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Piping Stress Handbook Second Edition -
-
Victor Helguero M.
Piping Stress Handbook Second Edition
Gulf Publishing Company Book Division Houston, London, Paris, Tokyo
Piping Second Library of
ISBN G87201_?03-6
Copyright @ 19_86 by Gulf publishing Company, Housron, Texas. All ngfts reserved. printed in the United Stabs;f
p-ar,b
ttrepf.
A;dca- itis book;; *itt out perJsio'i
may not be regoduced io a"y fo.rn
of the publisher.
$BN GE720r-nB{
.
.::
-i.j.
. -- ,,
Contents vlll
Preface
Chapter
1
Basic Theory of Pipe Stress and ANSI/ASME Codes 831.1, 831.3' ... . .. 1 831.4, and 831.8 Ptpe Stress Compliances . . . .
.
Pipe Stress Theory. Expansion Stresses. Cold Springing. ANSI 831.1 Fower Piping Code Stress Compliances (1983). ANSI 831.3 Chemical Plant and Petroleum Refinery Piping Code Stress Compliances (1984). ANSI B31.4 Liquid Fetroleum Transportation Piping Code Stress Compliances. DOT/B31.8 Gas Transmission and Distribution Piping Systems Stress Compliances. Standard Oudine for ANSI B3l Codes.
Chapter 2 Coefficients of Thermal
Expansion
,........17
Tables. Example Problem.
Chapter 3 Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 ..... 38 (1e83)
.
Tables.
Chapter 4 Allowable Stress Range for ANSI/ASME Petroleum Piping Code 831.3 (19M) . Thbles.
.
... ....73
Chapter 5 Stress Intensification and Flexibility Factors
tlz
Definitions. Thbles.
Chapter 6 Rotational Nozzle Flexibilities for Cylindrical Vessels
.
......l?a
Thbles.
Chapter 7 hessure and Shess Ratioo
.
.......177
Thbles. Instructions and Examples. Branch Reinforcement. Sample Calcula_ tions for Branch Reinforcement.
Chapter 8 Ihsign Criteria for Allowable loads, Moment, and Stresses
........257
Design Criteria for Pumps with Steel Nozzles anit Casings. Design Criteria for Pumps with Cast Iron or Aluminum Nozzles and Casings. Design Criteria ior Tirbine Drivers wilh Steel Nozzles and Casings. Design Criteria for Thrbine Drivers with Cast Iron or Aluminum Nozdes and Casings. Design Criteria for Compressors with Steel Nozzles and Casings. Design Criteria for Cornpres_ sors with Cast Iron or Aluminum Nozzles and Casings. ApI Code 661 Design Criteria for Air-Cooled Heat Exchansers.
Chapter 9 Simptified Solutions for Pipe Stress
265
Example Problem 9-1. Thbles. Example Problem 9-2.
Chapter 10
PropertiesofPipe Definitions. Thbles.
.........292
Chapter
11
Components
Weight and Dimensions of Pipe and
..
. 299
Weight of Pipe and Components. Tables.
Chapter 12 Allowable Pipe Span Formulas and
Thbles
...... ... 314
Pipe-Span Stress Limits. Pipe-Span Deflection Limits. Piping Wind Loads.
Chapter 13 Pipe Support Selection and
Design
..,...,
.
34
Pipe Supports. Spring Supports. Insulated Pipe Supports and Anchors for Cryogenic Service. Thbles.
Chapter 14 Fundamentalsof
ExpansionJoints.
........351
Types of Joint Movements. Nomenclature and Symbols. Types of Expansion Joints. Anchors, Guides, and Supports. Forces and Moments' Cold Springing of Expansion Joints. Cycle Life Expectancy. Corrosion. Erosion. Calculating Thermal Expansion. Precompression. Application, Pipe Guides and Guiding. Iocation of Expansion Joints. End Connections. Covers. Sleeves.
..... ....
Glossary Index
.
368
.,..373
vtl
heface
Determining piping stresses for the design
of
petro_
. chemical and.power plant piping systems iniolves ^many
complex mathematical calculations. These calculationi cal be solved with the aid of any one of several computer programs available provided they have the required ca_ pacity and an acceptable input/output format. The most formidable task facing the engineer is compiling the ex_ tenslve amount ot data needed to run the program. These data include physical properties. allowable stiesses, valve weights and dimensions. stress intensification factorsthermal expansion coefficients. spring hangers and expanslon Jotnt selectlon, and piping wind loads.
This reference book provides formulas, technical data. and other pertinent design information not readilv avail_ able in a single source for the piping stress analyit in the petrochemical industry who often has difficulry co ecting the required data and solutions to complete a piping stresi
analysis. .Depending on the magnirude and complexity of the job, the data needed to complete a given tasi may be scattered throughout a host of sources. The author's aim is to bring together in a single reference all the above mate_ rial and present it in a convenient form. Much of the information included in this book was ob_ tained from the work of others; some was used in its orisi_ nal form. while some was rearranged for this applicatio-n.
The author wishes to acknowledge his indebtedness to
Mr. Robert Kingshill, Virender Shukla, and Timothv W. Calk. for their assisrance in preparing this handbooki and the American Society of Mechanical Ensineers which generously permitted the author to use sevlral eouations to develop tabulations contained in this handbook. Suggestions and criticism concerning errors that may .9.T]l spite_of all precautions will be greatly appri ciated. They will contribute to the further improvement of
this reference handbook.
Victor Helguero M. , PE.
viii
Basic Theory of Pipe Stress and ANSI/ASME Codes 831..1, 831.3, 83L.4, and 831.8 Pipe Stress Compliances
The bending stress due to temperature, weight of pipe, contents, insulation, snow and ice, wind or earthquake is calculated by the following equatron:
Pipe Stress Theory To understand the basic criteria of the ANSI+ pressure piping code, it will be useful to explain the way different stresses develop when a piping element is subjected to a
number of loading conditions. There are four main
piping element, as shown in Figure l1. The following gives the intensity of these stresses and the manner in which they may be combined: stresses that
affe.t
t,
: Vqgrr'lt*+l Z
a
where
: :
S5
Ii L
* For
reasons of space these codes will be designated ANSI codes riroughout the text of the book, Some readers may be mor€ familiar with the desisnation ANSI/ASME as indicated in the headings.
=
Mi M" Z
: : :
Bending stress
In-plane stress intensification factor Out-of-plane stress intensif ication factor In-plane moment, lb-in. Out-of-plane moment, lb-in. Section modulus of pipe, in.3
The direct longitudinal stress due to t€mperature and weisht is calculated as follows:
lJ\J"
.
: Fu :
where A s
t \o S, I
The longitudinal stress due to internal pressure is calculated as follows:
^PD
"P Sr
=
= S, = Ss = Sc
Longitudinal stress and the sum of three component parts (see Equation 1-1). Circumlerential stress Radial stress Shear stless
Figure 1-1. Stress-free-body diagram.
Metal pipe cross-sectional area, in.z Direct force, lb
4t'
where P D
= =
:
Internal pressure Outside diameter of pipe (see Chapter 10)
Pipe wall thickness (see Chapter 10)
S:
:
0 (shear)
2
Piping Stress Handbook
Both significant stresses act in the same direction; therefore the stresses are "additive," i.e.
: S6+\+Sa
S1
(1-l)
Nofe: Inngitudinal stresses due to temperature are excluded from the combination when doing code calculations.
Circumferential stress, S., is primarily due to internal
The preceding method is known as the maximum shear theory (Iresca) and is the preferred method of the ANSI Code. A second method, known as the distortion-energy theory (Von Mises), also provides good results but is not used by the Code:
"'3S-+J--T-+ STTT$"
pressufe:
S^:.q,D -2t Radial.stress, S., is primarily due to internal pressue, which is equal to P.
S.=P
The ANSI pressure piping code recognizes that stress
Shear sfiess, S", is the sum of two component parts: tortional stress and direct shear stress (the second stress is usually negligible). (This condition occurs in three-dimensional piping systems.)
ss: where
Expansion Stresses
T
+2.0&
n
A
SS:
T: F,:
Shear stress Torque, lb-in. Resultant shear force Cross-sectional area of pipe Section modulus of pipe
z: sr: T/22, tortional
due to thermal expansion tends to diminish with time as a
result of local yielding or creep. This reduction of stress will appear as a stress of opposite sign in the cold condition. This phenomenon is known as self springing. Cold springing is similar, and although the hot stresses tend to diminish with time, the sum of the hot and cold stresses for any one cycle will remain practically constant.. This sum is called the stress range, ard, the code for pressure piping defines this allowable expansion stress range established for thermal expansion in terms of hot and cold tabu-
lar S values
S.
stress
:
F (1.25 S"
where S,
While the ANSI pressure piping code considers stresses due to therrnal expansion separately from primary stresses due to pressure, weight, and external loadi_ngs,/it is obvious that when combined stresses formulas and a specific yield criterion existr/stresses from all loadings should be included to delermine the principal stresses before confirming them. Resultant principal stresses at the outside
as:
=
: Sr, : F: S"
+ 0.25 Sh)
Allowable expansion stress range
(see
Chapters 3 and 4)
Allowable stress for the cold condition (see Chapters 3 and 4) Allowable stress for the hot condition (see Chapters 3 and 4) Stress range reduction factor for the cyclic
condition
fiber are as follows:
Sr
. sz
=
:
l/2
|2
Ib calculate
[Sr
+ S. +..//4St+ (S'=TFf
[g + s"
- "v4trTre-.l]zr
the principal stresses use 51 or 52, whichever
is greater, or the following equation:
\4* + C;=TJ'
(r-2)
Tbtal No. of Cycles Over Expected Life 7,000 and less
1.0
14,000 and 22,000 and 45,000 and 100,000 and 250,000 and
0.9 0.8 o.7 0.6 0.5
less less less less less
Basic Theory of Pipe Stress and ANSI/ASME Codes The stress due to thermal expansion, which must not :rceed the allowable expansion range , is callel expansion .;-ess and is defined by the piping code as:
n,:(1 -znci(fJn &=cR
s"={SJ'?+4-(sF xe Equation 1-2, where Sp
:
0 and Sr
:
Ss
The piping code further states that the sum of the long; ,-idinal stresses due to pressure, weight, and other sus:ined external loadings shall not exceed $,. Ifthe longitu:jnal stress due to sustained loadings is less than S1, the
:ode permits the unused portion to be applied to extend range available for expansion effects. There-
-.1e stress
:ore, the code, in effect, permits a total equal to 1.25 S. * Sr,), for thermal expansion stress combined with suesses
from other sustained loadings.
n=[r-tn"El* ' I s" Er,l
These relationships apply only to two-anchor piping systems with no intermediate restraints (use whichever equation is greater) and with the further condition that
sn*E
no cold spring to one for lO0% cold
se=
E": Er' : R: Cold Springing
spring
Maximum computed expansion stress Modulus of elasticity in the cold condition Modulus of elasticity in the hot condition Range of reactions corresponding to the full expansion range based on E"
R" and R1 represent the maximum reactions estimated to
A piping system may be cold sprung, or prestressed, to :educe anchor forces and moments caused by thermal expansion or contraction. This is accomplished by shortenng or lengthening the overall length of pipe by any desired amount not in excess of the calculated expansion. The amount of cold spring (C. S.) is usually expressed as a percentage or fraction of the total expansion or contrac-
Ion. This procedure is recognized by the ANSI Code for pressure piping which states: The beneficial effect of judicious cold springing in assisting the system to attain its most favorable condition sooner is recognized. Inasmuch as dre life of a system under cyclic condition depends pdmarily on the stress range rather than the stress level at any one time, no credit for cold spring is warranted with regard to sresses. In calculating end trusts and moments acting on equipment containing moving or removable parts with close clearanc€s, the actual reactions at ally one time mther than their range are signifi-
calt, and credit accordingly is allowed for cold spring in
the
calculations of thrusts and moments.
The reactions (forces and moments) & and & il the hot and cold conditions, respectively, obtained as follows from the reactions, R, are derived from the flexibility calculations based on the modulus of elasticiw at room temperature, E.:
occur in the cold and hot conditions, respectively. Thus, the ANSI piping code does not allow any credit for cold springing in the cornputation of stress. For reactions in the hot condition credit may be taken for twothirds of the actual cold spring applied; however, the full amount of cold sping must be taken into account in computing reactions for the cold condition. To understand the effects of stress range, self springing, and cold springing, see Figure 1-2.
ANSI 831.1 Power Piping Code Stress Compliances (1983) The standard terms, used in the equations set forth in the ANSI code, are defined as follows:
i: Z: rm : D" : :
Stress intensification factor. The term (0.75i) shall never be taken as less than 1.0 Section modulus, tn.,Z: r^2t^ r Mean radius, in. Outside diametet in. Nominal wall thickness. in.
Piping Stress Handbook SELF.SPRING
-
26000 Psl
NO COLD SPRING
24000 Psl
I I
=20 o
5 (,1q a' t! Ir
6ro
ll
-ltt ol
t: !; ii t:
I
dls\
|\)
N
/ ,---'1. r It ,l .tl t\
Irt! ti
.It
a !
m
T
L --t
I
t
\,{
, I
dld \ II
t-
, I
I r--1
It ltI
I
I I
I
I
I
a )< aa
ul tr.^ a I
Figure 1-2. Stress-range curve with and without cold spring.
: : Mr : P M"
: K: K:
M"
S,o
:
q,:
$" : S"
=
_ * S" :
Sr,
Internal design pressure Resultant moment loading due to weight and other sustained loads, in.lbs Resultant moment loading due to occa-
sional loads, including earthquake loads, trusts from relief/safety valve loads, in.-lbs Range of resultant moments due to thermal expansion/contraction, in.-lbs 1.15 for occasional loads actinq less than l0% of the operation period 1.20 for occasional loads actins less than l7o of the operation period Longitudinal stress due to pressure, psr Iolgitudinal stress due to sustained loads,
S"
:
stresses.
S.
S"
=
:
f(1.25 S" + 0.25
Sh)
(see Chapter 4) Basic material allowable stress at minimum
temperature from allowable stress tables, psl
$, =
DSI
Basic material allowable stress at maximum temperature from allowable stress tables, psi Stress range reduction factor fot cyclic conditions for total number N of fuIl-temperature cycles over total number of years of system operation (see " Expansion Stresses")
Longitudinal stress due to occasional loads, psi Thermal expansion stress due to thermal 9xpansion and anchor displacements, psi Longitudinal stress due to sustained loads plus the thermal expansion stress, psi
Allowable stress range for expansion
Wall thickness, in. Coefficient having values as given in the
SE=
ANSI Code 831.1, Table tV.t.2(A) Maximum allowable stress in material due to internal pressure and joint efficiency at the design temperature
Basic Theory of Pipe Stress and ANSI/ASME
'
Pressure Design The rninimum wall thickness for straight pipe under internal pressure and temperatures not exceeding those for various materials listed in the allowable stress tables, including allowances for mechanical strength, should not be
less than that determined by this equation (Section 1M.1.2, Equation 3):
,_ ''' = [_
_ro"- * ol + Pn I
(see Chapter 7)
The design pressure should not exceed:
(t - A) (see Chapter 7) D"-2Y(t--A) where t- : minimum required wall thickness, in. (mm) If pipe
5
where M" is combined in the following manner:
M"
: (Ml
+My2 +M:)t2
For full size outlet connections the equation is:
Z: r where
th
rnztn
:
Nominal wall thickness of the run pipe
For reduced outlet branch connections the equation is (see
Figure 1-3):
[2(SE
P=
Codes
2SE
Z: r where
r5
q tb
th
r3t"
: : = :
Branch mean cross sectional radius, in.
Effective branch wall thickness. in. = lesser of t5 or (i) t5 Nominal branch wall thickness. in. Nominal thickness of run PiPe. in.
is ordered by its nominal thickness, the manufac-
turing tolerances must be taken into account. This minimum thickness must be increased to provide the increase of manufactured tolerance allowed by the applicable spec-
ification or required by the process. The next heavier commercial thickness should be selected.
External Pressure
Sustained Longitudinal Stress The sustained longitudinal stress, 56' is the algebraic summation of the longitudinal pressure stress and longitudinal sustained weight stress. Sh is calculated using the following Code equation (Section 1O4.8.1, Equation 11):
To determine wall thickness and stiffening requirements for straight pipe under external pressure, the procedures outlined in paragraphs UG-28, VG-29, and UG-30 of Section VIII , Division 1 of the ASME Boiler and Pressure Vessel Code should be followed.
Longitudinal Stress LEG 3
The internal pressure stress, by the followilg equation:
^''
S1o,
should be determined
PD.
4t,
Thermal Expansion Stress The thermal expansion stress is calculated using the following Code equation:
5" = 1iv./z)
Figure 1-3. Header and branch connections'
Piping Stress Handbook
sk =
I& 19'frll4t . 4t^ z
1.s51,
(see Chapter 3 for 56)
ANSI 831.3 Ghemical plant and Petroleum Refinery piping Code Stress Compliances (1984)
As can be seen from the equation, the longitudinal stress due to pressure. weight, and other sustainid loads should be less than or equal to the Sh for the rnaterial.
Pressure Stress The minimum allowed wall thickness is calculated by using the design pressure in the following equation:
Occasional Longitudinal Stress The occasional longitudinal stress, S1o, is the algebraic summation of the longitudinal sustained weight striss the , longitudinal pressure stress, and occasionai stresr. S," i. 9{cu,tatea using the following Code equation (Seciion 104.8.2, Equation 12):
PD" 0.75iM, " _ ".-+t,--z*'
(P) (o. D.)
where O.
0.75iMh
: SE : P
D. =
y:
As can be seen from the equation, the longitudinal stress due to occasional loads should be less than-or eoual to k sh.
.875
Allowable Thermal Expansion Stress The thermal expansion stress is calculated usins the fol_
lowing Code equation (Secrion 104.8.3 tA), Equation
+
2 (SE
:
A:
yP)
+A
(see Chapter 6)
Design pressure, psig
Actual pipe outside diameter, in. Maximum allowable stress in material due to internal pressure and joint efficrency
A coefficient having values as given in the ANSI Code, Tabte 304.1.1, A; normally 0.4 A factor used to account to the industy's 12.5% mill tolerance on finished_ wall thicknesses Allowance for corrosion, erosion, etc., in.
The allowed pressure is calculated by using:
13):
S" :
iM"/Z <
S"
+
f(Sh
-
S)(see Chapter 3 for S")
As can be_ seen from the equation, the thermal expan_ . sion stress should be less than or equal to S".
2 (SE) (r-
Puo*
-
A)
O.D.-2y(t^-A)
where
tm
SE
(see Chapter 6)
= .875 x wall thickness, in. : Maximum allowable stress of the material for internal pressure considering the joint efficiency
Sustained-Plus-Thermal-Expansion Stress
Expansion Stress
The sustained-plus-thermal-expansion stress, Sh + Se, is the algebraic summation of the longitudinal stress due to sustained loads and the thermal exDansion stress. S1, * S. is calculated using rhe following iquation: sr,
+ sE =
I&
+
o75iM"
4t"ZZ
+it" .
,r- *
a",
As can be seen from the equation, the sustained-plusthermal-expansion stress should be less than or eouil to the sum of S1 and S,.
The expansion stress is calculated using the Code equation (Section 319.4.4, Eqtation 17).
S":
(S52
+
where S" :
4sr2)r/2
Computed expansion stress, psi
56 = Resultant bending stress, psi S5 = [(i1M), +(t"M"r2]t/2lz S, : Torsional stress, psi, = Mtl2Z Mr = In-plane bending moment, in.Jb M" = Out-of-plane bending moment, in.Jb
Basic Theory of Pipe Stress and ANSI/ASME
Mr
=
Z: i:
Torsional moment on cross section, in.-lb Section modulus of pipe, in.l Stress intensification factor (see Chapter 5)
For branch connections, the resultant bending stress (56) is calculated using the Code equations (Section 319.4.4, Equations 19 and 20):
I
For the header (Legs
and 2 in Figure 1-3):
Z
Pressure Stress The minimum allowed walfthickness pressure stress is calculated by using the internal pressure in the equation:
:PD"+A 2S
where
For the branch (Leg 3):
A S
Z.
56
z"
=
:
fm
t"
= =
: 1.
lo
li
= = =
=
1.21.
Effective branch wall thickness, in., = lesser of t1 and (L) (tb) Thickness of pipe matching run of tee or header exclusive of reinforcing pad or saddle, in. Thickness of pipe matching branch, in. Out-of-plane stress intensification factor In-olane stress intensification factor
319.4.4, Equation 18):
Longitudinal Stress The longitudinal pressure stress is computed in accordance with the Code using the equation:
PD" \. "rP= -_: 4t where S1o : Longitudinal pressure stress, psi P = Internal pressure. psig t : Actual pipe wall thickness, in.
D" =
Nominal outside diameter of the pipe, in. MI
Resultant bending stress, psi
[(i'MJ2
^
Allowance for corrosion, erosion, etc., in. (0.72) (E) (SMYS), psi Specified minimum yield strength, psi, Thble 1-l Weld joint factor, Thble 1-2
Mean branch cross-sectional radius, in.
For elbows and miter bends, the resultant bending
:
E:
,.
stresses (S5) calculated using the Code equation (Section
Su
SMYS
Resultant bending stress, psi Effective section modulus for the branch,
in.3,
Pressure, psig Actual pipe outside diameter, in.
P
D"
+ (LM"lll" Sr= fti,Mif where
7
ANSI B31.4 Liquid Petroleum Transportation Piping Code Stress Compliances
[(iiM)' + (i"M"t]r/'?
-\:-
Codes
+ (i"M.l]'/2
'o=-_.v-
where ii
stress intensification factor Out-of-plane stress intensification factor In-plane bending bending moment, in.-lb
= In-plane
lo:
Mi:
M"=
Z:
(see Figure
14)
"'&.
Out-of-plane bending moment, in.-lb (see
Figure 1-4) Section modulus of pipe, in.3
A conservative equation generally utilized for the calcuiation of the allowable expansion stress range is given in the ANSI Code 831.3 Section 302.3.58d, Equation 1:
s"
:
f(1.25 s"
+
.25
Sh)
Gee Chapter 4)
^,,Qr Figure 1-4. ln-plane and out-of-plane bending ments.
mo-
Piping Stress Handbook Table 1-1 Tabulation of Examples of Allowable Stresses for Reterence Use in Liquid petroleum Transportation piping systems Allowablestless values (s) shown in this Table
of the pipe.
are
equal to 0-72 x
t
(weldjoint factor) x specified minimum yield strength
Allowable stressvalues shown are for neE pipe of known specification. Allowable strcss values for new pipe ofunknown specification, ASTM A 120 specification orused (reclaimed) fipe shalr be dete,-ined in accordance $/ith 402.3.1. some code computations, particularly with regard to bianch connections .. .-For Isee 404.3.1 (d) (3)] and expansion, flexibility, structural atlachments, supports, and restraints (Chapter II, Part 5), the weiojoint factorZ. need not be considercd. For specified mintnum yield strength of other grades in ipproved specifications, reter to that particular specification. Allowable slress value for cold worked pipe subsequently heated to 600 F or higher (welding excepted) shall be 75 percent of value listed in Table. Definitions for the various types of pipe are given in 400.2_ Specified
(s)
Min Yield Specification
Gmde
(E\
Strength
Weld
psi
Notes
Joint
Faclor
Allowable Stress Value -20 F to 250 F psl
Seamless
API 5L A-PI5L, ASTM A 53, ASTM A 106 API5L, ASTM A 53, ASTM A I06 ASTM A 106 ASTM A 524 ASTM A 524
API sLU API 5LU API sLX API 5LX API 5LX API 5LX API 5LX API sLX API 5LX
425 A B c I II u80 ul00 x42 x46 x52 x56 x60 x65 x70
Furnace Welded-8utt Wetded ASTM A 53
API 5L Class t & Class fi API 5L (Bessemer), ASTM A 53 (Bessemer) F!rnace Weided-Lap Welded 5L Class I API 5L Class II API 5L (Bessemer) API 5L Electric Furnace
Elecrric Resistance Wetded and Elecrric Flash Wetded A25
Reptuduced
(2) (2)
B
B
1.00 1.00
(1)
25,200
30,000
(l)
1.00
r.00
80,000 42,000 46,000 52,000
(4) (1) (4) (l) (2) (4) (l) (2) (4) (l) (2) (4)
21,600 57,600
56,000
(l) (4)
60,000 65,000 70,000
(1) (4) (l) (4) (1) (4)
2s,000
(t) (2,
100,000
{l)
x65
x70 u80
l.
r.00
72,000 30,250 33,100
37,450 40,300 43,200 46,800 50,400
0.60 0.60 0.60
r0,800
25,000 (1) (2) (6) 28,000 (1) (2) (6.) 30,000 (l) (2) (6) 2s,00o (1) (2) (6)
0.80 0.80 0.80 0.80
14,400
100,000
ul00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
28,800
(2) (3) (2) (s)
56,000 60,000 65,000 70,000 80,000
x60
r8,000 21,600 25,200
(r') (2)
42,000 (l) (2) (4) 46,000 0) (2) (4) s2,000 (1) (2) (4)
x42 x46 x52 x56
1.00
r.00
40,000 35,000
25,000 (l) (7) 30,000 (2) 30,000 (l) 35,000 (2\ 3s,000 (l)
A
fron ANSI/ASME Code 831.4-1979, Tabte 402.3-
35,000
(l) (l)
2s,000 (l) 30,000 0)
A25
A-PI
API 5L API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A I35 API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A 135 API sLS, API 5LX ATI sLS, API 5LX API 5LS, API 5LX API 5LS, API sLX API sLS, API 5LX A}I 5LS, API 5LX API 5LS, API 5LX API 5LU API sLU
(l)
25,000
30,000
(l) 0) (l) (l)
(4) (4) (4) (4)
(1) (4) (l) (4)
Reprinted courtes!
1.00 0.85 1.00 0.85 1.00 1.00 1.00 1.00
r.00
10,800 12,950
t6,150 17,300 14,400 18,000 18,360 21,600
2l,420 25,200 30,250
33,r00 3',t,4SO
1.00
40,300 43,200 46,800 50,400
1.00
57600
1.00
'72,000
1.00
r.00
ofTh" e^"riron soi"ry of Munonirot rrxin"ug
Basic Theory of Pipe Stress and ANSI/ASME Codes Table 1-1 Continued (s)
Specified
(E)
Min Yield (iranorh
Weld
@o"
Specification
Notes
Joint
FactOr
Allowable S$ess Value -20 F to 250 F psi
Electric Fusion Welded ASTM A I34 ASTM A I39 ASTM A I39 ASTM A I55 ASTM A I55
A
A B x42 x46 x52 x56 x60 x65 x?0 u80 u100 Y35 v42 Y46 Y48 Y50 ]/52 Y60 Y65
API 5L, API 5IJ API 5L, API 5LS API 5LS, API sLX API 5LS, API 5LX API sLS, API 5LX API 5LS, API 5LX API 5LS, API 5LX API sLS, API sLX API sLS, API 5LX API 5LU API 5LU ASTM A 38I ASTM A 381 ASTM ASTM ASTM ASTM ASTM ASTM
A A A A A A
t'rooo
:
Submerged Arc Welded
38I 381
38I 38I 38I 38I
NOTES (l)Weld joint factor E
(1) (1) (2) (1)
30.000
0.80 0.80 0.80 0.90 1.00
(2) (2) (8) (8)
(l) (l)
1.00
21500 25,200
(2) (4) (r) (2) (4) (l) (2) (4)
1.00 1.00
r.00
30,000 35,000
(l)
42,000 46,000 52,000 56,000 60,000 65,000 70,000
(l) (l)
35,000 42,000 46,000 48,000 50,000 52,000 60,000 65,000
30,250 33,100 3',t,450
1.00 1.00 1.00
(4) (4)
(1) (4) (l) (4) (1) (4) (l) (4) (l) (2) (l) (2) (l) (2) (l) (2)
80,000 100,000
17,300 20,150
40,300 43,200 46,800 50,400
r.00 1.00
57,600
1.00 1.00
72,000 25,200 30,2s0
r.00 1.00 1.00 1.00 1.00
(l) (l) (l) (l)
33,100 34,550
36,000 37,450 43,200
1.00
1.00 1.00
,+6,800
(se€ Table 402.4.3) and allowable stress value a.e applicable to pipe manufactured after
1954.
(2)Weld joinr factor ,. (see Table 402.4.3) and allowabte stress value are applicable to pipe manuf.ctured befote l9 59.
(3)Class
It
produced under API sL 23rd Edition, 1968, or earlier has a specified minimum yield srrensth of
2a,OOO psi.
(4) Other Itades provided for in API sLS, API sLU, and API 5LX not precluded. (s)Manufacturewas discontinued and process deleted from API 5L in 1969(6)Manufacture was discontinued and process deleted ftom API 5L in 1962. (?) A25 is not produced in electric flash w€ld. (8)See applicable plate specification fo. yield point and r€fer to 402.3.1 for calculation
Allowable Longitudinal Stress The allowable stress value for by the Code in Section 419.6.4(c):
additive longitudinal
stresses is given
where SMYS
:
of(S).
Specified minimum yield strength, psi (see Thble 1- 17
Allowable Expansion Stress Range for Unrestrained Piping This is given by:
Sr
(allow)
where Su
:
= :
0.75
S"
The allowable expansion stress range, psi 0.72 SMYS
S"
:
0.72 (SMYS)
where SMYS
:
Specified minimum yield strength, psi (see Table l-lr
10
Piping Stress Handbook Table 1-2 Weld Joint Factor E Weld Joint
Specification Number
Pipe Mfrd. Before 1959
ASTM A 53
Seamless
1.00
Electric-Resistance-welded Furnace Lap-Welded Furnace Butt-Welded
Factort Pipe Mfrd.
Afler
0.85 (2) 0.80 0.60
1.00 1.00 0.80 0.60
1958
A
106
Seamless
1.00
1.00
ASTM A
I34
Electdc-Fusion (Arc)-Welded single or double pass
0.80
0.80
A
135
Electric-Resistance-Welded
0.85 (2)
1.00
A I39 ASTM A I55
Electric-Fusion-Welded single or double pass
0.80
0.80
0.90
1.00
ASTM A 381
Electric-Irusion-Welded, Double Submerged Arc-Welded
API 5L
Seamless
1.00 0.85 (2)
0.8s (2)
1.00 l 00 1.00 1.00
0.80 0.60
0.80 (3) 0.60
ASTM
ASTM ASTM
Electric-Fusion-Welded
Electric-Resistance-welded Electric-Flash-Welded
Electric-Induction-welded Submerged Arc-Welded Furnace Lapwelded Furnace Butt-Welded
API sLS
l-00
Electric-Resistance-welded Submerged Arc-Welded
API 5LX
1.00
t.00
Seamless
1.00 1.00 1.00
Electdc-Resistance-Welded Electdc-Flash-lvelded Electdc-Induction-Welded Submerged Arc-Welded
API
5LU
Known Unknown Unknown Unknown Unknown Unknown
1.00
1.00
Sean ess Electlic-Resistance-Welded Electdc-Flash-Welded Electric-lnduction-Welded Submerged Arc-Welded
-_ _ -
Known
(4)
Seamless
Electric-Resistance or F'lash-Wetded Electric-[jusion-Welded Furnace Lap-Welded or ovet 4lz" OD I:urnacc Butt-welded or 4%" OD and smaller
1.00 (6) 0.8s (6) 0.80 (6) 0.80 (7) 0.60 (8)
1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00
r.00 1.00
(5) 1.00 (6) 1.00 (5) 0.80 (6) 0.80 (7) 0.60 (8)
NOTES: (l) Definilions for the various pipe types (wetd joints) are given in 400.2, (2) A weld joint factor of I o may be used for electric-resistance-welded or etectric-flash-wetded pipe manufact ured prior to I 9 5 9 where (a) pipe furn ishe d un der this c tassifica ! ion has been su bj"" t"o to pp'r"'-"ni"i i""t"
and/or heat treatmenls as aFeed to by the supplier and the purchaser, and such sujplementat"u teits analor rreai treatment demonstrate the strength characteristics of the weld lo be equal to the rninimum tensite itrength for the pipe, or (b) pipe has been tested as requi.ed for a new pipetine in accordance with a3z.4.i ,^. speciried (r,| Il1anuracrure was discontinued and proeess deleted from AI,I SL in t 962. (4) Factors shown above for pipe manufactuled before r959 apply for new or used (rectaimed) pipe if pipe specification and pipe lvpe ate known and it is known that pile was manufacrured before r'9i9 ri.i r""*" whether manufactured after 19S8. ". (5) Factots shown above for pipe manufactured aft€r 1958 apply for new or used (rectaimed) pipe if pipe spec! ficarion and pip€ type are known and it is known rhar pip; was manufactured aiter 195s.(6) Factor apPlies for new or used pipe of unknown specific;tion and ASTM A t 20 if type of weld joint is known. (7) Factor applies fot new or used pipe of unknown specification and ASTM A l2o if iipe or *eta j"irr i" i"o*tl lo be furnace lap-wetded, or for pipe over 4% in. OD if type ofjoinr is unknown. (8) Factor applies for new or used pipe of unknown specification and ASTM A l20 if type of weld joint is known to be firrnace butt-welded, or for pipe 4% in. OD and smalter if type of joint is unknown.
Reproduced
from ANSI Code 831.419D,
Toble ,t02.4.3. Reprinad coutksy
of The Arncicai Sociey
oJ Mechanical Engineers.
Basic Theory of Pipe Stress and ANSI/ASME
M"
Longitudinal Expansion Stress for Restrained Piping
=
: ii :
Mt
For restrained piping, use the longitudinal expansion ANSI Code 831.4, Sec-
stress from the equation given in
tion 419.6.4
g: E= Sr.
Tr Tz
=
: :
Longitudinal compressive stress, psi Modulus of elasticity of steel, psi Hoop stress due to fluid pressure, psi Temperature at time of installation, 'F Maximum or minimum operating temper-
a=
ature, oF Linear coefficient of thermal expansion,
v:
Poisson's ratio
in./in./'F
= 0.3 for
The allowable stress value in shear is computed in accordance with the ANSI Code B31.4, Section 402.3.1 (e):
56 (allow)
=
(.45)
(S I,IYS)
The allowed internal pressure stress is S, where (0.72) (E) (SMYS), psi
S=
steel
DOT/831 .8 Gas Transmission and
Distribution Piping Systems Stress Compliances (1982)
0.90 (SMYS)
where SMYS
:
Allowable Internal Pressure Stress
This is calculated by using:
:
Bending moment out oi or transverse to, plane of member, in.Jbs Torsional moment, in.-lbs Stress intensification factor under bending in plane
Allowable Shear Stress
Allowable Expansion Stress Range for Restrained Piping
s"
11
ft):
Sr:E(a)(Tr-T1)-v(S) where
Codes
Pressure Stress
Specified minimum yield strength the pipe, psi (see Table l-1)
of
The design pressure for steel gas piping systems or the nominal wall thiclmess for a given pressure is determined by:
The expansion stress for unrestrained piping is calculated by using:
S.:
[56, + 4S,2]r2
where S" :
^.Z Sr
=
Mi =
2s' (F) (E) (T) D
(For limitations see Section
Computed expansion stress, psi
[(iiM), + (LI\AF]I"
:
P=
equivalent bending stress, psi MJ2Z torsional stress, psi Bending moment in plane of member (for
:
members having significant orientation, such as elbows or tees: for the latter the moments in the header and branch portions are to be considered separately), in.lbs
: S:
where P
D: F: E:
84l.l2l)
Design pressure, psig Specified minimum yield strength, psi (see Table 1-3). For special limitations on S see Section 841.121 (e) and (f). Nominal outside diameter of pipe, in. Nominal wall thickness, in. Construction-type design factor obtained from Table 14 I-ongitudinal joint factor obtained from Thble l-5 (see also Section 811.253 (d) Temperature derating factor obtained from Table 1-6
12
Piping Stress Handbook Table 1-3
specified Minimum Yield strength for steel and lron pipe commonly used in piping systems. Specilication
Tvpe
(l)
SMYS (psi)
A?I5L
BW, ERW, S
API5L
ERW, FW, S, DSA ERW FW, S, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, Fw' S, DSA
API 5L
A?t 5LS (2) API API API API
5LS 5LS sLS 5LS A?I sLS
API SLS API sLS API sLS API SLX (2)
A?I sLX API 5LX API 5LX API sLX API5LX API5LX ASTM A53 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM
A53 A53
ERW, ERW,
AI06
S
A106 AI 06
AI35 AI35
AI39 AI
B......... A.........
]9
A381
A38I ASTM A38I ASTM A38I ASTM A38I ASTM A381 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM
c.........
Clas Y-35 .. cla$ Y 42 .. Clas
Y46
.
class Y-48 . clas. Y-50 . Cla\s Y-s2 .
. . . .
A38I
Class
Y-56
..
A381
Class
Y60
.
A38I
Class
Y-65 . .
AI34 AI55 A333 4333 4333 A333 4333 A333 4333 A559
I
3s,000 42,000 46,000 52,000 56,000
60,000 65,000 70,000
42,000 46,000 52,000 55,000 60,000 55,000
S
70,000 25,000 30,000 30,000
S
3s,000
BW BW
ASTM 453
25,000 30,000 35,000 30,000
10,000 35,000
s s ERW ERW EFW EFW DSA DSA DSA DSA DSA DSA DSA DSA DSA EFW EFW S, ERW S, ERW
40,000 30,000 35,000 30,000 35,000
3s,000 42,000 46,000 48,000 50,000
52,000 s6,000 60,000 55,000 (3) (3)
,7
S, ERW S, ERW
8
S, ERW
30,000 35,000 35,000 35,000 35,000 75,000
9
S, ERW
46,000
ERW
35,000
3
S
6
(l) Abbreviarions: BW Furnace butl-welded; ERW- Electric resistance weld€d; S-Seamtess: EFw - Electric fusion weldedi DSA- Double subme.led,a.c welded.
FW
-
Fhsh w€lded:
(i!) Intermediate
Brades ar€ available in API 5LS and 5LX. (3) S€€ applicabl€ plat€ specification for SMYS.
Note: This tablc is not conplete. R)r minimum specified yield strength of other grades and erades in approved specifications, rcfer to the particulor specification. Iron ANSI/ASME Code 831.8-1982, Appenn& D. Repdnted courvsy of me Americon Societt of Mechanicat Engineers.
Reproduced
Basic Theory of Pipe Stress and ANSI/ASME Codes
Expansion Stress
Table 1-4 Values of Design Factor F Conslruclion Type (Scc 841.151)
This is calculated by using the Code equation:
Design Factor
Type A Type B Typc (' Type D
F
S"
0.11 0.60
=
where
0.5 0
0.,10
Ul
Reproduced Irom ANSI/ASME Code 831.&1982, Table courtesy of The Ameicon Society of Mecha ical Engineers.
IC.
Repnntud
(S6'?
Fr.tol
C
:
tion, in.lbs Torsional moment on cross section, lbs Section modulus of piPe, in.3
Stress intensification factor (see ANSI Code B31.8, Appendix E)
1.00
Llcctric Resistancc Weldcd
.60
Furnrcc Bult Welded Scrmicss
AS IN{ A 134 AST}'1 A] 35 AST\'1 A1]9
lllcclric Irusion Art Wcldcd Llectric ResislLrnce Wclded
lllcclric Fusion wclded
00 .80 1.00 .30
ASTM A]55
Llcctric Ijusion Arc Wclded
L00
ASTM ,42I
Spiral WeLded Stccl PiPe Doublc Submergcd'AIc-welded
r.00
Sc:rmLess
l .00
I
ASTM A38I API 5L
Sermlcss
L00
Elcctric Rcsistirncc Wcldcd Llectric I:lash WcLded
L00
Submcrgcd Arc Weldcd
llectric
S"
.80
Rcsistancc Welded
1.00 1.00 r .00
Note: Definitions for the virious chsses of welded pipe given in 804.243 n"proa*"a.Iro^ ,tNSttlSME Code 831 8-1982, Thble UI
Tcmpcrrtulc 150 t or 300 350 F
This is computed by using:
lA
less
400 tl 450 F For intermediLite temperatures
-'' srn=-
Reprihted
where
for Steel Pipe
TelnPcrirrure Dtrating
|
Specified minimum yield strength, psi (see Table 1-3)
Nre
courtesj of me American Society of Mechanical Engineers
Degfccs Fahrcnhelt
:
Longitudinal Pressure Stress
*Manufactu.ewasdiscontinued and process deleted from API 5L in 1962.
I
0.72 (SMYS)
where SMYS
l.00
Subnergcd Arc Welded
Table 1-6 Temperature Derating Factor
=
1.00 .60 .80
Furnace llut l Welded *l:urnace L!p-Wcldcd
API 5LS
This is calculated by using:
L00
Llcctric Rcsistxncc weldcd Elcclric Flash Wcld.d
API 5I X
Allowable ExPansion Stress Range
l
AST}I A106
frffiiififi
:
L00
ASTIU A53
Note:
4S,2)r/2
Se = Computed expansion stress, PSi iM/Z Resultant bending stress, Psi psi Mtl2Z St= Torsional stress, Resultant bending moment on cross sec-
z= :-
Longitudinal Joint Factor E Pipe Clrss
+
Sr: M: M, :
Table 1-5 Spec. Number
13
l:!ctor f
4r
P : n:
Design pressure, psig Outside diameter of pipe, in. Pipe wall thickness, in.
The sum of the longitudinal pressure and longitudinal bending stresses due to external loads such as weight of pipe and contents, wind, etc., should not exceed'75% of owable stress in the hot condition. The allowable for the sum of the longitudinal stresses is given by:
thl a
r .000 0.967
0.9 31
0.900 0.867
51
intcrp(tl!te for derating
B3t E-1982, rabtc 84l 'qNs ASME code courtesy of The American Sociery of Mechanical Engi eers
PD"
lB
Reprinted
:
(allow)
:
0.7s (S) (F) (T)
where S = Specified minimum yield strength, psi E_ .l|_
Design factor obtained from Table 1-4 Temperature derating factor, Table 1-6
14
Piping Stress Handbook
Standard Outline for ANSI Bg1 Codes
ANS|Code 831.1: Power Piping Includes
l.
Power and auxiliary service piping systems for electric generating plants. 2. Industrial and institutional plants (also see ANSI
3. 4. 5. 6. 7
.
Code 831.9). Central and district heating plants (also see ANSI Code 831.9). All piping and cornponent parts within or part of plants as previously specified, unless specifically excluded. Boiler external piping which is covered under the ASME Code, Section I, stamping requirements. Geothermal steam and hot water piping. Oil or gas piping , downstream of meter, within plant
identified in l, 2. or 3, above. and hydraulic distribution syslems.
8. Air
2. 3.
Code.
4.
Gas gathering, transmission, and distribution sys-
5. 6.
tems covered by ANSI Code B31.8. LPG in the liquid state. Fuel gas-air mixtures in the combustible or flammable range.
ly'ore.' This Code will be withdrawn when the new issue of ANSI Code 7223.1 (which does not reference ANSI Code B31.2) is released. This service will be covered by ANSI Codes 831.9 and 2223.1.
ANSI Code B31.3: Chemical Plant and Petroleum Refinery Piping lncludes 1. All piping within the property limits of facilities engaged in the processing or handling of chemical or petroleum or related products.
Exctudes
1. Piping specifically covered by other ANSI/ASME sections. 2. Components covered by ASME B and pV Code. J. Fuel gas in industrial and institutional plants. 4. Building heating and distriburion sream piping for 15 psi (100 kPa) gauge or less or hot water systems for 30 psi (200 kPa) gauge or less. 5. Roof drains, floor drains, plumbing, sewer or fire protecflon systems. b. Piping for hydraulic or pneumatic tools. 7. Piping for nuclear power plants.
ANSI Code 831.2: Fuel Gas Piping Includes 1. Natural
Fuel gas piping covered by the ANSI Codes B3l . 1 , B31.3, 831.8, Z2l.3O, or ZtO6.l Pressure vessels covered by the ASME B and pV
Excludes
1. Nonhazardous fluid piping with
pressures between 0 and 15 psi (100 kPa) and temperatures ranging from
2. 3.
4.
5. 6.
-20'F (-29"C) to 366'F
(186"C). Piping covered by the ASME B and PV Code, Section I or ANSI Code B31 . 1, which requires Section I, Inspection and Stamping @.E.P. Piping). Pressure vessels, heat exchangers, pumps, etc., including internal piping and connections for external piping. Piping within the property limits which has been designated for design according to the ANSI Code 831.4 or 831.8 or to government regulation (pipeline rights-of-way). Plumbing or sewers. Piping for fire protection systems (covered by insurance underwriter's requirements).
gas.
2. Manufactured gas. 3. LPG-air mixtures above the combustible limit. 4. LPG-in the gaseous state.
lncludes
Excludes
1. Fuel gas piping where the metal temperature is above 450"F (232"C) or below
ANSI Code 831.4: Liquid Petroleum Transporiation Piping Systems
-20"F (-29.C\.
1. Piping transporting liquid petroleum and petroleum products between the producer's facilities and delivery and receiving points.
Basic Theory ol Pipe Stress and ANSI/ASME
1.
1. Water air, steam, lube oil, gas, and fuel piping.
3.
4.
Pressure vessels, heat exchangers, pumps' meters' etc., including internal piping and connecUons to ex-
ternal piping. Piping systems designed for internal pressures less than 15 psi (100 kPa). Piping systems designed for internal pressures
6. 7.
Pressure vessels and piping covered by the ASME B
and PV Code.
systems with metal temperatures above 450'F Q32'C) or below -20'F (-29"C). Piping in chemical plant or refinery property limits' natural gasoline extraction plans' etc. ' covered by
2. Piping 3.
ANSI Code 831.3.
greater than 15 psi (100 kPa) where the design temperature is below -2O"F (-29"C) or above 250"F
4. Atmospheric vent piping for waste gases. 5. Low pressure gas which is covered by ANSI Code
Casing, tubing, or pipe used in oil wells, wellhead assemblies, and piping connecting those assemblies' Piping covered by the ANSI Code B31.3 or B31.8. Ammonia reftigeration piping systems'
6. Wellhead assemblies. 7. Proprietary items of equipment.
831.4.
(120'C).
5.
15
Excludes
Excrudes
2.
Codes
ANSI Code 831.9: Building Services Piping ANSI Code 831.5: Refrigeration Piping
lncludes'
,ncrudes
1. Piping
systems
for building services for industrial,
commercial, public, institutional, and multi-unit res-
1. Refrigeration and brine piping systems down to
idential buildings.
-350'F (-
196"C) either erected on the premises or factory assembled, unless specifically excluded.
Examoles:
Excludes
reother laboratories. piping Water systems. Piping systems with internal or external pressure of tS psi ltOO kPa) or less.
1. Self-contained refrigeration systems covered by quirements of Underwriter's Laboratories or nationally recognized testing
2. 3.
ANSI Code 831 .8: Gas Transmission and Distribution Piping
A. B.
C. D.
E. F.
G.
Excludes 1. Pressure limit exclusions:
A.
Steam: 125 psi (860 kPa) Gauge B. Nontuel gas: 125 (860 kPa) Gauge C. Liquids: 300 (2,070 kPa) Gauge D. Full vacuum for all fluids
,ncrudes
1.
Gas transmission pipelines.
2. Gas compressor stations. 3. Gas metering and regulation stations. 4. Gas mains. 5. Service lines to oudet of customer's meter set' 6. Gas storage lines and storage equipment of closed-pipe type.
Dual+emperature water for heating and cooling' Chilled water. Condensing water. Hot water. Steam and condensate return Compressed air and other nonflammable gases. Fuel gas over 60 psi (415 kP-a) _(tuel.gas ulder 60 psi is covered by the new ANSI Code 2223'1)
the
*
(as per latest draft.)
16
Piping Stress Handbook
2. Other exclusions:
A. Piping systems covered by ANSI Code B3l . I
B. Sanitary, potable water, and storm drain piping
Excludes
l.
c. Fire protection systems D.
4c:tylene, hydrogen, oxygen and medical gas
Plpng E. Fuel oil piping
Vessels, heat exchangers, condensers, pumps, com-
pressors, expanders, scrubbers, ana
ment.
2.
, J.
b*rer
equlp_
rr'acuum
piping systems which supply insulating vacuum !o vacuum jackets of cryogenic piping syJtems. rtpmg sysrems specifically covered by ANSI Codas
831.5 or 831.3 lwording of draft).
ANSI Code 831.10: Cryogenic piping* lncludest 1. Liquid-solid mixtures (or slush), operating at tem_ qg-ra1u1ej-rgcinS ftom r2OK (_ 244"F, _ 153 "C) ro (-4^59"8 -273"C), either erected on the prem_ 9K
ANSI Gode 831.11: Slurry piping Systems
ises or factory assembled.
lncludes * (Io
be included io tuture ANSI Code 831.3)
r (as per latest draft.)
t. Initial coverage will be coal transported in water. 2. Future coverages will include slurries ofother solids transported in nonhazardous liquids.
Coeflicients of Thermal Expansion
This chapter contains tables of the coefficients of thermal expansion (Tbble 2-1) and other tables relating to the physical properties of piping materials (Tables 2-2 through 2-4).
17
18
Piping Stress Handbook Table 2-1
Coefticients of Thermal Expansion (in./100 ft) Carbon Steel Carbon-moly Temp, (F)
Low-chrome (Thru 3 Cr Mo)
-32t -?.370 -320 -2.344 -315 -2.313 -3r0 -2.292 -305 -2.?.66 -300 -2.240 -295 -2.214 -290 2. | 8 -?80 2.135 -275 -2. l r0 -210 -2.084 -265 -2.058 -260 -2.A32 -255 -2.006 -250 -r .980 -245 -t .954 -240 - 1.928 -230 -1.e76 -225 -r .850 -2?0 -1 . A22 -2l5 -l .794 -210 -l . 765 -205 -1.738 -200 -1. 710 -r 95 -l .589 -190 -l . 658 -t a0 -l . 606 -r 75 -i .5B0 -170 -r . 554 -r 60 -1 .500 -r 55 -1 .47 4 -r 50 -r .450 -145 -r . 420 -r40 -1.390 -t 35 -r .350 -r 30 -t .330 -125 -r .300 -120 -1.210 -1l5 -t .240 -t t0 -1.210 -r05 -1. r80 -r00 -1 .150 - 90 -r .090 - 35 -r .050 - 80 -1.030
Austenitic
MO Siainless Thru Steels 9CrMo 18Cr8Ni
5 CR
-) ,ri -2.I72
-J.t'5 -3.806
12 Cr
'17
Ct
27 Cl
-2.040
-2.016
-r .992
25 Cr 20
Ni
Monel
3t12
67 Ni 30 Cu
Nickel
-2.620 -z .595 -2
.572
-t .944
-2
.524
-t .920
-2.500
-2. t48
-2.124 -2. I00
-3.586 -2.052
-1.896
-2.234 -2.202 -2. 185 -2
.170
-2.150
-1 .87?
-2.452
-2.004
-3.498 -3.454
-l.848 -l .824
-2.404
-2.090
-l .980
-3.410
-l .80
-2.380 .356
-2.070 -2.048
-2
nua
-I al,
-J.lOO
-2
-1.752
-l .908 1.884
-3,234
-l .704
-t .850
-3.r9
-l .68
-l.312
-3. 146 -1 ln?
-r.836
-3.058 -1 ,7 64
-3.014
-1.715
-2.960 -2.914
-l -l
-l .230 -t
-l
-r .570
-t.800
-!.540
-1.46 -r .438 -1 .4r6
-2.500
-2.454 -2.40a
-l .394
-2. t56 -2.114
-1.024
-l
.780
-t .760 -1
.996 -1 .704
-1 .948
-t .924
-t
.648
-r .350
-1 .90
.620
-1
-t.305
.8;8 -t.355
1
-1
.592
.284 -1.262
-1.s34
-r.536 -r.50s
-1.3t2
.240
-1.214
-t.188 -1.162
-t. -2.0r
.840 -1.820
-1 .37?
-1
-2.218
t36
-1.480 -1.750 -1.710
-t .670 -r .630
-1.110
-l .084
-1
.548
-l
.420
-1 .390
-t.360 -'t.330 -1.298
-r.05t
-r.506
-t .802
-r .454
-l .234
-1.006
-1 .422
-1 .202
-1./)
-0. 98
-1 .380
-t
0
-t .052
-1 .860
-t .482
-t .906
-l .080
-t.920 -t.900 -t .830
-2.778
. 170 . 140
-'t.
21?
-2. I88 -2 ,164
-2.824
-1.258
-r.200
-1.960 -1 .940
-1
-1 .370
-r.286
260
-? -1.614
-1
-l.314
-2
-2.?36
-2.092 -2.068 -?.044
-t .524
-1.342
-t .982
-1.525 -1.504
.548
-t.50 4.474 -l .448
-2.0c4
-2.284
-2. 1 16
.520
-t .57:
-2.30B
-t .548
-2.870
-1.558 -1.644
-2. I 30
-1
.854
-t .700 -r.550
-0.954
-t.34
-1.600 -1.550
-0.902
-1.25
-1
-0.876
.30
-1
.255
.170
-t.138 -t.105
-r .074 -1 .042
Coelticients of Thermal Expansion Table 2-1 Continued
Austenitic
Carbon Sleel Carbon-moly Temp.
Low-chrome
(F)
Ohru 3 Cr Mo)
- 15 -l .000 - 70 -0.97 - 65 -0.94 - 60 -0.91 - 55 -0.88 - 50 -0.84 - 45 -0. AoC - 40 -0.716 - lJ -u. /.4{ - 30 -0.712
25 .20 - 15 - t0 - 5 -
-0.680 -0.542 -0. 604
MO Stainless Thru Steels 9CrMo 18Cr8Nl
5 CR
-0.940 -0. 910
-
-0.880 -0.850 -0.820
-1 ,29?
-0. 790
-1.240
-0.758 -0,7?6 -0.594 -0.662
-r.188
-0.630 -.0596
-0.980 -0.928 -0.875
-0.552
-0.528
{r. !26 -0.494
0
-0.49
-0.450
5
-0.455
't0
-0.555
-l .500 -l . 44A
-l .135 -l .084
-0. s24
4.772 -0.720
-0.59 -0.65
-0.48 -0.45
-0.460
4.232
-0.350 -0.310
50 55 60
-0.140
-0.13 -0.098 -u.uoo -0.034
-0.210 -0. r 58
70
c
a0
0.039 0.076
-0.602
-0. 6r
-0.534
-0.57
-0.5c -0.464
-0. s3
{.33
-0 .4?a
-0.392
-0.30
-0.41
-0.356
-0.370
-0. 3?0 -0.285 -0.252 -0.213
-0.24 -0.21 -0. 19 -0. l5
-0.302 -0.?34
-0- 184
4.12
-0.200
-0.r5
-0.I50
-0. I l3
-0.105 -0.054
-0.06
-0.100 -0.050
-0.038
0
0
0
0
0
0
0.037 0.074
0.056 0.112
0.053 0. 106
0.047 0.094 0.140
0.038 0.076
0.212
0.t85
0.1 l4 0. I52
c.l l4
0.lll
0.152
0. 148
0. 190
0.1 85
0.230
0.22
0. 158
0.22s 0.2&.
0.033 0,066 0.099 0.137
-0.268
0.t65
4.076
0.r90
0.200
0.320
0.28
0.23
0.294
0.340 0.396 0.452
0.264
0.424
0.375
0.296 0.328
0.475 0.528
0.306 0.344
0.370
0. 508 0. 564
0.520 0.876
0.350
0. 58
0.268 0.306 0.344 0.382
0.258
0.420 0.458 0.496 0.534
0.40
0.121 0.762
-0.51
-0.300
-0.250
0.510 0.648 0.685
-0.670
-0. 554
-0. I 64
0.572
-0.77 -0. 73
-0.364
-0.175
-0.840 -0.805
-0.57
-0.36
-0.2t2
-0.938
-0.77?
-u.oto
40 45
-1. r0 -l .06 I .02
-0.895 -0.812
-0. 600
-0. 396
-0.284
100 '105 I t0 I 15 120 t25 'i30 135 I 40 145 t50 I 55 r 60 t55 I70
-0.690 {,. OJU
.010
-.976 -.942 -.908 -.874
-l.t4
4.746
31h Nickel
-1
-i. t6
-0.824 -0.798
-n la
:c
90
Monel 25 Cr 20 Nl 67 Ni 30 Cu
-u.6:
-0 - 668
4.428
-0. 388 -0.354
-0.070
Cr
4.772
?0
-0. t05
12 Cr 17 Cl 27
0.435 0,472 0.508 0.544 0.580
u-oto
6 t1t
0. 394
0.424 0.472
0.42 0.458
0,664
0.496 0.534
0.712
0.572
u.oto
0.462
0.8'14
0.496
0.584 0.735 0.783
0.90
0.530
0. 84
0,594
0.798 0.846 0.894
0.942
0.552 0.688
I .068
0.626
0,892 0.944 0.996
0,724
1.124
u. 056
I . 048
0.956
t.012
u.j64
0.568
0.788
0.428
0.268
0.61
0.548
0.724 0.752
19
Piping Stress Handbook Table 2-1 Continued
Carbon Steel Carbon-moly Temp.
(D
t30 tdJ
r90 r95
Low-chrome (Thru 3 Cr Mo)
0.30 0.834 0.876 0.914
1.180 0.796 0.832
0.858 0.904
0.97
0.85 0.89d 0.928 0.962 0.995
'1.37
i.2?
1.01
r.2t0
1.130 1.750 1.170 1.806 1.210 I .862 I.918 I .250 I .974 I .290 1.330 2.030 2.038 I .368 ?.146 I .405 2.244 I .444 1.4A2 2-262 2.320 I .520 ?.318 I . s58 .596 2.435 2.444 ]. 534 1.672 2.552 2.610 t .710 2.568 1 .748 2.726 r .786 2.744 I .824 1.862 ?.842 2.900 1 .900 1.940 ' 2.960 3.020 I .980 2.020 3.080 2.060 3.140 3.200 2. 100 2.140 3.260 2.180 3.320 2.2?0 3.380 2.260 3.440 2.30 3.500 2.340 3.560 3.520 2.3& 2.420 3. 580 2.450 3.740 2.500 3.800 2.544 3.860 2.588 3.920 2.632 3.980 2.616 4.040
r.362 .400
250
1
t55 t60
1
.442 1.484 1.526
?.7 A
t75 130
1.568 1.610 1.652 1.694
290 295
1.778
300 305 310
t.s2 I .864
1.908 1.952
qq6
320
I
325
2.040
330 335
2.123
340 345
2.112
355 350
2. ?16
2.304
) )
16F 142
2.436 3B0
J6f, 390
2.480 2.524 2.558 2.612 2
.656
1t0
?.700 2.746 ?.79?
115 120
2.884
r00
1.054
1.092
1
0.89 0.93
I .182
1.015
.286
0.85
1.308
1.078 1 .122
I .324
0.81
1.038 I .086 1.134
0.826
2t0
240
c.99
1.404 1.518
.248
1.10
0.792
.978
1
0.724
Nickel
348
I
I .46
1
0.59
3112
Monel 25 Cr 20 Nl 67 Ni 30 Cu
1.204 1.256
.940
225 ?30
Cr
0.758
0. 990 034
l
12 CJ 17 Cr 27
,?92
1
200
??a
a="
Austenitic
MO Stainless Steels Thru 'l8Cr8Nl gCrMo
5 CR
l
424
.258
r
1.478 I .364
1 .54 .03 .594 t.c65 '1.102 I-748 1.138 1.802 I.174 L865 1.210 I .910 1 .964 1 .244 1.278 2.018 2.072 1.312 'I .345 2.126 'I .380 2.I80 'I .416 2.234 2.288 I .454 ?.342 I .490 2.396 I . 526 2.450 1 .55 l .596 2.504 2.558 I .532 I .558 ?.612 2.666 I .704 2.7? 1 .74 1.77A 2.174 I.816 2.828 2.8A2 I .854 l.892 ?.935 2.99 I .93 3.044 I .956 2.002 3.098 2.038 3.152 2.074 3.205 3.26 2. r I 2.148 3.314 2.I86 3.368 2.?24 3.422 2.262 3.476 2.30 3.530 2.340 3- 584 2.380 3.538 2.4?o 3.692 2.940 3.746 1
'1.13
1.17
1.586
I
r.09
.460
1
.
1.556 I .504
I
'I .750 'I . S10 1
.378
652
t.710 .860
1.910
210
.252 .294
r.508
'I 1
.420 .462
1
.504
1.545
']
588
1.950
t.630
2.010 2.060 2.110 2.160
I .714 1.756 1 .798
2.210
t.s4
2.302
?.348 2.394
I .956
.44 2.488
2.050
2
2.532
2.092 2.134 2.176 ?.218
2.680 2.728
2.176
2.26 2.302 2.344
'2,872
2.428
A?L
2.386
2.910
2.470
3.084
2.595 2.638
3.250 3.304
2.690
l-J!6
2.77 4
3.412
2.816
2
.732
Coefticients of Thermal Expansion Table 2-1 Continued
Carbon Steel Carbon-molY Temp.
(n
Low-chtome (Thru 3 Cr Mo)
2.930
2.976 140
3.068
145
4
3.
3.160 3.205 460
3.298 3.344
1 lqn 480 435 490
3.435 3. 432
495
500
3.620
510
3.668 3.716 3.812
525
540 545
3.860 3.910 3.960 4.010 4.060 4.110 4.158
560
4.206 4.254 4.302
5B0
4.350 4.400 4.450
590
4. 500 4. 550
500
4.600 4 -652
610 615 520
625 630 640
4.704
4.756 4.408 4.360 4. 910
4.950 5.010 5.060 5-110
5.214 663 570
Austenitlc
MO Stalnlesa Thru Steels gCrMo lSCrSNl
5 CR
4.100 2.72 ?.76? 4.162 2.804 4.224 2.345 4.286 2.888 4.348 2.930 4.410 2.972 4.470 4.530 3.0 t4 3.055 4.590 3.098 4.650 4.710 3. l40 3.182 4.770 3.224 4.830 3.256 4.850 3.308 4,920 3.350 5.010 3.395 5.010 3.442 5.130 3.488 5.190 3.534 5.250 3.580 s.310 3.524 5.372 3.658 5.434 1.712 5.495 3.756 5.558 3.800 5.620 3.844 5.582 3.888 5.144 3.932 5. SC5 3.976 5.858 4,020 5.930 4.054 5.992 4.108 6.058 6. t20 4.'t5Z 6. 182 4. ',t96
4.240 4.286 4.332 4.378 4.424 4.470 4.514 4.558 4.602 4.646 4.690 4,776 4.7A2 4.828 4.374
6.240 6.302
5.354
6.426 5.488 6.550 5.514 6. 678
6.742 6.306 6.370 6.932
6.995 7.057
7.'l19
12 Ct
l7 Cr 27 Cr
25 Ct 20
, qnn 2.538 t .7a 2.514 2-652
Nl
Monel 67 Nl 30 Cu
3.800
3.520
J'
6i'.
3.57 4
3.908
3.628 3.682 3.736
J.vo. 4.015
2.690 4.070 2.735 4.124 2.770 4.178 2.810 4.232 2.850 4.286 4.340 2.890 , q2q 4.394 2.966 4.448 3.004 4.502 3.042 4.555 3.0a0 4.510 3.120 4.664 4. 718 3. I 60 3.200 4.772. 3.2& 4.825 3.280 4.880 1 1?2 4,934 3.354 4.988 3.405 5.042 3.448 5.096 3.490 5. 50 3.530 5.204 3.570 5.258 3.610 5.312 3.550 5.365 3.690 5.420 3.732 5.474 3.774 5.528 3.815 5.582 3.858 5.535 3.900 5.590 5. 144 3. 940 3.980 5. i98 4.020 5.852 4.060 5.905 4.100 5.950 4.142 6.014 4.184 6.068 4.226 6.122 4.268 5.176 4.310 5.230 4-352 6.284 4.394 6.338 4.435 6.392 4.478 6.M6 ',l
31h Nlckel
2.910
?.954 2 qqR 3.042 3.086
3. BI,4
3.130 3.174
3.898
3.21 8
3.790
3.952
1ta?
4.006
3.306
4.050
3.350
4. 114
4.168 4.222 4.276
3.442 3.988
J.lJ'. 3.580
4. 386
4.442
3.626
4.498 4.554
3.tt6
4.610 4.658
3.810
4.126 4.7 84
3.164
3.902 3.948
qqA
4.842
1
4.900 4,958
4.040 4.086
5.UtO 5.074 5. tJ4
4.132 4.178 4.224
5. 180
4.270
<
4,316
4.362 14R
5.404
4.408 4.454
5. 518
4.500 4,458 4.596
5.634
4.644
5.460
4.692 4.7 40
5.810 5.870
4.788 4.836 4- 884
5.990
4.932
6.050
4.980 5.028 5.076
6. 108 6. 156
6.224
6.282
21
Piping Slress Handbook Table 2-1
Continued
l Calbon Steel Carbon.moly Temp. Low-chrome (D (Ihru 3 Cr Mo)
680
5.474 690
4.tJO 4.588
700 705 710
Austenltlc
MO Slalnless Thru Steels ICrMo 18Cr8Nl
5 CR
4.920 4.954
7. 180
5.008
7.308
5.052
7
q no6
720
5.738 5.792 5.946
t'?5
5.900
730
5,2U
7.628 7 .592
5.332 5. 380 5. 428
6.004
.
.372
7.500 7.554
t.
7
o. u50
745
6. 108
5.5n
750
6. 150 6.z',t4
5.620
5.524
.U0
7.886 7
740
760
.244
166
5. 140 5. 684
7
.952
8.0r8 8.084 8.150 8,21 4
o.z06
J/b
770
o.
775
6.430
780
5. 484
190
6,592
795 800 805 310
5.754
l.
t
6DU
ont
8.342 8.406 8.470 6.5JO
!.v5b
8.602
8.568
6.645
5.004 6.052
6.700
6.100
8.80
6.308
5. 148 6. 196
8.855
6.862
6.244
a
6.29?
9.064 9. r30
7.082
5.340 6.390 5.440
440
7.138
845
7.194
6. 490
6.754
820
6.916
825 830
6.970
8.734
ooq
q tot
a 1rq 9.394
350
9.460 6.538
960 7.4
t3
7.174 840 435 890 395
/.5U6 7 .542 7.698
900
7.754
6. 686
9.542
5.734 6.182
9.724
6.830 6.878
9.856
a
7qn
9.922 6.974
q
aea
7.0?Z
r0.054
7.810
7.070
9t0
/.doo 7 472
7.1r8
10. 120 10. 188
7. 156
tu.250
7.978 8.034
7.214
10. 324
920
ln
1q2
12 C. 77 Cr
27 C.
25 Cr 20
4.520 4.562 4.504 4,645 4,688 4.730 4.776 4.814 4.A55 4.898 4.940 4.984 5.028
5,0n 5. I fO
5.
150
5.204 5.248 5.292 t. JJD
6.500 6.554 6.508
6.662 5.716
5.170 6.824 6.878
6.932 6.985 7.040
7.094 7.148
7.702 t.Z)E
Nl
Monel
3t/.
67 Nl 30 Cu
Nlckel
5.340 5.400 6.460 6.520 6.580
5.220 5.354
5.412
5. 640
6. 700 6. 750
5.508
6.820 6.880
5.604
5.940 7 .002
5.700
7.064 7.126
5.796 5.844
t.
o5z
7. 188
,250
7. 310
7
7.364 7.418
7. 310 7
7.472 I .a.n
7.490
5.940 5.988 5.036 6.084 o. tJz
/.55U
6. 180
5,380 7.580 s.424 7.634 s.458 7.688 5.5"2 7.742 5.555 7.796 5.600 7.850 5.544 7.910 5.688 7.970 5.732 8.030 4.776 8.090 5.820 8.150 5.866 8.210 5.912 8.270 6.004 8.390 6.050 8.450 5.094 8.510 6,138 8.570 5. r82 8.630 6.225 8.690 6.270 8.750 6.314 8.810 6.358 8.870 6.402 8.930 6.445 3.990 6.490 9.050 6.534 9. n0 6.578 9.1 70 6.522 9.230 6.666 9.290
.370
7. 510
7.130 7.790
6.280 O. JIU 6.380
7.850
6.430 6.480
8.036
6.580
7 417 7.974
o.5lu o, oJu
8. 160
6.580 6.730
8.288
5. 780
8.416
6. S50
8.480 3.544 8.508 8.672
6.930 5.980 7.030 7.080 7. t30
6.830
8. 735
9.800 8.864 8.928
8.992
7. 180
7.230 7 .280 7.330 7.380
9. r20
7.430
9,248
7.480 7.530
f.i84 a ?t,
7.630
Coefficients ol Thermal Expansion Table 2-1
Continued
Carbon Steel Carbon-moly Temp.
(R
Austenllic
MO Stainless Thru Steels gCrMo 18Cr8Ni
5 CR
Low.chrome (Thru 3 Cr Mo)
7. 310
I0.460
8.t88
7.360 7.410
10.528 r 0. 596
940 945
8.242
7
950
8.350 8.404 8.458 s. 512 8.556
s.080 8.134
960
970 980 985 990
.460
7. 510
8.674
8.128 s.782
7.560 7.610 7.660
I0.554 1d 71' 10. 800 t 0. 858
10.936
1.710 7.760
I1.004
7. 810
II
7.360 7.910
r
11.012
.140
r .208
t't.344
s.835
7.950 8.010
000 1005 'r010 t 0l5 1020 1025 1030 1035 1040 1045 I050 LU:: 060 I065
8.390
8.060
l t .480
8.946 9.002
0 8. 160
1
1075 r 030 r 085 090 r 095 I 100 'r 05 r0 IIr5 1120 |25 I 130 1r 35 I140 l145 'lt 50 r I55 I t60 r 165 I I 70
r
r
8.
l1 .412 I .548
8.210 8.260
1t.584
l4
9- 170
8.300
I I
t.820
I
t.956
9.058 9- l
9.228
9.236 9. 344
9.402
8. 400 3- 450 a. 500
1
.888
1?.C24 12.094
I2.
9. 460
150
1?.228
f, tO
3. 600
9.634
3. 700
Aoa
3. 750
9.750
r2.500 t2.558 tz.0Jo
9.982
8.800 8.850 8.900 s.950 9.000
10.040
9.050
I2.840
', 9.575
o
9.408
9.866 9.9?9
r
8.650
12.296 12.364
12.704 12.712
I0.094
o
no6
12.908
10.144
9.142
12.976
t0.202
9. 188
13.044
10.255
9
.234
I3.112
9.280
13. r 80
r
0.310
10.362 10.414 10.466 10.518 10.570 10.622 10.574 10.126 10. 773
9.330 9.430 9.480 9.520 9.568 9.554
I3.248 r
3.316
13.384
I3.452 13. 538
13.724 13.79?
12 CJ
17 Cr 27
Cr
Monel 25 Cr 20 Ni 67 Ni 30 Cu
6.710 9.350 5.756 9.410 6.802 9.470 5.848 9.530 5.894 9.590 6.940 9,550 5.986 9.710 7,032 9.770 7.078 9.830 7.124 9.890 .170 9.950 1.215 l0.010 7.262 10.070 7.308 10.130 7.354 10.190 7.400 10.250 I0.310 7 .444 7.488 10.370 10.430 t' .532 | .576 I0.490 10.550 1 .620 7. 586 10. 610 7. t-52 10.570 7.818 10.730 7.884 10.790 7.950 10.350 7.996 10.910 8.042 10.970 8.088 I I .030 8.I34 il.090 8.180 11.150 8.205 l l .2'10 8.232 11 .270 8.258 1 .330 8.284 11 .390 8.310 l l.4s0 8.354 1l .516 8.398 1l.582 8.442 1l .548 8.486 l .714 8. 530 l1 . 780 8.576 I .345 9.622 ri.912 8.658 l1 .978 8.714 I2.044 8.760 l2.l l0 8.804 12.176 8.848 12 -292 8.892 I2. 308 8.936 12.374 7
,]
1
1
7.680 7.730
9.440 9.505
a
31h
Nicket
7.780
a72
9.638 9.704
7.830
9.170
7.930
9.834 9.399
7.880
7.978 3.026 8.074
10.026
8.122
10.090 10.156 10.222 10.288 10.354
8.170 8.218 8.266
10.420
8.410
I0.486 r0.552 10. 618 i 0. 686
10.750
I0. sl8 10. sa6
11.42? '11
.090
It-158 11
.226 .294
|.352 I I .430 11
.498
I1.555 1
t .702
r1.770
| .838 I1.905 ' .974 12.042 12.
1
l0
12.182 12-254
\2.3?6
1'
laA
12.470 12.538 12.605 12.57 4
12.742
8. 314
23
Piping Stress Handbook Table 2-l Continued
Carbon Steel
Austeni c
MO Slainless Thru Sleels 9CrMo lSCrgNl
Carbon-moly Temp, Low-chrome (D CIh.u 3 Cr Mo)
t't75 I180
5 CR
0.830
9, 750
13.850
10. 884
9.808
13.928
9.904
t 195
10.992 I I .046
14.054
9.952
14.'t32
1200
It.t00
10.000
r
lt95 lt90
ll oot
10.938
l2t0
I | .212
r
t22n
I1.268 I1.324
r0. r55 0.208
14.200 14.268 't4.335 i 4.404 14.472
.380
r0.260
1230
14. 540
I I .436
314
14.603
10.368 10.422
r4.676 14.7M
10.476
14.812
'10. 530
14.880
l2l5
rt.ltl
I 1240
r250
1
r0.052
.492
ir.598
'll .504 l I .660
r
0. 104
r0
I 0. 582
't4.948
0.634
I5.0r6
'tl .884
r0.738
15.084 IJ. IJZ
l0.
1285
.940 .946 12.052
1290
r2.
1295
12. r 64
1300 1305
'12.22
ll.7t5
l2 60
11.772
1270
I
I
r280
r
t.328
1
1 1
108
790
r
0. 952 I I .005
15.424
II
15.560 15.628 15.596
't0.898 r
.060 .108 .156
r3t0 l3l 5
12.276
|l
12.388
I
1320
12.444
11.2s2
r325
12.500
I I . 300 I I .350
1330
I I .450 'I | . 500
t 345 r
350
r2.780
350 J05
12.892 12.948
1370
13. 004
r I
1375 1380 1385
L204
'll.€0
I340
15.220 5.288
10.844
I
L550
15.492
'I
5. 754
15.832
l5, 900
't5.968 r 6.036 t 6.104 r 6.172 't5.240
I t . 600
'15.308
I1.650
16.375 16.444 I 6.512
11 . 1t .
700 750
3.060
l1 .800
t6
't390
13.112 13.228
I1.850 I1.900 I1.950
1395
13.284
12.000
r
1400
13.340
12.050
15. 920 lF ooa
1405 1410
l4l5 1420
1
r3.l
'|
5.580 't5.643 16. 7l 6
r6.784 6.852
17
.072
17.'t48 17.224
12 Cr
l7 Cr 27
C.
8.980
Monel 25 Cr 20 Nl 67 Nl 30 Cu
12. 440
1' a1'
12.810 12.878 12.946
12.638 12.704
13.014 13.082
9.200
12.770
9.244
12.836
I3.',I50 13.220
9.288 9.332 9.376
12.902
9.024 9.068 9.112 9,156
r
13.290 13.350 '13.430
3.034
9.420 3. t00 9.465 13.166 9.512 13.232 9.558 13.29S 9.504 13.364 9.650 t3.430 9.696 13.496 9.742 13.562 9.788 ',t3.628 9. S34 13.594 9.880 13. 760 9,926 t 3.826 9.972 13.892 10.0r8 13.958 t0.064 14.024 l0.l l0 14.090 r0,154 t4. t50 10.198 14.2t0 10.242 14.270 10.825 14.330 10.330 14,390 10.375 14.450 10.422 14.510 10.468 t4.570 10,514 14.530 10.550 14.540 r0.504 't0,648 14.750 14.810 r0.692 14.870 10.735 14.930 10.780 14.990 '10.826 r 5.050 r0.872 l5.l l0 't0.913 t5.170 r0.924 15.230 I I .010 15.290
13.500
1
13.544 r
3.788
13.360
r3.932 14.004 r 4.076 14. t 48
14.22 14.292 't4. 364
t4.435 14.508
r4.580 14,552 14.724 t 4.796 14.868 14,940 1
5, 084
15.300 t 5.444
lt.tlo r
5.588
I
t- 60u
15.732 15.804 15.876
15.948 I
5.020
31h Nickel
Coefficients of Thermal Expansion Table 2-1 Continued
Austenltlc
Catlon Steel
MO Stainless Thru Sleels 9ClMo 18Ct8Nl
12 CJ 17 Cr 27 C.
5 CR
Carbon-moly Temp. Low-chrgmo (D (Thru 3 Cr ilo)
Monel
25c|20 Nl 67 Nl 30Cu
3th Nickel
't7.300
1425 1430
1435 1440 1445
17.534
17.6i2
1450 1455 1460
17.690
t465
17
17.768 17.846
.924 I8.002
t470
18.080
1475 1480 1485 1490
r8. r58 18.235
I495
13.31 4 le 102
500
18.470
r
Temp.
(D
-32 5
-320
Alumlnum
-4.68 -4.636
-315 -310 -305
-4.592
-300 -295 -290
-4.46
-4.548 -4.504 -4.41 -4.36
-2Aq -280
-4.26
-275
-4.21
-270
-4.162 -4.1
l4
Gray lron Bronze Brass
Caal
-J. v6
-3.932 -3.884 -i e1f -3.788 -3.692 -3.644 -3.596 -3.548
70 Cu 30
Nl Ni.Fe.Cr
-J-66
-J.lt
-3.64
-2.87
-3.832 -3.094 -3.784 -3.038 -1 t16 -? aa? -3.688 -2.926 -3.592 -2.836 -3.544 -2.&2
-1.49D -a. t06 -1..t.t5 -a- I J4
-3.4s2 -3.352 -3.404 -3.304
-3.5 -3.40
-2.70 -2.666 -2.632
-3.308 -3.208
-2.564
-260 -255
-4.066 -4,018
-250 -245
-3.97
-3.26 -3.16
-2.53
-?40
-3. 366 -3.8',r4
-3.164 -3.068 -3.I t6 -3.022 -3.068 -2.976
-2.462 -2.428 -2.394
-235 -230
-3.2'12 -3.114 -2.496
'J.Va -210
-3.602 -3.548 -3.494
-a.tJ
_2. JO
-2.972 -2.884 -2.326 -2.924 -2.833 -2.292 -2.82A -2.746 -2.224
Ni-Cr.Fe
Ductile lron
25
Piping Stress Handbook Table 2-1
Continued Temp.
(D
Aluminum
Gray Csst lron
-2.78
-3.44 -3.384 -3.328
-2.732 -2.684
-2.654
-180
-3.216
-2. t66
-2.5
-175
-3.16
-2.54 -2.47 -2.494 -2.424 -2.448 -2.378 -2.402 -2.332
-200 -195 -190
-185
n70 -t
65
-160 -155
-3. 104
-3.048
-?.992 -2.936 -2.88
-r 45
-2.8i8
-140
-2,756 -2.694
-lJ5 -llu -125 - r20
nl5
-6t
-80 -75 -70 -65 -ou -55 -45 -40 -30 -25 -20
30 35
40 45
-t
.49
-l .45
-2.086
-t.J60
-2.052
-1
.4t
-i .362
-l .984
-l.314
-2.24
-1 .95
-2.144 -2.096
-1.908 -|.aroo -1 .824
-1 .29 -1 .264
1AJ
-?.27 -2.21 -2. 15 -2.09 -? i1
-t.ot -l .76
-t.ro
-1.53 n .49
-1 .04
'l.ll _l.OO
-l.OO4 -l.OlO
-1.97
-t .56 -1.52 -t.512 -1.474 -1.464 -1.42A -l.4t6 -1.382
n.91 -l .85 -t .79
-1
71
-r.ot
-l.6
-l .46 -1.39
-2.048
-1 .856
. 6',14
-l
,306
.236
-1.292 -l .182 -1.278 -t .128 -1.264 -1.074
.25
-1
-t.lt
- ,962 -0.866 -
.858 .804
-
.696
-.902
- .834 -.766 - .698 -
.56 .49 .42 .35
-t.o50
I
-l .16 -1.136 -1
-l
.l t2 .
c88
.45
-1.014 -.988
-1 .41
-,962
-l
-1.33
-l .29 -l.21 -1.13
-1
-1.32 -1.25
n.18
-'1.74
-1.698
-t.506
-1.212
-, . 160
-l .952 -l .904
-1.712
-t.233
-.91
-.882 -.854
-,826 -.798
-1 ,67
-.97
25
-2.31 26
-1
-1.064
0
20
-2. Z60
-r .5l
-2.148 b
-2. JaC
-2
-2.162
Ductile lron
-1 .572
-l .04
l0
|
-2.19
Ni.Cr.Fe
-l .808
- t5 - l0 -5 5
-2.608
Nl Ni.Fe.Cr
-2.00
-2.57 -2.51 -2.45
-tu5
-95 -90
-2.70
30
-2.21 -2.16 -2. 1 l -2.06 -2.01 -r .96 -t.9l -r .86
-110 -100
Z0 Cu
Eronze Brass
-',!
.02
-t. t3.t -.9vo -l .058 - .912
.714 .658 .602 .546 .49 .436 .382 .328 .274
-
.642
-1 .082
-.77
_.74
-.71 -0.986 -0.938
- .89 - .844 - .799 -.752 - .706 - .66 -.612 -.564
- .65
-.62 -.588 -.556
-.524 -4.9?
-.414
.588 .534
- .5',16 - .468
-.276
.48 .426 .372
-.374
-.212
.318
-
.282
-. 194 -. 176 -.158
.264
-.236
-.322
Coefficients of Thermal Expansion Table 2-1 Continued Temp.
(R
50 55 60
Alumlnum
-.28
- .21 - .14 0
ta
.3066 . J6JJ
'100
120
.616 .694 .772
125
.85
130 135 140 145
.926
5
165 170
.312 .346
.54
.414 .448
.72
,482
.84
.622
.08 .14
.542
2.00 ?.082 2.164
1.26 .764 70'l
.972
2.41
230
2.494 2.578
'L I
'I
.08 .118
I.i56 I .194
.232
2.7 46
1
250 255 260 265
2.43 2.912 ?.994
1.27
270
J. lc6
I
275
3.24
1.45 1.488
295
'I
.
.21
.246 .282 .318 .354
.472
.56
.52 .568
.664
.oto
.716
.oo+ .712
.612 -bbb
.
.76 .805
.7 .744
.57
.852
.798
.
.97
.898
1.02
.944
,832 .876
.684 .72?
.92 .966
.788
1.012
.826
.olz ,
768
.82 .87 .54
.07 .122 .174
.288
1.
. 175
346 404 462
,226
.278
.5b6
oa
.038 'I .086 1
't
.
]34
I.182
.39 .4?6 ..+Oa
.498
'1.058 'I
'I
.62
l.ott 1.74
1,8 1.86 1 .922
,902
1.342
2.294 2.356 ?.418
.4]4
2,8
2.542 2. 604
I .564
1.602
I .434
t./06
l.tJ6
1
.83
1.486
1
.59
2.14
2.232
'1.378
1.644 1.705
2.17
306
.
.94
2.046 2. t08
.984
2.666 2.728
o.to
.864
.',t04
'I
'1
1.86
2.202 L 914 2.264 1.968 2.326 2.022 2.388 2.076
2.512 2.574 2.698
.252
.196
| . JJ.t I .386
.288
1
.892 1 .644 ,954 I .698 2.C]6 1.752 2.078 I .806
'I
tJ+
.60s
l.Jo
225
290
1.
.14
.424
1.114
t.Jt' I .44
. 105
.51
uto
1.172
.035 .07
.46
,94 .998
'l
1
044
3.412 3.498 3.584
.41
| .76 .82 .88
I .32
.866
2.328
3.076
2
.0933
.35
.
|.
.0433 .0866 .13 .1 73 .216 .26 .304 .348 .392 .436 .48 .524
.25
.408 .466 .524 .582 .64
.96
220
280 285
.l15
.5',16
r.008
240 245
.1866
.48
2.246
2.35
.206 .258
1.386 I .464
1.698 1.776 1.854 1.932
205 210
.t4
.24 .J
.233 .291
.lla
.02
| .62
200
.12
.586
175
190 't95
.0466
'L 308
1
0
.05'16 .1033
.278
.14 .105 .07
-_.035
.0s83 .1166
.uo
.658 .694
-
0
.66
.002 .078 .154
180 '185
-
.?44
110
Ductile lron
Ni-FeCr
- ,21 - .105 q2E
.21
't05
Itt
.055
.035 .07 .105 .14
80
t3u
.165
0
.016
85 90
Nl
-
-.07
70
70 Cu 30
Gray Caal lron
2.184 2.238 2.346
'I
.012
']
048
I . 084
.438
I .49
'I
L.38
544
1
.426
t.t7
I .598
1
.472
1
'|
.
'I
.?1
.652
1.5i3
1.706
't
.564
1.75
'l
,5l
1
.658
.37
706
.41
802
.45 .49
1
1
'l
.8',t4
.868
1
922
']
.25 1.29
'1,754
1.976
1.
2.03 2.084 2.138 2.192 2.246
't
.85
I .898
I .568
1.946 I .994 2.O42
1
'|
.606
.644 I .682
28
Piping Stress Handbook Table 2-1
Continued Temp.
(D
Alumlnum
300 305
3.67
3i0
3. 838
Gray Casl lron
1
't
.64
.678 1.716
'1. 754
Bronze Brass
274 2.954 2.918 t oat 2.046
320
4.006
't.792
325
4.09 4.176 4.262
I.atj 1.87
3.',t I
r .91
3.234
1.95 I .99
3.296
3.4
330 340 345
4.348
4.434
350 355 360 365 370
4.52
4.864
2,03 2.068 2.106 2.144 2.182
375 380
4.95
4.606
4.692 4.778
3.1n
3,484 3.548
3.612 J.O/O
2.22
2'A
lAE
5.038
3.7 4 3. 802
5.126
2,3
3.864
390 395
5.2 14
2.34
400 405 410
5.39
5.302
s.478
2.42 2.46
5.566 5. 654
2.54 2.58
3.926 3.988 4.05
4.
4
4. 178 4.242 4.306
420
5.742
425 430
5.92
4.434
4.498 4.562 4.626
4.37
6.0i
2.704
440 445
6.1
2.7 46
450 455 460 465 470
6.28
2.788 2.83 2.87
4. 69
2.76
70 Cu 30
Nl NLFe-Cr
2.40
2.30 2.358
Nt-Cr-Fe
2.09
3.48
4.248
3.648
4. 314
3. 704
2.56 2.606 2.652 2.698 2.744
4.38 4.448
3,76
2.79
4,516
3.872 3,928
3.386 3.434
3.984
3.482
4.l l6 4.1e.
4.584 4.652
z.4to
2.474 ? q1,
2.648 2.706 2.764
2 e)t
2.136
2.182
2 2r9
2.2't4 2.368 2.416 2.464 2.512
2.8
2.56 2.508
J.UO
2
2.94 3.00 3. l2 3.
l8
2.4
2.95
3.0 3.05 3.098 3. 146 3. 194
2.91
4. 856
6.544 6.632
2.95
4. 882
4.094 4. 148
4.946
4.924 4.992
4.202 4.256
3.68
475
6.72
3.03
5.01
s.06
4.31
480 485 490 495
6.81
3. 78
5.074
6.9
3.072 3. 114
5.128 5. t96
+.
6.99
4.422
3. 156
7.08
l10a
5.202 5.266
3.828 3.876
5.264
4.472 4.534
3.924
.17 7.262 7.354
3.24 3.284 ? 1'A
5.394 5.458
4.59 4.646 4.702 4.758
5t5
7
520
7.538
.446
525
3.46
5.65
530 535
7.724 7.818
3.544
7.912
a. t61
s40
J. J6O
5. 848
545
8.006
3.628
5. 9',I4
5.
7',1
2.97 4 3. 04
G4
JOO
2.882 2.928
3.088 3. 63 3.',]84
3. 73
3.28 3.384 3.436
3.488
5.68
4. At4
4.02 4.07 4.12 4,17 4.22
5.75
4.87 4.929
4.27 4,32
3. /'6 3.806
5. 89
4.986 5.044
6.03
5. 102
4.42 4,47
3.898 3.944
5.54
5.522 3. 416
2.44 2.48
3.816
4.
5.40 5.47
2.05 ?.09
2.80 2.85
4.72
7
.97 2.01
,704 2.752
2.656
2,9
1to,
.804 .846 .888
2.13 2.176 2.222 2.268 2.314
4.788
500 505 510
.7?
2.824 2.456 2.838 2.512 a.taz 1, to6 3.016 2.624 3.08 2.68 3.146 2.736 3.212 2.792 3.278 2.848 3.344 2.904 3.41 2.96 3.474 3.015 3.538 3.072 3.602 3. 128 3,666 3. 184 3.73 3.24 3.794 3.296 3.858 3.352 3.922 3.408 3.986 3.464 4,05 3.52
4.754 4. Bl8
6.368 6.456
Duclile |ron
6
3.54 J. 0Z6
3.672
l./to
Coetficients of Thermal Expansion Table 2-1 Continued Temp, (F)
550
Aluminum
8.
Gray Casl
tlon
1
8. 192
3.
8.376
7l4
Bronze
Brass
5.98 6.046 6.112 6. I78 6.244
6.10
560 565 570
8.2U 8. 468
3.758 3.802 3.846
575 580 585 590 5q5
8. 56
3.89
8.654 8.748
3.934
b.l I b. J/b
8.842
4.022
b.
8.936
4.066
600 605 610 615
9.03
4.n
620 625 630 535 64C
645
4. 156 4.202
4.428 4.294 4.34 4.386
4.432 4.478 4.524
550 655 660 665 670
4.57
675 580 685 690 695
4.8
4.616
4.662 4.708 4.754 4.846 4.A92 4.938 4.984
700 705
5.076
7t0
5.122
715 720
5. I68
5.214
7?5
5.26 5.308
730 735
740 745 750 755 760 765
5.404
5.452 5.548 5.596 5. 644
770 775 780
785 790 795
5.7 4
5.788 5.884
5.932
6.442 !u6 o.l/+
70 Cu 30 Nl
Ni"Cr-Fe
5. 16
Ductile lron
3.99
4.32 4.57
4.036
4.62
4.082
6.31
5.218 5.276 5.334
6.38
5.392
4.7?
4.174
o. +J
5.45 s.496
4.77 L.82 4.87
4.2? 4.264 4.308
5.608 5.664
4.92
4. 352
6. 17
6.24
o.3z 6.59 0.00
o./J
6.64 6. 80 6.704 6.872 6.944 6. 768 7.016 6. 832 6.896 7.088 6.96 7 .16 7.234 7 .026 7.308 7 .092 7.158 7.382 7.224 7 .456 7.29 7.53 7.356 7.602 7.422 7.674 7.488 '1.7 46 7.554 7.818 7. 89 7 .62 7.686 7 .964 7.752 8.038 7.818 8.1 12 7.884 8.186 7.95 8.26 8.016 8.336 8.082 3.412 8.148 3.488 8.214 8.564 8.28 8.64 8.348 8.716 8.416 8.792 8.484 8.868 8.552 8.944 8.62 9.02 8.688 9.096 8.756 9.172 8.824 9.248 8.892 9.324 8.95 9.40 9.028 9.476 9.096 9.352 9.',164 9.628 9.232 9.704
4.128
1.97 4.44
3.72
4.484
5.778 5.1?
t.17
4.528 4.572
3.?2
4.616
6.01
5.27
4. 66
6. 068
5.322
4.708
6. 184
s.426
6.242
5.478
4.756 4.804 4.852
6.30
6.524
5.53 5.582 5.634 5.686 5.738
6.58 6.64
5.84?
5.836 5.894
(
oE,
6.126
6.355
6.412 6.468
4.9 4.948 4. 996
5.044 5.092
5.394 5.946 5.998
5.24
6.938
6.102
6.996 7.054
6. 154
5.432 5.474
6.206 6.258
5.558
6.362
5.60 5.65
6. 414
5.70
6.70 6.7 6
6. 88
7.112 7.17 7 .23 7 .29
7.35
5.34
5.75
7
.41
o.f,kt
7
.47
.528
7.586
6.57 6.6?4 6.678
5.85
7
.644
6.732
6.00
7
6.05
7.702
7.76 7.82 7.88 7,94 8.00
5.90
6. 84
6.t0
6.894
6. l5
6.948 7.002
6.20 5.25
5.30
29
Piping Stress Handbook Table 2-1
Continued Temp. (F)
Alumlnum
Gray lron Bronze Brass
Cast
.800
805 810 815 820
825
9.30
5.98 6.028
v,
6.124 6.172 6.22 6.27 6.32 6.37 6.42
850 855 860 865
6.47 6.52 6.57
870 875 880 885 890 895
5.72
900 905 910 915 9?0
6.97
6.77 6.87
7.022 7.O74
7.216 7.178
925 930
7.284 7.338
940 945
,392 7 .446
950 955 960 965
7.5
970
7.708
7
7
,604
7.656
975 980 985 990 995
7.812 7.864 7.916
'1000
8.02
't005
l0l0 i0r5
't020 1025 1030 1035 1040 1045
7.968
'10.4 10.96 1.038 10.47 t'l.lt6 10.54 l't .194 10.61 11.272 1
10.748 10.8't6 10.884 '10.952
11.02 I1.09 'l l.l6 11.23 'l l .3 11.37 'I r .438 1l
'I
I
.506 .574
11,642 l
t
.71
11.778 '11
.846 I I .982 l
l.9r4
12.05
12.12 '12.19
12.26 12.33 12.4
12.472 12.544 12.616 16.688
8. 06
y.556 9.936 10.014 10.092
'10.33
'10.68
Nl Ni_Fe_Cr
9.78
9.436 9.504 9.572 9,64 i0. I 7 9.71 10.25 9.78 10.33 9.85 10.41 9.92 10.49 9.99 10.57 10.06 10.648 10. 13 10.726 10.2 t0.804 10.27 10.882
5.076
830 835 840 845
Jo5
70 Cu 30
8.118
Ni_Cr_Fe
7
Ductlle lron
.10
8. I76
6.398 6.446
8.292
6.542
8.412
5,59 6.642
6.494
8.474
8.598
6. 694
o. /40 6. 798
8,66 6. 898
B,784 8.846
8.908 8.95 9.012 9.074 9.135 9.198
6. 946 6. 994
7.042 7. 09 7. 138
/. tt'0 .234 7 .282 7
1l .35 1
l
.43
11.51
ola
.59
I .44
1 1
II.57 11.75 11 .832 11 .914 11.996
12.078 12.
t6
12.242
12.324 12.402
9.5 9,622 9. 684
9.746
10.242 10.304 I
u. Joo
10.428 10. 49
t3.062
'10.
13.i44
10.614
13.226 13,308
't0.738
s52
10. 80
13,474
'10.862
13.558
10.924
13.642 13.726
7.772
7.9r
10.t8
',t3.39
7
9.87 a o?, 9.994
12.57 12.652
12.98
.64 .684 7.728 7
/.6tb
10.056 10.118
12.816 12.898
.466 .524 7 .582 7
1
9. 808
12.488
12.734
7.408
I0. '11
.
986 048
7. 86
8.01
8.06
8.rI 8. ',t s8
8.206 8.254 8.302
Coetficients ot Thermal Expansion
2-l Cofitlrued Table
Temp.
o
1050 1055
t060 1065 1070 '1075 r
080
1085 1090
t095 00 1105
l l t0 'n
l5
1120 1125 1130 1135 1 140
lt45 50 '1
155
Aluminum
Gray l;on
Cast
8r6nze Erass '
12.76 12.83 12.90 1?.97 '13.04
l3.l'l
r3.182 13.254
13.32 13.39 13.47
70 Cu 30
Nl Nl-Fe-cr
13.81
11.11
13.894 13.978 14.062 14.146
'11
14.23 14.314 14.398 14. 492
14.566
n.172 11.234 .296
'1t .3
58
11.42
1t.484 11.548 't1.612 l1 .676
l4.65
Il.74 r
1
.802
11 . 864
11.926 .988 12.05
't2,I16 12.182 12.248
12.3]4 12. 38
12.442
lt60 '1165
12. 504
l l70
12.628
'1175
12.69 tz. tao
1180 85
I190
|
2.500
12.&2 't
2. 888
'I195
12.954
r200
13.02 13.088 tJ. t50
't205 '1210
l2l5 1220 1225 '1230
13.292 IJ.JO
'13. 43
1235
1240 1245 1250 'I255
13.64 '13.
71
1260
13.776 13.842
1265 1270
13.974
1275 1280
't285 1290 1295
'13.908
14.04 '14. l '14.
l
l8
'14.25 14. 32
Nl-Cr-Fs
Ductlle llon
31
32
Piping Stress Handbook Table 2-1 Continued Temp.
o
300 i 305
Aluminum
Gray lron Bronze Erass
Casl
70 Cu 30
Nl Ni-Fe.Cr
l310
14.39 14.46 14.53
1320
14.67
1
't315
'I4. 60
14.7 4 1330 IJJ' 1340 1345 1350
14.812
'14.884
r5.028 '15. 10
tt.l06 I JOU I JOa
15.304
1370
15.372
375 I 380 'l 385 1390
15.44
r
't 1
5.584 5.656
15.278 1400
'1405 t
4l0
l4l
15,80
13.872 15.944
5
I 5.01 6
1420
16.088
1425
16.
1430 1435
16.234
't440 1445
l6
16.308 16.382 16.456
1450 1455 1460 1465
16.53
1470
16.81
1475
76.88
1480 1485 1490 r 495
17.029 17.102
'1500
17.25
16. 60 16.7 4
16. 954
17.176
Ni-Cr-Fe
Ductile Iron
lable 2-2 Modulus ot Elasticity-Ferrous Material Modulus ot Etasticity, psi (MultiPly Tabulated Values by
106)
oF
-325 -200 - 100
Iaterial
:--lrn :r::
70
300 400 500 600 700
200
800
9oo 1000 1r00 1200 1300 1400 1500
steels
content
l-r
or
\:=:.31/2 ..::.rr
30.0 29.5
29.0
27
.9
27
.7
27
.4
27 .O
26.4 25.7 24.8 23.4 18.5 15.4 13.0
steels
:'::
Coment i^rl ie
lr l
31.0 30.6 30.4 29.9 29.5 29.0 28.3 27.4
"c
26.'7 25.4 23.8
21.5 18.8 1s.0
11.2
23.0 20.4
15.6
--:':r-moly i---s. low -_:tme :--r'rgh
3
,- \to
,::
i -:,aOlarc
31.0 30.6
30.4 29.9 29.5 29.0 28.6 28.0 21.4 26.6 25
29.4 28.5
28.1
30.4 29.9
29.4 28.3 27.7
7
24.s
,:at:ne
;-.s "1, :-
(5 Cr
:_qh 9
-- \lo)
.
- i::lllc --:tI ' 1rK -' 1l?) r:-L-:: :-_
27.4
27
.1 26.8 26.4 26.0 2s.4 24.9 24.2 23.5 22.8 2r.9 20.8 19.5
27.1 26.6 26.1 25.4 24.8 24.r 23.4 223 22.0 21.3 20.7 r9.3
17 9
ChrO-
-ll
30.8 30.3 29.8 29.2 28.7 28.3 27.7 27.0 26.0 24.8 23.r 2r.r 18.6 15.6 r22
i- l:t
13.4 r3.2 12.9 12.6 r2.2 11.'l 11.0 10.2
aa "t . ;-:;
are
for infornation, and it is not implied that materials are suitable for all lhe tempefatures
shovrn.
Table 2-3 Materials Elasticity-Nonferrous Modulus of E = Modulus of Elasticity, psi (Multiply Tabulated values by TemDerature, "F
,,
18.1
:€
67 Ni-30 Cu) and
106)
26.8 26.6 26,4 26.0 26.0 26'0 25'8 25,6 25'4 24.7 2.31 2|.o 18.6 16.0 14.3 13.0 Cu-Al) r--e:-\ickel - J.r-30 Ni) 21.6 Zl.5 21.2 2O.9 20.6 20'3 20 O l9'7 l9'4 -. -::--.tm alloys 10.9 10.6 10.1 10.0 9.8 9.5 8.7 7 7 ll.3 ' rrr:.99.98% Cu) 17.0 16.7 16.5 16.0 15.8 15.6 15.4 15 1 14.7 14213.7 | :- e:cial bmss (66 Cu-34 Zn) 15.0 14.7 14.5 14.0 13.9 13.7 13.5 13.0 12.7 l2'2 lf '8 -ia:i: :in bronze 14.2 13.8 13.5 13.0 12.9 12.7 12.4 12.0 i1.7 11.3 10.9 rl :r-6 Sn-1.5 Pb-4.5 Zn) :c \l-29
' ,t :=:
erc
for infonation, and it is not implied lhat materials are suitable fot all lhe tenperotures shown'
Piping Stress Handbook Table 2-4 Propertles of Salurated Steam v-cs|E I T6Fhtw. ,s.ff
i
P'
0..|{, 0.45
I H6t or I L.6r H6r I To!.t H..t
.lll}''|
!h. Liquid
lofEvle4.lis
I
of
s44
,9c..i6. 77
Coelficients of Thermal Expansion Table 2-4 Continued
rdpa.*.
i
.#E:1".j"
l"tffiltl I 'St*.
v
6.5!{l 6.,t58
76.0
n.0 78.0
5,lll
5.055 5.001 4.948
101,0 102.0 103.0
r04.0
4.19.1
4.157
{,110
112.0 113.0
lt89.l 1189.{
{.015 3.981
rr89,5
3.9r4
1190.7
t.at
llqt.8
u90.9
3.61{
1191.9 1192.0 1192.1
3.110 3.147 3.264 3,712
la6.
to.
l$. 0 lag. 0
35
36
Piping Stress Handbook Table 2-4
Continued Hqr Tod Ha! .Her.f.. II dr-tdr! @uq@ Ei.po..rr@ I| of sr..E
:.134
2.67 |,9992
i.999 r.9183
Expansion
Coefficients of Thermal Step
ExamPle Problem Use Figure 2-1 to calculate the F factor for the
i
2.
move horizontally to the left to find the t€mper-
atue correction factor, F, which in this example is equal to 0.22.
: 660"F : l0 ft-O in. = lin. K : I (shrt fully insulated) 'F : Ambient temperature Tr : Average temperature
T I t
1.
Klt
vl
Enter the chart at the point along the botom line where kh/Ji. Then move up vertically to
the point where the curve intersects' Then
follow-
conditions:
sep
Step3. T1 Step
4. Td
: T-70'F:530'F.
:
F x Tr
:
O.22
x
530"F
:
116.6'F
or 117"F.
I x 10ft :-=IU
Steps.
T" =
Tur
* 70'F :
117"F + 70"F
r87"F.
1
l.o .9
.t .,
Temperature at top ot skkt (oD Av€raqe temperature of skirt (oD Height of skirt, ft
Thickness of sklrt, in. 1 lor skirt lully insulated 1.7 for skirt flreback insulaled 2.7 for skirl not insulated Temperature corrgcllon lactor
1.6 l
.5
I .3
37
Example (see Page 2)
.2 .t
t4
t6 t8 20 22
24
26
2A
---------1>
Flgure 2-1. Curve for determination of average skirt temperature.
30
32
3ll
:
Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 (198t
This chapter contains allowable thermal stresses for petroleum piping. Values of Sh taken from ANSI/ASME Code 831.3-1980, Appendix A, Thble l. (Used courtesv of the American Society of Mechanical Engineers.)
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Stress Intensification and Flexibilitv trlactors
c Minimum radius. Tt'is dimension must not be less than .05 D65 except widr a branch diameter larger than 30 in. It need not exceed 1.50
The following is an explanation of the terms used in figuring flexibility and stress intensification factors. Refer to Tables 5-l through 5-3 for a tabular listing of the factors for different piping configurations. Figures 5-l and 5-2 illustrate these factors for widely spaced, two-weld and three-weld miter elbows, respectively.
t
.
i: T:
T: To: T.:
0:
Maximum radius, For outlet pipe sizes 8 inches nominal and larger, this dimension must not exc€€d 0.10 Dob + 0.50 in. For outlet pipe sizes less than 8 in. nominal, this dimension shall not be greater than 1.25 in.
When the external contour contains more than one radius, the radius of any arc sector of aF proximately 45" must meet the requirements for maximum and minimum of radii. o Machining must not be employed in order to meet the preceding requirements.
Definitions
h:
inches.
Flexibility characteristic Flexibility factor (never less than unity, factor for torsion equal to unity) Stress intensification factor (never less than unity, factor for torsion equal to unity) Nominal wall thickness of the fitting for elbows, and miter bends, in. Nominal wall thickness of the marching pipe for tees, in. Crotch thickness of tee, in. Pad or saddle thickness, when q is 1.5T, use h : 4Tlf . n. One-half angle between adjacent miter axes,
S = Miter spacing at centerline, in.
: Cr : C2 : D*
.
Closely spaced miter bend: S
o
Mdely
spaced miter bend:
(
12 (1 + tan 0) S >r2 (1 + tan 0)
O.D. of branch, in. Correction factor for curves with one end flanged, Cr : firre Correction factor for curves with both ends flanged, C2 : hr/3
deg
Rr:
Mean radius of matching pipe, in. Bend radius of welding elbow or pipe bend, in.
: S cot 0 /2 : [rz (1 * cot
o For closeV spaced miters Rr o For widely spaced miters Rr
0)lt2 Radius of curvature of the external contoured portion of the oudet measured in the plane containing the axis of the run and branch in inches. This is subjected to the following limitations:
The piping code does not speciff any particular distance from the end ofthe elbows arc or the centedine or a miter weld in which a flange will be effective in modiffing the K and i factors on these items. Until a better definition is published, the following rules can be applied: o Weld
elbows-Modifu the k and i factor when the butt weld of the flange is within one pipe diameter of the butt of the elbow. (Text continued on page 120.)
112
Stress Intensification and Flexibility Factors Table S1 Flexibility and Stress Intenslfication Factors Floxlbility
D.l6iprion
Outpl6n.
t
\lblding elbow
sirara lnt. F.ctorl'6
r.65
or pipe bend
Closely spaced miter bend s<12 (1 + tao 0)
F;t
Single miter bend or widely spaced
t.52
1.52
Fl.ribiliw Ch!r!ct!dnic h
li
'pz
0.9 'p;
tr'n
0.9
0.9
r;
314io + 114
(',)'
09
Cot 0
(")'
2
@#
l+coto r 2't
miter bend
s>/2 (1 + tan
-
ffi
lRt
0.9
0.75 'et
Skctch
d)
Weldins t€e
per -A.NSI 816.9
0.9
with
r,)I/a
D2
T
T"> 1.5 T
Reinforced fabricated
0.9
I
TE
I
TE
tee with pad or
314io+
ll4
saddle
UNeinforced fabricated tee
Extruded
welding tee
t
0.9
0.9
tt"=
3l1io+ rl4
3141o+ r14
T
(.f)f
T"<1.5 T Welded-in contour insert
r,)I/a
D2
0.9
1
t*
314
io+
T
ll4
T">1.5 T Branch weldedon finirg
0,9
0.9
(integra Y
3,3
T
-
reinforced)
ANSI/ASME 93l.3d-1984 Reproducedlfom ANSUASME Code 83l-3-1980, Appe dix D',lirble ical Engineers.
I. Repi
ted counesy ofThe At efican society of Mechatt-
113
rl 114
Piping Stress Handbook Table
+2
Str€ss Intensitication Factots for Branch Connections
40 80
f60 40 80
150 80
t20 160
xxs
'lt
1.00
1.00
I.OI 1.34
1.45
1.0 1.0
1.00 1.00
l.l0
0 0
1.00
2 0 0
t $
1.03 1.00 1.00 1.00 2.16 1.44 1.30
60 80
100 120 140 160
I .l
10 20 30
1.0 0 1.0 0 2.O4
1.84 1.60 1.36 L.20
t50 t0 20 ST 30 40
L.20
1.01
8
r.0
1.0
0
1.0 0
140
t60
40 50 80
100
L20
t.0 r I.0 0
1.0
0
l0
3.54
t.97 1.40
100
std
1.00 1.00
20 30
2.0 1.9
8 0
20 30 40
60 80
1.43
.250
30 40 60 80
100
0
r.0
0
4.39
1.0 2
1.00 4.0
0
2.90 8
1.10
stal
1.00
20 30 40
3.49
.250
1.00
.3r2 std 20 30 40
4.40 3.89 3.20
2.31 3.84
3.42 2.56 2.49 4.59
4.79 4.23 3.48 2.80 5.78
4.9
10
1.34
13
0I
4.64
4.42 IO
9
2.70
1.0
s!d
xs
l0
I.OI
4.0
stal
1.00
1.
1.49
10
2.54
1.00
r.
20
1.78
I.09
8
L.14 1.47
2.34
30 40 50 80
r.23
7.23
1.0
2.43
20
xs
1.88
100 120 140 150
1.10
140 160
t0
40
1.87 1.56
4 0
2.22
t
3.89
IO 20 30
1.0 1,0
1.00
2.09
1.0
2. a7
1.9
r.82
L20
2.40
1.00
2. r.0
80
I40 t60
0
2.59
100
I.00
1.0
0
60
r20
f.80 r. {8
1.00
r.0
xs
1.09 1.00
7
I.00
40
I.00 r.69 t.03
120 140
1.00
1.0
xs
l. l3
s9
1.45
std
L.O2
1.00
f.78
20 30
0
0
1.0
l.
I
I.0
r.22
1.0 L.0 1.0
rl
1.00
2.91
8
4.40
2.37 4.39 3.27 2.54
6.40 4.88 3.46
.
Slross Intensitication and Flexibility Factors
Table 5-2
Contlnued
40 80
160
1.00
d0 80
!.29
I50
{0 80
r20 r60
xxs {0 80 120 160
xxs
1.00
1.36
r.0 2.27 1.04 1.00
80
1.6
2.24 1.90
4
100
1.45
140
1. 16
160
1.05
30
{0 50 80
100
\20
l.l0
80
1.0
8
1.7
3
3.70 2.88
50
1.99
80 100
1.49
1.32
I00
IO
1.73
30 40
2.95 2.62
3.ss
60 s0 100 140 160
l0
!.L2
40 60 80
3.31
1.80
120 140 160
L.24
l0
5.66 4.86
std
4.39
20 10 20
30
s.36 4.11 3.91 3.34
1.08 s.80 4.24 3.6
4
7.0
3
3.41
140 10 20 30 40 60 80
I40
r00
t.4s
10 20 30 40
r60
100 120
1.70
1.49
r20
2.01
3.08
100 120 140 !.50
xs
40 50
2.5I
2.50
50
3.01
xs
30
40
xs
3.34
3, ?9
t.09
3.41 2.98
std.
sa
20
30
20
4.39
xs
140
t60
10
160
2.47
20
1.13
80
20 30 40
xxs
120 140
1.0
8
4.0 7
3.{9 3.09 2.09
t.52
6.08 5.36 4.39 3.34 7.82 s.96 4.A9
4.20 3.70
116
Piping Stress Handbook Table 5-2
Continued
f.70 0
1.00
1.58 1.30 1.04
1.40
L.0
40 80
L20 150
xxs
t.7
l.
4
41
l.14 t. 01
ll
1,00
1.83 1.70 1. 41
3,00
1.86
2
100 120 140
2.27
-t4
1.85 1.43
f0
2.64 2.Aa
xs 30 40 60 80
1.49
100 120 140 160
3,91
10
3.24
std
2.O 4
1. 41
I.29 4.74 3.06 2.85
2.O 4
I.7
4.23
f,49
3.7
7
3,0
7
1.22
.250
5.9
4
1.9
std 20 30 40
3.r7 2.44
2.60
10 s
3.82 3.32
4.75 3.9
r.50 r.25
20 30 40
3.68 3.20
4.57
.250
3.9
3
2.45 2.36
1.9I
5.3s,
tal
1.38 7.27
1.74
4.76
6.r7
8
2.O2
3,07 2.39
5.46
4.42
6.9I
6.01 5.31 4.69
10
3.38
2.38
5.99 4.56
6.34
0
4.35
20 30
2.94
1.,38
5.0
s.49
1.37
12
1.40
stil
1.28
t
1.54
2.03
.250
1.68
4
3.28
2.95 2.38
1.40 1.30
r.94
1,5r
4.0
7
t
l0
5.31
1.99
2.43
1.7
100
2.46
2.O7
1.94
10 20 30 40 60 80
3.28
20
2.Ar
7.12
1.29
20
2.69 1.6 7
2.00 I-7 4
1.20
3
5
3.09
100 120 140
3.49 3.0
3.'7
2.19
2.45
10 20 30 40 60 80
2.t9
1.68
1.37
4.94
6
3.45
40 60 80
140 160
1.20
2.a7
3,9
t20
1.23 20 30 40 50 80
7.52 f .35 1.25
XS
100
1.18
2.50 2.34
1.48 1.32
1.19
ST
I.20
1.31
rc
10 20 30
1,08 1.00
r.26
1.39
.3]-2 stal 20 30 40
6
5.78 4.'t
6
4.0
9
3.42 '7.89
6.80 6.00 4.9
5
3.44
4.25
6.8
r
8.75
5.9
0
5.24
6.66 5.4
8
4.72
*RXINFORCED FABRICATED TEE PAD THICKNESS EQUAI TO NOMINAT THICKNESS OF PIPE HEADER
.
Table
117
Stress Intensification and Flexibility Factors
.5F2
Continued
40 80
160 40 80
160
2.19
2-16 2.22 r.6 4
2.63
2.30 1.80
2,7
3.
r.88
7.34
3,90 3.03 2.50
xs
4.80 4.45
6.0?
4.57 3.34
2.10
2.41 10.44
1.76
2.Ol
8.0 8
4.61 4.31
5,49
r
4.21 3.64
2.07 2.02 4.71
4.2r
3.44
3.0 7
2,45 2.0
3
6.02 4.39 3.84 2.45
2.49 2.29
5. t4
4.60
4.9 5
2.80 2.43 6.85 4.25 3.?6
xs
4.0I 3.14 2,72 2.25
10 20 30 40
50 80
,94
4.61 3.9
4
3.39 3.0 3
2.24 9.09 4.14 3.17 3.24
2.59 2.37 't.69
4.78 a.40 3.30
9.60
2.70
2.44 r1.
?9
6. 8l 5.9 4
4.69
8.20
7.0
5
5.10
r0.73
6. r0
7.80
9.t2 8
10.44
1I.4
4
14.92
4.77 7.26 5.9
9.r2
6.92 6,04 5.36 4.45
8.89
3.18
3.9
6.81
1I.36 8.01
70.21
15.50 13.35
7.54 6.54 5.79
8,38 7.34
13.
f4
11.37 10.30
4.6 4 0
8.57 7.38
0
3.29
2.45
11. S2
8.0
11.8I
2,O9
9.'t5
10. s4
4.s3 2.94
l-2.46
8.30
9.9 0
6.40 5.54 4.92 4.44
7
3.0 2
2.40 10 20 30 40
4.58 3.92
3.68 2.76 2.33
2.98 2.67 2.35
120 140 160
30
2.79
3,4
r00
8.35
ST
l.8r
f.98
20 30 40 60 80
9.7!
10 20
4
2.07
t8
2.64
2.10
6.40
1I.82
17.f9
14.82 13.40
10.80 9.24 8.20
118
Piping Stress Handbook Table 5-3 Flanged Elbows-Flexibility Factors and Stress Intensiflcation Factors STZE
2.
I|ALL TIIICK
.154 .2La .436
2\ 2\ 2\ 2 tt" 2\ 2
.
083
,2"
3'
.120
.2I5 .300
3i
.600 .
3t" 3!"
on3
.1?o .314 .536 .0a3
.L20 .237 .337 .531 -674
'134 .258
.625 .750
50
.280
.432 .562 .718 .864 .148
3.2s 2.7r 2.24 L-74 7.73 L.44 1.32 l.03 1.00 1.00 I.00 1.o0 2.36 1.59
1.a3 1.24
I.OO
1.OO
l.0o 1.oo 3.54 2.95 2.74 2.24 2.7S I.48 1.38 I.15 1.01 l.OOj 1.00 1.00 3.85 3.21 2.97 2.47 r.88 I.56 L.44 L.20 1.O0 1.00
4.13 3.L9
3-44
r.22 L.04
1.Ol 1.00
2.66
I.OO l.O0
3.93 3.28 3.41 2.S4 2.13 l.?8 1.61 1.34 I.29 I.0o 1.07 1. o0 l.oo 1.00 4.41 3.68 1.65
1.3?
l.lo l.o0 1.00 1.00 5.20 4.34 4.23 3.52 2-92 2.44
.322
2.45 2.O4 2.06 t.72 r.77 r.47
.aL2 .875 .906
BqlC END FIANGED
i-
ii
.25O
.406 .500 .593 .718
8i
NOT A'JANGED
1.34 1.11 1.23 1.02 1.14 1.O0 r.11 l. o0
!2
1.42 1.lo t.25 I.O4 l.09 1.o0 1.00 1.00 l.o0 l.0o 1.20 1.06 r.00 I.OO
1.00 1.00 1.oo 1.00
1.73
1.49
1.2a I.06 1.12 1.OO 1.OO 1.00
1.00
1.00
1.64 1.36 I.30 1.08 r.I4 I.00 1.00 I.oo 1.93
1.61
1.16 1.0o l.os 1.00 1.00 1.oo 1.00 t.oo 1.88 1.57 1.76 1.46 1.38 1.16 1.20 1.OO I.09 1.O0 1.00 1.oo 1.OO 1.00
1.99 1.45 1.43 1.22 l.I0 r.o0 l.oo 2.16 I.96 1.57 1.49 1.36 1,18 1.11 l.06 l.ol l.oo
1.66
1.54
l.19 1.01
1.OO 1.OO
l.oo 1.81 1.63
qllE EI{D I:UINGED
it
2.35 1.78 r.47 1.20 1.00 I.OO 2.26 1.a5 L.3a 1.15 1.00 1.o0 2.52 1.50 1.00
iol 1.97
r.39 L.22
l.o0 t.oo l.OO
r.8A L.44
I.O8
l.oo
1.00 1.oo 2.09
I.25 1.oo
1.OO r.00
2.6e 2.23 2.20 1.83 1.28 r.07 L.00 1.00 2.S3 2.35 2.33 1.94 l.61 1.34 1.13 1.00 1.00 1.00 1.00 1.00 2.72 ?..27 2.45 2.O4 r..39 1.16 I.la I.00 1.O2 1.00 L.OO 1.00 2.96 2.47 1.ao 1.50 1.42 ].I8 1.05 1.00 1.OO 1.OO 3.35 2.80 2.88 2.39
1.31
!.24 1.14 1.0o
t.oo 1.o0
l.o0 l.oo
1.68 1.40 1.50 !.24 I.21 1.00 r.14 1.00 1.07 1.00 l.o5 1.OO
Note: l.o, iof, io2 are out-of,-p16ne intensifLcation factols i, 11r 12 are Ln plEne lntensiflcation factors
Stress Intensification and Flexibilitv Table 5-3 Continued
10" 10"
ro"
10" 10" Lo"
to" 10" 10"
ro" 10"
t2" 12" t2" 12"
.156 .180 .250 .330
12" L2"
.406 .500
12" t2"
5.23 4.55 3.4L 2.94
4.36 3.79
2.08
1.73
1.40 1.22 1.11
1. t7
5.26 4.'t9 3.8t 3.14 2.a7 2.7a 2.33
4.39
2.44
2.45
1.00 1.Oo
3.99 3.18 2.61
2.39 2.26 1.94
1.85 r.54 .443 1.000
1.39 1.16 1.27 r.06 r.12 1.o0
14" .250 l.4n .312 14" .375 14" .434 14" .500 14" .593 14" .750 14" .937 14" r.093 14" r.250 14" 1.406
3.90
3.25
2.92
2.44
16" ,250 16" .312 16" .375 16" .500 16" .556 16" .843 16" 1.O31 16" r".2IA t 6" 1.438
18n 18" la" 18" 18" la" 1am 18" 18" 18"
2.33 r.94 1.79
1.49
1.34 1.21 1.09
1.12 1.01
4-27 3.A1 3.23 2.63 2.17 1.81
3.55 3.18
1.o0
2.'7O
2.19 1.81 1.51
1.20 1.10
1.00 1.00
4.62 3.94
3.85 3.32
.475
.{34 .500 .352 .750
2.A7 2.39 2.63 2.t9
.93'l
1.82 1.56
1.52 1.30
1.23 1.11
1.00
t_.156
1.375 l-.562
t .78r
1.OO
2.r1 2.03 1.75 1.53 1.37 f.2a 1.19 1.12 t.o5 1.00 2.18 2.08 1.85 1.69 1.56 1.45 l.4t r.29 1.19 1.12 1.07 1.00
J..'t4 t.62 1.5? 1.45 1.38 1,27 1..17 f.10 1.05 1.00 r.96 1.83 1.71 1.54 1.40 r.2a f.18 1.11 1.04 1.03 2.O4 1.9O 1.78 1.69 1.61 1.54 L.39 1.28 t.r8 1.11 t.os l.oo
3.37
2.Af
2.44 2.18
2.O4
I.t4
1.69
r.40
1.0O
1.37
1.14
1.13 1.05
1.O0
3.16
2.63
1.41
2.30
l.9I
1.30
2.06 1.84
1.72 1.53
1.37 I.25 1.17 t.06
1.15 1.04
2.70 2.4r
2.25
1.84 L.t3
f.53 r.44
l.a1 1.69 1.45
r.2A
1.07
1.OO
1.00
1.oo
t.a2 1.73
r.54
1.2r 1.1? 1.04
1.00 t.Oo 1.00 1.00 1.45 1.35
r.3f 1.21 1.15 1.06
r.
r.73
1.42
1.00
r.44
1.O0
1.oo 2.0O
OO
o.92
L.oo
1.13 1.00 1.O4 1.00
1.64
2.9O 2.60 2.34 2.OL L.'74
2.41
1.35 1.23 l.l2
1.13 1.03
t.00 I.52 1.42
r.2a 1.r7 1.06
l.oo
L. oo
r.00 l-.00 r.7O 1.58
1.49 1.41 1.34
\.24 1.15 1.07 0.99
1.00 1.00
l.
oo
2.16 1.96
l.6a 1,45
1.00
r.05 1.00 3.07 2,56 2.75 2.29 2.51 2.O9 2.31 1.93 2.15 t.79 2.01 1.68 1.73 1.44 1.36 1.14 1.23 1.02 1.14 1.O0 1.05 l.o0
Note: i^, i^f i-2 are out-of-plane intensification factors i; jt; i2 ire in plane intensification facEors
Factors
119
120
Piping Stress Handbook Table 5-3 Continued
20" 20" 20" 20" 20" 20" 20" 20" 20" 20" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24n 30n 30" 30" 30"
I
t. t:l
.
.250 .375 .500 .593 .812 1.031 1.241 1.500 1.750 1.96A
.250 .375 .5OO
.562 .6A1
.968 1.21a
I.531 1.a12
2.062 2.343 .2so .375 .500 .625
4.91 3.77 3.0a
4.14 3.L4 2,5?
2.r8 r.82 1.a4 1.53 1.56 1.30 t.3a r.t5 L.22 t.02 1.11 1.OO 5.63 4.69 4.29 3.5'l 3.24 2-70 2.80 2-34 2.20 1.83 1.56 1.30 L.24 r.O3 1.12 1.00 5.63 4.97
4.69 4.L4
o8
2.57
Miter bends-Modify the K and i factor when the butt weld of the flange is located within one and one half pipe diameters of the nearest miter weld measured from the centerline of the pipe.
Although not specified by the Code, this will apply to both closely and widely spaced miters. Note: Large-diameter thin-wall piping elbows and miters are affected by internal line pressure. According to a *Batelle" report to dre AGA, the flexibility factors on these items are seriously impaired by internal pressure. To
correct the values from Table 5-1:
Divide K by: (P) (r)]" (Rt)t"
(1 + o 'E"tz
I2
2-L2 1.A4 'L.67
1.77 1.53
1.39
L.29 1.0? 1.19 1.00 1.11 1.OO 1.O5 1.00 1.O0 1.00 2.25 1.84 L.97 1.64 1.7a 1.48 r.71 L-42 1.59 1.32 1.30 l.oa t.oo l.r9 1.13 1.00 1.06 1.oo 1.OO 1.O0 2.43 2-O3 2-25 l-.84 1.93 1.61 1.7A 1.49
3.24 2.70 2.64 2.2O 2.26 r.a9 2.OA 1.73 r.75 1.46 1.54 r.28 1.36 1.13 1.24 1.03 1.13 1.OO l.05 t.o0 2-9L 2.51
2.42
4.76
1.46
2.O9
1.23 1.04 1.r5 r.00 1.06 1.00 3,24 2-A2 2.51
2
-70
2-34 2.O9
Factors and Characteristics h, k, and i
Butt-weld joint Reducer Weld-neck flange
Double-welded slipon flange Fillet-welded joint-single weld Socket-welded flange Single-welded slip-on flange Lap-joint flange (with ANSI Code
816.9 lap-joint stub) Screwed pipe joint or screwed flange Corrugated straight pipe or corrugated or creased bend.
1 I I I I I I I
| 5
1.0 1.0 1.0
l'.t 1.3 1.1
t.3 1.6
2.3 2.s
Divide i by:
(r+3.2s)9qq# Ecrr
Nate.' Factors shown apply to bending
for torsion equal to 0.9.
flexibility facrr
Stress Intensification and Flexibility Factors
121
Widely Spaced Miters D = Pipe
2-weld Miter
Size
(inJ 12 T4
16
l8 20 24 26
30 JZ
36
40 42 48 54 60 12
0.375 Wall 2-Weld
0.250 Wall
14.2 15.4 r7.3 l9.l 20.8 24.3 26.0 29.3 30.9 32.6 34.2 37 .3 38.9 43.5 48.0 52.4 61.0
Miter
5.4 5.7 6.3 6.8 7.3 8.3 8.7
10.1
4.1
10.9 12.2 13.5 14.8 t7 .3 18.5
4.4 4.8
9.6
11.'l
20.8 22.0 23.2 24.3 26.6
r2.0
27 .7
r3.2
31.0 34.2
10.0 10.4 10.9
r4.2 15.3 l7 .3
.3 43.5
37
Dimensions (in decimals ot teet) A 0.878 1.025
t.171
5.2
I .318
5.6 6.6
1.464 1.757 1.903
7.3
2.196
7.6
2.343 2.489
6.3
8.0 8.3 8.9 9.2 10.0
2.636 2.938 3.075
3.514
3.954 4.393
10.9 11.9 13.2
5.272
K = flexibility faaor
i. -
ii =
outof-plane stress intensificatian factor in plane stress inlensification Jbctor
Figure 5-1. Flexibility and stress intensification factors of two-weld miter elbows. Widely Spaced Miters D = Pipe
0.250 wall
Size
3-Weld
(in.)
Miter
12
t4 lo 18
20 24 26 30 34 36
40 48 54 60 72
ir=i"
i0.8 tt.1 13.1 14.5 15.9 18.5 19.8 22.3 23 .6 24.8 26.0 28.4 29.6 33.1 36.6 39.9 46.5
Wall 3-Weld Miter
0.375
4.3 7.7 4.6 8.3 5.1 9.3 5.5 10.3 5.9 lr.3 6.7 l3.l 7.0 1,4.1 7.7 1s.9 16.8 8. 1 8.4 17.6 8.'7 18.5 9.4 20.2 9.7 2r.1 10.6 23.6 11.5 26.0 12.3 28.4 13.9 33.1
lt =lo
3.3 0.696 0.401 3.5 0.812 0.468 3.8 0.928 0.535 4.2 .044 0.602 4.5 1.160 0.669 5.1 r.392 0.803 5.3 1.508 0.870 5.9 1.740 1.004 6.1 1.856 1.071 6.4 1.972 1.138 6.6 2.088 1.205 7.1 2.320 1.339 .4 2.436 1.406 8. l 2.784 r.607 8.7 3.132 1.808 9.4 3.480 2.009 10.6 4.176 2.411 1
7
K = fleribilitf factor
i" = it =
outof-plane
stress intensification
Dimensions (in decimals ot feet)
factor
in-plane strcss intensification factor
Figure 5-2. Flexibility and stress intensification factors of three-weld miter elbows.
Rotational Nozzle Flexibilities for Cylindrical Vessels
It is customary for piping stress analysts to model a piping system with rigid ends or anchors at the equipment
time and money on these changes, let's model the nozzh data points 5 ard 30 with flexible end conditions using the flexibility factors from Table 61. The table shows that fa exchanger E-l the in-plane rotational flexibility (R.F.) is .626 x 106 in.{bs/deg, and the out-of-plane R.F. is
nozzles. This assumption is acceptable when the system is flexible and the anchor loads are low. But anytime the system shows high loads and stress€s, the analyst must determine how reasonable the assumption in modeling the nozzles as rigid anchors was. The author has developed tables of rotational nozzle flexibilities for cylindrical vessels ranging in diameters from 2 ft to 20 ft and connecting nozzles ranging in diameters from 2
in.-lbs/deg. The new computer calculatior show that the highest stress is 12,015 psi and the new forces at anchor are:
in. to 48 in. sTD. thickness.*
To demonstrate how these flexibility facton really affect the accuracy of stress calculations for a simple piping system, an example where a l4-in. O.D. pipe from an exis shown in Figwe 6-1. changer E-l ties to a tower The computer stress calculation with rigid ends or anchors show a high stress of 33, 616 psi in the system and forces and moments at the nozzles as:
Tl
(}D. 5 30
Tl
lff .4Oi xltr
the in-plarc .209 x in.Jbs/deg. For the tower R.F. is 1.22 x lff in.-lbs/deg, and the outof-plane R.F. b
F,
(rb)
-il,113 l l.l l3
F,0b) -28,r4
28.182
n4 (ft-tb) 85,749
t49.174
Tb reduce these high forces and moments, we will have to modit the piping configwation with more elbows or an additional expansion joint. But before we spend more
D.P. 5 30
F.0b)
Fy
-2,tOO 2,100
-6,04
0b)
6,082
n4 (ft-rbo 3,3@
-20,741
These forces are obviously much lower ftan the frst assumption with rigid ends. Now we know tlnt the piprng system is not overstressed. The shell of the exchanger E-l or the tower T:-l needs to be checked for local stresses with the new loads. It is quite possible that they are acceptable to the exchanger and vessel designer and manufacturers. The following is a method for determining the spnng rate of nozzles attached to vessels or stubbed into larger piping. Only in- and out-of-plane rotational spring rat€s are included, since the radial flexibility is normally ignored. Nozde flexibilities sttould not be used if the nozde
122
Vessels
Rotational Nozzle Flexibilities for Cylindrical or pad diameter is greater than one third of the run or vessel diameter.
Nozde flexibilities were calculated in accordance with the phase report ORNL 115-3, Equation 8, page 6.
K:
c ws
DB
(-D/Wf"
WD
. MDBK o=-
(6-l)
(6-2)
EI
Spring Rate
:
EIPI
(6-3)
2160DBK
Solving Equation 6-2 tot (Ml?) and converting units to ftJbs/deg we have Equation 6-3.
where
C
c:
D: Ds: E= I: K: M: PI:
123
.09 for in-plane bending .27 for out-of-plane bending
Diameter of vessel or run, in. Diameter of branch, in. Modulus of elasticity, psi Moment of inertia of branch, in.a Flexibility factor Moment, in.{bs Circumference of a circle divided by the diameter
Angle of rotation, radiam e: of or run, in. Wall w: of branch, in. ws: Wall thickness thickness
vessel
In-plane bending refers to bngitudinnl bending in the run or vessel in the plane formed by the intersection of the branch and vessel or run centedines. Out-of-plane bendtngreferc to circumferentialbendng it a plane perpendicular to the vessel or run diameter.
PIPE:
MAT. -
C.S.
o.D. - 14"
THCK. - .375" TEMP, - 450'F EXCHANGER E.1:
MAT. -
C.S.
o.D. - 5'-0" THCK. TEMP,
- 1lz' - 45OOF
b I I I I
t
--TI
I
TOWER T-1:
MAT. -
o.D. THCK.
TEMP
C.S.
10'-o"
- %" - 450"F
I I I
Figure 6-1. An example diagram of a piping system where 14-in. O.D. pipe trom an exchanger ties to a tower'
124
Piping Stress Handbook Table 6-1 Rota Stiff calculation, Gyl. vessel ROIA 00.F1
vEss€L TCK,IN
2.000
.2 50
VESSEL
2.000 2.000 2.000 2.000 2.000 2.000 ?.000 2.000
.500 .6?5 J
1.?50 1.500 1.750 2.000
.250 .325 .500
2.C00
2.000 2.000 2.000 2.000 2.000 2.000
.000
.750 1 .000 1-250
2.OOO
1.500
.000 2.C00
2.000
2.000 2
2.00c 2.000 2.000 2.000
2 -OOr)
?-000
2.000 2.000 2.000 2.000 2.000 ?.000 ?.000 2.000 2
.000
.250 .375 .500
STI'F
CALCULATIOTI, CYL. VESSEL NO2 T
2.375 .375 .375
2 2
2.375 2.375 2.375 ? -375 2
.t75
?-375 2.3?5
.000 1.250 1.500 1
3.500 4.500 4.500 4. 500 4 -500
4
.500
4.500
6.625 6.625 6.625 6.625 6.625 5.625 6.625
2.500
.250
2.500
. t00
2.375 2.375 2.375 ?.3?5 2.375 2-375 2.375 2.375 2.3?5 2.375 3.500
2.50 2.50
.625
0
-750
0
2.500
1
.000
1.25(J
I .500 I .750
2.50 0 2 .500 2 .500
2.OfJO
2.500
.250
2.5C0
.37 5
2.500 2 .500 2 .500 2.500 2.500 2.50[r
.500
.625 .750 1.000 1-250 1.500 1.750
.154
.499 E +0 5 .871E+05
.4128r06 .8 47€r 06 .1 48 E+07
.233E+07 .343E+07 .479e +07 .394E+05
-216
.500 3 .500
3
6.625
.t75
.154
.2618+06
.1 50E r06
.22O8+07 .347 E+A7 . 510€+07 .712E +oz
3.500 3.500
2.OOO
.7 50
.154
.2438+05
3. 500
2.000 2.000 2.000 2.000
't
.154 .154 .154 .154
6
.6?5
6.6?5
.216 .216 .215 .216 .216 .237 .237
.237 .237 .237 .237 .237 .237 .?37 -280 .280 . ?80
.280
.280 .280 .280 .280 .280
.154 .151 .154 .154
.882Ef04
.265E+05 .729 Er 05
.223E+05 .389E+06
4.500 4.500 4.500
.7 50
-154
-216 -216
3.500 3.500
1.000 1-250
1.750 2.000 .250 .375 .500 .625
-154
.154 .216 .216
4.500
1. 500
CK,I
.500
3
-625
.7 50
ZLE ROT STIF IN.LB/DEG N INPLANE OUTPLAI.IE STD LOI,I6I CIRCU
r{ozzLE
OD,]N
.t0EE+06
.6'l4E+06
.126E+ C7
,520E|05 .143Er06 .294E+06 -514E+06
.81t8+06
.166E+07 .29'l E+Ol .459E+07 .67 4E107 .942E+07 .790E+05
.21EEf06 .4 478+ 06 .781E+06 .123E+07
.253E+07 .142E+A7
.697E+07 ,'102E+08 .143E+08
.1378+06 .28?E+06 .493 E +0 6 .7 78E+O 6 .114e+O7 .160E+07 -131E+05
.362E.05
.712E+o5
-130F+06 .205E+06 .420E+06 .733EtO 6
.1168+07
-170E+07 .2378+Q7
.l738+05 .478E+05
.981€+05 .1718+06 .27OE+D6
.555F+06 .9 69 E+06
.153E+07 -225t+O7 .314€+07 .263E+05 .726E+O5
.149E+06 .?608+06 .4118+06 .843E+06 .117e+A7 .232E+o7 .3428+07 .477E+47
-237E+05
.789E+O4 .217E+Os .446E+Q5
-154
.134E+06 .234E+06 .369E+06 .7 578+05 -132a+07 .2C9E+07
.154
.6528+05
.7798+05 .123E+O6
.2528+46 .4418+06 .695€+06
.'t 54
. 3C7E+ 07
.154
.128E+07 .552E+05
.1'l7E+O'
3.500 3.500
.216 .216 .216 .216
.970E+ 05
.323E+05
.199 E+06 .348 E +06
.56
.500
.?16
.5 49 Er 06
.183Ef06
.'113E+07 .197E+07
.376E+06
.3'10€+C7
-103E+07
5
3.500 3
.500
.216 .216 .216 .216
.456E+O?
-102Ef07
.143ErO7 4E
r0 5
-116etO6
.656Ef06 .152E +O7
20+ SSZL' 9O+3 L6L'
10+lS2t'
ZZ'
90+1299.
90+3tEt' 9O+3
L
90+l0t!' st]1rt08' S0+r06t' so+tzrL' to+1r 61' to+)6tL' 90+r9t6'
90+r 66S'
90+rttt' 9O+1L9
L'
90+:1901'
s0+3909'
s0+3952'
s0+rl.0l' 1.0+:0tl'
90rltt6'
90+35t9' 90+3?0t' 90+1052'
9Ot )Z I L' SO+) t, L'
90+ltor' S0+386t' t0+r0zl.'
tLtz'
l0+39t1' 9Crl0Zt' 90r10rz' 9A+tLtl' S0
+13Zr'
lar )z8g' to+ 12Lt' zo+ atgz' 10+108!'
20+lt0!' 90+ll0s' 90+l8tt'
Itz' tiz' z'
Lt
lt2'
L2' 9LZ' 9
tz' 9tz'
9
912' 9
LZ'
9C+rZ8l' !0+r968' s0+l tz t' lO+z L6r' z0+J082' to+ )o6L'
9LZ' 9LZ'
90+l169'
ts L' ,s L'
to+3lzL' 9O+a
Ltt' ,'
It
L2' 9A + 9O +1ZZ S0+3S65'
9tz'
t9 L' ts L' ts L'
ts ts
00s't 00E't 00s'?
00s't 005't
't 009' ,
005'
00s't 00s't
osz' 0c0'z
00('t
't 00s' t 00s't 00E' t 00E
00E't
00s't 009't 009't
stt'z slt'z glt'2
t' l'
,s L'
sLt'z
20+)r9S'
80+;1691'
g29'I
Lo+1s2?'
+3rz t' LO+1ZZS'
zzt' azt'
to+3rLt'
]166' 90+lE8r' 90+tg0t' 90+ 91+
f9lL.
80+3lzl'
20
20+)9' L' 90+3t26' 90+t6zs'
E0+r8E8'
90+ 1L92.
l0+SLzr' 101390t' lo+)eoz' L0+3ztl'
r. 10+i LL 6'
90+lllt.
9O+1'
S
l'
9O+3t9t'
90+rttz'
90+lttl'
s0+16t9' S0+39t2' lo+) L?z' l0+a LOZ' LO+) Lt l'
E0+rtt6' g0+rgZ
lo+39?9' 1.0+rg6t' L0 + )9 ZZ' L0
+
10L
t'
90+1669'
90]303t' 90+356t'. I0 +:l,l0l. 20+12' g'
/0+1t09'
90+1e98'
t0+30Lr. LC+ 10? Z.
90+ 39
20+36r
6i' 90+3ZrZ' 90+rEs l' s0+31.28'
SO+rlzr'
LO+
3
2LZ'
r.
9t+)SzL' 9C+109t' 90+lt9Z' 90+3 8Z
I'
90+lS9t' lo+1Ltg'
I9NO'] NJUI] I Nv-l dNI lNvldIn0 9rc/€'t'NI i Its 10u
sz9'
I
EZ9'8
sz9'a EZ9'
10+1662'
I
szg'8
zzt' zzt'
otiz' 082' 08 z' 08
z'
082' 03
z'
082' 082'
082' 082'
).tz'
Itz' 2t2'
lrz' Itz' Itz'
2t?' 9
L?'
09t'L 0c9'L 052't 000' I ost' szg' 00s'
09z' 000'z
00s't 09?'I 000' I
000'z OSL'L
009' I
osz'L 0c0' I os
L'
E29'S
a9
000
z' 'z
szg'9 szg'9 szg'9 szg'9 sz9'9 s z9'9 szg'9 szg'9 szg'9
as2'L o9s'L
oos't 00E't 00s't 00s -t 009't 005' t 00s't
OSL'L
00s't
l-tzz0N
-tJss3A'"llJ,NOllvlnllvl tlrls penu!luoc t-9 etqer
000't 000'5
0c0't 000't 000't 000'
t t
090'
5
000'
t
0c0'
t
0c0'
I t
00c'
000't 000't 000't 000'5
000't 000't 00c't 000'I
000'
sz9- 9
00E't 005'?
00c'l
009'
s29'8
t
000't
091'
szg' 00s'
008'
t I
000' 000'
000't 0c0't
E29'8 szg' I
(ls NI')]I
slassen lPcr.rpurdc Jof ssll!l!qrxell elzzoN leuollPlou
009't o9?' t 000'I r)s 2' szg'
00s
s0+39t?'
lo+lrot'
;
10+
osz't
000't 000't 0cs'z
cos 'z 00E' z
00s'z 009'z 009'z
00s' z
00s'z 00s'z c0g'z c35'Z
005'z oo3'z o09'z
'z
000' I 0Ez'
00E
00E'
00s'z 1xs'z 006'z 00s'z oos'z 00t' z
sz9'
09z' 000'z 00s' t osz'L
000't
0s2' sz9' 00s'
osz' 000'z
NI')JI -13 ss 3A v10u
00E'z oDs'z
00E' z
00E'z 005'
z
00E'z 00E'z
0cs'z 009'z 00s'z IJ'OO -l3sslA
126
Piping Stress Handbook Table 6-1 Continued ROIA STIfF CALCULAIIOII, CYL. VESSEL
OD,fT
3.000 3.000 3.U00
3.000
3.0c0 3.000 3.000 3.00c 3.000 3.000 3.000 3
.000
3.000 3.000
3.0c0 3.000 3.O00
3.000
L
l, l:i
l
t,
'
I
3
.000
3.000 3.000 3.000 5.000 5.000 5.000 3.000
3.000 3.000 3.000 3.000 3.0c0
VESSEL TC
K,IN
1.750 2.000 .z5g .375 .500 ,6 25 .7 50 1.000 1.250 'f . 500 1.750 2.000 .250 .375 . 500 .625 .750 I .000 t. ?50 1 .5s0 1.750 2.000 .250 .375 .500.625 .750 1.000 1.2r0 1.500 1.750 ?.000
3.500
3. 500
.250 .375 .500
1.500
.6?5 .7 50
.000 1.250 '|
f.500
3.5C0
1
.500
.750 2.000 .250 1
3.500 3
.50C
3.500 3.500 3.500 3-500 3.5C0
3.500
t.500
.500
.625 .750 1 .000 1.250 1.750 2-000
3.5C0
4.500 4-500
6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.625 4.625
. 500
.625 .7 5b
1.000
t.250
NOZZLE ROT STI f II{.LB/DE6 T
CK,I
SID
.280 .280 .280 .280 .280
.6458+05
.?15E+05
.2 E0
.?07E+07 .361E+07
10 -759 10 - 750
.l
78
E+
06
.365€+06
.638Ei06
.5938.05 .1228ro6 .2t3Er06
.569E+07
.2E0
.8t7E+07
280
.1'l7E+08
.389E+07
-853E+05 .235E+06
.284E+05
E.06
.161E+06
.135c+07 .?73E+07
.443E+06 .910E+06
.752e+07
.159E+07 .251E+O7 .569E+0 7
.280 .280 -
.32? .322 .322
.1018+07
.?56E+07
.3f,5E+06 .6888+06 .120E+07 .190E+07
-322 .322 -322
8.625 8.625 8.625 8.625 10.750 10.750 | 0.750 10.754 10.750
CIRCU . l84E +0 7
E.625 8 .625
8.625
OUTPLA}'IE
.551E +O7 .7 69 E+07
.237
.625
8
N INPLANE LONGI
.237
.322 .322 .322
4 92
.
.843Er06 .477Er07
-3?Z
.ttlE+08 .l 54Er 0E
.
-
t65
.365
.165 .36 5
107E+06
.279E+O7 .78
3
E.0 5
.e8l E+06
.51'E+O7 .358Ero5
.986Ei05 .?03Er06
.2968+06 .608E+06 .106E+07 .167a+07 .311E+07
.3548+06
.316E.07
.558E+06 -115E+07
.200E+07
10.750 10.750 10.750
- 565
.600E+07 .9 47 E+ E7
-365
.194Er08
2.375 2.375 2.375 2.375 2.375 2.375
.154
.2C0E+05 -551C+05
-154
2.375
.154
-640Er06 .112E+07
.154
.176E+07
.5888+06
-154
.259E+07 .362E+07
.1?1E+O7
.216 .216 .216 .216 .216 .216 .216
.298
2.37'
?.375 3.500 3.500 3.500 3.500 3.500 3,500 3.500 4
3.500
3.500 1.500 3.500
t{0zzLE OD,IN
VESSEL
.500
4.500 4.500 4,500 4.500 4.500 4.500
.365
.365
.t
54
.151 .154 .154
.154
. '139 E+0 8
.113Er06 .198Ff06 .312E{06
.659Er05 .1048+06
.213E+O6
.373Er06 .864Er06
.561E+05 .980E+05
.4648+O6
.952Ef06
.539Er07
.237 .237 .237
r04
.294E+ 06
.168Er06
-2'16
.2t7 .?t7
E
-184E105 .377E+Os
.99ZtrO4 .27iE+05
+C5
.166E+07 .?62E. 07
.237 .237
.6 67
.820E+05
E
.?16
.216
.464E+O7 .646 Er0 7
.386E+07
.155E+06 .317ErOo
.554E.06 .875E+06 .1?9e+O?
.1 80E+0 7 -t
.108€+06
.222Er06
31€r0
5
.361E+05 .741€+05
06
.i30E'06
.613 Ei 06
.204€+06
.389r
+
.126E+07 .2208+07
. 419 E+0 6
.733E+06
Rotational Nozzle Flexibilities for Cylindrical Table 6-l Continued ROTA STIFF CALCULATIONT
VESSEL NOZZLE ICKTIN 0D,Iil
VESSEL
0D,fI 3.5C0
1.500
1.500 3.500
'l
.7 50
2.000
.250
3.500 3.500 3.500 3.500 3.500 3.500 3.500
.500
.625
6.625 6.625
.7 50
t.00rJ 't
.250
1.500
3.50 0
.750 2.000 .250
5.500
.500 .625
.500
3
.625
6
1
3.500 3.5C0 .500 .500 3 .500 3 .500
3
3
3.5 00
3.500 3.500 3.500
E.625 E .625
.527E+C7
.2 80
.7 7 5E+ 07
.280
.1088+08 .790E+05 .218E+06
.4178+06 .780E+06 .123E+C7
10, 750
.500
1
0.750
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1
1.750
10 ,750
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2
10
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3.500 3.500
.500 .625 .7 50
12 -750
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.500
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12.750 12.750 12.750
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2.375 2.375 2.375
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4.00 0 1, .000
4.000 .000
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3. 500
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3. 500 3 .500
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3.500
3.500 3.900
.3'l0Er06
.637 E+O6
.1 'l1 E+07
.176E+07 .258E+07 _3617+07 .263E+0 5 .7?5E+O5
.149E+06 -260E+06 .410E+06
.23?E+07 ,34'l E+C 7
.11'3E+08
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.991E+05 .27 4E+06
.331E+0
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.913€+05 .187E+06
.562E+06 .9838+06
.328E+06
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.517E+o6
.l
.106E+07 ,185E+07
,3 65
.877E+ 07
.292E+07
.365
.129 E+ 08 .180E+08
.6008+07
.750
12.750 1? .750 12.750 12.750
.549E+05 .113E+06
-696E+ 07
.3'l8E+07 .5568147
10.750
3.500 3.500
3.500
.365
.199E+05
,842€+05
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.50>
10.750
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0. 750
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/.
.2E0
.9318+o6 .191E+07 .3348+07
.3?2
a
1.250
4
.1978+06
.t55E+06
4.625
0, 750
3
.2 80
.338E+C6 .590E+06
.280
1.750 2.000 .250
r
3.500
.2E0
-t?2
-7 50
J
.237E+ol
.2a7
8.6?5
.?50 I .500
1-000
3
.1169+02
E
1
.500 3. 500
3
CIRCU
+07
.347
E -625 8 .625
.7 50
LOI1GI
,5108 +07 .7'l ?E + c7 .597e+ A5
.322
10.750 10.750
.500 3 .500
SID
8.625
.500
3
ZLE ROT STIF II{.LB/DE6 C(,I N II,IPLANE OU]PLANE
.280
3-500 3 .500
3,500
T
6.625 6.625 6.625 6.625 6.625 6.625
1.000
VESS€L
N02
4. 500
4.500 4.500 6.6?5
CYL'
.'l 20E+06
.375 .375 .375
.329 E+C6 .676E+ 06
.118E+07
.430E+A7 .399E+05
.1'l0Ef06
.225E+06 .394E+06
.i86E+07
.621 E+06 .'128F+07
.666E+07 .'1058+08
.223E+oz .351E+07
-375
.2168+08
.7?1E+O7
.15 4
- 187E+05
.624E+O4
.106Er06
.353Er05
.375 .375
. I 55 E+08
.154 .154 .154 .154 -'t 54
,154 .151
.'t54 .216 .2.16
.z't6 .2'16
.?16
.515E+05
.185E+06 .292E+06 -5999+06 .105E+07 . 't 65 E+ 07
-517 E+07
.172E+05 .61
6E +0 5
.972E+05 .200E+06 .349 E+ 06
.550E+06
.2438+07
.808E+06
.339E+O7 .2?8 € + 05 .7 67E+05
.928E+04 .256E+05
.157E+05 .27 5E+ 06 -454F+06 . 891
E+
06
.1'l3E+07 ,525Er05 .917E +O5
.1458+06 .29
7 E+O
6
Vessels
127
128
Piping Stress Handbook Table 6-1 Continued R0TA
vEssEL
VESSEL
4.000 4
.000
4.0c0 4.00 0 4.C00
1
1.750 2.000 .250 .375 .500 .6?5 .7 50
4. 500
1.000
4.C00
2.OOO
4.000 4.000 4.000 4.000 4
.000
/..000 4.000 4.000 4.000 4.000 4.000 4.000 /,
.00 0
4.000 4.000 4
.000
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.0c0 4.000 4.000
1.000
.250 I .500 1.750 2.000 .250 1
.37 5
.500
a -625
.7 50
8.625 8.625 I .625
8.625
.625
1.0c0
.250 1 .500 1
1.759 2.000
E
.500
.625 .7 50
.000
.2 ro
.500
.750
2.000 .250
.t7
5
.500
1.500
1.750 2.000 .250 .375 .500 .625 1.000
1.250
.625
8.625 6.625
l0 .750 1
4.00 0
4.000 4.0c0 4.000 4.000
6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.6?5 8.625
.7 50
t-000 1.254
4.00 0
4.500
.625
.625
4.000 4.000 4.000 4.000 4.000
4. 500
.37 5
4.0 00
4.000 4.000
4.500 4.500 4.500
.250
.000
4.000
.500 .500 4. 500
3 3
4.500 4.500 4.500
1.250 1.500 1.750
4
OD,IN
3.500 3.500
.250
1.500
4.000 4.000 4.000
4,000 4.000 4.000
i{0zz LE
ICKTIN
OD,fT
4.000 4.0c0 4.000 4.000 4.000
SfIFF CALCULATION, CYL. VESSEL
0
.750
10.750 't 0.7s0 10.750 10.750 I 0.750 10.750 r 0.750 10.750 12.750 12.750 12.750
NOZZLE ROT SII F IN.LB/DEG
TcKrIt{ INPLANE
STD
LONGI
0uTPLAt{E CIRCU
.216 .216 .216
.156E+A7
. 519
C7
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.1 208 +07 .l6E E+07
.237
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.237 .?37 .237 .237 .237 .237 .237 .237
.215E
+
E+
05
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.324E+ 07 .477E +07
. 108E
.666E+07 ?80
.559Er05
.280 ,260
- 316E r 06
.
.2E0
.1 54E+06
.552E+C6
.?80 .280
.8718r06
.2E0
.312E+07
.280 .280 ,280
.t22
.322 -3?Z .322
.322 .322 .322
.179
*
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.493E+07 -7 ZsE+ 07
.1018+c8
.7398r05
.1218+06 .1 91 Ero6 -392E+06 .68
5
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.159E+0? .22?E+O7 .1E6E+05
.513E.05
.105E +06
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.365 .365
.930E+05 .256E+06
.134€r08 .526E+06
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.175E+06
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.145E+07
.4E5E+06
.296E+07
.992Ei06 .17
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6 E+
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'12.750
14.000 1 4.000 I 4.000 14.000 1 4.000 14.000
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.561 E+06 .119E+O7 .2O8E+87 -329E+07
.4838+o7
.675E+O7
-112E+O7
.?31E+Ol
Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued ROlA
vEssEL lCK,lN
vEss€L OD,FT
4.000 4
.000
4.000 5
1.500
1.750 2.000
.000
5.000 5.000 5.000 5.080 5.000 5 .0c0 5.000 5-000 5.C0C
5.000 .00c 5,000 5.000 5.0c0
SIIfF
5
.000
5.000
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. t 65€+06 .261e+06
-154
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-375 .375
4.500 /..500 4.500 4.500 /, ,500 4. 500 4 .500
.15 4 .1 54 .15 4
.154 .216
.3c3E+07
.820E+05
.386E+06 .797 E+ 06 .139E+07
- 129E+06
.2?OE+07
.7 32E+O6
-?16
.216 .216 .216 .216
.323E+07
I .625 I .625
1.?50 'l . 500
1.75n 2.000
8.625 8.625
8.625 10.750
.500
10 .750 10 .750
.? 50
1
10.750 0
.750
1
.000
10.750
't
.2 50
1
0
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.229E +O5
.469Er05 .?66a+06 -464Er46 .108E+07
-216
.451E+07
.150E+07
.329
-237
.907E+05 .186E+06 .325E+06
.110E+05 - 102€+05
.237 .237 .237
E
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.105E+07
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.322 .3?2 .322
.32?
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.322 .322 -322 .365
.108E+06 .171E+
.?37 .280 .280
.2 E0
.6208+05
.5r3E+06
8.6?5
.000
.830E+C4
.216E+ A6
.500
a -625
-723E.O6 .10'18r07
-2't6
.250
.7 50 2. 000
.3',12E+O6
.492E+06
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.280 .280 .280 .280 .280
.000 .250 .500
.176€+06
.2498 + 05 .686E+05 .141E+06
6.625 6.625 6.6?5 6.625 6.625 6.625 8.625
- 625 .7 50
.315E+05 .551E+05 .869E+05
.216
6 -625
/..500
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5.000
.154
.2908+A7 .427 E+07
.250
1
.154
-237
.500 ,750 2.000
5.C00
5.000 5.000 5.000 5.00c 5.000
.154
.500 3 .500 4 .500
.000
.000
5.000 5.000 5.000 5.000 5.000 5.000 5.000
2.375 2.375
3. 500
.250
5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.0c0
.'154Ei05
3
2. 000
5.0[0
5
.461E+05 .946E+05
.500 3. 500 3 .500
1.750
.7 50
5.000 5.000 5.000 5.000 5.000 5.000
2.375
3
,000
5
.7 47 ErOT
.7 50
1.500
.364F+07 .535E+07 .558E+04
.500 .6?5 .2 50
60E+ c8
.1 67E +05
3.500 3.500 3.500 3.500
1.000
1
.224€+08
2 z
2.000 .250
.500
.
.154 .154
2.375 2 .375
.000
5.000 5.000
.'109E+08
.000
4.000 14.000 2 .375
-7 50
5 - 000 5. 000
E ROT STI F IN.LBlDEG ICK,IN INPLANE 0UlPLAl'/t CIRCU STD LONGI
NO2 ZL
1
.500 -625
'|
r{022L€ 0Dr1N
't 4
5
5.000 5.000
CALCULATIOiIT CYL. VESS€L
.7
79
E
+a6
.160€+07 .279 E+47 .411F + 07
O
6
- 199E+07 .1 67 E+A 5
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.618E+C7 .905E+07 .6618+ 05 . J82€+06
.216E+07 .3028+O7 .220E+05
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20E +0E
.832E+05 .?29 E+06
.471E +06
.E228+06
.130E'07 .2
07 .4 65E+07 66E+
.1?
3E
+
07
.285F +07 .399 E+o7
.277 E +O5 .7 64E+O5 .157E+06 .271E+o6
.4328t06
.887€106 .155E+o7
Vessels
129
130
Piping Stress Handbook Table 6-1 Conlinued nOTA VESSEL OD, FT
5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 ).UOU
5.000 5 .000 5.000 5.000 5.000 5.000 5.000 5.000 5 .000 5.000
5.000 5.000 5.00 0
5.000 5.000 5.000 5.000 5
.000
.750 ?.000 .250 .375 .500
.750
2.000
.t75 . 500
.625
.t50
6.000 6.000 6.000 6.000 6.000 6.000 6.00 c
'1.500
.750 2.000 1
.250
.375 .625 .750 1.000 1.250 I .500 1.750 2.000 .250
6.000 6.000
- 500
.625 .750
6.0 00 6.0 00
6.000 6.000
?50
'l
-000
1.?50
. t 44E +0E
.478E
.200E108 - t 288+06
.4?6E+O5
-000
.409 E +07 .715 € + 07 .113E+0E
16.00 0
.166E+ 0E
.231E+08
.145E+06
rE.000 r8.000 18.000 t 8.000 18.000 1 8.000 18.000 18.000
.151 .154 .154 .154 -154 .154 .?16
.216 .216 .216 .216 .216 -216
E+0 6
.1368+07 .2388+O7 .376E+O7
.552ErO7
.771Ero7 .483€+05 -273E+06 .4778+D6
.226E+07
.75
?8E+ 08
188€+08 .262E+08
2.375 2.375 2.375 2.375 2.375 ?.375 3.500 5.500 3.500 3.500 5.500 3.500 3.500
2.t75
.664
.14tE+07
.
.154 .154
.421E+06
.133Efo6
.810 E r 07
-154
.117E+06 .2 418+06
.8 20 s+ 06
.l .154
r07
.668 Ef07
.399E+06
.464Er 97
2.375 2.375 ?.375
.569E+05 .10?E+06 .209E+06
.619E+07 .976E+07
- 199 E+07
16.000 't 8.000 18.000
.4328+Ol .604Er07
.365E+06 .575E+06 .118E+07 .206E+07 .325E+07
.352Ef 06 .723E+06 .1268+07
6.000 6.000
. l07E+07
-1738+07 -351E+07
.109E+07
r6.000 16.000 't
.
08
.626Er06
16.000 16.000 16.000
1.500
1.000 1 .250
E +
. t 11 E+06
14 -000 14 -000
16 1
1.750 2.000 .250 .375 .500 .625
.2 94 E+0 7
.130Er08
.305E +06
I .000
1.250
.186e+07
.8 82 Er 07
14 -000
14.000 14.000 14.000
.245E+07 .359€+07
.559E+02
.3208f07
'11.000
CIRCU
.9e9E+06 .156E+07
.566Er06
14.000
OUTPLAI{E
.502Er07 .333Er05 .9'l9Er05 .189Er06 .J30Er06 .520Er06
.100E+06 .2?6e+06
.'l8l
.250 1.t00
1
LONGI
12 -750
14.000 14.000
1
STO
1?.750 12.750 1?.754 12.?50 12.750 12.750
.6?5
.750 1 .000
TCXTII{ INPLIN€
.151E+C8
1Z -750
.500
NOZZLE ROT SII F IiI-18/DEG
10.750 12.750 12.750
.500
1 1
VESSEL
.734E+07 .108E+08
I0.750
.625 .750 I .000 1 .250
cYL-
| 0.750
1.750 2.000 .250
6.000 6.000 5.00 0 6.00 0
0DrIl,l
TCKeIx
'1.500
CALCULATIONI
0zztE
VE SSEL
5.0 00
5.000 5.000 5.0c0 5.000 5.000 5.000
SlItr
.l
3E +0 6
.155E+O7 .278e rO7 -426E+O? .6?6E+O7 -E75 E+07
53E+05
.509€+04
.421Er05
.1 40E+05
.864Er05
.l5lE+06
.288E+05 .503E+05
.2388+06
.794E+05
4E9E+06
.1638+O6
-
.854E+06 .'155E{07 .198E+07 -276e+07 -227E+05 .626E+05 .129E+06 .225E+06
.285E+06 .449E+06 .660 E+06 -9228+gb
.757Er04 .209E +05
-428E+05
.749€r0
5
.5 54E+06
.ll6Er06
-727e+O6 .127Er 07
.423E+06
.242E+O6
Rotational Nozzle Flexibilities tor Cylindrical Table 6-1 Continued
sTltr CALCULATIONT CYL- VESSEL NOZ ZLE ROT STIF IN.LB/DEG VESSEL NOzZLE lCK,It{ INPLAxE 0UTPLANE TC(,II{ OD,IN CIRCU STD LONGI ROTA
VESSEL
OD,FT
6.000 6.000 6.000 6.000 6.000 6.000 6
-000
6.000 6.000 6.000 6.000 6.000 6.000 6.00
0
6.000 6.000 6.000 6.000 6.000 6.000 6.00 0
6.000
6.0c0 6.000 6.000 .).
1.500
1.750 2.000 .37
5
.500
.625 .750 '| .0c0 1.250 1.500 1.?50 2 .0c0 .250
1.750 2.000
6.r100
,000
6.000 6.000
2
.000
.250 .500
1
6,000 6.000 6.000 6.000 6.000 6.000
.000 6.00 0
6
6.000 6.000 6.000
6.00 0
6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000
.000
.411E+07
.1378+O7
.237
.3008105
.100Er05 .27 6E+O5
.?37
.82EE+05 . I 70 E+06
.237
.2t7
.
?80
.2 80
.280 .280
.280 .322
.322 .322 .32? .322 .37? -322
.365
10.75 0
1
.000
1.250 I .500
.750 2.000 1
.250
.500 .6?5 .?50
1.000
7.250 1.500 'l .750
2.000
0.750 10.750 10.750
10. 750
.365 .36 5
.365
10.750 10.750 r 0.750 10.750 1? .750
.625 .7 50
i.000
1.250 1.500
.468E+06
.961€r06 .168E+07 .265E+0?
.389E+07 .5
44e r
07
.4568+05 .126E+06 .2 58 E+ 06 .451E+06 .711E+06
.146Er07 .?558+07 .402E+07
.5928r47
.826E+ 07 . 603 E+05 . 166 E+ 06
.341E+06
.5968r06 .940E+06 .193E+07 -317e+O7
.532Er07 .782E+07
12.750 12.750 12.750 12 .7 50
4.000 14.000 14.000 14.000
t4-000 I 4.000 14.000 14.000
.320E+06 .5608+06 .883E+06 .130E+07 .181E+07 .152E+05 .4'19€+05
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.850€+06 .131E+07 .197 EaOT .27 5E+07
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.643E+06 .112E+07 .1778+07 .261E+07 .364E+ 07
-253€r05
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.698E+05 .143E+o6
.250Er06 .395Er06
.E10Er06 .142E+07
.670E+O7
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.984E+07
.328E+07
.517E+06
12 -750
.'l 568+06
.1098|08
12
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.566E+05 .989E105
.759E+05 .209E+06 .430E+06 .750E+06 .118E+07 .243E+47
1? .7 50
.902E+06
.4588+O7
.304Er05
.839E+05 .172E+06 .301E106
.375
.142Er07
.37 5 .37 5
.292E+07
.47 4E+O6 .97 4E+06
.510E{07
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.1188+08 . 16 5E +0t
.f95E+07 .551€+07
.101E+06 .279E+06 -57?E+06 .999 E+06
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1
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.137E+08 .913E+05 .252E+O6
12.750 1?.750
-668€+06 .9828+06
.216
.280 .280 .?80 ,280 .280
4.625 a .625 I .625 10.750
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0
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6.625 6.625 6.625 6 .625 6.625 6.6?5 6.625 6.625 6.625 6.625 4.625 8 .625 I .6?5 8.625 I .625
.200E{07
-216
.237 .237 .23?
4.500 4.500
'| . 500
.216
.500 4. 500 4
.000 1.250
.750
.500
4.500
1
0
6.0c0 6.000 6.000 6.000 6.000
4
.7 50
6.00
6
4.500 4.500 4.500
-oa>
0
.500
4. 500
.500
6.00c
6.000
3
.37 5
6.0c
6.00
3.500 3.500
.375 .3?5
.375 .315 .375
.158E+07 .323E. 07 .565E+07 .89'l E +07
.928€+05 .191E+06
.lf,3Ef06 .5258+06
.1 08 E+07
.188E+07 -297E+O7
Vessels
131
132
Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULAII0tI, CYL- vESSEL v€ssEL
OD,FI
6.000 6.000 6.000 6.000 6.000 6.000 6.00
I
I I
lr
1.750
2.000
.250 .375 .500
.625 .750 .000
0
6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0 00 6.0 00
6.000 6.000 6.0c
VESSEL ICX,IN
6.00c 6.000 6.000 6.000 6.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.0 00 7.0 00
7.000 7.000
7.0 00
7.000 7.000 7.000 7.000 7.000
6.00 0
CK,I
.375 .37 5
-375
.759 2.000 .250 . t75 .500 .625
.375 .375 .375 .375
t .000 1.250
18.000 18.000
.t7 5 .375
.250 .500
1
t.
500
1.750 2.000 .250 .37
5
.500
.625 .7 50 I .000
1.250 1.500
.750 2.000 1
.3?5 .500
6.000 6.000 6.000
T
16.000 1 6.000 16.000 16.000 't6.o00 18.000 1 8.000 18.000 18.000
0
6.0 00
NOZ
OD,IN
14.000 14.000 16.000 16.000 16.000 16.000 J
ZLE NOT STIf IN.LB/DEG N INPLANE OUIPLAT.IE LONGI CIRCU SID
NOZZLE
.625 .750 I .000 1 1 1
.250
.500
.750
?.000
.250 .375 .500 .625 .?50 I .000 1.250 I .5C0
.150 2.000 .250
1
.t75 .500
.625 .750 1 .000 1.250
18 .000
.37 5
.375 .375
.375 .375 .37 5
.375 .375
?.375 ".375 2.375 2.375 3. 500
1.500
.343E+07 .504E+07 .7 01E+o7
.44'lE+o5 .122E+06 .2t19E+06
.141E+07 .?47E+O7 -3a9E+07
.148Er06 .4088r06
.572c_+O7
.798 E+07 .493E+05 .'136€+05
.837E+06
.279E+06
.146E+O7
.487E+O6 .769 E+O6
.231E+07 .473E+07
. 1 92 E+08 +
06
.451Er06 .925E+06
.255E+07
.'t58E+07 .2768+47 .435E+07 .639E+o7 .893€+0? .545E+05 .
1
50 E+06
.308F+06 .519E+06
,850E+06 .17 4E+07
.375 .375
.523E+ a7
.3? 5
.1448+08
.305E+07 .481E+07
.212E+08 -?96E+06
.797p+O7
.9878+07
.141E+05 .390E+05
.471E+04
.800El05
.267E+05
.140E+06
.4 66 E+0 5
.375 .375 .154 .'t 54
.154 .15 4
.'l56 .154 .154 .154 .154
.'t54 .216 -216
.216
3. 500
.216 .216 .216
3.500
.217E+O7
.423E+ A7
.7 40t+07 .1178+08
.162Er07
3. 500
3.500
.'l2 4E+07
.436€+06 .687ErO6
. 164E
-37 5
.389E+05 ,107E+06 .220E+O6 -384E+06 .606E+06
-131E+07
.206E+07
.2688+08
22 .00 0 22 .000 22 .000
2.375 2.s75 2.375 2.375 2.375
.748E +06
.375 .375
22.000 22.d00
.2l l E+08
-375
22.000
22 .000
.1 51 E+08
.827E+07 . t 30 E+08
22 .000
22.000 22.000
.373E+07 .652E+A7 .103E+08
.172E+08 .239E+08
20.000 20.000
.610E+07
.3658+46
18.000 18.000
20.000 20.000 20.000 20.000 20.000 ?0.000 20.000
.437E+O7
.132E+O6
18-000
20.000
. 131 Er08
.1838+08 . t l7E+06 .3228+o6 .6608+06 .l l5E+07 .182E+07
-216
.914E+O7
.130E+05
.220E+O6
.735Ero5
.452E+06 .790E+06
.151E+06
.263E +06
.125e+07 .183E+07
.416E+06
.580E+05 .119E+06 .208E+06 .328E+06 .67 3E 106
. 195 E+0
.l1EE+07
.39?E+06
.256Er07 .?10E'05
.611E+o6 .E53E+06 .7018+O 4 5
.J97E+05 .693E+05 .109 E+06
.?248+06
Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued R0TA vEssEl-
OD.Fl
STIFr CALCULATION, CYL. VESSEL
VESSEL lCKrIf{
NOZZLE
OD,IN
NOTZLE ROT SII F IN.LB/DE6
TCKTIN It'lPl-AllE
SID
LONGI
0UTPLANt CIRCU
.500
1.500
.216 .216
.186E+07
4.500
.381Er07
.237
.278E+05 .766E+05
.927e+04 .255E+05
.237 .237 .237 .237
.157E+06
.524E+O5
7.OOO
.250 .375 .500 .625 .7 to 1.000 1 .250
.618 E r0 6 -909E+06 .1278+O7
7.00 0
't
7.000 7-000 7.000 7.000 7.000 7.000 7.000 7.000 7.000
1
3-500 J .500
1-750 2.000
4
4.500 4.500
4. 500
4.500 4
4.500 4.500 6 .625
2.000
.250 .375 .500 .625 .750
7 .OOO
7.000 7.000 7.00 0
7.000 7.000 7.000 ?.000 7.000
7.00 c 7.00 0
7.000 7.OOC
.37
.7 50
I .000
1.000 1.250 1 .500
I .5C0
1.750 2
.000 .25D
.625
4.625 10 .750
10.750 10.750 10.750 10.750 10 .7 50 t 0.750
12.750 12.750 12.750 12.750 12.750 12.750 J4.000 14.000
.6?5
1
7.O0tJ
I .000
7.000
. 239E
+
06
.2AO
.4188+06
.260
- 659E+06
-280 .2E0
.135E+07
.
?80
.322 .322
.322 -322 -322
.62t
7 .OOA
1.250 1.500
.2E0
8 6
'14.000
7.000
.422t+05 .tJ6E+06
.322
. 500
.? 50
.280
4.625 4.6?5
7.00 0
7.000
.360E+07 .503E+07
.?36t+07
4.000 14.000 14.000 14.000 14.000
.365 .56 5
.365 .365
.870E +06
-179E+07 .3'l2E+ 0? .192E+07
.375 .375
.1648+O7 .337E+O7 -234E+O5
.398E+06
.133€+06
.695E+06
-232E+06
.194E +06
.110Er07 .225E+07 .393E+07 -911E+07
.646E+05
.565E+06 .750E+06 .131E+07 .207E+07 .3048+07 .424E+07
.2828|05
.777E+O5 -159 ErO6 .27aE+Q6 .439E +06
.13?ErO7 .271E+07 .4738+07
.902E+06
.7 45E+07
-24EE+O7
.l'l0E+08
.1 53E+0E - 936E+05 .752e +06
.529E+06 .9 25E+06
.146E+07 .2998
.375
.596E+06 .'l o 4E+o7
.101E+08 .703E+05
-E458+05 .23f,E+06 .4 78€ r06 .E35E+06
.375 .375
.105E+06 .184E+06 .290E+06
.241E+Ol
-375
.37 5
.183E+07 .?55E+ 07
.7 24E+ 07
.1278+08
-5at
.1f,9 E +06 -220E+O6 .4 5'l E+06 .78 7E +06
.1868+05
.365
.t75 -37'
.168E+07 .111E+05 .3EE€r05 .797E+Ot
E|05
5 5E
.620E+07
.37 5
.1208+O7
.124E+07
.365 .365
-36'
.518€+06 .817E+06
-3738+07
.5 48 E+07 .7 65E+0?
I .625
1? -750
1.000 1.250
-237
.245E+07
.154E+D6 .316E+06 -552E+06
-625
.7 50
.297E+O6
-
.500
.750 2.000
.7 41e+O6
.890E+06
.1558+07
.280
.916E+05
.4338+06
8.625
10.750 10.750 10.750 12.750 12.750 12.750
1
.2758r06
-217
.237 .237
.2 80
.500 .625
7.00 0
7.000 7.0c0 7.000 7.000 7.000 7.000 7.000 7.000
6.625 6.625
5
1.250 1.500 1.750 2.000 .250
-625
6 -625
.500
7.00 0
7.000 7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.000 7.000
6
1.750 2.000 .?50
7.00 0
7.000 7.000 7.000 7.00c
6.625 6 .625 6.625 6.625
I .000 1.250 1
.500
4. 500
.500
7.OOO
7.000 7.000 7.00c 7.000
.500
rAl
.'l
58 E+0 7
.365E+07 .510ErO7 .312E+05
.859E{05 .17 6E+06 .30EE+06
.4E68r06
.998E+06
.SZ3E+Oz
.17 4E+O7
.825E+07
.275e+07
Vessels
133
134
Piping Stress Handbook Table 6-1 Continued ROTA VESSEL OD, FT
7.00 0
7.000 7.0 00
7.000 7.000 7.000
7.00q 7.000 7.00 0
?.000
7.00 0
7.000 7.00
0
7.000 7.000
7.0 00
7.000 ?.000 7.000 7 -DOO
i
7.000 7.000 7.000 7.000 7-000
7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.00 0
7.000 7.000 7.000 7.0c0 7.000 7.000 7.0c0 7.000 7.0 00 7 .OOO
7.000 7.000 7.000 7.000
7.00 0
7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.0c0 7.000
SIIFF CALCULtII0NT CYL. VESSEL
VESSEL TCKTII{
1.759 2.000 .250 .375 .5rr0 .625 .750 I .000 1.250 I . 500 1.750 2.000 .250 .375 .500 .625 .750 1.000 1.250 1.500 1.750 2.000 .250 .375 . 500 .625 .750 1.000 I .250 1.500 1.750 2.000 .250 .375 .500 .6?5 .750 't .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1 .250 1 .500 1.75A 2.000 .250 .375 .500 .625 .750 r.000 1 .250 1.500 1.750 2.000
ZLE ROT STtF IiI.LB/D€G N INPLANE OUTPLANE CIRCU STD LONGI
NOZZ L E
NOZ
OD'IN
ICKTI
.f218.08
14 -000
14.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000
-375
.375 .375
.404E +O7
,loEE+06
.565E}07 .360Ef05
.298E+06 .611 E+06
.204€+06
.
t 69E+ 0E
.107Er07
.992E+O5
.3568rO6 .561E+06 .l l5E+07 .2018+07 .318E+07
.375 .375
.168E+07
.375
.9538+07 .140€+08 .1968+08
.375
.
.408 E+05
.346E+07
.604Er07
.467E+O7
.652e+07
18.000 18.000 18.000 18.000
.375
I 22 E+06 .338 E+06 .693E+06
.375
.121E+ 07
.113E+06 .23'l E+O 6 .4038+06
.191Er07
.636E+06
18.000 18.000
.375
.392E+07 .685E+07
.131E+07 .226E+07
.375
.1 C8 E+0E . 1 59E+ 0E
.360E+0 7 -529E+Oz
.222E+08
.739ErO7
.375
.1378+06
.457E+05 .126E+O6
.375 .375
.377E+06 .775E+06 .135E+07
1E.000
'18.000 1E.000
18.000 20.000 20.000 20.000 20.000 20.000 ?0 -000
20.000 20.000 20.000 20.000 22.000 22.000 22 -OOO
22.000 22.000 22.000
.375
.37 5 .37 5
.255E+O7
. 121E+08
.5058+05 . 139
.150E+07
.499E+06
.857€+06
.37 5
.236E +07
.s75
.485€+07 .847E+07
.16?E+a7 .?82ErO7
.134E+0E
.445E+O7 .654E+07 .914E+07
.37 5
.'l96E+08 .27 4erOE .166E+06
.375
.4578+06
.375
.259E+07 .531E+07
24.OOO
-375 -375
26 -OOO
E'06
.266Er06
.375
24.000
26.000 26.000 26,000 26.000 26.000 26.000 26.000
.5928r07 .626Er07
.417 E+06
.37 5
24.000 24.800 24.000 26.000 26.000
.4038+07
.151E+06
.938E+06 .1 648 + A7
24.OOO
.146E+07
.375
2?.ogo
24.000 24.000 24.000
.71?Ero6
.436E+07 .7 66a+07
.37 5
22.000 24-000
.451E+06
.2138+07
.178E+08 .248E+08
.3?5
22 -OOO
22.OOO
.258E+06
.9?7E+07 .1 46Er08 | 5E+08 .3 00E +08
.3 75
-2
-37 5 .37 5
.180Ei06
.375
.497ErO6
.375 .375 .375 .375 .375 .375 -375
.lcz€.07
.787E+O6
.5 53E+0 5
.152E+06 .313E+06 .546E+06
.862E+06 .177E+O7 .309 E +0 7 .488 E +0 7
.717E+07 .100€+08
.60',|Ef
.l
05
66Er0 6
.340E+06
.17EE+07
.594E+06 .9378 +06
.577E+07
.192E+07
.28'lEr07
.101 E+0E .'159E+08 .2 348 | 08
.3?7er08
.336€+0 7
.530Er07 .779E+O7
.109E+08
Rotational Nozzle Flexibilities for Cylindrical
Vessels
135
Table 6-1 Coniinued R0TA VESSEL
OD,FT
E
SS€L ICK,IN
VE
-00tJ
8.000
E.0c0 E.000 E.00 0
.375
?.375 2.375
.7 50
2
.000
1
1.250 1.500
1-750
E.000
2. 000
E.000
.37
.250
8.000 E.0c0 E.000
8.000 6.000
2.3?5 2.375 2 .375 2.375 3.500 .500 .500
.7 50
3. 500
.000 'l -250 't .500
3. 500 3 .500
5
.625
1
1.750 2.000
-250
8.0c c
.500
E.000
.750 I .000
6.000 8.000 8.000 8.000 8.000 8.0c0
2 -375
.500
[.0c0
8.000 8.000
.375
3 3
8.000 6.000
E.000 8 .000
NOzZL€
OO,IN
.500
8 .000 8.0c c E.0c0
6.000
STIFf CALCULAII0N, CYL. V€SSEL
.625
1.250 1.500
3.500 3.500
3.500 3. 500
4.500 4.500 4.500 4.500 4
.500
4.500 4.500 4
.500
/.. 500
.500
.000
4
.000
.500
E.000
.7 50
6.625 6.625 6,625 6.625
8
8.000
?
1
.000
8.000 8.000
1.250 1.500 1.750
8.CCC
2-AAO
E.000
8.000 3.000 8.000 6.000 8,000 8.000 t.000 8.000 8.000 6.000 1i .00c 8
8.000 E.0c0
6.000 8.000
tt.625
8
8.625
1.?50 .500
.500
.625 .7 50
.625
8.625 8.625
.750
1.750 2.000
-6?5
8.625
I .000 1
.6?5
6.625
8
I .625 8.625
10 . 750 10 . 750 10 .75 0
0. 750 1 0 .750 't
10.750
.000 1.?50
'10.750
't .
10
'I
500
8.CC0
E.000
6
.500
.000
.000 .000
6.625
.2 50
8.00c 3.000 E E
6.625
2. 000
.250
.750
10-750 't 0 .750 12.75t)
12,750
ZLE ROT STI f IN.LB/DEG N INPLANE OUTPLANE CIRCU LONCI STD NOZ
rCK,I
-154 54 .'154 .l54 -151 -154 .154 .154 -154 .154 .216 -2'.t6 .216 -216 .216 .z',t6 .216 .?16 .2'16 -2't6 .237 .?37 .237 -237 -237 .237 .23? .?37 .237 .237 .280 .280 .280 .280 .2 80 .280 .280 .280 .280 .280 .322 .322 -322 .32? .322 -3?Z -322 .322 .322 .3?? .365 .365 .365 .365 .365 .365 .365 .36, .365 .365 -3?5 .375
.1
. 132 €+0 5
.364€i05 .718E105 .',l31€+06 .2A6E+06 .423E+06 .7-19
E
+06
.117E+47
.171E+ol
.441E+04 -121ErO5
.2 49 E +O5
.436E+05 .687E+O5
.1418+06 .2{,68+O6 .389 E +06 .57?E+O6
.239E+O7
.7988+06
.197 t+Os .5 4ZE+05
.181F+05
.1118+06 .194F+06
.307Er06
.6 30€ +06
.1108+07 -17 4E+07
.255E+ol .356t+07
.260 E+ 0 5 .717E+05 .117E+O6
-?57 E+C6 .4058 +06 .832E+06
,1158+07
-2?9E.07 .3378+07 .4?18+07 .195F+A5 .109E+06 .?24E+46
. 391 E+ 06
.6r6E+06 .126E+07 .221E+ 07 .349E+O7 .5'12E+O7 .715E +O7
,656E+O4 .371E+05
.6488+05
.102Er06 .210Er06 .367E+O6
.578E+06 .8508+06 .119€+07 .8678+04
.27
L
7
E+O6
.4858+06 .7 64E+O6
.112E+07 ..|.57
E+
07
.132€+05 .363E+05 .745E+05
.130E+06 .2058+06 .422E+06 .7368+O6 .116E+O7 -'171
E+ 4 7
.238Ef07 -17 4E+05
-480E+05
.1 67 E +O7
.292E+47 .4618+O7
.9858+05 .17?E+46 .271E+06 .557 E+O6 .973E+06 .1548 +O7
- 677E+07
.2268+07
.9 45E+07 .658€+05
.315E+07 .219 E+45
.181E+06 .37?E+06 .650E+06 .',l03E+07 .2108+ 07
.6048+05 _124ErO6 .217E+o6 .3 42E+O6 .701E+06
.
3 68 E+
07
.580 €+07 .853E+07
.1198+08 -791E+05 .216E+06
(
i
.144E+46 .29 5 E f06 .e14E+06
\
.239E+05 .490E+05 .857E+05 .135E+06
.5228+05
.516Er06
l:
.1?3E+o7 .193E+07 .284E+17 .397 e+O7 .2 64e+ 0 5 -726E+OS
(
136
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATION, CYL. VESSEL VESSEL
VESSEL
OD,FT
ICK,'N
.500
8.00 0 8 .000
8.000 8.000 8.000
8.00 0
8-0cc 3.000 8.000 8.000 8.000
.7 50
I .000
1.250 1.500 .000
2
.2 50
E.000
8.000 6.000 E.000 8.0c0 6 .00c 6.000
.625
8.000 8.000 8.00
0
8.000 E.000
8.000 8.000
.75A I .000 1.25O 1 .500 1 .75A
2.000 .250
E.000
8.000 8.000 5.0 00 E.C00 3
.000
.0c0 8.000 6.000 8.000 8.000 8.000 E
8
.000 I .000 E.000 6
.000 8.000
E
E.000 E.000
6.000 6.000 6.000 8.000
.'136E+07
.230E+07
.489E+07
-163E+O7
.257 E+O7
.375
.7 72E+ 07 .113F+08
.1018+06
.337Ef05
.27EF+06
.9?8E+05
.375
.000
1 1
.500
.750
2.0 00
.250
.375 .500
.t91E+06
.999 r+06
.333E+06
.1588+07
.525Er06 .1088r07
.565E+07 .891E+07
.188E+07 .297E+07 .437E+C7
.131E.C8
.375
,163E+08
.64tE+06 .1?9E] 07
6.000
18.000 8
.000
20.000 20.000 20.000 20 .000
0.000
20 .000
20.000 20.000 20.000 20.000
.367E+d7 .641E+ 07
.375 .375 -375
.375 .315
22.000
1.250
.5?8E+o7
.572E+O6
.323Er07
22 .OOO
1
.378E+07
,610E+07
.377E+06 .595E+06 .122E+O7 .214E+O7
1
. ?50
.15EE +08
.113E+07
.7 5A
,500
.804€+05 .1658+06 .288a+06 .455F+06 .934E+06
.1058+06 .216E+06
2
.0c0
.292E+05
.316E+06
I
E.000 E.000
.875€+05 .241E+ 06
I E. 000
.625
.000
.342E+O7 .47 7 a +o7
.382E+05
.000 1 6 .000
1.250 I .500 1.750 2.000
-143E+08
.1 15E+06
18.000
.7 2. 0c0 'ti
E.C00 8
6.000 6.000 16.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000 16.000
18.800 't E.000 1 E .000
1
oz
E+
.375
1 1
1E
.625
.4'l1E+O 6
.'l0f €r08
14 .000
1.000 1 .250 1.500
.000
8.000 E.0c0 8.000 8.000
.000
.149E+06 .260E+06 .E44E+06 .117E+O7 .232E+O7
.E65E+06
4
CIRCU
.123E+ A7
.697 -375
OUTPLANE
.253E+07
.4128+07
'|
.500
1
.731r+06
.000
1
.000
.4 47E+06
.495€.06
1
.500
TCK,IN INPLANE STO LONGI
11 .000
t .000 1-?54 'I .500
8.000 E
't2.750 I 4.000 I 4.000 4.000 1 4.000 1 4.000 14.000
E.000
NOZZLE ROT STI F It.I.LB/DEG
1?.750 12.750 12 .750 12.750 12.750 12.750 12.750
14
.7 50
.750 2.000 .250
t,000
0zzL€
OD,III
2? .OOO 22 .O00
22.000 22.000 22.000 22.000
.5f>
22 .OOO
22.000 24.000 24.000 24 .000
.37
5
.101E+08 .'149Er08 .207E+08
.1288+06 .355E+06 .725E+ 06 .127E+O?
.200E+o7 .410E+07
.7',16E +07
.337E+07 -495E+07 .691 E! 07 .427E+05 .118E+06 .Z 4ZE+O6
.122E.O6 ,6668+06 .137E107 .239E +O7
.1'13E+08 .166E+0E .212E+0E .112E+06 .390E+06 .E0'l E+06
.377E+07
.1 40E+07
,2218 + A7
.467E+O6 .736E+O6
.453E+07 .79?E+07
.264Er47
.1 25€+0E .184E108 .256E+0E
.155€+06 .428€+06 .8
7EE
'
o6
.55 4E+07 .7738+O7 .472E+O5
.130E.06 .267E+O6
.15'lE+07 -4'16E+07
.6128+O7
.855E+07 .517E+05
.143E+06
.293Er06
! Cylindrical Rotational Nozzle Flexibilities lor
Vessels
137
Table 6-1 Continued ROTI STITF CALGULATI0N' CYL'
VESSEL
NOZZLE ROT STI F ItI'LB/DEG.,
:::?i' Y:l:ih i8:ii' iii;io lii:l-' 8.000 8
.000
8.000 8 .000 8.000 8.000 8.0c0 8.000
E.000
8.000
.7 50
t .000
1.250 1.500 1.?50 2.000 .500
.000
.625
8.000 8.000
.0c0
8
.7 50
.2 50
E.000 8 -000
8.000 8.000 8.000 8.000 8.000 8.CC0
8.000 .000
6
8.000 8.000 8.000
.000 .000
8
6
8.000
.000 I .000
8
8.000 8
.000
8.000 8.000 8.000 8.00 0
.500 .7 50 2
.000
-250 .500
.625
.750 1.000 1 .250 1.500 1.75u 2.000 - 500
.750 I .000
1.250 1.500 1.150 2. 000
24.000 24.000 24.000 24.000 24
-000
24.000 24.000 26.000 26.000 26 .00 0
26.0c0 26.000 26.000 26.000 26.000 26.000 26.000 28 .000
28.000
28 - 000
28.000 28.000 28.000 28.000 28.000 28.000
28 .000
30 .00 0
30.000 30.000 30.c00 30.0c0 30.000 30.000 30-000
30.000 30.000
9.000 9.O00
t00 .625
.
.000
9
9.000 9.000 9.000
1
9
1
.000
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.000
9.J00 9.000 9.000 9.000
.7 50
.000
.250 'r.500
1.750 2.000 .2 50
.500
2.175 2.375 ?.375 2 -375
2.375 2.375 2.375 3.500 3.500 3
.500
.7 50 1.O00
3'500 3.500 1.500 3.500 3.500
1.750
3
.000 .250
4
1.250 1.500 2
.500
3.500
.500
4.500
'i;i 'iti
'-1?i 'i;;
+07 -212F --istz'oz
-doee*oz . t:zt* oc
3!l:i^*' .E06E+06 7 ' 166E+o
.2q?!.91
'-1;t .zott+oa -456E+o7 '9!1,t-'9! .23'1E+0E 'Yl!:':' -375 'izi 'i;; '1;a
'.1it
1695+06 { 06 954g+06
- 465€
'5 621+o5
.155€+06
'3'l8Eio6
167E'07 '119!'96 ' :.. .E778+06 t A\F +o7 'it'. liioE'oz '.1?; i a31+ o7 '180E+67 '3\tq-+o^! 0E '1:9'-:Y' -375 .'l1et '-.ii -2196+08 '7298+o7 ':'-i an
:i;i;-o; :i+; '\zi 5ozF{06
.991!:95
167F +06
o7 '.314E+o6 .taOr*oz .600F+06 -28|E+oz '9 47 E+06 .igre. oz '1918+G7 . i ozr.oa '340F+07 .1615+08 '5368+07 .2 36g+oE .788E+07 .!366+oa '119:lo8 - 196E +06 '653F+05 sloE+c6 '180E+06 -l6eE+06 -ittt'oz --1s4E+o7 '9!28-+D6 3o5E+o? '102E+07 '-i?; -.iriE+07 '!9:!*07 16e5+08 '1!5.1-.ol .1i; '.;;;'17r8+08'1.6.1'.07 'i;i '8168+o7 'i545+08 ' z:le + o8 '-i?t
'iii 'i.;i 'i;4 'i|i '-i?t 'i;i 'iri, '.ir; ';;< 'i;. '|;i '.3;; 'i;.
-
163 6+
'118E+08
1at '-a;i ;;; '-;;i '.4;i
'-;ti
-'l25t+05 '416€+04 314t+ 05 ' 1 'l 5 +o s io5r+05 '235E+os5 :123E.06 ''le4E+06 ' 411E+o '6488+c5 -3eeE+o6 '111!'06 E
'.::: -lziiili ':l; ':l', ';'.; '.i;i rni '.tiz rie 'r;A
'.ia; ';;; ';;; '-i;; "r;i '.i;?
' i ))i ' )Jli,iz 'iz
aii
'.1":,i::"2 .53eF+06
-t5zE+o6
'618E+o/' os '170E+05 :5118 'os -105E.06 .35oEro5 -r
+
1E3F+06
-289F+06 -594E+06
'91.1E-+o5
'964E+05 .198E+06
16r,E+07 '119I'06 - 164E + 07 ' 51'55+06 .? L1E+o? .8 0 2 +06 +oz 3362+a? |z-tE+oL 't15E+05 "t '4768 +o5 +05 'E't7 '225F F
l,
Piping Stress Handbook Table 6-1 Continued
R0lA SllFr CALCULATI0NT CYL. VESSEL
OD,IT
VESSEL TCK,IN
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.500
.625
.750 I .000 1.250 'l .500 ?.000 .250
.375 .500
.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
.7 50
1.000 I .250 I .500
1.750 2.000 .?50 .375 .625 .750 .000
.250 .500
9.0 00
9.000 9.000 9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.00c 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
. 750
2.000 .500 .625
.750
I .000
1.250 '| .500 1.759 2.000 .250
.375 .500 .625 .750 I .000
1.250
NOZZL€
NO?ZLE
0DrIN
TCK,IN
4.500
4. 500 4 .500
4.500 4.500 4.500
.75C .000
.250 .500
.750 2.000 .250 .375 .5 00
.462e+o,
-2 42e+06
.808 E+05 .1?7E+O6 .262E+O6 .457E+O6 .7218+O6
.237 .237 .237 .237
.382Er06
.785E+06 .137E+O7
6.625 6.625
.148E+07
.2E0
.373E+05
.121ErO5 .3 4?E +0 5
6.62
.2E0 .2E0
-103€+06
.?118+06
.703€i05
.3688+C6
.123E+06 .194E+06
5
6.625 5.625
.237
6 -625
.280 .?80
6 -625
.280
6 -625
6.625 6.625 8.625 8.625 4.625
I .625 I .625
8.625 6.OZ)
.62> 8 .625
6
8.625 10.750 10.750 10.750 10 .750 10.750 10.750 r 0.750 10.750 10.750 10. 750
12.750 12.750 12.750 12.750 12.750 12.750 12 .750 '12.750
.625
. '1 39 Er 06
-237
.444E+07
2. 000
.500
.237
.216e+07 .318E+07
12.75D
.250
f IN.LB/DEG INPLANE OUTPLAI{E Lol,Gl CIRCU ROT STI
-237
,.. 500 4. 500
1
,500 t .750
slD
V€SSEL
14.000 '| 4.000 'r 4.000 14.000 't 4,000 14.000 14 .000
14.000 I 4.000 't4.000 16.000 16.000 16.000
.2 80
.280 -322 .32?
.58'l E+06 .1198+07 .208€+07 .329F+07 .433E+07
-1O6E+O7
.f,97E|06 -694E.06 .t10E+07 .161t+07
.67 4E. 07 .492E+05
.?25E+07 .164E+05 .452ErO5
.3ZZ
.279E+06
.92E E+0 5 -162E+O6
.322
.158E+07 .275E+87
.525Er06
.322 .3?2 .3?2
.322 .322
.365 .365 .365
.56 5
.365 .365
.136E+06
.437Fr06 .?68Ef06 -4348.07
.6388+07 .691E+07 .620€+05
.17'l
E+
06
.351E+06 .613E+06
.256E+06
.918E+06 .145E+07 .2138+O7
.297E+07 .207E+O5 -
5
70E+0 5
-117
E+O 6
.204E+06
.967Er06
-322E+O6
.'198Er07 .3 478+07 .5478+07 .804E+07
.661E106 .116E+07
.1'l2Er08
.1E2Er07 .2688+C7 .374E+07 .249E+05
.37 5
.746E+05 .205E+06
-375
.737E+06 -116E+07
.387Er06
.375
.239E+07
.795E+O6
.417 E+07 .657a+ A7
.219E+07
.375 .37 5
.175 .375
.422Er06
,685E'05 -141E+06
.246E+06 -'t 39 E+O7
.9 6?E+07
.322E+ol
.275Er05
-375
.135E+08 .825E+C5 .227E+06 .4 67 E+ 06
.815E+06
- 156E+06
.3? 5
-375
.129 E+07 .264E+07
.429E+O6 .880 E +06
.37 5
.4618+07 .728E107
.154E+O?
.37 5
.107E+08 .1 49€+ 08
.37 5 .37 5
.375
.375 .375
.953Er05 .263E+ 06
.375
.539 E+06
.450E+07
.758 E+05 .272E+O6
-243E+o? .357E+0?
.498€+07 .5
'13 g
r05
.875E+05
.lE0Ero6
Rotational Nozzle Flexibilities for Cylindrical
Vessels
139
Table 6-1 Continued ROTA VESSEL
OD,FT
9.0c0 .000
9
9.0c0 9.00
0
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9 .0c0 9.000
9.000 9.000 9.0c0 9.000 9.00
.625 .750 1 .000 1.500 1.750 2 .000
.250 .500 .625 .7 50
9.000 9.000 .000
9
9.000 9 9
.000 .000
9.000 9.000 9.000 9
.060
9.000 9.000 9 .000 9 .000 9 -0 00
9
.000
9.000 9 9
.000 .000
9.000 9.000 9.000
.000
E. 000
1
18.000
t8.000
18.000 18.000
20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
.500 .000
.2 50 1.5C0 't
1.750 2
16.000 16.000
.250
?. 000
1
16 - 000
18 .000
.000
'1E 1 '|
.00 0
8.000 8.000
18 .000
.?50
22 .000
.500 .6?5
22 .OOO 22 .00 0
.7 50
2
I .000
1.250 1.500 1.750 2.000 .?50
9.000 9.000 9.000
9.000 9.000 9.000 9-0c0 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
16.000 16.000
.000 .25D .500 -750
0
.000
6, 000
1
16
9.000 9
VESSEL
VESSEL NOZILE NOZZLE ROT STIF IN'LB/OE6 TcK,IN TNPLANE oUTPLANE oo,rH ;;i;;N CIRCU LONGI STD
.000
9
SIIFF CALCULATION' CYL.
.500
.625 1.000 1.?50
t.500 1.750 2
.000 .250
.375 .500 .625 .?50 r .000
1.250 1.500 1-750 2.000 .250 .500
.625
22.000 2
.000
22.000 2? .OOO
22.000 ?2 .OOO
22.000 24 -000 21-OOO
.000 24-000 24
24.000 24.AOO
24.000 24.000 24.000 24.000 26.000 26.000 26.000 26.000 26.000 ?6.000 26,000 26.000 26.000
26 - 000 26 .00 0
28.000 2E
.000
28.000
.375 .375 .375 .375 .375 .375 .375 .375 .375 .3?5 .3?5 .3tS .3?5 .375 .3?5 .3?5 .375 -375 .375 .375 -3?5 .375 .375 .3?5 .375 .375 _37, .375 .375 .375 .3?5 .375 .3?5 .3?5 .375 .375 .3?5 _375 -37, .375 .3?5 .375 .375 .375 .375 .3?5 .375 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 -3?5 .375 -375 .375
,941E+06
.149Fr07
.3148+06 .495E+06
.305 E+07
.'l02Er07
.533E+07
.
.840E)07 . 1 24 E+ 08
1
78€ +07
-280E+0? .412E+O?
.172E+08
.5'58+07
.6118f06
.2L
.108E+06 .2988+06
.3,,0E+05 .9928+05
.1O7E+O7
.3568f06
.168E+02
.346Er07 .604E +O7
.953E+O7 .',|40E +08
.196E+08 . 121 E+06
4E
+46
.561 E+06 - 11
5
E+Ol
.201F+O7 .318E107 .467E+07
.652E+07
.403E+0t
.53fE+06
.1118+06
.683E+06 .119E+07
.3988}C6
.188 € + 07 .3FZa+O7
.228E +o 6
.628E+06 .129E+07
.675E+07
.2258+07
.1078+0E .157E+oE .219 Er 08 .1J4 €+06
.7 29 E+A7
.368E+06 .755€106 -132t +o7 .208E+07
- 427 6+O7 -7 47E+07
.,'166+06
.355E+07 .5??E+a7 .445C+05 .123E+06 .252E+06 -440E+06 .694E+06 .14?E+ 07
.?49E+07 -J93E+07
.173E+08 .2129+oE
.577 E+O7 .806E+07 .488E+05
.4639+06
.134E+06
.1A6t+46 .EZ8E+06 -1458+ 07
.228E+07 .468E+07
.27
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rO6
.482ErC6 .760E+06 - 15 a,E+07
.1908+0E
-273E+O7 .430E+07 -632E+o7
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.'l57 E+O7 .2 482+07
.521E+06 .827E+O6
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18
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+
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.129Er08 .265E +08 .1 59E+06
.5098r07 - ',149E+08
.206E+08 .288E+08 .172E+o6 .4718+ C6 .972E+ 06 .170E +O7
.883E+07
.17oE+ol
.468Ei07 .68?E+07
.960E{07 .573Er05
.1588i06
.32 4E+o6 -566E+06
l,
140
Piping Stress Handbook Table 6-1 Continued ROTA STIFT CALCULATION,
EL TCK,IiI
VESSEL
VESS
OD,FI
9.000
9.000 9.0c0 9.000 9.000 9.000 9
.000
1.000
1.2rO 1.750 2. 000
.250
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.000
9.000
.500
.625 I .000
1.250 1
9.000
.500 .625 .?50
9.00 0
9.000 9.000 9.000 9.000 9.000 9.000
t.000 t.250 1.500
.750 2.000 1
10.000
.250
r0.000 1
0.00 0
r0.000 10.000 10.000 10.000 10 .00 0
10.000 10.000 '| 0.000 't0.000 I 0.000 10.000 10.000 10.000 10.000 '10.000
10.000 10.000 10.000 10.000 10.000
. 500
-625
-750
I .000 1.?50 I .500 1.?50 2-000 .250 .37 5 - 500
.625 .750
I - 000 I .250 1 .500 1
10 .000
10.000 10.000 10.000 10.000 10.000 10.000 10.000
.750
2. 000
.250 .500
.625
10 .00 0
10.000
.500
1.750 2.000 .250
.750 1.000 1
.250
1.750 2.000 .250 .500
VE SS EL
NOZZLE
NOZ ZLE
ROT STI
OD,IN
TCK,IN
INPLANE
STD
LON
28.000 ?E.000 2E.000 ?E.000 28.C00
28.000 30.000 30.000 30.000 30.000 30.000 30.000 30.000 30 .000
30.000 30.000 5 2.000 32.000 52 .000
52.000
.000 .000 52 .000 3 2 3 ?
.375 .375
4. 500
4.500 4.500 4.500 4.500 4.500 4. 500
4.500
6.625 6.625 6.625
- 268
E
+07
.550E+07
.37 5
-31tE+0E
.375
.375 .375
.2 23E +08
.185f+06
.509E+06 .104E+07
.182Ei07 -375
.375 .375 .375
.268€+07 .591E+07 .103E+0E
.163E +08
.239E+08 .334E+06
OUIPLANE CIRCU
.E93E+06
.183€+07 .320E+07
.5058i07 .7 438+O7
.1048+0E .6158+05 .1 708+06 +06
- 348 f
.608 Er06
.959Er06 .197E+O7
.344ErO7 .543E+07 .7988+07 .1 'l I E+08
.375 .375 .375 .375
.197E+06 .544E+06 .1t2E+Oz
.l8J
.195E+o7
.37 5
.3088+07
.650E+06 .1of,E+07
.375
2.375 2.3?5 2.375 2.375 2.375 2.375 2.375 2.375 z .375 2.375 3.500 1.500 3.500 3.500 3.500 3.500 5.500 3.500 4.500 4.500
6I
.t75
.3?5 -375
-500
F It{.LB/DEG
.9 61e+07 - 1 52Er08
32.000 32.000 52.000
3
CYL.
-
632E+07
. 1 10E +08 - 174E+ 08
.658Er05
E+06 .372E+O6
.211E+o?
.3688+07
.5808r07
.375
.256€+0E .357E+08
.E538+07
.'t 54
.'tt8E+05
.594E+04
.326E+05
.109 F +0 5 .2?3e+O5
.1t4
.154 .754
.669€+05
-154
.1848+06
.151 .154 .154 .154 -154
.216 .216
-216 -216
.216 .216
.117E+06 .3?9E+06 .661E+06
.104E+07 .153E+07 "214E+07 .176E+05 .485E+05 .996E+05 .17 4E+06 .27 4E+ 06
.563E+06
.?16
.216
- 9 84 E+06 .155E+ O?
.z',t6
.2?88+o7
.216
.?37 .237 .?37 .237 -237
.319e+ 07
.119Er08
.390€+05 .6158+05 -126E+O6
.2208+06 .348€+06 .511E+06
.714Ero6 .587erO4 -162E+05
.332E+0 5
.580E+05
.915€+05 .18EE+06 -328E+06
.517Ei06
.7618+O6 .106E+07
.2338+05 .6418+05
-775E+O4
.132E+06 .230E+06
.439E+05 .766ErO5 .121E+06 -2488+06
.363€+06 .714E+06
.433Fr06
.237 .237 -237
-205E+07
-684E+06
-237 .2E0
.35fE+05
.140ErO7 .1'l8E+05
.97 4E+05
.325E+05
.280 .280
.130€+07
.2148+Os
.302E+07 .42'lE+07 .2C0
E+
06
.'101 E+07
.667Eros
Rotational Nozzle Flexibilities for Cylindrical Vessels
141
Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL
OD,FT
'l
0.000
1
0
VESS€L NOZZLE NOZTL€ RO] STIT IN'LB/D€G TCKu IN TNPLATJE oUIPLANE 0D,rN i;i;iN CIRCU STD LONGI 6.625 .7 50
.000
.000
10. 00 0
10.000 10.000 10.000
1.750
10 .0 0c
2
.2 50
.500 .000
.2 50
10.000 '| 0.000 10-600
.500
10.0c0 10.000 10.000 10.000
.7 50
'10.000
.000
,250
6.625 6.625 6.625 6.625 6.6?5
I .625 I .625
8.625 8.625 a a
.6?5 .625
a.625
.750 .2 50
10 .750
.000
2
10.000 't 0.000
.6?5
8 .625 a - 625
.500
't 0 .000 't 0.00 0
6
I .625
0
.500
10.000 10.000 10.000
10.750 10.750 10.750
.7 50
10 .7 50
1u.0
0
0.0 00 '10.000 1 0.00 0 10.00 0 10.00 0 1 0.00 0 1
1 1
.000
1
.500
.250
1.?50 2.000
.250 .37
5
10.750 10.750 10 .750 'ro.750
l0 . 750
1Z -750 '12 ,7 50
10.000
.500
1Z .750 12 .7 50
1C.000
.7 50
12.750
.625
10.0c0
10.000
t .000
'10.0c0
1.250
10-000
1
1
0.000
10-000
.500
1-750 2.000
.250
10.000 10.000 10.000
'10-000 1 ri . ti00 1 0. 00c
.625 .7 50 '|
.000
1.250 1.500
'10
2
10.000
10.000 10.000 10.000 10.000 10.000 1 0.000 I 0.000 10.cc0
'i0.c00
.250 .500 .625 .7 50 1
.000
1
.500
1,254
.000
.500
0
1
0.00
0
12 -750 1
4
.000
000
.t/,-000 I 4 .000 14.000
.00c 14.000 't 4.000 14
.000 14.000
16.000 16.00u 16.000 '16-000
16.000 16.000 16.000 16 .000
6.000 6.000 18.000 18.000 18.000 1 8.000
't
2.0c0
1
1Z -7 50
14
.000
10 .0c 0
10.c00 1 0.000
.750 12.750
12
11, -
.500
10.000 10.000 .00 0
'12.750
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1
.280 .2 80 .280 .280 .280 .280 ,280 .3zz -322 .32? -t?? .322 -32? -32? .3?2 .322 .322 .365 -565 -365 .365 -365 .365 .365 .355 .365 .365 .t75 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 .375 -375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .3ZS -375 .375 -375 .375 .375 .3?5 .375 .375 .3?5
.319 E. 06 .551E+06
.113E+al
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.6408+07 .467E+05 .129E+06
.116E+O6
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.153E+o7 .213E+47
.156E +05
.264E+ a6
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.846€+07 .538E+05
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.'154€.06 .498€+06 .870E+06 .'t 37 E+47 .2629+O7 .282E+07
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06
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E+
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-306E+07
.427E+07 .261F+05 .719Er05 .1488+O6 .2 5E E+0 6 -407E+06 .835E+06
.j
46E+O7
.23a8+o7 .338E+07 .4728+07 .30 | E+0 5 -830E+05 .120 E+ E 6
.893E+c6
.?9Et+O6
.2 89E + 07
.964Er06
.141E+Ol .5ArE+07 .797 E+07 .'117E+0E
.'164E+08 .102E+06 .ZEZE+46
.5f0E+06 .1c1.E
+
A7
I
.1'lIE+06 .306E+ 0 6 .62ZE+O6 .11OE+07
.917
I
.470E+06 .1688+O7
.266E+07 .391E+07 .545E+07 .31?t+O5 .911t+O5
-'l 938 +06 .338E+06
-l
142
Piping Stress Handbook Table 6-1 Continued ROTA
10.000 10.000 10.000 10.000 10.000 10.000 10.000 1 0.000 10.000 10.000 10.000 10.000 'r0.000 10.000 10.000 I 0.0 00
10.000 10.000 I I
NOZZLE
TCKrlftl
TCK,IN
1.250 1.500 1.750 2.000
1E.000
18.000 .000 .000 18 .000 1E.000
1.750 2.000 .250
20.000 20.000 ?0.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 22 .000
.37 5
22 .00 0
-375
.500
-625 -750
.000 1.250 1.500 'l
- 160E+ 07
.3?5
.573E+07 .904E+07
-533E+06 .1098+O7 .191E+O7
.13fE+08
.375 .375 .375
.lt5Er06
-t75
.375 .37 5 .37 5
.375 .375 -175
I 0.00 0 '10.0 0 0
22 .OOO
1.000
22.000 22.000 22.000
.37 5 .37 5 .3? 5
10.000 10-000 I 0.000 10.000 I 0.000 10.000
't0.000 10.000 10.000 10.000 10.000 10. c00
'10.000
0.000 10.000 10.000 10.000
'|
t 0 -000
10.000 10.000 't 0.000 10.0 0 0
10.000 10.000 10.000 10.000 10.000 10.000
.t75
.375
IRCU
.301E+07 .413E+07
.6'l8Ei07 .382E+05
.316E+O6
.105Ef06
.6488+06
,2168+06 .377E+86
-11tE+07
.179 E+07
.367E+07 .641E+o7 .101E+08 . 149€+0E
.247E+06 .127 E+ 06 .349 E+06 .7178+O6
- 59 5 €+06
.122E+47 .214E+07 .3378+47 .4958+07 .691E+O7 -422E+O5 t t 6E+06
.
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E+0 6 . 417E +06
07 -'l97E +87
.658E+06
.708 El07 .112E+06
.3728rO7
.125E
+
.405E+07
.135Er07 .236Ef07
22.OOE
.375
. 164E'08
2? .000
.37 5
24.000
.375
. ?29E+08 . 1398+C6
.7 64ErO7 .463E+05
24 .000
-375
.3838+06 .78tE+O6
.262E+O6
-375 .375
.1378+O7
.457Er06
.721E+96 .148E+07
-547E+O7
.f288r06
.625
.?59
I .000
24 .AOO 24 .000
.375
.216E+07 .441E+07
1.250 I .500 1.750 2.000
24.000
.375
.776E+O?
.259e+O7
-122E+08 .180E+08
.600E +07
.375 .500
.625 .750 1 .000 1.250 1.500 1.750 2.000 .250 .375 .500 .625 .7SO
I .000
10 -000
l0 -000
.375 .500 .6?5
I 0.00 0
.375
.186E+0E
C
21.000 24.000
.500
1.250 1.500 1.?50 2.000
10.000 10.s00 10.000
.328Er07
-375
.37 5
1.500 t .750 2 .000 .250
F I{.LB/DEG
.3 75
22.000 ?2.000
1.25C
ROT STI
OUTPLAI{E
.500 .625
10.000 10.000 10.000 10.000
VESSEL
STD
t8 1E
CYI.
I!IPLAN€ LOIIGI
'l0.000
t0.000
.l
CALCULATION,
VESSEL
1.000
I 0.00 0
x,
STIfF
. a>u
.7 50
24 .000
24.000 24
.000
26.000 26.000 26.000 26.000
.375 .375 .375 .37 5
26 -000
.375 -375
6.00 0 6.00 0
.375 .375
z
6.00 0
26.000 2 2
26.000 28 .000
28.000 28.000
30.00 0 3 0 .000
30.000
.784E+06
.483Ef07
. l6'l
.8448i07 .133E|08 .196E+08
E+0 7
.281E+O7
.141ErO7 .652E+07 .911E+07
.375 .375
.972E+O6
-307E+O6
.375
50.000
.497E+O6
.235E+07
.5438f05
0.00 0
3
.139E+06 .?85E+06
.163E+06 .449€ + 06
?8.000 ?8.000 28.000 2E.000
.854Ff06 .149Et07
.503€r05
.273€+08
.375 .375 .375 .375
28 -000
.416€+06
.8388+07
.t75
eE.000
28.000
.2 5l E +08 . 15'l E+06
.408Er07
.375 .3?5
.375 .375
.161E+07
.150E+06
.5378r06
.2 54F+07
.847r +06
.522E+07
.17 4E+07
.911e+ 07
.504E+07
.1 44 E+ 0E
.479E+O7
,211 E+0E .295 E+06 .175E+06 .483E+06 .991 E | 06
- 705
.273e+Oz
-910E+06
.l73E+07
Fl07
.984E+O7 .584E+05 - 1618+06
r0 5 -577E+O6
- 330E
Rotational Nozzle Flexibilities for Cylindrical
Vessels
143
Table 6-1 Continued ROTA VESSEL
0D,fT
10.000 .000
10
10.000 10.000 't0.000
STIff
I:i:ii il:ii' I .000 1-?50 1 .500
I .750 2.000
.00 0
'10
10.000 10.0
.500
0 0
0.000 0.030 10.006
.625
1 1
10. c0c '10.000 10
.000
10.000 10.000 10.000 10.000
CALCULATION'
.7 50 1
.000
1.250 1.500 2. 000
.250
30.000 30.000 30.000 50 .00 0
.375 . 51>
.375
.375
32.000 32.000 32.000
.37 5
32 .00 0
3 2 3 2
,000 .000
32.000 32 .00 0
32.000 32.000 36.000 3
10.000 'l0.000 10.000
.150 1.000 1.250
3 6.00 0 3 6 .000
1G.C00
1
36.0c0
-375 .37 5 .37 5
-375
.375
11 .0 00
.250
2-375
.154 .154
.500
2-375
.15 4
2 -375
.15 4
I
'l
'l
l .000
.000 11 .000 11.000 11
11.000 -000
11
11.000
1l.0c0
.000 11.000
'11
1',| .0 00
11.000 11.000
11.000 11.000 'l1.000 11.00c 11.000 11 .00 0 1
I .000
11 .00 0
11.000 11.000
.154
2.375
1.000
2.375
.15 4
.000
?.375 2.375 2 .375
.154
.250
3.50t1
.216
.500
3 3
.216
'r
.2 50
1
.500
1.750 2
1't.000 11.000 'l1 .000 11.000 11 .000
36 -000
.625
{10 0
.
11.000 11.000
.6?5 .7 50
I .000
1.250 1.5C0 1
.750
2
.000
.250 .500
.625 .7 50
I .000
1.250 I .500
1.750 2.000
.37t .500 .625
F IN'L8/DEG
INPLANE LONGT
OUTPLANE
CIRCU
.187E+a?
.560€+07 .979E+07
-326E+07 .51 5E+07
.154E+08 .227 E+08 .317E108
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.172E+06 .353E+06
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+
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36.fjc0 36.000
2.375
ROT STI
.583E+06
1.750 2.000
11 .000
EL
V ESS
.Z1ZE+O6
10.000 10.000
1'l .000
L.
.516E+06
6. 000
36-000 3 6.000
.500
lli:li
30.000
.500
10 .000
CY
.
.110E+07
.226E+07
.394ar07 -622E+O7
.187E+CE .2 74 E+ 08
.911a+O7
-383Er0E
. '128E+08
.113Er05 .3'l 'l E+ 0 5
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+04
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.21
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.176€+06 .361€+06
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.995Er06
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-68',|E+06
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.500 .500
.216
.1548+05 .316€+05 .553Er05
3.500
.216 .216 .216 .216 .216
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.725E+ 06
f.500
3-500 3 .500
3.500 3.500 3.500 4.500 4.500 4. 500 4. 500
4.500 4.500 4.500 .500 .500 4 .500
4 4
6.625 6 -625
6.625 6.625
.?16
.2'16
.237 .?77 .23? .?37 .237 .237 .237 .237 .2 80
.280 .280 .280
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.958E+06 .310Er05
.636€r05 .1',|1 E+0 6
,.i t
.5 t,.
lt ,l t: \l
144
Piping Stress Handbook Table 6-1 Conlinued ROlA STIFF
VESSEL ICX,IN
VESSEL
OD,FT
11.000 t 1 .000 11
.000
.000 11.000 J1.000 I1
1
't
.000
.7 50 1
'| 1
6
.500 'l
10.750 10 -754
.000
2.000
't
.7 50
11 .0 00
t 1 .000
.000 11.000 11
.625 .750
11.000 11.000 11 .000 11 .000 11 .000
t1-00c
r 1 .0 00
11.000 t'l .000 11.000 1 1 .000 1't .000 11.000 1t - 000 1t .000
11.000 11.000 11-000 11.000
11.000 1t -c00 t 1 .000
11.000 11.000 11 .00 0
11.000 11.000
1 1
.000
.250 I .500 1 .750 2.000 -250 .500
.750
J.000 't
.2 50
.000
'ls -75Q
5
0.750 10.750 12.750
't2.750 12.750 12.750
12 -750
12.750 1?.750 12.750 12.750 12.750
?. 000
.3'l7E+06
.365 .365
.554E+06 -874E+06 .179 E+ 07 .31 1E+O7 .195E+07 .727E+O7 .102E+CE .67 4E+05
.375 .375 .375
.131E+07 .1928+O? .2 69 E +O7
.187E+05
.t06E+06 .1E5Elc6 .291E+O6
.5988+06 .105E+07 .1 65 E+o 7 .?42E+O7 .338E+07
.'186E+06 -3E2E+06 .666E+06
.619E+05
-t058+07
.3508+06
.216E+07 .377 E+07
.595E +a7
.87
1E + A7
.1 22E +08
-127E+ 06
.?2?E+0
6
.719 E+C6 .1?
6 t +O?
.1988+07 .291E+07 .4O7 E+07
.206E+06
.73EE+06
.2468+06
.239a+07
-'l16E+ 07
.388E+06 .79 6E+06
.417a+ A7
.139E+O7
.96EE+07 .135E+08 .862E+05
.323E+ o7
.237E+O6
.7 92 t+O 5 -162E1O6
4.000 4.000 14.000 'I 4.000 1 4.000
.4228+06
I
'I
4. 000
4.000
.658E+07
I 4.000
16-000 16 .000
t6-000 1 6.000 16.000
I 6.000 18.000 18 . J00
18.000 I 8 .000
.7 50
.1 558+06
.231E+06 .47 5E +06 . Ef 0Ef 06
't
16 .000
1.750
.2 49E+07
.393E+07 .5778+07 .806E+07 .56'tE+05
.147EtO6
.2 49E+o5 -686F+05
1.000 500
.113e+07
.17 5E+O6 .360E+06 .628E+06 .991E+06 .'l46E+O? -203E+07 .146E+05 .409E+05 .840E+05
.7468+05
.7 50
t.
-252E+06 .4 40E+06 .694E+06
OUTPLANT CIRCU
t4.000
16.000 16.000 't6.c00
'1.250
.365
't
14-000
't1.000 11.000 11.000 11
.750 10.750
1
.37
-3?2 -322 .32?
10
'l
.500 .625
.297E+a7
.437E+07 .6108+07 .4158+05 .1238+06
10 .-t 50
1.500
.750 2.000
.2E0
.322
10.750
.525E+ A6 .10E € +07 .1EEE+07
.280 .260 .322
-322
.500 .7 50
.280
8.625 t 0. 75r]
.3?5
TCK,IN STD LONGI 'NPLANE
.322
.250
VESSEL
NOZZLE ROT STI F IN.LB/DEG
-625
8
1-750 2.000
11.000 11
.625 8.625
.5A0
1
ULATION, CYL.
_625
.000
I .000 1 .25A t .500
'11.000
8 8
1-250
11.000 11.000 11.C00
-625
6.625
.000
r1.000
.500
E.625 8 .6?5
11 ,0 00 '| 1
6.625
-250
.000
11.000 11.000 'I1.000 11.000 11.000 11.000 11.000
OO,IN
1.750 2.000
11.000 1 I .000
LC
NO22LE
.000
1.250 't
CA
18.000
.4 87E + 06
.852E+06 - 1348+Oz
.27 6a+07
.482E+07
-375 .3?5
-
7
6OEr 07
.112E+08 .
1
56E+ 0E
.977E+05 .2 69 E+ 06
.553E+06
.9 66E +a6 .152E+ C7
.1 4'l E+O6
.219E+tl .450E+07 .287E+05
.284€+06
.4 48E+o6 .919E+06 .1618+O7 .?53E+O7 -3?2E+o7 -5?OE+07
.326E+05 .898 E+05
.184E+06 .322E+o6
. 508E +06
!
Rotational Nozzle Flexibilities for Cylindrical
Vessels
145
Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL
0DzFT
VESSEL NOZZLE TCKTIN OD,tN
NOZZLE
TCK'IN S
11.000
't.000 1.250 1.500
t l .000
2
11.000 1
.000
1
,1.000
18.000 .000 1 8 .000 't 8
1.750 .000
18.000 '18 -
000
1l.000
.2 50
20.000 20.000
.000
.500 .625
20 .000 20 .000
1't.000 11
11.000 11-000 11 .000
11.000 11.000
.750 I .000 1 .250 1 .500
.7tb
20.000 20.000 20.000 20 .000
2.000
11.000 't1.000
.250
20.000 20.000 22.000
11 .00 0
.500
22 -AOO 22 .00 0 22 .AAO
.000 11.000
11
11.000
l
.0 00
11
.000
'l
11.000
1
.7 50
1.000
22.000 22.000 22.000
t1.00c
1.250 't .5c0
0c
2.000
22 .COO
.37
Zr'.000
11.000 11 .0
11.000 11
.000
't1.000
l .000
't
11
.000
11.0CC
1't.000 't
'r
,000
11 .000 11 .0 00
5
.500 .? 50
.000 .25u .500 .7 50
2.000
.2 50
11.000 11.000
?? .ooo
22.O00
24.400 24.000 24.000 ?a.oao 24 -OOO
24.000 24.000 24 ,O00 24
-
000
26.000 26.000 26.000
'l 1
.500
'11.000
-7 50
26.000 26.000
. ?50
26.000
.000 11.000
.000
11.000 11 .00 0
11.000 1 1 .000
11.000 11.000 11.000
.500
.750 2.000
1'1
.00 0
11.000 11.000 11.000
11.000 't1.J00
28.000
.750 1 .000
23.0C0
1.250 'I
.5C0
1 -750 2 .OAO
.250
28.000 28.000 28.000 28.000 28.000
28.000 30.000 30.{.i00
11,000
,tic0
.500
11.0CC
-625
.7 50
11.000 '11.cti0
26.O00 26.000
.500
11,0C0 1'1
26.000
28.000
1'l .000
11.000
26.C00
1
,000
30.000 30.000 30,000 30.000
TD
.375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -3?5 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .375 -375 -375 .375 .375 -375 .375 -375 -375 .375 .3'?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 -375
ROT STI
F IN.L8/DEG
INPLA!,IE LONGI -313E +07
-5 46E+07 -86?E+07 .127E+oE .1 77E+08 -',|09E+06 .30',1E +06 .6'l8E +06 .108E + 07
.170E+07 .3 50 E +07 .6'11€+07 .963E+ 07
.142E+08 . 198
E+
08
.1?1E+46 .333E+06 ,683E+06
.119E+07
OUTPLANE CIRCU
Jo4E+az .182E+07 -287E+07 ,422E+07 .590E+07
.364€105 .1008+06
.206€ +06
-360€+06 .568F+06 .117E+ 07
.204E+o7
.321€+07
.472E+O7
.6598+07 .4038+05
.t11E+06 .228E+06
.398F+06
07 .387E+O7 - 67 5E +47
.628E+06 .1?98+A7
.1578+OE
.522E+07
.219E+08 .132E+06 .365E+46 .719E+06 .'131E+07 .286E+A7
,729E+O7 .141E +O5
.138
E +
.1078+C8
.225E+07 .355E+07
.1?2E+A6
.250F+06 .436E+06
424E+A7
.688E+06 .141E+o7
.7loE+o7
.247 E+07
-
.117E+08 .1 72 E | 08
.?1OEr08 .1448+06 . 397E+ 06
.814E+06
.112E+o7 .224E+07
.4608+07 .EC4E+07 .127E+O8
.
187E+ 08
.260E+06 .1 55ErC6
.42E€+06 . E79 E+ 06
.154E+O7 .? 12E+ 07 .197E +47 -E69E+A7 . 137E+08
.202E+08 .281 E+ tl8 . 'l 67 F+ 06
.460E+06
.945€+06
.3t9E+07
.5?2e+87
.799E+07 .480E+05 .'l32E +06 .2 7'l E+o 6 .47 4E+06
.718E+06 .1538+O7 .2 68E +O7 .123E+07
.62?E +07
.868€+07 .518E+C5
,143€+06 .293E +0 6
.512E+06
.803E+06 .166E+07 ,29AE+O7
.457t+C7
.672E +a7
.938E+07 .557E+05 .153E+06 .315E+06
,165E+A7
.550€+06
.2 (OE + C7
.E68F+06
.534E+07
-'178E+07
1,,
t
146
Piping Stress Handbook Table 6-1 Continued
ROI^ STIFT CALCULAIIOI,, CYL.
SS€L ICKIIN
VESSEL
11.000 11.000 11.000
1
1'l .000
2. 000
11.000 11.000 11.000 t
.250
t .500 1
.750
.500
l .000
11.000 1t .000 1t .000 1t .000
NOZZLE
VE
OO,FT
.625 .7 5s
1.0c0 1.250 1.500
OO'IN
30.c00
12. 000
32.000
32 .OOO 32 .00 0 32 .000 32 .000
36.00 0
11.000
'11.000 11 .000
I I .000
.000 1J.000 '| 1
t1.000
1.000
1r .000 11.ADO
'r1.000 t I .000
-375 .500
40 .000
.7 50
t.000
1.250
t. t00
I .750 2.000
12.000 12.000
-250 .375
'12.000
12.C00
12.000 12.000 12.000
.500
.625 -7 50
I .000 I .250
1.500 1.750 2.0c0 .250
.500
12.AOO
12.000
t2.000 | 2.000
.625 .7 50
I .000
12.000 12.000 12,000
1.250 1 .500
12.000 12.000 12.00c 't 2.000
-250
t2.000
t2.000
36.00 0 36.00 0 4
11.0C0
't2.000 12.000 12.000 12.000 12.000
.000
.750 2.000
0.000
40.000 40.000
5
.375 -375
.375 -375 -375
.375 .375
.302Er08 .179E+06 - 49ZEr06
.164Er06
.101E+ 07
.337E+06 .588E+06
.1768+07 .278E+oz ,571E +07
-333E+O7
.2028+06
.672Ero5
.556E+06
.380E{06
.664E+06 .1058+07
.375
.375 .375 -3?5
.t7
5
.t75 .375
.113E+08
.178€+06
.2 61 E +08
.365E+08 .225E+06 . 619 E+ 06
.127e+87 .222E+07
-375
.1 26E+ 08
.375 .375
.291E+08
2.375 2.375 2.375 2.3?5 2.375 2.375 2.375 ?.375 2.375 2.375
.154
3.500
.216 .216 .216 .216
.500 .500 3-500 3 3
3.500 3.500 3.500 4-500 4 .500
4.500 4. 500 4-500
.185E+06
.199E+07 .314E+07 .645E+07
.375
3. 500
.77?E+O7 .108E+08
.375
40 .00 0 40 .00 0
.r25E+O?
.1 14E+07
40.000
40.000
.19AE +A7
.998E+07 .157E+08 .231E+08 .3 23E + 08
,3508+07 .719E+07
40.000
.92E€+06
.37 5
40 .00 0
1
.37
.375 .375
36 .000
36.000 36.000
11.0C0 t 1.000
t't .000
6.000
3 3 6
1.250 1.500 1.750 2.000
11.000
.311E+07
.722e+C7 .101 E+08 .595E+05
. >UU
.625 -750
CIRCU
.216E+08
0.000 3?.000 3
.37:
't'1.000
.934Er07
OUTPLANE
30 .000
1t.000 11.000
.37 5
N INPLANE LONGI
.191E +o7
r't.000 ,l
.250
r CK,I
STD
.147E+o8
52.000 3 2.000 32.000 56.000 36.000
1.000
NOZZLE ROT SII F IN.L8/DEG
30. 000
1.750 2.000
11.000
VESSEL
.1988+08 .4078+08
.215E+O7 -376E+07
-5938+07
.E71ErO7 .12?E+oB .749E+0 5 .2068+O6
.424E+06 -7 40E+O6
.117e +O7 -240E+07
.419E+07 .661E+O7
.971E+07 .136E+08
.106E+05 .298 E+05
.3608+04
-154
-f56Er05
.6llE+05
.15 4
.'t07E+06 .1689r 06
-992E+04 .204E+05
-154 .154
.346E+06 .604E+06
-561E+05 .115E+06 .201 E+06
.154
.154 .154 .154 .216
.216
.216 .216 .216 .237 .237 .237 .237 -237
.9528+96
.11OE+07
.195E+07
. t6lE+05 .443E+05 .909E+05 .159E+06 -250E+06
.317E+O6
.467E+O6 .652e+D6
.536E+o1 .14EE+05 .303E+05
.529E+05 .835E+0 5
.5'l4E+06
.1718r06
.898E+06
.2998+O6
.112E+oz
.472E+O6
.208€r07
.694E+06
.291E+07 .212t+ 05
.970 E+0 6 .706 E+04 .195E+05 .400 E+0 5 .700E+05
.585E+05 .120E+06 .210E | 06 .
J3t E+06
.1 10E +06
Rotational Nozzle Flexibilities for Cylindrical
Vessels
147
Table 6-1 Continued ROTA VESSEL
0D,ll
,090 12.000
12
't2,000 12.000 12.000 'l2.000 12.000 12.00c 1Z
1.000
1.250 1 .500 1.750 2. 000
.375
12.00c
1
.500
.000 12.000
2. 000
't2.000
12 .00 0
12.000 't 2.000 12.000 1?.000 12,000 '12.000
12.000 12.000 12.000 12.000 12.000 12
,000
12.000 't2.000 .000 12 .000
12
6.625 6.625 6.625 6.6?5 6.625 6.625 6.625 8.625 E.625
.250 .500
8.625
-f>u 1.000 1.250 I .500 1.750
8.625
8.625
2. 000 .37
5
.500
.625 -750
1.000 1.250 1.500
1.750 2.000 .250
12.000 12.000 12.000
.500
12.00 0
0. 750
10.750 10.750 1 0. 750 1 0 .750
t0.750 10. 750 't 0
.750
10.750 10
12 1?
.750
.750 .750
1?.7 50
.000 .500
1
.000
12.O00 1 2 .000
.500 -7 50 2
1
12.750 12.750 12.750 12.750 12.750 12.750 12.750
12.000
'tz.ou0 '| 2.000 12.000 12.000 't 2 .00! 12.000 12.000 12.000
6 -625
1.750
.290
.500
4.500 6.625 6.625
1.250
12.000 12. 00 c
4
.7 50
.000
12
4.500 4.500
.625 1
t?-000
,.. 500
.500
't2.000 t 2 .000
'14.000 14-000
4.000
14. 000 -7 50
.000 12 ,000
4.000 14.000 t 4.000
.500
12 . 000
.7 50 2. 000 .2 5A
't 4 14 ,l
12
12.000 12.000 12.C00 1? -004
12.000 12.000 12
.000
VESSEL
VESSEL NOZZLE NOZZLE ROl SIIf IN.L8/DE6 TCK,IN INPLANE OUTPLANE TCX,IN OD,IN CTRCU STD LONGI
.000
12 .OOO
Sttf F CALCULAITONT CYL.
.000
.500 - 1>U
I .000
1
.000 .000
4.000 1 6.000 't 6.000
'16.000 16 .000
16.000 I 6.000
.237 .237 .237 .237 .237 .280 .280 .280 .2 80 ,280 .2 80 .280 .280 .280 .?80 .322 .322 .322 .322 -322 -322 -32? .322 .322 .322 -365 .365 .36, .36' .365 .365 .365 .365 .365 -365 .375 .375 .375 .375 -375 .375 .375 .375 -375 -375 .375 -375 .375 -375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -3?5
.680E+06 .119E+O7
.187E.07
.275E+07 .384E+07 .3?3E+05 .889 E +05 .133 E+06 .319E+06
.5038+06 .1c3F+07
.l80E+07
.2n58+O7 .418E+07
.584E +47
.426E+05 .118E+06 .241E+O6
.4218+06
.665€t06
.22'l E+ O6 .396E+06 -621ErO6 .91EE+06
.'l28E+07 .108E+05 .?96E+05 .608E+05 .106E+06 . t d8E+06 44F +o 6
,t
.601 €+06 .949E+06 .139E+07 .195E+O7 .142E+05
t
.3
.3929+05 .804E+05 .140E+06 .?22E+o6
. 136E+07
.4558r06
.238E+o7
.79 5E+ O6 .125E+A7 .184E+O7
.37 6E+O7 .553E+07
.7728+ol
.?57E+o7
.537E+05 .14EE+06 .304E+C6
.l0lE+06
.531€+06 .837E+06 .172E+07 .300E+07
.47 4E.o7
.179E+05 ,493E+05
.177E +06 -279E+O6
.573E+06
.100E+07 .1 58 F+07
.696E+07
.232E+07
.972E+O7
.324E+O? .?15E+O5
.616E+05 .17E8+06 .3 6 5€| 06 .63E Ef 06
.1o1E+07 .2o7E+O7
.361E+07
.5938+05 .122Er 06 .2'l3E+O6 .3368+0 6 .689 E+06
.t20E+07
.569E+O7
.t90Er07
.E37E+07 . 1178 + 08 .715E+05 .197E+46 .404E+06
.279E+O7
.706E+ 06
.1't1E+O7
-zz9E+07
.l90E+07
.2399+05 .656E+05
-135Ef06 .235E+06 .371E+06 .762E+06
-4OOE+07
.133E+07
.6308+07
.21OE+07
.9?6E+ 07 .'l 29Er0E
.309E+07 .431E +O7
.825E+05 .2?7E+O6
.467 E+o6 .E15€+06 .129E+07 .261E+o7
.275E+05
.758Er05 .156E+06 .272E+O6
.4?9 E+06 .880E+06
t:
'i
ir\ I
il
it;
:l
iii
148
Piping Stress Handbook Table 6-1
Continued
SIIfF CALCULATIOII' CYL. VESSEL NOZ ZLE ROI STIF II].L8/DEG VESSEL NOZ2LE T CK,I N INPLANE ICKrIN 00rIN OUIPLANE STD LONGI CIRCU ROTA
v€ssEL 0D,FT
.000 12.000
1.250
12.000 12.000 12.000
2.000 .250
12
'12.000
t .500
1.750
r2.000
.500
.625
1Z-000 '12.000
1? .00 0
12.000
1
.000
16.000 16.000 | 6.000 16.000 .000 .000 18.000 18.000 18 18
't8.000 r 8.000
r8.000
.000
-375
18 .000
1.500
12 .00 0 12 .000
2. 000
18.000
12.4O0
.250 .375
12 .00 0
.500
20.000 20.000 20.000 20.000
2.000 '| 2.000 'r2.000 12.000 12.000 1?.000 12.000 12.00c 12.000
18
.625 1.0c0
1,250 1.500 'l
.7 50
2.000
20 .000
20.000 20.000 20.000 2
0
.37 5
.000
.?50
22.000
.00 0
22 .000
22 .00 0
12.000 1?.000 12.000 12.000
.500 2. 000
.375 .500 .625
12.000
12.000 12.000
12. 000
12.000 12.000 12.000 12.000
.750 I .000
1.250 1.500
.750 2.000 .250 1
12.C00
12.000 12.000 12.000 1?.000 12.000 72.DOO
12.000
.625
24.000 24.000 24.000 24.000 2 4
-000
.500
26.000 26
.000
28 .000
.000 2E.000 28
.625 I .000
1.250
26.000 28.000 28
.000
28.000
1 49E
+08
.936E+05 .2 5E€+06 .5 29 E+06 .9 248 +06 .146E+07
-37 5
.375
.486E{06
.105E+06 .288E106 .5928+06
.961El05
. l69E+08
.275E+o7 .564E+07 -3498+05 .197
E+o 6
.103E+07 .'163E+07
.3458+06
.585Er07
.195Er07
.3358+07
.544E+06 .1',\2e+07
.9228+07
.307E+07
.136E+08
- 452E+ O7
-631E+07 .386E+05
.116E+06 .319E+06 .654E+06 .114E+07
.106€+06 .2188+06
.370E+ 07
.123Er07
.647E+07
.216E+O7 .340E+O7
. 150E+08 . ?09t + 08
.381E+06
.6018+06
.5C0 E+07
.698E+07
06
.422E+O5
.319E+ 06
.116E+06
.717E+06
.239 E+O6 .417 E+O6
+
.125E+07 .1988+07 .4A5E+07 .706E+07 .112E+08 .164E+0E
.658E+06 .135E+07 .236E+O7
.372ErO7 .548E+07
.2?9E+ 08
.7 65E +07
.138E+06
.459E+05 .127E+O6
.441E+07 .7 7 0E+ 07
-375
.12't
.375 .375
.149Ef06
.375
.308E+06
- 404E+O7
.2'l5E+ol
.375
.E59E+05 .17 6E+O6
.121 E+08
.330E+06 .779 E+06 -136E+07
.375
.312Er05
.996 E +0 6 .17 4E+07
.523E+07 .825E+07
- 127E
.375
.3578107 .49aE+07
.299ri07
.175 .375 .3?5 .375
6.0 00
2 6.00 0 2 6 .000
.
.102E+08
.000
1.?50 1 .500
.243E+O7
-375
26.000 26.000 ?
.154E+O7
.72EE+07 .107E+08
.1808+07
24.OOA
26.000 26.000
't .7 50 2 .000
.37 5
21.OOO
.000
't
12.000 't2.000
24.000
.7 50 1
.250
12 .000 12 .00 0
24.OAO
26
12 .00 0
12.000 2.000
22.000 24.000 22.000 22.000 24.000
- 461Er07
.1898+08
22.000 22.000
12 .00 0
12.000
12.000
.373 .375
2?.OOO
.500
12.000
.37 5
20 .00 0
12.00 0
r2.000 12.000 12.000
.375 .375 .375 .375 .375
12.000 12.000
't
.375 .175 .375
E+ 0E
.179E]08
.2608+06 .4548+06 .716E+O6
.147E+07
.257t+07 .405E+O7
.249E+08
.595Ef 07 .8318+0? .496E+05
.4108+06
-137E+06
-842E+06
.2El E+06
.147E+07
.490E+06
.232E+O7 .47 6E+O7
. t 59E +0 7
.a32E+07
.773E+o6
.?77E+07
Rotational Nozzle Flexibilities for Cylindrical
Vessels
149
Table 6-1 Continued ROlA STIfF CALCULATION, CYL. VESSEL
OD,'T
VESSEL NOZZLE NOZZLE ROT STIF IN.L8lDE6 ]CKTIN INPLAN€ OUTPLANE TCK,IN ODU IN CIRCU STO LONGI
12 .00 0 12 .00 0
1.500
'12.000
-7 50
't
28 .000
.375
.1318+08
-37t
.269F+08 .160€+06
28.000 28.000
12.00c
2.000
.250
30 .000
12.000 12.000 12.000 't2.000
.500
30.00 0
't
2.00r1
3 0
'l
.000
30.000 50.000 30.000
.37
52 .000
12.040
2
.00
.500
1.750 .250
0
12.000 12.000 '12
.625
.0 00
12.000 12
.00
12
.000
0
12.000 .000
12.00c 12.000
5
.500
.500 .750 2.000
12.C00
.250
12.000 't2.000
.500
.000 t 2 .000 12 .000
.? 50
'12.00c
.625
12 .000 12 .000
12.O00 '1 2 ,000
1
,000
1
.250
1
.500
1,750 2. 000 .2 5A
I2.000
. 471E+ 06
.'157
2.00 0
.967E+06
.322E+O6
.266E+A7 .5 47 E+07 .956E+07
.1828+07 .3't 9 E+O7
ri
.502E+07 .739E+o7
lls
3
't3.000
13.000 13.000 'l3 .000
.500 .750 I .0c0
1.250 1.500 1.750 2
't3,000
.000
-2 50
13.000 13 .000
.500
13.000
. a>u
'13.000
13 .0 00
.169E +o7
32-000 32.000 32.000 J2.000 32.000 32.00c 32.000 36.000
.15'lE+08 .2728+O?.
.309€+08 .193E+06
6.00 0 36.00 0
.5f2E+06
36.0C0 36 -000
.301€+07
1
.000
,109E+07 .191E+07
36.000
6.000 36.000 36.000 3
3
6.00 0
,644E+0S .177 E+06 .364E+06
.6368+06 .100F+07 .568E+07 .834E+O?
.37 5
.349E+CE
.593E106 .213E+07 .33 jE107 .689E+07
.'l
.375
2.375
.'t54 .154
2 -375
.154
.500
.103E+08
.250E+06
4C.000 r.0.000
3
.563E+06 .888E+06
.1708+08
-122E+07
2.375 2 .375 3.500 3.500 3.500 3.500
6
.375
40 .000
2.375 2.375
E+ o
.?O6E+O7
,106E+08
.215E+46
2.375
.965E+O7 .5 70 E+0 5
- 618E+07
40.000
40.000 40.000
13.000 13 .000 13.000 13 .000 1 3 ,000 13 .000
.1718+07 .298E+a7 - 691e +O7
1.750 2.000
12.000 12.000
.470E+07
58E +07
.207E+08 .289E+0E .171E+06
.?50 1 .000
'12.000
.891E+ 07 . '1418+08
1
.37 5 .3? 5
12 .00 0
1.250 I .500
.2t9E+07 .5128+07
40.000 40.000 40.000 40.000
12.000 12.000
.898E+07
.375
.500
12.000
.137E+07 .64JE+07 .147 E+O6 .301 E+06 .527E+06 .831E+06
-441E+06 .
30.00 0
.00 0
12
.193F+0E
-904Er06
3
12
12.000
.375
.000
30.000 30.000
1.250
12
30.000
.750 1 .000
12.000 12.000
12.O04
VESSEL
?0E +08
.190E+08 .2798+0E .390E+08
.t04E+05 -286€+05 .587E+05 .103E+06
.15 4
.162E+ 06 .33?E+O6
.154
.580E+06 .915E+06
-154
.15 4
.1358+07
-'l54
.188E+07 .154E+05 .425E+05 .8 73 E+ 05 .1 53E+06 .?41E+06 .494E+06
.2'l6 .216 .216 .216 .2'16
.360€+07 .116E+08
.717F +05
.'198E+06 -406E+06 .709E106 .112E+O7
.230E+07 ,4018+07 .633E+07 .9308+07 .'l30E+08
.346Er04 .9Sj€+04 .196E+05 .342E+O5 .539E+05 .111E+05 .'193E+06 _305E+06
.4438+O6 .626E+O6
.515E+04 .142E+05
.2918+05 .509E+05 .802E+05 .165E+06
lx
it:
fl
150
Piping Stress Handbook Table 5-1 Continued
R0IA sTIfr CALCULAIIOI{r CYL.
VESSEL tIO2ZLE TOZZLE ROT STIF II{.LB/DEG ODrlN TCK,IN IiIPLANE 0UTPLAI{E rc(,Itl C IRCU STD LON6I
VESSEL
OD,FT
'13.000
13.000 13.000
13.000 13.000 't3.000 13.000 13.000 13 .0 00
13.0C0
13.000 13.000
13.000 13.0C0 l3 .000 13.000
13.000 '13
.750
1.500 3.500 3.500
.250
4
.500
4
1 -250
1.500 1
2.000
.625 .750 1.000 1.250 1 1
.500
.754 2.000 .500
.0 0c
13.000 13 .0 00
11.000 13.000 13.000 13 .000 l:i
1.000
1.250 I .500 1.750 2.000 .37
13.000 15.000 13.000 t 3 .000 13.000
13.000 13.000 13.000
'tf .000 13.000 13 - 000 13 .0 00
5
.500
.625 .750
't3.000
'13.000
13.000
.500 .500
4.500 4.500 4.500 4 .500 4.500 4
.500
6.6?5
6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.62
5
4.625 a.625 8.625 a
.250
1. 500
.750 2.000
1
.375 .500
t .000
13 .000
4
1
13.C00
13.000 13.000
4.500
I .000
.625 .750 't .000 1 .250 I .500 1.750 2.000 .250 .375
13 .000 13 .00 0
.500
-625 E.625
13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 15.000 13.000 't3.000 13.000 13.000 't3.000
3. 500
6.62t
15 .00 0 [:
VESSEL
.500
.625 1.250 1.500 1.?50 2.000
.250 .37 5
.500 .675 .7 50
1.000 I .?50
8
.625
8.625 a.625 8.625 10.750 10-750 10.750 10.750 10
-750
10.750 10.750 10. 750
10.750 10.750 1?.750 12.750 1?.750 12.750 12.750 12.750 't 2.750 12.750 12.?50 '12.750
14.000 14.000 '| 4.000 14.000 14.000 14.000 14.000
.?16 .216 -216 .216 .zt7 .237 .237 .237 -237 -237 -"37 -?37 -237 .?37 .280 .280 .280 .280 .2E0 -280 .280 -280 .280 .?80 -32? .3?Z -322 .322 -3?2 .322 .t2? .3?Z .322 .322 -565 .365 .365 .365 .365 .365 .365 .365 .365 .365 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 -37' -375 .375 .375
.863€ +06 . I l6E+07 .20081 07
.?79E+07 .204€+05
.562Ef05 .115Er06 .202Er06 .l'lEE+06
.288E+06 .454E+O6 .667e+ O6
.932Er06
.680E+04 .1 87Er05 .385€+05 -672ErO5
.1 06€ r0 6
.655€ +06
-2'l8Er06 .380Er06
.180€+07
.600E+06 -8828+06 .123E+Ol
.114er07 .265E+O7
.369E+O7 .310E+05 .854E+05 .17 5E+06 .
j06E+06
.103Er05 .285E+05
.5E5Ei05 .'102E+06
.483E+06 -992 E+06 -1?3E+07 .273E+07 .402E+o? .561E+07
.t61E+06
.113E+06
.376Er05
.4108+05
.331
E+0 6 . 578 Ef06
.911F+06 .134F+O7 .187 E+O7 .137E+05
.2328+06
.7738+O5
.40 5E+ 06 .639E+06
.213Eio6
.131E+07 .229E+a7
.361E+07
.135E+06 .437 E+O6 .7 63ErO6
.120E+07
.531E+O7 .7 42E+O7
.1778+O7
,516E+05 .142E+O6 .?92E+06
-172E.05
.247E+O7
.474E+05
.97iE+05
.510E+ 06
.170E+06
.804€106 .1658+07
.268E+06
.550E+06
. ?EEE+07
.96t E+06
.455E+07 .669 E+07 .934 E +07
.152E+O7 .223E+O7
.6 20E +05
.',l718+06 .351E106
.613€+06 .967E.O6 .199E+07 .317E+o7 .5 47E+O7 .aE4E+ 07
.1128+08
.687€ +05 .189E+06
.388E+06
.Jll
E+07
-2078+05 .570E+05
.1178+06 .2048+06
.662Er06 .116ErO7 .182E+O7 .268 E+07 .374E+07 .229E+O5
.631E+05 . 1 29 E+06
.679E+O6 -107E+O7
.226E+06
.384€ +07
.128E+07
.220E+07
.357E+O6
.732Er06
Rotational Nozzle Flexibilities for Cylindrical Vessels
151
Table 6-1 Continued ROIA STIFF CALCUIATI0Ne CYL. VESSEL
OD,TT
13.000
VESSEL TIOZZLE NOZZLE ROI STIF IN.L8/DEG TCK,IN INPLARE OUTPLANE TCK,IN OD,IN CIRCU LONGI STD .500
1
13.000 13 .000 13.000
1.750
11.000
.500
,000
2
-z>u
't3.000 13.000
.62 5 .7 50
13 - 000 13 .000
.000
'13.000 13
.500
.000
1f.000
.7 50
.000 .000 '| 3 .000 13 .000 13 .000 1J .000
2. 000
13.0C0 13.0 0 0
1
13
13
13 .00 0
13.000 13.000 13 .000 13
't 3
13.000 13 .000
13.000
1.250 I-500 2. 000
.500 .625 .7 50
,000 1.?50 1.500 1
1.7r0 2.000
.500
r3,000 '13.000
I .000
13 .000
1
.000 13.000
z
13.000 13 't
't4.000 't 6.000 16.000 'l6.000 16.000 16.000 1 6.000 't 6.000 16.000 I 6.000 't6.000 18.000 ,000 1E.000 8
I
13.000 13.000 .000
.000
.000
13 .000
15
4
.7 50
.000 .000
4.000
I
18.tto0 1 8.000
.625
.000
13.000 13.000
1
1
13.000 13
1.250 .500
1.750 .000
8
.000
8.000 18.000 18.000 16.000 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000
't
20-000 20 .000
22.000 2 2.000 22.000 22.000 22 -OOO 22.OOO 22 .000
22.000 z2 -aoo
22.000
24 -OOO
3. 000
tt.000
.500
1f. 000
,625
24.000 24.000 24.000
.7 50
?4.AOO
.000
24
13.000
13.000
13.000 l3 .000 13.000 15.000 '13.000
1
't.250 I .500
1.750 2
13.000 11.000
.000 .500
t3.000 1J.000
.7 50
.000
13.0C0
1
.000 13.000
1-5C0
1.250
.000
24.000 24.000 21 .OOO
24.000 26
13.0C0
13
VESSEL
.000
26.000 26.000 26.000 26.000 26 .000
26.000 26.000
.375 .60 5E + 07 .375 .890 + 07 -375 ,124E+ 08 .375 .791E+05 .375 .218 E+06 .375 .448E+06 .375 .783E+06 .375 .1?4E +o7 .375 .?54E+O? .375 .4t 3E+07 .375 .699a+C7 .375 .103E+08 .375 . 143E]08 .375 .8998+05 .375 .? 4EE+06 -3?5 .508E+06 .375 .EE8E+06 .375 .1 40 F+ 07 .375 .288E+ 07 -375 .502E+07 .375 .793E+ 07 -375 .117E+0E .375 .1d3E+0E .375 .1008+06 .375 .?77E+06 .375 .569E+06 .375 .993€+06 .375 .157E+O7 '12?F +l\7 "7< -375 -562E+O7 .375 .8E6E+07 .375 .1 30 E+08 .375 .182E+08 .375 .1118+06 .375 .306E+06 .375 .629E +06 .375 . t 10Ei07 .375 .173E+ D7 -375 .3 56 E+07 .375 .621E+o7 .375 .980 E+0 7 .375 .',144E+08 .375 .201 E+oE .375 .122E+O6 .37t .3358+06 .375 .639Er06 .375 .120E+O7 .375 .190E+ol .375 .390E+07 ,375 .681E+07 .375 .107E+08 .375 .t 58E+08 .375 .220€+08 .375 .1328+06 .375 .3658+06 .375 .749E+O6 -375 .',131E+O7 .375 .206E+07 -375 .4248+07 .375 .7 40E+A7 .375 .117E+08 E
.?D2E+O7
.297E+Oz
.414E+Ol -2648+05
.728Er05 .149E+O6 .2 6'l E+ O6
.412E+0 6 .E46E+06 .148E+02 .233E+O7
,t
.343E+O7 .478E+O7
.300€+05 .8268+05 .169E+06 .296E+06 .467E+O6
.959E+06 .167 E+Of .2 64E+oz . f88E +07 -542E+07 .33 5E +0 5
,9 23E+o, .1 90E+06
.331E+06
.5?28.06
.107E+07 .1878+07
.295Ei07
.4348+D7
.606E+07 .370E+05 .102E+06 .210E+06 ,366E+06 .577E+06
.1 19 E +07
.?a7E+07 .3278+07 .480E+07 .67OE+07 .406E+05 -'l1?E+o6 .230E+06
.401E+06 -633E+06
.130E+07 -227E+O7
.358E+07 .526E+07 .735E+O7 -44JE+05
.122E+06 .250E+06 _436E]06 .688E+06
.141E+07 .217 E +07
.389E+07
i{
.,1
itr\
.,|\
|4
,)
itt
152
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATIOTI, CYL. VESS€L VESSEL
vE
OD,FT
TC
13
.000
13.000
ssEL
1.750 2.000
13 .0 00
13.000
.37 5
13 .0 c0
.500 .625
I
.7 50
'|
3.000
t.000
13.000
1-000
15.0C0
1.?50
13.000 13.000
1.750 2.000
13.000
t3.000
'1.500
.250
15.000 .500
13 .0 00
13.000 13.000 13.000
r3.000 13.C00
r3.000 13.000
.625
13
.000
13.000 't3.000
.5C0
.625 1.0c0
t.25D I .500 1.750 2 .000
.t75
.500
13.000
.625 .750
13.000
13.000
13.000 13.000
13.000 13.000 13.000 13.000 l3 .000 13 .0 00
13.000 13.000 13.000 13.000
13.000 13.000
I .000
1.250 1.500 1.750 2.000 .500
.625 .750 1.000 1 .250 1 .500 1.750 2-0c0 -?50 .37
13
5
.500
13.C00
.000
1.000
13 .000
'1
13.000
1t.0c0
28. 000
- 143E106
28.000 26.000 28.000 28.000
.7 50
. t00 1.750 2.000
OE
.240€+08
.t94e+O6
OUTPLA C
E
IRCU
.572E+O7
.799E+Ol .477E+05
.?238+07
.15',lE+06 .270E+O6 - 471ErO6 .743E+O6
.375 .s75
.153Ef07
.2668+O7 .4?OE+07
2E.000
.37t
.4 58E + 07 .799 E+07 .'126€+08
.00 0
-3? 5
.259E+0E
.
28 .000
28.000 28.000 2E
.375 .375
.!75
30.00 0
.375 .375 .375 .375
30.00 0
.375
30.000 30.000 30.000
.5r>
.375 .375 .375
30.00 0
32.000 32.000 32.000 32.000 32.000 32 .000
52.000
32 .00 0
32.O0D
32.000 3 6.000
36.00 0 36.00 0 36.00 0
36.000
.375 .375 .375 .375 .37 5 .37 5
.375 .37
36.000 36.000
.375
5
36.00 0 36.00 0
40.000 40.000 40.000
40 .00 0 40 - 000
40.000 40.000 40.000 40 .000
40.000
4E.00 0
4E.000
48.000 48.000 48.000 46.000 48.000 48.000 48.000
.809 Er 06
.141Er07
.lE5E+08 .
t 54E+06
.4?3E+06 .869 E r 06 .152e+O7 .239E+A7 -492E+07
.375 .375
.375
.s75 -375
.51?E+05
.141E+06 .2908+06 .506 E+06 .798E f06 .164E+O7
.286E+07
- 199 E+08
.664E+07 .927E+o?
.lf5E+08
.4 52 E+O7 .5 47E+0
5
.t5tE+06
06
.3'l0E+06
-1628+07 .?56E+07
.541E+06 .E53E+06
.9 29
E+
.5?6E +07
.91E8+07 .145E+08 .213E+08 .297 E+08 .185E+C6 .511E+06 .105E+07
.1838+07
.175Er07 .3068t07
.483E+07 .710 E+O7
.991Er07 .d18E+05 .170E+06
.350E+06 .611E+06
.289E+07
.9648+06
.591E+07 .1048+08
.t
.346Er07
- t 64E+0E .2 40E +0E
.545E+07
.336Er08
.112Er08
9EEr07
.E02€r07
.?07E+06
.6E9 E +05
.117 E+07
.190E+06 .390E+06
.570E+06 .2048+07 .3228+ 07 -662E+07 .
.375 .375
.618E+07 E63Ei07
.659E+07 .276E+08 -1648+C6 .453E+06
I6.000
4E.000
't5.000 't3.000 13.000
TCK.IN II'|PLANE STD LON6I .17?E
30.000 50.000 30.000
.375
NOZZLE ROT STl F IN.L8/DEG
6.000 26.000
1.250 1.500 1.750 2.000
1.000
N
2
30.000
13.000
15.000 13.000 15.000
OD,I
.7 50
13.0C0
13.000 13.000 13.000 13.000 13.000 15.000 13.000
0t z LE
K,I I,I
1 16
E+08
.68tE+06 .107E+07 .?21E+07 .385 E+0 7
.'l82E108
.608Er07
.268E+08 .374E+08 .249 E+ 06 .687E+06
.893E+07
.141E+07
.375
.246E+07 .389 a+07 .7988+ 07
.375
. 1J9E+08
.220E+08 .323E+ oE .451E+0E
.'l ?5E+08 .831E+0 5 .?29E+o5 .470E+06 .821E+06
.130E+07 .?668+O7 -4648107
.733E +07
.1088108 .1 508+08
Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-l Continued ROTA
0DrfT
VESSEL TC K,IN
.000
-250
VESSEL
14
4.000 14.000 14.000 't
14.0CC
14.000 14. 000
't4.000 't4.000 14.000 14.000 14.000 14.600 14.000 14,000 t 4 .000
14.000 '|
STIfF CALCULAIIOI'1, CYL.
4.O00
14.000 14.000 14.000 14.000 14.000 't4-000
.500 .625 1.000 1-258 1.5C0
1.750
z. 000
NOZZLE
0D,I
2.375
2.375 ?.375 z
.375
?.375 2.375 2.375 2.375 2.375 f.500 3
.500
.500
3.500
1
.000
3.500 1.500
't
.2 50
.625
3.500
2
3
.500
.000
14.000 't4.000 14.000 r4 14
.000 .000
14.000
.490Er05
.216 .216
.2328+O6 .176E+06 .E32€+06 .'131E+o7
.7738+05
.269
.8988+06
.216 .?16
.193€+07
E+ 07 . 'l97E+ 05
.281
E+0 5
.159E+06 .277a +O6 .437E+06 .643E+06 .655E+04
.28 0
.1678+07
.557E+06
.2638 + 07 .387E+0? .541E+07
.129 E+07
6.625
-2E0 - z6u .2E0
. I 09 E+06
.363E+05
.625
-322 -3?2
.322
.7 14 E+05 .'130E+06
8 -625
.223E+06 .390E+06 .615E106
1.250 1.500
8.625
.322
.2218+07
2.000
I .625
8.6?5 '| 0.750 10.750 10.750 1 0.750 10.750 10.750 10.750
.322 -322
.500 .500
6.625
6.625
.50b
6.6?5
6.525 6.625 6.625
1.000 1.250 1. 500 1
.750
2. 000
.375 .500
E
.62'
11
14
.117E+ 06
.9E48+05
.6?5
14-000
14.000 't4.000 14.000
. ?16
.137E+05
.27 4E+O5
4 4
4.000
.842E+05
.E23E+05 .169E+06 .295E+A6 .466E+06 .956E+06
2. 000
t
-?16
49 E+0 5
.4t08.05
.119E+O7 .996 E +04
1.750
.000 t 4 .000
I 4.000
.l
.2't6
.3568+07
14.000
14.000
-216
.?108+06
4.500
14.000 'r4.000 14.000 14.000
.181E+07
06
.629E+06 .1 10f+07 .173E+07 .255E+07
1.500
.0AA 14.0C0
.154
4E +
.237 .237 .237
4
14.000 14.000 14.000
.432E+0{i .6O3ErO6 .496E+O4
.500
.250
t4.000
.29
.130E+07
.154 .154 .154
.9888+05
.64E E +05 .102E +C6
'|
14.000 14.000 14.000
.EE?E+06
.154
.194E+06
14,C00 I 4.00 0
4.00 0
.156E+06 .320E+06 .559E+46
.9'18€+04 .189E+05 -329E+05 .5?0E+05 -107E+46 .1E6E+06
.237
4.500
'|
.15 4
.1818+05
4.500
.750
14.000 '| 4.000 14.000 14.000
.333E+04
.?76a+O5 .5668 | A5
.542F+05
1.000
14
.1 00E+05
.'t54
.237
.375 .500
14.000
.000
.154
4.500 4.500
4. 500 4 .500
14
ZLE ROT STIF IN.L8/DEG TCK,IN INPLANE OUIPLANE CIRCU STD LONGI
NOZ
-216
1.750 .000
N
VESSEL
1
.000
.250 .500 -625
t .000
1.250 1.500
1.750 2.000 .500
1
-237
.280 .280 .280 .280
.5 65 .3 65
.365
0. 750
10. 750
.306€+06
.299E+i5
.3958+05
.1268r07
.318E +07
.5'128+07 .715E+ 07
.497E+85
.'l37E+06 .281E+06 .491E+06 .7 7 5E+ A6
,365
10.750 12.750 1? .750
.1118+06
.159E+07 .?7EE+ol
.3 66E+
0
6
,5788+06 .850E106
.561Er05 .155E+06 .319Er06 .678€+06 .tE0E+07 .132E+0
5
.205E+06 .421 €+0 6 .736E+96 .116E+O7 .171E+07 .238E+07 .166E+05 .457 E+05 .937E+05 .164E+06 .258E+06 .530E+06 .926E+O6
.438E+07 .6 45E+07
.146E+07 .215E107
.596E+05 .165E+06 .336E+06
.199E+05
.9008+07
.375
.371E+Os
.300E+07 . 549€+0 5
-113E+06
154
Piping Stress Handbook Table 6-1 Continued ROTA VESSEL
OD'F1
14
.000
14.000 14.000 14.000 14.000 14.000 14.000
t4.000 14.000
14.0C0
14.000 | 4.00 0 I 4.00 0
14.000 14.000 14.000
14.000 14.000 14.000 14.000 I 1.000 t 4.000 t 4.000 14.000 14 .000
.625 .750 I .000 1.250 1
.500
1. ?50
2.000 -250 .625 .750 1.000
1.250 1.500 1.750 2.000
14
.000
| 4.000
14.000 14.000 'l4.000 I 4.000 14.000 14.000
14.000 t 4.000 14.000 14,000 14.000 14.000 't4.000 14.000 14.000 14.000 't 4.000 14.000
14.0C0
16
.625 1.000 1-?50 I .500
.000
1.250 1.500 1.750 2.000 .250 . 500
.625
.750 1.000 1
14.000 t 4.000 I 4.000 14.000 14.000 14.000
.500
.375
'1
14.000 14.000 14.000 14.000 14.000 11.000
t 4 .000
.2to
74.OOO 14 .000
12.750 12.750 12.750 12.750 12.750 12.750 1?.750 I 4.000
t 4 .000 16 .000
1.750 2.000 .250 .375 .500 .625 .750
14.000
CALCULATIOI,IT CYL. VESSEL
VESSEL NOZZ LE TCXTIN 0D,Itl
r4.000 14.000 14.000 14.000 14.000 14.000
14.000
STIfF
.250
I .500
1.750 2.000
.250
.375 .500 .625
.5918+06
.197E+O6
.932 E+06 .191E+O7
.311E+06 .638e+06
.375
.3J4€+07 .527E+07
-111E+07 .176E+O7
.375 .375 .375 .375 .t7 5
.37t
.375 -375
.375 .375 .375
.7
75E
+
07
.'l0E€+08 .662E+05 .182E+06 .3? 4E+06 .654E+06
. t 05E r07 .21?E+07
.370Ei07
.375 .375 .375
.000
.375
1E.000
.375 .375
'l 6
18.000 18.000
.608 Er05
.125E+06 -21EE+06
.3448r06 -706E+O6
.123E+O7
.194E+07 .?E6E+07
.7 558+06
.37 5
.221Ero5
.8 58 E+07 . t 20E+ 08 .764E+05
-375
.375
.258E+07 .361E+07
.583E+07
.2108+06 .432E+06
16.000 1 6.000 16.000 16.000 '| 6.000 I 6.000
IRCU
.375 .375
.37 5
.119E+07 .2 448+07
.399E+07 .255E+05 .70?E+05 -1418+46
.25?E+O 6
.397E+O6
.8'l5E+06
.427e+O7
.142E+O7
4E+07
.225E+O7
. (r7
.990E+07 .138E+08
.866Ei05
.239 t +06 .490E+06
.330Ero7
.461E+o7 .289E+05 .796 E+C 5 .163E+06 .2E5E+06
.37 5
.8t6E+06
.37 5
.135E+o? .277E+07
.16'l
18.000 18.000
.375
-484E+07 .7 64E+O7
.112€+08
16 -000 20 .000 20 .000
.37 5
.157E+08
.375
.96E
.375
.2c7a+ B6 .548E+06
.37 4E+07 .523E+O7 .3238+O5 .890E+05
IS-000 16.000 18.000 '18.000
20.000 20.000 20.000 2
0
.000
20.000 20.000 20.000 20.000
22.000 22.000
1.250 'l .50c 1-750 2.000
C
.375
.500
1.000
LON6I
000
-
2? .000 22 .000
.625
STD
16.000
-750
.37 5
I{OZZLE RO' STI F I}I.18/DEG ICK,I N INPLANE OUTPLANE
.37 5
.375 .375
E +
05
.957E+06 .151E+07 .310E+07 .5 41E+07 .854E+07 .126E | 08
.l
.375
22 - 000
22.000
.924E+O6 E+O?
.255E+07
.183E+06 .519E+06 .503E+06
-10f8+07
.180€+07 .265E+07 .41E E +0 7
?5E+08
.5848+07
107F106 .295E+06
.357E+05 .984E+05
06
.2OZE+Oa
.
.37 5
.450E|06
- 606E
+
.106E+07
.3538i06
.'l67E+07 .343E+07
-
5
56E+
06
.114E+07
22 -OOO
.37 5
.599Ei07
.?00Er07
22 .0C 0 22 .000
.37 5
.9 44E+ 07
.315E+O7
.375
.139E+08
.000
.375
22.000 24
24.000 2 4 2
.000
4.000
.37 5
.315
.t94E+0E .1 17 E+o6
.323€+06 .6648+e6 .116E+07
.463E+07 .616E+07 .5918+05 .108E+06 .221E+O6
.386E+06
Rotational Nozzle Flexibilities for Cylindrical
Vessels
155
Table 6-1
Conlinued ROTA STIFF CALCULATIONT OD,FT
VESSEL NOZZLE TCKrItl OD,IN
.000
.7 50
v€ssEL
14
14.000 14.0C0
4.000 14.000 14.000 14.000 I 4.000 14,000
1
1
.000
1.254 't.500 1.750 2. 000
.500
.625
14.000
14.000 14.000 14.000 14.000 't4.000 4.00 0 .000 'l 4 .000
'I
.7 50
1.000
1.250 1
.500
1.750 2. 000
14
14.000 14.000 14.000 t /, .000
14.000 't4.000 14.000 14
.500
.625 I .000 'l -?50
1 .500 1
.750
2.000
. ?50
.375
.000
14.000 '14.000
14.000 14-000 14 .000
14.000 t 4 .000
28 -000
2E.000 28 .000
28.000 28.000 28.000 28.000
30.00 0
30.000 30.000 30.000
30.000 30,000
30.00 0 30.00 0
.t75
f2.000
.500
.625
.500
1.750 2.000 .250
.375 .500 .6?5
'l
.750 .000
32.000 32.000 32.000 32.000 32.000 32.000 32.000 32.00c 32.000 36.000 36.000 3 6.000 36.000 36.00c 36 .00 0
2. 000
36.000 36.000 36.000 36.000
.500
40.000 40.000
.7 50
40.000
I .500
1.750
.000
'14,000
11.000
28.000
2. 000
1
14.000 t 4 .00c
.000
30 .00 0
14 .0 00
'l 4
28.000
1.250 1.500
I .000
'l .000 'I .2 50
14.000 14.000 14.000 14.000 14.000 14.000 't 4.000 14.0c0 t 4.000
26.U00
l0 .000
14.o00 14.000 14.000 14.000 14.000
I 4 .000
24.000 24.000 24.000 24.000 26.000 ?6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000
.7 50
t 4.000 I 4.000
14.000 14.000
24 .000
28
't4.000 't 4.000 14 .000
24.000
.64>
40 .000
40 .000
NOZZL€
TCK'IN STD
CYL.
VESSEL
ROT
STIF IN.L8/OEG
INPLANE LOTIGI
.1838+07 .37' .375 .375E+07 .375 .656E+0? .375 .'103E+08 -3?5 .152E+08 .375 .2',12E+08 .375 . 128E+06 .375 .551E+06 .375 -7?2Eta6 .375 .1?6E+O7 -375 .'1998+07 .375 .408[+07 .375 -7'l3E+O7 .375 . '1 12s+08 .3?5 -1659+08 .375 .231 E+08 .375 .13E€+06 .375 .380E+06 .375 .779E+O6 .375 .136E+07 .375 .2158ra7 .375 .4418+07 .3?5 .770E+47 .375 .1?2E+08 .3?5 .1798+08 -375 .249E+08 .375 .'l18E+06 .37t '408E+06 .375 .637E +06 .375 .146Et07 .375 .231E+O7 .375 .47 4E+A? .375 .AZ7E+Ol .3'15 .131E+08 .375 .192E+OB .3?5 .268E+0E 06 .375 .1 58E++06 .375 .4368 .3?5 .695E+06 07 .3?5 -'156E++O7 .3?5 .?47E -375 - 506Er07 .3?5 -8858t07 .375 .140E+08 .375 .205E+08 -375 .286E+08 .375 .179E+06 .375 .493E+06 .375 .101 E+07 .175 .177E+o7 .375 .279E+07 .375 .57?E+o7 .375 .999E+07 .375 .'t 5EE+ 08 .375 '232E+08 .3?5 .3 24E + 08 .375 .199€+06 .375 .549E+06 .373 .113E+07 .375 .197 s+o7 .375 .311E+07
OUTPLANE CIRCU
-610E+06
.125E +o? -219 E+07
.345E+07 .507E+07 .708E+07 .425E+05 -117E+06
.Z1j
E+O6
.420 E+0r5 .663E+06 .136E+0 7
.238€+07 .375ErO7 .551E+07 -7708+A7 .459E+05
.j27E+06
.260E +0 6 - 45 4E +O6
-7168+06
-14?E +O7
lir :t
t|j
{
ils
'{l
.ZS7E+47
.4o58+o7 .595E+07 .831E+07 .493E+05 .'1368+06
i!
.2798+06
.488E.06
.769 E +06 .
j
588 +02
-276E+O7 -435e+O7 -640E+O7
.89fE+07 .jAEE+05 .145€+06 .29EE+O6
,521F+06 .8228+06 .169E +Oz
.295E+07 .465E+07 -684E+07
.9558+07 .596E+05
.164€+06 .33?E+06 .589E+06 .929E+06 .19',l E+07 .
i33E+07
.525E+07 .772E+O7
.'t08€+08 ,664E+05 .'183E+06
.3t6E+86 .656E+06
.104E+07
,\
156
Piping Stress Handbook Table 6-1 Contlnued ROTA STTfF CALCULATION, CYL. VESSEL VESSFL
VESSEL
lcKrIN
OD,FI
1
14.000 14.000 I 4.000
1
t .500 1
2.000
14.000
.2 50 .37 5
.500
.625 .750 1.000 1.2t0 1.500
'15.000
.250
15.000 15 ir
lt 1
5.000
r5.000 15.000 1
5.000
15.000
5.000 I 5.000 't 5.000 15.000 't 5.000 15.000 15.000 1
tl
i
.500
.000
.625
I 5.000 't
F
.750
14.0C 0
14.000 't4.000 I 4.000 14.000 14.000 14.000 14.000 14.000
q;
.000
.250
15-000 t 5 .000
15.000 15.000 'l
I .000
1.250 I .500
.758 2.000 1
.375 .500 . ?50
1.000
1.250 1.500 2.000
.250 .375
5.00 0
15
.000
15.000 1 5.000 15.000 15.000 15.000 I 5.000 15.000 15.000 I 5.000 15.000 t 5.000 15.000 I 5.000 15.00 0
15.000 't5.000 I 5.000 I 5.000
15.000
.500
.625 1
.000
1.250 1.500 2.000
.250 .37 5
.500 .625 .7 50
1.000
1.250 1.500 1.750 2.000 .2 50
t 5 .000
15.000 15.000
N0zeLe
NOZZLE ROT STI F II{.LB/DEG
OD,IN
T
.638E+07
40 .000
40.000 40.000 40.000 40.000 48.000
- 11'l E+C8
48 .000
48.000 46.000 48.000
{8.000 48.000
.375
-?13E +O7
.3718+O?
.1?6E+08 .2 58Er 08
.586r+07
-21OE+06
.8 0l Er05
.662E+o5 .1f,6E+07 .237E+07
-221e+O6
.36'l E+08
.t7t
OUTPLAI{E CIRCU
.3? 4e+07 .7 69E+07
.861E107
.120Ef08
,4 53 E+0 6
.791E+O6
.125Er07 .256E+O7
.000
.375 .375
.212E+08
.706Er07
48 .00 0
.37 5
.311 E+08
.104E10E
48.000
.375
.435€+08
2.375 2.375 ?.375 2.375 2-375 2.375 2.375 ?.375 2.375 2.375 3.500
.151
.9 668+04
.3?2E+O4
3
.500 3 .500
.?16
5.500 3.500 5.500 3.500 3.500 3.500 3.500
-216
4E
4. 500 4
.500
4.500 4.500 4.500
4. 500
4.500
.500 4. 500 4-500 4
6.625
6.625 6.625 6.625 6 .625 6.625 6
-6?5
6.625 6.625 a.625 6
.625
CK,IN INPLANE STD LO}JGI
a
-62>
.625
.1 34E+08
-418E+O?
.'l
45
Fro8
.154
.?66E +05
.151
.546€r05
.887E+04 .1E28+05
.,t 54
.955E+05 .151E+06
.3t8E+05
.309E.06
.502E+05
.15 4
.154 .154
.540E+06 .8 52 E+ 06
-1808+06 .2848+06
.154
-1?5E+07
-
.154
.154 -2't6 .216
.175e+07
.479E+O4
.396€+ 05 .813E+05
.13?E+os
.1l?E+06
.473E+O5 .7 47E+05
06
.153E+06
.803E+06
.268E+06 .422E+06
.1278+ 07
.23? .237 .237 .237
. 460E
+
.1E6€+07
.8 67 E +06
. l908+05
.633E+04
-523E+05
.17 4E+A5 .358E+05
+
.107€+06 .l8EE+06 .296E+06 .60EE+06
. t06€+07 .1 67 E +O7 .2 468+07 .3 44E+ 07
.2898+05 .795r + 05
.2EO
.450 E+06
.1 63E+ 06
.285€+06 .924E+ 06
.2E0
.161E+07 .255E+07
.2 E0
.37 4E+07
.280 .322
.t22
,322 .3??
.621Er06
07
.260E
.280 .?80 .280 .280 .28 0
.271E+05
.2248+06
-716
.23? .237 .?3?
117E+O6
.583E+06
.144E+ 05
.216 .216 .216
.216 .216
.103E+06
.522e+07
.3E1€+05 .105E+06 .216E+06 .377 E+06
.626E+O5
.987E+05 .203E+06 .354E+06
,558Er06 .621E+06 .115e+O7 .9 62E+04 -265E+O5 .544E+O5
.951Er05
.150€+06 .308E+06 .538E+06 .848E+06 -125E+07 .174E+07 .127E+05 -350E+05 .719E+O5 .1?6E +06
Rotational Nozzle Flexibilities for Cylindrical Vessels
'157
Table 6-1 Continued ROTA STIFF VESSEL
OD,FT
VESSEI ICKTIN
15.000 15.000 15.000
15.000 15.000 15.000 15.000
NOZZLE
0D,IN
8
.625
8
.625
.500
a.625
8.625
.250
5.000 15.000 .000 .000 l5 .000
ALC
.750 .000
't
't 5 15
C
.7 50
.000
2
8.675 .750 10.750
.2 to
10
.500
1A.750
.62' ,7 50
10.750
'10.750
10.750
t5.000
.000 1.250 1.500 'l .750 2. 000
10
15.000
.250
'15.000
.500
.000
15
15 .000
I t .000
1
'15.000
15.000 15.000 J5.000 15.000 15.000
0 .750 I 0. 750 '1o.750
1
.750 12.750 12 .750 12.750 12 .750
.7 50
12 -750
1.500
'12.750
.0c0
1
12.750 12 .750
2. 000
12.750 12.750
15.000 15.000
.500
14.000 1/,.000
.000
.000 .250 .500
.000
15
15.000 15.008 15.000
1.750 .250
15.000 15.000 t 5.000 15.000
.7 50
.7 50
2-000
.0C0 '15.000
.250
15.000 1s-0c0
.500
15
15 't 5
.000
15.000 15.000 15
.? 50
.000
15.000
.000
1
.000
't.?50 1.500 1.750 2
'15.000
.000
.000 .000
.625 .7 50
15.000 15.000
1
.000
't5.0c0 t 5.000 15.000
1,258 1
.750
'l
2
.000
.000 1 5 .000 I 5 .000 15.000 15.000 15.000 5
'I
.500
.000
,000
14.000 I 4. 000
14.000 14.000 14.000 14.000 16
.000
16.000 16.000 I
6
.000
16.000 1 6.000 16.000 1 6.000 16.000 1 6.000
.000 18.0C0 1
15.000 15 15
4
1
'15.000 15
'14
8
t8-000 18.000 't 8.000 13 .000 16
.000
18.000 18.000 't 8.000 20.000 20 .000
.500 .750
20.000 20.o00 20 .008
ULATI0N'
CYL
VESSEL
'
NO?ZLE ROT STIf IN.LB/DEG
TCK,IN INPLANF LONGI STD
.322 .322 .322 -322 .322 .322 .365 -365 .36' .3 65 .365 .365 .365 .365 .365 .36 5 .375 .3?5 .375 .375 .375 -375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 -375 -3_tj .375 .375 .375 -375 .375 -375 .375 .375 .3?5 .375 .375 .375 .375 .375 .3?5 .375 .375 .3tj .375
.595E+06 .1228 +O7 .213E+o7 .336E+07 .494E+07 .690E+07 .4 80E + 05 .13?E+O6
.272E+A6 .475E+ 06
.7 49E+O6 .154E+O7
.268E+07
.4248+07
-623E +O7
.869E+07 .578E+05 .159E+06 .32? E+ 06 .5?1E+ 06
.900E+06 .16
5 E+
07
.323E+a7 .5C9E+07
.7198+07 .105E+08 .639E+05 .17 6E+06
OUTPLANI CIRCU
.198E+06 .407F+06 .711E+O6
.1'l
?E+O 7
.'165E+07 .238E+O7
.160E+05 - 4 41E +O5
.906€+05
.'t5EE+06
.25OElo6 .512E
+
O6
.895E+06 .'11'lE+O7
.208E+07 .290E+07 .193E+05 .530E+05
.t09E+06
.190E+06 .300E+06 .616E+06 .108E+07
.250E+07 .34EE+07 .2't 3E+0 5 -587E+05 .1?1E+O6
.632E+06 .996E+06 .205E+07 .357E+07 -564E+07
.2'l1E+O6
.116E+08 .738 € + 05 -203E+06 .417 E+o6 .7 Z9E+O6
.115F+07 .236E+O7
.4138+07
.65'l
E+D?
-957E+07
.1J4E108
.837E+05 .231E+06 .4738+ 06
.827Ei 06 .130 E +0 7 .21EE+07
.332E+0 6
.682E+06
.119E +o?
.188E+07 .27 6E+07 .386E+07 -216E+O5
.678E+05 .119 E+06 .?43e+O6
.3838+06 .787E+06
.138€+07 .217 E+07
.319E+07 .4 4tE+01 -?79E+05 .769E+05 .158E+06 .?7 6E+o6 .435E+06
.893€]06
.738E+O7
.156E+07 -216E+07
.1oEE+08
.362E+O7
.4688+07 .
1
51E108
.505E+07
.936E+05 .258E+06 .529E+06
.t1?E+O5
.146E+07
.486€+06
.925!+06
,l
i: "l
t\
.170E +A7
.3 62 Ei 06
.829E+07
:
.859E+05 .17 6a+06 .308E+06
r{
I
158
Piping Stress Handbook Table 6-1 Continued R0TA SIIFF CALCULATIOIte CYL.
vEss€L
VESSEL
TC(rIN
0DrFT
15.000
r5.000 15
.000
15.000 15.000
t -000
.?50 1.500 1
1.750 2.000
15.000
.2 50 .37 5
15.000 15.000 15.000 15.000 15 .0
00
.500
.625 .7 50 1
.000
15.000 15.000
1.254 1 .500 1.750 ?.000 .250
5.00 0
.37 . 500 '
15.000 15.000 15.C00
r5.000 1
15.000 15.000 t 5.000 I 5.000 I 5.00 0
15.000 15.000 15.000 15.000
t5.000 1 5,000 15.000 I 5.000 15.000 15.000 15.000
15.000
t5.000 15.000 15.000 15.000 | 5.000 t 5 .000
'15.000 15 .000
15.000 15.000 15.000 15.000 ,| 5.000 15 .0
00
5.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 't
I 5.00 0
15.000 15.000 '15
.000
.625 .750
1
.000
1.250 I .500 1.750 2.000 . ?50
.500 -625
.7 50
1.000
.250 I .500 1.759 2.000 .250 1
.t75
.500
.625 .7 to 't .000 1.250 1.500 1.750 2.000 .250 .375 .625 .75A 1.000 1.250
t.5c0
1.750 2.000 .250 .375 .500 .625 .750 1.000
l{oztLE 0D,IN
20.000 20.000 20.000 20.000 20.000 22.000 ??.000
.ooo 22.000 22.000 z2-ooo z2
VESSEL
OZZL€ ROT STI F II{. LB/
lcKelt{ INPLANE STD LON6I .375 .375 .375 .375 .375 .375 .375 .375
.375 .375 .375
.299€+07 .52tE+ 07 .825 E+07 .1 2l E+08 .169 E+0E .103E+06 .285E+06 .565E+06 .102E+ 07
-37 5
.134E+08
22.OOO 24 .00 0 24.OOO
-375
, I E7E+ 0E
.375 .375
.312E+06
26 -OOO
26.000 28.000 28 .000
28.000 28.000 28.000 2E.000 2E .000 ?E.000
28.000 28,000 30.000 30 .00 0
30.000 30.000
30 .000
30.00 0
.3?5 .37 5
.375 .375 .3?5
.375
.37'
.375 .375 .37 5
.3?5 -375
.175 .375 .375
.375 .375 -375
.375 .37 5
.6348.07 .999E+07
.147Er08 - ?05 E+08
. 12f,Ef 05
.340€+06 .192E+O7 .39
4E +O7
.214E+O6 .373 E+06
.5E9Ef06 .721E+O7 . zl t E+q7 .333 E +07 .490E +07 .684E +07
.4llE+05 .t13Er06
.23OE+O7 -362E+O7
.1 60E+0E .2?3E+08 .133E+06
.532E+O7
.109Er08
.367E +06 .7538+ 06
.132E+07 .20EE+0? .426E+o? 44E+0?
.t75
.141El07
.173Ef06 .241E+A8
.375
.223E+07 .4588+07 .799E+07
.37 5 -375
-624E+O7
.578 E +0 5 . t 048+06
.689E+07
.394€+06
.000
.19f,E+07 .J04E+07 .447E+07
.232e+O5
.375 .375
.375 .375
.19 5e+06
.541Er06
.406E+06 .6408+05 .131E+07
. t 43E+ 06
-375
.950E+05
.122t+O7
-375
-375
-345E+05
.697E+06
.117E+08
.375 .375 .375 .375
32.000 5 2.000
.641 E+06 .112E+O7 .17?t+ 07 . 363 8.0 7
-375 -375
30.000 30.000 30.000 30.000 3 2.000 32.000 52.000 32
.1 13E+06
.?
.t75
.275E+07 .404ErO7 .565E+07
.538E+06
.5788+07 .9'l 2 E+ 07
24.000 24.000 24.000 2 4.000 24,000 24.000 24.000 2 4.000 2 6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000
r0 6
-110E+07
-375
.375
E
.17 4E+O7
.1 61 E+07
.375
22 .000
.998
.331e+O7
?2.000
22.OOO
DEG
0UTPLANE CIRCU
.809 E+06
.126E+0E .185E+06 .2 59E+ 08
.714E+07 .444E+05 .122e+O6 -251E+06 .438 E+06 .692E+06 .1 42E +0 7
.248e+o? .391E+07 .575e+07 .803 Er 0 7 .477E+O5 .131 Eio6
.270Er06
.4718+06 .743ErO6 .153E+07 .z66ErO7 .420
E+ 0
7
.618E+07 .863
€
+0 7
.J
.510Efo5
.421E+06 'f,E+06
.140E+06
.865Er06
.'l5l€+07
.238E+07 .489E+07
.28EE+06 .504E+06 -
7948r05 65Elo7
.t
Rotational Nozzle Flexibilities for Cylindrical Vessels
159
Table 6-1 Continued ROTr STTFF CALCULATION,
VESS€L TCK,IN
v€ssEL OD,FT
5.000 15.00c 15.000
.250
't
1
't
1.500 1.750 2.000
5. 000
.000 15.000 1 5 .000 'l 5 .000
15
.500 .7 50
.000
15.000 15.000 15.000 15.000 15.000 1 5.000 'l5 .00c 15.00c 15.000
-375
.855E+07 .135E+0E
32 .00 0
.375
.'198E+08 .27 7 E+ 08
.661E+07 .923E+07
.375 .51>
.'17 3E + 06
.37 5
.977E+A6
.576E+05 .159E+06 .326E+o6
32.000 .000 I6 -000
3 2
f6.000
36.000 36.000 36 .00 0
40.000 40.000 40.000
.500
.625 '|
.000
.000
1.250
40 ,000
40 .000
1
6.00
0
6.000 16.000 16.000 1 6.000 '| 6.000 16.000 1 6.000 16.000 16.000 t
't 6
.000
't6.000 '| 6.000 16.000 16.000 16.00 0
16.000 16.000 16.000 't6.000 1 6.000
1.000 1.250 1
.500
1.750 2
.000
1
.5C0 .7 50
.10/rEr08
.530E+06
.177E+o6 .363E+06
tl'l
.634€+06
"J
.5rt
,190F+07 .3008+07 .6168+Ol
.375
.108E+08
-319e+o7 .566E+O7 .832E+47
.192Ei06 .109
E+
07
.1708+08
.612E+O5
.100Er07 .?o5E+07
.438€+06
.2?9E+a7
.7 64E+O6
48.000 46 .000
.000
4E
.000
2.375 2.375 2.375 2.375 2.375 2-375 2.375 ?.175 2.375 2.375 3.500 3.500 3
.500
3-500 3.500 3.500 4.500 4.500 4.500 4.500
.2 50
.746E+O7
.1318+07
.000
4E
.500
2.000
.32?E+07 .50E8+07
.313E+08
.37 5
48.000
3.500 3.500
1.7t0
+06
.?13E+O6
.7 50
1.000 1.250
E
.897E+06 .184E+07
06
3-500
.500 .625
. 569
.7748+O5
1E
16.000
.449Er07
.?32E+O6
2. 000
.500
.9 658+07
-285E+07
48 .000
I 5 .000
16.000
.553E+07
IRCU
.250E+08 .348E+08
48.000 48.000
16.000 16.000
.171E +07 .2 69 Er A7 .152E+CE .221E + 08
40.000
1.750
.000
5
.4768+06
C
40 .000
15.000
15
.37
40 .000
,/.8.000
.000 .000
15.000
-375
.s75
15.000 15
32 .000
.500
1.500 1.750 2.000
OUTPLANE
LONGI
40.000 40.000
1. ?50
.000
TCKTIN INPLANE
2.000
1.000
5.000 15.000 15.000
NOZZLE ROT STI F IN.L8/DEG
6.000 36.000 36.000 3 6.000
. >uu
V€SSEL
STD
3
15-000
't 5 15
OD,IN
36.000
15.000 15.000 '| 5.000 t 5,c00
15 1
NOZILE
ClL.
4. 500
-5t>
.639
.375
.315 .15 4 .15 4
.154
.154
30E +08
.43?E +07
.205E+08 .301 E+08 .420E+08
.682E+Oz
.935E+04 .258E+05 .529E+05 .924E+05 .1 46E+06
.299E+06
.15 4
.5238+06 .8258+06 .121E+07 . t 69E+07
-154
.216 -2't6
.216 .216 .216 .216 .?16 -216
.?'t6
.237 .237 .237 .237
5;
.121E+07 .24EE+o7
+
.15 4
.154 .154
5r
07 .713E+ 07
-362E
.'l
.375
E+
.1168+08
.1008+08 . t 40E+08 .3'l2E+04 .859E+0rr .1 76E+05
.308E+05 .486E+05 .998E+05 .17 4E+o6 .275E+A6
.404E+06 .5 64E.
O
6
. 1l9E +05
.16LE+04
.3E3E+05
E0€+07
.128E+05 ,262 E+0 5 .45EE+05 .7?3E+05 .14EE+06 .259E+06 .409E+06 .601 E+0 6
.252E+07 .1E48+05 .507E+05 .104E+06 .'182E+06 .287E+06
.606E+05 .956E+05
.787E+05 .13EE+06 .217E+06 . 4 45 E+06 . 778 E+ 06 . t 25 E+ 07
-l
.840E+06 -6'l3E+04 .'l 69 E+0 5 .3478+05
ft
160
Piping Stress Handbook Table eFl
Continued ROTA V ESS
EL
OD,fT
VESSEL
TCK,IN
16.000 r 6.000 16.000 16.000
1.000
I 6.00 0
2. 000
16.000 16.000 16.000 16.000 16
.000
16.000 16.000 16.000 16.000 16.000 16.000
1.250 I .500 1.750 .250 .375 .500 .7 50
1.000 1.250 'l
.500
1.750 2.000 .?50
16.0 0 0
16.0c0
.500
16.000
-625
16.000 16.000
I .000
16.000
1.250 1.500
16.000
1
I 6.00 0
16.0C0
.750
2.000
16.000 16.000 16.000
16.000 16.000 16.000 16.000 't6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000
r6.000 'l6.000 16.000 16.000 16.000 16.000 16.000 16-000
-
z)u
.500
.625 .750 I .000 't
.2 50
1.500
1.750 2. 000
.250 .37 5
.500
.750 I .000
1.250 J.500 I .750 2. 000
.500 .625 1.000 1-250 1.500
1.750
16.000
1.000
2
.000 .37
5
.500
.625
vESSEL
NOZZLE NOZ2LE ROI STIF IN.L8/DEG ODEIIi TCK'IN INPLANE OUTPLAN€ CIRCU LONCI STD 4.500 4. 500 4. 500 4. 500
4.500 6.6?5
6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.625
.?37 .237 .237 .237 .280 .280 .280 -280
.625
4.625 4.625 10.750 10 .750
10.750 10.750 10.750 10.750 10.750 10.750 10.750 10.750
-162e+07
.238r+07 .335E+07 .?79E+05 .770E+05
.145E+06 .298E+06
.280
.2 46E+ 07
.2E0
.506E+07 .369E+05
.280
.3?2
.322 .32? -322
.322
.156E +07
.362€+07
.t02E+06 .2C9
E
+06
.365E+06 .576E+06
.ll8E+07 .206E+07
.365
.3268+07 .479E+o7 -669Er07 .165E+05
.3 65
.1 28E+ 06 . 263E +06
.365
.460E+06 .7?5E+06
.3?Z
.322 .322 .365 .365 .365 .365
.36 5
.365 .365
.1 49 E+07
.37 5
.375
.179E+07 .3138+07
.3?5
-493E+Oz .7 25E +07
.000
1 4.00 0 1 1 1 1 4 .000
.339E+0 5 -696E+05
.1?2E+06
.192E}06 -394r+06
.688E +06 .109E f0 7
.160E+0? .223E+07 .155E+05 .4?7E+o5
.a77ErO5 .
l53Er06
.2128+06 .496E+O6
.316E+06 .551E+06 .8?2E+06
.13? E+07
.201E+g?
.28'lEr07 .185E+05
.291E+06 5968+06
-
.1048+07 .161E+07 -2428+O7 .337 E+O7
.375
.1018+06 .619E+05 .1 71 E+06 .350E+06
.2068+05
.175
.965E+06
.322E +o6
4.000 4.000 4.000
14.000 14.000 I 4.000 14.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000
.123E+05
.5148+05 .1058+06 . 1 84 Ef06
.559Er05 .'154Er06
12.?50 12.?50 12.750 1Z .750
.121E+O7 .1 69 E+ 07
.867E+06
.375 .375 .3?5
.37'
.521Er06 .821E|06
.260E+07 .4108 +07 .603E+07 .8 428 +07
12.75A
12.750
.257E+O5
.280
.375
12 -750
.111E+07 .932E+04 .9?1E+05
12 .7 50
12.750
.795E+O6
.4368+06 .894Er 06
?80
.t2?
8
.343E+06 .5 4l Ei06
.276F,+O6
.
a .625
4.625 I .625 8.625 4.6?5
.196E+06
.1038+07
.527Ero5
.322
I .625
.589E+06
. 158E+05
.625
8
'14
16.000 16.00c 16.00c 16.000 16.000 16.000
t6.000
STrrF CALcULATIONT CYL.
.6'l2E+06
.375 .375
. 569 E+0 5
.1 l7E +06
.2848+06
.1988+07
.660€r06
.546Er07
.182E+07
.3 46E +07
.115€+07
.6c2E+07
. ?67E +o7
.1 'l ?E+08
.7'l5E+05
.373E+07
.2f8E+05 .656E.05
,375
.197E+06 .404E+06
.375
.706e+06 .111E+07
.371E+O6
.375
.229E+07
.7 62E+06
.135E+06
.235E+06
Rotational Nozzle Flexibilities for Cylindrical Vessels
161
Table 6-1 Continued ROIA STIFT CALCULATION, CYL. VESSEL
VE
OD,FT
TC
SSEL II
16.000
1-250
16.00 0
1.5C0
6.000 16.00c 16.000 16.000 't
.750 2.000 1
.250
.500
16.0 00
16.000 16.000 16.000 16.000 1
6. C00
16.000 16.000 't6.000 I 6.000 16.000 'l6.00
0
t6.000 t 6.000 16.000 16.00
0
16.000 16.0 0 0 'I 6.00 0
16.000 16.c00 16.000 16.000
.625
J
.000
OD,I
l6 ,000 't 6.000
-153E+06 -?67E+o6
E. 000
.259E+ 07 .4538 +07
.750 1 .000
6.00 0 16.0 0 0
'| -
1-?50
1.500
.711E+07 .105Er08
r
. 147E+0E
20 . c00
.906E+05 .250F+06
20 .000
.895€+06
20,G00
-'l 4'l
20 .000
20.000 20.000 20 ,000
22.aao 22.000 22.000 ?2.000 22.000 2a.000 22.000
.500
1
.7 50
24.OOO
16.0C 0
t6-000 16.000 t 6 .000
16.000 16.000
1
.000
.250 I .500 1 .750 1
2
.000 .250
.799E
.37 5
.117E+08 .164E+08 .1C0E+06
.375
16.!00 16.000
1
.375
.302E+06
16.000
7.25A 1.500
16.00
1
.1t0E+06 .62'l
E
+
o6
.375
26-000
.37 5
.42't e+o6 .864E+06 .151E+07
.?38E+o7
.3508f07 .4898r07
-3028+05 .832E+05 .'171E+06
.298E +06 .471E+ 0 6
.966E+06 -169E+07 .266E+O7 .391E+0? .547E+07 -134E+05 .920E+05 .189E+06
.330€+06 .5209+06 .107E+07 .'l87E+07 -29 4E+07
.433E+o7
.604E.07 .366E+05 .101E+06 .207E+06
.361E+06
.35'lE+07
.'117E+07 .2018+Oz
.570E+O6
.968E+07
.3238+07
.142E+08 .199E+08
.66?E.07
.1198+06 .329E+06
.6758+o6 .1'l6E+07 -375
.431F.D7
.108E+07 .1718 + 07 .613E +07
.000
26.000
.567E+06 .990E+06 .156F+ 07 .3?18+ 07 .560E+07 .883E+07
.s75
2,6.000
26
.000
1
07
.130E +0E .1 81 E +08
26.000 ?6.000
16.000
+
.?76E +06
24.000 24.000
24.000 24.000 26.000
07
.54>
26 -AOO
16.00 0
6.00 0 '16.000
24. ilo0
E+
.290E+07 .506€+07
22.OD1
16.000 16.000
6.000
.512€r06
20.000
24.000 24.000 24.000
16.000
.375
E. 000
22.000 22.000
16-000
.458€+06
1E.000
750 2. 000
1
.1298+08 .B l0Er05
.126E+07
18.000 'l
.3098+07
.801E+C6
8
20.000
| .000
.?1OE+o7
.000
18 .000
.580
.7 50
.131E+o7
.6J0E+07
.270E +O5 .7 44E+O5
.250
.500
.399E+07
,22fE+06
18.000
1
CTRCU
-375
t 8 .000
1
OUTPLAIIE
.9 26E+ 07
8.000 20.000
1.750 2,000 .250
ICK,IN INPLANE LONGI STD
.375
2. 000
1.250 1.500
NOZZL€ ROT SIIf IN.LB/DEG
'l6.000
18.000
1.750
N
16 .000
1.250 1.500
16.00 0
16.000 1 6.000
NOZZLE
X,I
VESSEL
.186E+07 .382E+07 .667E+07
.47 4E+07 .398E+05 .110E+06 -225E+06 .393E+06 .620E+06
.127E +07
.222E+07
26.OOO
.351E+47
.750
26.000
.'l05E+0E
16.000
2. 000
26.OOO
.216E+08
16.C00 16.0 0 0
-250
-'l29
06
.375
28.000 28.000
.7208+O7 .430E+05
.500 .6?5
28 .000 2E
.000
.355E+06 .729E+06 .127E+C7
.243E+06 .425E+C6
.000
.412e+ 07
.6705+06 .137E+a7
.7218+07
.240E+07
0
16.000 16.000 16.000 16.000
16.000
.750
I .000
1.250
28.000 2E
28.000
.t55E+08 E+
.201E+07
-516E+O7
.1'18 E+06
I {
it
I .l
162
Piping Slress Handbook Table 6-1 Contlnued
VESSEL
0DeFT
16.000 16.000 16.000 16.000
t6.000
16.000 16.000 16.000 16.000 16.000 16.000 16.00
0
6.000 16.000 16.000 16.000 16.000 1
f6.000 16.000 1
6.00 0
|
6
.000
16.00 0
16.000 16.000 t 6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.C00
16.000 16.000 16.000 16.00c
r6.000 | 6.000 16.000 1 6.000 16.000 16.000 16
.00 0
16.000 16.000 16.000
t6.c0c t6-000
16.00c 16 .000
16.000 16 .00 0
16.000 17.000 17.00c 17.000 17.00n I 7.00 0
17.000
nOft STIFf CALCULATIONT CYL' VESSEL NOZ ZLE ROT STIF IN.LB/DEG NOZ Z LE VE SSEL IcKTIN It{PLAt{E 0UTPLANE 0DrIN TCk,ll{ CIRCU LONGI STD I . 500 1.750 2.000 .250 .375 .500 -625 .750 I .000 1.250 1.500 1.750 2.000 .250 .375 .500 -625 . ?50 I .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1.250 I . t00 I .750 ?.000 .250 .375 .500 .625 .750 1.000 I .2 50 I . 500 1.750 2.000 .250 -375 .500 -625 -750 '| .000 't.250 1.500 1-750 2.000
.250 .375 . 500 .625 .750 1 .000
2E.000 2E.000 2E.000 30 -00 0 50.00 0
0.000 30.000 30.000
3
30.00 0 30.00 0 30.00 0
30.000 30.000 3 2.000 32.00
0
e.000 32.000 32.000 3 2.000 32.000 3
52.00 0
2.000 52.000 3 6.000 36-000 36.000 3 6.000 3
36.00
0
6.00 0 36.00 0
3
36.000 36.000 36.000 40.000 40.000 40.000 40.000 40.000 40.000 40.000 40.00 0
40.000 40.000 46.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 2.375 2.375 2.375
2.375 2.375 ?,375
.375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -375 -375 .375 .375 .r7, -375 .375 -375 -175 -375 .375 .375 -375 .375 -375 -375 .t75 .375 .375 -375 .375 .375 .375 -315 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 .375 .37t .375 .375 .375 .375 .375 .375 .375 .154 .154 .154 .154 .151 -154
.1148+08
.3798+07
.167E+08 -235E+08
.778E+07
.138E+06 .
f,82E+06
.783E+06 .137E+07 .216E+o7 .4438+07 .774E+O? .1 22E+08
.'l80E+08 .251E+08
.1{EEr06 .408E+06
.8378+06 .1468+07 .231E+07 .47 4E+07
.828Ef07 . 131 E+06
.192Er08
.268E|08 .'l C7E+O6 .461E+06 .946E+06
.557 E+O7
.462E+05 .127E+06 .261 E+06
.4568+06 .719e+06
.148Er07 . ? 58
E+07
.407Er07 .598€+07 .636E+07 .493 E +0 5 -136E+06 .279E+O6
.488€+06 .769 E+06
.'l588+07
.27 6E+07 .435 E+0 7
.640€i07 .893Er07 .557E+05 .154E+06
.315Er06
.'l65E+07 .2618+07
.551 Er0 6
.535E+07
.17AE+07 -31?ErO7 .491E+O7
.9 35E+C7 -14?E+Oz .217E + 08
.303E+08 .186E+06 .514E+o6 . '105 E+ 07
. 1948+07
.291E+oz .596E+O7
.'l04E+08 .1648+08
.2 42 E+08 .337E+08 .225E+O6 .619E+06
.127t+O7 -22?ErO7
.350E+07
.8698f06
-7238+D7
.101E+0E .621E+05
.'l 71 E+06 .351Er06
.614E+06 .968E+06 .199E+07 .3478+O7
.548Er07 .805E+07 .112E+08
.7 498+OS .2068+06 .424E+O6 .740E+06 .117 E +07
- 291 E+08
.2408+07 .419E+07 .660F+07 .971E+07
.4078+08
.136€r0E
.907 E+04
.302E+04
.719e+O7
.1?6E+08 .'l9EE+08
.250€+05
.51fE+05 .8978+05
.1 r.1E+06 .290 E+ 06
.E338104 .171E+05
.299€+05 -471Er05
.968 E+0 5
Rotational Nozzle Flexibilities for Cylindrical
Vessels
163
Table 6-1 Continued ROTA STIf
VESS€L TCK,IN
VESSEL OD. FI
17.0
0
0
17.000 1 7.000 I 7.000 17,000 17.000 17.000 17.00c 17.000 't 7.000 17.00 c
17.000 17.000 17.000
1.250 I .500 1.750 2.000
1 1 1
0
17.000 17.000
17.000 '| 7.000 17.000 17.000 17.000 17.OOO
17.000
17.000 t 7.000 17.000 17.000 17.000 17.000 17.000 't7.000 17.000 17.000 t 7.000 .000 17.000 17.000 17.000 17
1
7.000
17.000
7.000 17.000 17.000 17.000 17.000 1
17.C00
ION,
.15 4 .15 4
.500
.675
4
.500
.500 4-500 /. .500
.1248 +05 .255E+05 .445E+05
.2'l0E+06
.701E+05
.432 €+06
.144E+O6
.,.500 4. 500
6.625 6.625 6.625 6.625
.250 .500
.6?5 .000
1.500
.375 .500 .625 .750 I .000 1.250 r.500
1
.000 .250
1.500 .250
.375 .500
.625 1.000
1.250
.33 6E +0 5 .588E+05
.27EE+ O6
.9?7E+ 05
E
+
07
.1758+07 .244E+07 .4928+05
.571E+06 .997F+ E6 .157 E+07
.231E+07
.190E+06 .332€+06 .524E+06 .771E+O6
-3?3E+07
.108E+07
.271t+05
.904E+04
.717E+05 .1538+06
.51',|E+05
.268E+06
.2 49E+05
.893E+05
.152E+07 .239E+O7
.797E+O6
6 -625
.280
.3518+07 .4918+07
- 1178+07
.625
.3?2 .3?2 -322
.625
8.625
I .625 I .625 8.625 10.750 10. 750 10 .750
750
I 0.750
,28 0
10-750 0. ?50
I 0. 750
12.750 12.750 12.750 1?.750 12.750 12 -750
12.750
.358E+05
.987Er05 .203E+06 .35 4E+O6
.164E+D7 .119E+05
.329€+05
.676e+O' .118Er06
.3?2 .3??
.5588+06
.1E6E+06
.1 15L+ 07
- 3E2E
.122
.Jt6E+07 .464E+ol
.105E+07 .1558+07
-322
.649E+07 .451E+45 .124E+06 .?55E+06
.t22 .32? .365 .365
.2oOE+ol
+06
.668E+06 .216E+07
.'l 50E+05 .414E+05
.851E.05
.1 49 E +06
.365
.4 468+06 .703€+06 .111e+07
.365
.25?E+ 07
.2348+06 .48'l E+ 06 .841E+06
.39E€+07
.133E+07
.365
.585E107 .E17E+07
.272E+A7
0. 750
'10. 750
.4236+06 .668€+06
.375
.542€+05 .149E+06
-375
.1958+07 -181Er05 .498E+05
.3078+06
.102Er06
.536E+06 .846E+06 .171E+07
.179E+06
.303€+07
1\
-t64E+05
.28 0
a
1
.101 E+ 06 .176E+06
.119
6 -625
8.625 8.625
'|
.178E+05
.252 E+06 -397E+06 .583E+06 .E15E+06 .595E+04
.755E+06
6.625
10 -
1
.280 .280 .280 .280
.133Er06
.4508+04
.'l41E+O6 .289 E+06 .505E+06
8
.375
-237
.'135E+05
.280 .?80
6.625
2.000
2.000
.237
.2EO
.7 50 1
-2't6
4
1.750 2.000
.592€+06
69 E+06 E + O6
.37 ?E + 05 .7 64e+05
-216 .?37 .237 .237 .237 .237
1.000 1.250 1.500
.1t8E+07
1
.?16
.216
4.500
.
.547 E+O6
J
.500
.507E+06
.'l64E+D7
.154
3.500
4
0UTPLANE CIRCU
.'t54 .216
.2',16
4.500
IN.LB/DEG
.267
3, q00 .500 4 .500
€L
.800E+06
.500
5.500
VE SS
ZLE ROI SIIF I NPL Allt STD LONGI
.500
.250
L.
TCXTIN
3
3.500
CY
NOZ
.000
.500 3 .500
.750
17.000 17.000 17.0C0
LCULAT
.216 .216 .2't6 .?'t6
17.OA0
t7.000 ,7.000
.500
5
2.00 0
7.00c 17.000
7.00
2.375 2.375 2.3?5
.500
1.750
r
't
OD,IN
3.500
17.000
17.000 17.000 't7.000
CA
NOZZL€
3
17.0 00
17.000
F
.?82E+O 6
.579€+06 .101E+07
!
164
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULAIION, CYL. VESSEL
v€ssEL
OD,fT
17.000 17.000 17.000 17.000 I 7.000 1
vE TC
1.500
I .750
?.000
.250
7.00 0
.625 .750
17-000
17.000 17.00c 17.000 17.000 17.000 17.000 17.O00
17.c00 17.000
I .000
1.250 I .500
1.750 2.000 .250 .37 5
17.C00
.500 .625
r7.000 17.000
I .000
17.AOO
1. 500
17.000 I,
i: "
'17.000
; I li ii
7.000 17.000 17.000 17.000 17.000
)rt
17.000 17.400 17.000 17.000
a:
l.
ssEL K,IT{
't
17-000
17 .00 0
1.250 1
.500 .625 .7 50
I .000 '| 't
17.0t/0
1
.37 5
't
14-000
14.000 14.000 14
.000
r6.000 16.000 I 6.000 1 6.000 1 6.000 16.000 16.000 16.000 16.000 16.000
.375
.375 .37 5
.375 .375
.000
.500
.625 .750
I .000
.250 1.500 1
1.750 2.000 .250
.375 . t00 .625
t7.oac
.7 50
I .000
1.250 1
1
8. 000
8.000 't8.000 18.000 18.000 1
.375 .37 5 .37 5
-375
.3 75
.375
.37 5
.5C0
.375
.000
.375 .375
20.000 20.000 20.000 2
0
.375 .37 5
?2 .000
22.000 ?2 .OOO 22 .00 0 22 .000
22.000 22.000 22.000 22.000 22 .000
.375
24
.000
24.000 24.000 21-OOO
.37 5
.192E +07
.336E+07 .529E+07
.375
24-OAO 24.OOO
.3? 5
.375
.200E+05 .552E+05 t 3E+ 06 E
+06
.312E+06 .640E+06 .112E+07
.176e+07
.7 78E+ a7 -109E+08 .693E+05 .191E+06 -39?E+06 .685E+06
.259 e+07
-222E+47 .388 E+07 .611E+A7 .E99E+07 .'125E+08
- 7t9E+O6
.362E+O7
.231
E+0 5
.6378+45 .13'lE+06 .??ae+o6 .360Er06 .1298+07 .204E+07 .300E+07 .418E+07
.786E+O' .2178+06 .445E+06
.26?E+O5 .722E+O5
.777E+06 .123E+ 07
.259E+06 .40EE+06
07
.838E+06
07 .69t8 + 07
.146e+O7
.102E+C8 .14?E+08
.340E+07 .47 4E+o?
.439E
+
.? 42E+ o6 .49?E+06 .868E+06
.137E+07 .281E+07 .491E+Oz
.l
488r06
.231E+O7
.293E+05 .607E+05 .'166E+06 .2 89
E
+06
.457 E+O6 .937f+O 6 .164E+Oz
.775E+ 07
.258E+07
.114E+08 .1 59E+0E .972E+05 .26E€+06
.380E+07
.550F+06
.5308+07
.3248+O' .895E+05
.183Ef06 .520€+06 .505E+06 . t 04 E+07
.5 4te+07
.lE1E+07
.857E+07 .'l26E+ 08 .176F+0E .106E+06
.286e+O7 .42OE+07 .586E+o7 .355E+05 .978 E+05
.2938+46 .6028+06 .105E+07
.000
24
.327E+O7
. 198
.311E+07
.37 5
.159E+07
.234E+o7
.593E+06 .936E+06
.151E+O7
21.OOO
CIRCU
.1
.960E+06
.37 5
OUTPLANE
.340€+06
.8 79E + 05
.000
20.000 20.000
.1 65 E+06
. ?5?E+
18.000 18.000 20.000 2 0.000 20.000 20
.478E+07 .703E+07 .982E+07 .6008+05
.108F+07
.37 5
1.250 1 .500 1.759 2.000 .250 .375
17.000 17.000 17.000 17.000 17.000 17.000 17.000
.375 .375
E.000
.7 50
7.000
17.000 17.000 17.000 17.000
-375
1
1
17.C00
4.000 14.000
.375 .375
.500
.525
'17.000
14 . C00 14 .000 14 -000
TCX,IN INPLANE STD LON6I
.375
,375 ,500
7.000
17.000 17.000 17.000 | 7.000 I 7.000 't 7.0c0
12.750 12.750 12.750 '| 4.000
NOZZLE ROT STI F IN.LE,/DEG
18 .000
t 7-000
t7.000
N
.2 50
1.750 2.000
I 7.000
17.O00
L E
OD,I
1E.000 .37 5
17.000 ,|
.750
2.000
t'l0zz
.166a+07 .341E+Ol .595E+07 .939E+07
-2O1E+O6
.351E+06 .553E+06
.114E+07 .'198E+Oz
.313E+O7
Rotational Nozzle Flexibilities lor Cylindrical Vessels
165
Table 6-1 Continued
SIIfF CALCULAIION, CYL. VESSEL NOZZLE ROT STIF IiI.LB/DEG VESSEL NOZZLE OUTPLANE T CK,I N INPLANE TC(,IN OD,II{ CIRCU STD LONGI ROTA
VESSEL
OD,FT
17,0 00
17.000 't
1.750 2
?.0 00
17.000
t 7.00 0
17.000 1 7.000 1 7.000
t 7-000
7.000 17.000 '| 7.000 17.000 1 7.000 17.000 17.000 17.000 17.000 17.000 17.000 1
-750
26.000
.150E+08 .2'l0E+0E
-500E+07 .698E+07
2.000
.500 1.0c0 1.?50 1-750 2.000 -z>tJ
.500 .000 .7 50 2. 000
.500 .6?5 .000
1.25O
1.500 1.750 2
.000
.500
1
.250
I .500
7.00 0
.500
17.000 t 7-000
17.000 17.000
.647
1.754 2
.000
.250 .375
I .000 't .2 59
't.500
E+
07
+06
.12ta+06
.417E+O5
28 .000
.345E+06 .7 Q7E+06
2E.000
.124E+07
.115E+06 .236E+06 .412E+06
28.000 28.000
.650E+06
28.000 28 .000
.195E+07 .400E+07
28.000 28.000 28 .000
.699E+07
.233E+o7
.375
.'110E+08 . t 62E+08
.36EE+07 .540E+07
28.000
.375
30 .00 0
-375
30.000 30.000 30.000 30.000 30.G00
30.000 30.000 30.000 30.000 .000
.375 -375
.375
.226E+08 .154E+06 , 370E+ 06
.760€+06 .133E+07 .2098+07 .430E+07 .751E+07 .'1188+06
.3?5
.375
.17
4E +
08
.243Er08 -144E+06
32.OOO
.396€+06
3 2
-E t 2E+06
.000
32.000 2.00 0
52.000 32.000 32.000 5
2.00
.375 .375
J2.000 56.000 3 6.000 36-000 56 .000 36
.000
36.000 3 6.000 J6.000 36.000 40.000
.375
40.000 40-000 40-000
40.000 40.000 40.000 40 -000
.375 -375 .375 .3?5
.375
.442t+O6 .698E+06 .1438+07 .?50E+o7 -395E+07
.5818+07 .8118+07 -479 E+05
.132€+06 .?7'l E +o6 .475E+06
.127E +08
.422E+O7
.26EE+07
.6218+07 .E67E+07 -541E+05
.4 47E+A6
.1tt9E+O6
.918E+06
.306E+06
. 160E+07
,534E+06
.253E+07
. E43E+06
.519
.'173E+07
E+
07
.907F+07 . t 43E+08 .2't0E+08 .29 4E+ 08 .181E+06
40 .000
.7518+07 .448E+05 .123E+06 .253E+06
.7 46E+06 .1538+a7
.16?E+06 -5()
.133E+O7
.142E+07 .224E+07 .460E+07 .803€+07 .'186E+08 .260E+0E
0
36.000
17.000 17.000 1 7.000 17.000 17.000 7.000
.37OE+ 07
26 ,000
3
't
.37 5
26.OBO
32
17-000
7.0C 0
- 601E
1
t . t)00
1
.1808+07 .1028+08
17.000 17.00c 17.000 17.000
1
.218E+06 .381E+06
?6 -OOO
17.OOO 17.OC0
't
.106€i06
.655E+06 .114E+07
.500
17.000 17.000 17.000 1 7.000 17.000 17.000 17.000 '17.000
.319E'06
1
7.000
7.0C 0
.37 5
.123E+07 .?16E+07 .340a+07
7.C00 17.O04 1
26 .000 26 . C00
.460E+07 .642E+o7 .386€+05
26 -OOO
'|
17.000 17.000
.193E+0E .116E+06
t .000 1-?50
17.C00 1
.138E*08
24.000
26.000 26.000 26.000
't
17.000 17.000 17.0c0 17.000
? 4 .OOO
.500
I 7.00 0
7.000 17.000
.000 -250
.302E+07 .4778+07 .7 0'l E.07 .979E+o7
-6038r05
.4988+06 .10?E+07 .179E+07
.166E+06 .341Ea06 .596E+06
.282E+07
.939
F+
C
6
07
.193€+07
.101E+08
.337E+O7
.579E
+
.1598+08 -234E+08
.551E+07 .78'lE+o7
rf
:l :
166
Piping Stross Handbook Table 6-1 Continued
R0lA STIFF CAI-CULATION, CYL. VESSEL VESSEL
OD,'T
17.000
ICK,IN
2.O00
17.000
.250 .315 . t00
I 7.00 0
-625
t 7.000 I 7.0 00
17.000 17.000 17.0 00
.7 50
1.000
1.250 I .500
48.000
18.000
.250 .375
2.375 2.375 2.375 2.375 ?.375 2.375 2.375 2.375 2 .375 2.375
.00 0
18.000 1E.000
tE.000 1
E.00 0
18.000
.500
.625 .750 1.000 1 .250 1
.250
.500
1E.000
18.000 18.000 18.0C0
16.000 18.000 't6.000 16.000 18.000
.500
1-750 2.000
I 8.0 00
iiI
4E.000 4 8 .000 48 .000
4E-000
t8.000
ir
40.000 48.000 48.000 48.000 48.000
1.750 ?.000
18.0c0 18.000 18.000
li
0zzLE OD,II{
17.000 17.000 17.000
18
i,:
vEssEL
.750 1.000 1.250 1.500 1.750 2.000 .250 .37 5
1E.C00
.500 .625
18.000 1E
.00 0
16.000 16.000 18.000 18.000 1E
.00 0
1E.000
.7 50
.000 1 -250 1
1.500 1 .?50 2.000
z>u .37 5
18.000
.
'tE.000 18.000 18 .0 18 .0
.500
.625
00 00
-7 50
18.000 't6.000
1
16.00 0
't
16.000 18.000 '16.000 18.0 0 0
'| 1
.000
3
.500
3.500 3.500 3. 500 3 .500 3 .500
3.500 3. 500 3.500 3.500 4. 500 4. 500
4. 500
4.500
4. 500 4 .500
4.500 4. 500
4.500 4.500 6-62> 6 .6?5
6.625 6-625 6.625 6-625
.250
6.625 6-625 6.6?5 6.625 4.625
500
8.625
.250
.500
.750
2. 000
I E.000
48.000
-
.625 .7 to
18.000 18.000 18.000
1
.000
18 .00 0 18 .00 0
1
.500
1.250
.6?5 8 .625
8
a
.625
a.625 4.625
NOZ2LE ROT SII f II{.LB/DEG OTJTPLANE T CK,I N IIIPLA E
SID
LOIIGT
CIRCU
.3278+08 .218E+06
.109E+08
.601E+06
.200E+06
.123E+ 07
.411E+O6
.3? 5 .37 5
.215e+07 .540E+07
.718E+06
-375
- 698E+07
-375
.'192E+08
.375 .375
.375
.375 .375
.'l22E+08 .283E+ 0E .395 E +08
.7?7e+Oj
.1138+07 .2t3E+O7 .406E+0? -641e+O7 .942E+D7 -'13
2
E
+08
-88?E+04
.2948+O4
54
.2438+05
.81 08 +0 4
-154 .154 .154
.499E+05 .871E+a5 .157E+06 .282E+06
-166Er05
.493E+06
-164E+06 .2 59 E+06 .381 €+06
.154
.t
.'154
.154 .154 .154 .154
.216 .216 .216 .216 .216 .216 .216 .216 .216 .216 .237 .237 .237 .237 .?37 .237 .217 .237 .280 .280 .28 0
.280 .280 .280 .280 .280 .280 .280
.322 .322
.778E+06 .111E+A7
.372 .322
.9418+05
60Er07
.sf,?E+06
.131E+05 .362E+05 .742E+05
.437E+O4
.130E+06
-43?E+O5
.t
.205E+06 .420E+06 .733E+06 .1 168+07 .170E+07 .237E+07 . l73E +05 .478 € + 05
.121E+05 .247E+O5 .682 €+0 5 .'140E+06 .z 44E+O6
.386E+06 -567Er06 .792E+O6 .
5 78E
+04
.159E+05
.9818+05 .1718+06 .2708+o6
.327E+O5
.555E+06 .969F+06
.22tE+97
-185E+06 .321E+06 .510E+06 .7 49E+06
.311E+07 .263E+05 -726e+Os ,|
.1 05E +07 .8 78 E+04
.2428+O5
49E+06
.497Er05
60E+ 06
.868E+05 .137 e +O6 - 2El E+06 .491E+06
.153E+07
. .
2
.411E+06
.843€+06 .147E+O7
.232e+07
. 571 E+0 5
.901E+05
.477E+Ol .348Er05
.774E+06 .114E+07 .159E+07 .1 l6E+05
.9 59E + 05
.320E+05
.342E+07
.197E+06
.322 .322 .3?2
.?90E105 .4 58 E+0 5
.314E +06
.543E+06 -111E+07
.195E+07 .307E+07
.657E +05
.1158+06 .18'l E+06 .371 E +06 .6 49 E +06
.102F+07
Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-1 Continued ROTA STIFF CAICULATION, CYL. VESSEL
vEssEL TC K,I I'I
VESSEL
00,fT
0zzLE OD,I N
NOZZLE
TCK,IN STD
0
1.750
18 .00 0
2,0 00
1E.00
18.000 1E.000 18.000
18.0
't
't
I C. 750
-ol>
10
.000
18 .00 0
'1
18.C00
1.750 2.000
. 500
1E . C00
18.00c
.375 .500
1E.000 1E.000 18 .000
18.000 '16.000
't8-000 1E.000
18.000 16.000
.750 1 1
18
16.000 1E.000 .000
18
?8.000 't8.000 1E.000 18-000
18.000 't I .000
.375 .500 .625 .750 .000
2. 000
.250 .37
5
.500 -750
1.000 1.250
t.500
-250
.7 50
r .000 't -250
?-000
-
000
18.000 18.0 00 18.0 0 0 1E.0 00 18 ,000 18 .0 00
18.000
12 -750
. 169F+07
12 .750 12 .7 50
11-OOO
.750
16 .00 0 18
.'l45E+06 .2968+06
14.000 1 4 .000 14 .000 1 4 .000
.500 .62
5
.750
1 .000 1.250 1.500 1,750
14
1
6
.375
.295E+07
.9E2E+06
1E
.000
1E .000 1E.000 1E .000 I E.000
18,000 20.000 20.000 20.000 20.000 20.000 20.000 20 .000
20.o00 20.000
+06
E
+
07
-515E+a7 .7 56E+ 07 .106E+08
-5ft
-375
.37 5
6
.155E+07 .22EE+Ol .318€+07 -195E+05 .536E+05 .110E+06 .192E+O6
.303E+06 .622E+O6 .1098+O? -1?2E+07 .?52E+O7
.352E+07 .619E+05
.666E+ A6 . 105E+07
.8738+07 .J?2E+08 .7 64E+05
.127E +O6 .222E +06
.350E+06 .719 E+O6 .126E+07
.'f98E+07 .291E+07 .106E+07 .2558+05
. 210E+ 06
.702E+O5
.432E+06
.144E+o6
,755€+06
.375
+O
.225E+O5
-594E+E7
-375
-5 62E
.186E+06 .3E1E+06
.377 E+07
.375
-27 4E+o6
.67 4E+05
.2168+07
18 ,000
18.000
.577t
.326E+07
.000
18.000 1 6.000
05
.3108+06 .1P'7
.000
t6-000 '| 6.000
+
.910E+06
.375
.9948+05 .'17 4E +0 6
.161E+06
16.000 16
-129E +07
.189E+07 -265E+07 .17 6E+Os .4E4E+05
.521E+06 -E22E+o6
.9 5 4E+07
.000
16.000 1 6.000 1 6.000 1 6.000 16.000
-468E+06 .817E+06
.527Er05
.750 12.750 12 .750 12.750 12
1
tE.000
1E.000
.79LE+07
12 -750
1.5C0
1.?50
1.500 1.?50
16 .00 0
I 0. 750
14.000 't 4.000 't 4.000
1
1E.000
18-000
.568E+07
12.750
-2288+06
.387E+ 07
10 . 750
- 5648
2. 000
t 6 .000
.245E+07
.375
1E.00 0
18.000 16.000
.365
I 4 .000
1-750
'18.000
10 .750
-114E+O6
.140r+07
.000 .250
2
.403€r05 ,827Er05
.24E8+06 .433E+06
.4658+07 .683E+07
18.0C0 1E.000
.146E+05
.375
.000 .000
.000
.438 E +05 .121E+06
.683 E+06
.750
-150E+07
.210E+0?
.365
0
CIRCU
.6J08+07
.750 10.750 't 0.750
I
OUTPLAT.IE
.1512+A?
'12.750
t8.000 r8.000 18.000 18.000
.000
F IN.L8/DE6
INPLANE LONGI
.250 1.500 1.750
1E.000
tE 't 8
0.750
.500
00
18.000
.322
10 . 750
18.000 18.000 1E.000
a.ol>
ROT STI
.119 E + O? .? 44E+07 .427E+07
-252E+06 .397E+06
.8'l5E+06 -142E+O?
-674t+e7
.225E+07
-99oE+07 .'138E+08
.330E+07
.235E+06 .483 E+06 .844E+06
.785E+05 .161E+06
. 1 33E +07
- 4 44E+06
.854€+05
.?738+A7 .477?+07 .753E+07
.11tE+08
- 461E+O7
.2858+05 .
z
8'l E+06
.9t'lE+06
.159E+07 .251E+o7
.369E+07
167
168
Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULATI0NT CYL' 0DufT
VESSEL TI(TIN
3.00 0
2.000
VESSEL
1
2? -OOO
18.0 00
13.000
.500
18.000 1E,000
.750
18.C)00
18.000 18.00c 18 ,000
18.000 1b.000 18.000
OD,IN
20 .000 22 .00 0
.250
18.000
NOZ2LE
r.0c0 1.250
22.000 22.000 22.000 22.OOO
22.000
1.500 1.750
22 -000
.000
22 -OOO
2
22
.000
24.000 24.000 24.000 24.000
18.C00 18.0 00
.500
1E.000 1E.000
-750
24.DAO
1.000
1.2t0
18.000 18.00c
1.500 1.750
24.000 24.000 24.000 2/..000 2 6.000
'tE.0G0
18.000
2. 000
24 .000
1E.0 00
.250
18.000 1E.000 1E.000
5
?6.OAO
.500
26.000
- 750
I .000
26-000 26 ,000
18.000 18.00c 't8-000
1.250
.500 1.750
26.000 26.000 26.000
.000
2-000
1E-000
1E.000
1E
't3.000 18.000 18 .000 1E.000 18 .000 16.000 13.000 16.C0C
18.000 't8.000 18.C00 18.0U 0
16.000 18.000
.37
.625
1
.?50
28 .000
.500
E.000 28.000
.625
2E-000
.750
28 .000
.000 1 .250
28.000 2E.000
'I
1.500 'l ,7 50
?.000
.250
.375 .500
28.000 28.000 28.000 30.000 30.000 30.000 30-000
.750 .000 .250
50.000 30.000 30.000 30.000 30.000
2.000 .250
30.00 0
.500
32.000
18.000 18.000 16.000
18.000
18.000 18.00c 18.000 1E.000 18 .000
1
16 .00 0 18.00 0
1
t6.000
26.000 2
18.000
18.000 18.00c 16.000
26.OOO
1
.000 32 .000 3 2
.625
3? .OOO
.000
32 .000
.250
.500 1-750 2 .000
32.000
3 2.00 0 3 2 .00 i:J 3 2 .000
32 .000
VESSEL
f IN.L8'/DEG TCX,IN TNPLANE OUTPLANI CIRCU LONGI SID
NOZ2LE ROT STt
.375 .15 5E + 08 -375 -944E+05 -375 . ?60E+06 .375 .5348+06 .375 .933 +0 6 .375 .1478+O7 .3ZS .3OZE+07 .3?5 .528E+07 .3?5 .8 33E + 07 .375 .122E+08 .375 .171E+08 .375 .103Er06 .375 . 285 E+ 06 .375 .585E+06 .375 . 102E+07 .375 .161E+Ol .3?5 .331E+07 .375 - 578E+07 .375 .91?E +07 .375 .134E+08 0E -375 . 1872 E+ -375 .1t E+06 .375 .3',10E+06 .375 .636F+06 .375 -'l11Eto7 .375 -115E +O7 .3?5 -3608+07 .3?5 .629E+07 .375 -992a+O7 .375 .146€+08 .3?5 .204E+0E 06 .375 .122E++06 .375 .33 5E -375 .667E+06 .3?5 -12o8+oz .375 .139E+07 .375 .5898+07 -375 .1C7E+08 .375 '679E+Q7 .375 .1 58E +08 .375 .220E+03 .3?5 ' l31E+06 .375 .360E+06 6 .3?5 .7 3E Elo .375 .1298 +o7 -3?5 .204e +A7 .375 .4'l8 €+ 07 -375 .730 E+ 07 .3?5 .1 1 5E+08 .375 .169E+08 .375 .236E+08 .375 .1169 + 06 .375 .3R5€+06 .3?5 .790€+06 -375 - 133 5+0 7 .375 -?18E+O7 .375 -4t ?E+O7 .375 .760E+07 .37, .123E+08 .375 .181E+08 -375 .253E+o8 F
.515€+02 .3'l5E+05 .867E+05 .178E+06
.311Fr06 .491E+06 .101E+07 .17 6E+07
.2788+07 .408E+07 .570E+07
.345€+05 .950E+05
.'t95E+06 .3418+06 .53EE+06
.1'l0Ei07
.1938+07 .304E+07
.447E+07 .624E+O7
.3758+05 .103E+06 -212E+O6
.371E+06 .585E+06 -120E+07
.2'l0E+07 ,331E+o7
.486E+07 .679t+O7 .405E+05 .1128+O6 .229 E+06 .400E+06 .631E+06
.'l30 .22
E+0 7
6E + O7
.357E+07 .5?5e +o7 .733e+O7 .435E+05
.120E.06 -246E+06 .430E+06 .678E+06 , tJ9E+07 .243E+O7
.3E4Er07
.564Er07 .788e+07
.465E+05 .'128E+06 .263E+06
.460E+06 .7?5E+o6
.149Er07 .260E+D7
.4'l0E+07 .603€+07 .E12E+07
Vessels Rotational Nozzle Flexibilities for Cylindrical Table 6-1
Continued ROTA VESSEL
0D,rT 'tE.000 18.000 't
8
.000
18.0CC
1E.00c
tE.00ri 18.006 't 8.000 18.000 1E.000
18.000 18.000 18.000 1 8.000 18.000 18.000 16.000 't8.000 18 .00 0
15.C00
16.0c0 16.000
16.000 18,000 16.000 18.000 18 .000
18.000 16.000 18.000
STIf'
NO2ZLF
VE SSEL
OD,IN
TCK,IN
.250 .375 .500 .625 .? 50 1 .000 1 .250 1-500 1.750 2.000 .?50 .375 .500 .625 .75O 1.000 1.250 I .5OO 1 .7 50 2.000 .250 .375 . 500 .625 .750 't .000 1 .250 1.500 1 .750 2.000
CALCULATION'
36.000 36.000 36.00 0 36 - 000
6.000 6.000 36.000 36.000
3 3
36. ooo
6.000 40.000 /.0.000 40.000 40.000 40.00o 40.000 40.000 40.o0o
3
40 .000 40 -000
4E.ooo
48.000 48.000 48.000 48.000 48.000 48 .000
48.000 4E.000
48.000
CY
L.
VESSEL
NOZZLE
ROT STI
TCK,IN
INPTANE LONGI
slD
-375 -375 .375 -175 .375 .3?5 -375 -375 .375 .375 .37t .3?5 .375 .375 -375 -375 .375 -375 .3?5 -375 .375 .375 -3?5 .3?5 .375 -375 -375 .375 .3?5 .375
f
It{.LB/DEG
.158Er06 .434t+06 .892E+06 .156E+O7
.2468+07 .504E+07
.8El€+07 . 1f9 E+ 08
.204€+08 .285E+08
OUTPLANE
CIRCU
.525E+05
.115E+o6 _297E+O6 . 519 E+06 .819 E+06 . 168€ +07
-2948+07 .463E+07 .681E+O7 .951E r07
.176E+06
.586t+05
.484E+06 .99481 06 .17 4E+07
.f31E+06
.271E+07 -562E+O?
.9a2E+o7 .155E+08 .?28E+0E
.3135+08 .212E+06 .584E+06 "120E+07
.16',| E+06
.579F+06
.9.13E]06 -187E+o7
-327E+A7 .5168+O? -759'-+o7 .106E+08 .706E+05 -195E+O6
.209E+07
.399E+06 .698E+06 .'110E+07
.678E+07 .118E+08 .187E+08
.395Ef07
.330€i07
-226E+O7
-623E+O7
.383E+08
.9'l5E+07 .128€+06
.858E+04
.286E+04
.4t6Et05
.1628+05 .283F+05
.275€+08
rt,
2 -375
19.000
2 -375
19-CC0
19.000 19.000 't9.000 19 .000
19.000 19 .0
00
19.000 19.000 19.000 19.000 19.000 19.000 19.000 19
-
000
19.000
'19.000
19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000
.500 .625
2.375
.000 1.250 1.500
.500
2.375 ?.375 2.375 2.375 2.375 3.500 3.500 3.500
1.0c0
3.500
't
1.750 2.000
'l .250
.5c0 1-750 z-000
't
.250 - 500
3. 500
f.
500
3.500 3.500 3.500 4-500 4 .500 4. 500 4
.500
4.500 1
.000
1.250 1.500 1.750
4. 500
4.500 4. 500 4
.500
-154 -151 .'t54 .154 -154 .154 .154 -151 -154 -154 -216 -216 -216 -216 -z'16 .216 -216 -216 -216 -216 -23? -237 .237 -237 .237 .237 .237 .237 .237
-237E +o5
.78E E+04
.848E+05 .134 E + 06
-446E+0j
-275e+o6 .4808+06
.757E+ 06 - 1'l1E+o7
-155ErO7 . 128 E+05
-3528+05 -722E+O5
.915E+05 .160 E +06 -ZSZE+O6
-371E+O6
.5'188+06 .426F+O4
.117€+05
.241E+O5
.126E+06 .199E+06 -409E+06 -714E+o6
_42.1E+O5
- 166E+07
-5528+O6 -771E+o6 .563E+04
.113E+07 .231E+Oz
' 169E+05 .465E+05
.9 55 E+05
.167E+06
-2638r06
-6648+O5
.136E+06
.2388+06 .375E+O6
.155E+05
.318 E +0 5 .556E+05 -8778+O5
-
.180E+06
-119E+O7 -219E+O7
.196ErO6 .7292+o6
540€+06 -94f, E+ 06
.31 4E+06
Table 6-1 Continued RO]A STIFF CALCULATION, CYL.
VESSEL TCK,IN
vEss€L OD,FT
NOZZLE
NOIZLE
OD,!N
TCK,IN STD
19.000 19.00 0
19.000 19.000 19.000 19.000 19.000 't9.000 19.000 19.000 19 .00 0
19.000 19.00c 19.000 19.000 19.00 0
19-000
:l
2. 000
.250 .37
n
.750
19.000
19
10 .7 50 10 .750
5
1
.7 50 'l
1.750
2.000
.000
19.000 t 9 .000 19 . C00
19.000 19.000 19.000 19.000 9.00
.625 1 '1
19.000 19.000 19.000 19.000 19.ai00
.500
z. 000
.500 ,7 50 '|
.000
1.250 1.500
.3?2
.322 -3??
10.750 10.?50 12.750
12.750 12.750 12 .750 't2-750 12.750
.365
1
.5538+07 .5138+05
-375
.5i7E+o6 .800Ei06
.1648+ A7 .247E+07 .452E +07
.665E+C7
.9298+07 .568E+05 .157E+06
14
.32'l €+06 .561E+06 .885E+06 .132E+07 .317 E + A7 ,501E+07
.000
14.000
1
6.000
't
6. c00
16.000 6.000 1 6.000
t
.7 36e+07
.5 r>
.000
16.000
2. 000
.111E+A6 .290E+06
4.000 14.000 14.000 14.000 1 4.000 14.000
.7 50
1.500 1.750
.422E+06 .665E+06 .137 E+07 .?39E+07 .3768 +07
1
16.000 16.000
1.25A
t t8E+06
12 -750
c25
.000
.108E+07 .189E+07 .299E+07 -4398+07 .6118+07 .427E+05
-772t+Ol
12.750
16 .
.52EE+06
.241E +06
12 -750
.?50 .500
.934 E+05
.
0.750 10.750
t4-000
'l9.00 0 19 .000
.332E+07 .464E+07 .339E+05 .192E+06 . 3f5 E+06
't
1 4.00 0 1 6 .0C0
19.C00
.400E+06
.'143E+D7 .2 26E+ 07
10 .7 50
10 . 750
-855E+04 .236E+O5
.2E0
.322
.375
-375
.
NE
.1O?E+O7
.821Ei06
.322
A
CIRCU
.256E+Os
260
.280 .280 .280 .322
OUTPL
.3068+07 .7olE+C5 .145E+06 .253E+06
.280 .?80
0. 750
't -750
2. 000
9.000
19.000 19.000 19.000 19.000 19.000
.000
1.750
0
19.00 c
.280
'12.750 .500
19.0c c
1
.500
.600
19.000 19.000
'|
.000
1.250
19.000 19
8.625 8.625
.37
19
1
.6?5
3.625 'l0.750
.500
.000 't 9 .000
a
SII F IN.LB/DEG
INPLANE LOt./ GI
8.625
.000
.250
ROT
8 -625
t .0c0
.000
19 ,000
_
8.625
2
19.000 19.000
-625
6.625 6.625 6.625 a .625
.?50
19-C00
t9.0cc
.28 0
6
1.250 1.500 1.750 2.000
't.250 1.500 1.758
19.000 19.000
-625
6.625 6.6?5
.000
19.000 19.000 19.000 '19
-2E0
6
.75A 1
'19.000 'l
5
.500
4.500 6.625 6.625
VESSEL
tC3t+08
.484€+05 .845E+05 .133E+06 .27 4E+O6 .47EE+06 .7 51E +O 6 .111E +07 . 155E+07
.1t3E+05
.3'l l E+05 -
639E+0 5
-112F+06
.1 76E+06
.561E+06 -631E+06
.996E+06 .146E+C7 -204E+C7
.142ErO5
. 392 E+0 5
.805E+05 -141E+O6
.222E+06
.455E+06 .79
5 E+o 6 - 125E+O?
.'184E+oz
.257€+07 .17'l E +Os .171E+O5
.968Er05 -t69E+06 -267ErO6
.5 47 E+O6
.956E+06
.15t E+07
. ?22E+A7
.310E+07
.'189E+05 .522E+O5
.1078+06 .'l t 7E+o6 .295E+06 .606E+06
.106E+07 .1678tO7 .245E+07 .313E+07
.656E+05 .1E1E+06 .371E+06
.219E+05 -602E+05
6IEE + C6
.216E+O6
.102E+07 .21OE+07 .367 E+07
.341E+06
.850E+07
-2838+07
-
.578F107
.'l
19E+ 08
,'12
4 8+O
6
-699€+06 .122E+a7 .193E+O7 .39 6E+Ol
Rotational Nozzle Flexibilities for Cylindrical
Vessels
171
Table 6-1 Continued ROTA STtFF VESSEL
OD,fT
VESSEL I€KTIN
.375
19.C0C
1
.750 ,0c0
19.C00
'1
.?50
19.000 19.00c
1.750 2.0c0
19.000 19.000 19.000 19.000
.375
19 ,000
19. 000
E,000
18.000
-3?1E+07
.7 648+O5
20 .000
.229 g +O6 .470E+06
.25U
20.co0 20.000
.82'l E+06
.5O2E+07 .306E+05
19 .000
.500
22.000 ?2.000
.000
22 .OOO 24 .000
.520€+06 .9cBE+06
.173E +O6
.3038+06 -980E+06
2+ O7
.1718+87 -270E+O7
.3978+A7 .555E+07 .336E+05 .925s+05 .190E+06
.532E+06 -523E+06
.322E+07
.107E+07
.250 .500
24 -000 24 .000 2/, -000
.8E8E+02 .131E+08
.?9 6E 107
.7 50 2. 000
.500 -625
19.000 19.000 19.000
1
19 .00 0
't
.000
21 .OOO
26 .000
26.000 26.000 26.000 26.000 26.000 26
1.500 2
'19.000 19 .00 0
26.000 26.000
.608E+07
.109E+06 .302E+06 .619 E+ 06
.365Er05
.101 E+06
.'17'l E+o7
.569 E+06
.108Er07 .
j508+07
.6'l2E+O7
.965E+07
.206E+06 .3 61 E+06
J17E+A7
.204E +07
.322E+A7
.198E+08
.118Er06
.473E+07 .6618+o7 .394t+O5
.500
2E.000 28 .000
-326E+06 .669 E +06
.223E+06
.7 50
28.000
.0c0
28.000
.1 42€+08
28.O00
.117E+O7
2E.000 2E .000 28 .000
. 184€+07
1.750
28.600
.?50
30.00 0
.127E +06
'1
.435E+07
.'tE2€+08
-378E+07 .6 6'l € +07 - J 04 Er08 .1 53E+0E
1
.188E+07
26-000
.7 50
-250 .375
r9.000 19.000
.000
.563€+07
.000 .250
I .500
28.900
.2'l4E+08
I
.844E+05
.478Er06
-157
I I
.155E+07 .2448+07 .359E+07
-?94E+07 -514E+07 .811E+07 .119E+08 .'t 66E+08
?4.OOO 24 .000
*'l
E+06
. 143E+07
.10'l E+06 -ZtZE+46 .5708+06 .995E+06
24.000
7
24.O00
19 .00 B 19 .00 0
19.0 00
't
24.000
.000
19 .0C0
19.000 19.000 19.000 19.000 19.000
.
.7 50
19.000 19.000
19.000 19.000
22 -00 0 22 .000
1
0
19.000 19.000
.27qE+o6 ,432E+06
.108E+08 .150E+0E .919 E r 05 .253E+06
.2 50
19 .000
19.00
.157ErA6
20.000 2 0.000 22.000 22.000
20 .000
'I
.500
.449E +07 .277E+O5
.465E+ 07 .733E +07
-000
19.000 19.000 19.000
.219E+O7
20.0c0
22.000
250
.1 39E+0 7
.88
-?50 1 .000
-
.;93 E +06
30E+07 -2668+07
.625
2
.248E+05 .683E+05 .140E+06 .245e+O6
.9 61E+07
.ll5E+08 .831E'05
1.750
CIRCU
18.000
.000
19.O00
.421E+O6 .735E+O6
OUlPLANF
1t.000
.500
t9 -00c 19.000 19.000 19.000
.205Er 86
l8 .000 20.000 20.000
19.000
.0c0
.743E+05
.6568+07
.000
19.000
TCK,IN TNPLANE LONGI STD
.lE6E+06
t 8 .000
22 .000 22 .000
C
NOZZLE ROT STI T IN.LB/DEG
t 8 .800
-75n
19.000 19.000 19.000
VESSEL
.116e+D7 ,238E+07 .416E+Qz
18.000
20 .000
19 .0C
'| 9
1
1.000 J.250 1.500 1 .750 2.000
9.000
19
OD,III
ION' CYL'
'l .500
.500
.000
9
't
19
NOZ?LE
1E.000
19 .00 0
't
LCULAT
l8 .000
19.006 't9.000 19.000 'r9.000
19
CA
.109E+06 .390E+06 .615E+06 .126E+O7
.220F+07 .348 F+07
.5119+07 .714s+C7 .424E+Ot
It/
172
Piping Stress Handbook Table 6-1 Continued ROIA
VESSEL OD,FT
TCK,IN
00
19.000 19-000
19,000
r9.000 19.000 19.000 r9.000 19.000 19.000 19.000 19.000 t 9 .000
'19.00c
19.000 19.0c0
'19.000
19.000
t { il
'19.000
.500
30.000 30.000
.6?5
30.00 0
.750
I .000
1.25C
1,500
1.750 2.000 .250 .375 .500 .625 .750 1 .000 1.250 1-500
1.750 2.000 .2so
19.000 19.000 19.000 'r9.000 19.00c 19.000
't
19 .00 0
I .500
19.0C0 19 .00 0
19.000 19.000 J9.000 19.000 19.000
.37 5
.500 1
.000
.250
1.750 2.000 .3?5 .500 .6?5
19. 00 0
.000
J
-
9.C00
19.000 19.000 19 -000
19.000 19.000
.500
.750 2.000
19 .0 00
r9.000 19.000
.625 .7 50
'19.000
.000 .250 .500
19.000
t9.000 19.000 19.000 20.000 20.000 20.000 20.000 20.o00 20.000 29.000 20.0c0 ?0.000 20.000
250
.75A
2.000
.250
.375 .500
.625 . 750
I .0c0 1 -250
.750 2.000 1
.37 5
.375 -375
30 .00 0
.375
30 .00 0
-375
30.000 3
0.00 0
30-000
30.000 3?.000 32 .000
32.000
32 .00 0
32.000 32.000
52.00 0
f2 .0c0
52.00 0 32 .000
36.000 36.000
36.00 0 36 .00 0
.750
CtL. VESSEL NOZ ZLE ROT S'I' IN.L8/DEG TCK,I N I NE OUTPLAiIE '{PLA STD LONGI CIRCU
CAI-CULATl0lrlr
VESS€L
19.00c 19 .0
STIff
36.000 36.000
56 - 000
6.000 36-000 36.000 40.000 40.000 40.000 40.000 40.000 3
40
.000
40.000 40.000 4
0
.000
.375 .37 5
.375 .375 .375 .375 .375 .375 -375
.375 .375 .375 .375 .37 5
.375 .375 .375 -375 -375 .37 5
.375
.375 .375
40.000 4E.000 4E.000 48 .000
_37 5
4E.000
.5t>
48.000
48.000 4 8 .000 48 .000 4E -OOO 48 .000
2.375 2.375 ?.375 2.375 ?.375 2.375 2.375 2.3?5 2.375 2
.3?5
.350E+06 .7198+06 .1268+07 .198 E+07 .4O7E+07 .71Oa+07 . I 12E+08 .165E+08
.117E +O6 -24OE+06
./,19€+06 .660E+06 -136E+o7
.237E+07 .373E+07
.230E+08
.549E+O7 .767E+O7
-136E+O6
.453E+05
.374E+06 .7 69E+ 06
.134E+07 .21?E+07 .435E+07 .7598+ 07 .1 208+08 .17 6E+OE .2468+0E . t 55E+06
.42tE+O6 .66E
E+
06
-152E+07 -239E+07 .491e+ 07 .8 58 E +07 -135E+08 .'199E+0E .2?8E +08
-125E+06
.256E+06 .448E+06
.7068r06
.115E+O7
.253E+07 -399E+O7
.587E+O?
.820E+07
.5t1Er05
.141E+O6 .289 E+06
-505E+06
.797E+O6 -1648+O7 -Za6E+07 .451E+O7
.171E+06
.663e+07 .926E+07 .570E+05 .157E+o6
-967e+O6
-322E+O6
-267 E+O7 .5 47 a107
.889 E+06 .1828+O7
-171E+06
.169E+07 .956a+07 . 151E+08
.222E+08 .310€+08 .206E+06 .5688+06 -117E+Ol .204E+07 .321E+07 .660E+07 .115E+08
.5638+06
.3198ro7 .5038+07 .7398+O7 .103E +08
.687E+05 .1 89 E+06
.369 E+06 .679 ar06 -1O7E+07
.?67E+08
.220E+07 .384e+A7 .606E+07 .891E+07
-3?3e+DB
.124F-rOE
.1 54
. 837 E+ 04
.279E+O4
-154
.231e+O5 .473p+O5
. 768 €+04
.s75
.154 .154
.182E+08
.8278+05
.1 54
.130E+06
.154 .154 .154 .154 .154
.268€+06 .468 E+06 . 73E
E
.'108
E
+06 r 07
.1 5l E+07
.1 5E E+05 -276E+O5
.435E+05 .892E+05 - I 56E+06 -246E106
.362E+06 . 50 5Ef06
Rotatlonal Nozzle Flexibilities for Cylindrical Vessels
'173
Table 6-1
Continued ROTA STI f VESSEL
OO,FT
20. c0c
NOZZLE ODZIN
V€SSEL ICK,IN
.500
3.500
20-000
,500
3. 500
2C.000
-7 50
5. 500 3-500
20-000
.500 1-750
2C.000
.250
4.500
2C,000
.500 .6?5
4.500 4.500 4.500 4.500
?0.000 20.000 20.000 20.000 20.000
.000
20,000 20.000 2C-000 2C.000 2C
.000
2A.O00
20.000 20.000 20.000 20,000
4. 500
1
,000
't.250 .500 1-750
't
.500 4-500 4 .500 4
2.000
4.500
.500
6.6?5 6.6?5
,250
6 -625
-750 .000 .500
2C.000
2.000
26.000 20.000 20.000 20.000 u 0.000 20.000
.500 .500
3 3
.375
20 -0 00
20.060
3.500
3 -5AO
20.000 2C.000
3.500
2. 000
20,000 20.0c0
.7 50
6.6?5
6.625 6.625 6.625 6.625 8.625
.500 .750
E.625 I .625 E.625
- 000
.625
2C.C00
.250
20 .000
1.750 2.000 .250
10 . 750
- 500
'1o.750
20.000
20.000 20.000 20.0c0
8 8
- 500
20.c0i.J
20.000
a
.625 .625
8.625
'to.?50 1
0. 750
10 .750
20.000 20.000
.000
1
20.00iJ
.5C0 .7 50
19.750
20,000 20.000
20.000
2
.000
2C.000
.254
20 .000
.500
20.000 20.000 20.000 2C.000
20.000 ?0.000 20.000 2C.000
0.750
10 .750
1A.750 0. ?50
1
12.750
12 -750
.7 50
.000
't?.750 12 -750 12 -750
.500
12 ,750 12.750 12 .750
.2-50
14
.750 2-0c0
NOZZL€
TCK'IN STD
3
20.000
CALCULATION,
F
.000
CYL.
VESSEL
F IN.LB / DEG OUTPLANE INPLAN€ CIRCU LONGI ROT STI
.216 .1246+o5 .2'16 -3438+05 .2'16 .791'5+05 .?16 -123t+o6 .216 .19/+E+06 -216 .398E+06 .2'16 .696E+06 07 .216 - 'l 10 E++O7 .216 .161E .216 -?z5E+O7 .23? . 164E+05 .237 .153E+A5 -237 .9f l E+05 .237 .163E+06 ,237 .256E+06 .?37 .526t+O6 .237 .920€+06 -237 .145E+07 .?37 -?138+07 07 .237 .298 € ++C5 .25OE .?ttl .2E0 .689E+05 .280 .14'1E+O6 .280 -?47E+06 .280 .390E+o6 .280 .800E+06 -2E0 .140E+07 -280 -220E+07 .280 .3216+A7 .2EO .152E+07 -322 . j30E+05 .32? .910 E+ 05 .322 . t87E+06 .3ZZ .326E+06 _3ZZ .515 +06 .32? .106€+07 .32? . 185F+C7 .322 -291 E+o7 -3zZ .4288+C7 .3?z .598 E+07 .365 .416F-+O5 .36t .1 155+06 .365 .Zj5E+06 .365 .411E+06 .365 .643E+06 .365 -133E+Q7 .365 .233E+O7 .365 .367E+D7 .365 ,.539€+02 .365 .753E+07 .375 .,DgE+05 .325 ..t 38 E+06 .375 .?83Ef06 .375 .4E4E+O6 .375 .7S0E +06 -375 . 160E+07 .37, .280E+07 .375 -41'lE+O? .375 .648E+07 -375 .9 05 E+07 .375 .5 54 E+ 05 E
.4
15E+O4
.114E+05 .235E+05 .410E+05 .647E+05 .'133E+06 .23?E+O6
.366E+06 .538E+06 .751E+06 .548E+04
.'l5'l E+05 .f10E+05
i,i
.542E+05 .855E+05 _1ZSE+O6
.307E+06 .484E+06 -7118+O6
.993E+06
.6 33E +0 4
.230E+o, .171E+A5
.3239+05 .1 30E+0 6
.267 E+O6
.4666+O6 -735E+O6 . 108E+07
.1519+07 .110E+05 .303E+05
.62jE+05 .'l 09 E+06 .17 2E+o6
.3SZE+46 .616E+06 .971E+06
.143t+Oz
.199E+07
.139E+05 .3E2 E+0 5
-784E+05 .1378+O6 .216E+O6 .4 44E+o6 .7?SE+O6 -122E+O7
.180E+07 .251E+O7 .161E+D5 .459E+05 .943E+05
-1658+06 .260F+06 .533€+06 .932E+06 -147E+O7 -?16E+O7
.302E+O7 .185E+05
u
174
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCUIATION, CYL. VESSEL V ESS
VESSEL ICK,II{
EL
OD,FT
20.000 20.000
.375 .500
20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
.7 50
2C.000
20 -000
20.000 20.000 20.000 20.000 20.000 2
0.00
-625
t.000
1. ?50 'l .500 1
"750 2.000
.750 1 .000 1-250 1.500 1
-750
2. 000
.500
-750 2.08O
20.000
1.250 1.500
.625 .000 .25A
.500
- 500
.7SO 't
2C.000
20.000 20.000 2U.000
20.000 20.000 20.000 20.000 ?0.0c0 20.000 20.000 20.000 20.000 2C.000
20.000
.000
1.750 2.000 .250
2ri.00G
?0.000 20.000 20.000
NOZZLE ROT STIF IN.LB/DEG
TCK,IN IfuPLANE STD LONGI
14.000 14 .000 14 - 000
14.000 1 4.000 .000 14.C00 14
14.000 t 4 .000 16 .000
16.000 16.000 16.000 16.000 t 6 .000
16.000 1 6.000 16 -
.663E+06
-375
.309E+07 .4888+07
.375 .375 .375 .375
.37 5
.375
.500 .7 50
.000 1-250 1.500 1-750 2.000 't
.250 .500 .7 50
.000
18 1
.375
20.000
.587E+05 -121E+O6
.632E+06
.211e+06
.205E+07
.332€ +0 6 .6E2E+06
.357 E+07 .5 64 E+ 07
-137E+O6 .239 Et0 6 .377 E+06
.l'13€+07 .2328+O7
.405E.07 .639Er07 . 131€+08 .Et0€+05
4E
+
07
.'ltJ5E+08
.5078+06 .885E+c6 .140€+07
.'t 62F+08
.9t2E+C5
?4.LOO
.27OE+A6
24.OOO
.555F+06
24.000
.500
2. 000
24 ,000
24.000
26.000 z6.ooo
.37
5
.970E+06 .153E+07 .314E+07 .519E+Oz .E66E+07
,127Er08
.375
-313E+Cz -
437E+O7
.270E+05
,864€+06
-79OE+07
24 .000 24 -LAO
.135E+07 .213E+o7
.259E+ o?
.'116Fr08
24-000
.773E+O 6
.7 41E+ 05
.237E+07 .501E+07
22.000 22.000
.666F+05
-223E+06 .45E€+06 .601E+06
.247E+ A5
22 .000 ?2 -OCO
.386E+07
.410E+06
.E96E+05
22.000
-276E+O7
.242E+O5
.147€+08
22.OOO
.119E+07 .188E+07
.725E+05 .200E+06
.71
.375
E+0 7
.213€r05
6E + A6
.453:+07
?2.000 22.000 22.AOO 22.AOO
.17
.334
-3628rD6
.126E+07
.3-t5
.t03E+07
.100E+08 .639E105
-9 39E+47
.37 5
20 .000
20.000 20.000
z4 .ooo 24 -OOQ
.750
375
.000
20,000 ?0.800 20.000 20.000 20.000 20.000
-718E +07
.163E+07 .239e+07
. 716 E+06
.000
I .000
.590E+06
.ll6E+0E
-
.182Er06 .288E+06
07
7 E+
.629E+07
.000
I 6.000
.17
.996Er06
t 8 .000 1E
.547E+06
.375 .375
000
t 8 .000
. 508 €+0 5 . l04E+06
.313€+06
18.000 16.000 18
OUTPLANI CIRCU
.153E+06
I E.000
?0.000 20.000 20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
20.0c0 20,000 20.000
OD,IN
'16.000 . 500
0
20.jco
NOZZL€
. 1 78E+ 0E .1o7E+A6 .291E+06
.153E+06 .2 6?E+06
-421E+o6
.1j'lE+07 .238E+07 .350€+07 4g9E+07 .299E+05 .323E+05
"
.169E+O6 - 295E+o6
.466E+06
.9t6E+06 -167E+o7 -263E+07
.387E+07 .5 4'l E+o7 .3?7E +o5 .902E+05 .'t 85E+06 .321E+06 .510E+06
.105E+07 .1E38+0 7 .289 E +O7
.424E+07 .592E+07 -356E+05
.980€+05
Rotational Nozzle Flexibilities for Cylindrical 'liable 6-1
Continued
SIITF CALCULATION, CYL. VESS€L NOZ ZLE ROT SlI f IN.L8/DEG VESSEL NOZZLE OUTPLANI TCK,IN INPLA}JE TCK,II'I OD,]N CINCU LONGI SID ROTA
VESSEL
0DrFT
2C.000
20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20 .00c 20.000 20.00c 20.000 20.0c0 20.000 20.0c0 20.000 20.000 20.000 ?0.000 20.000 20.0c0 20,0c0 20.000 20.c60 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000 20.000 20.000 20.c00 20.000 2C.000
20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 2C.000
20.000 20.000 20.000 20.c00 20.000 20.00c 20-000
20.0!0
20.000 ? 0.000 20.000
26.000
.500
26.0C0
26.000 26-000
1-000
26.000 26.000 26.000 26.000
1.250 1- 500
1.750 2. 000
2E.000 2E.000
.375 .500
28.000 28-000 2E.000
.7 50
28.000
.000
28 .000
28.000 28.000 2E.000
2.000 .?50
10.000
.625 .750
30.000 30.000 30.000 30.000
30. 000 30.00 0
t .000
1.250 I .500 1.?50 2.000 .500 .6?5
1.000 1.250 1.?50 2.000 .250
50 .000 30. 000 30
.000
32.000 3 2 3
.000
2.000
32 .00 0
32 .00 0 32 .000
2.000 32.000 32.000 3
r2.000 56.000 36-000 6.
.500
3
.7 50
36-000
't.500 I .750
3 6 -000 36. 00 0 36 -000 3 6 .000
.625 1.000 I .250
2. 000
.250
.500 I .000
1.500 1 .750 2.000 .250 .37
5
.500
COo
56.000 36.000
40.000 40.000 40.000 40.000 40 .00 0 40 .000
40.000 40.c00 40.000 40.000 4E.000
48.000 48.000
.375 -375 .375 -375 -375 .375 .375 .375 .375 .375 .375 -375 -375 .375 -375 -375 .375 .375 .375 .375 .3?5 -375 .375 -3?5 .3?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .3?3 .375 .375 .375 -375 .375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375
.604E+06
-201€+06
.166E+O7
.555ErC6 .'l11E+o7 .1998+07
.1658+07 .341E+07 .597 E+o7 .941E+O7 . 'l38E+08 -'t sf E+06 - 115
E
+06
.318E+06 .652E+06
.352E+06
.314E+O7 .461E+O7 .644E+O7
.384E+05 .'106Et06
.1148+o7
.217E+06 .380 E +0 6
.',|E0E+07
. 599 E+06
1F''f
.123t+o7
-644E+A7
.102E+08
.2152+07 .339E+07
.1 49E+08 .209€ +08
.696E+O7
z AA
E
.',1?4E+06
.341€+06
-498E+O7
.413E+05 .1148+06
.701E+06
.234E.06
- 12ZE+07 . ',l93E+ 07
-40E8+06 -644E+o6 .13? E+0 7
lOAc.a\7 -6928+07
.1098+08 . i 6iE+08 .224E+O8
.1328+06 .365E+06
.?3'l
E+O7
.364E+A7 .535E+07 .7 47E+O7 .441 €+05 .1?2E+O6
.719E+OC .13',1 E +07
.2 50E+06
-zo6E+07
.688E+06
.7 4OE+07
.217E+07 .389E+07 .57?E+07 .799E+07 .499E+05 .1378+06
.424t+07
.1178 +08 .17?E I oE .240E+08 . l50E+06 .112E+O6
.8 46 E+ 06
.118E+07 -233E+07 .479E+07 .E36E
r07
.132E+08
.'l948+0E .271E+O8 .1 67 E+ 06
.459E+06
.943E+06 .165E+O7
.436E+o6 .141e+O?
.282E+06 .4938+O6 .777s+O6 . t 608r07 .279 E+a7
.44OEr07 -646Er07 .90?€+07 .556E+05 .153E+06
.3148+06 .549E+06
.260E+O7
.E668+06
.533E+07
.'178E+A7
.9328+07 .147Er08 .2'l6E+08
.72OE+O7
.302E+08 .201E+06 .554E+06
.114Er07
.311E+o? .490E+A7
.101€.0E
.670 E+0 5
.185€+05 .379 E+06
Vessels
175
176
Piping Stress Handbook Table &1
Continued ROTA STIFF CALCULATION, VESSEL
OD, FT
20.000 20.0c0 20.000
20.0cc
20.000 20.0c0 20.000
vEssEL TCK,ll{ .625
ilozzLE
OD,Ill
48.000 .000 48 .000 48 .000 4E.000 4E.000 48
I .000 1
.250
1
.500
I .759
2.0c0
48.000
CYL.
VESSEL
ZLE RO' STIF IN.LB/D€G T{ INPLA'.IE OUIPLA}IE SID LOI{GI CIRCU
NOZ T
CK,I
.375 -375
- 199E+07
.313Er07 -643E+07
.1128+08
.177Er08 - 261
E
+08
.364E+08
-662E+O6
.1C4E+07 -214E+07
.3748+o7 .591E+07 .868 E+07 . 12t E+08
Pressure and Stress Ratios
By merely multiplying or dividing, P/S ratios may be used to readily determine: Ferritic Smls Temperature (Carbon and AlloYs
l.
Allowable working pressure 2. Working stress 3. Wall thickness required
900 950 1,000 1,050 1,100
This extreme simplicity arises because in the formulas devised to predict the stresses in a pipe under internal pressure, the P/S ratio may be equated to a quantity that is dependent only on the diameter and thickness of the pipe and the applicable allowance for threading, mechanical
D-2y(t -A)
.4 is known as the "modified lame" formula. In Sections 4 and 8 of ANSI 831 the Barlow formula is used, which is a special case of the general formula in which y 0. kr addition, Section 8 is based on nominal thickness rather than minimum thickness; the tabulated P/S ratios for y = 6 tut 6" placed on a nominal wall basis by mul-
:
as:
2(t.
:
tiplying by 8/7. Tables 7-1 through 7-4 give the precalculated values
=
t : A: D: y :
for
the right-hand side of the preceding general equation for each pipe size and weight based on a wall thickness 87Uz% of nominal and for values ofC varying from 0.0 to 100 in. in increments of .005 in. For any pipe size, wall thickness, and corrosion allowance the allowable working pressure is found merely by multiplying the P/S ratio by the allowable stress. Obviously, this relieves the designer from making annoying multiple arithmetical manipulations which might be subject to error.
lbs/
in.2
Ss
0.7
=
- A) D-2y(t.-A) where P : Maximum internal service pressure, P/S
o.7
The y value in the general formula reflects the effect of creep at high temperatures. In some ANSI Code sections that do not cover temperatures over 900'F, the y value of .4 is directly inserted in the formula; the formula with y
2SE(t--A)
This formula may be written
u.) 0.'l 0.7
strength, and/or corrosion. The general formula, adopted by the ASME Boiler Code in the section on power boilers and the ANSI Code for Pressure Piping is:
D_
0.4
Austenitic Steels (Cr-Ni stainless, such as Types 304, 316, and 347) 0.4 o.4 0.4 0.4 0.5 0.7
Allowable stress in material due to internal pressure Minimum pipe wall thickness, in. Allowance for threading, mechanical strengih. and/or corrosion, in. Outside diameter of pipe, in. Coefficient having values, as follows:
(Text continued on page 250.)
177
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Pressure and Stress Ratios
249
250
Piping Stress Handbook
Tbbles are presented
y y y y
for four values of y:
: 0 @arlow) : 0.4 (Modified lame) = 0.5 (Average diameter) : 0.7 (Creep)
3. The following two solutions can be used to determine the maximum allowable working pressure perCtable
7-l)
(lable 7-2\ Clable 7-3)
missible.
r
(table 74)
Ushg the design formula from the ASME Code, Section VItr, Division 1, 1983, and the symbol definitions contained therein:
SEt
P: Instructions and Examples
Example 1: Determining Allowable Working Pressure Determine the maximum allowable working pressure in accordance with the ASME Boiler and Pressure Vessel Code, Section VIII Division |, 197'7 , for a 10-in. , schedule 80 steam line, A106 Grade B materials, operating at
750'F.
R + 0.6t
S
=
E
:
12,900 psi 1 .00 (See the 1983 ASME Code on joint efficiencies) t"r,, .518 in.
lnsloe
D-
(12,900) (1) (.518)
4.8s7 6 69.)
).lo/
Solulion.'
r 1. List known information about the pipe. Size:
Weight (or schedule no.): riy'all thickness
:Ze t
".:
Material: Code section:
Operating temperature: Corrosion allowance:
l0-in. nom. (10.750 o.D.) Schedule 80 .593 nom. (.518 rnin.) ,{106 Grade B ASME, Section VIII
Division 1, 1983 750'F 0 (The 1983 ASME Code formula does not include allowance for corrosion, therefore, it is the responsibility of the designer to adjust the wall thickness where corrosive conditions exrst.)
2.
=
12,900 psi
raOrUS
+
tnri "-'
(.6) (.s18)
: l.lv:
osl
A simplet quicker method is to obtain the applicable P/S ratio from the pressure/stress ratio table listing Y = 0.4 (Table 7-2). Nore: In the ASME Code, Section mula:
*:?-,* thus
P:
P/S
:
SEt R + 0.6r
Et R + 0.6t
E:1.0 P/S
: D" 2
Obtain from 1983 ASME Code the allowable stress:
S
.. OrD" 2-
R:
P/S
:
-r+0.6t 2t
D"-2r+1.2t
VItr,
1983, for-
-w Pressure and Stress
pE:
D"
2t
Design factor (F) for Type
-
consrucuon
0.81
C
:
Ratios
251
0.5
thus, y in the basic ASME formula The foliowing two solutions can be used to find the stress or required yield strength.
P/S: 2(t -A) D-2y(t--A)
.
must equal 0.4
With the allowable stress(s) obtained from the ASME Code, Section VItr, Division 1, 1983,
therein:
(12,900 psi) and the P/S ratio obtained from Table
7-2
P: P:
?ST
P:---XFXEXT
(.r0M)
D
PD
^
SXP/S 12,900
Using the design formula from the ANSI Code 831.8, 1982, and the symbol definitions contained
2tFET
x.1004
=
l.295psi
Example 2t Determining Stress or Required Yield Strength
P
=
1,100
T1
-
1't 7<
11""*;
:
.562
F:.5 E:1.0 T : 1.0
Determine the stress or required yieid strength in accordance with the ANSI Code 831.8, 1982, on gas sion and distribution piping systems for a 12-in., schedule
transmis-
60, gas line, A106 Grade B materials, operating at 1,100 psi at 250"F.
s=
Solut'ons.'
s-
(1,100) (12.7s)
Q) (s62) (.5) (1) (1) 14'025 .562
=
24.955 psi
1. List known information about the pipe:
Size: 12 in. nom. Weight (or schedule
no.):
831.8,
t982 Operating temperature: 250"F
P:
1,100 psi
.
A simpler, quicker method is to obtain from Thble 7-1 where y = 0, the applicable P/S ratio, and then multiply to determine the stress or required yield strength.
Corrosion allowance: 0 P/S
2.
or required yield strength of
24,955 psi is less than the minimum yield strength of35,000 psi for A106 Grade B pipe, the pipe correctly meets Code requirements.
Schedule 60
section: ANSI Code
Operating pressure,
Since the stress
o.D.)
Wall thickness: .562 nom. Material: 4'106 Grade B Code
(12,750
ratio
:
.0771
Obtain from the Code section on gas transmission:
Minimum yield Y factor
strength : 35,000 psi =0
Because we are using a construction factor of .5 from the ANSI Code 83l .8 and because this Code is based on nominal wall, we must use the .5 fac-
Piping Stress Handbook
v:.4
tor and an 817 factor in the following formula along with our P/S ratio.
S: S:
A:0
P-P/S(8/7)(.s) 1,100
-
.0771 (8t7)
(.s)
:
(e00) (6.62s)
24,967 psj
2 tl3.000
<06?<
Example 3: Determining Wall Thickness Required
t^:'""-"
26,720
(900) (.4)]
.223
The nominal wall, T".-, is equal to .223 817 : .254. Because the ANSI
In accordance with the ANSI Code B31.1.0, 19g3, for power?iping, determine the pipe wall thickness required for a 6-in. steam line, A106 Grade B pipe, operating at 900 psi at 750'F at maximum allowable stress, with a iorrosion allowance of .050 in.
87lz% .223 x
Code B31 . 1 .0 design formula makes no allowance for corrosion and/or erosion, the corrosion allowance determined by the designer must be added to the nominal wall calculated. Therefore Tnon,,:
.254+.05O: .3M.
Sorutions.'
Then, refer to Chapter 10 "properties of pipe,' to determine the next thicker commercially available pipe. which is schedule 60, having a nominal
1. List known information about the pipe:
Size: Material: Code
wall thickness of .375.
6 in. (6.625 O.D.) A106 Grade B
.
section: ANSI Code B3l. 1.0, 1983
P: C:
:
Using Table 7-2 (where y 0.4) across from the 6-in. nominal pipe size under the column for .050 in. corrosion allowance, pick the pipe wall thickness having a P/S ratio equal to or greater than that just calculated. This value is .0869. Therefore, tno,o = .375 based on a P/S ratio of.0869 as
Obtain from the ANSI Code section on power piping (1983) the allowable srress:
S
=
=
y factor
A simpler, quicker method is to calculate the minimum required P/S ratio by dividing P by S:
P/S:900=13.000:.0692
Operating tempetature: 750.F Operating pressure, 900 psi Corrosion allowance, .050
2.
:
+
13,000 psi
0.4
shown in the table should be used.
The following two solutions can be used to find the
required wall thickness.
Note: Interpolation For values ofC and y intermediate to those shown in the tables, linear interpolation may be used.
.
Using the design formula from ANSI Code 831.1.0 and the symbol definitions contained therein:
PD^" 2(SE + Py)
L: ''' P
=900
D"
:
6.625
S = 13,000 E:1.0
+A
Note: Special calculations: Only the lhree most important uses for the P/S values have been illustrated. Those who would like to examine all of the uses are reminded that the tables may be employed to indicate the effect of operatmg temperature, corrosion allowance, material, and pipe size.
Branch Reinforcement The various ANSI piping codes give formulae for the reinforcement of nozzle openings in two respects:
Pressure and Stress Ratios 1.
The pressure area cut by the opening must be replaced by reinforcing the area within a prescribed
T = t :
zone around the opening.
which attach the reinforcement to the pipe must meet certain (essentialiy shear strenglh) requirements. The Petroleum Refinery Piping Code
2. The welds
831.3 (1980) gives detailed requirements in Section 304.3.3. The Power Piping Code B31.1 (1983) refers to Section 1O4.3.1 for a detailed description of this nozzle reinforcement design and calculation. For convenience, reprinted here is ANSI Code 831.3, Section 304.3.3 in Figure 7-1.
Nominal thickness of pipe, in. Pressure design thickness of pipe according to the appropriate wall thickness equation or procedure in 304.1 in. When the branch does not intersect the longitudinal weld of the run, the stress value for seamless pipe, of comparable grade, may be used in determining t for the purpose of reinforcement calculation only. When the branch does intersect the longitudinal weld of the run, the weld joint factor of the run shall enter the calculation. When the branch contains a weld, the weld joint factor of the branch shall enter the calculation.
Section 304.3.3 of the ANSI Code 831 .3-Reinforcement of Welded-Branch Connections Additional reinforcement is required when it is not provided inherendy in the components of the branch connection. This paragraph gives rules governing the pressure design of such branch connections for cases where the angle between the axes of the branch and of the run is between 45 and 90 degrees, inclusi.ve.
Required Area
-
The quantity (trdr) (2 sin B) is known as the required area; in the case of right-angle nozzles, the required area becomes t5d1 square inches. The branch connection must
be designed so that the reinforcement area defined in 304.3.3 (c) is not less than the required area.
Reinforcement Arca The reinforcement area shall be the sum of the followrng two areas.
Notation The notations described below are used in the pressure
design of branch connections. The notations are illustrated in Figure 7-2. Note the use of subscripts b for branch and h for run. Note also that Figure 7-1 does not indicate details for construction or weldins. B : Angle between axes of branch and run, degrees b = Subscript referring to branch : Corrosion allowance. in. c D" : Outside diameter of pipe, in. ,l : Actual corroded length removed from run pipe, in. : [D.o - 2(Tr - c)]/sin B : d1 or [T6 - c) + (Th - c) * dr/z] whichever is greater, but in any case not more than Dol : h Subscript referring to run or header L+ : Altitude of reinforcement zone outside of run pipe,1n. : 2.5 (Tr, - c) or 2.5 (Tb - c) + L, whichever is lesser : L Nominal thickness of reinforcing ring or saddle, in. T : Actual thickness ofpipe, in. @y actual measurement, or minimum thickness permissible under purchase specification)
1. The area lying within the reinforcement zone [defined in 304.3.3 (d)l resulting from any excess thickness available in the main run pipe wall and branch pipe wall over that required by the proper wall thickness equations, i.e., the thicknesses Tr - tn - c and T6 - to - c multiplied by appropriate lengths. Any line having a thickness greater than
2.
that required for corrosion allowance and for pressure and other loading considerations will occasionally be in service until the excess thickness is also corroded away. If this is the basis of the design, the excess thickness cannot be used for reinforcement of pipe+o-pipe branch connections. The area ofall other metal within the reinforcement zone (defined in Section 304.3.3 (d) provided by
weld and other reinforcement metal properly attached to the run of branch. In computing areas of weld metal deposits, the minimum dimensions required shall be used unless a definite procedure is employed to instruct the welder to provide specific larger dimensions, in which case lhe latter dimensions may be used in calculations. Fortions of the reinforcement area may be composed of materials other than those of the main run pipe, but if the allowable stress of these materials is less than that for the
254
Piping Stress Handbook
BRANCH REINFORCEMENT
DESIGNCONO|IONS:....... psig.......'F
Sfaigfn Pipo Und€r lr{om€l Pr€aslrg (a) For motallic pip6, thg inlornal prgssrro d6ign thicknoss 0) shall bs not legs than calculat€d by the lollowing Equalion 3, itt is loss han Do/4: 3O4.1 .2
HEADES
BRANCH
Nominal Siz6 Outside Oiameler
PY)
Dotr
Dob
T6
T6
S6
NominalWall Tabl6 304. t .l Values ot Y for Fenous Mato.ials
rempsraure
O€gr6o"F
Actual or min. Wall Matorial Spgc. ASTM
900&
115{, &
Below 950 lO00 1050 1100 Abovo
Ferritic
St€€ls Auslonidc
Sle€k
0.4 0.5 0.7 0.7 O.7
O-?
0.4 0.4 0.4 0.4 0.5
0.7
Allowabig Str€99
sh
Joint Elficiency
E6
Co€fliciont
Y6
Y6
Me
C6
eb
lhtorssc,iion Angl€
p
Y
REQUIREO THICKNESS OF HEAOEB AND BRANCHI PDoh
th=-= '' 2S6E6
2t.......x..,
+ 2YhP
2r.......x.. ..x....... . t 2x.,.....x..
.. +
PDcb
t 2Y6P 2t.......x...
2S6Ep
LIMITS OF REINFORCEMENT: Oqb
- 2(T6.C6)
... ...
.
-
2
r
(.......
-
.......)
sin P
(....... -.......) + (....... -.......) + 0.sx....... Sefecf farger ol lhe values, but not lo Exceed Ooh dZ = . .. ... , L4=2.5(th.Ch)=2.5(.......-.......)ot=2.5(lu-Co)+te=2.5(.......-.......)+.......
d2=d1
or
=
{Tb -
Cb) + Oh- Ch) + 0.S1 =
S€l€ct lossor of the valu69 (te = 0 if pad oi saddlg i9 not used) L4 = . . .
.
=
...
REOUIRED ANO AVAILABLE REINFORCEMENT AREA:
Ar€a =
...... . sq. in. required. (2x....... -....... ) (....... -.......
thdi = .... ... x... .... =
Ai =
(2d2 -
A2 =
214(Tb-tb.Cd =
A3 =
tf
dt)
(Th - th - Ch) =
= 1.......12
2r....... (....... -.....
-.......
- A3 =....... r....... +....... i..... AreaA-(At-Aa-Ad At + A2
A4 + 2 = sq. in. ol pad on €ach side ot nozzle =
sq. in. available. . . sq. in. ol area in pad requrred -
A4
+2-.......
Ac-2=L=.......* OEDusopadts
=.......
xL
=......,
Figure 7-1. Reproduction of ANSUASME Code 831.3, Section 304.3.3 giving detailed requirements for branch reinlorcemenl.
.
Pressure and Stress Ratios main run pipe, the corresponding calculated area must be reduced in the ratio of the allowable stress values before being counted toward the reinforcement area. No additional credit shall be taken for materials having higher allowable stress values than for the main run pipe.
Sample Calculations for Branch Reinforcement Example 7-l
Reinforcement Zone
The reinforcement zone is a parallelogram whose
length shall extend a distance d2 on each side of the centerline of the branch pipe and whose width shall start at the inside surface of the main run pipe (in its corroded condition) and extend to the distance La from the outside surface of the main run pipe measured perpendicular to this outside surface. (See Section 3M.3.3(c) (1)).
An NPS 8 run (header) in an oil piping system has an NPS 5 branch at right angles (Figure 7-3). Both pipes are Schedule 40 API 5L Grade A seamless. The design conditions are 300 psig at 400'F. The fillet welds at the crotch are minimum size in accordance with Section 327 .4'4. A corrosion allowance of 0.10 in. is specified. Is additional
reinforcement necessarv?
Figure 7-2. This figure illustrates the nomenclalure used in ANSI Code 831.3, Seciion 304.3.3, 1980. ll does not
inJicate complete w;lding details or a preferred melhod of construction. (Reprinted courtesy of the American Society of Mechanical Engineers.)
REINFORCEMENT ZON E
10.,*,".1 c=o'roin'
L4 = 0.268 in.
C
= 0.10 in.
4,286 in.
4.286-
Figure 7-3. Figure of branch reinforcement for use in Example
8.625 in. OO 7-1 '
7-
256
Piping Stress Handbook
t" : O.7 (0.237) = 0.166 in., or = 0.25, whichever is less : 0.166 in. t
Solution
SE:
Tr, =
Tr:
16.0 ksi. (0.322) (0.87t =,A.2{2
:
n.
(0.23? (0.87s) O.2U7 m. L'4 = 2.5(0.282-0.1) = 0.455 in., or 2.5(0.207 -O.l) + 0 0.268 in., whichever
:
t4 : dr: dz=
d,: tr, =
b:
is less 0.268 in.
I4.s -2(0.2s7 (0.207 2.432 4.286
-
in n.
-
0.l)l/sin (90') = 4.286 in.
0.1) + (0.282
-
o.D
+4':'6 z
or d1, whichever is grex er
+ (2) (0.4)
(300)
(300) (4.5m) (2) (16,000) + (2) (0.4) (300)
: :
0.080 in.
0.042 in.
:
0.166
o.1ut 0.235 in.
Thus, the required area, A1 (90)l 0.343 sq. in.
:
= (0.080) (4.28O t2 -
The rcinforcement area:
- I1l*o wall;
A.z
0.437 sq in.
:
In branch wall,
:
(300) (8.625) (2) (16,000)
Minimurn leg dimension of fillet weld
@.286) (0.282
A3
-0.08 -0.10)
sin
:
: (2) (0.268) l(0.207 -
0.042) - 0.101 0.035 sq in. In branch welds, Q) Q/2) (0.235)2 .
&:
ln. The total reinforc€ment area
:
:0.055
sq
0.527 sq in.
This is more than 0.343 sq in. so that no additional reinforcement is required to sustain the internal prcssure.
Design Criteria for Allowable Loads' Moments, and Stresses
Design Criteria for Pumps with Steel Nozzles and Casings
larger reactions. The vendor must submit comparable cri-
teria for pump cases constructed of cast hon. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expansion or contraction of prping. Piping reactions should be computed in conformance with ANSI Code B31 . or
API Code 610: Steel Pump Force, Moment, and Stress Limitations
I
The following criteria apply for pumps with 12-in. discharge nozzles or smaller. The forces contained herein are
considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting
ANSI Code 831.3 for pressure piping and should be designed within the limiting criteria set by this standard. The modulus of elasticity must be adjusted for the operating temperature condition. Each nozzle should be capable of withstanding double the forces and amounts listed in Table 8-1 applied simulta-
Table 8-1 Nozzle Loadings
Fotce/
oment
Nomlnal Size ot Nozzle Flange (in.)
<
Each top nozzle E
160
F, (compression)
200
Fy (tension)
100
F,
130
Each side nozzle
R Fy
160 130
F,
200
Each end nozzle F" F
F,
200 130 160
Each nozzle
Mr
340 260 170
My
M" M= x=
Moneu Axis
Reprcduced
ft-h
parolzl to shaft
6810
2
240 300 150 200 240 2W 300 300 2W 240 700 530 350
320 400 2W 260 320 260 400 400 260 320 980 740 500
12
14b
'| 6D
530 700
1,000
1,500 1,800 920 1,200
560
850
1,200
1,500
4ffi
1,000 1,500
1,zffi
700
7W I,100
I ,800
1,600 1,900 2,000 2,3w 1,000 1,200 1,300 1,500 1,600 1,900 1,300 1,500 2,000 2,300
700
1,100
1,500
1,800
2,000
2,300
4@
700 850
1,000 1,200
r,2w
1,300 1,600
1,500
2,6N
3,700 2,800 1,800
4,500 3,400
4,7N 3,500
5,400 4,000
2,2W
2,300
2,7W
560 700 350 460
850 1,100
560 1,700 1,300
1,900 1,300
870
t,2N 1,500
750
1,500
I,900
J = Verticalgo" to shaft z = Hoizontalgo' to shaJt
from Centritugal Pumps for ceneral Refinery Services, Suth Edition,
Institute.
257
1981
, Standad 610 Table 2. Repinted courtes, of the Ameican Petroleum
25A
Piping Stress Handbook
neously to the pump through each nozzle, in addition to internal pressure, without causing an hternal rub or adversely affecting the operation of the pumps or seal. The baseplate and pedestal support assembly should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when subjected to the loads shown in Table 8-1. These loads represent the total effect of all external mechanical forces that may be applied to a fully grouted pump base. They are to be applied to the pump through the suction and/or discharge nozzle (see Figure 8-1): For purposes of evaluating computed piping-imposed external moments and forces, these forces be transferred from both suction and discharge flanges to the intersection of the X, Y, and Z axes. An algebraic surffnation should then be made for comparison with the moment limitation just given. The vendor should submit alternative criteria for pumps larger than 12 in. Because a particular nozzle on a pump will not always be subjected to the maximum allowable resultant force and moment simultaneously, an increase in either the resultant applied force or the resultant applied moment may be made if the following limitations can be satisfied at that nozzle:.
(F"iF.) + (M^/M.)
where C M"
: = =
<
2, F"/F,
<
2, and M"/M.
(
C
M. F, D
=
: :
=
forces and moments from Table 8-2 on both nozzles simultaneously, taken about a point defined by the intersection of the axis of the shaft and the centerline of the pedestals. For heavy-duty baseplates the total applied resultant forces and moments on the suction and discharge nozzles should not be more than twice the eouivalent of those given in Thble 8-1. For applied resultant forces and moments that are greater than these, allowable values shall be mutually agreed upon by the purchaser and the vendor.
Design Criteria for Pumps with Cast lron or Aluminum Nozzles and Casings
Aluminum Pump Force, Moment, and Stress Limitations
2, for nozzles 6 in. and smaller (D + 6)/D, for nozzles 8 in. and larger resultant applied moment at the nozzle, ft-
lb E
The resultant applied force or moment may be increased up to double the values in Table 8-2 if the maximum combined limit on the installed equipment is not exceeded. This limit is determined by the summation of the
resultant applied force at the nozzle, lb resultant moment (from Table 8-2), ft-lb resultant force (from Table 8-2) lb nominal diameter of nozzle flange. in.
The following criteria apply for pumps with 4-in. or smaller discharge nozzles (suction nozzles may be larger). The forces contained herein are considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting larger reactions. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expan-
sion or contraction of piping. Piping reactions shall be computed in conformance with the petroleum refinery piping code for pressure piping ANSI Code 831.3, Section 319, and should be designed within the limiting criteria set by this standard. The modulus of elasticity should be adjusted for the operating temperature condition.
Table 8-2 Suggested Allowable Resullant Forces and Momenis (For Vendor's Standard Baseplates) E io^
-de..
Resultant Force/Moment F
Figure 8-1. Pump coordinate system.
M.
Nominal Size of Nozzle Flange (in.)
23
4
640
6
810
124
860 1,500 2,300 2,',700 2,900 690 1,400 2,000 3,500 5,200 6,600 8,200 430
Design Criteria for Allowable Loads, Moments, and Stresses Each nozde should be capable of withstanding forces from external piping determined by the following formuIas:
.
Limit tension and comDression forces to 500 lb
where F r X
Suction nozzles:
v z
F"(1.6w(50D r
w D d
Discharge nozzles:
F,6
(
S
(2w
F.,)
-
<
259
Force, lb Resultant of forces Axis parallel to shaft Vertical 90' to shaft Horizontal 90' to shaft Weight of pump only, lb Diameter, nominal diameter Discharge or exhaust Suction or intake
50D
o Top suction and top discharge nozzles are further limited by:
F. is the resultant shear force in the plane of any specific flange face.
and for suction nozzles
Each suction and discharge nozzle should be designed to withstand the forces described for the specific configuration. Unit stresses in each nozzle should be limited to: 4 one-third of the allowable hot stresses for pipe sizes
F*(1.3w(40D
in.; one-half of the allowable hot stresses for pipe sizes > 4 in.; as shown in ANSI Codes B31.1 and 831.3.
F.. and F,.a
:
(Fx2
+
Fz2)L/'z
(
(
1.2w Fr" (in compression) 25D Fr, (in tension)
( F",(w(35D
(
50D
The baseplate and pedestal support assembly on pumps
having a discharge nozzle of 4 in. should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when
and for discharge nozzles
F*a
(
(1.8w
r
F*) <
(
40D
t
(2w Fr") Fra (in compression) Fra (in tension) 0.5w < 25D
(
subjected to the following loads. These loads represent the forces tliat may be applied to a ful1y grouted pump base. They are to be ap-
tot;l effect of all externil mechanical
<
50D
nozzle.
F,a((wtF,,)<35D
o End suction and top discharge pumps are further limited by:
F":
G^'?+Fy.)-
and
F,6: (Fl and
+
M, :
3.0 W*
ftlb
: 2.0 wx ftlb = 1.5 W+ ft-lb M* : Moment in Y-Z plane My : Moment in X-Z Plane M, : Moment in X-Y plane W : Weight of pump only, lb Mv Mz
F"a'?)"'
For purpose of evaluating computed piping-imposed
for suction nozzles
external moments and forces, they should be transferred from both suction and discharge flanges to the intersection of the X, Y and Z axes. An algebraic summation should then be made for comparison with the moment limitation just given. The vendor must submit alternative criteria for pumps having a discharge flange of 4 in. NPS. It is suggested that these criteria be developed as a result of tests'
F".(1.2w(50D Fr.(0.6w(35D F.,< w(40D and
plied to the pump through the suction andior discharge
for discharge nozzles
F"a((1.8wtF*)<40D
(
Fra (in compression) 2w + Fy. Fra (in tension) 0.5w 25D
(
F.a((w1F".)935D
(
<
50D * Minimum W is 500 lb in tlpse
computations.
260
Piping Stress Handbook
D. :
Design Criteria for Turbine Drivers with Steel Nozzles and Casings Steel Turbines Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus "E," resultant bending moments are permissible up to a value that would cause a bending stress of S5/4 in a connection having a section modulus equal to the connecting piping for the same size where the comection is 4 in. IpS or larger. On smaller size connections a stress of S"/3 is permitted. (56 is as defined by ANSI Code 83l . I or ANSI Code B31.3 (current issue) for the material of construcnon. ) The resultant shear force at the face of the flanee and any individual component may not exceed 2,000 lb. The resultant forces and individual components are limited
The combined resultants of the forces and moments
the centerlines of the exhaust connection and shaft must not exceed the following two conditions: (2s0 D.
F.
where
F, : M, : D. :
F(
F,<
( ( w(
F."
F
160D
'vr
F
Algebraic summation of F." Algebraic surnmation of Fo Algebraic summation of F,'
( ( (
F-r)'"
w
l.6w
(
2w
Use up to 100% cold spring and satisfl the operaring condition only. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:
(s0oD"
where
F : M:
-
Combined resultant
of inlet.
extraction.
and exhaust forces, lb
Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ftJb Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction and exhaust openings up to a value of 9 in. in diameter. For values beyond this, use D. (i8 * equivalent diameter)/3 ln.
<
< <
50 D., 125 D., 100 D.,
M_
<250D, My. < 125D. M., < 125D.
1.6w
Combined resultant:
(F.*), + F.y, +
M.)
Components of these resultants should not exceed:
160D 130D
o Resultant components:
r
-
:
o Individual comDonents:
1.3w .6w
of
the inlets, extraction, and exlaust connections, resolved at
further as follows:
F-<
Pipe size of the connection (IpS) up to g in. in diameter. For sizes greater than this use Dc : (16 + IpS)/3 in.
M)
(lb), including pressure forces where unrestrained exoansion joints are used at the connection. except Resultant force
on vertical exhausts Resultant moment, ftlb
Vertical Exhaust Connection For installation of turbines with a vertical exhaust and an umestrained expansion joint at the exhaust, an additional amount of force caused by pressure loading is allowed. (The additional force referred to is perpendicular to the face of the exhaust flange and central.) For this type ofapplication, calculate the vertical force component on the exhaust connection, excluding pressure loading, and compare with the value of t/o the pressure loading on the exlaust. Use the larger of these two numbers for a vertical force component on exhaust connections in making the calculations just outlined. The force caused by the pressure loading on the exhaust is allowed in addition to the values established bv the Dreceding up to a maximum value of vertical force (ib) o; the exhaust connection (including pressure loading) of 151/: times the exhaust area (in.2). These values of allowable force and moment Dertain to
the turbine structure only. They do not pertain to the forces and moments in the cormecting piping, flange, and
Design Criteria for Allowable Loads, Moments, and Stresses flange bolting that should not exceed the allowable stress as defined by applicable codes and regulatory bodies. (See
Figure 8-2.)
261
resultant forces and individual components will be limited
further as follows: o Individual components:
F"(1.3w(40D Design Criteria for Turbine Drivers with Cast lron or Aluminum Nozzles and Casings Cast lron or Aluminum Turbine Force, Moment and Stress Limitations
Fr(.6w(35D F"< w(40D .
Resultant components:
Algebraic summation of F,* Algebraic summation of Fo Algebraic summation of F'"
.
( ( (
1.6w w 1.6w
Combined resultant:
At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a
(F*2+F,r2+F''?),n<2w
value which would cause a bending stress of 56/4 in a connection having a section modulus equal to the connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller size connections a stress of Sr,/3 is permitted. (56 is as defined by ANSI Code B3l. 1 or ANSI
Use cold spring, but comply to these limitations in both
Code 831.3 (current issue) for the material of constructlon.) The resultant shear force at the face of the flange and anv individual component should not exceed 500 lb. The
operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:
F< where
(s00D.
F
/
M)
= Resultant force (lb), including pressure forces where unrestrained expansion joints are used at the comection, except
RIGHT ANGLE TO
TURBINE SHAFT-
-
M: D":
on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to an S-in. diameter. For sizes greater than this (16 + IPS)/3 in. use a D"
:
The combined resultants of the forces and moments of the inlet. extraction, and exhaust connections, resolved at the centerlines of the exhaust connections must not exceed the following two conditions.
l.F.<
(2s0
where F.
D.
:
M,: Figure 8-2. Turbine coordinate system.
-
M)
Combined resultant of inlet, extraction, and exhaust forces, lb Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ft-lb
262
Piping Stress Handbook
D.
:
Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction, and exhaust openings up to a value of 9 in. in diameter. For
values beyond this, use D. (18 + equivalent diameter)/3 in. 2. Components
F*
o Combined resultant:
(F*2+Fry2+F.z;rnE2* Use 100% cold spring and satisf the operating condi tion only.
of these resultants should not exceed:
D., < M* < Fy. 125 D., < My. < F". 100 D,, < M". < 50
250 D. 125 D, 125 D,
The total resultant force ald total resultant moment imposed on the compressor at any comection must not exceed the following:
F< Design Criteria for Compressors with Steel Nozzles and Casings
where
F
= Resultant force (lb), including pressure forces where unrestrained expanston
M:
Centrifugal Steel Compressor Force, Moment, and Stress Limitations
value that would cause a bending stress of $,/4 in a connection having a section modulus equal to the comecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size comections a stress of S1/3 is permitted. (S1 is as defined by ANSI Code B31.1 or ANSI Code 831.3 (current issue) for the material of construc-
1.F.<
(463
where
D.
F. : MI:
( ( F" ( F,
1.3w .6w 1.0w
< < <
160D
l30D 160D
Resultant components:
Algebraic summation of Fo Algebraic summation of Fo Algebraic summation of F-
2. l.6w 1.6w
-
M.)
Combined resultant of suction, interstage and discharge forces, lb Combined resultant of suction, interstage and discharge moments result-
ing from forces, ftlb Diameter (in.) of a circular opening equal to the total areas of the suction, interstage, and discharge openings up to a value of 9 in. in diameter. For values beyond this, use D, = (18 + equivalent diamerer)/3 in.
Individual components:
F*
.
joints are used at the connection. Resultant moment, ftlb Pipe size of the connection (IPS) up to 8 inches in diameter. For sizes greater than this use D" : (16 + IPS)/3 in.
The combined resultants of the forces and moments of the suction interstage and discharge connections, resolved at the centerlines of the discharge comection must not exceed the followins two conditions.
tion.) The resultant shear force at the face of the flanee and any individual component should not exceed 2,60 lb. The resultant forces and individual components will be limited further as follows:
r
M)
J
D:
At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a
-
(925D.
Components of these resultants should not exceed:
F," Fy.
F,,
< <
<
92 D.,
M_ <
230 D,, My.
460 D, 230 D,
r85 D,.
230 D,
< M. <
Design Criteria for Allowable Loads, Moments, and Stresses
Design Criteria for Compressors with Cast lron or Aluminum Nozzles and Casings
where
F :
(lb), including pressure forces where unrestrained e xpansion joints are used at the connection. except Resultant force
M= D"
:
Cast lron Compressor Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus, "E," resultant bending moments are permissible up to a value that would cause a bending stress of S;/4 in a connection having a section modulus equal to tle connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size connections a stress of 56/3 is permitted. (Sr is defined by ANSI Code 831.1 or ANSI Code 831.3 (current issue) for the material of construc-
:
The combined resultants of the forces and moments of the inlet, extraction, and exhaust connections, resoived at the centerlines of the exhaust connection must not exceed the followine two conditions.
1.F.<
(250
where
hon.) The resultant shear force at the face of the flange and any individual component shall not exceed 500 lb. The re-
.
-
MJ
Combined resultant
of suction, in-
terstage and discharge forces, lb
Combined resultant
of
suction, in-
terstage, and discharge forces, lb Diameter (in.) of a circular opening
eoual to the total areas of the suction, interstage, and discharge openings up to a vaiue of 9 in. in diameter. For values beyond this use D, = (18 + equivalent diameter)/3 in.
2.
ComDonents of these resultants should not exceed:
<
< 460 D. < 230 D, < F. < 185 D., M- < 230 D,
F."
F.y
Resultant components:
Algebraic summation of F* Algebraic summation of Fo Algebraic summation of F,"
F. : D, :
o Individual comDonents:
Fr(.6w(35D F"< w(40D
D.
M. =
sultant forces and individual components are limited further as follows :
F.(1.3w(40D
on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to 8 in. in diameter. For sizes greater than this (16 + IPS)/3 in. use a D"
( ( <
92 D., M,230 D., M.y
1.6w 1.0w 1.6w
o Combined resultant:
(F*2+F.y2+F-'?)'n<2w
API Code 661 Design Criteria for Air-Cooled Heat Exchangers
Use cold spring, but comply to these limitations in both
operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the followins:
F<
(s00D"
-
M)
Each nozzle in the corroded condition must be capable of withstanding the moments and forces defined in Table 8-3. The design of each fixed header, of the fixed header to sideframe connection, and of other support members should be such that no damage will occur due to the simul-
264
Piping Stress Handbook
taneous application of the following design iotal nozzle loadings on a single header:
For the direction of loads see Figure 8-3. The total of all nozzle loads on one multibundle bav should not exceed three times that allowed for a singli header.
Moments.
ftlb
Forces.
The maxirrum allowable moments and forces for floatirlg headers are a matter of agre€ment between the pur-
lb
F,FyF"
MM, IvI, 3,000 4,000 2,000
r,500 3,000
chaser and the vendor.
2,500
This recogrrizes that the application of th€s€ moments and forces will cause movement and that this movement will tend to reduce the actual lmds. Tabte
&3
Allowable External Forces and iloments tor Air-Cooled Heat Exchangers Nozzle
NPS Moments ft-lb Inches ilr lily M:
Slze,
lth 2
6 8 10
t2 14
50 70 50 70 120 70 200 300 2N 400 600 400
1,050 1,500 800 1,500 3,000 1,100
2,W0 2,5W
3,000
3,m0
1,250
3,000 1,500 3,500 1,750
Forces, lb
F,
F,,
F2
100 150 100 150 2ffi 150 300 250 300 500 400 500 600 750 750
850 2,000 1,000 2,000
1,200
1,500
1,250 2,W 2,000 1,500 2,500 2,500
Figure 8-3, The direction of the loads defined in Table & Exchangers for General Refinery Se/.v,bes, Second Edition, i978, Standard 661, Figure L Reprinted courtesy of the American Petroleum Instilute.
3. Reproduced lrcm Air-Cooled Heat
Simptified Solutions for Pipe Stress
These tables are developed as a tool for the piping stress
can readily be seen that the smaller expansion
engineer or the piping designer by which he can quickly evaluate a proposed layout before he proceeds with his deslgn worK. It is important for the reader to understand that the tables presented herein do not compose a rigorous solution to the pipe stress problem. Computer calculations must be made for borderline cases. The tables are approximate values onlv for two-anchor oroblems.
Example Problem 9-1 Consider the piping arrangement in Figure 9-1.
Size: 8 in. Schedule: Sch 40 Material:
O.D.:
=
F:
A-53 Grade B 8.625 in.
where
Temperature: 600'F Coefficient of thermal expansion: .046 in./ft
:
The expansion for the 20-ft leg is X .92 in., and the expansion for the 10-ft is X = .46 in. By inspection, it
will deflect
the longer leg more easily than the larger expansion will the shorter leg. To develop Tables 9-1 and 9-2, a guided cantilever formula has been used to calculate stresses. If we observe our Example Problem 9-1 for an expansion ofX -92 in., the required offset is about 13 ft for a stress of 15,000 psi (See Thble 9-1) and 23 ft for a stress of 5,000 psi (See Table 9-2). If Point A is attached to a piece of rotating equipment, you will need to have about 23 ft to make the system more flexible. If the system is attached to a piece of nonrotating equipment, a 13-ft offset will be sufficient. To find the thermal forces Table 9-3 is to be used, which shows forces for a unit reflection with various leneths of offset. Note that in identifuing pipe sizes the tables show wall thickness and moment of inertia as well as O.D. All forces are calculated from the formula:
6 Ell1728 L3 (guided cantilever)
F: E=
{:
Force, lb E O-.ton, t tn., Young's modulus of elasticity, (30 psi) Moment of inertia of pipe, in.a Length of the shorter leg, ft
I : L: I
I
Fys
=
F.B
x
106
434lb
=
Figure 9-1. Diagram for Example Problem
6,949lb.
9-1
.
(Text continued on page 291.)
265
256
Piping Stress Handbook
Table 9-1
Lengths ot Offset Required to Safely Absorb Various Expansions tor Piping Between Two Solld Anchors (Stress Limit is 15,000 pst)
Pipe O.D.
(in.) ol
1.3 1.9 2.3 4.5 6.6 l'.D
rs .7 74.9
16,S 18 .0
.g 24.5 2g
30 .s 36 .g
42,9
4A.S
54.9
1.5 2,6 3.5 3.3 4.2 5.1 5.3 5.7 5.1 6.4 7.9 7.8 9.3 tg .5
tength (ft)
Bequired to Absorb Expansion A (in.)
o.2
0.3
2.3
.8
3.4
3.0 5.2 5.9 6.6
l1,l
t4.l
I4.9
8.4
ro ,4
11.8 L3 .g
IS .1
14.3 16.3 L8 ,2
74.0
19 ,9 2g .8
L6 .O
l8 .0 26,0 24,9
3g .g 36 .S 42 .0
48,9
54.5
22.3 23.6
24.9
u.d
9.7
12.o 13.6 15.1 15 .5
l8 .9
2I.0
22.9 24 .T 27 .3
29.8
Jt.5
8.1 8.9 9.9 .5 11.1 10
tJ.o l4 .9
r6.l u.3
18.3
36.1 38,5
4r,s
9.9 10.9 13.4 L5.2 l5 .9 l8 .5 21.1 23 .5 25.6 26 .9 28.8 30.5 32.2 9.4 .2 .7 .9 a2.9
3
38.6 44.6 47 .3
5.1 6.7 7.4 8.4 9,4
5.il
tength (ft) Pipe O.D. (in.) -r-:3 2.9 2.5 1.3 1.9 2.3
3.9 4,3
4.6 5.2
4.3
7.6 8.1 8.5 9.1 9.9
0.4
43 a6 49
rg .2 16 .7
t2 ,2 12.a
t4.l
IE ?
17.3 18 .5
2L.I
0.5 3.6 4.4 4.8 6.5 5.8
9.4
10.5
IL.4 12 .g t2.a l4 .4
!7,6 2g ,8
0.6 4. 4.8 6.6 7.4 8.2 9.0 l0 .3 12,5
13.2 14
.l
14 .9
15.7 17 .3
l9 .3 2t .7
22.A
o.7 .3
5,2 ?1
8.5 8.9 11.1 L2.4 IJ.5
14.2 15.1 L7 .S
t8.5 2g
22
.8 .8
.4 28.0 26
23 .6
0.8 4.6
0.9 4.9
6.1 8.6 rs .4
lr.:t
l4 .5 .2 16.3 17.3 t8 .2 15
8.9 9.1 tg ,r
.3
1.1
1.2
6.2 5.9
5,4 6.5 7.2 8.9
6,8
t0.6
.l
9.3 10.5
12.2
I2 .8
7S
Lt.2
tl.l
lt.7
l4 .1
14.9 16.2
15.6
L7 .g
12,6 16.1
27 22 24 26 28 29
1.0
.r
23,6 .9 28.9
.4
25
.4 .2 .9
29 .9
18.2 l9 .3 26 .3 22 .3
24.9
29
,s
1',t t
14,9
14 .5
r7 .0
17.8
17.8 l8 .6
,2
2L .T
2S
23.4
22,3 24.4
26 .7
27 .3
33.1
34.5
28.6 39,9
JJ.5
Required to Absorb Expansion A (in.) 3,0 9.9 l0 .8 11.9 o.5 20 .2 .l
.r .l
23 za .6 28
29.5
38.6 43 .2 47 .3
51.1 54.7 5A.g
4.5 9,7 12.9 15.9
I8 .g 26 .g 2L .9 25 .0 27 .9
35,4 31.9 34.1
tg ,4
11.0
13.8
14 .6
17 ,g
2I.3 23
.4
29 .8 36 .4
36.1
38,5
JO.I
4g .7
4r .7 46 .7
51.1 55.2
59,1 62.6
5.9
44.6
49.9 54.7 53.1 67 .S
t3.3 78,5
26.5 24
.8
3r,5 34.4 36.1
ll.5
!4 .6 15 .4 t9 .6 2I .6 23 ,9 29 ,9
36,3 JU.I 4S
43.2
,'l
47 .3
45.6 49.9
58,6
51.1
67 .S
70.6 7 4,9
6.6 L2, 2g 22 25 27 31
23 ,6 26
.L
.3
4I.7
45.3
47 .3 49 .9
47.8
52 ,3
5 8.6 64.1 7
4.I
I7 .6
24.6
54.7
61.t
67,9
16.5 .2 22.5
18
39.9 41.4
43.5 46.5 49,3 52 ,S s5 .9
63.6
39 .4 43
.s
45,1 48.2
sl.1 53 .9
55,0 ?a I
8S
a2.6
7,0
28 ,2 34 .6 38 .S
4S
.6 42 .1
13 ,2 L6 .g
28 .6
34.9
66 ,O
7t.s
.0 .6 .g .4
16.9 29.8
6.5
,5
88.5
267
Simolified Solutions for Pipe Stress
Table 9-2 Lengths of Oftset Required to Safely Absorb Various Expansions tor Piping Connected to Rotating Equipment (Stress Limit is 5,000 psi)
Pipe O.D.
(in.) -6:i t.9 3,5
3.4
6,6 8.6
5.4 7.3
4.6
ro.7 8.r r2.7 8.9 74.s 9.3 L6.0 9,9 t8,0 I0,5 1t.r 28 .0 24 ,O 12.2 13,5 30 .o 36.s L4.9 42.A 15.1 48.0 L7 .3 54,6 18.3 Pipe O.D.
(in.) i.s 1.3 rl .0 1.9 13.3 2.3 14,6 3.5 18.0 4.5 29.5
8.6 24,3 ls.7 31.6 L2.7 34.4 14.0 36,L L6.0 3 8.5 18.0 4L.O 26.9 43.2 24.6 47 .3 30 ,0 52.9 5a.S 36 .0 42.O 62.6 48.5 67.0 54.9 7 r.g
Required to Absorb Expansion A (in')
Length (ft) o.2
4.9 4.8 6,6 7 .4 8.2 9,9 r0.3 12.5 t3,2 14.9 r7.3 19.3 21.1 22.8 24.4 25 ,9
0.3 4.9 5.9 8,9
9,r
t0.r
1r.1
12.6
15.4
16.r 18.3
27,r
23.6 25,9 28.9 29.9 31.7
Length (ft) 2.O
2.5
0.4
0.5
0.6 6.9 8.4
9,3 .5 11.7 12.8 14 .6 16.3 L7.8 18.6 19.9 2r ,r 22.3 24.4 27.3 29 .9 34.6 36 ,7 L6
70,4 1r .8 13.0
11 .4
14.3
15 .7
L2.9 14 .3
16 ,3
L8.2 19.9 2q .8
20 .0
2r .8
22.3
24.4
23.6 24.9
25 .9 27 ,3
27 ,3
0.5 33 .5
29.9
3
38.6 4L.0
36 .7
39.6 42 .3
44.9
o.7 7.5
0.8
rg .0
10 .7
74,0
8.0
r5,4
l6 .5
lo I
20
16.9
2r.6 24,7
r8.t
.7
26 .4
0., 8.t
76.1
1t .3
1.0 9.0 l0 .8 11,9 14.7
29.5
39.6
45 .7
48.5
11 .9
47 .A
43.2
44,9 48,5
47 ,3
55 ,g
58.0
6.q
7.9
17 .5
19.2
26.2 23
24.5 28 .g
.r
28,1 29.5
38.6
34,6 38.6
9,4
tr .4
1.2 9.8
.4 16 .1 r 9.4 29.2 24.2 25,3 29.5 36,8 32.3 30 .9 34.6 33 .l 3 8,5 37 .6 40.5 42,3 49.7 sl .9 56 .0 53 .6 57.3 59 .9 60,8 6 3.5
r4.0 t5 .8
28 .0 32 ,3
1.1
48.9
5I
.I
15
Required to Absorb Expansion A (in.) 3.0
15.6 16 .8 18.8 26 .3 15.9 18 .9 20 ,7 22,4 20.8 23.3 25,5 27 .6 23.6 26,4 29.s 31.3 29.2 32.0 3 4 .6 26 .L 28.6 32,0 4g.r 43.3 36,5 4q.8 44 .'t 48.3 44.5 48.'t 52.6 3 9,8 4r,7 46 .7 Fl I q( ' 44,6 49 ,9 54.7 59 .r 47.3 52.9 58 .0 62.6 49,9 5s.8 61, t 66.0 54.7 61.r 67 .0 72.3 61..1 68.4 74,9 8q.9 67.9 7 4.9 82 .S 88.6 72.3 89.9 88.6 95.7 77 .3 85.5 94 .7 r02.3 82.O 91.7 109.5 rsg.5
4,9 18 .0
29.5
4.5 23,g 25 ,4
5.0 20.L 33.0 37 ,4
37.9 49,5 46 .3
43,5
49.r 54,8 62.6 67 .0
61 ,0
70.6 86.5 L02.3
L09.4 116.0
77.0 74,9
4t .4 45.3
51.7
74.9 7 8.9 85,5
L00.5
ro5 .9
108.5
114 .4
rt6,g
123.1
28 .g
34.6 39.2
r22 .3 L29 .7
22,9 26.6
35,r 4t,0
43 .4 41 ,5
45.3
66 ,5
63.2 68.9 72.3
66.9 65.0
82 .0
9r.7
21.1
24.3
74.L 78,5 82,8
90.7
49 .7 56 ,7
22.9 27 .7
3t ,5 39.6
42 .7 49 .0
59.0
65.8
78.r
77 .3
80.5
85,5
96.0
94 ,7
98 .6
a2.g
23 .8 28 .8
88.6 93 .4
IO2 .3
I6L,4
10s.9
110 .3
]f
r2g ,o
125,3 134,0
130.5
135.4 L44.7
ItL.r
r36.1
1r5.0
I42.I
I2A .a 139 .5
L4't,9
4.4
r25.3
Piping Stress Handbook Table 9.3 Force (lb/ln.) ot Expansion tor L-Shaped pipe (No Etbow)
?.375
{IFF-
l. J/J
,,t65
FI i J 5 6
t I 7 LE
t.3ls 190 l,!li 5t3 :6? i52 9$ 5{ 45 J3 ?5
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Simplitied Solutions for Pipe Stress Table 9-3 Contlnued
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Piping Stress Handbook Tbble 9-3 Continued
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Simplified Solutions for Pipe Stress Table 9.3
Contlnued
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4r
THICrjI/ESS, AND MOMENT OF INERTI,A-
Piping Stress Handbook Table 9-3 Continued
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Simplified Solutions for pipe Stsesg TEible 9-3 Contlnued
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3 UNFS ARE AD., WAIT TIIICKNESS, AND MOMENT OF NERTU.
Simplified Solutions for Pipe Stress Table 9-3
Continued
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UNES ANE O.D.
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TEICKNESS. AND MOMENT OF
NERTU.
276
Piping Stress Handbook Table
$3
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WAIL TH]CKNESS, AND MOMENT OF INERNA.
16,864
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Simplified Solutions for Pipe Stress Table 9-3 Continued
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WAIL zIIICKNESS, AND MOMENT OF INERNA.
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277
Piping Stress Handbook Table 9-3 Continued
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3 UNES ARE AD., WAIL T'IIICKNESS, AND MOMENT OF NERNA,
Simplified Solutions for Pipe Stress Table 9-3
Continued
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FIRST 3 I.]NES ARE
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WAIL TIIICKNESS, AND MOMENT OF INERTU.
113,:94
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Piping Stress Handbook Table 9-3 Continued
r.6?3 T!
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915.lBl 46u,573
2
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i7 6,t4i 449,6?? 7l0,4it
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3 UNES ARE O.D.. WAIL MICKNESS, AND MOMENT OF INERTA.
Simplified Solutions for Pip€ Str€ss Table $3 Contlnued
l.it5 T! l?,73 Ii{. stH. uS PIFE tiF-
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s9g
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FIRST 3 UNES ARE
l 7t
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4n il
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TTIICKNESE, AND MOMENT OF INERTU.
Piping Stress Handbook Table 9-3 Continued
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11.90S 697,31t
1,9.
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l.
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?9S 1833.46t ?771.61S :67t.839
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tt6, !t6 gl0,4i: :88.71F 5t0,tli
51,ifl 90.494 143.491 : l,l, 9l: {43, sgs 4l,4lJ tt,TrtJ l lS.5:4 167, I S.il.9gi 3?,tgg 54! 924 86.939 l ,4ll 169.9ii :$, $l! 43,5t5 6t,6fl lr5, 5 r15,ll I !l !It4 35, $St 5i.:S? 85.544 175, S:6 17,479 l9!4f6 46,6i8 ;g!496 !44,141 l4t57l ?4,316 38!t74 58t 764 l!6.15= n! ?76 ?t!6i3 3?t 748 49,504 lfl.t66. tg,43E t7. t6' :7.t45 4?! 99? 56,137 8,t49 t5!S:6 ?i,8?3 36.tgl ;3,8:: t73l l3,fi6 :9,6!3 ll, 175 il,796 6, ii4 rJl! 17.9J6 ?;, i14 55.,tS! 5.ESi 9tlqg 15,6t7 !-:! 7:9 49,559 7
:.1i9
s,713
t3.sls
4,591 7!;99 12,2?i 4,S7i 6,953 tS.!64 l,617 6,llt 9! 793 l,:61 5!4i7 F,7FS ?! 936 4,9t9 i, E3t :. s"? 4,4il 7,17 4 2,4i3- 4!S4l S,li l :.165 3.6i$ 5, 1,iE2 3,:5? 5!:t4 t!g?; 3!d,i5 4.85t S?B
1,67C ?.SS?
1,5i5 :.38? 1,4!l ?,37S l9 l,s3t 9b6 939 !,i0 7St 736 699
3t1ifr
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l.8Br t, i4g !!i!& 1,515 1,414 1,3:t l!:37 l. t6u
i.954 :! 771
t,287 r,Srt
l,l
4!4:4 ,1. $93
t,::o !.5i8 1,402
?.:4: :,596
lttS? 1,94t
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lss l?t ii3 :r 7fg i l, i64 5.?i? ig,i|i {,t67 9.969 4,511 9.? 4,139 g!3i:i l! 997 7,1i 3,631 ,411 l.lst i! 936 Ir 1ig 6!494 i! 966 6117g 6!
l
4
1
1 lrtl
q ,igl
3 UNES ARE O.D., WAIL THICKNESS, AND MOMENT OF INERTA.
Simplified Solutions for Pipe Stress Table 9-3 Contlnued
:.3;5 rS 1?,i5 li,l, slil. Bts PIFE
IFF-
t.375
:.59t
iEl
t. ?lg t,8rF
F.389
:t
ll,tsl :s,?0i 1i9,ll7 ;6!!i4? 5?7,::? 1.34i 15,0?{ 3i,t?s i9,149 l:6,?14 4t7!856 8lt.716? l,4ll i.3lr li,i4: li!i44 63,?SI i7t.f64 314.971 5tB.45S i?3 3,?4i 8,tfi9 l:,!?6 3l'74I 88!597 176,6;t 301,?8t ,119 1,S78 4!&35 l!968 19.5?; 5i!182 it?r?14 1t{.:56 3i{ l.iBl ?,9t9 6,!7i l?!ig7 3i!lt5 64!JrE id9'79t i77 79? l!955 4,?{5 8,239 ?1.5S8 43,1?l l3!i56 t:{ 55$ t!37J ?,954 3!7lA 13,ld6 39,?s6 5iii61 496 1,8c1 :!153 4,:18 llrFlz 2ztg18 $.661 tg 69 3t5 i5! 1,618 3' 161 8,174 16,58S !8'295 5?. ?35 579 1!?46 t,,141 6.3i3 l2t77i 11,794 4t Ig5 45S 9lt 1,9?6 l!91? 19!649 17t14? J63 ?85 1,537 4.gll 8!646 13,72: 13 l{8 ?97 618 l!t5t 3,:&3 t.542 1!,1:9 27 tln q9 :44 li6 1!g3i :,58? lrllt t.lts 72 l8 83 2$4 438 8t8 ?,:41 4.41{ ir6i6 76 1;2 3i9 i73 1!8Eg J!79! 6'{i8 16 lI 5? 146 3i4 6i5 1,6i3 3r?19 i,491 ;69 5?? 1,3?7 ltltr 4.;0u fl 51 l:5 ig 44 ls8 ?33 455 l.l8t itSg{ 41967 ,4 767 3l$ 1.s34 1,613 3,537 s 3r a2 177 34i 9S5 1,815 3!S95 7 ll 717 1,5?7 2,i24 71 156 lt5 7 it ri ?6 64 lJE 27* ;t5 l'4ll l!{ifl it7 l!!55 :, i4l 1f3 2$ it i 13 5 ?l 51 169 ?14 559 1,1:: t,9il t8 19? 35: !,St6 i!716 46 4 l8 452 955 1,144 88 lis 4 t7 4l lsa 40t Slg l'195 *t 3 15 J7 175 741 1ri64 7r t4l 3 l{ 34 j: lJ6 t7{ 1! 149 l:f 3l si i2 3s6 614 lrg4s 6E tl7 I 1l :8 s5 Li7 ?SS 562 ti8 15 : 10 515 u7t 95 ::7 5S r I t3 ,fl :J6 471 E7 4i 2 I :t g3 2t7 436 114 43 ? i 7fr 281 4t? 686 i7 i It 7 1S 3i2 6i5 71 ii6 36 2 7 t7 34 5g 112 145 383I 6 16 gt 169 3rg t46 Jl 1 6 15
; 4
5 6 7
t t LU
l? l3 l1 :s 1l
l9
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3. EtS
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3
LTNES
ARE O.D.
,
WAIL TTIICKNESS, AND MOMEITT OF NETN'1.
Piping Stress Handbook Table 9-3 Contlnued
?,3;5
i;5
rFF.
?.
3iT
9.436
9T
i,ili:
2
T0
J,sSt 4.".J9fl 5,:63 6.6?5 !.61I S.itS0 9.b74 ,.73t 0.S64 9 giS 5.ttg i5.iEg lJ.6Jt i6.3t0 i6t.9git
UiY
78,921 ?l 1!q
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174
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tl ll ti
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378
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11,495
32,95i
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ils :t3
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it
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49.194
6, t 16,871 5! 191 17,{17 J.9t9 !t i65 3.1{5 7,6gi ?,518 d.l{t 2,847 5.106 t,687 4, tit l!416 3!{34 1, 1.35 :! 893 |,'tgi ?r,i6g F64 ?,!89 ;46 t,8?; r49 1.:85 5{8 I,3S7
It
t7
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4,642 lg!ill
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gt3,;t6
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t6l
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556
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103
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i35 1:6 ii6 lfit Lli'
iit
566
3:5 4,19
42' 3?4
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?84 261
:,i3
3 UNES ARE OD., WAIL T'HICKNESS, AND MOMENT OF INERNA.
Simplified Solutions for Pipe Stress Table $3 Contlnued
d.6i5 Tl ?4 iH.
,itt:!T
:;
s.6:5
g,5
i,J.
i5S
S.1r8
i2,75S S.443
iit.3?s :86.139 16l.65g
sCH. lEg PIFE
14.u6g 16,99t 13',Jrio 2g'fr88 :4'oti
r.937 l.g3t 1.156 l.:81
S?4.41{ lJ64.,l3t ?179'6SS
l3l5'ttS
1.5:l
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3
+
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tfr
ll l? l3 l{ l5 t7 i9
i: :3 :,1
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157.467 46i,7t9 914 t 144 tgl. tt3 ?38,441 4S8,i4? 58.559 1:;,9BS ?7,J!854 16!t45 86,896 179'569
6g7r63g 397.5S7
659!99?
?59!375
41{,36t
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il FIFST
t$l.955
:4!693 58, 4 114.2i8 l!7!73? 277,513 445!{5S rzi.+lr -: 17,tJ6 4t,E!5 St! ?54 ll?:gg4 t94,?i4 3ll!455 473!6Bt 9it.Sl7 t?,63s :t.8s5 5S,5t5 gi,g7f r42.1?8 r?7. S5l 343rJl5 i13.7tB 9,495 ?!.393 43,956 64!322 196,?93 l7t,5B7 259,44S 5lg.??; 7!It1 i7,?4S Il!E5t 4?.699 93t ?59 lll!195 ll ?. aJs 413!t51 5!75? 13.166 ?4.619 39,SBl 64! S9t 103,146 l5?! 175 3:4! 969 4!656 ig! 8&? :1!lil il!?97 5lt7i6 BI!iq4 t?5,S41 169.lgl 1,745 8,83t 17,335 ?5,446 4?,1l? h7 t274 1g?,315 ztr,47t J,585 7,?7,1 14,:E4 :g! 946 i4.699 55,,11: s4.rt5 174.?18 ?!3?t 6,967 11,9dS 17.,lso ?8.939 4i! !14 7g,2g| 145, i7l
:1,17t
38,51?
zg,72t !7t766 t5,347
?St
13t348
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lt!69!
33,19; !4,51?
is!281 9,dr6 a,da7
7r:?l $,4i5
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164
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?:,1SS
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1$4,956
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tlg
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40.
11.515 16,343
17,144.
3s, ?6i
t!
319
t64 8.469 7!6!l 4,ii | {.:3t 6.1:9 3.953 6! 319 1,616 iri'ii 1,315 :t:96 It {;16 ,i, Ai6 ?.896 4,1g: 2!77t !, s6:
4J.
l
t?,!lg
5,
;,i9s i,;t6
5?! 6 3S.3{r
4.1:r
3,9!t 1,518
J,:94
3 UNES INN O.D., WAIL THICKNESS, AND MOMENT OF INERNA.
6t8
13,;3i !i! l:?
3?!:13
12,73?
:6.41,i :i! t5g
ll,igl
iq!164
Ig,33X:' ;1r;dl 9,&S9 l9,i6f
iu6 l8! i59 8,t54 i6,6,io i,4tt 1:,;t7 6!El? 14, ttF 6,t9-r !l,tt7 5.8?l l:,il: 5! 196 llr l:]
f,
5,019 li! l:6
Piping Stress Handbook Table 9-g
Continued
4.i i0 l:.i5 I{. UiFSET
F1
2
;
I
1 a
I It l? i3
l5 l,: 17
ts
it 2g
?l :? :3 t5 ;b ?; !$
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tl i5
li
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ti ;9 4t
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lit
FIPE
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l:1,
s4t
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115!
14,99? ?9!?7!
igl 7ig
a4t! 9tl 191,3!9
5,1:,lBt
I s9,746 ?is, i36 5?i.7ll ?t 443 4i!J4? lli,lll ??f. tEg 3t4, i?s 5!g?4 t!,4t9 23t 9?5 67,77{ 156,t59 3i?,445 i! 54t 7!9t3 15.SS6 4?,S8t 9S.465 l?4, Eit ?.371 5,t35 l0.tt3 ig! 59? 65, ?$4 lt$,547 l, &$i 1ttt77 7,989 ?fi!081 46,3?? 91rgE7 t,?15 :,6S6 5.16S 14,639 il,7;3 6,5,541' 3 t,014 3rg8l t0! 999 ?5,375 59,118 ;0J 1.551 t!t9t c.47? 19.545 lB,rdl
lg!
9J
h
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4t 17 34 31 ?i ?6 i,i t: 1fi 11 iu
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srt s? 75 6S 63 57 53 49 4i 1t lY
rr
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l!531 1, ?6?
I
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i74 331
294 ?S3
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6,66J 15,3?3 5,115 l?.1t8 4!338 l$!997
1,374 It ?8t 2.:10 ?, ii4 I,EJd i,:Br
3S.4?3
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8.t45 16.JiA 6!87{ ll,6Fi 7!1 i1,461 4!9?4 9! 745 51
4r7ZZ
1,647 11175 3.17: 1, ?S3 2,17& 1.f59 ?! 443 937 3! 16! i44 661 6SS 54? 491 447 487 37: 141 il1 7AS t67 217 ?2i ?l?
8!l:5 7,;i? 6, i7; 5,494 1.435 4, ?79
t!71d 3,196 1.53? I,945 f! 355 I! i,li l!:31 :1476 1,134 ?,244 1,031 I,E4B 94S l!96g S5? i.;91 789 1,55t j74 i!43r 6i7 1,l2j; &!5 l!?18 ;,)t 1,1:i 5:g I,944 ,ifr 4t,
3 UNES ARE AD,, WAIL THICKNESS, AND MOMENT OF NERru.
Simplified Solutions for Pipe Stress Table 9-3 Contlnued
I,t 10 !4 il{. scll, 1i0
cFt-
iEI
l4.E9t ri.g00 lE'tlgg ig'g$n :4.d0, l.gt3 l.tlg l.3lt 1.-5Eg i.sl! 9ir.5:r' l:55.419
lsr.11: Il$,441
'J
,i It t2
i3 t.l
249S.irgt 3;5{.13S 568,!34
l]?,819 !22,i32 :36!tsl 96,s:5 16?,S?? :oS! ?lB 7:,746 l?l 710 195t3{5 56,933 93!761 159,589 r
4{![7] 73,]{7 tl8!4{? J5!?96 59,i{6 94.83?
15
l6
76
1
gl5,t57
?93.gsl 6ii.l65
:?6.36i
4il
t77t996
379t987
!61?
l{?!514 ?i7,933 lt3!8A9 ?4t.49d
l2!978
5?,965
27,182
44t6i9
6i,p54
37,9J8
57,914 I lB! 839 48,8S? lSl!88?
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J?,5?7
19,455 17.495
?s,69S
15t
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7!958 13,3t7
:3
539,43S
lil,g58
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9!i9l
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77,19? 63!539
16!
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28,6t9 48,967 ?3!619 3Yr33&
l9,7rg 6t? l4,tt7 t?,1f5
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lo
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l3?! 756
4?!2?6 3&.7?6 3?! 141 :8.r8€ 2:,0:8
83.01S 76.546 66! 999
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!5
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45
47
FIRST
PIFE
3
LINES ARE O.D.,
WAII TIIICriI{ESS,
5t,?6s
AND MOMENT OF NERNA.
Piping Stress Handbook Table 9-3 Continued
E,iir5 T0 iS. r'55 l:.75d d.El: L.t1g l. ltS
S,6?5
iiFF5EI
ci
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7
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9
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tr6,565
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4rs,
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l.9st f, i54 ti,31,5 l, ?59 7! 799 14, S5; ?,746 i,569 t?r5lJ ?,135 i.5s6 10,639 l, s-g! 4,799 9, t?t 1,7?9 41177 i tEEg r,:94 ttl98 6. E53 1! llE 3,149 5,ItS l, l5g ?\i7 | 5, iit i, fii5 714";7 4.67d 91r ?,l"qs .i, t:: s14 l, t4? 3, is? 7:i I,;4: 3.;:4 i57 l,:i! :,99? 59J t.4!? 2. 51.3 I,:Si :,i5t l$l i, li9 'j,:?i 44s l, i66 :, d3l 4St 9?i 1, a57 l7i 3t4 L,,19? t4l !:l 1,:d4 lli 7i6 i,441 i?: i?r t. s :;i i4t l, ?35 ::t i99 t, l4g ?37 556 l.r5? r=83
Btt
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l5gt6:?
r
5{iB.:lB
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9:l 196,l4l 48,793 83!,18t
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195,595
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63,330
19i,
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?6.71s
ri.965 4,{.6tt 37, ?38
,5!7
S05 ?9. s?8 lit,i4t 17,:?5 :4,418 8.7t4 15.i71 :i,lBi
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l
LNES ARE OD., WAIL THICKNESS. AND MOMENT OF INERTA.
l?
408,93t t?7.,1l9 i66, !S4
?09 t1t,i45
89.381
tB7,97A
75.?C6 l5,i, dsi
64,d:? :4,ECl t7.4i
i
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ii 1l
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fii
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fl5
Simplilied Solutions for Pipe Stress Table 9-3 Continued
r.;i5 i0 1:.;5 I}{ Stii. !i-F-
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5ai
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FT
l.5rs 4.5t0 3, ti: t.4:8 9.5;1 F. ElE 5.F3ii l:. i;i -l.l,sl,
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8.
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O.D., WALL THICKNESS, AND MOMENT OF INERTIA.
l,iY) i! /tJ r r c..o
-,'ilJ :,:ti
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Piping Stress Handbook Table 9-3 Continued
14
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Simplified Solutions lor Pipe For the example shown in Figure 9-1, it will take 7,552 lb for a l-in. expansion for a 10-ft offset for Ax '9214 ex' oansion the force F- = 6,949 lb' For a 20-ft offset the iorce will tr-g44lb for a l-in. expansion. for Ay 46 in' 434 Ib. the force Fv
:
The nomograph in Figure 9-2 is used to size piping loops, depending on the size of the pipe and the thermal exoansion between anchors. This nomograph is conserva-
tivi for a refined design' An exact
calculation by com-
puter should be required.
What size piping loop will be required for a 300-ft straight pipeline under the following conditions: TbmDerature: 400"F O.D.: 12,750 Schedule: Sch 140 Materials: A-53 Grade B C.S. Use the nomograph in Figure 9-2, and join points A' B, and C. This will ihow a need of a 70-ft loop (L = 70 ft).
11
A
J&
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L = 2A+B
100
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Example Problem 9'2
B
l-t -]JL
Stress
o1000
IJJ
Flgure 9-2. Stress nomograph'
0)
10 Properties of Pipe
: Fifth power ofd, in.5 = DrlL2: outside pipe surface, ftrlft (ength) : dtr/12 : inside pipe surface, ff/ft Qength) : @2 - &)n 14 : metal area, in.2 : d'z rl4 : flow area, in.2 : 3.4A. = weight of pipe, lb/ft W* : 0.433 Ar : weight of water in pipe, lb/ft Rg : (UA)', : (V + &1*4 : radius of gyration. m. I : A.Rl : 0.0491 (Da - 6+; : moment of inertia, in.a Z : 2llD : 0.0982 (D4 - d4yD = section modulus : in.3 ds A" Ai A. & W
The following are the definitions of the tefms used in the table.
Definitions
D = Outside diameter of pipe, in. Sch : Pipe schedule, nondimensional t : tl6ll thickness, in. d : lnside diameter of pipe. in.
Table 10-1 Properties ot Pipe
T
Sch
D
losi
V8
40
sT 40s
D'.40S
80
xs
80s
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40
sT {0si
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3/s D
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80 )
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r87
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160
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Properties of Pipe Table 10-1
Continued
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160
55
D
Ao
.2249
8Gs
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.742 .or5
80
.t8rl D
d
4.51
?.58
3.61
l.gn
l.l2l
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iqo
t.l9{
3.49 3.32 3.20
1.186
2.t94
l.l6f
t a6t
l.D.to
3.018
t.724
l.8so
1.080
294
Piping Stress Handbook Table 10-1 Continued
t
Sch
D
(continuod)
3 D -3.500
.241 .254 80
xs
80s
160
55
-4.000
t oot t ot, 2.900
Ao
40 80
sT
xs
1A.'
244
.9t6 attl
3.834
88
1.04? 1.047
t.021 1.4&l
oa
1.047 1.04?
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r.047
.9,19
2.Al
10.94 10.78 r0.31
562 480
1.04?
2.680
t.04?
.929 ,900
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3.€8 3.364
431
1.047
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.t.ol6
8.89
tz.sl
3.9st
9E t.Jo
13.€
3.?44
1.004 .984 .980
.134
3.732
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.
t48
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3.?04 3.624
.tn t28
taz
3.548
,lta
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alt .r.t,
t20
69?
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t.04? 269
4.334
1.04? 1.047 1.178
4.244
t371
1.178
t.1l
I.t?8
4.2t6
1358 1332
1.108 1.104
4.t24 4.090 4.026
1193 1144 1058
4.000
i024
3.900
3.500
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3.152
tno .t34
5,34S
$ sT 40s
5 D:5.563
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xs
80s .438
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4.563 4.313 4.063
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tJo
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1.080
902
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t.021
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1.178
1.015 1.002
I t7q I t7e I l?a
ott
4.86
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5.59
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1.178 4363
1.399
270a
t.456
t.272
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1.456 1.456
1.250
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1.456 1.456 1.4s6
l.38ri r.321
l.n7 l.l9{ I l2q
1.064
1.349
4.10
t.3!9 1.298
t ,ro
6.09 6.04
1.544
1.546
t.542
8.66 1.520
ta! 7c|
5.44
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21.36
1.4.t4 1.425
4.O2
1.416
\t.Jtt
1.3?4
a tt
o
tt
t4.61
11.34
12.97
JO-JJ
2.81 J.JO 4.ZL
t.2{8
4.@
2.054
s.93
2-64 2.84
1.262 1.869
i.949
7.88
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4.27 10.42
9.ld
t't t, o.,t9
8.€
l5.l?
8.66 8.03
41Cr
t.928 1.920
9.70
4,925
4.02
1.464
27.04 32.9?
4.tn
8.?8 9.05
4.4t
23.95
3.33t
3.?0
4.78
7.9S
3.Ul
8.08 q i,t
19.00
?.4.74
2.394
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1.505 1.498 1.495
16.52
18.54 18.19 17.26
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1,664 2.050
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I1.04 'tn 1l
t4-62
ata
r.sa
1.510
4.98
20.01
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1.461
1.534
14.99
u.43 a.o2
4.79
1.210
l.{8:i 1.4?
1.88 2.?S 4.30
7.04
3.04 it.,at
5.98
27.54
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1.368
1.549
9.28
2.74a
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.r.6t 3.19
2.?A4
2.78
1.489
7.80
1.962
1?q
t.372
l.coz
13.46
I lar
3.{3
3.42S
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1.455 1.4s6 1.456
t492
4.41
4.02
t2,t8 o4
3.29
5.04 0.Ylt
4.67
t2.24
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1.094 1.047
6.1? 6.13
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1.031
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7.64
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l.l40
6.39
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3.9t
I1.80 I1.50
t. t?8
l.8o
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12.s7
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480
17.69
5.84 tt
3.34 3.60 3.74 ,l oa
1.047 1.036
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2.34
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1.054
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14.33
3.47
2.247
t.178
4t62 4.859 4.813 4.688
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l.l?8
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l.tIIt
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1.I78
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1.628
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4.01 4.81
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3.90
2.81
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2.86
10.64
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6.49
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6.60
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3.016 3.129 3.950
2.624
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40
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3.10 3.04 2.90
l4{t
.344 .469
55 losi
Z.5IJ
8.81 9.91
2.462 2.5S0
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2-68i
40si
80s
|.l
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250
20s
Af
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.
D
3.018
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tosi
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1.84? 1.839
l.?99
5.45 7 tf,
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1.819
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3.03
8.38 25.74 30.c3
:n.64
10.80
Properties of
Pipe
295
Table 10-1 Continued
D
S
t
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.109 .134 .180 .188 .219
5
q
d 6.407
d"
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Ai
10.80
1.734 1.734
t.6?7
10.38
9.82
I.734 r.?34
6.249
6.071 4{,
80
sT
xs
4osi 80si
:o( lnq
8.2t
.2.&
9.lol
.500
5.O25
.s62 .?18 .864
5.501
.109 .148 .158
8.407
4.897
5.04 ,t 7a
3.$
1.640 l. qlo 1.620
3.80
1.604 1.589
r.?34
t.588
I t.?34
t.440
4.41
J.5at
2.?'58
36.8
8.149 20
8
40
sT
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D-8.625 60
80
lm
xs
34.2
2.248
7.93?
1t<
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', otl
al ,
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7.875 7.813
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t. oor
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7.439
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xx
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lEo
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10
.250
.u9
D = 10.750
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10.482 10.420 10.374
2.2€8 2.258
10,020
18.94
36.40
2cl
53.4
18.26
2.143
t9.66
2.133
2t.32 2237
cl a
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8.50
2.195
€.5
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49.6 2.104 2.060
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3.00
35.4
23.40
30.43
2.99
49.3
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10.48
47.9
t2.02
46.4 45.?
55.2 22.45
1.882 1.833
to
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1.800
21.30
2.?.8
l.?84
2t.97
2.81
2.74 2.73
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53.4 60.6
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!8.5
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15.2 18.?
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2.89
12.80 14.69
te to
78.4 82.9 88.8
20.58
100.3 105.7
23.25 24.52
lzt.4
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140.6
32.60
ta
tt
J!.qt 162.0
38.48
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3?.4
14.30 \t.lJ
87.0
36.4 100.9
3.7t
84.5
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7.24
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2.84
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84.S
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t6.81
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84.0
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63.4
2.94
18.8
40.6
86.3
5.{9 8.2t
20.8
t0.29
r3,39
2.92 40.9 43.4
9.lo
a.z 5l.l
22.94
8.7
2-062
8.2t 8.74
44.4
2t.42
14.98 11.81
6.13
23.44
2I.68
50.0 49.5
4.42
45.4
1a^ 8.40
6.83
2.246 2.248
10.29
54.0
14.9t 16.9{
4.35 5.40
19.?l
10.76
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2.81
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28.58 3?,.7!
4.39
l5.l I
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24.9
4.2A
2.A t.$r
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25.O1
21.O4
21.8
10.192 10.136 10.0s4
2.?AO
14.40
?,1
9.91 13.40 14.25
14.95
118
2'I.l
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54.5 54.2
2,EA
2.Al
t8.gtl
3.94
2.ttI
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2.86 c.a
8.16
n.8
10.344 10.310 10.250
4.9
t0
ce t?
1.996 1.944
tn
v.o2
7
l€4
2.304 2.295
n.64
18.8
2.089 2.O78
15.4
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29.5
2.t52
2.2,58
to t lo.o
14.99
15.64
2,180
2.045
o.t'lJ
lGs
() sT
2.?58
32.4
80s
120 140
35.4
.344
30.1
4€t.30
2.160
38.2
9.29
13.28
2.201
42.O
I
Rq
Ww
13.44
10.70
2.?Sa
q 1q7
31.?
8.40
J5.O
8.249
l,J
12.39
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t..J.to L?.42
2.82
40.l
1.664 1.646
1.734 1.734
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.€2
Am
18.78
l13.? 125.9
2.81 2.81
10.07
It 1t z.Ez
I
l.9l
80.7 79.4 ?8.9
34.2
34.9 34.4
J.b9 3.68
I54-0
lAt
160.8
4.6
296
Piping Stress Handbook Table 10-1 Continued
n
?
Sch
(continurd)
..JYC
60
to D
-
10.750
xs
80s
80
l0o
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12.85
?.55 2.54
16.t0
9.564
80.0
85.3
9.314
l?.06
2.81
2.50
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2.4
4'8
18.92
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54.? 58.0
tt.a
64.3
68.1
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9.064 q ?q/t
61.2
z,8l
2.37
2.81
2.4
6.U
9I.J
30.63
2.8t
2-26
t.t2s
8,500
44.4
2.81
55
.156
12.{nt
298
t0s
.td)
12.390
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t?^344
82 u7
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12.312
2A3
8.625
40st
tlJw
t,J
?t.9
tt.2
xst 80s
32.3
3t.9
3l.t 29.5
172-5
3?-
2t2.0
3!'.4 41.5
3.60 J.50 3.stt
244.9 ?€.8.2
{t.5 sit2
296.3
55.1
36-t.9
@.3 68.4
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89.2
n.9
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32.3!t
58.4
109.9
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3.52 3.4? 3.4It
*4.3
60.l
384.0
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3,l.Oa
56.?
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24.6
3.{il
399.4
?4.3
3.34 3.34 3.34
3.25 3.24
6.17
12t,5
2t.o
120.6
52.6 s2.2
8.(x!
1t9.7
4.45 4,44 4.44
1?9'4 140.5
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24.2 27.2
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3.2t 3.Zl
8.62 9.36 9.82
I0.93
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t2.t92
3.19
12.090
3.34 3.34
3.t8 3.I?
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269 zo:t 258
3.3{
r2.150
12.88
n4.8
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t2.062
it5!l
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249 242
3.16 3.14 3.13
I14.3
12.000
3.34 3.34 3.34
13.4t
.t' ID
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4It.6 49.6 53.5
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I1.844 I l.?50 I1.648
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3.34 3,34 3.34
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108.4 106.2
65.4 73.2
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103.9 101.6 96.1
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3.66 3.63 3.62
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t.938
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51.6
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4.4t 4.40
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49.0 48.5
183.2
26.6 28.7
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212.7
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4.39 4.38 4.3?
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144.4 143.6
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26 24
32.3 34.8
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62.0 60.8
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4.86 4.84 4.82
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36.s 45.0
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59.0 63.4 67.8
59.1
4.81
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4.80
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58.6 58.0
4.79
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61.4 65.3
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4.78
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4.74
80.3
55.3
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562 589
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13.5{n
448
3.6"f
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13.3?5 13.2s0
408
4A:,
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13.188
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l3.l2s
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r3.062
389 380
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13.0@ t2.814 t2.?50
40
xst 60
to2
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3?1
345
3:l?
2.98 2.90
taa
23.8t ?.6.&
118.3
15t.5
t9.2
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I t.500 I t.s16
160
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23.56
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14.000
2.81
88.1
2.42
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98.0
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2.81
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ol.l
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9.960 9.?!t0 9.68?
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9.250
lb
D-12-7fi
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140
t2
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31.5!l
10,29
3.53 3.50 3.47
10.80 IO.UJ
l4il.1 l4(,.s t3?.9
3.6? 3.67 3.67
3.45
17.34
136.6
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t8.66
3.42
19.94
134.0
3.6? 3.6? 3.67
3.40
2t-zt
132.?
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t29.0
3.34
24.9A 26.26
84.9 89.3
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t3.44
tn.7
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242
lno o 116.4
84.1
Properties of
Pipe
297
Table 10-1
Continued
I
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Sch
D
q
t
d
Ao
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Al
Am
Rq
hI
I
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I
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(contiaucd)
.ooo .?50
80
I
t2.r?s
I00
l4 D-
1.093 1.250 1.344
120 140
14.000 160
.r
262
u.814 .t.ot
I1.500
1.406
I1.188
,I88
t5.624 I5.524
ott
4.19
902
4.
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15.500
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4.t9
842
4.19 4.19 4.19
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15.438
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la tt l5.loo
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15.124
30 ST
l6 D-
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80
4.19 4.19 4.19 4.19 4.19
126.4 12,,.7
c.t I
614
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4.69
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38.4?
lr5-5
t30.8
50.0
4.63
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98.2 117.9
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4d32
109.6
150.7
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47.5 4{i.0
4.58 4.53
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181.6
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4.50
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4.09 4.06 4.06
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40.1 42.1
82.0
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80.4
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3.98 3.94
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4.8 24.35
l1e a 114
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5.52 5.50
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t4.500
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4.19 4.19
3.80
35.S0
601
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40.14 48.48
160.9
lJo.c
4.19 4.19
t52.6
16,{.8
co.00
144.5
14.3r4
t3.124 13.000
38!) rtll
t60
t2.at4
345
l0
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l?.500 It itq
l64l
4.5{t
1584
4.55 4.52
4.
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4.19 4.19
t7.?.fi
.€8
t472
4.71
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t?.000
t420
4.?l
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16.876
1369
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t6.813
1344 IJI''
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16.750 16.562 16.500
1247 1?23
t090
80 100
t5.066
120
15.250
t40
I
950
1.688
14.625
t4.438
4.?l
3.44 3.40
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x, 'l
t69.4
IUI.J 1t2.4
68.0
4.48 4.4Ii 4.42
13.94 17.36
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144.6
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194.5
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5.t2
1815 1894
236.7
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61.0
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14.688 14.625
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103.6
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1
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5.84 5.80
L
2908 3020
8I-A $!!.5 323.1
als.6
298
Piping Stress Handbook Table 10-1 Continued
Sch
D
t0
20 D
-
20
sT
30
xs
l9.s@
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t9.3?5 r9.250 t9.124
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40
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18.814
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.8tz
I8.?50
6{'
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1.99
1.500
17.000
1.42
140
l.?50
16.500
l60
1.844 1.968
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23.000
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22.876
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4.750 4.626 22.064
80
t.2r8
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t.531
l.oall
I.812
140
2.0t2
160
2.188 ?-3+3
sa
xl;
20
ST
xll
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20.938 20.376
r9.8?6 19.52s
r9.3t4
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2.9.t25
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29.000
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42 42.000
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2.82 2.73 2.64 2.56 2.48
18.250
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5.24 5.24 5.24 5.24 5.24 5.24 5.24
5.Zt
5.0? 5.04
(nt
4.9? 4.94 4.93 4.91
4.8t 4.?8 4.?6 4.70 4.58
4.'r 4.4{t
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1.07
4.9 4.n
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4.21
4.59 4.3it 4.08
o.to
5.dl
c.,t0
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6.8
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o-15
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!9.36
ta t,
26.9 30.6 34.3 36.2 38.0 48.9 52.€ 54,3 61.4 J!t.o
?5.3 87.2
Af 298.6 294.8 291.0
?at.z 283.5
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135.8 161.9
2249 2550
212.5
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129.5 140.7
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5.92 5.89 5.78 5.74
50.3 54.8 70.0
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L1 Weight and Dimensions o{ Pipe and ComPonents
Weight of PiPe and ComPonents
c
lhbight of iwulntion of the PiPe
I = Insulation density, 1b/ft3 T : Irsulation thiclness, in.
qnd compoWhen determining the weight of the pipe nents, several factois must be taken into consideration:
D=
Outside diameter of PiPe' in.
Weight of insulation Weipht of pipe : lJse the values for properties for carbon steej pipe as a standard. These values can be found in
o
Values
Chapiei tO. The relative weight factors for other mate-
Aluminum Brass Cast ircn Copper
Thermobestos
=
0'35
: l.l2 : 0'91 = l,l4 Fefrtic stainless steel : 0'95 Austenitic stainless steel = 1.@
{arbon
Depleted uanium
(D+f; = 67n
ll
lb/ft3
10
to 11 1b/ft3
11.53 lb/ft3
KAIJO
r9-2rlbltr
Super-X Foly-Urethane
?5tbltr 2.3rbltr
Amosite asbestos
16 lb/ft3 9 rb/ff 91b/ft3
Foamglas
Cellular glass
0.98
,
IT
Diatomaceous earth = 2rrbltr ?AIbItr High temperature
!
Wrbught
.0218
for insulati.on densitY:
Calcium silicate 85% magnesium
rials are:
:
,r)
Mineral wool
8lb/ff
Tables 11-1 Orough 11-10 give the weiglt of insulation and various pipe componens by size.
t
Wigtrt of water in pipe: See the proper.ties of pipe in Chapter 10.
The following pages are tables and figures showing fittings' valves, anct ptpe
standard dimensions of flanges, bends.
299
Piping Stress Handbook Table 11-l Weight of Insulation (lb/linear ft) Plpe Slze
Thickness of Insulation
21h" I
.72 .84
1.35
3
1.01 1.25
4 6
2.tl
t.62
3112"
1.94
2.',|6
| .71
2.52 2.53
3.47 3.48
2.08
3.01
4.O',l
2.5s
J.Ol 4.5'7
4.66 6.09
5.64
7.8s
t2 t4
3.28 4.13 5.20 6.04
.07
6.r6
16
6.90
8.38 9.33 10.4
8.45
11.6
8.93 10.5 10.7 12.0 13.3 14.6
t3.4
r7 .0
21.0
21.1 24.8
14.1
18.0 19.2
2r.9
26.0
23.4 25.0 26.5
27 .8
28.O
JJ. I
29.s
34.8 40.1
40.3
45.9
46.4
52.2
1.5
2
8
10
l8 20 24 26 28 30 J2
7
8.
10.0 10.4 11.2 I 1.9 12.7 13.4
36 42 * me tublc
15.
l3
I
16.1 t7
.l
t4.2
18.2 19.2
16.5
22.2
is based on calcium silicate at
I
20.5 21.7 23.0
t tb/ff
28.0
3.70 4.52 4.42 5.24 6.07 7 .60 9.48
5.59 6.65 7
11.5
t3.2 15. I
11.0 12.7 13.
l
15.8 t7 .5 19.3
14.6 16.3 l7 .7
29.5 31.3
34.0
and nust be adjutt"d 1o,
olnt
^ot"riol".
Table 11-2 Weight of Flanged Gate Valves (tb) Size
(inJ I 1.5
150# 300# JI
55
3
95
4
140
6
240
8
/100
t0 t2 t4 16
l8 20 24
900#
68 75 t4s 215 420 700
1500# 2500#
1,050 1,530 1,490 2,0w 1,150 2,170 2,410 1,580 2,800 3,500 630 830
1,910 3,720
136
115
194 270 530 940
330 720
256 460 610 1,410
1,220 |,560 2,600 1,880 2,350 2,630 35W
3,2W 4,680 4,230 6,500 7,2W
2,350
4,90
9,800
3,900
7
,380
I 1,800
CourEsy of Crane Co.
314 430 900
.4
20.4
1'7
18.
I
18.5
2t.3
20.5 22.6 24.6 28.7 30.2 32.2 JZ+. J
23.6 25.9
39.r
36.3
41.1
38.3
43.'7
rn" tort"
28.1
32.9 34.6 36.9
41.6 44.1 46.6
51.4
54.4 57 .5
49.1 51.7 59.2
iiuaiionaig *d-o*rin.
60.5
bJ-) 72.6 ."ighr.
(tb) Size
(in.) I
9l
16.0
Table 11-3
35
45
2
600#
9.10 11.5 13.8 15.5
weight ot wetd End cate valves
Rating 400#
.48
9.82
150# 300# 20
Ratlng 400#
1.5 29 55 245 60 380 120 4 120 170 220 6 210 360 460 8 340 590 830 l0 550 9r0 r,250 12 730 1,220 1,800 14 990 |,960 2,210 16 1,460 2,550 3,100 18 |,730 33N 3,76s 20 2,200 4,350 24 3,350 6,700 Courtesy of Crane Co.
600#
900#
25
80
70
125
80
155 270 &0
190
260 350 750
410 520 1,250
1,080 1,300 1,610 1,970 2,240 3,2N 3,000 4,350 4,030 6,000
1,910
6,760 8,950 10,500
. Weight and Dimensions of Pipe and Gomponents 301 Table 11-4 Welgtrt of Flanged Check (Swing) valves (tb)
Size
weight of wdd
3OO# 4OO# 600# 900# 1500# 2500#
160 70 23462 280 180 140 120 3 65 630 4 100 180 2W 260 3401,360 6 2N 330 395 530 640 8 390 620 680 900 1,180 2'100 l0 510 9m 9N 1,440 2'170 t2 775 r,2n 1,250 |,970 t4 1,200 1,650 16 1,450 2,050 2,420 18
.t
J
80
t40
6
250
8
a0
l0
598
t2
824
139 214 396
a8 686
14 16 18
20 24 Councst oI craie co.
zto
155
190 210 240 310 420 500 580 740 890 820 880
390 780 1,320
Counesy of Crane Co.
150# 300# 400#
4
100
2500#
130
18
Co.
79
900# 1500#
55
20 24
Table 11'7 End Globe \ralves weld tlreight of (tb)
slze
Ratlng
2
600#
1,015 1,150 r,200
t2 t4 t6
Table 1 1-6 vrteight of Flanged Globe \hlves (lb) Slze
47 80 130 zffi 510 760
1<
10
a^
Ctaw
Ratlng 400#
350 4 100 6 160 8 360
20
Courtesy of
(lb)
Size
Ratlng
(ln.) 150#
Table I l'5 End Check (Swing) l/alves
90 160
600# 115 191
233 476
318
820
1,2:U.
782
900# 1500#
2t5 46 4fi 490 65 920 1,890 215
2500#
Ratlng
(in.) 150# 3OO# 4OO# 600# 900# 1500# 2500#
234757897 3 75 115 130 L6 170 185 + 120 179 206 272 2N 285 6 220 332 401 656 630 680 8 363 530 900 1,100 1'1'+0 l'370
10 12
1,056 1,160
535
794
L4
l6 18
20 24 Courtesy of Cratv
C'a.
r,730
2,7N
3,850
2,400 3,024 4,lm0
Piping Stress Handbook
Table 11-B Wbight of Flanged Angle \hlves 0b) Ratng 150# 300# 400# 600# 900#
238 130 160 230 4 110 2N 235 280 370 6 zl0 370 385 675 1,000 8 360 634 685 985 10 552 1,130 1,950 12 r,720 3,100 2,350
14
lo 18
20
Counes! of Crune
Co.
Table 11-9 Weight of Weld End Angte Valves (tb) Rating
(inJ
r50# 300# 400# 600# 900# 15oo# 2soo#
2
70
3
8l
r70
4
155
490
o 8 10
530
330 880
t2
t4 16 18
20 24 Courtesy
ol Crane
Co.
r30
Table 11-10 Wbights ot Flanges (tnctuding Botts)
2WN 6 10 13 13 31 31 48 2SO 6 9 11 tl 32 32 48 2 BLD 5 10 12 12 31 31 49 3 WN 11 19 27 27 38 61 113 3SO 9 17 19 19 36 60 gg 3 BLD 10 20 24 24 38 61 105 4WN t7 29 4t 48 g 90 r77 4SO 15 26 32 43 6 90 158 4 BLD 19 31 39 47 67 90 164 6 WN 27 48 67 96 130 202 451 6 SO 22 45 54 95 r28 2U 396 6 BLD 29 56 71 101 133 197 418 8 WN 42 76 104 137 222 334 692 8 SO 33 67 82 135 207 3t9 60i 8 BLD 48 90 115 159 232 363 gg l0 wN 60 110 152 225 316 546 1,291 10 so 51 100 117 213 293 528 1.148 r0 BLD 78 146 t8l 267 338 5gg t.245 f2 wN 88 163 212 272 434 843 1.919 12 SO 72 140 1& 261 388 820 1,611 t2 BLD 118 209 26t 341 475 928 1,775 14 WN 11,3 217 277 406 642 1,241 14 SO 96 195 235 318 4@ 1,016 14 BLD r42 267 354 437 s74 16 WN 108 288 351 577 785 1,597 16 SO t85 262 310 42 559 1,297 16 BLD 160 349 455 @3 719 18 wN 140 355 430 652 1.074 2.069 l8 so 229 33t 380 s73 797 t,694 18 BLD 196 440 572 762 1,030 20 wN 43r 535 8lt 1.344 2.614 20 so 181 378 468 733 972 2,114 20 BLD 298 545 7tt 976 r,287 24 WN 295 632 777 1,157 2,450 4,153 24 SO 245 577 676 1,056 1,823 3,378 24 BLD 446 Ur 1.355 2.442 Courte\) of Crane Co.
303
Weight and Dimensions of Pipe and Components
Steel Butt-Welding Fittings (in.)
,."n a/rf-/..'t( '(tiiJ t!ng t.dlu.
t ilt
9Oo
llbow
on
aA T/f 4 LJJRodlu.
9Oo Shorr
:tbov,
on. lnd
.N -A/ > lons Rodlut Elbow "1.-J
45o
1 | | tl F\ i /i -t-:-L
I
5l..l9hl Cror!
r-l-T Ill t*tl _n Ll
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1r/z 2
6
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20rh
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24
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9
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40 40 40
80 80 80 80
40 40 40 40
80 80 80
40 40
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80 80 80
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81/z
1Yt
Stror
l2E/rs 165/re
28
6
e
63/rs I -/L6
4r/s 43/t 51
Extr
S 2
4
L-/r6
7r/z 9
lrr/re 2 2r/z
lVs
30
6 6r/z
15'
2r/z
rt
t
llr/t t3rh.
lr
3 33/t
10
ll.
12r/2
M
J
2Y1
r1h.
t'/2
t'/a
tL____J)
---r
H
I tta
6t/t
3r/z
s
lr6/ts
rYL
2Vz
[\
tl
F
D
s/t
lr/z
[_-\ l!--/-l k-
k
long Rodlur R.lurn B.nd
R.lnfor.lns
lYz
Shap!d Nlppl.!
20xlE'
w.ldlnr 5!ddl.
Yz
Dincnrion "T" it rhown in tobl. beloe; r.f.r lo lors. loblc for diln€nrion "E".
9oo Typ.
Stub End
R.turn a.nd
Size
R.ducinr Crott
ml url
t-M+l
Shorl Rodlur
M
R.du.lns T..
therein, to lhe American Standard, B r 6.q- r qi8; see page 2gr. Thickness: Stendard Fittings r z-inch and smaller ate made for use with Standard pipe (heaviest weight on 8, ro, and r zjinch sizes);sizes r4-inch and larger are made for use with O.D. pipe fu-inch thick, Exrra Strong Fittings rz-inch and smaller are made for use wilh Exlra Strong pipe; larger sizes are made for use with O.D. pipe \/2-inch Lhick. Schedule r60 Fittings are r''"'le for use with Schedule r6o pipe. Double Extra Strong Fittjngs are made for use with Double Extra Slrong pipe
Iong Tang.6t
Stroighl or
lll
l._E-*Ei
Arnerican Standard: These fittings conform, in sizes and types included
Lonr Rodl'rr
i
--r-'llf ill" T U- b .--ul
160,
ad Doubl. Exrro Strcns FitrinE. trov. tr|. ro,n. outdd. din.ttiott.
L__-r-'
1
T-/:
S.cndad, Exrrc st'ots. S.rrcduL
1
n
9oo
Courtesy of Crane Co.
F-c.---
F--A---l
30 36
40 48
x3 17r/t
20
304
Piping Stress Handbook
Forged Steel Flanges (in.) Courtesy of Crane Co.
150 ond 3oO-Pound
Slip-On W6lding Flqn!. 150 ond 30O-Pound
Class
Pipe Vz 3/t
3Vz
1/ts
31/8
I lr/t
4Y.
Yz e/rs
45/^
3A
2W
6 7
7r/t 3Y2 150
Pound E
8Vz 9
l3/s
2YE
r/-
lrr/ra
13/t
Y2
2 2y2
3Yg
I Vre
2TB
3A
35/e
%
rtl" I B/ts
l0
r,/rs
T1
I
l3Y2
lyE l3/rs
l6
150 ond 3O0-Pound
lyg
Tta
8
5/z
7Yz
E
5/e
t-/lB
8r/z
E
x/t
17/rs
9Vt
8
ll3/t
E
l3Aa 23/t
l6
27r/^
xqr/,
20 20
l3/e
Ls/e
11h
'rr
45/e
I
4YB
rr/ra
lr/z
6YA
t3/--
'/a
2
6th
2U
7V2
I
3
8Ut
lYs
%
l6
lrr/ra 3r/t 2 2,r/t
3W
27/8
4rh
37/e
4Y8
'/1
t3/t
f6 %
1rs/re 2r/r,
1
2Y2
4Y2
ru
lTAc 6.63 8.63
14.00 16.00
lr/t
3U,
6
24.O0
Y2
7/s
2r/ra
5/s
1
0.84 1.05
'/a
lr/rs
2r/e 27Aa
3/t
l3/ra 2rt/ta
4
rllc
3/t
6./e
8 8
ts/rel 3
,i\i,"l
3Ve 33/rs
1.90 2.38 2.88 3.50 4.00 4.50
5Y2
7V
E
"/a
7TE
8
lTg
33/s
l1
l3/s
75Ae 8r/z
9Y1
8
'/1 '/l
2
37/g
105/n
t2
3/"
2rAa
37/a
TE
27/te
43/s
I
x'/s
45/e
lr/s
27h
5Y8
3
55/e
6.63 8.63 10.75 12.75 14.00
l0
17Y2
t2
20Yz
2Vt
lo3/e
12t/t
1sY1
16
t7t/t
l5/rs
lY2
lrr/r, Lfa
77As
33/t
4
20
lVa
22W
20
lY.
3Y4
53/t
r6.00
4t/r
24t/e 27
x4
lr/e
3W
6r/t
1E.00
t'/a
24 24
lYa
33/t
6t/a 6./a
5V2
2
3Y2
20.00 24.00 4.50
l6
25W
xY1
l8
2E
23/e
21
20
30rh
2Yz
36
23/r,
27tA
l0
l3/e
6sAs t -/16
77/a
8
9ra
E
% %
to6/^
t2
7h
t2
I IYB lY4
ll
tr/z
12r/z
1s/*
8!z
17r/z
l1/B xYE
lo'/a l2t/e
loYz
2Yt
t73/a
l6 20 20 24 24
l5Y1
2s/p.
r6Yt 20r/t
16 18
25Yz 2a
2r/z
tgt/z
25/c
21
x0
3or/z
2r/t
36
3
77r/^
l3As
20r/a
16r/, lEYz
E
r3a
I
r.66 )
63/ts
l5/a l7/a 2
3Y" 37/re
lrAa
lr/t
t4c
l3/t
lYa 2rYre 5r/2 r E.00 lr3/rt lYe 27/8 5rr/te 20.00 4r/ra
l3/rs
t2r/,
te/,"
to-75 lr5/rt 2t/re
9
6 8
l0
xl/rs
I
s/e
s%
3 3Y2
3r/z
E
3./a
rY1 2r3/rs
0.84 '/e 1.05 "/a 1.32 rr/re txt 1.66 1.90 % 2.38 1 2.88 lY8 3.50 13/,, 4.00 4.50 t -/16
l0
l4
40O, 600, 9O0, 1500, ond 2soo-Pound
5/s
6 7
223/t
33/e
l,
W.ldins No
5lz
5 5r/z 6sAs / -/16 ar/z los/a
2T
u
5
Pound
4Yg
lrr/ra
t4
400
21/re 2Y2
27Yz
lrh
W!ldlng N.Gk Flans.
I
l8Y2
18 20 24
Pound
%
l7/re le/ra
l6
3Y2 4
^/2
x3r/z
lr/r
21
tL/-^ 23/re
-/a
18./t 2lY4
19
l4
2r/ra
4r/.
t6rL
17,
l7/e
'/a
37/8
13/,
150 ond 3oo-Pound
H
|3/.-
4
l4Yt t7
10
300
Yz
E
r/
3t/c
123/t
C.oh.l.p Flong.
Cron.lop Fl.nso 4OO, 600, 900, | 500, o.d 250o-Poqnd
Bolts
D
Siie
1r/z 2
Scr6v.d Flon9. 400, 600, 9O0, 1500, ond 2500-Pou.e
5lip-On !Y.ldi.s Fldns! 400. 600, 9O0, ond l5o0-Pound
21Yz 2434 27
lr/" z\g
6 2
zrh
2r/t 4t/," 2rrAe
6.63
2V,
E.63
rr/rs
27/B
47/B
r0.75
4
3YB
53/e
lr/t 3sle
12.75
4V.
57/a
l3/s 3rr/rs t./E 31h
6 6Y2
lr/z
6E/a
14.00 16.00 18.00 20.00 24.00
t3a
4r/,
67/*
53/s
5t/t
Weight and Dimensions of Pipe and
Forged Steel Flanges (in.) Continued. Courtesy of Crane Co. Class
Pipe Size
rY1
5r/t
r3/,"
2 2r/2
lYz
6Yg
7/e
x7/8
2
z\z
6Y2 7r/z
IYB
3
81/^
lYt
lo3/t
lr/z
63/ra
13
l3/e lr/p.
t -/16
I
Y2
'/e '/a
31h.
'/L
0.84
xr/t
1.05
1r/rs rYa
21/ra
l|/t
23/t 27h 3Y8 3r/^
L5/e
8
-/B
t/t
6s/e,
3A
lr3/rc
8r/z
8 8 8
11/ta l5/e
1/B
2r/B
loYz
I
gYz
rrv
8 11
I
1,5/^
45/e
lo5/s
t33A
t2
lYg
J
5Y1
33/s
6 6Yg 6Vz
Lr/^
l4
10
20
2r/,
123/a
t7
l6
lr/t
20
lY4
233/L
2r/e X3/t
19Y1
l4
16r/a
X03/a
z0
3rr/ts
l8Y2
233/e
20
l3/t lr/z
18
29Yt
2.53/t
20
l5/e
46/a
7 7\/a 7Yz
l7/a
$t/z
E
3Yz 9Yz 133/t 15
900
t
23/e
ll
lra
8rh
11,y,
t2
rVa
33/e
5r/z
12
l3/e l3/e l3/e
4Yz
4V
7Yt
6.63 8.63 10.75
4V8
77/a
12.7 5
5s/s
83/a
14.00
6Va
24
3YB
t6rh
22
l6
X73/t
33/t 3r/z
lSYz
2Ar/q
27Vt
l6 20 20
3Y6 63/e
11/z
r'/a
t'/a
81/z
r6.00
6Y2
l7/s 2
6
9
6V
93/t
35r/z
xo
ZYz
E
llr/z
18.00 20.00 24.00
/ '/2
29U
20 20 20
x7
l3/s
3Y4
lY1
23/e
9r/e
I
"/a
'/1
lrr/rs
3Y2
-/A
l3/e
23/a
I
57/g
lr/s
2
7/E
lt/e
27/B
lY1
6r/r,
rVR
2r/z
43/z
4
1/"
F/a
27/e
lYz
7 8r/z
lr/n lYz
x7/e
47/s
I
lr/a
3V
35/e
6r/,
E
%
2V
96/e
l5/s l7/e
4YB
7r/z
d
I
21/z
4Y8
t0rh
E
E
rYa
lxr/t
zYB
9Y2
8
143/t
27/B
63Aa TsAs
llYz
rv
27h.
E
lr/z
6
t5y,
3r/^
8r/,
12r/2
tz
8
19
35/a
t05/B 123/t
tx l4
4r/t 47h
3e/ts
47/e
4.50
3e/re
4Y8
6Ys
l3/a
4rr/ts
63/t
4rrA,
rsYz
l6/t
5'/a
83/s
6.63 8.63
l9
6V
16
l7/8 2
l6
'),r/^
22\/2
5Y4
lB/ra
l3/e
3Y2
ta
sw 6V
Ita
lrr/te
33/t
3/a
I
13/e
7r/
lV2
4r/a 5Va
%
lr,
2 2r/z
8
ls/t
27/s
534
4
2
33/e
63/t
E
I
23/e
zYl
4r/s
734 9
8
IYB
E
8
ev
2Y2
lor/z
3
tt
l5/a
4s/a
l6r/t
lYz
lx/s
2Yt
5r/t
2
0.84 1.05
8r/t
t0v lYl
1.66 1.90 2.38 2.88 3.50
26Yz 29r/2
Yz t/a
5r/z 6 6Yz 2Ys
25r/^
l0
4s/s
14.00 16.00 18.00 20.00 24.00 3.50
t4
3
3
4.50
l5t/2 l8Y2
2W
43/a
4Yz
lx"/o
2
6.63 8.63 10.75
2e/t 3Yg
1o7s
%
zY8 L"/e
lYa
73/t
4t/t
--)
8 8
2Y2
5r/z
lr3/r'
9r/t
23Ae
4l
rv
lTAa ls/e
2Y8
75/ra
4Ya
tv"
7/B
2
133/t
1.66 1.90 7.38 2.88 3.50 4.50
8
5 63/ra
t8t/z 2lYz
18 20 24 r/z
1
lr/ra
'/2
lY2 t3/t
l0
E
43Ae
L'/A
28r/z
27r/t
I/s
2Yra
l6t/z
3 3r/a
H
I
5 4YE
G 7h
E
llY2
Pound
rt/ts
lr
Dia.
6
3
2500
4Y2
47h
20 24
1500
3r/z
I
27
Pound
t./a 3r/t
41/s
t2
Pound
l3/e Yre
3x/e
-/1
600
Pound
D
lz
116 '/a
Bolts
c
B
t4 l6Yz
3
63/ra
lo3/t
35/e
123/t
t
l9
41A
l4r/,
E
r/t
t2
13/t
IYz
4YB
t0.75 lrYB t2.75 10
55/a
7
8%
tt3/a
14.00
9r/"
27/8
0.84 1.05
lsAe
r'/t6 lLYra
3Ys
I
1I/s 2rAa
3r/z 3t/^
lYs
23/s
1r%o
t.32
tlA 2rAa
43/e
1.66 1.90 2.3E
2./t
3Y8
5'/e
2.88
3Y8
lVt
35/e
6r/e
lVz
4V
7Yz
4.50
4Yl
5VE
9
6
tosa
5th
8
2lt/t
5
t -/t5 8Yz lo5/s
10
26y.
6rh
123/t
2trh
2r/z
9
l6Yz
1o.75
9
t2
30
7Yt
t5
243/e
2.4
t0
l8r/t
12.75
l0
5 6
17
2
l1Y2
2
6.63 8.63
Components
305
Piping Stress Handbook
Cast Steel Wedge Gate Valves 150- to 1500-Pound Dimensions Courtesy of Crane Co.
E-T FEh ltf JIK D
E-T l-E$r--l ,-t
|tI
I
I
JIL D fltt ory" ./-i\ |
I
Ylf i*
I
_5=a r- I
T-
/- i\
I I I
T--T--T -=] fi=-l='il1 r-i--l l-c----l
I
-1 I -t- -l-
f---r-l F-A----l
Bun-W.lding
Dimensions, in Incher Cless
Size of
B
Valve
6r/t
t'/2
zrh 3r/z 4 5 6
1S0-Pound
734
8
8
8Y2 9
c
D
E
Er/z
Lt'/l 16Yz
8 8
201/.
9
grh
llVt
25.4
l0
3r/z 4
B
c
D
E
\rYz
llYz
l3
l3
l8r/+ 22r/t
6 9
t4
l4
253/a
10
32
l5 t7
t7
20 22
20
6 8
26
3l
363/t
14 14 16
423/t
20
52Y1
24 27
3lr/z
10
l5
30%
157/e
JnYa
t4
8
tlr/z
t6r/z
4
l6
10
13 14
18 193/t
52Yz
IE
l0
ffir/z
l8
t2
70
7or/t
27
14
77r/t
30 30
l4 l6
79s/t
l8
97Y1
27 30
20
trh
z0
32
ll23/t
30
163/t
8
7
IE
8
2r/z
l9
3 5
7r/z 8Y2
E9
15
27r/t 3tr/2
4
18
t2
t2
28r/t
l0
15
15 t57/e
33r/z
t7
l0
38r/z
14
t2
3E
l6 16
4oY2 44r/z
30
30
7s%
l6 IE
33 36
9lr/z
30
20
39
993/t
45
36 39 45
t2oy2
36 36
l6
16
303/a
18 19r/z 23r/z
1E
26Y2 30 32Y2
1E
22
900-Pound
20
6
24
E
29
I lr/t
20
38 40Y2
44r/z
10
l0
ll
11
l6
423/t
20
52\h
24 27 30 30
62V1 73r/z
77r/t
a5t/t
l6t/z
t2
11
10
9
l4r/z
22YB
l0
263/E
12
16r/z
l6Y2
Itrh
l8Y2
11
4
2lY2
ttr/z
5
26Yz
3t3/t
6 8
273/a
26rh 27%
323/t
323/t
i'5
t9r/z
40r/t 5or/z
20
26r/z 30 32r/z J5'/2
593/t
67./t
74
74t/.
27
8 8
l4r/2
L'/2
73Yz
t4
363/t
3
1500-Pound
t2
2
1t./-
8l
14 16
36
126
11
t4
l4 l6
t04r/z
23r/t
l9t/t
10
47
llr/z
IE
t
20
llYE
t9./t
6
43
8 9
47 56Y2 64Y1
39
62V
l8
9th
l6Yz
31
833/t 933/t
8Yz 9Y2
r6Yz IE
l0
39
7 8 9
Ls% 8
600-Pound
l6
24 26 28
18
400-Pound
Valve 2rh
9
t2
Size of
l0Y2
t2
300-Pound
Class
'A
l4 16
20
Weight and Dimensions of Pipe and Components
Cast Steel Globe and Angle Valves Courtesy of Crane Co.
Claes
Butt-Welding
Flanged
2
z\z 150
Pou
r
t500
Pound
E
16r/2
11Y2
t93/a
rrlh
t9t/t
53/a
173/e
14
23
l6
2ot/e 7.134 X3r/z
E
8 9 9
lTYt
10 10
x4Y2 26
l9t/z
24r/z 26
7 8 93/t
loYz
173/t
Sr/a
173/e
t9
53/a
19
2oY2
6Y4
xo\2
9 10 10
65/s
22r/z
tx
7
24t/t
t4
7Ye
x6v
l6
293/e
36lz
IE x4
12Y2
xoYz 22r/z
121/2
14
l2Y2
l3x/t
91h
ttth
l3t/r.
HIK
4t/t 4t/t
t9
3r/z
Flaneed or
All alves
Butt-W€ldingt
t4t/2 t6r/z
173/t
243/t
14
243/.
11
16
5 6
t53/t t7r/2
26rh 293/.
t7r/z
293/t
E
22
36U
L2
36y2
834 l1
l6
25Y1
16
8
xSYa
l4
28Y2
It
x1t/r
18
28Y2 3lV1
9
28Y2
1E
93/a
31r/n
20
38r/a
ll3/a
38t/t
x7
23Yz
6Yz 7 7Y2
2tr/1 23rh
z7r/z
8Yz
27rh
r8
l0
303/a
x0
191/z
3lr/t
191/z
E
23r/z
3ara
23r/z
2 zYz
llY2 l3 l4
l9
1lY2
21r/e
t7
27r/2
20 22
303/t
x3Yz
t4
20
l5 18
29Y2
IE
37t/a
6
303/e
22
3
2
l4lrz
25V8
l4Y2
2r/2 3
r6yz
28r/s
18r/z
33Y2
t6t/z l8t/2
10
t9
2lr/t
3Y2
b
900
133/t
$Yz
rrrh
Pound
Pound
I
l4Y2
t0r/2
400
Pound
t33/t
8 8V2 9Yz 10r/z
2U Pound
600
JJ
2 +J
300
K
K
19rh
8
Screwed
HH
HH
l4 l6
5 6
Angle Valves
Globe Valves
Size
t2
l4
II
24
24 29r/2
7Y2
9
24 791/z
373/t
t2
37 3/a
20
l4 28r/a 331/2
IE
308
Piping Stress Handbook
Cast Steel Swing Check Valves Courtesy of Crane Co. Weighlr cnd Dimension:
Js I P F+ T'---'-'T t--N
Prea-
Size
Class
Pounds, Each Valves
,r.l
2V2
3rh r50
5
Pound
5
50
30
Flanged or Butt-Welding
P
E
l0
100
100
140 200
120
390 510
360
5
8
slz
!
$rh 9r/t roYz
1rh
5
rlYz
300
Pound
400
Pound
80
100
120
l2YE
27Yz
133/a
on 39 60 80
9rh lo3/t
63/t
torh
6t/t
E
ll3/t
llr/z
E
EYl
l2Yz
130
l4
g3/t
153/t
t03/t
6
260
lTVz
t\3/"
8
620
510
2l
t4
l0
920
760
12
1290
1015
24t/z 2a
200 270
190
16
l0
IE
t2
6
310
19r/z
8
6E0
l0
900
580 820
13Yz 26r/z
t2S0
I150
30
38
32 40 70
l3
100
14
4
260 400 530
17 20
6
170 300 420
E
900
l0
1440
740 880
t2
1970
1200
180
6
340 640
t
I lE0
l4Yz
t$r/t
63/t
llY2
70
J
l5 I
6V 9Yz
140
900
500
t0r/t
240
2r/z
t
lgYz 24th
180
2
Pound
8 9
250 330
lr/t
Pound
13
160
4
1Y2
600
6 6Yz
ltr/z
1200 1450
40 70
P
8
12
2 zYz
M
$rh 9rh
94 96
M
N
u 40 50
Screwed
Valves Weldinp Valves
FD&SF
Inches 2
Dimeneions, in Inches
Butt-
$r/t
I
tor/r 123/.
tir/t 31
t8t/t 2lr/z
15
Ith ll
240
l8
500 890
29
t6r/, EY1
t0r/z
t33/t
trh
ll0
EO
2 2r/z
160
130
t2 t4rh
245
t70
l6V2
2E0
210
l8Vz
ttut
630 950
Ltr/z
l3r/t
1360
390 480 780
26r/2 273/t
t51/t
2100
1320
3
Pound 6 8
93/t
rsv
Weight and Dimensions ot Pipe and Compononts
Miter Welding
30"
Siz.
6o'
45"
+v2
3/4 15/r 6
5ta
7la
6
I
c
R
r-3/8
r- r
5/16
3/4 15t16
6
1-5l16
I 1-0
t3/a 1-13/16
1-1/8
I,13/r 6
2-1t2
10
1.1t16
2.114
3rl8
12
r
2.5la
3-11/16
l-6
+1n6
1-9
2-1lA
+5la
2-O
35/16
11/16
11la
lA
2.7
2.11A
35/16
18
2.7 t16
r3l4
20
2.11t16
+1ta
t6
22 26
71116
i6
4 13^6
1-7 7-7
| 16
3a
t1l16
.t0
5.3/8
t2
5-An
8,11/16
6,7/16 1.1/4
9,15/
"q 1)
5/8
lA
1r
-3/16
'|
-
o-1/16
1
-
2.r5/16
7 15t16
t
911/16
8-1t/16 s 15/r6 11,Vt6
r-05/16 1
,2.1116
1-
3-r3/16 5'9/r 6 7 5/16
-
3-O
5
1
-
2-15/16
9-1t4 9- | 3/16
103/8 1l I t -9/',t6
l6
1,G7t16
8,3/16
63/8
&5/8
4-5116
4-t5l16
1-7t16
1r-91/16
8-1/16
+9/r6
r
r
tr3/r6
34
3/16 1G9/16
r-11/16
5,3/8
- 0-t/8 1- r7ta
1-
+1tA
'|
-
5-318
2
7.1ft 8 5/r6
1I2
7.7t4 9-1/a
8-lt/16
2,2.1t4
6-0 6-9 7-6
915/16 113/16
2
9-O
1
3-6 3-9 40 4-3 4-6 4-9 5-0
r
r ,3-9/16 r
-
8-13/16
Source: Tclas Pipe Bending Co., btc., Houston' Texas'
5,3/8 5-13/16
1
6-3/16
6-5/8
1
1-v16
1
1.7 | 16
1
-
0-7/16
2-15t16
10-3/8 11,5/8
GT/A
8-3/4
-
-
22-
to.tla o-S/A 2.31a 4-1/A
2-5714
2 7-5tA 2 - 9-3ft 2- 11-1tA 3-O.7lA
43
- 9-S/16 3- 1-1t4
3
6-5/t6
5
0-7116
!t/2
4.r
9-15/16
1-9/ 16
r
6-r5/16 1.1/2
1-7/16
1
I-
5
3 r/8
10-3/ 16
I
+1lA 4.5t16
6
2.114
5
5.1t4 8- r
2.5rc
3.3t4
3-314
2-9
+9/r
32
v2
3.
2-
3-3/16
4
2-5la
t8
5-3t4
2-15lr6
6
E
5-1t4 6-7 lA
2-1t2
2.t14
3-3t4
63/r6 6sta
30
't-7
3
6-3/16 11-7/A
4.314
5-3114
11-
2 2
11,1/8 2-1t2
5.7la
2-9-1/A
- 2-15lt6 r - 5-3/8 1-7 7/a I - 10.3/8
2
0.1t4
r/t6
11.5/8
1,
t-14
1-
21ta 45tA
1
- 0-7116 2 3-5t16 1 - 6,3/16 2 5-13t16 1-1.13116 3 - 3-13/16 1 - I,S/16 3-7.1 6 2 8-5/16 1- 11.3/t6 2 - 10-13/16 3 - 10-7lr6 2- O-1ta 3 - 1-114 4,1-5/8 4-5 2 - 4-1/a 3 6-114 4 - 8-3/8 2 - 5-1ta 3 a-3t4 4 - 11,5/8 2- 7-1t2 3 - 11.1/4 5-3 4- 1-11/16 2 - 9.r/16 5 - 6-5/16 2 - tor3/16 4 - 4.3116 5 - 9-9/16 3 - 3-314 4 - r I,5/8 3 - 8'3/4 5 -7.11A 7 - 5-1t2 a, 3.7t16 6 - 2,9/16 4- 1-11/16 4,11.94 I - 1t-3/8 3
309
310
Piping Stress Handbook
Miter Welding Dimensions
K
H
13/r6
3.5/16
3.1n6
2-1116
1-7 /16
1-5/8
+Aa
4.1116
3-3/16
1t8
2-1/16
6 9/16
69/ l6
4-13/16
r.l5/ r 6 3-rlr6
l/8
33/r
8,13/t 6
8.11/',r6
6-7lr6
ll
lG15/16
8-1/16
9.58
6 t/4
1t2
l-
6
1.7116
I
M
11/16 +13/ t6
t7 la 2-1/a 2.7
/16
5.5/8 6.7
/16
1.1/4
1-
1-3/16
1
1
3-3/8
r
5-9/16 7-314
211/t6 81/r6 2.15/16
8, t
3/16
3-3/16
$5/8 10.7
t16
3.3/4
11-114
4
1
+5/16
1-O.7la
+gfi6
1
-
1-
5.51A
- 4.7t4 - 7.5t16 1 - 9-1r/16 2 - O.1lA
6.7116
7.1t4
8-1/r6
1
'|
Source: Texas
G3/16 2.3t4
r
2
+9t16
2
2-
6.3t4
2 -
2
-
11.1|a
1.11/16
5 3/8
4-1116
-
2
0-1/16
413/16 1-2-7/16 5.r/16 1 - 3.114
l-3 t-51/8 1 - 7.5/16 - 9.1t16
3,9/t6
3 7.15/t 6 3 - 1(}t/8 4- +t1t16 4- t1-5/16 5-5-7tA
6-7
'|
3 7tA
t1-9/16
1
-
1C1t2
-
a.1la
2
-
O.1/8
2
-
rG5/r6
2
-
1,
3 3 -
3
0-7116
29/16 4- 1tlt 6 6-7tA
3-9 4- 3.1t16 4-9.7lA
5 4,3/8 6-51/4
PW Bending Co., Inc., Houston, Tlxas
22 2 22 3 3-
4
7la
23tA
l1l16
3
1-114
3 9/16
r0 1rlr6
-
Gr5/16 t-7 /8
-
+1/A
t1t16
3-5/16
+15t16 6.9/16 4.1/a S-3t4
2-9t16
73ta 0-1t4
4-10
- 8-7/16 - 9-3/8 1- 1O1/? 2- 1-111t6 2- 4-7 tA 2- 8-1/8 3 - 2.3t4 1
r
4.13/
5 3/16
11-13/16
1
t-3116
4 3/16
9-9/16
1
&5la
1- r
7-1/2
1
7ta
3/a
1ll16
8-5/8
2-1t16
- 4-ll16 r - 5lr/16 1 - 7.5t16 1 A-7 la
2 3
3
1t-114
1-O7lA
s
N
3/16
l6
7.3/16 9-5/A
I -O
T
29/16
t
3-114
4-15/16 6-1/2
8-1/16
3
-13/ 16
23t8 9/r6 43/4 515/16 7 3t16
11/16 1-.1/2
2.3/1C 3
3.13/16
q.iirrc 9.1rl16 - 2-1t16 t.3/8 4,3/16 1 - 4.13t16 11.1t8 8 3/8 s.slu '| 7-114 t.s/16 4-3t4 r - 0-r1/16 I9/',t6 6.7/ 16 l.r3lr6 5-3/8 1 I5/8 1 - 2 3t4 10-3/4 7,rta 2 515/16 2- 0-1/16 r 1-15/r6 t.'ts,1c 2-3t16 6-3/t6 2 - 2-7t16 1- 5.112 1,11t4 q 914 2.3/a 7-3/t6 2 - 4.13/16 1 ,7.1t16 \- 2:9t16 , e:9/16 2.9t16 7.3/4 2 - 7.1t4 | 8,5/8 1 - 3.112 lo 3,/8 2.13n6 8.3/8 2 S-a/a I 10,5/16 t 1:1/l6 3 8-15/16 3 - Or/16 1- 11-1t8 1 - 5.1t4 11.7tB 3,3/16 I9/16 3 - 2-1116 2 - 1-112 1 - 7.1/a 1 0.3/4 1G r/8 1- 1.9/1C 3-3/8 3 - 4-7/a 1 8,5/16 1G3/4 1 9- 12 3-9/16 3- 7 1t4 2 - 4-5/A 1-23!a I t-5116 3-3t4 I - 10.11/r6 1 - 3.3/1€ 11- 15/16 4, G1/16 2 7.71A 4 1- 11-l ta r - 3.7/6 4 3/16 1 -O.112 4 2.1/2 2 - g-7 t16 2- 1-11t6 1 1111. 4.3/4 4- 9,11/16 2 - 4-5ta l-71l',8 1 - 4-1/8 5 - 4-7la 5-3/8 3-7 2 A 1t4 1-9.1/2 6.15/16 1 - 5-718 6 - 0-1/8 3 - 11-5/8 2 - 11.3t4 I - I1.7,t 7.3/16 1 -9.1/2 7 -2-1/2 4 - 9-3/8 2, 45ie 3-1 1
a_
Weight and Dimensions of Pipe and Components
L€ngth of Pipe in Bends Courtesy of Crane Co.
Radius of Pip€ Bends
-'l
f*.9\ |
90" Bends
|
180' Bends
the length of prpe in d bend having a radius not qiven above. add together the Iength of pipe in bends whose combined radii equal the required radius.
ro nna
270' B€nds
540' Bends
length of pipe in 90'bend of 5'9'radius. Ersmolcr ' Find Lenetli of prpA r; o0" bend of 5 radius = o+ra' Lengrh of prpc rn 90'beno of a' ,adius = W Then, l€ngth of pipe in 90" bend of 5' 9' radius
=
109rl'
311
312
Piping Stress Handbook
Calculation ot Pipe Bends Courtesy of Crane Co.
4i'
Eromple No.
8-Given A,
9o
:
sin
B, C, D,
R
tH : lllc K:tanlH L:A-K P: B _K N:F*2K
E : D -A _B F :YE'+ E
zc
x
R
Exornple No. I
B:
3.414
2.828 0.828
t+A--E
,
l.-s1
Eromple No.
E:D_A-B F:2N_C e :11o"+
$:
tan
r'
zH
K:14c
Exomple No.
E=D-A-B e -tVl-lT" " =
=
stn
ltJ
z,
tso
x x
x
^R
R
l--€ivcn R ond 45o Angler T = T ans.ent
Length oipipe in bend
R
9.425
x R +27
:
-
9-Given A,
M
B, C' D,
R
:llK'-n,
{:sinzN lP :90" *
to:r4tP
ZH
- tN
S:tanlOxR
lO-Givan A, B, C, D,
otf
l2-Given A,
P:2D C:A-2R n _tl,op,, r--, E:D-n F :2E
R
tH:tltc K=rantHxR v =A-K \. _ R .K ':-"-
Erornple No.
Exomple No.
C:%B
D=R+C
E = A -2R F =l/D'+E'
R
C/2R:
sin
tG
lH:90'+ lG lK = 180'-2 tG
l3-Given A,
EiF = sin lG H =%F x = 1ln-' K/H : sin lL
n'
B,
R
tJ[:tG-tL
lN = r80'+2lM t?==s2o; +
trI
Weight and Dimensions of Pipe and Components
313
Galculation of PiPe Bends Courtesy of Crane Co.
Exomple No.
D:B-C F =ll I
Ii = H: --l
aA
Sln
Exomole No.
l--Given A, B, C, R
zr F lS: tP * tG tK : 9O" - tS tL : t4 tS_ M = rar] lL xt( N:H+M O:B_C-M = stn
E,
Zu
llr;-
n'
4-Givsn A,
E:V a'+ D'
€xonple No.
2--Given A, B, C, N fxomple No.
D: B -C E:A -R F
:lo,
+ o'
E
F=s:nz\l H
:
lr'- n'
D:B -C
E:la'+a A
E --'-'
-A
c
:y
S-Given A,
(2R)"
R (1
- B'
lp:
sin
tD
R
7:sinlP t8:zP+tG lS lK:9O' lL : 1/2 lSM=tanlLY,R N:H+M _M O :B -C
Exomole No. 3---Given
R
LU:sinzF H:tanlG Xft tG:y2tF P:C -H
D:B-C
B =2R
B, C'
A, B, C,
fxomole No.
C:thB D: t4A
tG:%tF H:tanlGxR P :C -H
D
E --'--
E:IC'+ U
G
Exomple No.
R
E
=D
6-Given A,
=%E
B
lH:90" - tF A, + R1 -' 4A | _ rtl
Z-Given A, B, C, D,
G/H:sinlK
-A-B F:R-C t':lzH G:n+F H=lE+ G" rI:V L'-R'
R
IIlL=sintN to :90' - tK , t\ 7p =/2 tO S:tan IPXR
12 Allowable Pipe Span trlormulas and Tables
Pipe-Span Stress Limits
^M -Z
5
WL' 42
In order to have a workable set ofpipe-span tables or to
find an allowable span that will require a minimum of manual calculations, the limit for dead load stresses is set at S1/2. This eliminates the need for checkins the sum of
'=!@
the longitudinal pressure stresses plus dead load stress. (Sr, allowable stress at maximum temperature. ASA
:
Code 831.1 and 831.3.) The formula used to determine the maximum soans in the tables (Thbles 12-l through l2-9) is a mean berween a uniformly loaded beam simply supported at both ends and a uniformly loaded beam with both ends fixed. This mean formula most nearly depicts the conditions actually existing in a refinery. (See Figure 12-1.) By inspection, if the two moment diagrams in Figure 12-1 are superimposed, the point of the maximum bending moment will still be at mid-span.
Mean=
M:vz(Y.y-)
A safety factor of 1.25 is required because of the discrepancy between theoretical assumption ald the actual field situation.
M:wL'xl 124
Pipe-Span Deflection Limits Maximum allowable pipe deflection between supports must not exceed 1 in. or ll2 the nominal pipe diameter. whichever is the smaller. This is the basic piping practice: however,.it is subject to compliance with the customer,s specfrcanon. The formula used to determine the deflections in Thbles 12-1 through 12-9 is a mean between a uniformly loaded beam simply supported at both ends and a uniforn r loaded beam with both ends fixed. (See Figure l2-2.) In order to maintain homogeneous units, "Lt' must be in in. and "W" must be in lbs/in. , however, for ease of handling we wish to have "L" in ft and "W" in lb/ft, whicL we must now convert to inch units. The preceding equation becomes:
5 WL2 48
In order to maintain homogeneous units, "L" must be in lb/in.; however, for ease of handling we wish to have "L" in feet and 'W" in lb/ft, which we musr now converr to
.
wL4 I28EI
^
13.5WL4
inch units. Thus the preceding equation becomes:
M =-
5WI
-
48
2
60
wL,
5 WL2
48
l3.5WL4 EI
EI (Text continued on Dase 3:0
314
a Allowable Pipe Span Formulas and
Tables
Fixed Ends
simply Supported
frrnT 1_,-N
Load
I Shear
t uoment
2-l
z-l--
uJf Fixed Ends
Simply Supporled WL ., V =-
., "-
"'-=Y
rvrl -
2
,., -
WL 2
WL, ;;
by figuring the and a uniformly both ends at supported mean between a uniformly loaded beam loaded beam with both ends {ixed.
Figure 12-1. Diagram showing how stress limits are determined
!
r,
Fixed Ends
Simply Supported 5WL4
WL4
384E1
384E1
Mean: =
A1 +A2
3WL4 384E1
WL4 128E1
by figuring and a uniboth ends al supported the mean between a unitormly loaded beam fixed. formlv loaded beam with both ends
Figure 12-2, Diagram showing how deflection limits are determined
t
315
316
Piping Stress Handbook Table 12-1 Piping Spans Based on the Following carbon steel Materials: seamless A53 Gr. A, A106 Gr. A, Apt 5L Gr. A; Wetded A53 cr. B, Apt 5L Gr. B, A155 C55 Ctass 2 >200.F wilh Water,
(L =
No Insulation
7,650 psi)
201'F-600.F wilh Commodity
(f. =
6,175 psi)
=
Wetghi ot Waler, Minimum Insutation
Maximum
'
Exceeds maximum dettecrion. Courtesy of Po$,er Piping Company.
Tabte 12-2 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A312 Tp316, Ag12 TP317, 4430 FP316H, A376 TP317 >200"F with Warer, No Insutarion
(L =
Pipe
Size
'
SCH.
9,375 psi)
Maximum Span
Exce€ds maxiftum deflection,
Co nesy of Power Piping Conpany.
201'F-600oF with Commodity
(L =
8,550 psi)
Maximum Span
=
Weight ot Water, Minimum tnsularion
Recommended
Allowable Pipe Span Formulas and
Tables
Table 12-3
TP304L' A312 Piping spans Based on the Following stainless steel Pipe Materials: seamless A213 FP304H A430 TP304, A376 TP3o4L, 201.F-600.F with commodity
>2OO'F with Waler, No Insulation (1, = 7,550 psi)
(r3
=
5'800 ps4
weight ol water, Minihum Insulation
Becommended
Maximum
'
=
Exceeds ma)(imum dellection. Courtesy of Power Piping ConPanY.
Table 12-4
piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A213 TP304L' A312 TP3O4L >2Oo"F with W.ler, No Insulaiion (1, = 7,650 Psi)
Maximum Span
'
Exceeds maximum delleclion. Courtesy of Power PiPing Compan
Becommended
201.F-600.F wirh commodity
{L =
a,500 Psi)
Maximum Span
=
weigh! ol water, Minimum Insulallon
Recommended
317
318
Piping Stress Handbook Table 12-5 Piping Spans Based on the Following Nickel pipe Material: Seamless 8161 Annealed >200'F with Water,
(L =
No Insulation
4,ooo psi)
Maximum
201dF-450cF wlth Codmodity 1,000 psl)
[. =
Recommended
=
Weight of Waier, Mtnlmum Insutation
Maximum
Courtesy of Po,,er Piping Company.
Table 12-6 Piping spans Based on the Following Aluminum pipe Material: seamless B24l Gr.3oo3 H112 >200'F wlth Wbter, No Insutation (1. = 4,000 psi) Maximum
Cowteq of Power Piping Compaat
Recommended
201'F-400.F wilh Commodity
(r. =
1,7s0 psl)
Maximum
=
Wetght ot Warer, Mtnimuh tnsstation
Recommended
Allowable Pipe Span Formulas and
Tables
319
Table 12-7
PipingspansBasedontheFo||owingA|uminumPip"M"tg'iM >2oooF with water, No Insulation (1. = 3,000 Psi)
Pipe Size
'
scH,
201.F-4O0dF with Commoclily d- 2.ooo Dsi)
=
=
Weight ol Waier, Minimum lnsutalion
Recommended SPan
Maximum Span
Maximum Span
Exc€eds maximum dell€ction. CourresJ of Power PiPing Comqany
Table 12-8 8235 Piping spans Based on the Following Aluminum Pipe Materials: seamless B21O' 9'234' and H18 Gr. 3003 Gr. 6061 T4, 8241 >200'F with Waler, No Insulatlon (1. = 4,500 psi) Maximum
'
Exceeds maxlmum dellectlon.
CouneE of Power Piping ComPant
Recommenaled
201.F-6OO.F with Commodity (t! 9s0 psi)
=
Maximum
=
welght o, water, Minimum Insulation
Becommended
320
Piping Stress Handbook Table 12-9 Piping spans Based on the Following Red Brass pipe Materiar: seamress B43 >200"F wilh Waler, No Insulatton
(l =
tot
1,500 psi)
Maximum
u:o'o:offn
il.
=
weisht ot warer' Minimum Insuration
""""oditv
Fecommended
Courkq of Power Piping Conpany.
: : W:
where SB
L E I Z f
=
: : : :
Longitudinal bending stress, psi Maximum deflection, in. Weight of pipe, including commodity and insulation if any, lb/ft Length of span, ft Hot modulus of elasticity of pipe, psi Moment of inertia of pipe, in.t Section modulus of pipe, in.3 Unit stress = Sr/2, psi. 56 per ASA Code 831.3
To solve for an allowable pipe span with a known __ llectlon, use the foliowing lormula:
.
4i EIA Y 13.5W
de_
Piping Wind Loads Wind Loads Tables 12-10 through 12-12 can be used to calculate wind loads. The wind pressure (P) in lb/ff on a flat surface normal to the direction the wind for any given velocity (V) in miles/hr is given quite accurately by the formuli
P
:
0.004v,
Table 12-11 gives the pressure per square foot on a flat surface normal to the direction of the wind for different velocities as calculated by the preceding formula. The design wind pressure at the location of a given pipeline should be applied ro the projected area ofthiout-
I
l
Allowable Pipe Span Formulas and Tables side of the pipe (or insulation) to determine a uniformly distributed load as follows:
w_ where
(P) (c") (D)
The design wind pressure depends on the location of the vessel or stack. The U.S.A. Standard Building Code Requirements for Minimum Design Loads, in Buildings and Other Structures, A58.1-1972, and the Uniform Building
Code include a table showirg wind pressure at various
t44
P: C": D: W:
I
heights, and a map where these values apply.
Design wind pressure, 1b/ft2 Shape factor (See T};ble 12-12)
Outside diameter of pipe (or insulation)' in. Wind load 0b/in) pounds per linear foot of plpe
More tables have been developed according to wind velocity in miles/hr, wind pressure lb/ft2, wilh reference to a pipe outside diameter. These tables are very usefirl for computer data input to model uniform wind load on pip-
ins.
Table 12-12 Shape Factors
Table 12-10
Ofticial Designations of Winds
Shape Less than
Calm
Ito
Light wind
1
Cylinder
/
8to12
Gentle wind Moderate wind Fresh wind Strong wind Gale Whole gale Hurricane
Factor
General Use
13 to 18 19 to 24 zf, to J6
Octagon Sphere
Flat
39 ts 54 55 to 75 Above 75
* Beoufon Wind kole, U.S. Weather Burca-.
Towers, stacks, drums, tanks, exchangers, prping, etc. Piers for towers and drums
0.6
Tbnks
0.60
Open signs Solid signs Closed buildings, framing, and com. parts Frames, open-type structure
1.60
0.80
1.40 1.30
1.60 Open plan
0.80 Sec. plan 0.00 other Plan
Table 12-11 Pressure per Sq Ft on a Flat Surface Normal to the Direction of the Wlnd Corespondlng Pressule Velocity
(miles/hr)
(lbflrl
To
10
0.4
Gende wind
20
1.6
30
3.6
Fresh wind Strong wind
40
6.4
)U
10.0
60
t4.4
80 100
25.6 40.0
Gale Gale
Whole gale Hurricane Violent hurricanes
322
Piping Stress Handbook Table 12- l3 Wind Load (lb/in.)
t5
rb/tt2 lil
il
0
40
45
50
55
9l
to0
105
lt2
117
85
.r4 .2t
.19
.24
.29
,29
.35
.43
.51
.25
.31
.41
.50
.58
.37
.,t5
.56
.65
.75
.69
.81
.68
.42
.89
.
.4r
rl5
.55
8.625
r0.750
.67
.89
12.7 50
,79
t.06
I4
35
80
4.500
5.525
30
7! es,/ti R
2.375
4.0
20
l.tl
.39
.49
.58
.55 .83
.84
.93
.92
1.04
1 t5
L.27
.96
1.10
1.23
1,38
1.51
r.0?
1.25
I.44
I.61
1.34
1.56
2,r2
t.38
1.32
2.01
.47 r -15
1.45
1.75
2.04
2.3
3
2.61
1.00 r.33
1.66
2.00
2.3
3
2.67
2,99
l8
t.r2
1.87
3.35
20
t.25
22
r,37 1.83
24
1.50 1.99
t,62
1.4
9
2a
r.7
30
r.87 2.49
5
2.62
3.00
2,50
2,9I
3.34
2.75
3.20
2.49
3.00
3.45
4.00
2.70
3.25
1.79
4,34
4.85
2.9t
3.50
4.0
8
4.61
.12
4.75
4.31
s.01 5.3
2.08
2.13
3
2.00 2.56
3.32
4.00
4.66
34
2.t2 2,83
3.53
4.25
4.95
35
2.25
2,99
3.7
4
'1.50
5.21
38
2.17
3.r6
3.95
4.75
40
2.50
3.33
4.16
5.00
12
2.62
3.49
{.35
5.25
44
2,75
3.56
4
46
2.al 3.83
t ,74
48
3.0 0
3.99
4.99
50
3.r2
4
.16
5.20 5.40
I.9l 2.39
1.46 2,92
2.9r 4 -1,2
a,16
4.58
rt
4.58
5.0r1
4.48
4.99
5.45
5.45
5.9S
4.
6.41 5.51
5.8?
5.9 8
6.65
7.33
6.35
7 -08
7 .7A
5.0I
6.?3
7,49
8,24
-34
7.10
7.91
8.?0
6.68
7,48
8.3 3
9.15
8.?4
9.62
6
5.83
.9t
4
.01
7.85
6.4I
7.34
8.22
9.r5 10.0I
5,75
6.70
7.68
8.60
9.58 10.s3
6.0
0
6.99
8.01
s.97
9.99 l0 .99
6.25
7 .29
8,35
9.35
10.41 I1.45
8.68
9.t2
10.83
,57
4.33
.80
.71
7
rl.9I
5{
3.37
4.49
s.6t
6.75
55
3,50
4.66
5.82
?.00
8.
58
3,52
4.83
1.25
60
3,75
4
6.24
7.50
4.14
10.02 Ll.22
t2.49
1.3
3.87
5.16
6
.44
7.75
9.03
10.35
tr.59
12.9t
14.20
.99
54
4.00
5.33
6.5
56
4.12
5.49
5.
9.01 10.09
1t.24 \2.X7
r5
9.3 5 10.47
1r.66 !2.42
4.45
9.58 10.84
12.08 13.28
7
.87
5
.008
10.68 1r.95
g5
8.25
1I.02 12,34
.7 4
14.66 13.74
15.12
Table 12'13 Uniform Wind Loads (lb/ln.)
.59
1.02
.9{ 4.00 /t.500 5
1.00
l.l2
8.625
r0.750
I4 18 20
1.08
2.15 2.58
1.3r
1.2r t,?
"525
.79
.84
1.09
l.16
r.23
r..25
1.33
r.
.54
1.40
9
2.69
2.33
2.34
2,47
3.05
2.91 3.45
1.33
/t.50
4.8?
5.00
5.41
1.3I
r./15
2.14
1.78
r.87
2.62
2.76
3.41
3,59
4.03
t.25
t.17
4.78
5.02
3.99
1.21
l.5r
1.37
.4.56
{.95
1.65
5.00
5.33
5.83
6.25
?.08 8,25
8.?0
9.00
9.49
9.20
9.7 5
10.29
9.91
10.50
r1.08
t.08
4.00
.98
1.66
1.49 2.20
.94
r.50
!11
3.80
3.50
.89
5.54 5.00
5.99
22
5.50
5.95
6.41
6
.87
7.79
21
6.00
5.49
7 .OO
?.50
8.49
25
6.50
8.56
?.54 7.58
8.15
?.91
10.83
2S
7.00
30
?.50
32
8.00
r0.00
r0.56
11.33
8,50
r0.62
11.33
12.03
13.45
r4.16
L2.7 4
L1.24
15.0
15.04
15.83
34 36
40
9.00
10.0
9.99
9.20 4
10.50
r0.29
II.OE
9.7
10.83 L2.23
a2
ta
II.O 12.45
45 !t5
14.00
r2.0 12.5
13.54
13,0
t{.08
5a
r3.tl
L4.62
15.75
15.70
16.9t
54
t5,0
12.00
13.45
14.25
13.3
1{.1
rt.00
13.12
13.99
14.87
13.75
t{.66
15.00
16.5
17.4I r8.20
19.16
16,99
r 8.00
18.99
20,00
17.?0
18.?
5
19.79
20.83
16.25
17.33
t8.al r9.50
20.58
16.87
17.99
19.12
20.25
2!.37
17.50
18.56
r9.82
21.00
r 8,75
15.78
19.37
20.55
17.33
20.00 20.52
2L.21
2a.!.6
22,50
23 .7 4
25.00
23.25
24.53
25.83 25.66
24.00 23.27
22.50 23.22
2L.75
18.12
\5.24
0
17.50
15.28
14.37
19.99
!7 .A7
rt .8?
2
12,50
r1.87
14.58
14.0
50
11.99
10.5
24.75
25.L2
27.50
13 Pipe Support Selection and Design
Pipe Supports
t Because piping is aflected by thermal expansion. supports in a piping system move thermally in different directions. Weight is supported by two kinds of supports-rigid
tions are critical (very expensive). They have been use
and flexible.
c Rigid supports are supports in a piping system which stay fixed. They generally move thermally in two directions-horizontally and laterally, but not vertically. The weight at this point is usually supported by shoe supports, bracket supports, dummy legs, or a rigid hanger. There are hundreds of ways these supports can be designed and every company seems to have its own way. (See Figure 13- 1.)
c Flexible supports move in all three directions. Weight is supported in this application by use of spring supports.
Spring Supports The types of springs offered for industrial support applications can be segregated into three classifications: are the springs most commonly used in the petrochemical industry for supporting loads. They are used almost exclusively in the construction of pre-engineered and calibrated variable- and constant-support spring hangers. They are also used in less expensrve forms in the construction of hold downs, field supports, and vibration dampeners. c Disc spings (BeIlviIIe springs) are seldom used in the construction of variable- or constant-support spring hansers, but are available if desired when space limita-
o CoiI spings
Variable Spring SuPPorts The word "variable" in this description refers to the fact that the load-carrying capacity of the spring varies considerably as the spring is compressed or extended from a fixed reference point. In other words, as the pipe moves up, the spring is extended and the load that it exerts is decreased. The opposite effect is experienced when the pipe moves down. In either case, the force exerted must not vary when extended or compressed by more than 25 % (maximum) from the calculated load. Manufacturers offer a large variety of variable-load spring hangers with standard and nonstandard scales. (See Figure 13-2.) The scale is attached to the spring support
frame and indicates the vendor's recommendation for range of load. Normally, a safety scale is provided above and below the scale. Beyond these points the unit either loses all load carrying capacity or it reaches its fully compressed position, therefore prohibiting frrther displacement. In every case, an attempt should be made to select a spring so that the calculated load falls in the center of the spring-scale range. The maximum deflection, which will compute to be not more than a 25% variability, can be found by dividing the full range of the spring scale, in inches, by a factor of 2.5. Where the equipment loading is sensitive or critical, larger-range scales may be beneficial in reducing the variability percentage. Typical applications are shown in the next pages along with an explanation on how to size and how to determine the type of spring to be used. Dimensions for variable {Texl conlinued on Page 327
324
E
\
"'l
J
.,|
",1
\tf\ET
" , 'S+
I
x
;
e
!4
t
E
F.l
t6 t
HI
I
1
g
o.l
FI
|
-.ll
tlsstA
trTli |t /
ill $
tl
E
Ie
ol
;l
ll.l tl
u_!J
lP
l+
Pipe Support Selection and
I _l
r.
fl
J
o RI
c)l
.{l
.i
a
Design
o
f
oo-
6 o l
o (9
o
.9 lt
325
326
Piping Stress Handbook
Type A
Typr A
Typo B
!t
T=
I
m
T
,t
Special variable spring hangers can be fabricated for
.d\ V
i|fr
l|\ Typc C
fi
lo D.Lrnio. Type: The type of variable sorine hanger to be used depends upon the physical ihari acteristic-s_ reqlired by the suspension problem; i,e., amount,9f head room, whether pipe is to be supported above the spring or below the spring, etc. Conslderation _should be given to the seven standard types of-
Typr
How
fered (see line cuts of types ,,A', througlr',,6"r, unusual conditions.
How io Dctcrminc Sire: Conplete sizing infornation is given above the hanger selection chart This information is applicable to sizing hangers of all series.
It will be noted
on the hanger selection charts that
the total spring deflection in the casing leaves a leserve above and below the recommended working
D
load mnge.
Trovol Stop: lrrtr-l PICCEI
lrnev:L
f
i LrIrTl
sroP
PtEqg
Typr F
Typc
F
Wirh Roller
L--,1 rH
The functional design of the pre-compressed variable spring hanger pereits the incorpo.ation of a two-piece travel stop that locks the hanger spring against up-
Type E
Typr
G
ward or downward movement for temporary conditions of underload or overload, The complete travel stop, the up litnit stop only for cold set purposes or the down limit stop only which rnay be ernployed during erection, hydrostatic test or chenical cleanout will be fumished only when specified. The travel stop is painted red and is installed at the fsctory with a red ..cautio!,' tag attached calling attention that the device rnust be removed before the pipe line is put in service.
Figu.e 13-2. variable supports. (courtesy support rechnology and piping Technology products,
Inc_)
Pipe Support Selection and springs are generally the same for all the malufacturers. That is why loading tables and dimensions that can be used for application in supporting piping have been included.
Constant Spring SuPPorts The word "constant" in this description implies that the spring will exert the same lifting effort as the pipe moves up and down. Actually, the spring rate in most cases rs minimized by transferring the load through a series of levers so that the elongation or compression of the spring is
negligible. Constant-support spring hangers are considerably more expensive than variables and are therefore used sparingly. They are used in conjunction with large deflections where variability becomes a problem, large loads where erren small variabilities are a problem, and at strain-sensitive equipment. (See Figure 13-3.) Manufacturers offer a wide variety of load ranges, deflection ranges, and frames for their constant-support springs. Loading tables given in Thbles 13-1 through 13-5 and in Figures 13-3 through 13-6, generally are the same for all the manufacturers, but dimensions are different and should be obtained from each manufacturer. (See Figure 13-7 for typical arangements of constant supports.)'
Travel Stops
All hangers have built-in stops to limit the travel at the top and bottom to a small percentage beyond the specified range. In addition, temporary stop pins are provided at the initial travel position for the purpose of hydrostatic testing and to facilitate erection. All stops are of rugged construction to withstand appreciable overloads. It should be remembered, however, that hangers will function only when temporary stops are removed and the hangers load-rods are adjusted properly to enable the hanger to operate within the specified range oftravel. An arrow traveling on a scale readily indicates the travel posi-
tion at all times. Load Ad justment
All
hangers are equipped with a load-adjusting nut that permits up to a 10Vo increase or a 10% decrease in loadcarrying capacity. However, since all hangers are carefully tested ald preset in the factory to specified loads, it is recommended that no field load adjusfinent be made until it is accurately determined that a change is necessary.
Otherwise, the proper distribution of pipe stresses in the system may be disturbed.
Design
327
Standard Hangets Load-travel data, physical design features, and dimensions are shown on the following pages, for convenience in selecting the proper type and size hangers for any specific requirement. Since the load-supporting capacity of a given size is inversely proportional to the travel function, excessive overfavel when specified may require a larger and more costly hanger size than actually needed.
Sway Brace Support This type of support is also a spring, but is not used to take care of the weight effect. It is recommended for controlling vibration, absorbing shock loading, guiding or re-
straining thermal expansion, and bracing a pipe line against sway. Figure 13-8 shows different sway braces and tables for loading and sizes.
Insulated Pipe Supports and Anchors for Cryogenic Service Gryogenic Pipe Supports and Hangers The design of supports for piping used in cryogenic service diffbrs from those designs used for standard piping. In this application the support is designed to avoid metal-to-metal contact of the support with the pipe. Such contact would create a heat sink whereby heat would be transferred from the ambient environmental conditions to the cold pipe through the metai support. To avoid this metal-to-metal contact, a support is manufactured from rigid polyurethane foam. Polyurethane offers both the insulating properties necessary to maintain the cryogenic temperature, and also the high strength necessary to support the pipe. Figure 13-9 illustrates a typical cryogenic support. The insulated support is normally furnished with the foam, vapor barrier, protection shield, and a galvanized cradle. These components are all adhered together into a unit that is easily installed. The saddle as ihown in this figure may be removed and replaced with other types of supports such as a pipe clamp for use with rigid and spring hangers, or with graphite teflon slide Dlates.
The design of the polyurethane support includes the following considerations: . Required insulation property (K-factor). o Thickness ofthe insulation on the remainder ofthe pip(Text conlinued ofl page 3,15.)
324
Piping Stress Handbook Table 13-1 Load Table for Variable Spring Supports for Selection ot Hanger Size
Lood Toblc in Poundrr lor Sclection of llonger
site
0
3
3
1
6
I 6
2
hir
I
21/.
sp.in, S.dl.
- lb, p.r i.,
Courtes! of Support Technolog, Products, Inc., and Piping Technolog)t Products, Inc.
il'
Pipe Support Selection and Design
Figure 2680
TY PE -8.
TYPE-A
329
TYPE-C
-
Type B and C opringe are furnished with one ot two luge ae ehown, welded to tlre toP cap of epring'
Typc A rpringc are furnirhed with r threedcrl buchirg in the toP Platc, providing for a rimplc rod attachment for the upper connection. ugt naiad
ha|t9al !12a
load
tb
20 3'o
00 124
v, c
713
tu9
cadn0
crdng
thd lgth
holc
lengtn
dlan
c
3l2a
v2
th
813/rs gqa
5 27 29
Vr
950
6
1Ol/s
1235
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6
12Vs
62
t/.
1615
1\h 11/1
1
79
1Vs
7
th
a4 100 124
11h
7
1
lU!
7
1V2
154
14t
5130
16o 7125 170 q5fl0 18o 12645 19o 1680s 200 22325
21o 29688 19591
l.ngth
6
lt
x
R
s
T
tht
1Y2
101/rs 1013/re
1Ua
7h
1V2
301
2
3,18
2U1
456 528 684
21/,
2!e
I
1Ya
a
I I
t0 10 11
2% 27/a
3Ys
9154e 1oe/r o
85/6
8% 8%
131/ro 131316
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1U4
t/s
V4
1V2
121/^
11/a
7/e
V4
125h
1313/,e 14s/ro 1sYa
11/2
1Ua
121/B
15
11/2
12 13%
1Ua
1st/g
16%
11/2
137/s
14rh
167/a
'|
11/2
14V2
11/4
1U4
1
1V2
1Sla
1U4
11/^
16la
17Y2 18Ya
''|
2
147/a
1Ya
15%
177e
15%s
11/2
187/rs
1V2
2171rc
187ls
11/2
1515he 1815/rs 181s/rs
qa
2131le 2471rc
23111le 261s/ro
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2V2
2811rc
3 3 4
41/2
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Figure 13€, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products, Inc')
330
Piping Stress Handbook
TYPE-D
Figure 2680
TYPT-T
EJ
TY PE-F
--,
c=_: .-- rl
Type D spring permits adjustment from the top, by lurning lhe nuls on the hanger rod against a piece ot tubing. The tubing is securely welded to the spring cap. Type D spring is set above the supporting steet_ Type E permits rod adjustment from either above or below the spring. Type F spring assembly is designed to suppofi piping lrom below, direclly lrom the tloor Adjustment is made by inserting a bar into holes in the load column. and turning the load column as a jack screw The base plate is welded to the case and has lour holes for fastening.
type F csBlng
Lnglh a
0o
6r1/,0
cr3lng
!hipplng l.ngth K
4
10
M
9'3/,6
3Vs
8s/,a
50
8%
4
3Ys
5s/16
5s/,6
60
%
80
5/s
90
tto
7h
813/,6
6%
11/2
6s/s
1Y2
1O1/a
67a
-lY2
101h
8s
1
9'si,^
150 160
8%
1t/a
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12'h6 131r/i6
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13v4 13Y.
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8% 8
2Y2
16Ya
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169r
31/2
19'/i6
4
21VE
1qa
181/6
85/s
1AY6
12Ya
21A
201h 235h
124b
5
23%
123/a
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265h
123/4
61/t
295/,6
32
1211$ 137/,0
16th
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3
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155h
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3 3 3 3 3 3 3 3 3
3 3
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18%
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16!r^
13U. 13U. 13U.
1@1.
16V2
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16h
5
15r^6
171116
179!
19%
13Y. 13Y.
25%
197/,n
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25r1/,5
191^6 2151'6
21\lt6
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2gqe 3231,a 35e/i
6
295116
127e
lG6
17U.
15,1/.
17U.
159t 15Y.
l7U. 17U.
Figure 13-3. Continued.
10'/!6
1g/.
6,a 161, r
6V16
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8U.
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aU. Y.
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18o 190
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1431a
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131k 151h
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170
200 21o 220
10'5/,6
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120 130 140
lenglh
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tt
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6
Pipe Support Selection and Design
i80
Figure 2680
ROO
SrZ€ A',
--
l
L
z
N\
-c Type G trapeze type spring assemb,y is formed by welding lwo standard spring assemblies to the ends of
a pair ot channels. Type G assembly is especially adaptable tor use where headroom is limited, lo avoid interference, or lo accommodate unusually heavy loads. The assembly can be furnished wiih center to center dimensions, as specified by purchaser. When ordering Type G, divlde the total pipe load in half to select the proper spring size. Ihe travel range of the springs remain unchanged-
r F
hanger
.alod load
(appror)
!tza
tb
each, lb
0o
138
1o
200
20 3o 40 5o 6o
256
70
8o 9o 10o 110
12o 130 140 150 160
170 18o 190
200
21o 22o
rod
caslng
lenglh
79142
min thread cngegornonr
channtla
V2
6rr/re
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38 39 63
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la
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131/s
183
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224 270 326 630
1U4
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8% 8%
11/g
11/z
161/re
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231rc
2Va
13/a
lAYs
Bsh
271rc
21/e
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%
lt 1
6% 6%
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1b
933 1137 1436
z
P
28 29 30
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446 598 798 1064 1426 1900 2470 3230 4276 5700 7600 '| 0260 14250 19000 25290 33610 44650
caslng dlamater
1Ya
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11/4
1
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3Vs
4
Figure 13-3, Continued.
31t
4
3il
l
332
Piping Stress Handbook
Figure 980 TY PE-B
TYPE-C
--I-
RiS
rElh r
rll
I
stzE'A'
Type A springs are furnished with a threaded bushing in the top plate, providing for a sjmple rod attachment for the uDoer connection. Type B and C springs are unfurnished with one or two iugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached direc y to building steel by a pair of angles, eye rod or a single plate.
rypr
B Aa,c o,Ec oo
lo
20 30 40
].t
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170
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A.h.
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936 I
l7t
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015
842
196
64
210
t1t0
1154
2506
Figure 13-4, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
Figure 980
***-ffj
___l_
T-ffi-r I FC-t I
xllE
llrll Ll-l-L---i TYPE-D
TY
T YPE -G
TYPE-F
PE-I
!
0o 'lo 20 30 10
50 80 70
19%
2.Y.
1Y. 1U. 1Y.
2OY.
1U.
22 23v.
1Y.
21lt
23\'tr th 25Y.
80
5h 5\t 5\t
1Y.
5h
29h
O
25Y.
120
27Y. 32Y.
130 140 150
1.900
AYa
tl
1.9m 1.9m
7V2
8Y.
Y.
vh
a%
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AY.
7Vr
7
1\'
90 100
th
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8
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13U
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stt
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16Y. 16v, 16v,
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160 190
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200 210 220
35'1. m+t
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h
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h h
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a%
2Vr
al
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17v.
l5V.
llUa
r
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22
2
U.
*
It
Figure 13-4. Continued.
2h
8Vt
5.563 5.56:]
51{
h
2\l
5.563
6Y.
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{ 4
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h
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6n
lt lt
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2.875 2.475 2.475
'16Y7
13U.
2Y.
AY.
2'h
3}t
3ti
1
{ a 1
a 1
333
334
Piping Stress Handbook
Figure 820
TYPE-A III' ROD S|ZE
"A"
TYPE-C
TYPE-B
r-l-t
- --_<,1
__JH
I
B
__t
ROD SIZE
"A"
Type A springs are lurnished wilh a threaded bushing in the top plate, providing lor a simple rod attachmenl for the uooer connection. Type B and C springs qre unlurnished with one or two lugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached directly lo building steel by a pair of angles, eye rod or a single plate.
S
r.rqhl {lp9ror)
lug in9
c
\E,C o,E
f
00 20
10 10
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6
'
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17
29
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r
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80 9o r00
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2
16
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ro
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m2
Figure 13-5. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
Figure 820
ROD & NUT NOT
FURNISI]ED LENGTH TO SUIT CUSTOMER
TYPE-E
TYPE.t) r-r--
--
ROD SIZE
.
LOAO FLANGE NOT FUFNISHED
\\\ INDICATOF
00 10
20 30 40
7v,
7 7 7
AYa
7Ya
9Yt
ala
1 900
2.475 2.875 2 475
AYa
50 70 80 90
9
I
9
8
1Ot/r
I I
1oth 1O7/.
13Y. 13%
16v2
13%
161/,
120
13V.
16V.
130
13%
16V,
13U.
16Y2 16Y2
't6Vz
100 110
2
13% 13V. 5
25
%
h
16V,
3
3i3/,e 3r3^6
1
I
1.9m 8%
50
140 150 160 170 180 190 200 210 2.O
1.9m YB
16v2
l5Y.
22
17U
15Y. 15V.
22 22
17Y. 17Y.
157. t 5Y.
22 22
v,
3.50 3.50 3.50
5% 5%
I
5Va
1
1
I
65/,6
1
4.50 4.50 4.50
41.,a
2 2 2 2
S1/.
1Y. 1V.
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8%
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4.50
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4.fi
8V. a%
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3
450
aV.
21h
1
4.50 4.50
8% 8th
2v.
2 2
5.563 5 563 5.563
Figure 1&5. Continued.
8Va
v,
214
12V2
2%
121h
2rt
121h
27/.
12V, 12V.
3th 3%
v,
1
335
336
Piping Stress Handbook
2Il2"8H
SERVICE: Recommended for light loads where vertiCal movement does not exceed 1% inches. APPROVALS: Compties with Federal Soecification WW-H-171D (Type a9) and Manufacturers Standardization Society SP-69 (Type 4B). INSTALLATION: Designed tor attachment to its supporting member by screwing a rod into the top cap of the hanger the full depth of the caD.
THO,
4'FN. TIiD
LIGHT DUTY SPRING HANGER Corbon Steel Spring Coil ond Coge The Light Duiy Spring Honger is used for the support of rniscelloneous lield run piping systems subiect to slight (up to l,/4") verticol displocement. lt is designed for incorporotion in rod hongers with o lood coupling provided for spring Iooding. lhe unit does not hove o lood scole ond trovel indicotor. Amount of spring looding con be opproximoied by reloting "8" dimension with spring deflecfron role.
Selection of correcl spring size is normolly done by opproximoie methods toking into occount weight o{ pipe, covering, contents ond mojor fittings. Ordering: Order by port number ond spring size nurnber,
DIMENSION5 IN INCHES Sl1in e
a
c
No. %
l)
D
E
Def
6/,
2
6'/.
l'/1
7)/.
t1
81"
6'/^
I0'/s
Lood
1,/, 2
V/"
Spr in o
Defle
oio
w n
sighr Lbs.
per 100
52
26
160
266
66 87 152
00
200
238 287 350 680
600
210
982
5 3',/,
6t/,
6
ledion
,4
Figure 1$6. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
I
f
L. T +
T
----'l
.[w7-.,
-es.;-
Figure 13-7. Typical arrangements oi constant supports. (Courtesy of Elcen Metal Products Company.)
Piping Stress Handbook Table 13-2 Load Table for Constant Spring Supports (lb for total fuavel in in.) hango. 3lzo
load in oounda for lolal truvel in lnche3
Pipe Support Selection and Design Table 13-3 Load Table for Constant Spring Supports (lb tor total travel in in.) losds in Dound3 lor lotal trevel in inchas
340
Piping Stress Handbook Table 13-4 Load Table for Constant Spring Supports (lb for total travel in in.) load In pound! lor total lraval In Inchca
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46187
4467
58848
56788
53000
48177
61344 63888
58156 60525
50472 52615
fi222
42t71 4€G4 4@r0 50000
47315
628q|
54313
5't 953
49700
7?943
68888
65261
9757 56$0 5943
52m8
66388
56358
53909
51666
75884
71666 74444
57500 59750 620@ 64500
61423
58G31
56003
5374t
67000 6S500
63804
m96 ws1
720m
64566
87500
81540
75716 78930
70665 73665
66250
6q)53
96
a2145
71a75
97
&5360
74688
875m
82665 85998
875&
77500 80625 8i]750 86875
875m
6235s 66@2 67649 70296
78826 81767 84708
87500
110
1$m
12641
18350
44665
107
11939
13244 13940
19573
i5819 600m
i06
12508
20@3
53091
94
11nO
2172
61400
s
I
0756 103(n
25a5 m972
584m
9.
921
!t611 10179 10747
a5m0
1
8o1l
10042 11235
11149
52500
5111
/u,
9043
3299
57500
tt
aaTa
231f7
s8
91
9808
t2
13907 14680
87
90
1769
'fl 1{
v21
70524
38378
[email protected]
cx30
Stgla
71351
62604 65430 68250
6ta1,l
743t 1 77265
71c62
dJ122
80946
739€
70831
84469
80628
v125
73914
875m
83992
80342
a7446
s3646
770m m183
875m
86050
830
8@@
73156 75787
83610 47221
79210
75250
71661
43176 65444 68402
82629
785m
74756
67500
86050
81750
n851
87500
850@ 87500
66185
64708
Pipe Support Selection and
Design
Table 13-5 Load Table for Constant Spting Supports (lb for total travel in in.) load In pound3 ior
nangJ aLa no.
l2V.
13v2
14
14Ya
't5
5696
5492
5303
5126
4961
4a06
42
5544
5359
518 7
5025
1SV2
16
64
6152
5915
65
6432
6184
66
7062
67$
6538
6304
6087
5884
5694
5617
67
7@0
7394
7120
6966
6629
6408
620 r
m0a
6a
8320
sm
7m3
7428
7172
6933
6709
65@
8843
8503
8188
7895
7623
7365)
7131
6909
9005
8671
8361
8073
7804
7552
7317
a m
57
lotll tievol 15Y2
In
inchc
17
llth
t8
1AV2
le
19h
m
71
9888
9507
9155
8428
8523
8239
7973
n25
72
10507
10103
9724
cts
9057
8755
4473
82G
73
11126
10697
10301
9932
9590
9270
8971
8692
74
11714
1
t292
r0873
10484
10123
9786
9470
9175
12416
1r
ct8
11496
11084
10703
10346
10012
9700
76
1$88
12544
12118
11584
11282
10906
10554
10225
77
!3760
13230
12740
122€4
11861
1
1466
11096
10750
78
14507
1399
13432
12951
12505
12088
11698
|l34
79
15254
r4666
t
4123
13618
13149
12710
12300
11917
&)
16000
153€4
14814
fi2€4
13792
12902
125.O
81
16m0
r6153
15555
14S8
14482
14m0
1354 7
13125
8it
't7€o0
'16922
16295
15712
15171
1465s
14r92
13750
83
18400
17602
17(B6
16427
15861
15332
14lX)7
14375
19680
18522
142.1
1756S
16364
16398
15859
r5375
20960
20153
19406
1A712
18068
17465
16902
16375
86
22160
213o7
m517
19783
19102
18465
17869
173r3
87
23:t60
?2461
21628
20855
20't36
19465
18A37
18250
88
24560
23614
2739
21C26
21171
20465
't9805
19188
89
25384
2757
219e8
21288
20625
2€3o7
24413 2725a
23569
m
26400 29440
26283
25377
24331
23740
23000
g1
3?210
31@0
29&50
a7a2
27791
26864
25998
25188
g2
35280
as22
32665
31496
301r I
29397
28449
27563
3aan0
37g)E
35944
34639
33446
32330
31247
3)313
12!00 40788
39257
37853
$549
3530
34t90
33125 321 19
31175
3@45
29442
2fl647
27494
27179
26500
442@
42494
40g24
39460
381m
36830
35642
34531
33482
32498
31570
30691
29863
29078
28332
27625
4amo
44ZiO
42590
41067
39652
38330
370€3
35938
34445
32856
31941
31080
30262
29486
?€750
47800
,r5960
44257
42873
41204
39829
39545
37344
35209
43822 35r 45
3r'141
3l}191
32295
31448
30640
?3875
4SOO
47690
45023
4428[
42755
41329
4m00
38750
37572
36468
35/27
34441
33511
32631
31794
310m
99
51600
49613
47n5
46066
44479
429S6
41609
40313
39087
37939
36855
3584t0
3/,862
3:}946
33076
32250
tm
$6m
51536
49627
47451
46203
44662
43221
41A75
406m
39r09
38284
37219
36214
35a62
34358
335m
u
s 91
95
98
tol
55800
53459
51479
49637
47927
46329
44434
43434
42117
40880
39712
34607
37565
36578
35640
34750
102
57600
56382
5330
5142 4S51
47995
4&47
450m
4S32
42350
41141
39996
38916
37894
36922
38000
1(x,
802m
5788e
55738
53744
51892
50r 62
44544
47031
456(P
44262
429S
41801
40673
39604
385€8
37625
104
62800
60382
58
54r 34
52324
50640
49063
47571
$174
44455
43607
42429
41315
&255
39250
105
65400
62882
m552
58346
56375
54495
5e737
51094
49541
4€085
46712
45412
44196
€025
11921
40875
106
68000
65382
62960
60707
58616
56661
54834
53125
51510
5mm
48569
47214
45943
44736
435€8
42500
107
700m
6€228
657m
63350
5116€
59127
572m
55438
53752
52r 73
506a3
49273
47942
46683
454 85
44350
t0a
7"3920
68441
65992
63719
61594
59607
57750
55994
54350
52797
51328
49942
€6i]0
47343
a6200
109
70960
7to14 74m0
71255
6530
u127
62059
60125
58297
5459
53439
5200
50€30
49331
48rm
1t0
80000
76920
74070
68706 71120
64960
66€60
64510
62500
60600
57140
55550
54050
52630
51280
5m00
r45
58820
341
342
Piping Stress Handbook
Figure 550
VIBRATION COIIIROl AND SWAY BRACT
The FIG 550 vibrotion conlrol ond swoy broce presents o neol, conpoci oppeqronce
Sire Ronge: For pipe sizes 2 through 24 inch. Service: Recommended for conttolling vibration; absorbing shock loadings; guidittg or restraining the movement of pipe resulting from thermal expansioni bracing a pipe line against sway. Instollotion: Shipped ready foi installation
Adiustment The sway brace should be in the neutral position when the system is Hot and operating, a: which time the tension test collar should be hani tight, If it is not, the sway brace should be adjusted to the neutral position by use of the loai coupling. The screws in the tension test colla: need not be loosened, since they serve o[ly to secure it to the load coupling. Feotures:
rVibration is opposed with an ilstantaneous counter foice bringing the pipe back to normal position. rA single energr-absorbing pre-loaded spring provides two way action.
Cut.owoy section shows simplicity
of exclusive .single spring
design
o
One spring saves space and simplifies design.
o
Spting has 3-inch travel in either direction.
r Accurate neutral adjustment assured.
oEnclosed spring excludes ditt and gives a clear. compact aPpeaaance.
Speci{icotions: Fulfills the requirements of the ASi Code for Pressure Piping as to fabrication details and materials.
Deflection of single spring occurs when thrust exceeds pre.compress ion
Tension couses dellection of sin. glo spring in opposite direction
Figure 13-8, Vibration control and sway braces. (Courtesy Support Technology and Piping Technology
Produc:-.
Inc.) Fi
Pipe Support Selection and Design
lmportont: Rod lengths should be cut and final tension adjustments made for the hot or operating position of the pipe. If, with the pipe in its hot position, the
Siue Selection: The vibration control and sway btace
gives full deflection forces from 200 to 1800
pounds
initial precomptessed spring forces from 50 to 450 pounds to dampen vibrations, oppose pipe sway and has
tension test collar can not be turned by hand or if it tums very freely, loosen the jam nut adjacent to the rod coupling and rotate the coupling until the coliar
and absorb shock forces.
The exact amount of energy needed to control piping should be in proportion to the 6ass, amplitude of movement, and nature of disturbing forces acting on the pipe. When it is possible to calculate the exact restraining force required, the size of the vibration control and sway brace capable of providing this force
can just be turned by hand. Retighten the jam nut.
When correct tension adjustments are completed, the btace exerts no force on the pipe in its operating
position. Undei shut-down conditions, the brace allows the pipe to assume its cold position. It exerts a nominal cold strain force equal to the pre.load force plus the amount of travel from the hot to cold position, times the spring scale of the particular size of the vjbratron control €nd sway brace.
should be selected.
To simplify the selection of size, engineets have designed the vibration control and sway brace in three sizes that are readily related to nominal pipe size. For pipe sizes 3%-inch and smaller, the small size is recommended; for 4 to 8-ioch, the medium size; and for 10-inch and larger, the large srze. Instollotion: The vibration control and sway brace is shipped ready for installation. The rod coupling rotates with slight resistance and the tension test collar can be rotated by hand while holding the rod coupling statiorla!y,
vibrqtion control crnd sway brrrce END
El'lD
PLATE
PLATE
SPR]NG PLATE
rN SIO
343
-.
SPRING PLATE
,-ROD
COUPLTNG
STD. JAIV NUTT
JAM NIJT,'
E E
loads
.
L
FtG 550
weights
o
FtG 555
dimensions (inches)
FtG.550 preload
1
2 3
21o
spring
weight
to
(approx) each. lb
4to I
50 150
10 to 16 18 to 24
450 900
31/,
5 6
1350
1800
ID
200 600 1800 3600 5400 7200
rod size,
trkeoul
3ize,
E '11/z
22 1
36
plpe
1
11/a
2 2 2
79 95
212
41/z
135/o 14TB
41,'
1 1
3/a
1
11/2
'|
1Yz
11/2
'lrz
Y2
11/z
6tb
15/B
177/s 185/s
173/4
15/s
22
17
21/a
141.h
21/a
2011
2lt
13/B
23r3/ro
6Ys
1 ,1
87/a
1
13
63/q
lYz
111i2
63/a
112 112
13 15
63/a
11/a
95/a 11/a
1
r3i, o
FrG. 555 spfing ror pipe size
l 2 3
4 5
6
2lo 4lo
tb 31/2
8 16
10 to 18 to 24
50
150 450 900 1350 1800
A As specified by customer.
Figure 13-8. Continued.
pipe size,
weight (3ppror,
rod M,
each, lb
E
200 600
23 26
11/?
1
1
2
1
1800
38
1
2
1
3600 5400 7200
1v2
2 2vz
'| Y2
a2
11/2
6s/s
98
1t'2
21/2
1\',2
65/s
3/a
11/a
41i2 3/a
1Y2
65/e
20
24Va
77/a
I
2O3/a
25
77/a
1
241/s
283/B
7?/3
1
2451.o 6s/rs 2513/, o 6'g/,s 2713 rc 6'g/,s
31Ya 33Ls
295/B
g'/a 91/a
11,, 11.,
9Ya
1)ta
93i r6 91si, e
135/,s 12
13lz 15Yz
11/a
1l/a
344
Piping Stress Handbook
FIG 550 A **il:"1iu *ll *
FIG 555 A dimension
i! 2It 0 in
recornmended when W dimension is
or les!
2
lt
0
in, o! lo38,
-
FIG 555
FIG 55OB recommended when W dim€nson is 2
Il I in.
B
recomm€nded when W dimeBion is 2 lt
or rnot€
I in.
or more
-r.
_
PIPE
olAp
-
tl!alqace
corior oI plpa noDLnol plpa
drs
rwoy broce
!l:e
2
2% 3
I
6% 2
I
l4 l8 20 24
7 8,,16
sX" r0%
l0 t2
s% s% sr\e 8Xe
3% 4 5 6
lo olltlld6 stud ol ptD6 cloEp
3
rr%
t2tlft r3,\"
I4tXc rs% r7%
Dimenaions lor ssgemblies lor lsrger pip€ sizes dvdilobl€ on opplicalion. psrogroph "How lo sir6 qsBemblios" obove.
S€€
Figu.e 13-8, Continued.
t
-a-
\
Pipe Support Selection and
Design
Molded rigid polyurethane foam supports may also be to support other types of piping systems where the medium being transferred in the pipe is to be maintained at a high temperature and protected from a cold environment. This type of application is typical of a pipeline pumping oil at a design temperature of 180'F through a cold environment at approximately -50"F. The insulating properties of the polyurethane foam are necessary to keep oil in a low viscous state for pumping over long distances. The supports for this type of application are designed in the same manner as those for cryogenic appli-
ing system. The thickness of the polyurethane support should match that of the line pipe. . Support load, o Environmental conditions-The exposed cradle may require special coatings or galvanizing. From these design conditions, a suitable foam density is selected for the supports. Thbles 13-6 through 13-11 include some typical properties of molded rigid polyurethane foam used to fabricate supports. Examining these tables, it is apparent that as the foam density at ambient temperature is increased, both the thermal conductivity factor and the compressive strength also increase. At cryogenic temperatures, however, higher density rigid polyurethane foam has approximately the same thermal conductivity factor as lower density foam. This results from the fluorocarbon within the foam cells becorning a liquid at the cryogenic temperature, thus creating a partial vacuum. Thus the normal support design procedure involves first determining the required K factor to insulate the piping based upon the thickness of the matching pipe insulation. Secondly, the foam density needed to produce the required K factor is selected. Lastly, the length of the support needed to
used
cations.
lnsulated Anchors For special designs where it is necessary to anchor the piping system, it is also necessary to avoid the metal-tometal contact for the conditions already stated. Anchors are fabricated for this application by foaming between an actual piece ofthe line pipe and an outerjacket. See Figure 13- 10.
support the pipe is determined using the selected density.
P0WERFoAM/P0WEBSLIDE Beference Guide
POLYUBETNANE FOAM
sEcTloN "B.s'
AOLTEO PLATE TO STR1JCTUBE
l-g-
*..o.o
"*r.
ro
"t"r"tu".
Al ligure numbers ir lhis section
are ava lable in any POWEFFOAM thickness, sin91e, double
or lriple layefing lo conform to the line
Figure 13-9. POWERFOAM/POWERSLIDE"
345
reference guides. (Courtesy of Power Piping Company.)
346
Piping Stress Handbook
POWERF0AM lnsulated Pipe Anchor Stainless, copper and alumanum pipe can be made
into PowERFoAM anchors.
ULTRA HIGH DENSITY POWERFOAM STEEL PIPE EXACT DUPLICATE OF LINE PIPE TO BE WELDEO TO LINE PIPE
ON/CONTRACTION
Figure 13-10. POWERFOAM" insulated pipe anchor. (Courtesy of Power Piping Company.)
Pipe Support Selection and Design
347
Table 13-6 POWERFOAM- Thermal Properties
oella "T"/2 ll. lb./cu.ll. 10 10 14 14
160.0
20 20
320.0 320.0
Cou
Hol Face
Kq./cu. m,
+43 5 +42.9 +41.6 +42.4 +44.3 138.7
160.0 224.O 224.O
esy of Power
cold
Hol Face
Cold Face 1S3 7
I
162 193.4 159 6 193.4 157 6
l.
''K" Faclor Blu. ln. Hr. Fl.2
264
88.7
0 0213
o 141
0.0219 0.0241 o.0244 0.0297
0.r52 0167 0169
110 3 109 2 106
-3I6.7
103.2
-261 2
760
232
792
-316.1
104 6
-58 4
109
986 860
-746
111 7
102.2
357
-59 4
101 7
-255.3 ,316.1 251 7
24.9 25.2
750
31 8
121 7 108 6
1
Conduclivity
Blu/Hr.
Face
-15 1 -60 0 -75 9
I
Apparent Thermal
Power Input amount ol Energy Pow€r Loss To Malntain
TemDeralure in Fahrenheil
Temperalurein Cenligraale
Powerloam Den3ilier
"F
0.206 o.223
0 0321
PipW ConpanJ.
Table 13-7 POWERFOAM* Physical Properties Engineering Oata Slrenglh Compressive
At Yield with a Safety Faclor
Ske.glh
Srrenglh
Or 5:1
Densilies Kq.
t0
160 0 160.0
10
224.0 224.O
320.0
20 20
320 0
-256 -318 -256 -318 -256
160 194.5 160
60
194.5
,318
194 5
6.0 6.0 6.0
r60
60 60
152 152 152 152
152 152
5900 4500 9200 9200 r 4600 18000
2625
I191
2550
3575
1157 1667
2800
1270
4204 3900
1905 1315
PSI
PSI
PSI
PSI
2676 2441 4173 4173 6522 8165
534 408 833 833 1322
38 29 59 59 93
1630
115
234 231 333
17
2.8 1.9
23
3.1
3.2
254 380 354
PSI
27
32
25
4.8
19500 22104 27200 27004 40000 34900
1371 1483 1912
1898
2812 2453
106.8 81.6 166.6 166.6 264.4 326.0
5.74 11.71 11.71 1€.59
22.92
ar Yrerd
Courtesy of Power Piping Conpan!.
"o*',l'-?;ly ST?31'.':Tf;",:"':$f3$'j1".'#ij::l'.'h Table 13-8 POWERFOAM" Temperature Range
lrsrimum (Hol)
Temperalure
Temperelure
Den3illes lb./cu.
Kg./cu. m.
10 14
160 0 224 0 320 0
20
Minlmum (cryogenic) seflice
Servace
'c +275
135
425
+275
r35
-425
-245 ,254
,275
135
-425
-254
Data is all based on tests performed on POWERFOAIiI made with our tormula and molding techniques. Independent testing laboratory corroborating iesl data available upon request.
Courtesy of Power Piping Compant
SUPPORT CONTACT 30" each side of vertical center line.
60"
-
SUSTAINABLE LOAD FORMULA:
/n'D'L I lc\ Sustainaute Loao \ 6 l\ t = C = Compressive strength with safety lactor O = Ouier diameter in inches L = Length in inches
Piping Stress Handbook Table 13-9 Engineering Data
IEIGHI
OF PIPE, WATEi {PEe Footl
r'rl|sutaTtol{ 1J2
22 2.052
i5 192.01
I 5
402.n
'u
f .375 t "r^"",1 PIPE I
t7912 39.59 23
1323.,15
'.62
257.&A 751"O
r3233 9
i
"Are
nol regular p pe
sz6
*"SUSTAINABLE
LOADS OF INSULATED PIPE SUPPORTS
2 fb./cu. tl. 32 Kg./cu. n. COMPaESSIVE STRENGTH = 5.8 pst (.40774 Ks./Cm.t W|TH 5:1 SAFETY FACTOR
-
'rrBased on ioam .c,mpresston (with
a S:1 salery
Courtes! of Power Pipin| Company.
tacroi,
tengrh ot slpports and pipe sizes.
FOAM BY AMBIENT TEMP
-it
Pipe Support Selection and Design Table 13-10 Engineering Data
*-SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS 4 lb./cu. tt. - & Kg./cu. d. 13 PSI ( 9139 KS /Cm, WITH 5:1 SAFETY FACTOR
COMPAESSIVE STRENGTH =
*rBased on loam compression (with
a
AMBIENT TEMP,
5l
saietv laclor) length ol supporb and pipe srzes
96 Kg./cu. m' 6 lb./cu. fi. COMPBESSIVE STRENGTH ='I6 PSI (1.1248 KS./CM.4 WITH 5:1 SAFETY FACTOB (NON-MOLDEO FOAM AY OTHEFS AMBIENT TEMP
-
"'Based
on road compression (wnh a 5:1 salely lacior). length oi supports and pipe s[es
Courtesy of Power Piping Conpany.
Piping Stress Handbook Table 13-1 1 Engineering Data
-*SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS t tbJcu. fi. - 128 Kg./cu. m. COiIPRESSIVE STRENGIII = ZI PSt (1.5466 Kg./Cm.,) WITHi:1 SAFETY FACTOR lt{ON-MoLDEo
FoAM ay
OTHERS AMBIEXT TEMP.
ot supporrs and pipe si:es.
fi'8as.d
on foam densirios (wnh a
""Comprossive strength ol
5r
salety lacto4, iength ot supporls and pip€ sizos.
POWERFOAM onty.
Counesy of Power Piping Conpan!.
J
t4 Fundamentals of ExPansion Joints
Thermal movements in pipelines and ducting result from variations in temperature of the flowing medium or from variations in ambient temperature where piping is exposed to weather. If not compensated for in system design, these movements may cause high stresses, possibly resulting in failure of the piping or connected equipment. Compensation for thermal movement in a piping system . can be achieved by three basic methods:
Nomenclature and SYmbols Standard nomenclature used in discussing expansion joints and the symbols used in applications drawings are presented in Figure 14-2.
Types of Expansion Joints
1. Designing a flexible piping system that utilizes
2. 3.
-
changes of direction to absorb movement. Using pipe loops or bends to absorb the movement. Using expansion devices, such as expansion joints, swivel joints, ball joints, ard flexible hose.
There are two general categories of expansion jointsthe slip type and packless (or bellows) type. The packless, corrugated metal expansion joint is most frequently used in modern piping applications. It does not require maintenance, and its hherent flexibility to absorb thermal movements in several planes permits greater freedom in piping design. The slip joint, a pair of telescoping sleeves made pressure tight by a packing gland, can absorb a greater amount of axial movement than a comparable bellowstype joint. However, it requires periodic maintenance and is restricted to axial movement only.
Types of Joint Movements
The type of expansion joint used depends on the qpe movement to which it will be subiected.
of
Single Expansion Joint This is the simplest type of expansion joint . As its name
implies, it is constructed with one bellows and is used mostly to absorb axial movements. A single joint can also be used to absorb angular ald lateral movements, as well as a combination of these three basic movements. Figure 14-3 typifies good practice in the use of a single expansion joint to absorb axial movement. Note that the expansion joint is placed between two main anchors (MA) and that it is located near one of the anchors. Q'{otice also that the first alignment guide (GD is placed close to the joint. The second guide (G2) is close to the frst, and intermediate alignment guides (G) are provided along the balance of the line.
Expansion joints installed in piping systems are subject to thee types of movement-axial movement, angular rotation, and lateral deflection. These movements can occur individually or in combinations. The four examples in Figure l4-1 show how single and universal expansion ioints absorb these movements.
Double Expansion Joint This consists of two single joints joined by a common connector that is anchored to a rigid part of the structure by means of an anchor support base. Double expansion
351
Piping Stress Handbook
I r*F AESORPTION
OF AXTAL
I
MOVEMEIiT
(SINGLE JOTNT)
ABSORPTION
OF ANGULAR ROTATION (SINGLE.'OINT)
--I -t-' 1+
-
-li rl
L EGEND
- X: +X: 9: Y:
ABSORPTION OF LATERAL DEFLECTION AND AXIAL MOVEMENT (UNIVERSAL.JOINT)
COMPRESSION
EXTENSION ANGLE OF ROTATTON L
ATERAL DEFLEcTIoN
Figure 14-1. Expansion joint movements. (Courtesy of Badger Expansion Joint Company.) joints are supplied with or without an anchor support base depending on the customer's preference. See Figure 14-4. A double joint is used when the axial movement to be absorbed is too large to be handled by a single joint. The intermediate anchor on the center nipple divides this movement so that each bellows of the double joint is usually located in the center of a pipe run: so both ends are subjected to the same movements and have the same num-
ber of corrusations.
Universal Expansion Joint This consists of two bellows joined by a common connector which is not anchored to the structure. This per-
mits the universal expansion joint to absorb any combinaand angular-where these movements are too sreat to be handled by a single joint. Universal joints usually have tie rods with stops that distribute the movement between the bellows and siabilize the corrunon connector. The joints find increasing use in steam and hot-water distribution systems because there
tion of three basic movements-axial, lateral.
are impressive cost savings for the large amounts of movement they can absorb with a minimum of guiding and anchoring.
Figure 14-5 illustrates a universal expansion joint used to absorb lateral deflection in a single plan Z bend. Both anchors are intermediate anchors because the pressure loading is absorbed by the tie rods. Only directional guid-
Fundamentals of ExDansion
T
MAIN ANcHoR
Xf--f
T
Ft DMA l2\-------------1
mmr
F__x--? IA
.
-ffi-
Joints
353
sTNGLE E*PANSToN JorNT
DTREcnoNAL
DOUBLE EXPANSION JOINT
MA|N ANcHoR
WITH INTERI\4EDIATE ANCHOR
INTERMEDIATE ANCHOR PRESSURE BALANCEO
T
EXPANSION JOINT
I
t
\DIRECTIONAL INTERMEDIATE
m7f DIA
'ANcHoR wtrH
GUTDE
SINGLE EXPANSION JOINT
l----
PrPE ALTGNMENT GUTDE
WITH TIE RODS
rr---r l
'" lfi:11 tEt mmm sroE vrEw
UNIVERSAL EXPANSION JOINT
END VIEW
WITH OVERALL TIE RODS
PLANAR PIPE ALIGNMENT GUIOE
ra*/L 't
t
c-------E-------
)
sPRrNc suPPoRr
UNIV€RSAL EXPANSION IOINT WITH SHORT TIE RODS
+
P,PE REDU.ER
GUSSET
UNIVERSAL PRESSURE EALANCED EXPANSION JOINT
l--'-4
-Ff
HTNGED EXPANSToN
rorNr
GIIvIBAL EXPANSION JOINT
Figure 1'l-2. Expansion loint symbols. (Courtosy ol Badger Expansion Joint Company.)
Piping Stress Handbook
di
'1il-
l|l Figure 14-3. Single expansion joint. (Courtesy of Badger Expansion Joint Company.)
Figure 14-4. Double expansion joint. (Courtesy ot Badger Expansion Joint Company.)
fI
-LATERAL
MOVEMENT HOT
Figure 14-5. Universal expansion joint. (Courtesy of Badger Expansion Joint Company.) ing, if any, is required because the compressive load on the pipe consiss onJy of the force necessary to deflect the expansion joint.
Where dimensionally feasible, the expansion joint
should be designed to fill the entire offset les so th;t its expansion is absorbed within the tie rods as ixial movement.
Pressure Balanced Expansion Joint This is a combination of single joints that oppose each other in the same way the internal pressure loads oppose the other. This prevents excessive loading due to presiure thrust from being transmitted to pipe anchors, turbines, or
Figure 14-6. Pressure balance expansion joint. (Courtesy of Badger Expansion Joint Company.) process equipment. The compressive forces of the two bellows are additive, but these are usually negligible in comparison with the pressure forces. This type ofjoint is used where a pipeline changes direction. It absorbs axial or a combination of axial and lateral movements. _ Figure 14-6 shows a tlpical application of a pressurebalanced expansion joint for combined axial movement and lateral deflection. The anchor on the piping run and that on the turbine are intermediate anchors, and onlv directional guiding is required. By proper design. the guide directly above the turbine can be made to absorb the axial movement forces of the expansion joint without transmitting these to the turbine. The only force imposed on the turbine is that which is required to deflect the expansion ioint laterallv.
Fundamentals of Expansion Joints Hor
Hinged Expansion Joint This is a single expansionjoint designed to permit angular rotation in one plane only by use of a pair of pins through hinge plates attached to the expansion joint ends. Hinged jo-ints are used in sets of two or three to absorb pipe movement in one or more directions in a single plane piping system. Each individual joint in the system is restricted to pure angular rotation by its hinges. However, each pair of hinged joints, separated by a section of piping, will act together to absorb lateral deflection in much the same manner as a universal expansionjoint in a singleplane - application. Expaniion joint hinges are designed to transmit the fu1l pressure thrust of the expansion joint and, in addition' may be designed to support the weight of piping and
----------.1
rA(:
HEJ:
Hings Expansion Joint
PG:
Planar Guide
equipment, and absorb thermal loads, wind loads, and other external forces. A hinged system permits large movements to be absorbed with the minimal anchor forces.
Figure 14-7 illustrates a two-hinge expansion joint system. In this application the expansion joints absorb only the differential vertical growth between the vessel and pipe riser. Any horizontal movement due to piping elpqiion, vibration, wind loads, etc. will be absorbed by bending of the vertical pipe leg. A planar guide may be installed near the top of the vessel to protect the hinged joints from wind loads at right angles to the plane of the piping.
Figure 14-7. Hinged expansion joint. (Courtesy Badger Expansion Joint ComPanY.)
Gimbal Expansion Joint This is a single expaqsion joint designed to permit angular rotation in any plane by the use of two pairs of hinges affixed to a cornmon floating gimbal ring' Unlike the hinged joint which can absorb angular rotation in a single plane ofun the gimbal joint can absorb angular rotation in any plane. The ability of the gimbal expansion joint to atsorb angular rotation in any plane is most often applied by
using two gimbal joints which act together to absorb movement. Gimbals, like hinges, are designed to transmit the pressure thrust and are used in pairs, or in conjunction with a hinged joint. Figure 14-8 illustrates a gimbal-joint application. Because pressure loading is absorbed by the gimbal structure, only intermediate anchors are required. Planar zuides are provided to restrict the movement of each piping leg. Ai in a hinged-joint installation, the location of pipe suppo.t. is simplified by the load-carrying ability of the simbal.
Figure 14-8. Gimbal expansion joint. (Courtesy Badger Expansion Joint Company.)
of
Piping Stress Handbook
Anchors, Guides and Supports Pipe Anchors The.function of pipe anchors is to divide a pipeline into individual expanding sections. Since thermaj movement cannot be restrained, it is the function of pipe anchors to limit and control the movement that expansion joints, lo_ cated in the line between the anchors, must abiorb. In some applications, major pieces of connected equip_
ment such as turbines, pumps, compressors. and reaciors, lI desrgned to wlthstand the forces acting upon them. can
function as anchors. Additional pipe ichors are com_ monly located at valves, at changeJ in pipe direction, at blind ends of pipe and, at major branchionnections. ix_ pansion devices must be installed in each of the pipe sec_ tions to provide flexibility.
Pipe Guides A pipe guide is a sleeve or frame fastened to a risid structure that permits the pipeline to move onJy along-its 9wn lxls: The guide is needed to prevent the pipeline from buckling due to the pressure thiust or ftelbiiity of
the expansion joint-or both. planar pipe guide is a pipe guide modified to permit .. A limited movement in one direction other than loneitudi_
nal. It is used in
"L" or "2"
Cold Springing of Expansion Joints "Cold springing" means prestraining the elements of a piping system at the time of installation so that thermal stresses occun'ing when the piping is hot are appreciably reduced. The purposes of cold-springing expaniion joints may be considerably different, although the mechanics are basically the same. Cold springing is generally applied to expansionjoints absorbing only lateral deflection or angular rotation. Cold springing should not be confused with ..orecompressing" or "presetting" an expansion joint. Tire laner terms apply to adjusting an expansion joint in an axial direction to allow for specified amounts of axial compression or extension without physical interference between the corrugations or overextending the corrugations, yhich mighl damage them. If deshed, cold springing can be done at the factory before shipment to facilitate installation. The endurance or cyclic life of an expansion joint is dependent on the maximum mnge of stress to which the bellows is subjected, the numerical maximum stress value being a far less significant factor. Cold springing an expansion joint to reduce the maximum numerical stress would not result in any great improvement in cyclic life. There are, however, a number of other reasons for coldspringing exparsion joints as foliows:
piping configurations (see
figurg J+j) where rhe expansion idints ar6 subiected to lateral deflection or angular rotatton. Pipe guides should be located and spaced carefullv in a piping system. (See Figure l4-9.) A pipe support carries the dead weight ofthe insulation, . piping. and its contents. Pipe supports are not pipe guides. supports do not lim.it the free movement of piping or con_ tribute to guiding it in any way. The recommendations for pipe anchors and guides given in this chapter represent the mlrxmum requrements tor controlling pipelines contain_ ing expansiotr joints. However, standard piping practice usually requires additional pipe supports b;twe;n guides.
Forces and Moments To calculate the loads on piping, supports, and equipment, the forces and moments to move an expansion joint must be known. The expansion joint manufacturer will provide axial, lateral, and angular spring rates.
Force Reduction
Il
a wide range of applications, the force required to deflect an expansion joint is significant. Where the expansion joint is used to relieve the loading on sensitive equip-
ment, where anchor structures are limited to extremely small loads, and in other similar cases, cold-springing the expansion joint at installation can cut the maximum deflection force in half. In some cases, a 100% cold spring will reduce deflection forces to a minimum at extremely high operating temperatures.
Stability Figure l4-1 shows the movements ofbellows due to angular rotation and/or lateral deflection. In both cases, one side of the bellows is extended and the other compressed. so the bellows may become distorted when subjected to
Fundamentals of ExPansion Joints MAXll,4UM RECOMMENDED SPACING FOR TNTERMEDIATE PIPE GUIDES AXIAL MOVEMENT ONLY (VALUES BASED ON STANDARD WEIGHT CAREON STEEL PIPE
400
357
)
400
350
350
300
300 250
200
200 r80
t80
r60
t60
r40
r40 r20
6
roo
=a^
feo r..r 70
e lao
(9 -k--
6
>40 CE
F
z-30
toL
400
250 MAXIMUM PRESSURE-PSIG NOTE: I.ADOIIIONAL PIPE SUPPORTS ARE USUAILY iEOUIREO A€TW€EI'I GIIIDES II{ ACCORDANCE WITH STANOARO PRACTIC€. 2 ARROWS REF€R TO EXAMPLE GIVE^I IN TEXI
Figure 14-9. Spacing for guides with expansion joint. (courtesy of Badger Expansion Joint company.) internal pressure. Reducing either the internal pressure or the displacement of the corrugations will improve the stability of the expansion joint. By cold springing the expansion joint 50% at installation, the maximum displacement per corrugation is cut in half and the exparsion joint is far more stable. For this reason, where expansion joints are subjected to large lateral deflections, or where operating pressures are high, it is good practice to install the joint in a 50% cold-sprung condition.
Component Clearances Where an expansion joint is furnished with internal sleeves, external covers, or tie devices spanning the be1-
lows, these components must have enough clearance to accornrnodate the lateral deflection or angular rotation of the joint. The required clearance can be reduced to a minimum if the joint is cold sprung 50%. By this means, hter-
358
Piping Stress Handbook
nal sleeves of maximum diameter can be furnished, the overall diameter of an expansion joint incorporating external covers or tie devices minimized, and the desien of external structures simplffi ed.
Use of Internal Sleeves in Expansion
Joints
. I?"r:lJ
sleeves should be specified in expansion joints
ln me Iollowlnq cases:
l.
transmitted through the flange bolts to the mating ange and then to the connecting pipe.
In some instances cold springing is recommended to keep tie rods closer to the bellows. thereby minimizing moments. When ordering, advise if joints are to be insul lated. If so, speci$ the insulation thickness, because this will affect the hardware desien. . Consideration must also be-given to the crushing of piping. Attachments must be designed to distribute -the l-oid as much as possible.
to
When smooth flow and/or minimum friction losses are desired.
2. Where flow velocities are hish. 3. Where there is a danger of pitting or erosion. 4. In high-temperature applications. 5. When copper bellows are used and the application
is
for high-pressure drip, super-heated steam, hot water^or condensate, or where there is any possibility of flashins.
In some
increase the thickness
cases
it becomes necessary
of the pipe wall and/or
the lengths of the pipe nipples in orderlo distribute the load. Proper design of attachments is extremely important. parJicularly for critical applications with high piessures and temperatures. In such cases, hardware-cai cost as much as or mrcre than the expansion joints. For greater systgm rgliab_ilrry, it is important that emphasis be put on engineerirg design rather than price. Upon receipt of per_ unent apptlcatron data. sp€cial requirements can be deter_ mlneo,
Internal sleeves should not be used where tars or other
il;;;;;t-";;;;
Calculation of Forces and Loads highly viscous fluids are nowing. 'jplcking up," "coking," or "caking" and result in joint failure..If purging will prwent these conditions, sleeves The forces or loads to be calculated for tie rods, hinges should be used in conjunction with purging
comections.
Tie Rods, Hinges, and Similar Accessories In a piping system with expansion joints, it is often impractical to provide main anchors to absorb pressure thrusts. In these cases. tie rods. hinges, or gimbals may solve the problem as long as their attachments are designed to transmit the forces imposed by pressure in the expansion joint.
Method of Attachment
and attachments are: 1. Pressure thrust. 2. Force to extend or compress the expansion joint due to thermal growth within its tied lensth. .'- Weight of joint. 4. Unsupported weight of prptng and insulation between a pair of bellows. 5. Weight of fluid carried in the joint and unsupported piping. In large joints, consideration should be eiven to the weight o[ water used in hydro testing.
6. Wind loading effects, if
present.
In addition, effects of temperature and flow conditions must be accounted for.
Tie rods, hinges, and gimbals are attached in two basic ways:
1. By a structure whose function is to transmit the loads to the pipe or equipment. This concentrated loading may introduce high localized stresses into the prping in addition to the stresses due to internal pressufe.
2. By direct attachment to
flanges, which then carry the loads on the rods or hinges in addition to their normal flange load. In this method the total load is
Cycle Life Expectancy The cycle life expectancy of an expansion joint is affected by various factors in physical Construction. These are:
1. Operating
pressure.
2. Operating temperature. 3. Bellows material.
Fundamentals of Expansion
4. 5. 6. 7.
The movement per corrugation. The thickness of the bellows. The center-to-center distance of the corrugations. Depth and shape of the corrugation.
Any change in these factors will result in a change in the life of the expansion joht. The life expectancy is defined as the total number of complete cycles that can be expected from the expansion joint based on data tabulated from tests performed at room temperature under simulated operating conditions. A cycle is one complete movement from the full-open to the fi.rll-closed to the full-open position. It should be noted, however, that laboratory tests rarely if ever duplicate actual service conditions. Cycle life is only one factor in the design of an expansion joint and may be tle least important. Many life cycle tests have been conducted and expansion joints can be manufactured to meet any specification. However, experience has shown that few applications have a real need for high cycle-life design, which adds unnecessary costs to the expansion joint.
Joints
359
prevented by covering the bellows and using an antispatter compound when welding. External conditions should also be considered. External corrosion can result from fumes or sprays that may contact the bellows or in tunnel and manhole installations where water is allowed to collect. Direct application of insulation to the expansion-joint bellows and direct burial in the ground are not recommended. Many corrosion problems encountered in the field can be reduced, if not completely eliminated. Where corrosion problems are complex, consult a qualified corrosion engineer.
Erosion This is the mechanical wearing away of the metal surfaces in a joint. It usually results from the irnpact of solid particles entrained in the flowing medium. Where there is a possibility of severe erosion, such as in lines carrying abrasive media, heavy liners should be used to protect the bellows of the expansion joint.
Corrosion Corrosion can significantly reduce the service life of an expansion joint. The design and operating characteristics of expansion joints are such that they may be exposed to corrosive attack under conditions that do not affect piping and fittings of similar materials. Types of corrosion most frequendy experienced in expansion-joint applications are as follows:
1. Stress-corrosion (a cracking of the material as the
2. 3. 4. 5. 6.
result of a combination of stress and corrosive environment). Intergranular-corrosion, characterized by a preferential attack along the grain boundaries in metals. Pitting, which is a localized attack on metals. General corrosion or the gradual eating away of the metals in a system. Impingement and corrosion erosion, associated with the impact of a liquid or gas medium on the surface of the material under attack. Elevated temperature oxidation, most comrnonly encountered in hot ak and exhaust lines.
Calculating Thermal Expansion Metallic, packless expansion joints are normally designed to move in axial compression only, and unless otherwise specified, the minimum and installation temp€ratures are assumed to be 60'F. Here is how to determine the amount of thermal expansion in a piping system:
Example Assume a 10-in. steam line fabricated from carbon steel is carrying superheated steam at 300 psig and the distance
between pipeanchors is 1,10 ft-O in. The minimum ambi ent temperature is 70"F and the maximum operating temperature is 460'F.
Sorution The corrosion resistance of stainless steel depends on the formation of a thin, unbroken, chromic oxide surface, which will form slowly in the atmosphere on clean stainless steel. Particles of steel from welding spatter should be
From Chapter 2, Table 2-1, we find that the expansion of carbon steel pipe at 460'F is 3.25 in. per l0O ft, and at 70'F the expansion per 100 ft is 0 in.
Piping Stress Handbook Total expansion:
(r4O ft) (3.2s
in.)
-
100
0 in.
Example
:
4.55 in.
Therefore, we find that we should select an exDansion joint that will absorb ar least 4.55 in. of axial
"o*o."._
slon.
Assume that the installation temperature will be 70"F. The required precompression is then calculated as follows:
6(70.F P_ (460"F
Precompression
- 0.F) _ - 0.F)
0.913 in.
Note: If the amount of precompression is very small (Va in. per corrugation or less), it may be neglected. When precompression is required, remember to deduct the amount of this precompression from the normal overall length dimensions.
If the minimum operating temperature is lower than the qggput d installation temperature, the expansion joint will be subjected to both enension and compression-dur_ ing^operation. Because most expansion jointjare designed to runcuon rn compression only. any expansion joint used rn lyclr an apphcatlon must be precompressed (prior to in_ stallatton) to prevent extension of the expansion joint beyond its original. overall length. If advised of the minimum. maximum, and installation temperalures when the order is placed. the expansionjoint wlll be tactory precompressed and may be installed as re_ ceived. In the case of expansion joints specified for low-temperature service only, the installation and maximum temoeratures are normally the same. so thejoints function eniirely in extension. Where such service conditions are clearly specified, the expansion joint will always be factory precompressed, ready for installation.
Where it is not possible to anticipate the installation temlerature, the expansion joint may be precompressed in the field. The amount of precompression is determined as follows:
-4(Tz-Tr) (Ts - Tr) D-
Application Pipe Anchors The first step is to determine the tentative locations of pipe anchors. By proper location, any piping system can be reduced to a number of individual eipanding pipe sections having relatively simple configurations. The number and location of pipe anchors will depend upon piping configuration, amount of thermal expansion, the proximiry of structural members suitable for-use as anchors, and-the location ofpipe fittings, connected equipment, and branch connections.
. Start out with the assumption that single expansion joints in straight axial compression will provide the simplest and most economical layout. Wherever possible, the distance between anchors and amount ofexpansion should be kept uniform so rhat the expansion joinis used will be interchangeable. Ib minimize the number of exDansion joints adjust the distance between alchors so thai exoansion joints having a maximum number of corrugations in each bellows (consistent with stabilitv) can be ised.
Total amount of precompression, in. Total rated axial movement of the expan-
Galculation of Forces Acting on Main Pipe Anchors
Installation temperature determined by actual temperatue reading of adjacent piping. Do not use the ambient atmospheric temperature for this purpose.
A main pipe anchor must be designed to withstand the forces and moments imposed upon it by each of the pipe sections to which it is attached. In the case of the installation illustrated in Figure 14-10, the force acting on the main anchor consists of the full line thrust due to pressure , -the the force required to deflect the expansion joint, rated
sion joint, in. Minimum temperature
Maximum temDerature
Fundamentals of Exoansion Joints
'1 0z
I
Figure 14-10, Diagram illustrating the forces that act upon the main
anchor.
Figure 14-11. Diagram illustrating the forces that act upon the main anchor in applications involving straight pipe selections and in applications involving anchors at pipe bends and elbows.
movement, and the frictional force due to the pipe align-
where
ment guides. Formulas for calculating anchor forces in various applications follow. The steps for calculating the main anchor forces for applications involving straight pipe sections (see the center anchor in Figure
14-ll)
are:
: F, : F. : F,nn
Fg :
I 2.
t
Static thrust due to internal pressure' lb Force (ftom data sheet) required to extend or compress the expansion joint, lb Frictional force due to pipe alignment guides. Note: This can be obtained from the manufacturer of the
1. Calculate the firll line thrust:
F":AP where F, : A: P:
Force on main ancho! lb
guides. Static thrust due to internal pressure,
lb Effective pressure thrust area (in.2) taken from data she€t Maximum pressure (p6i) based on the most severe conditions whether design, operational or test
Assuming that the weight of the pipeline and its contents are carried by supports. To calculate the total by any one force imposed on the main anchor pipe section use the following equation:
(F)
F':F"+F.+F"
To determine the net load on the anchor, it is necessary to add vectorially the forces imposed upon it by
each
of the three pipe
sections
to which it is at-
tached.
To calculate the main anchor forces for applications involving straight pipe sections containing expansion joints ofdifferent diameters (see center anchor in Figure 14-12), use the following equation:
4:(Ar-&)P
Piping Stress Handbook
Figure 14-12. Diagram illustrating the torces that act upon the main anchor in applications involving straight pipe selections containing expansion joints of ditferent diameters.
where
A1 :
Effective area, corresponding to the mean diameter of the corrugations of the expansion joint in the larger pipe section,
,q.2
:
P :
m.' Effective area, corresponding to the mean diameter of the expansion joint in the smaller pipe section, in.2 Maximum pressure (psi), based on the most severe conditions, whether design, operational, or test.
Here again, it is necessary to consider the differences in the forces required to extend or compress the expansion joints and the differences in the frictional forces due to pipe alignment guides and supports. Thus, the total force on the center anchor
will
be:
F,":F"+F-r+Fgr-Fgz where F.1
=
F- : Fr1 Fez
: :
Force (from data sheet) required to extend or compress the expaniion joint in the larger pipe section, lb Force (from data sheet) required to extend or compress the expansion joint in the small pipe section, lb
Frictional force (from guide manufacturer) due to pipe alignment guides in the larger pipe section, lb
Frictional force (from guide manufacturer) due to pipe alignment guides in the smaller pipe section, lb
To calculation the main anchor forces for applications involving anchors at pipe bends and elbows (see Figure 14-10) the following calculation must be used. In the case of an anchor located at a pipe bend or elbow, it is necessary to consider the forces imposed by the pipe sections on both sides of the anchor. Thus, assuming that each section contains an expansion joint, the line thrust due to pressure (F" : AP) and the forces F- and F", explained previously, become biaxial components and-must be added vectorially. In addition, the effect at the elbow of
the centrifugal thrust (Fo) due to flow, must be considered. Fo may be calculated as follows:
rp:
2ADV2
0
: Internal where A-slnD e
o
: : : :
ff
area of pipe, DensiU of fluid, lb/ft3 Velocity of flow, ft/sec Acceleration due to gravity, 32.2 fllsec2 Angle of pipe bend
Calculation of Intermediate Pipe Anchor Forces An intermediate pipe anchor must be designed to withstand the force and moments imposed upon it by each of the pipe sections attached to it. However, an intermediate anchor does not have to be designed to withstand the full line pressure thrust, because this force is always absorbed by main anchors or by devices on the expansion joint. such as limit rods, tie rods, gimbals, or hinges. Assuming that the weight of the pipeline and its contents is caffied by supports, the following calculation will determine the forces acting on an intermediate pipe anchor in a pipe section containing expansion joints (see Figure 14-13):
Fre : F.r * where F^1
Frr
Fno
=
: :
Fr1
*
Fn2
*
Fgz
The force (ftom the data sheet) required to extend or compress expansion joinr
EIl
shown in Figure 14-13.
The total force due to friction of all the
pipe alignment guides installed on the pipe section to the right of the intermediate anchor in Figure 14-13. The force required to extend or compress expansion joint EI2 shown in Figure 14-
tJ-
-Fundamentals of Expansion Joints
363
Figure 14-13. Diagram illustrating theJorcesthat act upon an intermediate pipe anchor in a pipe section containing expansion joints.
Fgz
=
The total force due to friction of all tlte pipe alignment guides installed on the pipe section to the left of the intermediate anchor in Figure l4-13.
Nore: The frictional force due to pipe alignment guides can be obtained from the manufacturer of the guides.
If the pipe is the same diameter on both sides of the intermediate anchor, and if the guides on both pipe sections are similar in number and design to F,,z and Fgr, respectively, but opposite in sign, F1a will be equal to zero. However, it is possible that the pipeline may heat up gradually from one end, thereby causing one of the pipe sgctions to expand before the other. It is therefore considered good practice to design the htermediate anchor to resist the forces exerted by one of the two pipe sections (i.e., F1a : F*1 *Fgr).
used only in applications involving lateral deflection or angular rotation resulting from L- or Z-shaped pipe configurations . Proper alignment is very important in the installation of all expansion joints. Expansion joints will not function properly unless the pipeline in which they are installed is securely anchored and guided.
Spacing of Pipe Guides Where an expansion joint is located close to an anchor, the first pipe guide should be located no more than four pipe diameters ftom the moving end. The second should be located no more than fourteen pipe diameters from the first. The recommended spacing for intermediate guides along the balance of the pipeline can be determined from Figure 14-9. For any known pressure and pipe size, the guide spacing can be determined by locating the pressure on the scale at the bottom of Figue 14-9. Follow the pressure line vertically until it intersects the diagonal line for
Pipe Guides and Guiding A pipe alignment guide is a sleeve or frame fastened to some rigid structure that permits the pipeline to move freely along its own axis and limits it to this type of motion. A roller support, U bolt, or pipe hanger, which orily supports the weight ofthe pipe, cannot be substituted for a pipe guide. Pipe guides are required to prevent buckling ofthe pipeline. Buckling is caused by compressive loading on the pipe due to the internal pressure thrust and the flexibility of the expansion joint which causes the pipe to act like a column with end loading. In axial movement applications, avoid using a single pipe-alignment guide because such a guide may act as a fulcrum, which might impose lateral deflection or angular rotation on the expansion joint due to movement of the piping in a dhection other than axial. Planar pipe guides are modified to permit limited movement and/or bending of the piping in one plane. These are
pipe size. From this intersection, follow across horizontally to the guide spacing column (left to right) and read the recommended spacing. For example, the recommended intermediate guide spacing for a 6-in. pipeline containing an expansion joint under a pressure of 125 psig is 43 feet. The first guide should be no more than 24 in. from the expansion joint, and the second pipe guide 84 in.
from the first.
Location of Expansion Joints Wherever possible, an exparsion
joint should be lo-
cated irnmediately adjacent to a pipe anchor. If it is not possible to locate the expansion joint near a pipe anchol pipe guides should be used on both sides of the expansion joint ir accordance with the instructions given in the precedhg paragraphs under "Spacing of Pipe Guides."
Piping Stress Handbook
Figure 14-10 shows the preferred practice in the use of a single expansion joint (EI) to absorb axial pipeline expansion. Note the use of one expansion joint between two main anchors (MA) , the nearness of the expansion joint to an anchor, the closeness of the fimt alignment guide (G1), the spacing between the fint alignment guide and the second alignment guide (Gr), and the spacing of intermediate guides (G) along the balance of the line. Expansion joints should not be located immediately
downstream from turbulence-pnrducing devices (such as butterfly valves). plug valveJ, and su-dden increases in pipe size, mitered elbows, etc. If it is impossible to locate
joint an adequate distanceiway from tubulence producers. the joint slould be equipped with a heavy sleeve. Figures 14-14 and 14-15 show the information required for standard and special expansion joints specification sheets. the expansion
End Connections The type of end connections selected depends upon the operating conditions and the customer's re.guirements. See Figure l4-16 for illustrations. The following is a briefdescription of the various g?es available.
Fixed Flanges (Type SF) The flanges are welded directly to the bellows material without the use of intermediate pipe nipples. In this construction the flanges are in direct contact with the flowins medium.
Fixed Flanges (Type F) The flanges are welded to pipe nipples, thereby provid-
ing greater overall length. In this construction bbth the pipe nipple,s and flanges are in direct contact with the flowing medium.
Combination Ends Expansion joints can be supplied with one weld end and one flanged end to meet installation requirements.
Covers Covers protect expansion joints from mechanical damage and serve as a base for insulation.
Van Stoned Flanges (Type V) The flanges are slipped over the ends ofthe bellows and the bellows material is flared out or "Van Stoned" over the faces of the flanges. The \r'an Stones are roughly equivalent to the raised faces on standard forged steel flanges. The flanges are loose and free to rotate, thus permitting easy alignment with the mating pipeline flanges. This construction is generally used in applications involving product purity or corrosion, because the only material in contact with the flowing medium is the corrosionresistant bellows matefial.
Sleeves Sleeves minimize pressure drop and also streamline the
flow of gas or fluid through an expansion joint, thereby reducing friction losses and turbulence. They are recommended for all expansion joints, except in applications
where high-viscosity fluids such as tar are involved. Sleeves are required whenever the velocity of flow exceeds the following values:
Welding Ends (Type W) The ends of the expansion joint are supplied with pipe suitably beveled for welding to connecting equipment or piping. Standard joints are supplied with carbon steel weld ends. See individual data sheets for grade and type. Other thicknesses, lengths, and grades of carbon steel weld ends are available on order. Where alloy pipe is used, it may be advantageous to use weld ends that are shorter and thinner than carbon steel standards. Consult the factory for recommendations when alloy pipe is used.
Nominal
Size 3 to 6 in. ) 6 in. 3 to 6 in. > 6 in. Pipe
Medium in Pipe
Steam Steam Air (other gases) Air (other gases)
Velocity
of trlow 1,000 ft/min/in. dia 6,000 ff:/min 250 ft/min/in. dia 1,500 fl:/min
Fundamentals ol Exoansion
For additional data use the sheet for supplemental information for special expansion joints. Customer
Inquiry/Job No.
Project
1. Item No.
2. Quantrty 3. Size 4. Flowing Medium+ 5. Flow Velocity 6. Int. Design Pressure, psig 7. Int. Text Pressure, psig 8. Maximum Temperature, "F 9. Minimum Temperature, oF
10. Installation Temperature, oF 11. Axial compression, in.
12. Axial
extension, in.
13. Lateral deflection, in. 14. Angular rotation, deg. 15. Pipe specification 16. Weld end specification 17. Flange specification 18. Type or catalog number 19. Internal sleeves 20. External covers 21. Anchor base 22. Limit rods Use manufacturer's standard unless otherwise specified by purchaser.
23. Bellows material 24. Equalizing ring material 25. Total corrugations 26. Lenglh limitation
If flowing medium is corrosive,
erosive, or viscous explain in detail.
Figure 14-14. Standard expansion joint specification sheet.
Joints
365
366
Piping Stress Handbook
Customer
Project
hquiry/Job No.
1. Item No.
2. External design pressure, psig 3. External test pressure, psig 4. Pipe purge, instr. connection 5. Vibration amplitude 6. Vibration frequency Special Flange Design
7. Material 8. Facing 9. O.D. 10. I.D.
ll.
12. 13. 14. 15.
Thiclness
B.C. diameter No. holes Size holes
Hole orientation
Design Restrictions
16. 17. 18. 19.
Length Maximum O.D. Minimum I.D. Axial force 2O. LatercJ force (Shear) 21. End moment 22. Cychc design life 23. ASME Code partial Data forms required 24. Applicable codes and specifications
Figure 14-15. Supplemental information for special expansion joints, to be used with the standard expansion ioint specitication sheet.
Fundamentals of Expansion Joints
Figure 14-16. End connections.
15 Glossarv .,/
Aging-The term originally applied to the process or sometimes to the effects of allowing a metal to remain at ordinary temperatures. H;at treatment ar temperatures above room temperature for the purpose of accelerating changes of the type that might take place during aging at ordinary temperature is called artificial aging. The changes taking place
during artificial aging are due to the precipitation treatment. Aging is an approach to the attaitment of equilibrium from an unstable condition induced by a prior operation. The fundamental reaction involved is generally one of precipitation, sometimes submicroscopic. The method employed to bring about aging consists of exposure to a favorable temperature subsequent to (1) a relatively rapid cooling from some elevated temperature (quench aging) or (2) a limited degree of cold work (strain aging). Alclad-The common name for a type of clad-wrought aluminum product with coatings of high purity aluminum; or an aluminum alloy different from the core alloy in composition. Alloy-A metallic substance consisting of two or more elements, of which at least one is metal, and in which all elements are miscible in the molten state and do not separate when solid. Alloying elements-Chemical elements constitutins an alloy. In steel. usually rhe elements added to mo?ify the properties of the steel. Annealing-A heating and controlled operation to impart specific desirable properties generally concerned with subsequent fabrication of the alloy, such as softness and ductility. When annealing follows cold working for the purposes of stress removal, it is called stress annealing. Arc welding-Welding accomplished by using an electric arc formed between a metallic or carbon electrode and the metal being welded, between two separate electrodes, or between two separate pieces being welded (also called fusion welding). 368
Austenite-A solid solution in which
gamma iron is the
solvent, having a face-centered cubic crystal structure. Austenitic steel-Steel, which due to its comoosition has a stable structure at normal lroom) timperatures; as for example: the 18-8 types. It is not hardened by thermal treatrnent. Bend test-A test commonly used to determine relativ! ductility of a sample by bending it over a given radius and through a given angle. BilIet-A semi-finished rolled ingot of rectangular or nearly rectangular cross section. Brass-A copper-base alloy in which zinc is the principal added element. Brazing-Joining metals by fusion of nonferrous alloys with melting points above 800"F but below the melring point of the metals being joined. Brinell hardness-A hardness number determined br applying a known load to the surface of the mareriil to be tested through a hardened steel ball of known diameter. Note: Not suitable for measurins the hardness of strip and sheet because of insulfic-ient thick. ness.
Brittleness-A tendency to fracture without appreciable deformation. Carbon steel-Steel in which carbon provides the properties without substantial amounts of other alloyins elements.
Carburizing-Diffusing carbon into the surface of ironbase alloys by heating in the presence of carbonaceous materials.
Case hardening-Carburizing, nitriding, or cyanidinr
and subsequent hardening by suitable heat trearment, if necessary, all or part ofthe surface portion: of a section of iron-base alloy. Casting-Fouring molten metal into a mold or a meta. object so produced.
Cementite-An iron-carbon compound with the chem;cal formula Fe3C often called iron carbide.
--
Glossary Charpy test-A pendulum-q pe impact tesr in which
a
notched specimen, supported ar both ends as a simple beam, is broken by the impact of the falling pendulum. The energy absorbed in breaking the specimen, as determined by the deireased rise of the pendulum, is a measure of the impacr strength of the
metal. Chemical analysis-Separating an allor. into its component elements and identi! in-e them. In quantitative analysis, the proportion of each element is determined. Chromium-A hard crystalline metal used as an alloying element to give resistalce to heat. corrosion, and wear and increase strength and hardenability. Cold working-Permanent deformadon of a metal below its recrystallization temperature. Also defined as plastic deformation of a metal at a temperature low enough to ensure strain hardening. Mechanical properties, such as tensile strength, hardness, and ductility, are also altered. Compressive strength-The ability to withstand compressrve stresses.
, Compressive stress-Stress caused by a compressive load or in fibers compressed by a bending. Cooling stresses-Stresses caused by uneven contraction, external restraint, or localized plastic deformation during cooling. Corrosion-Gradual chemical or electrochemical attack on a metal by atmosphere, moisture, or other elements.
Corrosion embrittlement-Embrittlement in certain al- loys caused by exposure to a corrosive environment. Corrosion fatigue-Combined action of corrosion and fatigue in which local corroded areas act as stress concentrators, causing failure at the point of stress concentration and exposing new metal surfaces to corrosion. The failure is progressive and rapid. Creep-Plastic flow of metal, usually occurring at high temperatures, subject to stress appreciably less than its yield strength. It progresses through first, second, and third stages to fracture or results in stress relaxation. Cyaniding-A process of case hardening a ferrous alloy by heating in a molten cyanide salt bath, thus causing the alloy to absorb carbon and nitrogen simultaneously. Cyaniding is usually followed by quenching to produce a hard case. Ductility-That property of metal which allows the metal to be permanently deformed before final rupture. Elastic limit (limit of elasticity)-Maximum stress to which a metal can be subjected without permanent deformation at the point of stress. Electrochemical corrosion-Localized corrosion that results from exposure of an assembly of dissimilar
349
metals in contact with or coupled with one aa'drc: or of a metal containing microscopic areas di-isr::-
lar in composition or structure. The dissimilar er:ments form short-circuited electrodes. The corr.--
sive medium is the electrolyte, and an electrlc current is induced. which results in the disolution of the electrode that has the more anodic solution potential, while the other is unattacked.
Elongation-The amount of permanent extension in
the
tensile test, usualll' expressed as a percentage of the original gage lengrh. (e.g. , 25 percent in 2 inches). It may also refer to the amount of extension at any stage in any process which continuously elongates a
body, as in rolling. Endurance limit-A limir of stress below which metal will withstand stress without fracture; a specified large number of applications of such stress. Eutectoid steel-A carbon steel containine 0.80% carbon that becomes a solid solution ar anitemoerature in the austenite temperarure range between i ,333.F and 2,500"F.
Fatigue-The tendency of a metal to fracture under conditions of repeated cyclic stressing below the ultimate tensile strength but above the yield strength. Ferrite-A solid solution in which alphas iron is the solvent and having a body-cenrered iubic crystal structure.
Ferritic steel-Steel which, due to its composition, is not hardenable by heat trearmenr. Such stainless types as 405, 430, and 448 are essentially ferritic steels.
Free machining-The property of steel imparted by additions of sulphur, selenium, or phosphorus which promote chip breakage and permit increased ma-
chining speeds. Additions of sulphur or selenium also help to decrease friction between the chips and the tool face.
Galling-The damaging ofone or both rnetallic
surfaces
by removal of particles from localized areas during sliding friction. Galvanic corrosion-Corrosive action occurrins when two dissimilar metals are in contact and arJioined by a solution capable of conducting an electric current, a condition which causes a flow of electric current and corrosion of the more anodic of the f$.o metals. (Also see Electrochemical Conosion.) Gas welding-Welding in which heat is supplied b1' a manually or automatically controlled torch flame of oxyacetylene or oxyhydrogen (also called fusion welding). Grains-Individual crystals in metal. Hardenability-In a ferrous alloy, the propern that determines the depth and distribution of hardness ilduced by heat treating and quenching.
37O
Piping Stress HandbooK
Hardness-Resistance to indentation by standard balls. diamonds, etc.. under standard loais. Also, the degree of cold working. Heading-An upsetting process used to form rivet, screw, and bolt heads in making these products from wire or rod. Heat treatable-Refers to an alloy that may be hardened by heat treatment. Heat treatment-A combination of heating and cooling operations timed and applied to metal or alloy to produce desired properties. Homogenizing-A process of heat treatment at high temperature to eliminate or decrease chemical segregation by diffusion. Attainment of austenite that has a uniform distribution of carbon. Hooke's Law-Stress is proportional to strain in the elastic region. Hot forming-Working operations performed on metals heated to temperatures above room temperature. Hot working-Hot forming above the recrystallization rcmperature.
Hydrogen embrittlement-A brittleness sometimes engendered by contact with plating and pickling solution acid due to absorption of hydrogen by the
metal. The embrittlement is more evident in hardened parts, and can be removed by aging or heating the steel for a prescribed period. Hypereutectoid steels-Steels containing from 0.80% to above 2.0% carbon. Hypoeutectoid steels-Carbon steels containing less than 0.80% carbon. Impact test-A test designed to determine the energy absorbed in fracturing a test bar at high velocity. The usual impact test specimen is a standard size square bar with a V or keyhole type notch. (See Charpy test and Izod test.) Intergranular corrosion-Corrosion that tends to localize at grain boundaries, usually under conditions of prolonged stress and certain environments, and in association with poor heat reating or welding practice that has caused the precipitation of a more easily attacked constituent at these boundaries. Izod test-A pendulum-type of notched-bar impact test in which the specimen is supported at one end as a cantilever beam and the energy required to break off the free end is used as a measure of impact strength. Machinability-The rate and ease with which a metal can be machined. Magnetic particle testing-This method of inspection consists in suitably magnetizing the material and applying a prepared magnetic powder which adheres along lines of flux leakage. On properly magnetized material, flux leakage develops along surface nonuniformities. This method is not applicable to high
manganese or austenitic stainless steels and nonfer-
rous alloys, which are nonmagnetic.
Martensite-An unstable constituent in quenched steel, the hardest of the transformation products of austenite.
Martensitic steel-Steel which, due to its composition, has martensite as its chief constituent after cooling.
The hardenable stainless types are all martensite ste€ls.
Mechanical prop€rties-Those pfoperties that reveal the reaction, elastic or plastic, ofa material to an applied stress or that involves the relationship between stress and strain; for example, Young's modulus, tensile strength, fatigue limit. These properties have often been designated as physical properties, but the term mechanical properties is technically more accurate and therefore preferred. Modulus of rigidity-The ratio of the unit shear stress to the unit angular strain in the elastic range.
Nitriding-A
process of surface hardening in which a ferrous alloy is heated in an atmosphere of cracked ammonia gas or other suitable nitrogenous material thus allowing nitrogen to diffuse into the surfaca metal. Nitriding is conducted at temperatures below the critical temperature range and produces surface hardening of the metal without quenching.
Normalizing-A
process in which steel is heated to a suitable temperature above the transformation range and is subsequently cooled in still air at room teiperature. This operation is used for grain refining or to develop specified mechanical properties.
Notch sensitivity-The reduction caused in nominal strength, impact or static, by the presence of a stress concentration, usually expressed as the ratio of the notched to the unnotched strength.
Permeability-Magnetic permeability is the ratio of the magnetic induction to the intensity of the magnetizing field. Physical properties-Those properties familiarly discussed in physics, exclusive of those described under Mechanical Properties; for example, density, electrical conductivity; coefficient for thermal expansion. The term has often been used to describe mechanical properties, but such usage is not recommended. Pickling-Immersion in dilute acid or other suitable media for the removal of oxide scale from hot-rolled or otherwise sealed surfaces. Plasticity-The ability of a metal to be deformed exten-
sively without rupture. Plating-Deposition of a thin film of a metal or alloy on a different base metal from a solution containins ions of the plating metal.
G Glossary Poisson's ratio-Ratio expressing the relation of strain normal to the applied load as a proportion of direct strain within the elastic limit. Also relates moduli of elasticity ard rigidity. hecipitation hardening-Hardening of metallic alloys, by aging, which results from the precipitation of a constituent from a supersaturated solid solution, usually nonferrous alloys. Also termed as hardening. (See ,{grng.) Process annealing-An annealing operation carried out at a constant temperature just below the critical transformation temperature (also referred to as sub-
critical annealing) . Proof stress-In a test, stress that will cause a specified permanent set in a material, usually 17o or less. Proportional limit-The highest stress at which the material still follows Hooke's Law, similar to elastic
limit. Quenching-A process of rapid cooling from an
ele-
vated temperature.
Radiography-The use of X-rays or gamma radiation to detect internal structural defects in metal objects. . Reduction of area-In a tensile test, the difference between the original cross-sectional area and that of the smallest area ofthe point ofrupture. It is usually stated as a percentage of the original area. Also called contraction of area, it is not applicable to the mechanical testing of sheet and strip. It is also a measure of cold work. Refractory metals-Metals such as tungsten, columbium, tantalum, and molybdenum, which have rela- tively high melting temperatures. Residual stress-Stresses locked in a metal after the completion of nonuniform heating or cooling, working, etc. due to expansion, contraction, phase changes, and other phenomena.
Resistance
welding-A welding
process
in which the
work pieces are heated by the passage of an electric current through the contact area, combined with pressure causing joining by fusion. Rockwell hardness test-This test consists of forcins a cone shaped diamond or hardened steel ball int6 a metal specimen to determine the degree of penetration and. hence. the hardness. Rupture stress-The true stress given by dividing the load at the moment of incipient fracture by the area supporting that load. Salt spray tesl-An accelerated corrosion test in which the metal specimens are exposed to a fine mist of salt water solution. Scaling-Surface oxidation caused by heating in an oxidizing atmosphere. Seam welding-Resistance welding that consists of a series of overlapping spots forming a continuous weld .
37'l
Shear-Plastic deformation in which parallel planes of metal crystals slide so as to retain their parallel relationship. Also called angular elastic strain. Shear stress-Stress acting on a shear plane. Solution treating-A condition of complete solubility resulting in a single phase for compositions of two or more alloying elements at temperatures lower than the solids. Solid solutions may be limited in extent with respect to range of alloy composition or can be continuous, extending throughout an alloy series.
Specific gravity-A numerical value representing rhe weight of a given substance compared with the weight of an equal volume of water. Spot welding-A resistance-welding process in which the fusion is limited to a small circular or oval area. Stabilization-Prevention of the formation of carbides at the grain boundaries of austenitic stainless steels. Dimensional control of nonferrous castines. Strain-Deformation expressed in units pe-r unit of length produced by strain. Strain aging-Load per unit of area. Stress concentrator or stress raiser-Any notch, scratch, sharp change of contour, slot groove, hole, defect, or other discontinuity in an engineering material that has the effect of concentratins the stresses applied to the material or generated in-it by heating or cooling. Stress corrosion-Corrosive action induced and accelerated by the presence of stresses.
rupture-A test to destruction at elevated temperature, by which it is possible to determine the stress that causes failure at a given temperature and with the lapse of a given period of time.
Stress
Temper-A condition produced in a metal or alloy by mechanical or thermal treatment and havins chancteristic structure and mechanical propertiei. Temper brittleness-Brittleness that results when certain steels are held within or slowly cooled throug! a certain range of temperature below the transformation range. The brittleness is revealed by a notchedbar impact test at room temperature or lower temperatufes. Tempering-The process of reheating quench hardened or normalized steel lo a temperature belo*. t}le rars-
formation range and then coolhg at an) rare desired. This operation is frequently called sress relieving. "Drawing" is synonymous xith temperhg. but the latter is the preferred usage. Tensile strength-The maximum load il pou_n& ger square inch, based on the origiml cro=.-^.e.-tibn. which may be developed in rensile resrilg. isee a.L:o Uhimate Strength.)
372
Piping Stress Handbook
Thermal stresses-Stresses in metal, resulting from nonuniform temperature distribution.
Through-hardening-Thermal description of alloys that harden completely, so the center of a hardened section exhibits hardness similar to the surface. Torsion-Strain created in an object by a twisting action or the stresses created by such an action. Toughnesl-Ability to absorb considerable energy before fracture, usually represented by the area under a stress-strain curve and therefore involvins both ductility and strength. [Jltimate strength-The maximum strength or stress before complete failure or fracture occurs.
Vacuum melting-A process by which alloys are melted rn a near pertect vacuum to prevent contamination
by atmospheric elements. Vickers hardness test-An indentation hardness test utilizing a diamond pyrarnid and useful over the entire range of common metals.
process of joining metals whereby partial melting of the parent metals occurs except in the case of pressure welding when heating is only sufficient to cause recrystallization across the interface.
Welding-A
Yield point-The load per unit or original cross section at which a marked increase in deformation occurs without increase in load. In stainless and heat-resisting steels, this occurs only in the martensitic and ferritic chromium types. In the austenitic stainless and heat-resisting steels, the yield point is the stress corresponding to some definite and arbitrary total deformation, permanent deformation, or slope of the load deformation curve; this is more properly termed the yield strength.
Yield strength-Stress corresponding to some fixed permanent deformation such as 0.1 or 0.2% offset from the modulus slooe.
aa
Index
Air-cooled heat ex changerc, 263-264 Allowable expansion stress range, 2, 8-9, 11, 13 Allowable external forces and moments (tables), 264
Allowable internal pressure stress,
1l Allowable loads, 257 -264 Allowable longitudinal stress, 9 Allowable momenlq 257 -264 Allowable pipe deflection, 314 Alowable pipe span, 314 Allowable resultant forces and moments (table), 258 Allowable shear stress, 11
Disffibution Piping), 11, 13, 15, 251
ANSI/ASME Code 831.9 (Building Services Piping), 15 ANSI/ASME Code 831.10 (Cryogenic Piping), 16
ANSI/ASME Code B31.11 (Slurry Piping), 16 ANSI/ASME Code for Pressure Piping, 177 API Code 610, (steel pump force, moment, and stress limitations), 257 -258 API Code 661 (design criteria for
air-cooled heat exchangers),
263-2&
Allowable span, 314 Allowable stress(es), 8-11, 257 -264
ASME Boiler Code, 177
-
Barlow formula, 177 Baseplate support, 258-259 Bellows, 356
range (tables), 38-111 Allowable working pressure, 177,
250-251 Anchor(s), 122, 345, 356, 360-363 forces and moments, 3 intermediate, 362-363
main, 360-362 Angle valves cast steel, 307
flanged,302 ANSI/ASME Code 816.9, 120 ANSI/ASME Code B31.1 (Power Piping), 3-6, 14, 257 , 260 allowable stress range (tables),
38-'72 ANSI/ASME Code 831.2 (Fuel Gas
Piping),
14
ANSI/ASME Code 831.3 (Chemical Plant and ktroleum Refinery Piping), 6-7, 14, 25'l -260 allowable stress range (tables),
73-111 ANSI/ASME Code 831.4 (Liquid Petroleum Transportation Piping
, 9, 11, 14-15 ANSI/ASME Code 831.5 (Refrigeration Piping), 15 ANSI/ASME (DOT) 831.8 Code Systems),
7
(Gas Transmission and
Bellville (disc) springs, 324 Bending, 123 maximum, 314 stress, 1, 260 Bends, 120, 3ll-323, 350 Boiler external piping, ,14 Bracket supports, 324 Branch connections , ll4, 253-255 Branch reinforcement, 252-256 Buckling, 356, 363
Building Services Piping Code (ANSr/ASME 831.9), 15
Coil springs, 324 Cold springing, 2-3, 356-358 Combination ends, 364 Compliance codes, 3- l6 Components of pipe, 299-313
clearances,357 Compressors, 262-263 Connections
branch, 114, 253-254 end,364 purging, 358 vertical exhaust, 260-261 Cons^TLlt sprjng supports. 327,
load table, 338-341 Corrosion,359 Covers, of expansion joints, 364 Creep, 2, 177 Cryogenic hargers, 327 , 345, 349 Cryogenic Piping Code
(ANSr/ASME 831.10), 16 Cycle life expectancy, 2, 358-359 Cylindrical vessels, 122- 176
Deflection, 324, 329 lirnits of, 314-315 Design criteria air-cooled heat exchansers.
263-264 compressors, 262-263
pipe suPports, 324-350
pumps,257-259 turbine drivers, 260-262
Butt-welded fittings, 303
Design factor
Caking,358 Centrifugal steel compressor, 262
Direct longitudinal sness. I Direct shear stress, 2 Disc (Bellville) springs. 3?4
Chemical Plant and Petroleum Refinery Piping Code (ANSI 831 .3) , 6-7 , 14 , 257 -258 allowable stress range (tables),
73-111 Circumferential bendhg, 123 Circumferential stress, 2 Coefficients of thermal expansion
(tables),2-32
373
F,
13
Discharge nozzles. 257 -259 Distortion energy (von Mis€sl theory, 2 DOT Code B31.8. 13. 15. 51 Double expansion joim- 15l-351 Dummy legs, 324
ll.
Elbows, 112, 118-lll Electric generadng pla s. l-t
374
Piping Stress Handbook
End connections, 364 Ends, 121, 364
i
loops, 351
Erosion,359
factor (table), 120 Industrial plants, 14 Insulated anchors, 345 Insulated pipe supports, 348-350 Insulation of pipe, 299-300 Intermediate pipe anchor, 362-363
spans,314-320 rypes of, 325-329
Expansion devices, 351 Expansion forces, (tables), 278-290 Expansion joints, 351-367
anchors,356 application, 360-363 cold springing, 356 corrosion, 359
Internal sleeve, 358
k factor (table), 120, 327
erosion,359
Load adjustment, 327
265-291
't2
specified rninimum yield strength,
forces and moments, 356 guides, 356, 363-364 precompression, 360 thermal expansion calculations,
Loading, sustained external, Loads,257-2&, 326,357 Leaf springs, 324
359-360 types,351-355
Piping Systems Code (ANSUASME 831.4), 7-1r Longitudinal joint factor t, 13 Longitudinal stress, 1-3, 5,7,9,
Factors, k, h, i (table), 120 Flanged elbows, 118 Flanged valves, weight of (tables)
angle,302 check (swing), 301 gate,300
globe,30l Flanges
fixed, 364 forged steel, 303-305 weight (tabl€), 302
Flexibility, 122 Flexibility factors,
1
12
flanged elbows, 118- 119 miter elbows, 120-121
Flexible piping, 351 Flexible support, 324 Force reduction, 356 Forces and moments,3, 122,
257,26/.,356,358 Fuel Gas Piping Code (ANSI/ASME
83r.2),
14
Gas Transmission and Distribution
Piping Code (ANSI/ASME (DOT) 831.8), 11- 15, 2s1 Gimbals, 355, 358 Globe valves, 307 Guides, 356, 363
stress, l-2, 5-7 compliance codes, 3-16 simplified solutions (tables),
Joint movements, 351
cycle life expectancy, 358-359 end connections, 364-367
Expansions, offset lensths reouired (tables), 266-267' Expansion stresses, 2-3, 6, 13 range, 8-9, 11 External mechanical forces, 258 External pressure, 5
materials, properties (tables), 33 properties (table), 292 -298
3
Liquid ktroleum Transportation
tl,
13
Machining, 112 Main pipe anchors, 360-362 Maximum allowed wall thickness, 6 Maximum allowable resultant forces
supports. See a/so Supports. tor cryogenic service, 329, 345 design and selection, 324-350 flexible, 324, 356 insulated, 348-350 nsid, 324 Piping restrained, 11 three-dimension, 2 two-anchor, 3
unrestrained,9 Piping codes, 3-16 Piping wind loads, 320-323
(tzble),324-325
Planar piDe euide. 356. 363 POWER,FOAMTM, 345-347
and moments, 258 Maximum bending, 314 Maximum def lection, 324
Fower Piping Code (ANSI/ASME 831.1), 3-6, 14, 257 , 260 Precompression, 356, 360
Maximum radius, 112 Maximum shear (Tresca) theory, 2 Mechanical forces, 258-259 Minimum radius, 112 Minimum thickness, 177 Miter(s)
Pressure
bends, 120 elbows, 120-121 spactng, 112, 120-121
welding,308-309 "Modified lame" formula, 177 Modulus of elasticity (table), 33,257
external, 5
working, 176, 250-251 Pressure-balance expansion, 354 Pressure design, 5 Pressure stress, 6-7, 11
rutios,
177
, 250-256
(tables), 178-249 Prestressing,3 Pumps, 256-258 Purging connections, 358
Moments. See Forces and moments
Nominal wall thickness, 11, 111, 177
Nozzles, 122-123
flexibilities, 122-
176
loadings (table), 257 snction, 257 -259 Occasional longitudinal stress, 6 Offset lengths required (tables),
266-267
Oil piping,
14
Radial flexibility, 122 Radial stress, 2 Refrigeration Piping Code
(ANSr/ASME 831.5),
15
Reinforcement area, 253, 255 Reinforcement zone, 255 Required area for branch connections,253 Required yield strength, 350-351 Restrained piping, 1l Resultant applied forces and
moments, 258 Pedestal support, 258-259 Pipe(s)
Hangers, 324, 327, 345, 349 Heat exchangers, 263-264 Heating plants, 14 h factor (table), 120 Hinged expansion joint, 355, 358
anchors, 356, 360-363
Hot \pater piping, 14
insulation, 299-300
Resultant bending stress, 6-7 Resultant shear force, 259
deflection, 314
Right Rigid Rigid Rigid
guides,356,363
Rotational nozzle flexibilities
bends,311-323,351 components, 299 -313, 357
angle nozzles, 253 ends, 122 hanger, 324 support, 324
(tzbles), 122-176
-
{d ---r
Index {Is Saturated sream. properties
(tables). 3-l-36 -
Self sprineins.
l
Shaft displaciment
of
. 258-259
Shape factors. 321 Shoe suppon. 3!-1 Shear strissSingle expansion ioint, 351
l
Sleeve.356.358,364
Slurry Piping Code (ANSt/ASME 831.11). t6 Spans, allouable, 313. See also ptpe sPans.
Specified rninimum yield stren eth (SMYS.,, 9, Spring rate of nozzles, 122 spnng suppons, 324_341
ll
Stabiliry,356
Standard hangers, 327
standard terms, 3_4
Stress(es). .te€ aho piDe stress.
allowable. 8-l l. 38--l I t, 257_264 deadload, 314 intensificarion factors, l. I12. I L4-121
limits,314-315 pressure/stress r atios,
prtmary, 2
lj 7 _256
range, 2 shear,
ll
Structuraj supports, 325
suctron nozzles, 257_259 Supports. 324-325, 327, 342. 356. Slee a/so Pip€(s) supports. baseplare. 258-259 pedasral, 258-259
-'
Support load, 345 Sustained longitudinal stress. 5 )usralned-pIus_thermal expansion stress, 6 Sway brace support, 327. 342 Swing check v-aives, 30gTemperature derating factor terms, standard. 3_4
Thermaf expansion, 2-3,
359-360
f,
l.]
5-6. 324,
_.coefficienrs of (tabtes), 2_32 r nerma movements, 351 Three-dimension pipine. 2 Three-weld-miter elbo;s. 12 I tte roos, JJ6 Torsional stress, 2 Travel stops, 327 Tresca (miximum shear) theory, 2 rwo-anchor Ptplng systems, 3
turbines,260-267
Thrbulence-producing device, 364
Uni{orm Building Code, J2l unrtorm wind loads, 323
U.S.A. Standard Buildins Code R^equirements for Deiign Loads. Universal expansion joint, 352_J54 unrestratned ptplng, g
rtical exhaust connecrion. 160_16 l vrbratron control, 342_ J4.t Von Mises (distortion energr r l.betrrVe.
2-'
Wall thickness pressure stress, 7. 251
wall thlckness
maxrmum allowable. 6
nominal, l l, l12, required, 177 Weather,35l
177
Wedge gate valves. 306 Weld elbows, l12 Weld-end valves (tables)
angle,302 check (swing), gate,300 globe,301
301
Welding ends, 363 Weld joint factor E,
l0
Wind loads, 320-321 (table),322-323 Wind pressure, 320
Working stress, 172
y values (tables), 177_250 y : Q Garlowy, 178-195, 250
y=
Van Stoned flanges. 3& Variable spring iupports, 324_327 load tabte, 328
y
U.4 (modified lame). 196_214,250 = 0.5 (average diameter).
y
:
2t4_231, t50
0.7 (creep), 232_250
-
Victor Helguero M.
Piping Stress Handbook Second Edition
Gulf Publishing Company Book Division Houston, London, Paris, Tokyo
Piping Second Library of
ISBN G87201_?03-6
Copyright @ 19_86 by Gulf publishing Company, Housron, Texas. All ngfts reserved. printed in the United Stabs;f
p-ar,b
ttrepf.
A;dca- itis book;; *itt out perJsio'i
may not be regoduced io a"y fo.rn
of the publisher.
$BN GE720r-nB{
.
.::
-i.j.
. -- ,,
Contents vlll
Preface
Chapter
1
Basic Theory of Pipe Stress and ANSI/ASME Codes 831.1, 831.3' ... . .. 1 831.4, and 831.8 Ptpe Stress Compliances . . . .
.
Pipe Stress Theory. Expansion Stresses. Cold Springing. ANSI 831.1 Fower Piping Code Stress Compliances (1983). ANSI 831.3 Chemical Plant and Petroleum Refinery Piping Code Stress Compliances (1984). ANSI B31.4 Liquid Fetroleum Transportation Piping Code Stress Compliances. DOT/B31.8 Gas Transmission and Distribution Piping Systems Stress Compliances. Standard Oudine for ANSI B3l Codes.
Chapter 2 Coefficients of Thermal
Expansion
,........17
Tables. Example Problem.
Chapter 3 Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 ..... 38 (1e83)
.
Tables.
Chapter 4 Allowable Stress Range for ANSI/ASME Petroleum Piping Code 831.3 (19M) . Thbles.
.
... ....73
Chapter 5 Stress Intensification and Flexibility Factors
tlz
Definitions. Thbles.
Chapter 6 Rotational Nozzle Flexibilities for Cylindrical Vessels
.
......l?a
Thbles.
Chapter 7 hessure and Shess Ratioo
.
.......177
Thbles. Instructions and Examples. Branch Reinforcement. Sample Calcula_ tions for Branch Reinforcement.
Chapter 8 Ihsign Criteria for Allowable loads, Moment, and Stresses
........257
Design Criteria for Pumps with Steel Nozzles anit Casings. Design Criteria for Pumps with Cast Iron or Aluminum Nozzles and Casings. Design Criteria ior Tirbine Drivers wilh Steel Nozzles and Casings. Design Criteria for Thrbine Drivers with Cast Iron or Aluminum Nozdes and Casings. Design Criteria for Compressors with Steel Nozzles and Casings. Design Criteria for Cornpres_ sors with Cast Iron or Aluminum Nozzles and Casings. ApI Code 661 Design Criteria for Air-Cooled Heat Exchansers.
Chapter 9 Simptified Solutions for Pipe Stress
265
Example Problem 9-1. Thbles. Example Problem 9-2.
Chapter 10
PropertiesofPipe Definitions. Thbles.
.........292
Chapter
11
Components
Weight and Dimensions of Pipe and
..
. 299
Weight of Pipe and Components. Tables.
Chapter 12 Allowable Pipe Span Formulas and
Thbles
...... ... 314
Pipe-Span Stress Limits. Pipe-Span Deflection Limits. Piping Wind Loads.
Chapter 13 Pipe Support Selection and
Design
..,...,
.
34
Pipe Supports. Spring Supports. Insulated Pipe Supports and Anchors for Cryogenic Service. Thbles.
Chapter 14 Fundamentalsof
ExpansionJoints.
........351
Types of Joint Movements. Nomenclature and Symbols. Types of Expansion Joints. Anchors, Guides, and Supports. Forces and Moments' Cold Springing of Expansion Joints. Cycle Life Expectancy. Corrosion. Erosion. Calculating Thermal Expansion. Precompression. Application, Pipe Guides and Guiding. Iocation of Expansion Joints. End Connections. Covers. Sleeves.
..... ....
Glossary Index
.
368
.,..373
vtl
heface
Determining piping stresses for the design
of
petro_
. chemical and.power plant piping systems iniolves ^many
complex mathematical calculations. These calculationi cal be solved with the aid of any one of several computer programs available provided they have the required ca_ pacity and an acceptable input/output format. The most formidable task facing the engineer is compiling the ex_ tenslve amount ot data needed to run the program. These data include physical properties. allowable stiesses, valve weights and dimensions. stress intensification factorsthermal expansion coefficients. spring hangers and expanslon Jotnt selectlon, and piping wind loads.
This reference book provides formulas, technical data. and other pertinent design information not readilv avail_ able in a single source for the piping stress analyit in the petrochemical industry who often has difficulry co ecting the required data and solutions to complete a piping stresi
analysis. .Depending on the magnirude and complexity of the job, the data needed to complete a given tasi may be scattered throughout a host of sources. The author's aim is to bring together in a single reference all the above mate_ rial and present it in a convenient form. Much of the information included in this book was ob_ tained from the work of others; some was used in its orisi_ nal form. while some was rearranged for this applicatio-n.
The author wishes to acknowledge his indebtedness to
Mr. Robert Kingshill, Virender Shukla, and Timothv W. Calk. for their assisrance in preparing this handbooki and the American Society of Mechanical Ensineers which generously permitted the author to use sevlral eouations to develop tabulations contained in this handbook. Suggestions and criticism concerning errors that may .9.T]l spite_of all precautions will be greatly appri ciated. They will contribute to the further improvement of
this reference handbook.
Victor Helguero M. , PE.
viii
Basic Theory of Pipe Stress and ANSI/ASME Codes 831..1, 831.3, 83L.4, and 831.8 Pipe Stress Compliances
The bending stress due to temperature, weight of pipe, contents, insulation, snow and ice, wind or earthquake is calculated by the following equatron:
Pipe Stress Theory To understand the basic criteria of the ANSI+ pressure piping code, it will be useful to explain the way different stresses develop when a piping element is subjected to a
number of loading conditions. There are four main
piping element, as shown in Figure l1. The following gives the intensity of these stresses and the manner in which they may be combined: stresses that
affe.t
t,
: Vqgrr'lt*+l Z
a
where
: :
S5
Ii L
* For
reasons of space these codes will be designated ANSI codes riroughout the text of the book, Some readers may be mor€ familiar with the desisnation ANSI/ASME as indicated in the headings.
=
Mi M" Z
: : :
Bending stress
In-plane stress intensification factor Out-of-plane stress intensif ication factor In-plane moment, lb-in. Out-of-plane moment, lb-in. Section modulus of pipe, in.3
The direct longitudinal stress due to t€mperature and weisht is calculated as follows:
lJ\J"
.
: Fu :
where A s
t \o S, I
The longitudinal stress due to internal pressure is calculated as follows:
^PD
"P Sr
=
= S, = Ss = Sc
Longitudinal stress and the sum of three component parts (see Equation 1-1). Circumlerential stress Radial stress Shear stless
Figure 1-1. Stress-free-body diagram.
Metal pipe cross-sectional area, in.z Direct force, lb
4t'
where P D
= =
:
Internal pressure Outside diameter of pipe (see Chapter 10)
Pipe wall thickness (see Chapter 10)
S:
:
0 (shear)
2
Piping Stress Handbook
Both significant stresses act in the same direction; therefore the stresses are "additive," i.e.
: S6+\+Sa
S1
(1-l)
Nofe: Inngitudinal stresses due to temperature are excluded from the combination when doing code calculations.
Circumferential stress, S., is primarily due to internal
The preceding method is known as the maximum shear theory (Iresca) and is the preferred method of the ANSI Code. A second method, known as the distortion-energy theory (Von Mises), also provides good results but is not used by the Code:
"'3S-+J--T-+ STTT$"
pressufe:
S^:.q,D -2t Radial.stress, S., is primarily due to internal pressue, which is equal to P.
S.=P
The ANSI pressure piping code recognizes that stress
Shear sfiess, S", is the sum of two component parts: tortional stress and direct shear stress (the second stress is usually negligible). (This condition occurs in three-dimensional piping systems.)
ss: where
Expansion Stresses
T
+2.0&
n
A
SS:
T: F,:
Shear stress Torque, lb-in. Resultant shear force Cross-sectional area of pipe Section modulus of pipe
z: sr: T/22, tortional
due to thermal expansion tends to diminish with time as a
result of local yielding or creep. This reduction of stress will appear as a stress of opposite sign in the cold condition. This phenomenon is known as self springing. Cold springing is similar, and although the hot stresses tend to diminish with time, the sum of the hot and cold stresses for any one cycle will remain practically constant.. This sum is called the stress range, ard, the code for pressure piping defines this allowable expansion stress range established for thermal expansion in terms of hot and cold tabu-
lar S values
S.
stress
:
F (1.25 S"
where S,
While the ANSI pressure piping code considers stresses due to therrnal expansion separately from primary stresses due to pressure, weight, and external loadi_ngs,/it is obvious that when combined stresses formulas and a specific yield criterion existr/stresses from all loadings should be included to delermine the principal stresses before confirming them. Resultant principal stresses at the outside
as:
=
: Sr, : F: S"
+ 0.25 Sh)
Allowable expansion stress range
(see
Chapters 3 and 4)
Allowable stress for the cold condition (see Chapters 3 and 4) Allowable stress for the hot condition (see Chapters 3 and 4) Stress range reduction factor for the cyclic
condition
fiber are as follows:
Sr
. sz
=
:
l/2
|2
Ib calculate
[Sr
+ S. +..//4St+ (S'=TFf
[g + s"
- "v4trTre-.l]zr
the principal stresses use 51 or 52, whichever
is greater, or the following equation:
\4* + C;=TJ'
(r-2)
Tbtal No. of Cycles Over Expected Life 7,000 and less
1.0
14,000 and 22,000 and 45,000 and 100,000 and 250,000 and
0.9 0.8 o.7 0.6 0.5
less less less less less
Basic Theory of Pipe Stress and ANSI/ASME Codes The stress due to thermal expansion, which must not :rceed the allowable expansion range , is callel expansion .;-ess and is defined by the piping code as:
n,:(1 -znci(fJn &=cR
s"={SJ'?+4-(sF xe Equation 1-2, where Sp
:
0 and Sr
:
Ss
The piping code further states that the sum of the long; ,-idinal stresses due to pressure, weight, and other sus:ined external loadings shall not exceed $,. Ifthe longitu:jnal stress due to sustained loadings is less than S1, the
:ode permits the unused portion to be applied to extend range available for expansion effects. There-
-.1e stress
:ore, the code, in effect, permits a total equal to 1.25 S. * Sr,), for thermal expansion stress combined with suesses
from other sustained loadings.
n=[r-tn"El* ' I s" Er,l
These relationships apply only to two-anchor piping systems with no intermediate restraints (use whichever equation is greater) and with the further condition that
sn*E
no cold spring to one for lO0% cold
se=
E": Er' : R: Cold Springing
spring
Maximum computed expansion stress Modulus of elasticity in the cold condition Modulus of elasticity in the hot condition Range of reactions corresponding to the full expansion range based on E"
R" and R1 represent the maximum reactions estimated to
A piping system may be cold sprung, or prestressed, to :educe anchor forces and moments caused by thermal expansion or contraction. This is accomplished by shortenng or lengthening the overall length of pipe by any desired amount not in excess of the calculated expansion. The amount of cold spring (C. S.) is usually expressed as a percentage or fraction of the total expansion or contrac-
Ion. This procedure is recognized by the ANSI Code for pressure piping which states: The beneficial effect of judicious cold springing in assisting the system to attain its most favorable condition sooner is recognized. Inasmuch as dre life of a system under cyclic condition depends pdmarily on the stress range rather than the stress level at any one time, no credit for cold spring is warranted with regard to sresses. In calculating end trusts and moments acting on equipment containing moving or removable parts with close clearanc€s, the actual reactions at ally one time mther than their range are signifi-
calt, and credit accordingly is allowed for cold spring in
the
calculations of thrusts and moments.
The reactions (forces and moments) & and & il the hot and cold conditions, respectively, obtained as follows from the reactions, R, are derived from the flexibility calculations based on the modulus of elasticiw at room temperature, E.:
occur in the cold and hot conditions, respectively. Thus, the ANSI piping code does not allow any credit for cold springing in the cornputation of stress. For reactions in the hot condition credit may be taken for twothirds of the actual cold spring applied; however, the full amount of cold sping must be taken into account in computing reactions for the cold condition. To understand the effects of stress range, self springing, and cold springing, see Figure 1-2.
ANSI 831.1 Power Piping Code Stress Compliances (1983) The standard terms, used in the equations set forth in the ANSI code, are defined as follows:
i: Z: rm : D" : :
Stress intensification factor. The term (0.75i) shall never be taken as less than 1.0 Section modulus, tn.,Z: r^2t^ r Mean radius, in. Outside diametet in. Nominal wall thickness. in.
Piping Stress Handbook SELF.SPRING
-
26000 Psl
NO COLD SPRING
24000 Psl
I I
=20 o
5 (,1q a' t! Ir
6ro
ll
-ltt ol
t: !; ii t:
I
dls\
|\)
N
/ ,---'1. r It ,l .tl t\
Irt! ti
.It
a !
m
T
L --t
I
t
\,{
, I
dld \ II
t-
, I
I r--1
It ltI
I
I I
I
I
I
a )< aa
ul tr.^ a I
Figure 1-2. Stress-range curve with and without cold spring.
: : Mr : P M"
: K: K:
M"
S,o
:
q,:
$" : S"
=
_ * S" :
Sr,
Internal design pressure Resultant moment loading due to weight and other sustained loads, in.lbs Resultant moment loading due to occa-
sional loads, including earthquake loads, trusts from relief/safety valve loads, in.-lbs Range of resultant moments due to thermal expansion/contraction, in.-lbs 1.15 for occasional loads actinq less than l0% of the operation period 1.20 for occasional loads actins less than l7o of the operation period Longitudinal stress due to pressure, psr Iolgitudinal stress due to sustained loads,
S"
:
stresses.
S.
S"
=
:
f(1.25 S" + 0.25
Sh)
(see Chapter 4) Basic material allowable stress at minimum
temperature from allowable stress tables, psl
$, =
DSI
Basic material allowable stress at maximum temperature from allowable stress tables, psi Stress range reduction factor fot cyclic conditions for total number N of fuIl-temperature cycles over total number of years of system operation (see " Expansion Stresses")
Longitudinal stress due to occasional loads, psi Thermal expansion stress due to thermal 9xpansion and anchor displacements, psi Longitudinal stress due to sustained loads plus the thermal expansion stress, psi
Allowable stress range for expansion
Wall thickness, in. Coefficient having values as given in the
SE=
ANSI Code 831.1, Table tV.t.2(A) Maximum allowable stress in material due to internal pressure and joint efficiency at the design temperature
Basic Theory of Pipe Stress and ANSI/ASME
'
Pressure Design The rninimum wall thickness for straight pipe under internal pressure and temperatures not exceeding those for various materials listed in the allowable stress tables, including allowances for mechanical strength, should not be
less than that determined by this equation (Section 1M.1.2, Equation 3):
,_ ''' = [_
_ro"- * ol + Pn I
(see Chapter 7)
The design pressure should not exceed:
(t - A) (see Chapter 7) D"-2Y(t--A) where t- : minimum required wall thickness, in. (mm) If pipe
5
where M" is combined in the following manner:
M"
: (Ml
+My2 +M:)t2
For full size outlet connections the equation is:
Z: r where
th
rnztn
:
Nominal wall thickness of the run pipe
For reduced outlet branch connections the equation is (see
Figure 1-3):
[2(SE
P=
Codes
2SE
Z: r where
r5
q tb
th
r3t"
: : = :
Branch mean cross sectional radius, in.
Effective branch wall thickness. in. = lesser of t5 or (i) t5 Nominal branch wall thickness. in. Nominal thickness of run PiPe. in.
is ordered by its nominal thickness, the manufac-
turing tolerances must be taken into account. This minimum thickness must be increased to provide the increase of manufactured tolerance allowed by the applicable spec-
ification or required by the process. The next heavier commercial thickness should be selected.
External Pressure
Sustained Longitudinal Stress The sustained longitudinal stress, 56' is the algebraic summation of the longitudinal pressure stress and longitudinal sustained weight stress. Sh is calculated using the following Code equation (Section 1O4.8.1, Equation 11):
To determine wall thickness and stiffening requirements for straight pipe under external pressure, the procedures outlined in paragraphs UG-28, VG-29, and UG-30 of Section VIII , Division 1 of the ASME Boiler and Pressure Vessel Code should be followed.
Longitudinal Stress LEG 3
The internal pressure stress, by the followilg equation:
^''
S1o,
should be determined
PD.
4t,
Thermal Expansion Stress The thermal expansion stress is calculated using the following Code equation:
5" = 1iv./z)
Figure 1-3. Header and branch connections'
Piping Stress Handbook
sk =
I& 19'frll4t . 4t^ z
1.s51,
(see Chapter 3 for 56)
ANSI 831.3 Ghemical plant and Petroleum Refinery piping Code Stress Compliances (1984)
As can be seen from the equation, the longitudinal stress due to pressure. weight, and other sustainid loads should be less than or equal to the Sh for the rnaterial.
Pressure Stress The minimum allowed wall thickness is calculated by using the design pressure in the following equation:
Occasional Longitudinal Stress The occasional longitudinal stress, S1o, is the algebraic summation of the longitudinal sustained weight striss the , longitudinal pressure stress, and occasionai stresr. S," i. 9{cu,tatea using the following Code equation (Seciion 104.8.2, Equation 12):
PD" 0.75iM, " _ ".-+t,--z*'
(P) (o. D.)
where O.
0.75iMh
: SE : P
D. =
y:
As can be seen from the equation, the longitudinal stress due to occasional loads should be less than-or eoual to k sh.
.875
Allowable Thermal Expansion Stress The thermal expansion stress is calculated usins the fol_
lowing Code equation (Secrion 104.8.3 tA), Equation
+
2 (SE
:
A:
yP)
+A
(see Chapter 6)
Design pressure, psig
Actual pipe outside diameter, in. Maximum allowable stress in material due to internal pressure and joint efficrency
A coefficient having values as given in the ANSI Code, Tabte 304.1.1, A; normally 0.4 A factor used to account to the industy's 12.5% mill tolerance on finished_ wall thicknesses Allowance for corrosion, erosion, etc., in.
The allowed pressure is calculated by using:
13):
S" :
iM"/Z <
S"
+
f(Sh
-
S)(see Chapter 3 for S")
As can be_ seen from the equation, the thermal expan_ . sion stress should be less than or equal to S".
2 (SE) (r-
Puo*
-
A)
O.D.-2y(t^-A)
where
tm
SE
(see Chapter 6)
= .875 x wall thickness, in. : Maximum allowable stress of the material for internal pressure considering the joint efficiency
Sustained-Plus-Thermal-Expansion Stress
Expansion Stress
The sustained-plus-thermal-expansion stress, Sh + Se, is the algebraic summation of the longitudinal stress due to sustained loads and the thermal exDansion stress. S1, * S. is calculated using rhe following iquation: sr,
+ sE =
I&
+
o75iM"
4t"ZZ
+it" .
,r- *
a",
As can be seen from the equation, the sustained-plusthermal-expansion stress should be less than or eouil to the sum of S1 and S,.
The expansion stress is calculated using the Code equation (Section 319.4.4, Eqtation 17).
S":
(S52
+
where S" :
4sr2)r/2
Computed expansion stress, psi
56 = Resultant bending stress, psi S5 = [(i1M), +(t"M"r2]t/2lz S, : Torsional stress, psi, = Mtl2Z Mr = In-plane bending moment, in.Jb M" = Out-of-plane bending moment, in.Jb
Basic Theory of Pipe Stress and ANSI/ASME
Mr
=
Z: i:
Torsional moment on cross section, in.-lb Section modulus of pipe, in.l Stress intensification factor (see Chapter 5)
For branch connections, the resultant bending stress (56) is calculated using the Code equations (Section 319.4.4, Equations 19 and 20):
I
For the header (Legs
and 2 in Figure 1-3):
Z
Pressure Stress The minimum allowed walfthickness pressure stress is calculated by using the internal pressure in the equation:
:PD"+A 2S
where
For the branch (Leg 3):
A S
Z.
56
z"
=
:
fm
t"
= =
: 1.
lo
li
= = =
=
1.21.
Effective branch wall thickness, in., = lesser of t1 and (L) (tb) Thickness of pipe matching run of tee or header exclusive of reinforcing pad or saddle, in. Thickness of pipe matching branch, in. Out-of-plane stress intensification factor In-olane stress intensification factor
319.4.4, Equation 18):
Longitudinal Stress The longitudinal pressure stress is computed in accordance with the Code using the equation:
PD" \. "rP= -_: 4t where S1o : Longitudinal pressure stress, psi P = Internal pressure. psig t : Actual pipe wall thickness, in.
D" =
Nominal outside diameter of the pipe, in. MI
Resultant bending stress, psi
[(i'MJ2
^
Allowance for corrosion, erosion, etc., in. (0.72) (E) (SMYS), psi Specified minimum yield strength, psi, Thble 1-l Weld joint factor, Thble 1-2
Mean branch cross-sectional radius, in.
For elbows and miter bends, the resultant bending
:
E:
,.
stresses (S5) calculated using the Code equation (Section
Su
SMYS
Resultant bending stress, psi Effective section modulus for the branch,
in.3,
Pressure, psig Actual pipe outside diameter, in.
P
D"
+ (LM"lll" Sr= fti,Mif where
7
ANSI B31.4 Liquid Petroleum Transportation Piping Code Stress Compliances
[(iiM)' + (i"M"t]r/'?
-\:-
Codes
+ (i"M.l]'/2
'o=-_.v-
where ii
stress intensification factor Out-of-plane stress intensification factor In-plane bending bending moment, in.-lb
= In-plane
lo:
Mi:
M"=
Z:
(see Figure
14)
"'&.
Out-of-plane bending moment, in.-lb (see
Figure 1-4) Section modulus of pipe, in.3
A conservative equation generally utilized for the calcuiation of the allowable expansion stress range is given in the ANSI Code 831.3 Section 302.3.58d, Equation 1:
s"
:
f(1.25 s"
+
.25
Sh)
Gee Chapter 4)
^,,Qr Figure 1-4. ln-plane and out-of-plane bending ments.
mo-
Piping Stress Handbook Table 1-1 Tabulation of Examples of Allowable Stresses for Reterence Use in Liquid petroleum Transportation piping systems Allowablestless values (s) shown in this Table
of the pipe.
are
equal to 0-72 x
t
(weldjoint factor) x specified minimum yield strength
Allowable stressvalues shown are for neE pipe of known specification. Allowable strcss values for new pipe ofunknown specification, ASTM A 120 specification orused (reclaimed) fipe shalr be dete,-ined in accordance $/ith 402.3.1. some code computations, particularly with regard to bianch connections .. .-For Isee 404.3.1 (d) (3)] and expansion, flexibility, structural atlachments, supports, and restraints (Chapter II, Part 5), the weiojoint factorZ. need not be considercd. For specified mintnum yield strength of other grades in ipproved specifications, reter to that particular specification. Allowable slress value for cold worked pipe subsequently heated to 600 F or higher (welding excepted) shall be 75 percent of value listed in Table. Definitions for the various types of pipe are given in 400.2_ Specified
(s)
Min Yield Specification
Gmde
(E\
Strength
Weld
psi
Notes
Joint
Faclor
Allowable Stress Value -20 F to 250 F psl
Seamless
API 5L A-PI5L, ASTM A 53, ASTM A 106 API5L, ASTM A 53, ASTM A I06 ASTM A 106 ASTM A 524 ASTM A 524
API sLU API 5LU API sLX API 5LX API 5LX API 5LX API 5LX API sLX API 5LX
425 A B c I II u80 ul00 x42 x46 x52 x56 x60 x65 x70
Furnace Welded-8utt Wetded ASTM A 53
API 5L Class t & Class fi API 5L (Bessemer), ASTM A 53 (Bessemer) F!rnace Weided-Lap Welded 5L Class I API 5L Class II API 5L (Bessemer) API 5L Electric Furnace
Elecrric Resistance Wetded and Elecrric Flash Wetded A25
Reptuduced
(2) (2)
B
B
1.00 1.00
(1)
25,200
30,000
(l)
1.00
r.00
80,000 42,000 46,000 52,000
(4) (1) (4) (l) (2) (4) (l) (2) (4) (l) (2) (4)
21,600 57,600
56,000
(l) (4)
60,000 65,000 70,000
(1) (4) (l) (4) (1) (4)
2s,000
(t) (2,
100,000
{l)
x65
x70 u80
l.
r.00
72,000 30,250 33,100
37,450 40,300 43,200 46,800 50,400
0.60 0.60 0.60
r0,800
25,000 (1) (2) (6) 28,000 (1) (2) (6.) 30,000 (l) (2) (6) 2s,00o (1) (2) (6)
0.80 0.80 0.80 0.80
14,400
100,000
ul00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
28,800
(2) (3) (2) (s)
56,000 60,000 65,000 70,000 80,000
x60
r8,000 21,600 25,200
(r') (2)
42,000 (l) (2) (4) 46,000 0) (2) (4) s2,000 (1) (2) (4)
x42 x46 x52 x56
1.00
r.00
40,000 35,000
25,000 (l) (7) 30,000 (2) 30,000 (l) 35,000 (2\ 3s,000 (l)
A
fron ANSI/ASME Code 831.4-1979, Tabte 402.3-
35,000
(l) (l)
2s,000 (l) 30,000 0)
A25
A-PI
API 5L API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A I35 API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A 135 API sLS, API 5LX ATI sLS, API 5LX API 5LS, API 5LX API 5LS, API sLX API sLS, API 5LX A}I 5LS, API 5LX API 5LS, API 5LX API 5LU API sLU
(l)
25,000
30,000
(l) 0) (l) (l)
(4) (4) (4) (4)
(1) (4) (l) (4)
Reprinted courtes!
1.00 0.85 1.00 0.85 1.00 1.00 1.00 1.00
r.00
10,800 12,950
t6,150 17,300 14,400 18,000 18,360 21,600
2l,420 25,200 30,250
33,r00 3',t,4SO
1.00
40,300 43,200 46,800 50,400
1.00
57600
1.00
'72,000
1.00
r.00
ofTh" e^"riron soi"ry of Munonirot rrxin"ug
Basic Theory of Pipe Stress and ANSI/ASME Codes Table 1-1 Continued (s)
Specified
(E)
Min Yield (iranorh
Weld
@o"
Specification
Notes
Joint
FactOr
Allowable S$ess Value -20 F to 250 F psi
Electric Fusion Welded ASTM A I34 ASTM A I39 ASTM A I39 ASTM A I55 ASTM A I55
A
A B x42 x46 x52 x56 x60 x65 x?0 u80 u100 Y35 v42 Y46 Y48 Y50 ]/52 Y60 Y65
API 5L, API 5IJ API 5L, API 5LS API 5LS, API sLX API 5LS, API 5LX API sLS, API 5LX API 5LS, API 5LX API 5LS, API 5LX API sLS, API sLX API sLS, API 5LX API 5LU API 5LU ASTM A 38I ASTM A 381 ASTM ASTM ASTM ASTM ASTM ASTM
A A A A A A
t'rooo
:
Submerged Arc Welded
38I 381
38I 38I 38I 38I
NOTES (l)Weld joint factor E
(1) (1) (2) (1)
30.000
0.80 0.80 0.80 0.90 1.00
(2) (2) (8) (8)
(l) (l)
1.00
21500 25,200
(2) (4) (r) (2) (4) (l) (2) (4)
1.00 1.00
r.00
30,000 35,000
(l)
42,000 46,000 52,000 56,000 60,000 65,000 70,000
(l) (l)
35,000 42,000 46,000 48,000 50,000 52,000 60,000 65,000
30,250 33,100 3',t,450
1.00 1.00 1.00
(4) (4)
(1) (4) (l) (4) (1) (4) (l) (4) (l) (2) (l) (2) (l) (2) (l) (2)
80,000 100,000
17,300 20,150
40,300 43,200 46,800 50,400
r.00 1.00
57,600
1.00 1.00
72,000 25,200 30,2s0
r.00 1.00 1.00 1.00 1.00
(l) (l) (l) (l)
33,100 34,550
36,000 37,450 43,200
1.00
1.00 1.00
,+6,800
(se€ Table 402.4.3) and allowable stress value a.e applicable to pipe manufactured after
1954.
(2)Weld joinr factor ,. (see Table 402.4.3) and allowabte stress value are applicable to pipe manuf.ctured befote l9 59.
(3)Class
It
produced under API sL 23rd Edition, 1968, or earlier has a specified minimum yield srrensth of
2a,OOO psi.
(4) Other Itades provided for in API sLS, API sLU, and API 5LX not precluded. (s)Manufacturewas discontinued and process deleted from API 5L in 1969(6)Manufacture was discontinued and process deleted ftom API 5L in 1962. (?) A25 is not produced in electric flash w€ld. (8)See applicable plate specification fo. yield point and r€fer to 402.3.1 for calculation
Allowable Longitudinal Stress The allowable stress value for by the Code in Section 419.6.4(c):
additive longitudinal
stresses is given
where SMYS
:
of(S).
Specified minimum yield strength, psi (see Thble 1- 17
Allowable Expansion Stress Range for Unrestrained Piping This is given by:
Sr
(allow)
where Su
:
= :
0.75
S"
The allowable expansion stress range, psi 0.72 SMYS
S"
:
0.72 (SMYS)
where SMYS
:
Specified minimum yield strength, psi (see Table l-lr
10
Piping Stress Handbook Table 1-2 Weld Joint Factor E Weld Joint
Specification Number
Pipe Mfrd. Before 1959
ASTM A 53
Seamless
1.00
Electric-Resistance-welded Furnace Lap-Welded Furnace Butt-Welded
Factort Pipe Mfrd.
Afler
0.85 (2) 0.80 0.60
1.00 1.00 0.80 0.60
1958
A
106
Seamless
1.00
1.00
ASTM A
I34
Electdc-Fusion (Arc)-Welded single or double pass
0.80
0.80
A
135
Electric-Resistance-Welded
0.85 (2)
1.00
A I39 ASTM A I55
Electric-Fusion-Welded single or double pass
0.80
0.80
0.90
1.00
ASTM A 381
Electric-Irusion-Welded, Double Submerged Arc-Welded
API 5L
Seamless
1.00 0.85 (2)
0.8s (2)
1.00 l 00 1.00 1.00
0.80 0.60
0.80 (3) 0.60
ASTM
ASTM ASTM
Electric-Fusion-Welded
Electric-Resistance-welded Electric-Flash-Welded
Electric-Induction-welded Submerged Arc-Welded Furnace Lapwelded Furnace Butt-Welded
API sLS
l-00
Electric-Resistance-welded Submerged Arc-Welded
API 5LX
1.00
t.00
Seamless
1.00 1.00 1.00
Electdc-Resistance-Welded Electdc-Flash-lvelded Electdc-Induction-Welded Submerged Arc-Welded
API
5LU
Known Unknown Unknown Unknown Unknown Unknown
1.00
1.00
Sean ess Electlic-Resistance-Welded Electdc-Flash-Welded Electric-lnduction-Welded Submerged Arc-Welded
-_ _ -
Known
(4)
Seamless
Electric-Resistance or F'lash-Wetded Electric-[jusion-Welded Furnace Lap-Welded or ovet 4lz" OD I:urnacc Butt-welded or 4%" OD and smaller
1.00 (6) 0.8s (6) 0.80 (6) 0.80 (7) 0.60 (8)
1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00
r.00 1.00
(5) 1.00 (6) 1.00 (5) 0.80 (6) 0.80 (7) 0.60 (8)
NOTES: (l) Definilions for the various pipe types (wetd joints) are given in 400.2, (2) A weld joint factor of I o may be used for electric-resistance-welded or etectric-flash-wetded pipe manufact ured prior to I 9 5 9 where (a) pipe furn ishe d un der this c tassifica ! ion has been su bj"" t"o to pp'r"'-"ni"i i""t"
and/or heat treatmenls as aFeed to by the supplier and the purchaser, and such sujplementat"u teits analor rreai treatment demonstrate the strength characteristics of the weld lo be equal to the rninimum tensite itrength for the pipe, or (b) pipe has been tested as requi.ed for a new pipetine in accordance with a3z.4.i ,^. speciried (r,| Il1anuracrure was discontinued and proeess deleted from AI,I SL in t 962. (4) Factors shown above for pipe manufactuled before r959 apply for new or used (rectaimed) pipe if pipe specification and pipe lvpe ate known and it is known that pile was manufacrured before r'9i9 ri.i r""*" whether manufactured after 19S8. ". (5) Factots shown above for pipe manufactured aft€r 1958 apply for new or used (rectaimed) pipe if pipe spec! ficarion and pip€ type are known and it is known rhar pip; was manufactured aiter 195s.(6) Factor apPlies for new or used pipe of unknown specific;tion and ASTM A t 20 if type of weld joint is known. (7) Factor applies fot new or used pipe of unknown specification and ASTM A l2o if iipe or *eta j"irr i" i"o*tl lo be furnace lap-wetded, or for pipe over 4% in. OD if type ofjoinr is unknown. (8) Factor applies for new or used pipe of unknown specification and ASTM A l20 if type of weld joint is known to be firrnace butt-welded, or for pipe 4% in. OD and smalter if type of joint is unknown.
Reproduced
from ANSI Code 831.419D,
Toble ,t02.4.3. Reprinad coutksy
of The Arncicai Sociey
oJ Mechanical Engineers.
Basic Theory of Pipe Stress and ANSI/ASME
M"
Longitudinal Expansion Stress for Restrained Piping
=
: ii :
Mt
For restrained piping, use the longitudinal expansion ANSI Code 831.4, Sec-
stress from the equation given in
tion 419.6.4
g: E= Sr.
Tr Tz
=
: :
Longitudinal compressive stress, psi Modulus of elasticity of steel, psi Hoop stress due to fluid pressure, psi Temperature at time of installation, 'F Maximum or minimum operating temper-
a=
ature, oF Linear coefficient of thermal expansion,
v:
Poisson's ratio
in./in./'F
= 0.3 for
The allowable stress value in shear is computed in accordance with the ANSI Code B31.4, Section 402.3.1 (e):
56 (allow)
=
(.45)
(S I,IYS)
The allowed internal pressure stress is S, where (0.72) (E) (SMYS), psi
S=
steel
DOT/831 .8 Gas Transmission and
Distribution Piping Systems Stress Compliances (1982)
0.90 (SMYS)
where SMYS
:
Allowable Internal Pressure Stress
This is calculated by using:
:
Bending moment out oi or transverse to, plane of member, in.Jbs Torsional moment, in.-lbs Stress intensification factor under bending in plane
Allowable Shear Stress
Allowable Expansion Stress Range for Restrained Piping
s"
11
ft):
Sr:E(a)(Tr-T1)-v(S) where
Codes
Pressure Stress
Specified minimum yield strength the pipe, psi (see Table l-1)
of
The design pressure for steel gas piping systems or the nominal wall thiclmess for a given pressure is determined by:
The expansion stress for unrestrained piping is calculated by using:
S.:
[56, + 4S,2]r2
where S" :
^.Z Sr
=
Mi =
2s' (F) (E) (T) D
(For limitations see Section
Computed expansion stress, psi
[(iiM), + (LI\AF]I"
:
P=
equivalent bending stress, psi MJ2Z torsional stress, psi Bending moment in plane of member (for
:
members having significant orientation, such as elbows or tees: for the latter the moments in the header and branch portions are to be considered separately), in.lbs
: S:
where P
D: F: E:
84l.l2l)
Design pressure, psig Specified minimum yield strength, psi (see Table 1-3). For special limitations on S see Section 841.121 (e) and (f). Nominal outside diameter of pipe, in. Nominal wall thickness, in. Construction-type design factor obtained from Table 14 I-ongitudinal joint factor obtained from Thble l-5 (see also Section 811.253 (d) Temperature derating factor obtained from Table 1-6
12
Piping Stress Handbook Table 1-3
specified Minimum Yield strength for steel and lron pipe commonly used in piping systems. Specilication
Tvpe
(l)
SMYS (psi)
A?I5L
BW, ERW, S
API5L
ERW, FW, S, DSA ERW FW, S, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, Fw' S, DSA
API 5L
A?t 5LS (2) API API API API
5LS 5LS sLS 5LS A?I sLS
API SLS API sLS API sLS API SLX (2)
A?I sLX API 5LX API 5LX API sLX API5LX API5LX ASTM A53 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM
A53 A53
ERW, ERW,
AI06
S
A106 AI 06
AI35 AI35
AI39 AI
B......... A.........
]9
A381
A38I ASTM A38I ASTM A38I ASTM A38I ASTM A381 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM
c.........
Clas Y-35 .. cla$ Y 42 .. Clas
Y46
.
class Y-48 . clas. Y-50 . Cla\s Y-s2 .
. . . .
A38I
Class
Y-56
..
A381
Class
Y60
.
A38I
Class
Y-65 . .
AI34 AI55 A333 4333 4333 A333 4333 A333 4333 A559
I
3s,000 42,000 46,000 52,000 56,000
60,000 65,000 70,000
42,000 46,000 52,000 55,000 60,000 55,000
S
70,000 25,000 30,000 30,000
S
3s,000
BW BW
ASTM 453
25,000 30,000 35,000 30,000
10,000 35,000
s s ERW ERW EFW EFW DSA DSA DSA DSA DSA DSA DSA DSA DSA EFW EFW S, ERW S, ERW
40,000 30,000 35,000 30,000 35,000
3s,000 42,000 46,000 48,000 50,000
52,000 s6,000 60,000 55,000 (3) (3)
,7
S, ERW S, ERW
8
S, ERW
30,000 35,000 35,000 35,000 35,000 75,000
9
S, ERW
46,000
ERW
35,000
3
S
6
(l) Abbreviarions: BW Furnace butl-welded; ERW- Electric resistance weld€d; S-Seamtess: EFw - Electric fusion weldedi DSA- Double subme.led,a.c welded.
FW
-
Fhsh w€lded:
(i!) Intermediate
Brades ar€ available in API 5LS and 5LX. (3) S€€ applicabl€ plat€ specification for SMYS.
Note: This tablc is not conplete. R)r minimum specified yield strength of other grades and erades in approved specifications, rcfer to the particulor specification. Iron ANSI/ASME Code 831.8-1982, Appenn& D. Repdnted courvsy of me Americon Societt of Mechanicat Engineers.
Reproduced
Basic Theory of Pipe Stress and ANSI/ASME Codes
Expansion Stress
Table 1-4 Values of Design Factor F Conslruclion Type (Scc 841.151)
This is calculated by using the Code equation:
Design Factor
Type A Type B Typc (' Type D
F
S"
0.11 0.60
=
where
0.5 0
0.,10
Ul
Reproduced Irom ANSI/ASME Code 831.&1982, Table courtesy of The Ameicon Society of Mecha ical Engineers.
IC.
Repnntud
(S6'?
Fr.tol
C
:
tion, in.lbs Torsional moment on cross section, lbs Section modulus of piPe, in.3
Stress intensification factor (see ANSI Code B31.8, Appendix E)
1.00
Llcctric Resistancc Weldcd
.60
Furnrcc Bult Welded Scrmicss
AS IN{ A 134 AST}'1 A] 35 AST\'1 A1]9
lllcclric Irusion Art Wcldcd Llectric ResislLrnce Wclded
lllcclric Fusion wclded
00 .80 1.00 .30
ASTM A]55
Llcctric Ijusion Arc Wclded
L00
ASTM ,42I
Spiral WeLded Stccl PiPe Doublc Submergcd'AIc-welded
r.00
Sc:rmLess
l .00
I
ASTM A38I API 5L
Sermlcss
L00
Elcctric Rcsistirncc Wcldcd Llectric I:lash WcLded
L00
Submcrgcd Arc Weldcd
llectric
S"
.80
Rcsistancc Welded
1.00 1.00 r .00
Note: Definitions for the virious chsses of welded pipe given in 804.243 n"proa*"a.Iro^ ,tNSttlSME Code 831 8-1982, Thble UI
Tcmpcrrtulc 150 t or 300 350 F
This is computed by using:
lA
less
400 tl 450 F For intermediLite temperatures
-'' srn=-
Reprihted
where
for Steel Pipe
TelnPcrirrure Dtrating
|
Specified minimum yield strength, psi (see Table 1-3)
Nre
courtesj of me American Society of Mechanical Engineers
Degfccs Fahrcnhelt
:
Longitudinal Pressure Stress
*Manufactu.ewasdiscontinued and process deleted from API 5L in 1962.
I
0.72 (SMYS)
where SMYS
l.00
Subnergcd Arc Welded
Table 1-6 Temperature Derating Factor
=
1.00 .60 .80
Furnace llut l Welded *l:urnace L!p-Wcldcd
API 5LS
This is calculated by using:
L00
Llcctric Rcsistxncc weldcd Elcclric Flash Wcld.d
API 5I X
Allowable ExPansion Stress Range
l
AST}I A106
frffiiififi
:
L00
ASTIU A53
Note:
4S,2)r/2
Se = Computed expansion stress, PSi iM/Z Resultant bending stress, Psi psi Mtl2Z St= Torsional stress, Resultant bending moment on cross sec-
z= :-
Longitudinal Joint Factor E Pipe Clrss
+
Sr: M: M, :
Table 1-5 Spec. Number
13
l:!ctor f
4r
P : n:
Design pressure, psig Outside diameter of pipe, in. Pipe wall thickness, in.
The sum of the longitudinal pressure and longitudinal bending stresses due to external loads such as weight of pipe and contents, wind, etc., should not exceed'75% of owable stress in the hot condition. The allowable for the sum of the longitudinal stresses is given by:
thl a
r .000 0.967
0.9 31
0.900 0.867
51
intcrp(tl!te for derating
B3t E-1982, rabtc 84l 'qNs ASME code courtesy of The American Sociery of Mechanical Engi eers
PD"
lB
Reprinted
:
(allow)
:
0.7s (S) (F) (T)
where S = Specified minimum yield strength, psi E_ .l|_
Design factor obtained from Table 1-4 Temperature derating factor, Table 1-6
14
Piping Stress Handbook
Standard Outline for ANSI Bg1 Codes
ANS|Code 831.1: Power Piping Includes
l.
Power and auxiliary service piping systems for electric generating plants. 2. Industrial and institutional plants (also see ANSI
3. 4. 5. 6. 7
.
Code 831.9). Central and district heating plants (also see ANSI Code 831.9). All piping and cornponent parts within or part of plants as previously specified, unless specifically excluded. Boiler external piping which is covered under the ASME Code, Section I, stamping requirements. Geothermal steam and hot water piping. Oil or gas piping , downstream of meter, within plant
identified in l, 2. or 3, above. and hydraulic distribution syslems.
8. Air
2. 3.
Code.
4.
Gas gathering, transmission, and distribution sys-
5. 6.
tems covered by ANSI Code B31.8. LPG in the liquid state. Fuel gas-air mixtures in the combustible or flammable range.
ly'ore.' This Code will be withdrawn when the new issue of ANSI Code 7223.1 (which does not reference ANSI Code B31.2) is released. This service will be covered by ANSI Codes 831.9 and 2223.1.
ANSI Code B31.3: Chemical Plant and Petroleum Refinery Piping lncludes 1. All piping within the property limits of facilities engaged in the processing or handling of chemical or petroleum or related products.
Exctudes
1. Piping specifically covered by other ANSI/ASME sections. 2. Components covered by ASME B and pV Code. J. Fuel gas in industrial and institutional plants. 4. Building heating and distriburion sream piping for 15 psi (100 kPa) gauge or less or hot water systems for 30 psi (200 kPa) gauge or less. 5. Roof drains, floor drains, plumbing, sewer or fire protecflon systems. b. Piping for hydraulic or pneumatic tools. 7. Piping for nuclear power plants.
ANSI Code 831.2: Fuel Gas Piping Includes 1. Natural
Fuel gas piping covered by the ANSI Codes B3l . 1 , B31.3, 831.8, Z2l.3O, or ZtO6.l Pressure vessels covered by the ASME B and pV
Excludes
1. Nonhazardous fluid piping with
pressures between 0 and 15 psi (100 kPa) and temperatures ranging from
2. 3.
4.
5. 6.
-20'F (-29"C) to 366'F
(186"C). Piping covered by the ASME B and PV Code, Section I or ANSI Code B31 . 1, which requires Section I, Inspection and Stamping @.E.P. Piping). Pressure vessels, heat exchangers, pumps, etc., including internal piping and connections for external piping. Piping within the property limits which has been designated for design according to the ANSI Code 831.4 or 831.8 or to government regulation (pipeline rights-of-way). Plumbing or sewers. Piping for fire protection systems (covered by insurance underwriter's requirements).
gas.
2. Manufactured gas. 3. LPG-air mixtures above the combustible limit. 4. LPG-in the gaseous state.
lncludes
Excludes
1. Fuel gas piping where the metal temperature is above 450"F (232"C) or below
ANSI Code 831.4: Liquid Petroleum Transporiation Piping Systems
-20"F (-29.C\.
1. Piping transporting liquid petroleum and petroleum products between the producer's facilities and delivery and receiving points.
Basic Theory ol Pipe Stress and ANSI/ASME
1.
1. Water air, steam, lube oil, gas, and fuel piping.
3.
4.
Pressure vessels, heat exchangers, pumps' meters' etc., including internal piping and connecUons to ex-
ternal piping. Piping systems designed for internal pressures less than 15 psi (100 kPa). Piping systems designed for internal pressures
6. 7.
Pressure vessels and piping covered by the ASME B
and PV Code.
systems with metal temperatures above 450'F Q32'C) or below -20'F (-29"C). Piping in chemical plant or refinery property limits' natural gasoline extraction plans' etc. ' covered by
2. Piping 3.
ANSI Code 831.3.
greater than 15 psi (100 kPa) where the design temperature is below -2O"F (-29"C) or above 250"F
4. Atmospheric vent piping for waste gases. 5. Low pressure gas which is covered by ANSI Code
Casing, tubing, or pipe used in oil wells, wellhead assemblies, and piping connecting those assemblies' Piping covered by the ANSI Code B31.3 or B31.8. Ammonia reftigeration piping systems'
6. Wellhead assemblies. 7. Proprietary items of equipment.
831.4.
(120'C).
5.
15
Excludes
Excrudes
2.
Codes
ANSI Code 831.9: Building Services Piping ANSI Code 831.5: Refrigeration Piping
lncludes'
,ncrudes
1. Piping
systems
for building services for industrial,
commercial, public, institutional, and multi-unit res-
1. Refrigeration and brine piping systems down to
idential buildings.
-350'F (-
196"C) either erected on the premises or factory assembled, unless specifically excluded.
Examoles:
Excludes
reother laboratories. piping Water systems. Piping systems with internal or external pressure of tS psi ltOO kPa) or less.
1. Self-contained refrigeration systems covered by quirements of Underwriter's Laboratories or nationally recognized testing
2. 3.
ANSI Code 831 .8: Gas Transmission and Distribution Piping
A. B.
C. D.
E. F.
G.
Excludes 1. Pressure limit exclusions:
A.
Steam: 125 psi (860 kPa) Gauge B. Nontuel gas: 125 (860 kPa) Gauge C. Liquids: 300 (2,070 kPa) Gauge D. Full vacuum for all fluids
,ncrudes
1.
Gas transmission pipelines.
2. Gas compressor stations. 3. Gas metering and regulation stations. 4. Gas mains. 5. Service lines to oudet of customer's meter set' 6. Gas storage lines and storage equipment of closed-pipe type.
Dual+emperature water for heating and cooling' Chilled water. Condensing water. Hot water. Steam and condensate return Compressed air and other nonflammable gases. Fuel gas over 60 psi (415 kP-a) _(tuel.gas ulder 60 psi is covered by the new ANSI Code 2223'1)
the
*
(as per latest draft.)
16
Piping Stress Handbook
2. Other exclusions:
A. Piping systems covered by ANSI Code B3l . I
B. Sanitary, potable water, and storm drain piping
Excludes
l.
c. Fire protection systems D.
4c:tylene, hydrogen, oxygen and medical gas
Plpng E. Fuel oil piping
Vessels, heat exchangers, condensers, pumps, com-
pressors, expanders, scrubbers, ana
ment.
2.
, J.
b*rer
equlp_
rr'acuum
piping systems which supply insulating vacuum !o vacuum jackets of cryogenic piping syJtems. rtpmg sysrems specifically covered by ANSI Codas
831.5 or 831.3 lwording of draft).
ANSI Code 831.10: Cryogenic piping* lncludest 1. Liquid-solid mixtures (or slush), operating at tem_ qg-ra1u1ej-rgcinS ftom r2OK (_ 244"F, _ 153 "C) ro (-4^59"8 -273"C), either erected on the prem_ 9K
ANSI Gode 831.11: Slurry piping Systems
ises or factory assembled.
lncludes * (Io
be included io tuture ANSI Code 831.3)
r (as per latest draft.)
t. Initial coverage will be coal transported in water. 2. Future coverages will include slurries ofother solids transported in nonhazardous liquids.
Coeflicients of Thermal Expansion
This chapter contains tables of the coefficients of thermal expansion (Tbble 2-1) and other tables relating to the physical properties of piping materials (Tables 2-2 through 2-4).
17
18
Piping Stress Handbook Table 2-1
Coefticients of Thermal Expansion (in./100 ft) Carbon Steel Carbon-moly Temp, (F)
Low-chrome (Thru 3 Cr Mo)
-32t -?.370 -320 -2.344 -315 -2.313 -3r0 -2.292 -305 -2.?.66 -300 -2.240 -295 -2.214 -290 2. | 8 -?80 2.135 -275 -2. l r0 -210 -2.084 -265 -2.058 -260 -2.A32 -255 -2.006 -250 -r .980 -245 -t .954 -240 - 1.928 -230 -1.e76 -225 -r .850 -2?0 -1 . A22 -2l5 -l .794 -210 -l . 765 -205 -1.738 -200 -1. 710 -r 95 -l .589 -190 -l . 658 -t a0 -l . 606 -r 75 -i .5B0 -170 -r . 554 -r 60 -1 .500 -r 55 -1 .47 4 -r 50 -r .450 -145 -r . 420 -r40 -1.390 -t 35 -r .350 -r 30 -t .330 -125 -r .300 -120 -1.210 -1l5 -t .240 -t t0 -1.210 -r05 -1. r80 -r00 -1 .150 - 90 -r .090 - 35 -r .050 - 80 -1.030
Austenitic
MO Siainless Thru Steels 9CrMo 18Cr8Ni
5 CR
-) ,ri -2.I72
-J.t'5 -3.806
12 Cr
'17
Ct
27 Cl
-2.040
-2.016
-r .992
25 Cr 20
Ni
Monel
3t12
67 Ni 30 Cu
Nickel
-2.620 -z .595 -2
.572
-t .944
-2
.524
-t .920
-2.500
-2. t48
-2.124 -2. I00
-3.586 -2.052
-1.896
-2.234 -2.202 -2. 185 -2
.170
-2.150
-1 .87?
-2.452
-2.004
-3.498 -3.454
-l.848 -l .824
-2.404
-2.090
-l .980
-3.410
-l .80
-2.380 .356
-2.070 -2.048
-2
nua
-I al,
-J.lOO
-2
-1.752
-l .908 1.884
-3,234
-l .704
-t .850
-3.r9
-l .68
-l.312
-3. 146 -1 ln?
-r.836
-3.058 -1 ,7 64
-3.014
-1.715
-2.960 -2.914
-l -l
-l .230 -t
-l
-r .570
-t.800
-!.540
-1.46 -r .438 -1 .4r6
-2.500
-2.454 -2.40a
-l .394
-2. t56 -2.114
-1.024
-l
.780
-t .760 -1
.996 -1 .704
-1 .948
-t .924
-t
.648
-r .350
-1 .90
.620
-1
-t.305
.8;8 -t.355
1
-1
.592
.284 -1.262
-1.s34
-r.536 -r.50s
-1.3t2
.240
-1.214
-t.188 -1.162
-t. -2.0r
.840 -1.820
-1 .37?
-1
-2.218
t36
-1.480 -1.750 -1.710
-t .670 -r .630
-1.110
-l .084
-1
.548
-l
.420
-1 .390
-t.360 -'t.330 -1.298
-r.05t
-r.506
-t .802
-r .454
-l .234
-1.006
-1 .422
-1 .202
-1./)
-0. 98
-1 .380
-t
0
-t .052
-1 .860
-t .482
-t .906
-l .080
-t.920 -t.900 -t .830
-2.778
. 170 . 140
-'t.
21?
-2. I88 -2 ,164
-2.824
-1.258
-r.200
-1.960 -1 .940
-1
-1 .370
-r.286
260
-? -1.614
-1
-l.314
-2
-2.?36
-2.092 -2.068 -?.044
-t .524
-1.342
-t .982
-1.525 -1.504
.548
-t.50 4.474 -l .448
-2.0c4
-2.284
-2. 1 16
.520
-t .57:
-2.30B
-t .548
-2.870
-1.558 -1.644
-2. I 30
-1
.854
-t .700 -r.550
-0.954
-t.34
-1.600 -1.550
-0.902
-1.25
-1
-0.876
.30
-1
.255
.170
-t.138 -t.105
-r .074 -1 .042
Coelticients of Thermal Expansion Table 2-1 Continued
Austenitic
Carbon Sleel Carbon-moly Temp.
Low-chrome
(F)
Ohru 3 Cr Mo)
- 15 -l .000 - 70 -0.97 - 65 -0.94 - 60 -0.91 - 55 -0.88 - 50 -0.84 - 45 -0. AoC - 40 -0.716 - lJ -u. /.4{ - 30 -0.712
25 .20 - 15 - t0 - 5 -
-0.680 -0.542 -0. 604
MO Stainless Thru Steels 9CrMo 18Cr8Nl
5 CR
-0.940 -0. 910
-
-0.880 -0.850 -0.820
-1 ,29?
-0. 790
-1.240
-0.758 -0,7?6 -0.594 -0.662
-r.188
-0.630 -.0596
-0.980 -0.928 -0.875
-0.552
-0.528
{r. !26 -0.494
0
-0.49
-0.450
5
-0.455
't0
-0.555
-l .500 -l . 44A
-l .135 -l .084
-0. s24
4.772 -0.720
-0.59 -0.65
-0.48 -0.45
-0.460
4.232
-0.350 -0.310
50 55 60
-0.140
-0.13 -0.098 -u.uoo -0.034
-0.210 -0. r 58
70
c
a0
0.039 0.076
-0.602
-0. 6r
-0.534
-0.57
-0.5c -0.464
-0. s3
{.33
-0 .4?a
-0.392
-0.30
-0.41
-0.356
-0.370
-0. 3?0 -0.285 -0.252 -0.213
-0.24 -0.21 -0. 19 -0. l5
-0.302 -0.?34
-0- 184
4.12
-0.200
-0.r5
-0.I50
-0. I l3
-0.105 -0.054
-0.06
-0.100 -0.050
-0.038
0
0
0
0
0
0
0.037 0.074
0.056 0.112
0.053 0. 106
0.047 0.094 0.140
0.038 0.076
0.212
0.t85
0.1 l4 0. I52
c.l l4
0.lll
0.152
0. 148
0. 190
0.1 85
0.230
0.22
0. 158
0.22s 0.2&.
0.033 0,066 0.099 0.137
-0.268
0.t65
4.076
0.r90
0.200
0.320
0.28
0.23
0.294
0.340 0.396 0.452
0.264
0.424
0.375
0.296 0.328
0.475 0.528
0.306 0.344
0.370
0. 508 0. 564
0.520 0.876
0.350
0. 58
0.268 0.306 0.344 0.382
0.258
0.420 0.458 0.496 0.534
0.40
0.121 0.762
-0.51
-0.300
-0.250
0.510 0.648 0.685
-0.670
-0. 554
-0. I 64
0.572
-0.77 -0. 73
-0.364
-0.175
-0.840 -0.805
-0.57
-0.36
-0.2t2
-0.938
-0.77?
-u.oto
40 45
-1. r0 -l .06 I .02
-0.895 -0.812
-0. 600
-0. 396
-0.284
100 '105 I t0 I 15 120 t25 'i30 135 I 40 145 t50 I 55 r 60 t55 I70
-0.690 {,. OJU
.010
-.976 -.942 -.908 -.874
-l.t4
4.746
31h Nickel
-1
-i. t6
-0.824 -0.798
-n la
:c
90
Monel 25 Cr 20 Nl 67 Ni 30 Cu
-u.6:
-0 - 668
4.428
-0. 388 -0.354
-0.070
Cr
4.772
?0
-0. t05
12 Cr 17 Cl 27
0.435 0,472 0.508 0.544 0.580
u-oto
6 t1t
0. 394
0.424 0.472
0.42 0.458
0,664
0.496 0.534
0.712
0.572
u.oto
0.462
0.8'14
0.496
0.584 0.735 0.783
0.90
0.530
0. 84
0,594
0.798 0.846 0.894
0.942
0.552 0.688
I .068
0.626
0,892 0.944 0.996
0,724
1.124
u. 056
I . 048
0.956
t.012
u.j64
0.568
0.788
0.428
0.268
0.61
0.548
0.724 0.752
19
Piping Stress Handbook Table 2-1 Continued
Carbon Steel Carbon-moly Temp.
(D
t30 tdJ
r90 r95
Low-chrome (Thru 3 Cr Mo)
0.30 0.834 0.876 0.914
1.180 0.796 0.832
0.858 0.904
0.97
0.85 0.89d 0.928 0.962 0.995
'1.37
i.2?
1.01
r.2t0
1.130 1.750 1.170 1.806 1.210 I .862 I.918 I .250 I .974 I .290 1.330 2.030 2.038 I .368 ?.146 I .405 2.244 I .444 1.4A2 2-262 2.320 I .520 ?.318 I . s58 .596 2.435 2.444 ]. 534 1.672 2.552 2.610 t .710 2.568 1 .748 2.726 r .786 2.744 I .824 1.862 ?.842 2.900 1 .900 1.940 ' 2.960 3.020 I .980 2.020 3.080 2.060 3.140 3.200 2. 100 2.140 3.260 2.180 3.320 2.2?0 3.380 2.260 3.440 2.30 3.500 2.340 3.560 3.520 2.3& 2.420 3. 580 2.450 3.740 2.500 3.800 2.544 3.860 2.588 3.920 2.632 3.980 2.616 4.040
r.362 .400
250
1
t55 t60
1
.442 1.484 1.526
?.7 A
t75 130
1.568 1.610 1.652 1.694
290 295
1.778
300 305 310
t.s2 I .864
1.908 1.952
qq6
320
I
325
2.040
330 335
2.123
340 345
2.112
355 350
2. ?16
2.304
) )
16F 142
2.436 3B0
J6f, 390
2.480 2.524 2.558 2.612 2
.656
1t0
?.700 2.746 ?.79?
115 120
2.884
r00
1.054
1.092
1
0.89 0.93
I .182
1.015
.286
0.85
1.308
1.078 1 .122
I .324
0.81
1.038 I .086 1.134
0.826
2t0
240
c.99
1.404 1.518
.248
1.10
0.792
.978
1
0.724
Nickel
348
I
I .46
1
0.59
3112
Monel 25 Cr 20 Nl 67 Ni 30 Cu
1.204 1.256
.940
225 ?30
Cr
0.758
0. 990 034
l
12 CJ 17 Cr 27
,?92
1
200
??a
a="
Austenitic
MO Stainless Steels Thru 'l8Cr8Nl gCrMo
5 CR
l
424
.258
r
1.478 I .364
1 .54 .03 .594 t.c65 '1.102 I-748 1.138 1.802 I.174 L865 1.210 I .910 1 .964 1 .244 1.278 2.018 2.072 1.312 'I .345 2.126 'I .380 2.I80 'I .416 2.234 2.288 I .454 ?.342 I .490 2.396 I . 526 2.450 1 .55 l .596 2.504 2.558 I .532 I .558 ?.612 2.666 I .704 2.7? 1 .74 1.77A 2.174 I.816 2.828 2.8A2 I .854 l.892 ?.935 2.99 I .93 3.044 I .956 2.002 3.098 2.038 3.152 2.074 3.205 3.26 2. r I 2.148 3.314 2.I86 3.368 2.?24 3.422 2.262 3.476 2.30 3.530 2.340 3- 584 2.380 3.538 2.4?o 3.692 2.940 3.746 1
'1.13
1.17
1.586
I
r.09
.460
1
.
1.556 I .504
I
'I .750 'I . S10 1
.378
652
t.710 .860
1.910
210
.252 .294
r.508
'I 1
.420 .462
1
.504
1.545
']
588
1.950
t.630
2.010 2.060 2.110 2.160
I .714 1.756 1 .798
2.210
t.s4
2.302
?.348 2.394
I .956
.44 2.488
2.050
2
2.532
2.092 2.134 2.176 ?.218
2.680 2.728
2.176
2.26 2.302 2.344
'2,872
2.428
A?L
2.386
2.910
2.470
3.084
2.595 2.638
3.250 3.304
2.690
l-J!6
2.77 4
3.412
2.816
2
.732
Coefticients of Thermal Expansion Table 2-1 Continued
Carbon Steel Carbon-molY Temp.
(n
Low-chtome (Thru 3 Cr Mo)
2.930
2.976 140
3.068
145
4
3.
3.160 3.205 460
3.298 3.344
1 lqn 480 435 490
3.435 3. 432
495
500
3.620
510
3.668 3.716 3.812
525
540 545
3.860 3.910 3.960 4.010 4.060 4.110 4.158
560
4.206 4.254 4.302
5B0
4.350 4.400 4.450
590
4. 500 4. 550
500
4.600 4 -652
610 615 520
625 630 640
4.704
4.756 4.408 4.360 4. 910
4.950 5.010 5.060 5-110
5.214 663 570
Austenitlc
MO Stalnlesa Thru Steels gCrMo lSCrSNl
5 CR
4.100 2.72 ?.76? 4.162 2.804 4.224 2.345 4.286 2.888 4.348 2.930 4.410 2.972 4.470 4.530 3.0 t4 3.055 4.590 3.098 4.650 4.710 3. l40 3.182 4.770 3.224 4.830 3.256 4.850 3.308 4,920 3.350 5.010 3.395 5.010 3.442 5.130 3.488 5.190 3.534 5.250 3.580 s.310 3.524 5.372 3.658 5.434 1.712 5.495 3.756 5.558 3.800 5.620 3.844 5.582 3.888 5.144 3.932 5. SC5 3.976 5.858 4,020 5.930 4.054 5.992 4.108 6.058 6. t20 4.'t5Z 6. 182 4. ',t96
4.240 4.286 4.332 4.378 4.424 4.470 4.514 4.558 4.602 4.646 4.690 4,776 4.7A2 4.828 4.374
6.240 6.302
5.354
6.426 5.488 6.550 5.514 6. 678
6.742 6.306 6.370 6.932
6.995 7.057
7.'l19
12 Ct
l7 Cr 27 Cr
25 Ct 20
, qnn 2.538 t .7a 2.514 2-652
Nl
Monel 67 Nl 30 Cu
3.800
3.520
J'
6i'.
3.57 4
3.908
3.628 3.682 3.736
J.vo. 4.015
2.690 4.070 2.735 4.124 2.770 4.178 2.810 4.232 2.850 4.286 4.340 2.890 , q2q 4.394 2.966 4.448 3.004 4.502 3.042 4.555 3.0a0 4.510 3.120 4.664 4. 718 3. I 60 3.200 4.772. 3.2& 4.825 3.280 4.880 1 1?2 4,934 3.354 4.988 3.405 5.042 3.448 5.096 3.490 5. 50 3.530 5.204 3.570 5.258 3.610 5.312 3.550 5.365 3.690 5.420 3.732 5.474 3.774 5.528 3.815 5.582 3.858 5.535 3.900 5.590 5. 144 3. 940 3.980 5. i98 4.020 5.852 4.060 5.905 4.100 5.950 4.142 6.014 4.184 6.068 4.226 6.122 4.268 5.176 4.310 5.230 4-352 6.284 4.394 6.338 4.435 6.392 4.478 6.M6 ',l
31h Nlckel
2.910
?.954 2 qqR 3.042 3.086
3. BI,4
3.130 3.174
3.898
3.21 8
3.790
3.952
1ta?
4.006
3.306
4.050
3.350
4. 114
4.168 4.222 4.276
3.442 3.988
J.lJ'. 3.580
4. 386
4.442
3.626
4.498 4.554
3.tt6
4.610 4.658
3.810
4.126 4.7 84
3.164
3.902 3.948
qqA
4.842
1
4.900 4,958
4.040 4.086
5.UtO 5.074 5. tJ4
4.132 4.178 4.224
5. 180
4.270
<
4,316
4.362 14R
5.404
4.408 4.454
5. 518
4.500 4,458 4.596
5.634
4.644
5.460
4.692 4.7 40
5.810 5.870
4.788 4.836 4- 884
5.990
4.932
6.050
4.980 5.028 5.076
6. 108 6. 156
6.224
6.282
21
Piping Slress Handbook Table 2-1
Continued
l Calbon Steel Carbon.moly Temp. Low-chrome (D (Ihru 3 Cr Mo)
680
5.474 690
4.tJO 4.588
700 705 710
Austenltlc
MO Slalnless Thru Steels ICrMo 18Cr8Nl
5 CR
4.920 4.954
7. 180
5.008
7.308
5.052
7
q no6
720
5.738 5.792 5.946
t'?5
5.900
730
5,2U
7.628 7 .592
5.332 5. 380 5. 428
6.004
.
.372
7.500 7.554
t.
7
o. u50
745
6. 108
5.5n
750
6. 150 6.z',t4
5.620
5.524
.U0
7.886 7
740
760
.244
166
5. 140 5. 684
7
.952
8.0r8 8.084 8.150 8,21 4
o.z06
J/b
770
o.
775
6.430
780
5. 484
190
6,592
795 800 805 310
5.754
l.
t
6DU
ont
8.342 8.406 8.470 6.5JO
!.v5b
8.602
8.568
6.645
5.004 6.052
6.700
6.100
8.80
6.308
5. 148 6. 196
8.855
6.862
6.244
a
6.29?
9.064 9. r30
7.082
5.340 6.390 5.440
440
7.138
845
7.194
6. 490
6.754
820
6.916
825 830
6.970
8.734
ooq
q tot
a 1rq 9.394
350
9.460 6.538
960 7.4
t3
7.174 840 435 890 395
/.5U6 7 .542 7.698
900
7.754
6. 686
9.542
5.734 6.182
9.724
6.830 6.878
9.856
a
7qn
9.922 6.974
q
aea
7.0?Z
r0.054
7.810
7.070
9t0
/.doo 7 472
7.1r8
10. 120 10. 188
7. 156
tu.250
7.978 8.034
7.214
10. 324
920
ln
1q2
12 C. 77 Cr
27 C.
25 Cr 20
4.520 4.562 4.504 4,645 4,688 4.730 4.776 4.814 4.A55 4.898 4.940 4.984 5.028
5,0n 5. I fO
5.
150
5.204 5.248 5.292 t. JJD
6.500 6.554 6.508
6.662 5.716
5.170 6.824 6.878
6.932 6.985 7.040
7.094 7.148
7.702 t.Z)E
Nl
Monel
3t/.
67 Nl 30 Cu
Nlckel
5.340 5.400 6.460 6.520 6.580
5.220 5.354
5.412
5. 640
6. 700 6. 750
5.508
6.820 6.880
5.604
5.940 7 .002
5.700
7.064 7.126
5.796 5.844
t.
o5z
7. 188
,250
7. 310
7
7.364 7.418
7. 310 7
7.472 I .a.n
7.490
5.940 5.988 5.036 6.084 o. tJz
/.55U
6. 180
5,380 7.580 s.424 7.634 s.458 7.688 5.5"2 7.742 5.555 7.796 5.600 7.850 5.544 7.910 5.688 7.970 5.732 8.030 4.776 8.090 5.820 8.150 5.866 8.210 5.912 8.270 6.004 8.390 6.050 8.450 5.094 8.510 6,138 8.570 5. r82 8.630 6.225 8.690 6.270 8.750 6.314 8.810 6.358 8.870 6.402 8.930 6.445 3.990 6.490 9.050 6.534 9. n0 6.578 9.1 70 6.522 9.230 6.666 9.290
.370
7. 510
7.130 7.790
6.280 O. JIU 6.380
7.850
6.430 6.480
8.036
6.580
7 417 7.974
o.5lu o, oJu
8. 160
6.580 6.730
8.288
5. 780
8.416
6. S50
8.480 3.544 8.508 8.672
6.930 5.980 7.030 7.080 7. t30
6.830
8. 735
9.800 8.864 8.928
8.992
7. 180
7.230 7 .280 7.330 7.380
9. r20
7.430
9,248
7.480 7.530
f.i84 a ?t,
7.630
Coefficients ol Thermal Expansion Table 2-1
Continued
Carbon Steel Carbon-moly Temp.
(R
Austenllic
MO Stainless Thru Steels gCrMo 18Cr8Ni
5 CR
Low.chrome (Thru 3 Cr Mo)
7. 310
I0.460
8.t88
7.360 7.410
10.528 r 0. 596
940 945
8.242
7
950
8.350 8.404 8.458 s. 512 8.556
s.080 8.134
960
970 980 985 990
.460
7. 510
8.674
8.128 s.782
7.560 7.610 7.660
I0.554 1d 71' 10. 800 t 0. 858
10.936
1.710 7.760
I1.004
7. 810
II
7.360 7.910
r
11.012
.140
r .208
t't.344
s.835
7.950 8.010
000 1005 'r010 t 0l5 1020 1025 1030 1035 1040 1045 I050 LU:: 060 I065
8.390
8.060
l t .480
8.946 9.002
0 8. 160
1
1075 r 030 r 085 090 r 095 I 100 'r 05 r0 IIr5 1120 |25 I 130 1r 35 I140 l145 'lt 50 r I55 I t60 r 165 I I 70
r
r
8.
l1 .412 I .548
8.210 8.260
1t.584
l4
9- 170
8.300
I I
t.820
I
t.956
9.058 9- l
9.228
9.236 9. 344
9.402
8. 400 3- 450 a. 500
1
.888
1?.C24 12.094
I2.
9. 460
150
1?.228
f, tO
3. 600
9.634
3. 700
Aoa
3. 750
9.750
r2.500 t2.558 tz.0Jo
9.982
8.800 8.850 8.900 s.950 9.000
10.040
9.050
I2.840
', 9.575
o
9.408
9.866 9.9?9
r
8.650
12.296 12.364
12.704 12.712
I0.094
o
no6
12.908
10.144
9.142
12.976
t0.202
9. 188
13.044
10.255
9
.234
I3.112
9.280
13. r 80
r
0.310
10.362 10.414 10.466 10.518 10.570 10.622 10.574 10.126 10. 773
9.330 9.430 9.480 9.520 9.568 9.554
I3.248 r
3.316
13.384
I3.452 13. 538
13.724 13.79?
12 CJ
17 Cr 27
Cr
Monel 25 Cr 20 Ni 67 Ni 30 Cu
6.710 9.350 5.756 9.410 6.802 9.470 5.848 9.530 5.894 9.590 6.940 9,550 5.986 9.710 7,032 9.770 7.078 9.830 7.124 9.890 .170 9.950 1.215 l0.010 7.262 10.070 7.308 10.130 7.354 10.190 7.400 10.250 I0.310 7 .444 7.488 10.370 10.430 t' .532 | .576 I0.490 10.550 1 .620 7. 586 10. 610 7. t-52 10.570 7.818 10.730 7.884 10.790 7.950 10.350 7.996 10.910 8.042 10.970 8.088 I I .030 8.I34 il.090 8.180 11.150 8.205 l l .2'10 8.232 11 .270 8.258 1 .330 8.284 11 .390 8.310 l l.4s0 8.354 1l .516 8.398 1l.582 8.442 1l .548 8.486 l .714 8. 530 l1 . 780 8.576 I .345 9.622 ri.912 8.658 l1 .978 8.714 I2.044 8.760 l2.l l0 8.804 12.176 8.848 12 -292 8.892 I2. 308 8.936 12.374 7
,]
1
1
7.680 7.730
9.440 9.505
a
31h
Nicket
7.780
a72
9.638 9.704
7.830
9.170
7.930
9.834 9.399
7.880
7.978 3.026 8.074
10.026
8.122
10.090 10.156 10.222 10.288 10.354
8.170 8.218 8.266
10.420
8.410
I0.486 r0.552 10. 618 i 0. 686
10.750
I0. sl8 10. sa6
11.42? '11
.090
It-158 11
.226 .294
|.352 I I .430 11
.498
I1.555 1
t .702
r1.770
| .838 I1.905 ' .974 12.042 12.
1
l0
12.182 12-254
\2.3?6
1'
laA
12.470 12.538 12.605 12.57 4
12.742
8. 314
23
Piping Stress Handbook Table 2-l Continued
Carbon Steel
Austeni c
MO Slainless Thru Sleels 9CrMo lSCrgNl
Carbon-moly Temp, Low-chrome (D CIh.u 3 Cr Mo)
t't75 I180
5 CR
0.830
9, 750
13.850
10. 884
9.808
13.928
9.904
t 195
10.992 I I .046
14.054
9.952
14.'t32
1200
It.t00
10.000
r
lt95 lt90
ll oot
10.938
l2t0
I | .212
r
t22n
I1.268 I1.324
r0. r55 0.208
14.200 14.268 't4.335 i 4.404 14.472
.380
r0.260
1230
14. 540
I I .436
314
14.603
10.368 10.422
r4.676 14.7M
10.476
14.812
'10. 530
14.880
l2l5
rt.ltl
I 1240
r250
1
r0.052
.492
ir.598
'll .504 l I .660
r
0. 104
r0
I 0. 582
't4.948
0.634
I5.0r6
'tl .884
r0.738
15.084 IJ. IJZ
l0.
1285
.940 .946 12.052
1290
r2.
1295
12. r 64
1300 1305
'12.22
ll.7t5
l2 60
11.772
1270
I
I
r280
r
t.328
1
1 1
108
790
r
0. 952 I I .005
15.424
II
15.560 15.628 15.596
't0.898 r
.060 .108 .156
r3t0 l3l 5
12.276
|l
12.388
I
1320
12.444
11.2s2
r325
12.500
I I . 300 I I .350
1330
I I .450 'I | . 500
t 345 r
350
r2.780
350 J05
12.892 12.948
1370
13. 004
r I
1375 1380 1385
L204
'll.€0
I340
15.220 5.288
10.844
I
L550
15.492
'I
5. 754
15.832
l5, 900
't5.968 r 6.036 t 6.104 r 6.172 't5.240
I t . 600
'15.308
I1.650
16.375 16.444 I 6.512
11 . 1t .
700 750
3.060
l1 .800
t6
't390
13.112 13.228
I1.850 I1.900 I1.950
1395
13.284
12.000
r
1400
13.340
12.050
15. 920 lF ooa
1405 1410
l4l5 1420
1
r3.l
'|
5.580 't5.643 16. 7l 6
r6.784 6.852
17
.072
17.'t48 17.224
12 Cr
l7 Cr 27
C.
8.980
Monel 25 Cr 20 Nl 67 Nl 30 Cu
12. 440
1' a1'
12.810 12.878 12.946
12.638 12.704
13.014 13.082
9.200
12.770
9.244
12.836
I3.',I50 13.220
9.288 9.332 9.376
12.902
9.024 9.068 9.112 9,156
r
13.290 13.350 '13.430
3.034
9.420 3. t00 9.465 13.166 9.512 13.232 9.558 13.29S 9.504 13.364 9.650 t3.430 9.696 13.496 9.742 13.562 9.788 ',t3.628 9. S34 13.594 9.880 13. 760 9,926 t 3.826 9.972 13.892 10.0r8 13.958 t0.064 14.024 l0.l l0 14.090 r0,154 t4. t50 10.198 14.2t0 10.242 14.270 10.825 14.330 10.330 14,390 10.375 14.450 10.422 14.510 10.468 t4.570 10,514 14.530 10.550 14.540 r0.504 't0,648 14.750 14.810 r0.692 14.870 10.735 14.930 10.780 14.990 '10.826 r 5.050 r0.872 l5.l l0 't0.913 t5.170 r0.924 15.230 I I .010 15.290
13.500
1
13.544 r
3.788
13.360
r3.932 14.004 r 4.076 14. t 48
14.22 14.292 't4. 364
t4.435 14.508
r4.580 14,552 14.724 t 4.796 14.868 14,940 1
5, 084
15.300 t 5.444
lt.tlo r
5.588
I
t- 60u
15.732 15.804 15.876
15.948 I
5.020
31h Nickel
Coefficients of Thermal Expansion Table 2-1 Continued
Austenltlc
Catlon Steel
MO Stainless Thru Sleels 9ClMo 18Ct8Nl
12 CJ 17 Cr 27 C.
5 CR
Carbon-moly Temp. Low-chrgmo (D (Thru 3 Cr ilo)
Monel
25c|20 Nl 67 Nl 30Cu
3th Nickel
't7.300
1425 1430
1435 1440 1445
17.534
17.6i2
1450 1455 1460
17.690
t465
17
17.768 17.846
.924 I8.002
t470
18.080
1475 1480 1485 1490
r8. r58 18.235
I495
13.31 4 le 102
500
18.470
r
Temp.
(D
-32 5
-320
Alumlnum
-4.68 -4.636
-315 -310 -305
-4.592
-300 -295 -290
-4.46
-4.548 -4.504 -4.41 -4.36
-2Aq -280
-4.26
-275
-4.21
-270
-4.162 -4.1
l4
Gray lron Bronze Brass
Caal
-J. v6
-3.932 -3.884 -i e1f -3.788 -3.692 -3.644 -3.596 -3.548
70 Cu 30
Nl Ni.Fe.Cr
-J-66
-J.lt
-3.64
-2.87
-3.832 -3.094 -3.784 -3.038 -1 t16 -? aa? -3.688 -2.926 -3.592 -2.836 -3.544 -2.&2
-1.49D -a. t06 -1..t.t5 -a- I J4
-3.4s2 -3.352 -3.404 -3.304
-3.5 -3.40
-2.70 -2.666 -2.632
-3.308 -3.208
-2.564
-260 -255
-4.066 -4,018
-250 -245
-3.97
-3.26 -3.16
-2.53
-?40
-3. 366 -3.8',r4
-3.164 -3.068 -3.I t6 -3.022 -3.068 -2.976
-2.462 -2.428 -2.394
-235 -230
-3.2'12 -3.114 -2.496
'J.Va -210
-3.602 -3.548 -3.494
-a.tJ
_2. JO
-2.972 -2.884 -2.326 -2.924 -2.833 -2.292 -2.82A -2.746 -2.224
Ni-Cr.Fe
Ductile lron
25
Piping Stress Handbook Table 2-1
Continued Temp.
(D
Aluminum
Gray Csst lron
-2.78
-3.44 -3.384 -3.328
-2.732 -2.684
-2.654
-180
-3.216
-2. t66
-2.5
-175
-3.16
-2.54 -2.47 -2.494 -2.424 -2.448 -2.378 -2.402 -2.332
-200 -195 -190
-185
n70 -t
65
-160 -155
-3. 104
-3.048
-?.992 -2.936 -2.88
-r 45
-2.8i8
-140
-2,756 -2.694
-lJ5 -llu -125 - r20
nl5
-6t
-80 -75 -70 -65 -ou -55 -45 -40 -30 -25 -20
30 35
40 45
-t
.49
-l .45
-2.086
-t.J60
-2.052
-1
.4t
-i .362
-l .984
-l.314
-2.24
-1 .95
-2.144 -2.096
-1.908 -|.aroo -1 .824
-1 .29 -1 .264
1AJ
-?.27 -2.21 -2. 15 -2.09 -? i1
-t.ot -l .76
-t.ro
-1.53 n .49
-1 .04
'l.ll _l.OO
-l.OO4 -l.OlO
-1.97
-t .56 -1.52 -t.512 -1.474 -1.464 -1.42A -l.4t6 -1.382
n.91 -l .85 -t .79
-1
71
-r.ot
-l.6
-l .46 -1.39
-2.048
-1 .856
. 6',14
-l
,306
.236
-1.292 -l .182 -1.278 -t .128 -1.264 -1.074
.25
-1
-t.lt
- ,962 -0.866 -
.858 .804
-
.696
-.902
- .834 -.766 - .698 -
.56 .49 .42 .35
-t.o50
I
-l .16 -1.136 -1
-l
.l t2 .
c88
.45
-1.014 -.988
-1 .41
-,962
-l
-1.33
-l .29 -l.21 -1.13
-1
-1.32 -1.25
n.18
-'1.74
-1.698
-t.506
-1.212
-, . 160
-l .952 -l .904
-1.712
-t.233
-.91
-.882 -.854
-,826 -.798
-1 ,67
-.97
25
-2.31 26
-1
-1.064
0
20
-2. Z60
-r .5l
-2.148 b
-2. JaC
-2
-2.162
Ductile lron
-1 .572
-l .04
l0
|
-2.19
Ni.Cr.Fe
-l .808
- t5 - l0 -5 5
-2.608
Nl Ni.Fe.Cr
-2.00
-2.57 -2.51 -2.45
-tu5
-95 -90
-2.70
30
-2.21 -2.16 -2. 1 l -2.06 -2.01 -r .96 -t.9l -r .86
-110 -100
Z0 Cu
Eronze Brass
-',!
.02
-t. t3.t -.9vo -l .058 - .912
.714 .658 .602 .546 .49 .436 .382 .328 .274
-
.642
-1 .082
-.77
_.74
-.71 -0.986 -0.938
- .89 - .844 - .799 -.752 - .706 - .66 -.612 -.564
- .65
-.62 -.588 -.556
-.524 -4.9?
-.414
.588 .534
- .5',16 - .468
-.276
.48 .426 .372
-.374
-.212
.318
-
.282
-. 194 -. 176 -.158
.264
-.236
-.322
Coefficients of Thermal Expansion Table 2-1 Continued Temp.
(R
50 55 60
Alumlnum
-.28
- .21 - .14 0
ta
.3066 . J6JJ
'100
120
.616 .694 .772
125
.85
130 135 140 145
.926
5
165 170
.312 .346
.54
.414 .448
.72
,482
.84
.622
.08 .14
.542
2.00 ?.082 2.164
1.26 .764 70'l
.972
2.41
230
2.494 2.578
'L I
'I
.08 .118
I.i56 I .194
.232
2.7 46
1
250 255 260 265
2.43 2.912 ?.994
1.27
270
J. lc6
I
275
3.24
1.45 1.488
295
'I
.
.21
.246 .282 .318 .354
.472
.56
.52 .568
.664
.oto
.716
.oo+ .712
.612 -bbb
.
.76 .805
.7 .744
.57
.852
.798
.
.97
.898
1.02
.944
,832 .876
.684 .72?
.92 .966
.788
1.012
.826
.olz ,
768
.82 .87 .54
.07 .122 .174
.288
1.
. 175
346 404 462
,226
.278
.5b6
oa
.038 'I .086 1
't
.
]34
I.182
.39 .4?6 ..+Oa
.498
'1.058 'I
'I
.62
l.ott 1.74
1,8 1.86 1 .922
,902
1.342
2.294 2.356 ?.418
.4]4
2,8
2.542 2. 604
I .564
1.602
I .434
t./06
l.tJ6
1
.83
1.486
1
.59
2.14
2.232
'1.378
1.644 1.705
2.17
306
.
.94
2.046 2. t08
.984
2.666 2.728
o.to
.864
.',t04
'I
'1
1.86
2.202 L 914 2.264 1.968 2.326 2.022 2.388 2.076
2.512 2.574 2.698
.252
.196
| . JJ.t I .386
.288
1
.892 1 .644 ,954 I .698 2.C]6 1.752 2.078 I .806
'I
tJ+
.60s
l.Jo
225
290
1.
.14
.424
1.114
t.Jt' I .44
. 105
.51
uto
1.172
.035 .07
.46
,94 .998
'l
1
044
3.412 3.498 3.584
.41
| .76 .82 .88
I .32
.866
2.328
3.076
2
.0933
.35
.
|.
.0433 .0866 .13 .1 73 .216 .26 .304 .348 .392 .436 .48 .524
.25
.408 .466 .524 .582 .64
.96
220
280 285
.l15
.5',16
r.008
240 245
.1866
.48
2.246
2.35
.206 .258
1.386 I .464
1.698 1.776 1.854 1.932
205 210
.t4
.24 .J
.233 .291
.lla
.02
| .62
200
.12
.586
175
190 't95
.0466
'L 308
1
0
.05'16 .1033
.278
.14 .105 .07
-_.035
.0s83 .1166
.uo
.658 .694
-
0
.66
.002 .078 .154
180 '185
-
.?44
110
Ductile lron
Ni-FeCr
- ,21 - .105 q2E
.21
't05
Itt
.055
.035 .07 .105 .14
80
t3u
.165
0
.016
85 90
Nl
-
-.07
70
70 Cu 30
Gray Caal lron
2.184 2.238 2.346
'I
.012
']
048
I . 084
.438
I .49
'I
L.38
544
1
.426
t.t7
I .598
1
.472
1
'|
.
'I
.?1
.652
1.5i3
1.706
't
.564
1.75
'l
,5l
1
.658
.37
706
.41
802
.45 .49
1
1
'l
.8',t4
.868
1
922
']
.25 1.29
'1,754
1.976
1.
2.03 2.084 2.138 2.192 2.246
't
.85
I .898
I .568
1.946 I .994 2.O42
1
'|
.606
.644 I .682
28
Piping Stress Handbook Table 2-1
Continued Temp.
(D
Alumlnum
300 305
3.67
3i0
3. 838
Gray Casl lron
1
't
.64
.678 1.716
'1. 754
Bronze Brass
274 2.954 2.918 t oat 2.046
320
4.006
't.792
325
4.09 4.176 4.262
I.atj 1.87
3.',t I
r .91
3.234
1.95 I .99
3.296
3.4
330 340 345
4.348
4.434
350 355 360 365 370
4.52
4.864
2,03 2.068 2.106 2.144 2.182
375 380
4.95
4.606
4.692 4.778
3.1n
3,484 3.548
3.612 J.O/O
2.22
2'A
lAE
5.038
3.7 4 3. 802
5.126
2,3
3.864
390 395
5.2 14
2.34
400 405 410
5.39
5.302
s.478
2.42 2.46
5.566 5. 654
2.54 2.58
3.926 3.988 4.05
4.
4
4. 178 4.242 4.306
420
5.742
425 430
5.92
4.434
4.498 4.562 4.626
4.37
6.0i
2.704
440 445
6.1
2.7 46
450 455 460 465 470
6.28
2.788 2.83 2.87
4. 69
2.76
70 Cu 30
Nl NLFe-Cr
2.40
2.30 2.358
Nt-Cr-Fe
2.09
3.48
4.248
3.648
4. 314
3. 704
2.56 2.606 2.652 2.698 2.744
4.38 4.448
3,76
2.79
4,516
3.872 3,928
3.386 3.434
3.984
3.482
4.l l6 4.1e.
4.584 4.652
z.4to
2.474 ? q1,
2.648 2.706 2.764
2 e)t
2.136
2.182
2 2r9
2.2't4 2.368 2.416 2.464 2.512
2.8
2.56 2.508
J.UO
2
2.94 3.00 3. l2 3.
l8
2.4
2.95
3.0 3.05 3.098 3. 146 3. 194
2.91
4. 856
6.544 6.632
2.95
4. 882
4.094 4. 148
4.946
4.924 4.992
4.202 4.256
3.68
475
6.72
3.03
5.01
s.06
4.31
480 485 490 495
6.81
3. 78
5.074
6.9
3.072 3. 114
5.128 5. t96
+.
6.99
4.422
3. 156
7.08
l10a
5.202 5.266
3.828 3.876
5.264
4.472 4.534
3.924
.17 7.262 7.354
3.24 3.284 ? 1'A
5.394 5.458
4.59 4.646 4.702 4.758
5t5
7
520
7.538
.446
525
3.46
5.65
530 535
7.724 7.818
3.544
7.912
a. t61
s40
J. J6O
5. 848
545
8.006
3.628
5. 9',I4
5.
7',1
2.97 4 3. 04
G4
JOO
2.882 2.928
3.088 3. 63 3.',]84
3. 73
3.28 3.384 3.436
3.488
5.68
4. At4
4.02 4.07 4.12 4,17 4.22
5.75
4.87 4.929
4.27 4,32
3. /'6 3.806
5. 89
4.986 5.044
6.03
5. 102
4.42 4,47
3.898 3.944
5.54
5.522 3. 416
2.44 2.48
3.816
4.
5.40 5.47
2.05 ?.09
2.80 2.85
4.72
7
.97 2.01
,704 2.752
2.656
2,9
1to,
.804 .846 .888
2.13 2.176 2.222 2.268 2.314
4.788
500 505 510
.7?
2.824 2.456 2.838 2.512 a.taz 1, to6 3.016 2.624 3.08 2.68 3.146 2.736 3.212 2.792 3.278 2.848 3.344 2.904 3.41 2.96 3.474 3.015 3.538 3.072 3.602 3. 128 3,666 3. 184 3.73 3.24 3.794 3.296 3.858 3.352 3.922 3.408 3.986 3.464 4,05 3.52
4.754 4. Bl8
6.368 6.456
Duclile |ron
6
3.54 J. 0Z6
3.672
l./to
Coetficients of Thermal Expansion Table 2-1 Continued Temp, (F)
550
Aluminum
8.
Gray Casl
tlon
1
8. 192
3.
8.376
7l4
Bronze
Brass
5.98 6.046 6.112 6. I78 6.244
6.10
560 565 570
8.2U 8. 468
3.758 3.802 3.846
575 580 585 590 5q5
8. 56
3.89
8.654 8.748
3.934
b.l I b. J/b
8.842
4.022
b.
8.936
4.066
600 605 610 615
9.03
4.n
620 625 630 535 64C
645
4. 156 4.202
4.428 4.294 4.34 4.386
4.432 4.478 4.524
550 655 660 665 670
4.57
675 580 685 690 695
4.8
4.616
4.662 4.708 4.754 4.846 4.A92 4.938 4.984
700 705
5.076
7t0
5.122
715 720
5. I68
5.214
7?5
5.26 5.308
730 735
740 745 750 755 760 765
5.404
5.452 5.548 5.596 5. 644
770 775 780
785 790 795
5.7 4
5.788 5.884
5.932
6.442 !u6 o.l/+
70 Cu 30 Nl
Ni"Cr-Fe
5. 16
Ductile lron
3.99
4.32 4.57
4.036
4.62
4.082
6.31
5.218 5.276 5.334
6.38
5.392
4.7?
4.174
o. +J
5.45 s.496
4.77 L.82 4.87
4.2? 4.264 4.308
5.608 5.664
4.92
4. 352
6. 17
6.24
o.3z 6.59 0.00
o./J
6.64 6. 80 6.704 6.872 6.944 6. 768 7.016 6. 832 6.896 7.088 6.96 7 .16 7.234 7 .026 7.308 7 .092 7.158 7.382 7.224 7 .456 7.29 7.53 7.356 7.602 7.422 7.674 7.488 '1.7 46 7.554 7.818 7. 89 7 .62 7.686 7 .964 7.752 8.038 7.818 8.1 12 7.884 8.186 7.95 8.26 8.016 8.336 8.082 3.412 8.148 3.488 8.214 8.564 8.28 8.64 8.348 8.716 8.416 8.792 8.484 8.868 8.552 8.944 8.62 9.02 8.688 9.096 8.756 9.172 8.824 9.248 8.892 9.324 8.95 9.40 9.028 9.476 9.096 9.352 9.',164 9.628 9.232 9.704
4.128
1.97 4.44
3.72
4.484
5.778 5.1?
t.17
4.528 4.572
3.?2
4.616
6.01
5.27
4. 66
6. 068
5.322
4.708
6. 184
s.426
6.242
5.478
4.756 4.804 4.852
6.30
6.524
5.53 5.582 5.634 5.686 5.738
6.58 6.64
5.84?
5.836 5.894
(
oE,
6.126
6.355
6.412 6.468
4.9 4.948 4. 996
5.044 5.092
5.394 5.946 5.998
5.24
6.938
6.102
6.996 7.054
6. 154
5.432 5.474
6.206 6.258
5.558
6.362
5.60 5.65
6. 414
5.70
6.70 6.7 6
6. 88
7.112 7.17 7 .23 7 .29
7.35
5.34
5.75
7
.41
o.f,kt
7
.47
.528
7.586
6.57 6.6?4 6.678
5.85
7
.644
6.732
6.00
7
6.05
7.702
7.76 7.82 7.88 7,94 8.00
5.90
6. 84
6.t0
6.894
6. l5
6.948 7.002
6.20 5.25
5.30
29
Piping Stress Handbook Table 2-1
Continued Temp. (F)
Alumlnum
Gray lron Bronze Brass
Cast
.800
805 810 815 820
825
9.30
5.98 6.028
v,
6.124 6.172 6.22 6.27 6.32 6.37 6.42
850 855 860 865
6.47 6.52 6.57
870 875 880 885 890 895
5.72
900 905 910 915 9?0
6.97
6.77 6.87
7.022 7.O74
7.216 7.178
925 930
7.284 7.338
940 945
,392 7 .446
950 955 960 965
7.5
970
7.708
7
7
,604
7.656
975 980 985 990 995
7.812 7.864 7.916
'1000
8.02
't005
l0l0 i0r5
't020 1025 1030 1035 1040 1045
7.968
'10.4 10.96 1.038 10.47 t'l.lt6 10.54 l't .194 10.61 11.272 1
10.748 10.8't6 10.884 '10.952
11.02 I1.09 'l l.l6 11.23 'l l .3 11.37 'I r .438 1l
'I
I
.506 .574
11,642 l
t
.71
11.778 '11
.846 I I .982 l
l.9r4
12.05
12.12 '12.19
12.26 12.33 12.4
12.472 12.544 12.616 16.688
8. 06
y.556 9.936 10.014 10.092
'10.33
'10.68
Nl Ni_Fe_Cr
9.78
9.436 9.504 9.572 9,64 i0. I 7 9.71 10.25 9.78 10.33 9.85 10.41 9.92 10.49 9.99 10.57 10.06 10.648 10. 13 10.726 10.2 t0.804 10.27 10.882
5.076
830 835 840 845
Jo5
70 Cu 30
8.118
Ni_Cr_Fe
7
Ductlle lron
.10
8. I76
6.398 6.446
8.292
6.542
8.412
5,59 6.642
6.494
8.474
8.598
6. 694
o. /40 6. 798
8,66 6. 898
B,784 8.846
8.908 8.95 9.012 9.074 9.135 9.198
6. 946 6. 994
7.042 7. 09 7. 138
/. tt'0 .234 7 .282 7
1l .35 1
l
.43
11.51
ola
.59
I .44
1 1
II.57 11.75 11 .832 11 .914 11.996
12.078 12.
t6
12.242
12.324 12.402
9.5 9,622 9. 684
9.746
10.242 10.304 I
u. Joo
10.428 10. 49
t3.062
'10.
13.i44
10.614
13.226 13,308
't0.738
s52
10. 80
13,474
'10.862
13.558
10.924
13.642 13.726
7.772
7.9r
10.t8
',t3.39
7
9.87 a o?, 9.994
12.57 12.652
12.98
.64 .684 7.728 7
/.6tb
10.056 10.118
12.816 12.898
.466 .524 7 .582 7
1
9. 808
12.488
12.734
7.408
I0. '11
.
986 048
7. 86
8.01
8.06
8.rI 8. ',t s8
8.206 8.254 8.302
Coetficients ot Thermal Expansion
2-l Cofitlrued Table
Temp.
o
1050 1055
t060 1065 1070 '1075 r
080
1085 1090
t095 00 1105
l l t0 'n
l5
1120 1125 1130 1135 1 140
lt45 50 '1
155
Aluminum
Gray l;on
Cast
8r6nze Erass '
12.76 12.83 12.90 1?.97 '13.04
l3.l'l
r3.182 13.254
13.32 13.39 13.47
70 Cu 30
Nl Nl-Fe-cr
13.81
11.11
13.894 13.978 14.062 14.146
'11
14.23 14.314 14.398 14. 492
14.566
n.172 11.234 .296
'1t .3
58
11.42
1t.484 11.548 't1.612 l1 .676
l4.65
Il.74 r
1
.802
11 . 864
11.926 .988 12.05
't2,I16 12.182 12.248
12.3]4 12. 38
12.442
lt60 '1165
12. 504
l l70
12.628
'1175
12.69 tz. tao
1180 85
I190
|
2.500
12.&2 't
2. 888
'I195
12.954
r200
13.02 13.088 tJ. t50
't205 '1210
l2l5 1220 1225 '1230
13.292 IJ.JO
'13. 43
1235
1240 1245 1250 'I255
13.64 '13.
71
1260
13.776 13.842
1265 1270
13.974
1275 1280
't285 1290 1295
'13.908
14.04 '14. l '14.
l
l8
'14.25 14. 32
Nl-Cr-Fs
Ductlle llon
31
32
Piping Stress Handbook Table 2-1 Continued Temp.
o
300 i 305
Aluminum
Gray lron Bronze Erass
Casl
70 Cu 30
Nl Ni-Fe.Cr
l310
14.39 14.46 14.53
1320
14.67
1
't315
'I4. 60
14.7 4 1330 IJJ' 1340 1345 1350
14.812
'14.884
r5.028 '15. 10
tt.l06 I JOU I JOa
15.304
1370
15.372
375 I 380 'l 385 1390
15.44
r
't 1
5.584 5.656
15.278 1400
'1405 t
4l0
l4l
15,80
13.872 15.944
5
I 5.01 6
1420
16.088
1425
16.
1430 1435
16.234
't440 1445
l6
16.308 16.382 16.456
1450 1455 1460 1465
16.53
1470
16.81
1475
76.88
1480 1485 1490 r 495
17.029 17.102
'1500
17.25
16. 60 16.7 4
16. 954
17.176
Ni-Cr-Fe
Ductile Iron
lable 2-2 Modulus ot Elasticity-Ferrous Material Modulus ot Etasticity, psi (MultiPly Tabulated Values by
106)
oF
-325 -200 - 100
Iaterial
:--lrn :r::
70
300 400 500 600 700
200
800
9oo 1000 1r00 1200 1300 1400 1500
steels
content
l-r
or
\:=:.31/2 ..::.rr
30.0 29.5
29.0
27
.9
27
.7
27
.4
27 .O
26.4 25.7 24.8 23.4 18.5 15.4 13.0
steels
:'::
Coment i^rl ie
lr l
31.0 30.6 30.4 29.9 29.5 29.0 28.3 27.4
"c
26.'7 25.4 23.8
21.5 18.8 1s.0
11.2
23.0 20.4
15.6
--:':r-moly i---s. low -_:tme :--r'rgh
3
,- \to
,::
i -:,aOlarc
31.0 30.6
30.4 29.9 29.5 29.0 28.6 28.0 21.4 26.6 25
29.4 28.5
28.1
30.4 29.9
29.4 28.3 27.7
7
24.s
,:at:ne
;-.s "1, :-
(5 Cr
:_qh 9
-- \lo)
.
- i::lllc --:tI ' 1rK -' 1l?) r:-L-:: :-_
27.4
27
.1 26.8 26.4 26.0 2s.4 24.9 24.2 23.5 22.8 2r.9 20.8 19.5
27.1 26.6 26.1 25.4 24.8 24.r 23.4 223 22.0 21.3 20.7 r9.3
17 9
ChrO-
-ll
30.8 30.3 29.8 29.2 28.7 28.3 27.7 27.0 26.0 24.8 23.r 2r.r 18.6 15.6 r22
i- l:t
13.4 r3.2 12.9 12.6 r2.2 11.'l 11.0 10.2
aa "t . ;-:;
are
for infornation, and it is not implied that materials are suitable for all lhe tempefatures
shovrn.
Table 2-3 Materials Elasticity-Nonferrous Modulus of E = Modulus of Elasticity, psi (Multiply Tabulated values by TemDerature, "F
,,
18.1
:€
67 Ni-30 Cu) and
106)
26.8 26.6 26,4 26.0 26.0 26'0 25'8 25,6 25'4 24.7 2.31 2|.o 18.6 16.0 14.3 13.0 Cu-Al) r--e:-\ickel - J.r-30 Ni) 21.6 Zl.5 21.2 2O.9 20.6 20'3 20 O l9'7 l9'4 -. -::--.tm alloys 10.9 10.6 10.1 10.0 9.8 9.5 8.7 7 7 ll.3 ' rrr:.99.98% Cu) 17.0 16.7 16.5 16.0 15.8 15.6 15.4 15 1 14.7 14213.7 | :- e:cial bmss (66 Cu-34 Zn) 15.0 14.7 14.5 14.0 13.9 13.7 13.5 13.0 12.7 l2'2 lf '8 -ia:i: :in bronze 14.2 13.8 13.5 13.0 12.9 12.7 12.4 12.0 i1.7 11.3 10.9 rl :r-6 Sn-1.5 Pb-4.5 Zn) :c \l-29
' ,t :=:
erc
for infonation, and it is not implied lhat materials are suitable fot all lhe tenperotures shown'
Piping Stress Handbook Table 2-4 Propertles of Salurated Steam v-cs|E I T6Fhtw. ,s.ff
i
P'
0..|{, 0.45
I H6t or I L.6r H6r I To!.t H..t
.lll}''|
!h. Liquid
lofEvle4.lis
I
of
s44
,9c..i6. 77
Coelficients of Thermal Expansion Table 2-4 Continued
rdpa.*.
i
.#E:1".j"
l"tffiltl I 'St*.
v
6.5!{l 6.,t58
76.0
n.0 78.0
5,lll
5.055 5.001 4.948
101,0 102.0 103.0
r04.0
4.19.1
4.157
{,110
112.0 113.0
lt89.l 1189.{
{.015 3.981
rr89,5
3.9r4
1190.7
t.at
llqt.8
u90.9
3.61{
1191.9 1192.0 1192.1
3.110 3.147 3.264 3,712
la6.
to.
l$. 0 lag. 0
35
36
Piping Stress Handbook Table 2-4
Continued Hqr Tod Ha! .Her.f.. II dr-tdr! @uq@ Ei.po..rr@ I| of sr..E
:.134
2.67 |,9992
i.999 r.9183
Expansion
Coefficients of Thermal Step
ExamPle Problem Use Figure 2-1 to calculate the F factor for the
i
2.
move horizontally to the left to find the t€mper-
atue correction factor, F, which in this example is equal to 0.22.
: 660"F : l0 ft-O in. = lin. K : I (shrt fully insulated) 'F : Ambient temperature Tr : Average temperature
T I t
1.
Klt
vl
Enter the chart at the point along the botom line where kh/Ji. Then move up vertically to
the point where the curve intersects' Then
follow-
conditions:
sep
Step3. T1 Step
4. Td
: T-70'F:530'F.
:
F x Tr
:
O.22
x
530"F
:
116.6'F
or 117"F.
I x 10ft :-=IU
Steps.
T" =
Tur
* 70'F :
117"F + 70"F
r87"F.
1
l.o .9
.t .,
Temperature at top ot skkt (oD Av€raqe temperature of skirt (oD Height of skirt, ft
Thickness of sklrt, in. 1 lor skirt lully insulated 1.7 for skirt flreback insulaled 2.7 for skirl not insulated Temperature corrgcllon lactor
1.6 l
.5
I .3
37
Example (see Page 2)
.2 .t
t4
t6 t8 20 22
24
26
2A
---------1>
Flgure 2-1. Curve for determination of average skirt temperature.
30
32
3ll
:
Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 (198t
This chapter contains allowable thermal stresses for petroleum piping. Values of Sh taken from ANSI/ASME Code 831.3-1980, Appendix A, Thble l. (Used courtesv of the American Society of Mechanical Engineers.)
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Allowable Stress Range tor ANSUASME Power Piplng Code
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Piping Stress Handbook
I
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Allowable Stress Range for ANSUASME Petroleum Piping Code
lA
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111
Stress Intensification and Flexibilitv trlactors
c Minimum radius. Tt'is dimension must not be less than .05 D65 except widr a branch diameter larger than 30 in. It need not exceed 1.50
The following is an explanation of the terms used in figuring flexibility and stress intensification factors. Refer to Tables 5-l through 5-3 for a tabular listing of the factors for different piping configurations. Figures 5-l and 5-2 illustrate these factors for widely spaced, two-weld and three-weld miter elbows, respectively.
t
.
i: T:
T: To: T.:
0:
Maximum radius, For outlet pipe sizes 8 inches nominal and larger, this dimension must not exc€€d 0.10 Dob + 0.50 in. For outlet pipe sizes less than 8 in. nominal, this dimension shall not be greater than 1.25 in.
When the external contour contains more than one radius, the radius of any arc sector of aF proximately 45" must meet the requirements for maximum and minimum of radii. o Machining must not be employed in order to meet the preceding requirements.
Definitions
h:
inches.
Flexibility characteristic Flexibility factor (never less than unity, factor for torsion equal to unity) Stress intensification factor (never less than unity, factor for torsion equal to unity) Nominal wall thickness of the fitting for elbows, and miter bends, in. Nominal wall thickness of the marching pipe for tees, in. Crotch thickness of tee, in. Pad or saddle thickness, when q is 1.5T, use h : 4Tlf . n. One-half angle between adjacent miter axes,
S = Miter spacing at centerline, in.
: Cr : C2 : D*
.
Closely spaced miter bend: S
o
Mdely
spaced miter bend:
(
12 (1 + tan 0) S >r2 (1 + tan 0)
O.D. of branch, in. Correction factor for curves with one end flanged, Cr : firre Correction factor for curves with both ends flanged, C2 : hr/3
deg
Rr:
Mean radius of matching pipe, in. Bend radius of welding elbow or pipe bend, in.
: S cot 0 /2 : [rz (1 * cot
o For closeV spaced miters Rr o For widely spaced miters Rr
0)lt2 Radius of curvature of the external contoured portion of the oudet measured in the plane containing the axis of the run and branch in inches. This is subjected to the following limitations:
The piping code does not speciff any particular distance from the end ofthe elbows arc or the centedine or a miter weld in which a flange will be effective in modiffing the K and i factors on these items. Until a better definition is published, the following rules can be applied: o Weld
elbows-Modifu the k and i factor when the butt weld of the flange is within one pipe diameter of the butt of the elbow. (Text continued on page 120.)
112
Stress Intensification and Flexibility Factors Table S1 Flexibility and Stress Intenslfication Factors Floxlbility
D.l6iprion
Outpl6n.
t
\lblding elbow
sirara lnt. F.ctorl'6
r.65
or pipe bend
Closely spaced miter bend s<12 (1 + tao 0)
F;t
Single miter bend or widely spaced
t.52
1.52
Fl.ribiliw Ch!r!ct!dnic h
li
'pz
0.9 'p;
tr'n
0.9
0.9
r;
314io + 114
(',)'
09
Cot 0
(")'
2
@#
l+coto r 2't
miter bend
s>/2 (1 + tan
-
ffi
lRt
0.9
0.75 'et
Skctch
d)
Weldins t€e
per -A.NSI 816.9
0.9
with
r,)I/a
D2
T
T"> 1.5 T
Reinforced fabricated
0.9
I
TE
I
TE
tee with pad or
314io+
ll4
saddle
UNeinforced fabricated tee
Extruded
welding tee
t
0.9
0.9
tt"=
3l1io+ rl4
3141o+ r14
T
(.f)f
T"<1.5 T Welded-in contour insert
r,)I/a
D2
0.9
1
t*
314
io+
T
ll4
T">1.5 T Branch weldedon finirg
0,9
0.9
(integra Y
3,3
T
-
reinforced)
ANSI/ASME 93l.3d-1984 Reproducedlfom ANSUASME Code 83l-3-1980, Appe dix D',lirble ical Engineers.
I. Repi
ted counesy ofThe At efican society of Mechatt-
113
rl 114
Piping Stress Handbook Table
+2
Str€ss Intensitication Factots for Branch Connections
40 80
f60 40 80
150 80
t20 160
xxs
'lt
1.00
1.00
I.OI 1.34
1.45
1.0 1.0
1.00 1.00
l.l0
0 0
1.00
2 0 0
t $
1.03 1.00 1.00 1.00 2.16 1.44 1.30
60 80
100 120 140 160
I .l
10 20 30
1.0 0 1.0 0 2.O4
1.84 1.60 1.36 L.20
t50 t0 20 ST 30 40
L.20
1.01
8
r.0
1.0
0
1.0 0
140
t60
40 50 80
100
L20
t.0 r I.0 0
1.0
0
l0
3.54
t.97 1.40
100
std
1.00 1.00
20 30
2.0 1.9
8 0
20 30 40
60 80
1.43
.250
30 40 60 80
100
0
r.0
0
4.39
1.0 2
1.00 4.0
0
2.90 8
1.10
stal
1.00
20 30 40
3.49
.250
1.00
.3r2 std 20 30 40
4.40 3.89 3.20
2.31 3.84
3.42 2.56 2.49 4.59
4.79 4.23 3.48 2.80 5.78
4.9
10
1.34
13
0I
4.64
4.42 IO
9
2.70
1.0
s!d
xs
l0
I.OI
4.0
stal
1.00
1.
1.49
10
2.54
1.00
r.
20
1.78
I.09
8
L.14 1.47
2.34
30 40 50 80
r.23
7.23
1.0
2.43
20
xs
1.88
100 120 140 150
1.10
140 160
t0
40
1.87 1.56
4 0
2.22
t
3.89
IO 20 30
1.0 1,0
1.00
2.09
1.0
2. a7
1.9
r.82
L20
2.40
1.00
2. r.0
80
I40 t60
0
2.59
100
I.00
1.0
0
60
r20
f.80 r. {8
1.00
r.0
xs
1.09 1.00
7
I.00
40
I.00 r.69 t.03
120 140
1.00
1.0
xs
l. l3
s9
1.45
std
L.O2
1.00
f.78
20 30
0
0
1.0
l.
I
I.0
r.22
1.0 L.0 1.0
rl
1.00
2.91
8
4.40
2.37 4.39 3.27 2.54
6.40 4.88 3.46
.
Slross Intensitication and Flexibility Factors
Table 5-2
Contlnued
40 80
160
1.00
d0 80
!.29
I50
{0 80
r20 r60
xxs {0 80 120 160
xxs
1.00
1.36
r.0 2.27 1.04 1.00
80
1.6
2.24 1.90
4
100
1.45
140
1. 16
160
1.05
30
{0 50 80
100
\20
l.l0
80
1.0
8
1.7
3
3.70 2.88
50
1.99
80 100
1.49
1.32
I00
IO
1.73
30 40
2.95 2.62
3.ss
60 s0 100 140 160
l0
!.L2
40 60 80
3.31
1.80
120 140 160
L.24
l0
5.66 4.86
std
4.39
20 10 20
30
s.36 4.11 3.91 3.34
1.08 s.80 4.24 3.6
4
7.0
3
3.41
140 10 20 30 40 60 80
I40
r00
t.4s
10 20 30 40
r60
100 120
1.70
1.49
r20
2.01
3.08
100 120 140 !.50
xs
40 50
2.5I
2.50
50
3.01
xs
30
40
xs
3.34
3, ?9
t.09
3.41 2.98
std.
sa
20
30
20
4.39
xs
140
t60
10
160
2.47
20
1.13
80
20 30 40
xxs
120 140
1.0
8
4.0 7
3.{9 3.09 2.09
t.52
6.08 5.36 4.39 3.34 7.82 s.96 4.A9
4.20 3.70
116
Piping Stress Handbook Table 5-2
Continued
f.70 0
1.00
1.58 1.30 1.04
1.40
L.0
40 80
L20 150
xxs
t.7
l.
4
41
l.14 t. 01
ll
1,00
1.83 1.70 1. 41
3,00
1.86
2
100 120 140
2.27
-t4
1.85 1.43
f0
2.64 2.Aa
xs 30 40 60 80
1.49
100 120 140 160
3,91
10
3.24
std
2.O 4
1. 41
I.29 4.74 3.06 2.85
2.O 4
I.7
4.23
f,49
3.7
7
3,0
7
1.22
.250
5.9
4
1.9
std 20 30 40
3.r7 2.44
2.60
10 s
3.82 3.32
4.75 3.9
r.50 r.25
20 30 40
3.68 3.20
4.57
.250
3.9
3
2.45 2.36
1.9I
5.3s,
tal
1.38 7.27
1.74
4.76
6.r7
8
2.O2
3,07 2.39
5.46
4.42
6.9I
6.01 5.31 4.69
10
3.38
2.38
5.99 4.56
6.34
0
4.35
20 30
2.94
1.,38
5.0
s.49
1.37
12
1.40
stil
1.28
t
1.54
2.03
.250
1.68
4
3.28
2.95 2.38
1.40 1.30
r.94
1,5r
4.0
7
t
l0
5.31
1.99
2.43
1.7
100
2.46
2.O7
1.94
10 20 30 40 60 80
3.28
20
2.Ar
7.12
1.29
20
2.69 1.6 7
2.00 I-7 4
1.20
3
5
3.09
100 120 140
3.49 3.0
3.'7
2.19
2.45
10 20 30 40 60 80
2.t9
1.68
1.37
4.94
6
3.45
40 60 80
140 160
1.20
2.a7
3,9
t20
1.23 20 30 40 50 80
7.52 f .35 1.25
XS
100
1.18
2.50 2.34
1.48 1.32
1.19
ST
I.20
1.31
rc
10 20 30
1,08 1.00
r.26
1.39
.3]-2 stal 20 30 40
6
5.78 4.'t
6
4.0
9
3.42 '7.89
6.80 6.00 4.9
5
3.44
4.25
6.8
r
8.75
5.9
0
5.24
6.66 5.4
8
4.72
*RXINFORCED FABRICATED TEE PAD THICKNESS EQUAI TO NOMINAT THICKNESS OF PIPE HEADER
.
Table
117
Stress Intensification and Flexibility Factors
.5F2
Continued
40 80
160 40 80
160
2.19
2-16 2.22 r.6 4
2.63
2.30 1.80
2,7
3.
r.88
7.34
3,90 3.03 2.50
xs
4.80 4.45
6.0?
4.57 3.34
2.10
2.41 10.44
1.76
2.Ol
8.0 8
4.61 4.31
5,49
r
4.21 3.64
2.07 2.02 4.71
4.2r
3.44
3.0 7
2,45 2.0
3
6.02 4.39 3.84 2.45
2.49 2.29
5. t4
4.60
4.9 5
2.80 2.43 6.85 4.25 3.?6
xs
4.0I 3.14 2,72 2.25
10 20 30 40
50 80
,94
4.61 3.9
4
3.39 3.0 3
2.24 9.09 4.14 3.17 3.24
2.59 2.37 't.69
4.78 a.40 3.30
9.60
2.70
2.44 r1.
?9
6. 8l 5.9 4
4.69
8.20
7.0
5
5.10
r0.73
6. r0
7.80
9.t2 8
10.44
1I.4
4
14.92
4.77 7.26 5.9
9.r2
6.92 6,04 5.36 4.45
8.89
3.18
3.9
6.81
1I.36 8.01
70.21
15.50 13.35
7.54 6.54 5.79
8,38 7.34
13.
f4
11.37 10.30
4.6 4 0
8.57 7.38
0
3.29
2.45
11. S2
8.0
11.8I
2,O9
9.'t5
10. s4
4.s3 2.94
l-2.46
8.30
9.9 0
6.40 5.54 4.92 4.44
7
3.0 2
2.40 10 20 30 40
4.58 3.92
3.68 2.76 2.33
2.98 2.67 2.35
120 140 160
30
2.79
3,4
r00
8.35
ST
l.8r
f.98
20 30 40 60 80
9.7!
10 20
4
2.07
t8
2.64
2.10
6.40
1I.82
17.f9
14.82 13.40
10.80 9.24 8.20
118
Piping Stress Handbook Table 5-3 Flanged Elbows-Flexibility Factors and Stress Intensiflcation Factors STZE
2.
I|ALL TIIICK
.154 .2La .436
2\ 2\ 2\ 2 tt" 2\ 2
.
083
,2"
3'
.120
.2I5 .300
3i
.600 .
3t" 3!"
on3
.1?o .314 .536 .0a3
.L20 .237 .337 .531 -674
'134 .258
.625 .750
50
.280
.432 .562 .718 .864 .148
3.2s 2.7r 2.24 L-74 7.73 L.44 1.32 l.03 1.00 1.00 I.00 1.o0 2.36 1.59
1.a3 1.24
I.OO
1.OO
l.0o 1.oo 3.54 2.95 2.74 2.24 2.7S I.48 1.38 I.15 1.01 l.OOj 1.00 1.00 3.85 3.21 2.97 2.47 r.88 I.56 L.44 L.20 1.O0 1.00
4.13 3.L9
3-44
r.22 L.04
1.Ol 1.00
2.66
I.OO l.O0
3.93 3.28 3.41 2.S4 2.13 l.?8 1.61 1.34 I.29 I.0o 1.07 1. o0 l.oo 1.00 4.41 3.68 1.65
1.3?
l.lo l.o0 1.00 1.00 5.20 4.34 4.23 3.52 2-92 2.44
.322
2.45 2.O4 2.06 t.72 r.77 r.47
.aL2 .875 .906
BqlC END FIANGED
i-
ii
.25O
.406 .500 .593 .718
8i
NOT A'JANGED
1.34 1.11 1.23 1.02 1.14 1.O0 r.11 l. o0
!2
1.42 1.lo t.25 I.O4 l.09 1.o0 1.00 1.00 l.o0 l.0o 1.20 1.06 r.00 I.OO
1.00 1.00 1.oo 1.00
1.73
1.49
1.2a I.06 1.12 1.OO 1.OO 1.00
1.00
1.00
1.64 1.36 I.30 1.08 r.I4 I.00 1.00 I.oo 1.93
1.61
1.16 1.0o l.os 1.00 1.00 1.oo 1.00 t.oo 1.88 1.57 1.76 1.46 1.38 1.16 1.20 1.OO I.09 1.O0 1.00 1.oo 1.OO 1.00
1.99 1.45 1.43 1.22 l.I0 r.o0 l.oo 2.16 I.96 1.57 1.49 1.36 1,18 1.11 l.06 l.ol l.oo
1.66
1.54
l.19 1.01
1.OO 1.OO
l.oo 1.81 1.63
qllE EI{D I:UINGED
it
2.35 1.78 r.47 1.20 1.00 I.OO 2.26 1.a5 L.3a 1.15 1.00 1.o0 2.52 1.50 1.00
iol 1.97
r.39 L.22
l.o0 t.oo l.OO
r.8A L.44
I.O8
l.oo
1.00 1.oo 2.09
I.25 1.oo
1.OO r.00
2.6e 2.23 2.20 1.83 1.28 r.07 L.00 1.00 2.S3 2.35 2.33 1.94 l.61 1.34 1.13 1.00 1.00 1.00 1.00 1.00 2.72 ?..27 2.45 2.O4 r..39 1.16 I.la I.00 1.O2 1.00 L.OO 1.00 2.96 2.47 1.ao 1.50 1.42 ].I8 1.05 1.00 1.OO 1.OO 3.35 2.80 2.88 2.39
1.31
!.24 1.14 1.0o
t.oo 1.o0
l.o0 l.oo
1.68 1.40 1.50 !.24 I.21 1.00 r.14 1.00 1.07 1.00 l.o5 1.OO
Note: l.o, iof, io2 are out-of,-p16ne intensifLcation factols i, 11r 12 are Ln plEne lntensiflcation factors
Stress Intensification and Flexibilitv Table 5-3 Continued
10" 10"
ro"
10" 10" Lo"
to" 10" 10"
ro" 10"
t2" 12" t2" 12"
.156 .180 .250 .330
12" L2"
.406 .500
12" t2"
5.23 4.55 3.4L 2.94
4.36 3.79
2.08
1.73
1.40 1.22 1.11
1. t7
5.26 4.'t9 3.8t 3.14 2.a7 2.7a 2.33
4.39
2.44
2.45
1.00 1.Oo
3.99 3.18 2.61
2.39 2.26 1.94
1.85 r.54 .443 1.000
1.39 1.16 1.27 r.06 r.12 1.o0
14" .250 l.4n .312 14" .375 14" .434 14" .500 14" .593 14" .750 14" .937 14" r.093 14" r.250 14" 1.406
3.90
3.25
2.92
2.44
16" ,250 16" .312 16" .375 16" .500 16" .556 16" .843 16" 1.O31 16" r".2IA t 6" 1.438
18n 18" la" 18" 18" la" 1am 18" 18" 18"
2.33 r.94 1.79
1.49
1.34 1.21 1.09
1.12 1.01
4-27 3.A1 3.23 2.63 2.17 1.81
3.55 3.18
1.o0
2.'7O
2.19 1.81 1.51
1.20 1.10
1.00 1.00
4.62 3.94
3.85 3.32
.475
.{34 .500 .352 .750
2.A7 2.39 2.63 2.t9
.93'l
1.82 1.56
1.52 1.30
1.23 1.11
1.00
t_.156
1.375 l-.562
t .78r
1.OO
2.r1 2.03 1.75 1.53 1.37 f.2a 1.19 1.12 t.o5 1.00 2.18 2.08 1.85 1.69 1.56 1.45 l.4t r.29 1.19 1.12 1.07 1.00
J..'t4 t.62 1.5? 1.45 1.38 1,27 1..17 f.10 1.05 1.00 r.96 1.83 1.71 1.54 1.40 r.2a f.18 1.11 1.04 1.03 2.O4 1.9O 1.78 1.69 1.61 1.54 L.39 1.28 t.r8 1.11 t.os l.oo
3.37
2.Af
2.44 2.18
2.O4
I.t4
1.69
r.40
1.0O
1.37
1.14
1.13 1.05
1.O0
3.16
2.63
1.41
2.30
l.9I
1.30
2.06 1.84
1.72 1.53
1.37 I.25 1.17 t.06
1.15 1.04
2.70 2.4r
2.25
1.84 L.t3
f.53 r.44
l.a1 1.69 1.45
r.2A
1.07
1.OO
1.00
1.oo
t.a2 1.73
r.54
1.2r 1.1? 1.04
1.00 t.Oo 1.00 1.00 1.45 1.35
r.3f 1.21 1.15 1.06
r.
r.73
1.42
1.00
r.44
1.O0
1.oo 2.0O
OO
o.92
L.oo
1.13 1.00 1.O4 1.00
1.64
2.9O 2.60 2.34 2.OL L.'74
2.41
1.35 1.23 l.l2
1.13 1.03
t.00 I.52 1.42
r.2a 1.r7 1.06
l.oo
L. oo
r.00 l-.00 r.7O 1.58
1.49 1.41 1.34
\.24 1.15 1.07 0.99
1.00 1.00
l.
oo
2.16 1.96
l.6a 1,45
1.00
r.05 1.00 3.07 2,56 2.75 2.29 2.51 2.O9 2.31 1.93 2.15 t.79 2.01 1.68 1.73 1.44 1.36 1.14 1.23 1.02 1.14 1.O0 1.05 l.o0
Note: i^, i^f i-2 are out-of-plane intensification factors i; jt; i2 ire in plane intensification facEors
Factors
119
120
Piping Stress Handbook Table 5-3 Continued
20" 20" 20" 20" 20" 20" 20" 20" 20" 20" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24n 30n 30" 30" 30"
I
t. t:l
.
.250 .375 .500 .593 .812 1.031 1.241 1.500 1.750 1.96A
.250 .375 .5OO
.562 .6A1
.968 1.21a
I.531 1.a12
2.062 2.343 .2so .375 .500 .625
4.91 3.77 3.0a
4.14 3.L4 2,5?
2.r8 r.82 1.a4 1.53 1.56 1.30 t.3a r.t5 L.22 t.02 1.11 1.OO 5.63 4.69 4.29 3.5'l 3.24 2-70 2.80 2-34 2.20 1.83 1.56 1.30 L.24 r.O3 1.12 1.00 5.63 4.97
4.69 4.L4
o8
2.57
Miter bends-Modify the K and i factor when the butt weld of the flange is located within one and one half pipe diameters of the nearest miter weld measured from the centerline of the pipe.
Although not specified by the Code, this will apply to both closely and widely spaced miters. Note: Large-diameter thin-wall piping elbows and miters are affected by internal line pressure. According to a *Batelle" report to dre AGA, the flexibility factors on these items are seriously impaired by internal pressure. To
correct the values from Table 5-1:
Divide K by: (P) (r)]" (Rt)t"
(1 + o 'E"tz
I2
2-L2 1.A4 'L.67
1.77 1.53
1.39
L.29 1.0? 1.19 1.00 1.11 1.OO 1.O5 1.00 1.O0 1.00 2.25 1.84 L.97 1.64 1.7a 1.48 r.71 L-42 1.59 1.32 1.30 l.oa t.oo l.r9 1.13 1.00 1.06 1.oo 1.OO 1.O0 2.43 2-O3 2-25 l-.84 1.93 1.61 1.7A 1.49
3.24 2.70 2.64 2.2O 2.26 r.a9 2.OA 1.73 r.75 1.46 1.54 r.28 1.36 1.13 1.24 1.03 1.13 1.OO l.05 t.o0 2-9L 2.51
2.42
4.76
1.46
2.O9
1.23 1.04 1.r5 r.00 1.06 1.00 3,24 2-A2 2.51
2
-70
2-34 2.O9
Factors and Characteristics h, k, and i
Butt-weld joint Reducer Weld-neck flange
Double-welded slipon flange Fillet-welded joint-single weld Socket-welded flange Single-welded slip-on flange Lap-joint flange (with ANSI Code
816.9 lap-joint stub) Screwed pipe joint or screwed flange Corrugated straight pipe or corrugated or creased bend.
1 I I I I I I I
| 5
1.0 1.0 1.0
l'.t 1.3 1.1
t.3 1.6
2.3 2.s
Divide i by:
(r+3.2s)9qq# Ecrr
Nate.' Factors shown apply to bending
for torsion equal to 0.9.
flexibility facrr
Stress Intensification and Flexibility Factors
121
Widely Spaced Miters D = Pipe
2-weld Miter
Size
(inJ 12 T4
16
l8 20 24 26
30 JZ
36
40 42 48 54 60 12
0.375 Wall 2-Weld
0.250 Wall
14.2 15.4 r7.3 l9.l 20.8 24.3 26.0 29.3 30.9 32.6 34.2 37 .3 38.9 43.5 48.0 52.4 61.0
Miter
5.4 5.7 6.3 6.8 7.3 8.3 8.7
10.1
4.1
10.9 12.2 13.5 14.8 t7 .3 18.5
4.4 4.8
9.6
11.'l
20.8 22.0 23.2 24.3 26.6
r2.0
27 .7
r3.2
31.0 34.2
10.0 10.4 10.9
r4.2 15.3 l7 .3
.3 43.5
37
Dimensions (in decimals ot teet) A 0.878 1.025
t.171
5.2
I .318
5.6 6.6
1.464 1.757 1.903
7.3
2.196
7.6
2.343 2.489
6.3
8.0 8.3 8.9 9.2 10.0
2.636 2.938 3.075
3.514
3.954 4.393
10.9 11.9 13.2
5.272
K = flexibility faaor
i. -
ii =
outof-plane stress intensificatian factor in plane stress inlensification Jbctor
Figure 5-1. Flexibility and stress intensification factors of two-weld miter elbows. Widely Spaced Miters D = Pipe
0.250 wall
Size
3-Weld
(in.)
Miter
12
t4 lo 18
20 24 26 30 34 36
40 48 54 60 72
ir=i"
i0.8 tt.1 13.1 14.5 15.9 18.5 19.8 22.3 23 .6 24.8 26.0 28.4 29.6 33.1 36.6 39.9 46.5
Wall 3-Weld Miter
0.375
4.3 7.7 4.6 8.3 5.1 9.3 5.5 10.3 5.9 lr.3 6.7 l3.l 7.0 1,4.1 7.7 1s.9 16.8 8. 1 8.4 17.6 8.'7 18.5 9.4 20.2 9.7 2r.1 10.6 23.6 11.5 26.0 12.3 28.4 13.9 33.1
lt =lo
3.3 0.696 0.401 3.5 0.812 0.468 3.8 0.928 0.535 4.2 .044 0.602 4.5 1.160 0.669 5.1 r.392 0.803 5.3 1.508 0.870 5.9 1.740 1.004 6.1 1.856 1.071 6.4 1.972 1.138 6.6 2.088 1.205 7.1 2.320 1.339 .4 2.436 1.406 8. l 2.784 r.607 8.7 3.132 1.808 9.4 3.480 2.009 10.6 4.176 2.411 1
7
K = fleribilitf factor
i" = it =
outof-plane
stress intensification
Dimensions (in decimals ot feet)
factor
in-plane strcss intensification factor
Figure 5-2. Flexibility and stress intensification factors of three-weld miter elbows.
Rotational Nozzle Flexibilities for Cylindrical Vessels
It is customary for piping stress analysts to model a piping system with rigid ends or anchors at the equipment
time and money on these changes, let's model the nozzh data points 5 ard 30 with flexible end conditions using the flexibility factors from Table 61. The table shows that fa exchanger E-l the in-plane rotational flexibility (R.F.) is .626 x 106 in.{bs/deg, and the out-of-plane R.F. is
nozzles. This assumption is acceptable when the system is flexible and the anchor loads are low. But anytime the system shows high loads and stress€s, the analyst must determine how reasonable the assumption in modeling the nozzles as rigid anchors was. The author has developed tables of rotational nozzle flexibilities for cylindrical vessels ranging in diameters from 2 ft to 20 ft and connecting nozzles ranging in diameters from 2
in.-lbs/deg. The new computer calculatior show that the highest stress is 12,015 psi and the new forces at anchor are:
in. to 48 in. sTD. thickness.*
To demonstrate how these flexibility facton really affect the accuracy of stress calculations for a simple piping system, an example where a l4-in. O.D. pipe from an exis shown in Figwe 6-1. changer E-l ties to a tower The computer stress calculation with rigid ends or anchors show a high stress of 33, 616 psi in the system and forces and moments at the nozzles as:
Tl
(}D. 5 30
Tl
lff .4Oi xltr
the in-plarc .209 x in.Jbs/deg. For the tower R.F. is 1.22 x lff in.-lbs/deg, and the outof-plane R.F. b
F,
(rb)
-il,113 l l.l l3
F,0b) -28,r4
28.182
n4 (ft-tb) 85,749
t49.174
Tb reduce these high forces and moments, we will have to modit the piping configwation with more elbows or an additional expansion joint. But before we spend more
D.P. 5 30
F.0b)
Fy
-2,tOO 2,100
-6,04
0b)
6,082
n4 (ft-rbo 3,3@
-20,741
These forces are obviously much lower ftan the frst assumption with rigid ends. Now we know tlnt the piprng system is not overstressed. The shell of the exchanger E-l or the tower T:-l needs to be checked for local stresses with the new loads. It is quite possible that they are acceptable to the exchanger and vessel designer and manufacturers. The following is a method for determining the spnng rate of nozzles attached to vessels or stubbed into larger piping. Only in- and out-of-plane rotational spring rat€s are included, since the radial flexibility is normally ignored. Nozde flexibilities sttould not be used if the nozde
122
Vessels
Rotational Nozzle Flexibilities for Cylindrical or pad diameter is greater than one third of the run or vessel diameter.
Nozde flexibilities were calculated in accordance with the phase report ORNL 115-3, Equation 8, page 6.
K:
c ws
DB
(-D/Wf"
WD
. MDBK o=-
(6-l)
(6-2)
EI
Spring Rate
:
EIPI
(6-3)
2160DBK
Solving Equation 6-2 tot (Ml?) and converting units to ftJbs/deg we have Equation 6-3.
where
C
c:
D: Ds: E= I: K: M: PI:
123
.09 for in-plane bending .27 for out-of-plane bending
Diameter of vessel or run, in. Diameter of branch, in. Modulus of elasticity, psi Moment of inertia of branch, in.a Flexibility factor Moment, in.{bs Circumference of a circle divided by the diameter
Angle of rotation, radiam e: of or run, in. Wall w: of branch, in. ws: Wall thickness thickness
vessel
In-plane bending refers to bngitudinnl bending in the run or vessel in the plane formed by the intersection of the branch and vessel or run centedines. Out-of-plane bendtngreferc to circumferentialbendng it a plane perpendicular to the vessel or run diameter.
PIPE:
MAT. -
C.S.
o.D. - 14"
THCK. - .375" TEMP, - 450'F EXCHANGER E.1:
MAT. -
C.S.
o.D. - 5'-0" THCK. TEMP,
- 1lz' - 45OOF
b I I I I
t
--TI
I
TOWER T-1:
MAT. -
o.D. THCK.
TEMP
C.S.
10'-o"
- %" - 450"F
I I I
Figure 6-1. An example diagram of a piping system where 14-in. O.D. pipe trom an exchanger ties to a tower'
124
Piping Stress Handbook Table 6-1 Rota Stiff calculation, Gyl. vessel ROIA 00.F1
vEss€L TCK,IN
2.000
.2 50
VESSEL
2.000 2.000 2.000 2.000 2.000 2.000 ?.000 2.000
.500 .6?5 J
1.?50 1.500 1.750 2.000
.250 .325 .500
2.C00
2.000 2.000 2.000 2.000 2.000 2.000
.000
.750 1 .000 1-250
2.OOO
1.500
.000 2.C00
2.000
2.000 2
2.00c 2.000 2.000 2.000
2 -OOr)
?-000
2.000 2.000 2.000 2.000 2.000 ?.000 ?.000 2.000 2
.000
.250 .375 .500
STI'F
CALCULATIOTI, CYL. VESSEL NO2 T
2.375 .375 .375
2 2
2.375 2.375 2.375 ? -375 2
.t75
?-375 2.3?5
.000 1.250 1.500 1
3.500 4.500 4.500 4. 500 4 -500
4
.500
4.500
6.625 6.625 6.625 6.625 6.625 5.625 6.625
2.500
.250
2.500
. t00
2.375 2.375 2.375 ?.3?5 2.375 2-375 2.375 2.375 2.3?5 2.375 3.500
2.50 2.50
.625
0
-750
0
2.500
1
.000
1.25(J
I .500 I .750
2.50 0 2 .500 2 .500
2.OfJO
2.500
.250
2.5C0
.37 5
2.500 2 .500 2 .500 2.500 2.500 2.50[r
.500
.625 .750 1.000 1-250 1.500 1.750
.154
.499 E +0 5 .871E+05
.4128r06 .8 47€r 06 .1 48 E+07
.233E+07 .343E+07 .479e +07 .394E+05
-216
.500 3 .500
3
6.625
.t75
.154
.2618+06
.1 50E r06
.22O8+07 .347 E+A7 . 510€+07 .712E +oz
3.500 3.500
2.OOO
.7 50
.154
.2438+05
3. 500
2.000 2.000 2.000 2.000
't
.154 .154 .154 .154
6
.6?5
6.6?5
.216 .216 .215 .216 .216 .237 .237
.237 .237 .237 .237 .237 .237 .?37 -280 .280 . ?80
.280
.280 .280 .280 .280 .280
.154 .151 .154 .154
.882Ef04
.265E+05 .729 Er 05
.223E+05 .389E+06
4.500 4.500 4.500
.7 50
-154
-216 -216
3.500 3.500
1.000 1-250
1.750 2.000 .250 .375 .500 .625
-154
.154 .216 .216
4.500
1. 500
CK,I
.500
3
-625
.7 50
ZLE ROT STIF IN.LB/DEG N INPLANE OUTPLAI.IE STD LOI,I6I CIRCU
r{ozzLE
OD,]N
.t0EE+06
.6'l4E+06
.126E+ C7
,520E|05 .143Er06 .294E+06 -514E+06
.81t8+06
.166E+07 .29'l E+Ol .459E+07 .67 4E107 .942E+07 .790E+05
.21EEf06 .4 478+ 06 .781E+06 .123E+07
.253E+07 .142E+A7
.697E+07 ,'102E+08 .143E+08
.1378+06 .28?E+06 .493 E +0 6 .7 78E+O 6 .114e+O7 .160E+07 -131E+05
.362E.05
.712E+o5
-130F+06 .205E+06 .420E+06 .733EtO 6
.1168+07
-170E+07 .2378+Q7
.l738+05 .478E+05
.981€+05 .1718+06 .27OE+D6
.555F+06 .9 69 E+06
.153E+07 -225t+O7 .314€+07 .263E+05 .726E+O5
.149E+06 .?608+06 .4118+06 .843E+06 .117e+A7 .232E+o7 .3428+07 .477E+47
-237E+05
.789E+O4 .217E+Os .446E+Q5
-154
.134E+06 .234E+06 .369E+06 .7 578+05 -132a+07 .2C9E+07
.154
.6528+05
.7798+05 .123E+O6
.2528+46 .4418+06 .695€+06
.'t 54
. 3C7E+ 07
.154
.128E+07 .552E+05
.1'l7E+O'
3.500 3.500
.216 .216 .216 .216
.970E+ 05
.323E+05
.199 E+06 .348 E +06
.56
.500
.?16
.5 49 Er 06
.183Ef06
.'113E+07 .197E+07
.376E+06
.3'10€+C7
-103E+07
5
3.500 3
.500
.216 .216 .216 .216
.456E+O?
-102Ef07
.143ErO7 4E
r0 5
-116etO6
.656Ef06 .152E +O7
20+ SSZL' 9O+3 L6L'
10+lS2t'
ZZ'
90+1299.
90+3tEt' 9O+3
L
90+l0t!' st]1rt08' S0+r06t' so+tzrL' to+1r 61' to+)6tL' 90+r9t6'
90+r 66S'
90+rttt' 9O+1L9
L'
90+:1901'
s0+3909'
s0+3952'
s0+rl.0l' 1.0+:0tl'
90rltt6'
90+35t9' 90+3?0t' 90+1052'
9Ot )Z I L' SO+) t, L'
90+ltor' S0+386t' t0+r0zl.'
tLtz'
l0+39t1' 9Crl0Zt' 90r10rz' 9A+tLtl' S0
+13Zr'
lar )z8g' to+ 12Lt' zo+ atgz' 10+108!'
20+lt0!' 90+ll0s' 90+l8tt'
Itz' tiz' z'
Lt
lt2'
L2' 9LZ' 9
tz' 9tz'
9
912' 9
LZ'
9C+rZ8l' !0+r968' s0+l tz t' lO+z L6r' z0+J082' to+ )o6L'
9LZ' 9LZ'
90+l169'
ts L' ,s L'
to+3lzL' 9O+a
Ltt' ,'
It
L2' 9A + 9O +1ZZ S0+3S65'
9tz'
t9 L' ts L' ts L'
ts ts
00s't 00E't 00s'?
00s't 005't
't 009' ,
005'
00s't 00s't
osz' 0c0'z
00('t
't 00s' t 00s't 00E' t 00E
00E't
00s't 009't 009't
stt'z slt'z glt'2
t' l'
,s L'
sLt'z
20+)r9S'
80+;1691'
g29'I
Lo+1s2?'
+3rz t' LO+1ZZS'
zzt' azt'
to+3rLt'
]166' 90+lE8r' 90+tg0t' 90+ 91+
f9lL.
80+3lzl'
20
20+)9' L' 90+3t26' 90+t6zs'
E0+r8E8'
90+ 1L92.
l0+SLzr' 101390t' lo+)eoz' L0+3ztl'
r. 10+i LL 6'
90+lllt.
9O+1'
S
l'
9O+3t9t'
90+rttz'
90+lttl'
s0+16t9' S0+39t2' lo+) L?z' l0+a LOZ' LO+) Lt l'
E0+rtt6' g0+rgZ
lo+39?9' 1.0+rg6t' L0 + )9 ZZ' L0
+
10L
t'
90+1669'
90]303t' 90+356t'. I0 +:l,l0l. 20+12' g'
/0+1t09'
90+1e98'
t0+30Lr. LC+ 10? Z.
90+ 39
20+36r
6i' 90+3ZrZ' 90+rEs l' s0+31.28'
SO+rlzr'
LO+
3
2LZ'
r.
9t+)SzL' 9C+109t' 90+lt9Z' 90+3 8Z
I'
90+lS9t' lo+1Ltg'
I9NO'] NJUI] I Nv-l dNI lNvldIn0 9rc/€'t'NI i Its 10u
sz9'
I
EZ9'8
sz9'a EZ9'
10+1662'
I
szg'8
zzt' zzt'
otiz' 082' 08 z' 08
z'
082' 03
z'
082' 082'
082' 082'
).tz'
Itz' 2t2'
lrz' Itz' Itz'
2t?' 9
L?'
09t'L 0c9'L 052't 000' I ost' szg' 00s'
09z' 000'z
00s't 09?'I 000' I
000'z OSL'L
009' I
osz'L 0c0' I os
L'
E29'S
a9
000
z' 'z
szg'9 szg'9 szg'9 szg'9 sz9'9 s z9'9 szg'9 szg'9 szg'9
as2'L o9s'L
oos't 00E't 00s't 00s -t 009't 005' t 00s't
OSL'L
00s't
l-tzz0N
-tJss3A'"llJ,NOllvlnllvl tlrls penu!luoc t-9 etqer
000't 000'5
0c0't 000't 000't 000'
t t
090'
5
000'
t
0c0'
t
0c0'
I t
00c'
000't 000't 000't 000'5
000't 000't 00c't 000'I
000'
sz9- 9
00E't 005'?
00c'l
009'
s29'8
t
000't
091'
szg' 00s'
008'
t I
000' 000'
000't 0c0't
E29'8 szg' I
(ls NI')]I
slassen lPcr.rpurdc Jof ssll!l!qrxell elzzoN leuollPlou
009't o9?' t 000'I r)s 2' szg'
00s
s0+39t?'
lo+lrot'
;
10+
osz't
000't 000't 0cs'z
cos 'z 00E' z
00s'z 009'z 009'z
00s' z
00s'z 00s'z c0g'z c35'Z
005'z oo3'z o09'z
'z
000' I 0Ez'
00E
00E'
00s'z 1xs'z 006'z 00s'z oos'z 00t' z
sz9'
09z' 000'z 00s' t osz'L
000't
0s2' sz9' 00s'
osz' 000'z
NI')JI -13 ss 3A v10u
00E'z oDs'z
00E' z
00E'z 005'
z
00E'z 00E'z
0cs'z 009'z 00s'z IJ'OO -l3sslA
126
Piping Stress Handbook Table 6-1 Continued ROIA STIfF CALCULAIIOII, CYL. VESSEL
OD,fT
3.000 3.000 3.U00
3.000
3.0c0 3.000 3.000 3.00c 3.000 3.000 3.000 3
.000
3.000 3.000
3.0c0 3.000 3.O00
3.000
L
l, l:i
l
t,
'
I
3
.000
3.000 3.000 3.000 5.000 5.000 5.000 3.000
3.000 3.000 3.000 3.000 3.0c0
VESSEL TC
K,IN
1.750 2.000 .z5g .375 .500 ,6 25 .7 50 1.000 1.250 'f . 500 1.750 2.000 .250 .375 . 500 .625 .750 I .000 t. ?50 1 .5s0 1.750 2.000 .250 .375 .500.625 .750 1.000 1.2r0 1.500 1.750 ?.000
3.500
3. 500
.250 .375 .500
1.500
.6?5 .7 50
.000 1.250 '|
f.500
3.5C0
1
.500
.750 2.000 .250 1
3.500 3
.50C
3.500 3.500 3.500 3-500 3.5C0
3.500
t.500
.500
.625 .750 1 .000 1.250 1.750 2-000
3.5C0
4.500 4-500
6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.625 4.625
. 500
.625 .7 5b
1.000
t.250
NOZZLE ROT STI f II{.LB/DE6 T
CK,I
SID
.280 .280 .280 .280 .280
.6458+05
.?15E+05
.2 E0
.?07E+07 .361E+07
10 -759 10 - 750
.l
78
E+
06
.365€+06
.638Ei06
.5938.05 .1228ro6 .2t3Er06
.569E+07
.2E0
.8t7E+07
280
.1'l7E+08
.389E+07
-853E+05 .235E+06
.284E+05
E.06
.161E+06
.135c+07 .?73E+07
.443E+06 .910E+06
.752e+07
.159E+07 .251E+O7 .569E+0 7
.280 .280 -
.32? .322 .322
.1018+07
.?56E+07
.3f,5E+06 .6888+06 .120E+07 .190E+07
-322 .322 -322
8.625 8.625 8.625 8.625 10.750 10.750 | 0.750 10.754 10.750
CIRCU . l84E +0 7
E.625 8 .625
8.625
OUTPLA}'IE
.551E +O7 .7 69 E+07
.237
.625
8
N INPLANE LONGI
.237
.322 .322 .322
4 92
.
.843Er06 .477Er07
-3?Z
.ttlE+08 .l 54Er 0E
.
-
t65
.365
.165 .36 5
107E+06
.279E+O7 .78
3
E.0 5
.e8l E+06
.51'E+O7 .358Ero5
.986Ei05 .?03Er06
.2968+06 .608E+06 .106E+07 .167a+07 .311E+07
.3548+06
.316E.07
.558E+06 -115E+07
.200E+07
10.750 10.750 10.750
- 565
.600E+07 .9 47 E+ E7
-365
.194Er08
2.375 2.375 2.375 2.375 2.375 2.375
.154
.2C0E+05 -551C+05
-154
2.375
.154
-640Er06 .112E+07
.154
.176E+07
.5888+06
-154
.259E+07 .362E+07
.1?1E+O7
.216 .216 .216 .216 .216 .216 .216
.298
2.37'
?.375 3.500 3.500 3.500 3.500 3.500 3,500 3.500 4
3.500
3.500 1.500 3.500
t{0zzLE OD,IN
VESSEL
.500
4.500 4.500 4,500 4.500 4.500 4.500
.365
.365
.t
54
.151 .154 .154
.154
. '139 E+0 8
.113Er06 .198Ff06 .312E{06
.659Er05 .1048+06
.213E+O6
.373Er06 .864Er06
.561E+05 .980E+05
.4648+O6
.952Ef06
.539Er07
.237 .237 .237
r04
.294E+ 06
.168Er06
-2'16
.2t7 .?t7
E
-184E105 .377E+Os
.99ZtrO4 .27iE+05
+C5
.166E+07 .?62E. 07
.237 .237
.6 67
.820E+05
E
.?16
.216
.464E+O7 .646 Er0 7
.386E+07
.155E+06 .317ErOo
.554E.06 .875E+06 .1?9e+O?
.1 80E+0 7 -t
.108€+06
.222Er06
31€r0
5
.361E+05 .741€+05
06
.i30E'06
.613 Ei 06
.204€+06
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+
.126E+07 .2208+07
. 419 E+0 6
.733E+06
Rotational Nozzle Flexibilities for Cylindrical Table 6-l Continued ROTA STIFF CALCULATIONT
VESSEL NOZZLE ICKTIN 0D,Iil
VESSEL
0D,fI 3.5C0
1.500
1.500 3.500
'l
.7 50
2.000
.250
3.500 3.500 3.500 3.500 3.500 3.500 3.500
.500
.625
6.625 6.625
.7 50
t.00rJ 't
.250
1.500
3.50 0
.750 2.000 .250
5.500
.500 .625
.500
3
.625
6
1
3.500 3.5C0 .500 .500 3 .500 3 .500
3
3
3.5 00
3.500 3.500 3.500
E.625 E .625
.527E+C7
.2 80
.7 7 5E+ 07
.280
.1088+08 .790E+05 .218E+06
.4178+06 .780E+06 .123E+C7
10, 750
.500
1
0.750
.000
1
1.750
10 ,750
3
2
10
.500
3.500 3.500
.500 .625 .7 50
12 -750
.250
'12.?50
.0s0
.5C0
3.500 .500
.500
.500
2. 000
12.750 12.750 12.750
.500
2.375 2.375 2.375
.750
4.00 0 1, .000
4.000 .000
4.000 4.000 4.000 4 .00c
.000 .?50 .500
0
4.000 4.000 4.000 4.000 /,.000 4.000
2
4.rJ00
1
.000
?.375 ?.s75 2.375 2.375 2.375
.250
3. 500
.500
3. 500 3 .500
.75rJ
.000
3.500
3.500 3.900
.3'l0Er06
.637 E+O6
.1 'l1 E+07
.176E+07 .258E+07 _3617+07 .263E+0 5 .7?5E+O5
.149E+06 -260E+06 .410E+06
.23?E+07 ,34'l E+C 7
.11'3E+08
.47 6E+
.991E+05 .27 4E+06
.331E+0
.147E+07 07 5
.913€+05 .187E+06
.562E+06 .9838+06
.328E+06
SSEaOl
.517E+o6
.l
.106E+07 ,185E+07
,3 65
.877E+ 07
.292E+07
.365
.129 E+ 08 .180E+08
.6008+07
.750
12.750 1? .750 12.750 12.750
.549E+05 .113E+06
-696E+ 07
.3'l8E+07 .5568147
10.750
3.500 3.500
3.500
.365
.199E+05
,842€+05
.441E+C7
.50>
10.750
-1708 +O7
-?53E+C7
.102E+08
0. 750
.0c
.280
.625
1
/.
.2E0
.9318+o6 .191E+07 .3348+07
.3?2
a
1.250
4
.1978+06
.t55E+06
4.625
0, 750
3
.2 80
.338E+C6 .590E+06
.280
1.750 2.000 .250
r
3.500
.2E0
-t?2
-7 50
J
.237E+ol
.2a7
8.6?5
.?50 I .500
1-000
3
.1169+02
E
1
.500 3. 500
3
CIRCU
+07
.347
E -625 8 .625
.7 50
LOI1GI
,5108 +07 .7'l ?E + c7 .597e+ A5
.322
10.750 10.750
.500 3 .500
SID
8.625
.500
3
ZLE ROT STIF II{.LB/DE6 C(,I N II,IPLANE OU]PLANE
.280
3-500 3 .500
3,500
T
6.625 6.625 6.625 6.625 6.625 6.625
1.000
VESS€L
N02
4. 500
4.500 4.500 6.6?5
CYL'
.'l 20E+06
.375 .375 .375
.329 E+C6 .676E+ 06
.118E+07
.430E+A7 .399E+05
.1'l0Ef06
.225E+06 .394E+06
.i86E+07
.621 E+06 .'128F+07
.666E+07 .'1058+08
.223E+oz .351E+07
-375
.2168+08
.7?1E+O7
.15 4
- 187E+05
.624E+O4
.106Er06
.353Er05
.375 .375
. I 55 E+08
.154 .154 .154 .154 -'t 54
,154 .151
.'t54 .216 .2.16
.z't6 .2'16
.?16
.515E+05
.185E+06 .292E+06 -5999+06 .105E+07 . 't 65 E+ 07
-517 E+07
.172E+05 .61
6E +0 5
.972E+05 .200E+06 .349 E+ 06
.550E+06
.2438+07
.808E+06
.339E+O7 .2?8 € + 05 .7 67E+05
.928E+04 .256E+05
.157E+05 .27 5E+ 06 -454F+06 . 891
E+
06
.1'l3E+07 ,525Er05 .917E +O5
.1458+06 .29
7 E+O
6
Vessels
127
128
Piping Stress Handbook Table 6-1 Continued R0TA
vEssEL
VESSEL
4.000 4
.000
4.0c0 4.00 0 4.C00
1
1.750 2.000 .250 .375 .500 .6?5 .7 50
4. 500
1.000
4.C00
2.OOO
4.000 4.000 4.000 4.000 4
.000
/..000 4.000 4.000 4.000 4.000 4.000 4.000 /,
.00 0
4.000 4.000 4
.000
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.0c0 4.000 4.000
1.000
.250 I .500 1.750 2.000 .250 1
.37 5
.500
a -625
.7 50
8.625 8.625 I .625
8.625
.625
1.0c0
.250 1 .500 1
1.759 2.000
E
.500
.625 .7 50
.000
.2 ro
.500
.750
2.000 .250
.t7
5
.500
1.500
1.750 2.000 .250 .375 .500 .625 1.000
1.250
.625
8.625 6.625
l0 .750 1
4.00 0
4.000 4.0c0 4.000 4.000
6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.6?5 8.625
.7 50
t-000 1.254
4.00 0
4.500
.625
.625
4.000 4.000 4.000 4.000 4.000
4. 500
.37 5
4.0 00
4.000 4.000
4.500 4.500 4.500
.250
.000
4.000
.500 .500 4. 500
3 3
4.500 4.500 4.500
1.250 1.500 1.750
4
OD,IN
3.500 3.500
.250
1.500
4.000 4.000 4.000
4,000 4.000 4.000
i{0zz LE
ICKTIN
OD,fT
4.000 4.0c0 4.000 4.000 4.000
SfIFF CALCULATION, CYL. VESSEL
0
.750
10.750 't 0.7s0 10.750 10.750 I 0.750 10.750 r 0.750 10.750 12.750 12.750 12.750
NOZZLE ROT SII F IN.LB/DEG
TcKrIt{ INPLANE
STD
LONGI
0uTPLAt{E CIRCU
.216 .216 .216
.156E+A7
. 519
C7
E.06 .818E+06
-216
.361E+07 .504E+07
.1 208 +07 .l6E E+07
.237
.366
-123t+O5
-101Er06
.237 .?37 .237 .237 .237 .237 .237 .237
.215E
+
E+
05
.694
.324E+ 07 .477E +07
. 108E
.666E+07 ?80
.559Er05
.280 ,260
- 316E r 06
.
.2E0
.1 54E+06
.552E+C6
.?80 .280
.8718r06
.2E0
.312E+07
.280 .280 ,280
.t22
.322 -3?Z .322
.322 .322 .322
.179
*
A7
.493E+07 -7 ZsE+ 07
.1018+c8
.7398r05
.1218+06 .1 91 Ero6 -392E+06 .68
5
E+06
r07
.159E+0? .22?E+O7 .1E6E+05
.513E.05
.105E +06
.184E+06 .290 Er0 6
.5968+06 .104E+07 .164E+07 -2428+87
.t378 +47
.2o4E+06 .4'lEE+06
.246€+05 .678E+05 . 139 E+06
.730Ef06
. 243 E+0 6
.115€+07
.3848106
.236E
.78EE+06 .138E+07 .217 E+o7 .319E+O7 -416E+07
+
07
.413E+07
.322
.651E'07
-322
.958E+07
.365 .365
.930E+05 .256E+06
.134€r08 .526E+06
.365
.338 t +0 5 E+ 05
.2OaE+06 .363E+O6 .573E+06 . t 18E+07 .206E+07
.310Er05 .854Er05
.175E+06
.9'l9Er06
.306E|06
.145E+07
.4E5E+06
.296E+07
.992Ei06 .17
-365
.5208+07 .E208+07
.375
.112f+06
.565
.375
3E +07 .2738+O7
.121E+08 .168E+06
.40?Ero7
.3CEE+C6
.103E+06 .21 I E +06
.633r+06 .t118+07
.5618+07 .373€+05
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12.75O
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.750 't2.750 12.750 12.750
-375 .375
I 4.000
.37 5
.124E+06
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.37 5
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.114E+O6
.375
.700E+06 .122E+87
.233E+06 .40EE+06 .643E+06
1Z
.6258r07 .9E
6 E+
07
.145E|0E
.202Ef08
'12.750
14.000 1 4.000 I 4.000 14.000 1 4.000 14.000
.174E+07 .358E+07
.575
.193Er07 .396E+07 .692E+A7
.561 E+06 .119E+O7 .2O8E+87 -329E+07
.4838+o7
.675E+O7
-112E+O7
.?31E+Ol
Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued ROlA
vEssEL lCK,lN
vEss€L OD,FT
4.000 4
.000
4.000 5
1.500
1.750 2.000
.000
5.000 5.000 5.000 5.080 5.000 5 .0c0 5.000 5-000 5.C0C
5.000 .00c 5,000 5.000 5.0c0
SIIfF
5
.000
5.000
.250 .5c0 .7 50
. t 65€+06 .261e+06
-154
.535E+06 .935E+06 .1 4EE+07 .217 E+ A7
-375 .375
4.500 /..500 4.500 4.500 /, ,500 4. 500 4 .500
.15 4 .1 54 .15 4
.154 .216
.3c3E+07
.820E+05
.386E+06 .797 E+ 06 .139E+07
- 129E+06
.2?OE+07
.7 32E+O6
-?16
.216 .216 .216 .216
.323E+07
I .625 I .625
1.?50 'l . 500
1.75n 2.000
8.625 8.625
8.625 10.750
.500
10 .750 10 .750
.? 50
1
10.750 0
.750
1
.000
10.750
't
.2 50
1
0
.750
.229E +O5
.469Er05 .?66a+06 -464Er46 .108E+07
-216
.451E+07
.150E+07
.329
-237
.907E+05 .186E+06 .325E+06
.110E+05 - 102€+05
.237 .237 .237
E
105
.105E+07
.351E+06 .613E+06 -967E+46 .'l42E+O7
.184€+07
.596t+ 07
.2t0
.500E+05 .138E+06 .283E+06
.2E0
.494E+ A6
.322 .3?2 .322
.32?
.322
.322 .322 -322 .365
.108E+06 .171E+
.?37 .280 .280
.2 E0
.6208+05
.5r3E+06
8.6?5
.000
.830E+C4
.216E+ A6
.500
a -625
-723E.O6 .10'18r07
-2't6
.250
.7 50 2. 000
.3',12E+O6
.492E+06
.?16
.280 .280 .280 .280 .280
.000 .250 .500
.176€+06
.2498 + 05 .686E+05 .141E+06
6.625 6.625 6.6?5 6.625 6.625 6.625 8.625
- 625 .7 50
.315E+05 .551E+05 .869E+05
.216
6 -625
/..500
.500
5.000
.154
.2908+A7 .427 E+07
.250
1
.154
-237
.500 ,750 2.000
5.C00
5.000 5.000 5.000 5.00c 5.000
.154
.500 3 .500 4 .500
.000
.000
5.000 5.000 5.000 5.000 5.000 5.000 5.000
2.375 2.375
3. 500
.250
5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.0c0
.'154Ei05
3
2. 000
5.0[0
5
.461E+05 .946E+05
.500 3. 500 3 .500
1.750
.7 50
5.000 5.000 5.000 5.000 5.000 5.000
2.375
3
,000
5
.7 47 ErOT
.7 50
1.500
.364F+07 .535E+07 .558E+04
.500 .6?5 .2 50
60E+ c8
.1 67E +05
3.500 3.500 3.500 3.500
1.000
1
.224€+08
2 z
2.000 .250
.500
.
.154 .154
2.375 2 .375
.000
5.000 5.000
.'109E+08
.000
4.000 14.000 2 .375
-7 50
5 - 000 5. 000
E ROT STI F IN.LBlDEG ICK,IN INPLANE 0UlPLAl'/t CIRCU STD LONGI
NO2 ZL
1
.500 -625
'|
r{022L€ 0Dr1N
't 4
5
5.000 5.000
CALCULATIOiIT CYL. VESS€L
.7
79
E
+a6
.160€+07 .279 E+47 .411F + 07
O
6
- 199E+07 .1 67 E+A 5
.459E+05 .943E+05 .165E+O6 .260E +o6
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.618E+C7 .905E+07 .6618+ 05 . J82€+06
.216E+07 .3028+O7 .220E+05
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.2188+06
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.607€+05 .125E +o6
.343E+06
A7
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.369E+ 07 .533E+ 07 .856E + 07
.191E+07
.2't1E|
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20E +0E
.832E+05 .?29 E+06
.471E +06
.E228+06
.130E'07 .2
07 .4 65E+07 66E+
.1?
3E
+
07
.285F +07 .399 E+o7
.277 E +O5 .7 64E+O5 .157E+06 .271E+o6
.4328t06
.887€106 .155E+o7
Vessels
129
130
Piping Stress Handbook Table 6-1 Conlinued nOTA VESSEL OD, FT
5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 ).UOU
5.000 5 .000 5.000 5.000 5.000 5.000 5.000 5.000 5 .000 5.000
5.000 5.000 5.00 0
5.000 5.000 5.000 5.000 5
.000
.750 ?.000 .250 .375 .500
.750
2.000
.t75 . 500
.625
.t50
6.000 6.000 6.000 6.000 6.000 6.000 6.00 c
'1.500
.750 2.000 1
.250
.375 .625 .750 1.000 1.250 I .500 1.750 2.000 .250
6.000 6.000
- 500
.625 .750
6.0 00 6.0 00
6.000 6.000
?50
'l
-000
1.?50
. t 44E +0E
.478E
.200E108 - t 288+06
.4?6E+O5
-000
.409 E +07 .715 € + 07 .113E+0E
16.00 0
.166E+ 0E
.231E+08
.145E+06
rE.000 r8.000 18.000 t 8.000 18.000 1 8.000 18.000 18.000
.151 .154 .154 .154 -154 .154 .?16
.216 .216 .216 .216 .216 -216
E+0 6
.1368+07 .2388+O7 .376E+O7
.552ErO7
.771Ero7 .483€+05 -273E+06 .4778+D6
.226E+07
.75
?8E+ 08
188€+08 .262E+08
2.375 2.375 2.375 2.375 2.375 ?.375 3.500 5.500 3.500 3.500 5.500 3.500 3.500
2.t75
.664
.14tE+07
.
.154 .154
.421E+06
.133Efo6
.810 E r 07
-154
.117E+06 .2 418+06
.8 20 s+ 06
.l .154
r07
.668 Ef07
.399E+06
.464Er 97
2.375 2.375 ?.375
.569E+05 .10?E+06 .209E+06
.619E+07 .976E+07
- 199 E+07
16.000 't 8.000 18.000
.4328+Ol .604Er07
.365E+06 .575E+06 .118E+07 .206E+07 .325E+07
.352Ef 06 .723E+06 .1268+07
6.000 6.000
. l07E+07
-1738+07 -351E+07
.109E+07
r6.000 16.000 't
.
08
.626Er06
16.000 16.000 16.000
1.500
1.000 1 .250
E +
. t 11 E+06
14 -000 14 -000
16 1
1.750 2.000 .250 .375 .500 .625
.2 94 E+0 7
.130Er08
.305E +06
I .000
1.250
.186e+07
.8 82 Er 07
14 -000
14.000 14.000 14.000
.245E+07 .359€+07
.559E+02
.3208f07
'11.000
CIRCU
.9e9E+06 .156E+07
.566Er06
14.000
OUTPLAI{E
.502Er07 .333Er05 .9'l9Er05 .189Er06 .J30Er06 .520Er06
.100E+06 .2?6e+06
.'l8l
.250 1.t00
1
LONGI
12 -750
14.000 14.000
1
STO
1?.750 12.750 1?.754 12.?50 12.750 12.750
.6?5
.750 1 .000
TCXTII{ INPLIN€
.151E+C8
1Z -750
.500
NOZZLE ROT SII F IiI-18/DEG
10.750 12.750 12.750
.500
1 1
VESSEL
.734E+07 .108E+08
I0.750
.625 .750 I .000 1 .250
cYL-
| 0.750
1.750 2.000 .250
6.000 6.000 5.00 0 6.00 0
0DrIl,l
TCKeIx
'1.500
CALCULATIONI
0zztE
VE SSEL
5.0 00
5.000 5.000 5.0c0 5.000 5.000 5.000
SlItr
.l
3E +0 6
.155E+O7 .278e rO7 -426E+O? .6?6E+O7 -E75 E+07
53E+05
.509€+04
.421Er05
.1 40E+05
.864Er05
.l5lE+06
.288E+05 .503E+05
.2388+06
.794E+05
4E9E+06
.1638+O6
-
.854E+06 .'155E{07 .198E+07 -276e+07 -227E+05 .626E+05 .129E+06 .225E+06
.285E+06 .449E+06 .660 E+06 -9228+gb
.757Er04 .209E +05
-428E+05
.749€r0
5
.5 54E+06
.ll6Er06
-727e+O6 .127Er 07
.423E+06
.242E+O6
Rotational Nozzle Flexibilities tor Cylindrical Table 6-1 Continued
sTltr CALCULATIONT CYL- VESSEL NOZ ZLE ROT STIF IN.LB/DEG VESSEL NOzZLE lCK,It{ INPLAxE 0UTPLANE TC(,II{ OD,IN CIRCU STD LONGI ROTA
VESSEL
OD,FT
6.000 6.000 6.000 6.000 6.000 6.000 6
-000
6.000 6.000 6.000 6.000 6.000 6.000 6.00
0
6.000 6.000 6.000 6.000 6.000 6.000 6.00 0
6.000
6.0c0 6.000 6.000 .).
1.500
1.750 2.000 .37
5
.500
.625 .750 '| .0c0 1.250 1.500 1.?50 2 .0c0 .250
1.750 2.000
6.r100
,000
6.000 6.000
2
.000
.250 .500
1
6,000 6.000 6.000 6.000 6.000 6.000
.000 6.00 0
6
6.000 6.000 6.000
6.00 0
6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000
.000
.411E+07
.1378+O7
.237
.3008105
.100Er05 .27 6E+O5
.?37
.82EE+05 . I 70 E+06
.237
.2t7
.
?80
.2 80
.280 .280
.280 .322
.322 .322 .32? .322 .37? -322
.365
10.75 0
1
.000
1.250 I .500
.750 2.000 1
.250
.500 .6?5 .?50
1.000
7.250 1.500 'l .750
2.000
0.750 10.750 10.750
10. 750
.365 .36 5
.365
10.750 10.750 r 0.750 10.750 1? .750
.625 .7 50
i.000
1.250 1.500
.468E+06
.961€r06 .168E+07 .265E+0?
.389E+07 .5
44e r
07
.4568+05 .126E+06 .2 58 E+ 06 .451E+06 .711E+06
.146Er07 .?558+07 .402E+07
.5928r47
.826E+ 07 . 603 E+05 . 166 E+ 06
.341E+06
.5968r06 .940E+06 .193E+07 -317e+O7
.532Er07 .782E+07
12.750 12.750 12.750 12 .7 50
4.000 14.000 14.000 14.000
t4-000 I 4.000 14.000 14.000
.320E+06 .5608+06 .883E+06 .130E+07 .181E+07 .152E+05 .4'19€+05
.8608+05
.l
508+06 .237 E+06 .487E+06
.850€+06 .131E+07 .197 EaOT .27 5E+07
.201E+05
.t14Er06 .199E+06 .513E+06
.643E+06 .112E+07 .1778+07 .261E+07 .364E+ 07
-253€r05
.4258+07
.698E+05 .143E+o6
.250Er06 .395Er06
.E10Er06 .142E+07
.670E+O7
.22i8+07
.984E+07
.328E+07
.517E+06
12 -750
.'l 568+06
.1098|08
12
.750
.566E+05 .989E105
.759E+05 .209E+06 .430E+06 .750E+06 .118E+07 .243E+47
1? .7 50
.902E+06
.4588+O7
.304Er05
.839E+05 .172E+06 .301E106
.375
.142Er07
.37 5 .37 5
.292E+07
.47 4E+O6 .97 4E+06
.510E{07
.170E+07
.375 .3?5
.EC5Er07
.2688+O7
.1188+08 . 16 5E +0t
.f95E+07 .551€+07
.101E+06 .279E+06 -57?E+06 .999 E+06
.33?E+05
.375
1
.500
.297E+ 06
.137E+08 .913E+05 .252E+O6
12.750 1?.750
-668€+06 .9828+06
.216
.280 .280 .?80 ,280 .280
4.625 a .625 I .625 10.750
.500
0
.2958+07
6.625 6.625 6.625 6 .625 6.625 6.6?5 6.625 6.625 6.625 6.625 4.625 8 .625 I .6?5 8.625 I .625
.200E{07
-216
.237 .237 .23?
4.500 4.500
'| . 500
.216
.500 4. 500 4
.000 1.250
.750
.500
4.500
1
0
6.0c0 6.000 6.000 6.000 6.000
4
.7 50
6.00
6
4.500 4.500 4.500
-oa>
0
.500
4. 500
.500
6.00c
6.000
3
.37 5
6.0c
6.00
3.500 3.500
.375 .3?5
.375 .315 .375
.158E+07 .323E. 07 .565E+07 .89'l E +07
.928€+05 .191E+06
.lf,3Ef06 .5258+06
.1 08 E+07
.188E+07 -297E+O7
Vessels
131
132
Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULAII0tI, CYL- vESSEL v€ssEL
OD,FI
6.000 6.000 6.000 6.000 6.000 6.000 6.00
I
I I
lr
1.750
2.000
.250 .375 .500
.625 .750 .000
0
6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0 00 6.0 00
6.000 6.000 6.0c
VESSEL ICX,IN
6.00c 6.000 6.000 6.000 6.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.0 00 7.0 00
7.000 7.000
7.0 00
7.000 7.000 7.000 7.000 7.000
6.00 0
CK,I
.375 .37 5
-375
.759 2.000 .250 . t75 .500 .625
.375 .375 .375 .375
t .000 1.250
18.000 18.000
.t7 5 .375
.250 .500
1
t.
500
1.750 2.000 .250 .37
5
.500
.625 .7 50 I .000
1.250 1.500
.750 2.000 1
.3?5 .500
6.000 6.000 6.000
T
16.000 1 6.000 16.000 16.000 't6.o00 18.000 1 8.000 18.000 18.000
0
6.0 00
NOZ
OD,IN
14.000 14.000 16.000 16.000 16.000 16.000 J
ZLE NOT STIf IN.LB/DEG N INPLANE OUIPLAT.IE LONGI CIRCU SID
NOZZLE
.625 .750 I .000 1 1 1
.250
.500
.750
?.000
.250 .375 .500 .625 .?50 I .000 1.250 I .5C0
.150 2.000 .250
1
.t75 .500
.625 .750 1 .000 1.250
18 .000
.37 5
.375 .375
.375 .375 .37 5
.375 .375
?.375 ".375 2.375 2.375 3. 500
1.500
.343E+07 .504E+07 .7 01E+o7
.44'lE+o5 .122E+06 .2t19E+06
.141E+07 .?47E+O7 -3a9E+07
.148Er06 .4088r06
.572c_+O7
.798 E+07 .493E+05 .'136€+05
.837E+06
.279E+06
.146E+O7
.487E+O6 .769 E+O6
.231E+07 .473E+07
. 1 92 E+08 +
06
.451Er06 .925E+06
.255E+07
.'t58E+07 .2768+47 .435E+07 .639E+o7 .893€+0? .545E+05 .
1
50 E+06
.308F+06 .519E+06
,850E+06 .17 4E+07
.375 .375
.523E+ a7
.3? 5
.1448+08
.305E+07 .481E+07
.212E+08 -?96E+06
.797p+O7
.9878+07
.141E+05 .390E+05
.471E+04
.800El05
.267E+05
.140E+06
.4 66 E+0 5
.375 .375 .154 .'t 54
.154 .15 4
.'l56 .154 .154 .154 .154
.'t54 .216 -216
.216
3. 500
.216 .216 .216
3.500
.217E+O7
.423E+ A7
.7 40t+07 .1178+08
.162Er07
3. 500
3.500
.'l2 4E+07
.436€+06 .687ErO6
. 164E
-37 5
.389E+05 ,107E+06 .220E+O6 -384E+06 .606E+06
-131E+07
.206E+07
.2688+08
22 .00 0 22 .000 22 .000
2.375 2.s75 2.375 2.375 2.375
.748E +06
.375 .375
22.000 22.d00
.2l l E+08
-375
22.000
22 .000
.1 51 E+08
.827E+07 . t 30 E+08
22 .000
22.000 22.000
.373E+07 .652E+A7 .103E+08
.172E+08 .239E+08
20.000 20.000
.610E+07
.3658+46
18.000 18.000
20.000 20.000 20.000 20.000 20.000 ?0.000 20.000
.437E+O7
.132E+O6
18-000
20.000
. 131 Er08
.1838+08 . t l7E+06 .3228+o6 .6608+06 .l l5E+07 .182E+07
-216
.914E+O7
.130E+05
.220E+O6
.735Ero5
.452E+06 .790E+06
.151E+06
.263E +06
.125e+07 .183E+07
.416E+06
.580E+05 .119E+06 .208E+06 .328E+06 .67 3E 106
. 195 E+0
.l1EE+07
.39?E+06
.256Er07 .?10E'05
.611E+o6 .E53E+06 .7018+O 4 5
.J97E+05 .693E+05 .109 E+06
.?248+06
Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued R0TA vEssEl-
OD.Fl
STIFr CALCULATION, CYL. VESSEL
VESSEL lCKrIf{
NOZZLE
OD,IN
NOTZLE ROT SII F IN.LB/DE6
TCKTIN It'lPl-AllE
SID
LONGI
0UTPLANt CIRCU
.500
1.500
.216 .216
.186E+07
4.500
.381Er07
.237
.278E+05 .766E+05
.927e+04 .255E+05
.237 .237 .237 .237
.157E+06
.524E+O5
7.OOO
.250 .375 .500 .625 .7 to 1.000 1 .250
.618 E r0 6 -909E+06 .1278+O7
7.00 0
't
7.000 7-000 7.000 7.000 7.000 7.000 7.000 7.000 7.000
1
3-500 J .500
1-750 2.000
4
4.500 4.500
4. 500
4.500 4
4.500 4.500 6 .625
2.000
.250 .375 .500 .625 .750
7 .OOO
7.000 7.000 7.00 0
7.000 7.000 7.000 ?.000 7.000
7.00 c 7.00 0
7.000 7.OOC
.37
.7 50
I .000
1.000 1.250 1 .500
I .5C0
1.750 2
.000 .25D
.625
4.625 10 .750
10.750 10.750 10.750 10.750 10 .7 50 t 0.750
12.750 12.750 12.750 12.750 12.750 12.750 J4.000 14.000
.6?5
1
7.O0tJ
I .000
7.000
. 239E
+
06
.2AO
.4188+06
.260
- 659E+06
-280 .2E0
.135E+07
.
?80
.322 .322
.322 -322 -322
.62t
7 .OOA
1.250 1.500
.2E0
8 6
'14.000
7.000
.422t+05 .tJ6E+06
.322
. 500
.? 50
.280
4.625 4.6?5
7.00 0
7.000
.360E+07 .503E+07
.?36t+07
4.000 14.000 14.000 14.000 14.000
.365 .56 5
.365 .365
.870E +06
-179E+07 .3'l2E+ 0? .192E+07
.375 .375
.1648+O7 .337E+O7 -234E+O5
.398E+06
.133€+06
.695E+06
-232E+06
.194E +06
.110Er07 .225E+07 .393E+07 -911E+07
.646E+05
.565E+06 .750E+06 .131E+07 .207E+07 .3048+07 .424E+07
.2828|05
.777E+O5 -159 ErO6 .27aE+Q6 .439E +06
.13?ErO7 .271E+07 .4738+07
.902E+06
.7 45E+07
-24EE+O7
.l'l0E+08
.1 53E+0E - 936E+05 .752e +06
.529E+06 .9 25E+06
.146E+07 .2998
.375
.596E+06 .'l o 4E+o7
.101E+08 .703E+05
-E458+05 .23f,E+06 .4 78€ r06 .E35E+06
.375 .375
.105E+06 .184E+06 .290E+06
.241E+Ol
-375
.37 5
.183E+07 .?55E+ 07
.7 24E+ 07
.1278+08
-5at
.1f,9 E +06 -220E+O6 .4 5'l E+06 .78 7E +06
.1868+05
.365
.t75 -37'
.168E+07 .111E+05 .3EE€r05 .797E+Ot
E|05
5 5E
.620E+07
.37 5
.1208+O7
.124E+07
.365 .365
-36'
.518€+06 .817E+06
-3738+07
.5 48 E+07 .7 65E+0?
I .625
1? -750
1.000 1.250
-237
.245E+07
.154E+D6 .316E+06 -552E+06
-625
.7 50
.297E+O6
-
.500
.750 2.000
.7 41e+O6
.890E+06
.1558+07
.280
.916E+05
.4338+06
8.625
10.750 10.750 10.750 12.750 12.750 12.750
1
.2758r06
-217
.237 .237
.2 80
.500 .625
7.00 0
7.000 7.0c0 7.000 7.000 7.000 7.000 7.000 7.000
6.625 6.625
5
1.250 1.500 1.750 2.000 .250
-625
6 -625
.500
7.00 0
7.000 7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.000 7.000
6
1.750 2.000 .?50
7.00 0
7.000 7.000 7.000 7.00c
6.625 6 .625 6.625 6.625
I .000 1.250 1
.500
4. 500
.500
7.OOO
7.000 7.000 7.00c 7.000
.500
rAl
.'l
58 E+0 7
.365E+07 .510ErO7 .312E+05
.859E{05 .17 6E+06 .30EE+06
.4E68r06
.998E+06
.SZ3E+Oz
.17 4E+O7
.825E+07
.275e+07
Vessels
133
134
Piping Stress Handbook Table 6-1 Continued ROTA VESSEL OD, FT
7.00 0
7.000 7.0 00
7.000 7.000 7.000
7.00q 7.000 7.00 0
?.000
7.00 0
7.000 7.00
0
7.000 7.000
7.0 00
7.000 ?.000 7.000 7 -DOO
i
7.000 7.000 7.000 7.000 7-000
7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.00 0
7.000 7.000 7.000 7.0c0 7.000 7.000 7.0c0 7.000 7.0 00 7 .OOO
7.000 7.000 7.000 7.000
7.00 0
7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.0c0 7.000
SIIFF CALCULtII0NT CYL. VESSEL
VESSEL TCKTII{
1.759 2.000 .250 .375 .5rr0 .625 .750 I .000 1.250 I . 500 1.750 2.000 .250 .375 .500 .625 .750 1.000 1.250 1.500 1.750 2.000 .250 .375 . 500 .625 .750 1.000 I .250 1.500 1.750 2.000 .250 .375 .500 .6?5 .750 't .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1 .250 1 .500 1.75A 2.000 .250 .375 .500 .625 .750 r.000 1 .250 1.500 1.750 2.000
ZLE ROT STtF IiI.LB/D€G N INPLANE OUTPLANE CIRCU STD LONGI
NOZZ L E
NOZ
OD'IN
ICKTI
.f218.08
14 -000
14.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000
-375
.375 .375
.404E +O7
,loEE+06
.565E}07 .360Ef05
.298E+06 .611 E+06
.204€+06
.
t 69E+ 0E
.107Er07
.992E+O5
.3568rO6 .561E+06 .l l5E+07 .2018+07 .318E+07
.375 .375
.168E+07
.375
.9538+07 .140€+08 .1968+08
.375
.
.408 E+05
.346E+07
.604Er07
.467E+O7
.652e+07
18.000 18.000 18.000 18.000
.375
I 22 E+06 .338 E+06 .693E+06
.375
.121E+ 07
.113E+06 .23'l E+O 6 .4038+06
.191Er07
.636E+06
18.000 18.000
.375
.392E+07 .685E+07
.131E+07 .226E+07
.375
.1 C8 E+0E . 1 59E+ 0E
.360E+0 7 -529E+Oz
.222E+08
.739ErO7
.375
.1378+06
.457E+05 .126E+O6
.375 .375
.377E+06 .775E+06 .135E+07
1E.000
'18.000 1E.000
18.000 20.000 20.000 20.000 20.000 20.000 ?0 -000
20.000 20.000 20.000 20.000 22.000 22.000 22 -OOO
22.000 22.000 22.000
.375
.37 5 .37 5
.255E+O7
. 121E+08
.5058+05 . 139
.150E+07
.499E+06
.857€+06
.37 5
.236E +07
.s75
.485€+07 .847E+07
.16?E+a7 .?82ErO7
.134E+0E
.445E+O7 .654E+07 .914E+07
.37 5
.'l96E+08 .27 4erOE .166E+06
.375
.4578+06
.375
.259E+07 .531E+07
24.OOO
-375 -375
26 -OOO
E'06
.266Er06
.375
24.000
26.000 26.000 26,000 26.000 26.000 26.000 26.000
.5928r07 .626Er07
.417 E+06
.37 5
24.000 24.800 24.000 26.000 26.000
.4038+07
.151E+06
.938E+06 .1 648 + A7
24.OOO
.146E+07
.375
2?.ogo
24.000 24.000 24.000
.71?Ero6
.436E+07 .7 66a+07
.37 5
22.000 24-000
.451E+06
.2138+07
.178E+08 .248E+08
.3?5
22 -OOO
22.OOO
.258E+06
.9?7E+07 .1 46Er08 | 5E+08 .3 00E +08
.3 75
-2
-37 5 .37 5
.180Ei06
.375
.497ErO6
.375 .375 .375 .375 .375 .375 -375
.lcz€.07
.787E+O6
.5 53E+0 5
.152E+06 .313E+06 .546E+06
.862E+06 .177E+O7 .309 E +0 7 .488 E +0 7
.717E+07 .100€+08
.60',|Ef
.l
05
66Er0 6
.340E+06
.17EE+07
.594E+06 .9378 +06
.577E+07
.192E+07
.28'lEr07
.101 E+0E .'159E+08 .2 348 | 08
.3?7er08
.336€+0 7
.530Er07 .779E+O7
.109E+08
Rotational Nozzle Flexibilities for Cylindrical
Vessels
135
Table 6-1 Coniinued R0TA VESSEL
OD,FT
E
SS€L ICK,IN
VE
-00tJ
8.000
E.0c0 E.000 E.00 0
.375
?.375 2.375
.7 50
2
.000
1
1.250 1.500
1-750
E.000
2. 000
E.000
.37
.250
8.000 E.0c0 E.000
8.000 6.000
2.3?5 2.375 2 .375 2.375 3.500 .500 .500
.7 50
3. 500
.000 'l -250 't .500
3. 500 3 .500
5
.625
1
1.750 2.000
-250
8.0c c
.500
E.000
.750 I .000
6.000 8.000 8.000 8.000 8.000 8.0c0
2 -375
.500
[.0c0
8.000 8.000
.375
3 3
8.000 6.000
E.000 8 .000
NOzZL€
OO,IN
.500
8 .000 8.0c c E.0c0
6.000
STIFf CALCULAII0N, CYL. V€SSEL
.625
1.250 1.500
3.500 3.500
3.500 3. 500
4.500 4.500 4.500 4.500 4
.500
4.500 4.500 4
.500
/.. 500
.500
.000
4
.000
.500
E.000
.7 50
6.625 6.625 6,625 6.625
8
8.000
?
1
.000
8.000 8.000
1.250 1.500 1.750
8.CCC
2-AAO
E.000
8.000 3.000 8.000 6.000 8,000 8.000 t.000 8.000 8.000 6.000 1i .00c 8
8.000 E.0c0
6.000 8.000
tt.625
8
8.625
1.?50 .500
.500
.625 .7 50
.625
8.625 8.625
.750
1.750 2.000
-6?5
8.625
I .000 1
.6?5
6.625
8
I .625 8.625
10 . 750 10 . 750 10 .75 0
0. 750 1 0 .750 't
10.750
.000 1.?50
'10.750
't .
10
'I
500
8.CC0
E.000
6
.500
.000
.000 .000
6.625
.2 50
8.00c 3.000 E E
6.625
2. 000
.250
.750
10-750 't 0 .750 12.75t)
12,750
ZLE ROT STI f IN.LB/DEG N INPLANE OUTPLANE CIRCU LONCI STD NOZ
rCK,I
-154 54 .'154 .l54 -151 -154 .154 .154 -154 .154 .216 -2'.t6 .216 -216 .216 .z',t6 .216 .?16 .2'16 -2't6 .237 .?37 .237 -237 -237 .237 .23? .?37 .237 .237 .280 .280 .280 .280 .2 80 .280 .280 .280 .280 .280 .322 .322 -322 .32? .322 -3?Z -322 .322 .322 .3?? .365 .365 .365 .365 .365 .365 .365 .36, .365 .365 -3?5 .375
.1
. 132 €+0 5
.364€i05 .718E105 .',l31€+06 .2A6E+06 .423E+06 .7-19
E
+06
.117E+47
.171E+ol
.441E+04 -121ErO5
.2 49 E +O5
.436E+05 .687E+O5
.1418+06 .2{,68+O6 .389 E +06 .57?E+O6
.239E+O7
.7988+06
.197 t+Os .5 4ZE+05
.181F+05
.1118+06 .194F+06
.307Er06
.6 30€ +06
.1108+07 -17 4E+07
.255E+ol .356t+07
.260 E+ 0 5 .717E+05 .117E+O6
-?57 E+C6 .4058 +06 .832E+06
,1158+07
-2?9E.07 .3378+07 .4?18+07 .195F+A5 .109E+06 .?24E+46
. 391 E+ 06
.6r6E+06 .126E+07 .221E+ 07 .349E+O7 .5'12E+O7 .715E +O7
,656E+O4 .371E+05
.6488+05
.102Er06 .210Er06 .367E+O6
.578E+06 .8508+06 .119€+07 .8678+04
.27
L
7
E+O6
.4858+06 .7 64E+O6
.112E+07 ..|.57
E+
07
.132€+05 .363E+05 .745E+05
.130E+06 .2058+06 .422E+06 .7368+O6 .116E+O7 -'171
E+ 4 7
.238Ef07 -17 4E+05
-480E+05
.1 67 E +O7
.292E+47 .4618+O7
.9858+05 .17?E+46 .271E+06 .557 E+O6 .973E+06 .1548 +O7
- 677E+07
.2268+07
.9 45E+07 .658€+05
.315E+07 .219 E+45
.181E+06 .37?E+06 .650E+06 .',l03E+07 .2108+ 07
.6048+05 _124ErO6 .217E+o6 .3 42E+O6 .701E+06
.
3 68 E+
07
.580 €+07 .853E+07
.1198+08 -791E+05 .216E+06
(
i
.144E+46 .29 5 E f06 .e14E+06
\
.239E+05 .490E+05 .857E+05 .135E+06
.5228+05
.516Er06
l:
.1?3E+o7 .193E+07 .284E+17 .397 e+O7 .2 64e+ 0 5 -726E+OS
(
136
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATION, CYL. VESSEL VESSEL
VESSEL
OD,FT
ICK,'N
.500
8.00 0 8 .000
8.000 8.000 8.000
8.00 0
8-0cc 3.000 8.000 8.000 8.000
.7 50
I .000
1.250 1.500 .000
2
.2 50
E.000
8.000 6.000 E.000 8.0c0 6 .00c 6.000
.625
8.000 8.000 8.00
0
8.000 E.000
8.000 8.000
.75A I .000 1.25O 1 .500 1 .75A
2.000 .250
E.000
8.000 8.000 5.0 00 E.C00 3
.000
.0c0 8.000 6.000 8.000 8.000 8.000 E
8
.000 I .000 E.000 6
.000 8.000
E
E.000 E.000
6.000 6.000 6.000 8.000
.'136E+07
.230E+07
.489E+07
-163E+O7
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.7 72E+ 07 .113F+08
.1018+06
.337Ef05
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.9?8E+05
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1 1
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.750
2.0 00
.250
.375 .500
.t91E+06
.999 r+06
.333E+06
.1588+07
.525Er06 .1088r07
.565E+07 .891E+07
.188E+07 .297E+07 .437E+C7
.131E.C8
.375
,163E+08
.64tE+06 .1?9E] 07
6.000
18.000 8
.000
20.000 20.000 20.000 20 .000
0.000
20 .000
20.000 20.000 20.000 20.000
.367E+d7 .641E+ 07
.375 .375 -375
.375 .315
22.000
1.250
.5?8E+o7
.572E+O6
.323Er07
22 .OOO
1
.378E+07
,610E+07
.377E+06 .595E+06 .122E+O7 .214E+O7
1
. ?50
.15EE +08
.113E+07
.7 5A
,500
.804€+05 .1658+06 .288a+06 .455F+06 .934E+06
.1058+06 .216E+06
2
.0c0
.292E+05
.316E+06
I
E.000 E.000
.875€+05 .241E+ 06
I E. 000
.625
.000
.342E+O7 .47 7 a +o7
.382E+05
.000 1 6 .000
1.250 I .500 1.750 2.000
-143E+08
.1 15E+06
18.000
.7 2. 0c0 'ti
E.C00 8
6.000 6.000 16.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000 16.000
18.800 't E.000 1 E .000
1
oz
E+
.375
1 1
1E
.625
.4'l1E+O 6
.'l0f €r08
14 .000
1.000 1 .250 1.500
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8.000 E.0c0 8.000 8.000
.000
.149E+06 .260E+06 .E44E+06 .117E+O7 .232E+O7
.E65E+06
4
CIRCU
.123E+ A7
.697 -375
OUTPLANE
.253E+07
.4128+07
'|
.500
1
.731r+06
.000
1
.000
.4 47E+06
.495€.06
1
.500
TCK,IN INPLANE STO LONGI
11 .000
t .000 1-?54 'I .500
8.000 E
't2.750 I 4.000 I 4.000 4.000 1 4.000 1 4.000 14.000
E.000
NOZZLE ROT STI F It.I.LB/DEG
1?.750 12.750 12 .750 12.750 12.750 12.750 12.750
14
.7 50
.750 2.000 .250
t,000
0zzL€
OD,III
2? .OOO 22 .O00
22.000 22.000 22.000 22.000
.5f>
22 .OOO
22.000 24.000 24.000 24 .000
.37
5
.101E+08 .'149Er08 .207E+08
.1288+06 .355E+06 .725E+ 06 .127E+O?
.200E+o7 .410E+07
.7',16E +07
.337E+07 -495E+07 .691 E! 07 .427E+05 .118E+06 .Z 4ZE+O6
.122E.O6 ,6668+06 .137E107 .239E +O7
.1'13E+08 .166E+0E .212E+0E .112E+06 .390E+06 .E0'l E+06
.377E+07
.1 40E+07
,2218 + A7
.467E+O6 .736E+O6
.453E+07 .79?E+07
.264Er47
.1 25€+0E .184E108 .256E+0E
.155€+06 .428€+06 .8
7EE
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o6
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.15'lE+07 -4'16E+07
.6128+O7
.855E+07 .517E+05
.143E+06
.293Er06
! Cylindrical Rotational Nozzle Flexibilities lor
Vessels
137
Table 6-1 Continued ROTI STITF CALGULATI0N' CYL'
VESSEL
NOZZLE ROT STI F ItI'LB/DEG.,
:::?i' Y:l:ih i8:ii' iii;io lii:l-' 8.000 8
.000
8.000 8 .000 8.000 8.000 8.0c0 8.000
E.000
8.000
.7 50
t .000
1.250 1.500 1.?50 2.000 .500
.000
.625
8.000 8.000
.0c0
8
.7 50
.2 50
E.000 8 -000
8.000 8.000 8.000 8.000 8.000 8.CC0
8.000 .000
6
8.000 8.000 8.000
.000 .000
8
6
8.000
.000 I .000
8
8.000 8
.000
8.000 8.000 8.000 8.00 0
.500 .7 50 2
.000
-250 .500
.625
.750 1.000 1 .250 1.500 1.75u 2.000 - 500
.750 I .000
1.250 1.500 1.150 2. 000
24.000 24.000 24.000 24.000 24
-000
24.000 24.000 26.000 26.000 26 .00 0
26.0c0 26.000 26.000 26.000 26.000 26.000 26.000 28 .000
28.000
28 - 000
28.000 28.000 28.000 28.000 28.000 28.000
28 .000
30 .00 0
30.000 30.000 30.c00 30.0c0 30.000 30.000 30-000
30.000 30.000
9.000 9.O00
t00 .625
.
.000
9
9.000 9.000 9.000
1
9
1
.000
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.000
9.J00 9.000 9.000 9.000
.7 50
.000
.250 'r.500
1.750 2.000 .2 50
.500
2.175 2.375 ?.375 2 -375
2.375 2.375 2.375 3.500 3.500 3
.500
.7 50 1.O00
3'500 3.500 1.500 3.500 3.500
1.750
3
.000 .250
4
1.250 1.500 2
.500
3.500
.500
4.500
'i;i 'iti
'-1?i 'i;;
+07 -212F --istz'oz
-doee*oz . t:zt* oc
3!l:i^*' .E06E+06 7 ' 166E+o
.2q?!.91
'-1;t .zott+oa -456E+o7 '9!1,t-'9! .23'1E+0E 'Yl!:':' -375 'izi 'i;; '1;a
'.1it
1695+06 { 06 954g+06
- 465€
'5 621+o5
.155€+06
'3'l8Eio6
167E'07 '119!'96 ' :.. .E778+06 t A\F +o7 'it'. liioE'oz '.1?; i a31+ o7 '180E+67 '3\tq-+o^! 0E '1:9'-:Y' -375 .'l1et '-.ii -2196+08 '7298+o7 ':'-i an
:i;i;-o; :i+; '\zi 5ozF{06
.991!:95
167F +06
o7 '.314E+o6 .taOr*oz .600F+06 -28|E+oz '9 47 E+06 .igre. oz '1918+G7 . i ozr.oa '340F+07 .1615+08 '5368+07 .2 36g+oE .788E+07 .!366+oa '119:lo8 - 196E +06 '653F+05 sloE+c6 '180E+06 -l6eE+06 -ittt'oz --1s4E+o7 '9!28-+D6 3o5E+o? '102E+07 '-i?; -.iriE+07 '!9:!*07 16e5+08 '1!5.1-.ol .1i; '.;;;'17r8+08'1.6.1'.07 'i;i '8168+o7 'i545+08 ' z:le + o8 '-i?t
'iii 'i.;i 'i;4 'i|i '-i?t 'i;i 'iri, '.ir; ';;< 'i;. '|;i '.3;; 'i;.
-
163 6+
'118E+08
1at '-a;i ;;; '-;;i '.4;i
'-;ti
-'l25t+05 '416€+04 314t+ 05 ' 1 'l 5 +o s io5r+05 '235E+os5 :123E.06 ''le4E+06 ' 411E+o '6488+c5 -3eeE+o6 '111!'06 E
'.::: -lziiili ':l; ':l', ';'.; '.i;i rni '.tiz rie 'r;A
'.ia; ';;; ';;; '-i;; "r;i '.i;?
' i ))i ' )Jli,iz 'iz
aii
'.1":,i::"2 .53eF+06
-t5zE+o6
'618E+o/' os '170E+05 :5118 'os -105E.06 .35oEro5 -r
+
1E3F+06
-289F+06 -594E+06
'91.1E-+o5
'964E+05 .198E+06
16r,E+07 '119I'06 - 164E + 07 ' 51'55+06 .? L1E+o? .8 0 2 +06 +oz 3362+a? |z-tE+oL 't15E+05 "t '4768 +o5 +05 'E't7 '225F F
l,
Piping Stress Handbook Table 6-1 Continued
R0lA SllFr CALCULATI0NT CYL. VESSEL
OD,IT
VESSEL TCK,IN
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.500
.625
.750 I .000 1.250 'l .500 ?.000 .250
.375 .500
.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
.7 50
1.000 I .250 I .500
1.750 2.000 .?50 .375 .625 .750 .000
.250 .500
9.0 00
9.000 9.000 9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.00c 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
. 750
2.000 .500 .625
.750
I .000
1.250 '| .500 1.759 2.000 .250
.375 .500 .625 .750 I .000
1.250
NOZZL€
NO?ZLE
0DrIN
TCK,IN
4.500
4. 500 4 .500
4.500 4.500 4.500
.75C .000
.250 .500
.750 2.000 .250 .375 .5 00
.462e+o,
-2 42e+06
.808 E+05 .1?7E+O6 .262E+O6 .457E+O6 .7218+O6
.237 .237 .237 .237
.382Er06
.785E+06 .137E+O7
6.625 6.625
.148E+07
.2E0
.373E+05
.121ErO5 .3 4?E +0 5
6.62
.2E0 .2E0
-103€+06
.?118+06
.703€i05
.3688+C6
.123E+06 .194E+06
5
6.625 5.625
.237
6 -625
.280 .?80
6 -625
.280
6 -625
6.625 6.625 8.625 8.625 4.625
I .625 I .625
8.625 6.OZ)
.62> 8 .625
6
8.625 10.750 10.750 10.750 10 .750 10.750 10.750 r 0.750 10.750 10.750 10. 750
12.750 12.750 12.750 12.750 12.750 12.750 12 .750 '12.750
.625
. '1 39 Er 06
-237
.444E+07
2. 000
.500
.237
.216e+07 .318E+07
12.75D
.250
f IN.LB/DEG INPLANE OUTPLAI{E Lol,Gl CIRCU ROT STI
-237
,.. 500 4. 500
1
,500 t .750
slD
V€SSEL
14.000 '| 4.000 'r 4.000 14.000 't 4,000 14.000 14 .000
14.000 I 4.000 't4.000 16.000 16.000 16.000
.2 80
.280 -322 .32?
.58'l E+06 .1198+07 .208€+07 .329F+07 .433E+07
-1O6E+O7
.f,97E|06 -694E.06 .t10E+07 .161t+07
.67 4E. 07 .492E+05
.?25E+07 .164E+05 .452ErO5
.3ZZ
.279E+06
.92E E+0 5 -162E+O6
.322
.158E+07 .275E+87
.525Er06
.322 .3?2 .3?2
.322 .322
.365 .365 .365
.56 5
.365 .365
.136E+06
.437Fr06 .?68Ef06 -4348.07
.6388+07 .691E+07 .620€+05
.17'l
E+
06
.351E+06 .613E+06
.256E+06
.918E+06 .145E+07 .2138+O7
.297E+07 .207E+O5 -
5
70E+0 5
-117
E+O 6
.204E+06
.967Er06
-322E+O6
.'198Er07 .3 478+07 .5478+07 .804E+07
.661E106 .116E+07
.1'l2Er08
.1E2Er07 .2688+C7 .374E+07 .249E+05
.37 5
.746E+05 .205E+06
-375
.737E+06 -116E+07
.387Er06
.375
.239E+07
.795E+O6
.417 E+07 .657a+ A7
.219E+07
.375 .37 5
.175 .375
.422Er06
,685E'05 -141E+06
.246E+06 -'t 39 E+O7
.9 6?E+07
.322E+ol
.275Er05
-375
.135E+08 .825E+C5 .227E+06 .4 67 E+ 06
.815E+06
- 156E+06
.3? 5
-375
.129 E+07 .264E+07
.429E+O6 .880 E +06
.37 5
.4618+07 .728E107
.154E+O?
.37 5
.107E+08 .1 49€+ 08
.37 5 .37 5
.375
.375 .375
.953Er05 .263E+ 06
.375
.539 E+06
.450E+07
.758 E+05 .272E+O6
-243E+o? .357E+0?
.498€+07 .5
'13 g
r05
.875E+05
.lE0Ero6
Rotational Nozzle Flexibilities for Cylindrical
Vessels
139
Table 6-1 Continued ROTA VESSEL
OD,FT
9.0c0 .000
9
9.0c0 9.00
0
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9 .0c0 9.000
9.000 9.000 9.0c0 9.000 9.00
.625 .750 1 .000 1.500 1.750 2 .000
.250 .500 .625 .7 50
9.000 9.000 .000
9
9.000 9 9
.000 .000
9.000 9.000 9.000 9
.060
9.000 9.000 9 .000 9 .000 9 -0 00
9
.000
9.000 9 9
.000 .000
9.000 9.000 9.000
.000
E. 000
1
18.000
t8.000
18.000 18.000
20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
.500 .000
.2 50 1.5C0 't
1.750 2
16.000 16.000
.250
?. 000
1
16 - 000
18 .000
.000
'1E 1 '|
.00 0
8.000 8.000
18 .000
.?50
22 .000
.500 .6?5
22 .OOO 22 .00 0
.7 50
2
I .000
1.250 1.500 1.750 2.000 .?50
9.000 9.000 9.000
9.000 9.000 9.000 9-0c0 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000
16.000 16.000
.000 .25D .500 -750
0
.000
6, 000
1
16
9.000 9
VESSEL
VESSEL NOZILE NOZZLE ROT STIF IN'LB/OE6 TcK,IN TNPLANE oUTPLANE oo,rH ;;i;;N CIRCU LONGI STD
.000
9
SIIFF CALCULATION' CYL.
.500
.625 1.000 1.?50
t.500 1.750 2
.000 .250
.375 .500 .625 .?50 r .000
1.250 1.500 1-750 2.000 .250 .500
.625
22.000 2
.000
22.000 2? .OOO
22.000 ?2 .OOO
22.000 24 -000 21-OOO
.000 24-000 24
24.000 24.AOO
24.000 24.000 24.000 24.000 26.000 26.000 26.000 26.000 26.000 ?6.000 26,000 26.000 26.000
26 - 000 26 .00 0
28.000 2E
.000
28.000
.375 .375 .375 .375 .375 .375 .375 .375 .375 .3?5 .3?5 .3tS .3?5 .375 .3?5 .3?5 .375 -375 .375 .375 -3?5 .375 .375 .3?5 .375 .375 _37, .375 .375 .375 .3?5 .375 .3?5 .3?5 .375 .375 .3?5 _375 -37, .375 .3?5 .375 .375 .375 .375 .3?5 .375 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 -3?5 .375 -375 .375
,941E+06
.149Fr07
.3148+06 .495E+06
.305 E+07
.'l02Er07
.533E+07
.
.840E)07 . 1 24 E+ 08
1
78€ +07
-280E+0? .412E+O?
.172E+08
.5'58+07
.6118f06
.2L
.108E+06 .2988+06
.3,,0E+05 .9928+05
.1O7E+O7
.3568f06
.168E+02
.346Er07 .604E +O7
.953E+O7 .',|40E +08
.196E+08 . 121 E+06
4E
+46
.561 E+06 - 11
5
E+Ol
.201F+O7 .318E107 .467E+07
.652E+07
.403E+0t
.53fE+06
.1118+06
.683E+06 .119E+07
.3988}C6
.188 € + 07 .3FZa+O7
.228E +o 6
.628E+06 .129E+07
.675E+07
.2258+07
.1078+0E .157E+oE .219 Er 08 .1J4 €+06
.7 29 E+A7
.368E+06 .755€106 -132t +o7 .208E+07
- 427 6+O7 -7 47E+07
.,'166+06
.355E+07 .5??E+a7 .445C+05 .123E+06 .252E+06 -440E+06 .694E+06 .14?E+ 07
.?49E+07 -J93E+07
.173E+08 .2129+oE
.577 E+O7 .806E+07 .488E+05
.4639+06
.134E+06
.1A6t+46 .EZ8E+06 -1458+ 07
.228E+07 .468E+07
.27
6E
rO6
.482ErC6 .760E+06 - 15 a,E+07
.1908+0E
-273E+O7 .430E+07 -632E+o7
.438E+06 .900 E+ 06
.530E+05 .'116E+06 .300E+06
.'l57 E+O7 .2 482+07
.521E+06 .827E+O6
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.296e+o7
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18
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+
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.129Er08 .265E +08 .1 59E+06
.5098r07 - ',149E+08
.206E+08 .288E+08 .172E+o6 .4718+ C6 .972E+ 06 .170E +O7
.883E+07
.17oE+ol
.468Ei07 .68?E+07
.960E{07 .573Er05
.1588i06
.32 4E+o6 -566E+06
l,
140
Piping Stress Handbook Table 6-1 Continued ROTA STIFT CALCULATION,
EL TCK,IiI
VESSEL
VESS
OD,FI
9.000
9.000 9.0c0 9.000 9.000 9.000 9
.000
1.000
1.2rO 1.750 2. 000
.250
9.000
9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9
.000
9.000
.500
.625 I .000
1.250 1
9.000
.500 .625 .?50
9.00 0
9.000 9.000 9.000 9.000 9.000 9.000
t.000 t.250 1.500
.750 2.000 1
10.000
.250
r0.000 1
0.00 0
r0.000 10.000 10.000 10.000 10 .00 0
10.000 10.000 '| 0.000 't0.000 I 0.000 10.000 10.000 10.000 10.000 '10.000
10.000 10.000 10.000 10.000 10.000
. 500
-625
-750
I .000 1.?50 I .500 1.?50 2-000 .250 .37 5 - 500
.625 .750
I - 000 I .250 1 .500 1
10 .000
10.000 10.000 10.000 10.000 10.000 10.000 10.000
.750
2. 000
.250 .500
.625
10 .00 0
10.000
.500
1.750 2.000 .250
.750 1.000 1
.250
1.750 2.000 .250 .500
VE SS EL
NOZZLE
NOZ ZLE
ROT STI
OD,IN
TCK,IN
INPLANE
STD
LON
28.000 ?E.000 2E.000 ?E.000 28.C00
28.000 30.000 30.000 30.000 30.000 30.000 30.000 30.000 30 .000
30.000 30.000 5 2.000 32.000 52 .000
52.000
.000 .000 52 .000 3 2 3 ?
.375 .375
4. 500
4.500 4.500 4.500 4.500 4.500 4. 500
4.500
6.625 6.625 6.625
- 268
E
+07
.550E+07
.37 5
-31tE+0E
.375
.375 .375
.2 23E +08
.185f+06
.509E+06 .104E+07
.182Ei07 -375
.375 .375 .375
.268€+07 .591E+07 .103E+0E
.163E +08
.239E+08 .334E+06
OUIPLANE CIRCU
.E93E+06
.183€+07 .320E+07
.5058i07 .7 438+O7
.1048+0E .6158+05 .1 708+06 +06
- 348 f
.608 Er06
.959Er06 .197E+O7
.344ErO7 .543E+07 .7988+07 .1 'l I E+08
.375 .375 .375 .375
.197E+06 .544E+06 .1t2E+Oz
.l8J
.195E+o7
.37 5
.3088+07
.650E+06 .1of,E+07
.375
2.375 2.3?5 2.375 2.375 2.375 2.375 2.375 2.375 z .375 2.375 3.500 1.500 3.500 3.500 3.500 3.500 5.500 3.500 4.500 4.500
6I
.t75
.3?5 -375
-500
F It{.LB/DEG
.9 61e+07 - 1 52Er08
32.000 32.000 52.000
3
CYL.
-
632E+07
. 1 10E +08 - 174E+ 08
.658Er05
E+06 .372E+O6
.211E+o?
.3688+07
.5808r07
.375
.256€+0E .357E+08
.E538+07
.'t 54
.'tt8E+05
.594E+04
.326E+05
.109 F +0 5 .2?3e+O5
.1t4
.154 .754
.669€+05
-154
.1848+06
.151 .154 .154 .154 -154
.216 .216
-216 -216
.216 .216
.117E+06 .3?9E+06 .661E+06
.104E+07 .153E+07 "214E+07 .176E+05 .485E+05 .996E+05 .17 4E+06 .27 4E+ 06
.563E+06
.?16
.216
- 9 84 E+06 .155E+ O?
.z',t6
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.714Ero6 .587erO4 -162E+05
.332E+0 5
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.915€+05 .18EE+06 -328E+06
.517Ei06
.7618+O6 .106E+07
.2338+05 .6418+05
-775E+O4
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.439E+05 .766ErO5 .121E+06 -2488+06
.363€+06 .714E+06
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.237 .237 -237
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.97 4E+05
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.280 .280
.130€+07
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.302E+07 .42'lE+07 .2C0
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06
.'101 E+07
.667Eros
Rotational Nozzle Flexibilities for Cylindrical Vessels
141
Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL
OD,FT
'l
0.000
1
0
VESS€L NOZZLE NOZTL€ RO] STIT IN'LB/D€G TCKu IN TNPLATJE oUIPLANE 0D,rN i;i;iN CIRCU STD LONGI 6.625 .7 50
.000
.000
10. 00 0
10.000 10.000 10.000
1.750
10 .0 0c
2
.2 50
.500 .000
.2 50
10.000 '| 0.000 10-600
.500
10.0c0 10.000 10.000 10.000
.7 50
'10.000
.000
,250
6.625 6.625 6.625 6.625 6.6?5
I .625 I .625
8.625 8.625 a a
.6?5 .625
a.625
.750 .2 50
10 .750
.000
2
10.000 't 0.000
.6?5
8 .625 a - 625
.500
't 0 .000 't 0.00 0
6
I .625
0
.500
10.000 10.000 10.000
10.750 10.750 10.750
.7 50
10 .7 50
1u.0
0
0.0 00 '10.000 1 0.00 0 10.00 0 10.00 0 1 0.00 0 1
1 1
.000
1
.500
.250
1.?50 2.000
.250 .37
5
10.750 10.750 10 .750 'ro.750
l0 . 750
1Z -750 '12 ,7 50
10.000
.500
1Z .750 12 .7 50
1C.000
.7 50
12.750
.625
10.0c0
10.000
t .000
'10.0c0
1.250
10-000
1
1
0.000
10-000
.500
1-750 2.000
.250
10.000 10.000 10.000
'10-000 1 ri . ti00 1 0. 00c
.625 .7 50 '|
.000
1.250 1.500
'10
2
10.000
10.000 10.000 10.000 10.000 10.000 1 0.000 I 0.000 10.cc0
'i0.c00
.250 .500 .625 .7 50 1
.000
1
.500
1,254
.000
.500
0
1
0.00
0
12 -750 1
4
.000
000
.t/,-000 I 4 .000 14.000
.00c 14.000 't 4.000 14
.000 14.000
16.000 16.00u 16.000 '16-000
16.000 16.000 16.000 16 .000
6.000 6.000 18.000 18.000 18.000 1 8.000
't
2.0c0
1
1Z -7 50
14
.000
10 .0c 0
10.c00 1 0.000
.750 12.750
12
11, -
.500
10.000 10.000 .00 0
'12.750
.2 50
1
.280 .2 80 .280 .280 .280 .280 ,280 .3zz -322 .32? -t?? .322 -32? -32? .3?2 .322 .322 .365 -565 -365 .365 -365 .365 .365 .355 .365 .365 .t75 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 .375 -375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .3ZS -375 .375 -375 .375 .375 .3?5 .375 .375 .3?5
.319 E. 06 .551E+06
.113E+al
.198E+02 -312E+a7 .458E+07
.6408+07 .467E+05 .129E+06
.116E+O6
.184E+06 .377 E+06 .659E+06 .104E+07
.153E+o7 .213E+47
.156E +05
.264E+ a6
.429E+05 -EE'l€+05
.46?E+06 .7 zEE+ 06
.243E+O6
- 1198+07
.261E +D7
.112E107 .606E+ 07
.846€+07 .538E+05
.162Et06 .533F+06 .5818+06
.'154€.06 .498€+06 .870E+06 .'t 37 E+47 .2629+O7 .282E+07
.1968+05 .540€+05 .194€+06
-329E+07
-7 63E+O7
.254E+07
.707E+0, .l95E+06
.2368+O5 .650E+05
06
E+
.'l88€+07 -519E +O7
.173E+Oi
. ',l06E+08
.355E +47
.400E+06 .699 €+ 06 .1,t 08+02
.l33E+06
.2?68.07 .395E+07 .6?48+07 .917E+07 .128E+0E .7E3€+05 .216E+46 .443E+06 .774E+06 .122E+O7 .251E +07 . 4 3EE +07
.690E+o7
.lClE+08 .',I12E+0E
.904E+05 06 .5J',l E+06 .Z 49
E+
.233E+06 .368E106 .754E+06 .132E+A7 -20EE+o7
-306E+07
.427E+07 .261F+05 .719Er05 .1488+O6 .2 5E E+0 6 -407E+06 .835E+06
.j
46E+O7
.23a8+o7 .338E+07 .4728+07 .30 | E+0 5 -830E+05 .120 E+ E 6
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.?9Et+O6
.2 89E + 07
.964Er06
.141E+Ol .5ArE+07 .797 E+07 .'117E+0E
.'164E+08 .102E+06 .ZEZE+46
.5f0E+06 .1c1.E
+
A7
I
.1'lIE+06 .306E+ 0 6 .62ZE+O6 .11OE+07
.917
I
.470E+06 .1688+O7
.266E+07 .391E+07 .545E+07 .31?t+O5 .911t+O5
-'l 938 +06 .338E+06
-l
142
Piping Stress Handbook Table 6-1 Continued ROTA
10.000 10.000 10.000 10.000 10.000 10.000 10.000 1 0.000 10.000 10.000 10.000 10.000 'r0.000 10.000 10.000 I 0.0 00
10.000 10.000 I I
NOZZLE
TCKrlftl
TCK,IN
1.250 1.500 1.750 2.000
1E.000
18.000 .000 .000 18 .000 1E.000
1.750 2.000 .250
20.000 20.000 ?0.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 22 .000
.37 5
22 .00 0
-375
.500
-625 -750
.000 1.250 1.500 'l
- 160E+ 07
.3?5
.573E+07 .904E+07
-533E+06 .1098+O7 .191E+O7
.13fE+08
.375 .375 .375
.lt5Er06
-t75
.375 .37 5 .37 5
.375 .375 -175
I 0.00 0 '10.0 0 0
22 .OOO
1.000
22.000 22.000 22.000
.37 5 .37 5 .3? 5
10.000 10-000 I 0.000 10.000 I 0.000 10.000
't0.000 10.000 10.000 10.000 10.000 10. c00
'10.000
0.000 10.000 10.000 10.000
'|
t 0 -000
10.000 10.000 't 0.000 10.0 0 0
10.000 10.000 10.000 10.000 10.000 10.000
.t75
.375
IRCU
.301E+07 .413E+07
.6'l8Ei07 .382E+05
.316E+O6
.105Ef06
.6488+06
,2168+06 .377E+86
-11tE+07
.179 E+07
.367E+07 .641E+o7 .101E+08 . 149€+0E
.247E+06 .127 E+ 06 .349 E+06 .7178+O6
- 59 5 €+06
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.
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E+0 6 . 417E +06
07 -'l97E +87
.658E+06
.708 El07 .112E+06
.3728rO7
.125E
+
.405E+07
.135Er07 .236Ef07
22.OOE
.375
. 164E'08
2? .000
.37 5
24.000
.375
. ?29E+08 . 1398+C6
.7 64ErO7 .463E+05
24 .000
-375
.3838+06 .78tE+O6
.262E+O6
-375 .375
.1378+O7
.457Er06
.721E+96 .148E+07
-547E+O7
.f288r06
.625
.?59
I .000
24 .AOO 24 .000
.375
.216E+07 .441E+07
1.250 I .500 1.750 2.000
24.000
.375
.776E+O?
.259e+O7
-122E+08 .180E+08
.600E +07
.375 .500
.625 .750 1 .000 1.250 1.500 1.750 2.000 .250 .375 .500 .625 .7SO
I .000
10 -000
l0 -000
.375 .500 .6?5
I 0.00 0
.375
.186E+0E
C
21.000 24.000
.500
1.250 1.500 1.?50 2.000
10.000 10.s00 10.000
.328Er07
-375
.37 5
1.500 t .750 2 .000 .250
F I{.LB/DEG
.3 75
22.000 ?2.000
1.25C
ROT STI
OUTPLAI{E
.500 .625
10.000 10.000 10.000 10.000
VESSEL
STD
t8 1E
CYI.
I!IPLAN€ LOIIGI
'l0.000
t0.000
.l
CALCULATION,
VESSEL
1.000
I 0.00 0
x,
STIfF
. a>u
.7 50
24 .000
24.000 24
.000
26.000 26.000 26.000 26.000
.375 .375 .375 .37 5
26 -000
.375 -375
6.00 0 6.00 0
.375 .375
z
6.00 0
26.000 2 2
26.000 28 .000
28.000 28.000
30.00 0 3 0 .000
30.000
.784E+06
.483Ef07
. l6'l
.8448i07 .133E|08 .196E+08
E+0 7
.281E+O7
.141ErO7 .652E+07 .911E+07
.375 .375
.972E+O6
-307E+O6
.375
50.000
.497E+O6
.235E+07
.5438f05
0.00 0
3
.139E+06 .?85E+06
.163E+06 .449€ + 06
?8.000 ?8.000 28.000 2E.000
.854Ff06 .149Et07
.503€r05
.273€+08
.375 .375 .375 .375
28 -000
.416€+06
.8388+07
.t75
eE.000
28.000
.2 5l E +08 . 15'l E+06
.408Er07
.375 .3?5
.375 .375
.161E+07
.150E+06
.5378r06
.2 54F+07
.847r +06
.522E+07
.17 4E+07
.911e+ 07
.504E+07
.1 44 E+ 0E
.479E+O7
,211 E+0E .295 E+06 .175E+06 .483E+06 .991 E | 06
- 705
.273e+Oz
-910E+06
.l73E+07
Fl07
.984E+O7 .584E+05 - 1618+06
r0 5 -577E+O6
- 330E
Rotational Nozzle Flexibilities for Cylindrical
Vessels
143
Table 6-1 Continued ROTA VESSEL
0D,fT
10.000 .000
10
10.000 10.000 't0.000
STIff
I:i:ii il:ii' I .000 1-?50 1 .500
I .750 2.000
.00 0
'10
10.000 10.0
.500
0 0
0.000 0.030 10.006
.625
1 1
10. c0c '10.000 10
.000
10.000 10.000 10.000 10.000
CALCULATION'
.7 50 1
.000
1.250 1.500 2. 000
.250
30.000 30.000 30.000 50 .00 0
.375 . 51>
.375
.375
32.000 32.000 32.000
.37 5
32 .00 0
3 2 3 2
,000 .000
32.000 32 .00 0
32.000 32.000 36.000 3
10.000 'l0.000 10.000
.150 1.000 1.250
3 6.00 0 3 6 .000
1G.C00
1
36.0c0
-375 .37 5 .37 5
-375
.375
11 .0 00
.250
2-375
.154 .154
.500
2-375
.15 4
2 -375
.15 4
I
'l
'l
l .000
.000 11 .000 11.000 11
11.000 -000
11
11.000
1l.0c0
.000 11.000
'11
1',| .0 00
11.000 11.000
11.000 11.000 'l1.000 11.00c 11.000 11 .00 0 1
I .000
11 .00 0
11.000 11.000
.154
2.375
1.000
2.375
.15 4
.000
?.375 2.375 2 .375
.154
.250
3.50t1
.216
.500
3 3
.216
'r
.2 50
1
.500
1.750 2
1't.000 11.000 'l1 .000 11.000 11 .000
36 -000
.625
{10 0
.
11.000 11.000
.6?5 .7 50
I .000
1.250 1.5C0 1
.750
2
.000
.250 .500
.625 .7 50
I .000
1.250 I .500
1.750 2.000
.37t .500 .625
F IN'L8/DEG
INPLANE LONGT
OUTPLANE
CIRCU
.187E+a?
.560€+07 .979E+07
-326E+07 .51 5E+07
.154E+08 .227 E+08 .317E108
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.172E+06 .353E+06
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.973E+06
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zc9E+07 .330E+07 -677E+07 .11E8+08
-697E+O6
+
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.'1948106
o?
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36.fjc0 36.000
2.375
ROT STI
.583E+06
1.750 2.000
11 .000
EL
V ESS
.Z1ZE+O6
10.000 10.000
1'l .000
L.
.516E+06
6. 000
36-000 3 6.000
.500
lli:li
30.000
.500
10 .000
CY
.
.110E+07
.226E+07
.394ar07 -622E+O7
.187E+CE .2 74 E+ 08
.911a+O7
-383Er0E
. '128E+08
.113Er05 .3'l 'l E+ 0 5
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6E
+04
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.21
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.176€+06 .361€+06
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3
5
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.1 54
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.487E+06
.995Er06
-332E+06
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-68',|E+06
.1688i05
.559E+04
.500 .500
.216
.1548+05 .316€+05 .553Er05
3.500
.216 .216 .216 .216 .216
-462E+05 .949E+05 .1e6E+06 .2628+ 06 .537 er06 .938E+06
.872E+O5
.218f+07
.725E+ 06
f.500
3-500 3 .500
3.500 3.500 3.500 4.500 4.500 4. 500 4. 500
4.500 4.500 4.500 .500 .500 4 .500
4 4
6.625 6 -625
6.625 6.625
.?16
.2'16
.237 .?77 .23? .?37 .237 .237 .237 .237 .2 80
.280 .280 .280
.179t+O6
.3t3E+06
.148€+07
.493E+06
.3048+ 07 .222E+05 ,611 € +05 . 1?5€+06 .219E+46 .316E1C6 .? 10E+O6 .124E+07
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o7
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.958E+06 .310Er05
.636€r05 .1',|1 E+0 6
,.i t
.5 t,.
lt ,l t: \l
144
Piping Stress Handbook Table 6-1 Conlinued ROlA STIFF
VESSEL ICX,IN
VESSEL
OD,FT
11.000 t 1 .000 11
.000
.000 11.000 J1.000 I1
1
't
.000
.7 50 1
'| 1
6
.500 'l
10.750 10 -754
.000
2.000
't
.7 50
11 .0 00
t 1 .000
.000 11.000 11
.625 .750
11.000 11.000 11 .000 11 .000 11 .000
t1-00c
r 1 .0 00
11.000 t'l .000 11.000 1 1 .000 1't .000 11.000 1t - 000 1t .000
11.000 11.000 11-000 11.000
11.000 1t -c00 t 1 .000
11.000 11.000 11 .00 0
11.000 11.000
1 1
.000
.250 I .500 1 .750 2.000 -250 .500
.750
J.000 't
.2 50
.000
'ls -75Q
5
0.750 10.750 12.750
't2.750 12.750 12.750
12 -750
12.750 1?.750 12.750 12.750 12.750
?. 000
.3'l7E+06
.365 .365
.554E+06 -874E+06 .179 E+ 07 .31 1E+O7 .195E+07 .727E+O7 .102E+CE .67 4E+05
.375 .375 .375
.131E+07 .1928+O? .2 69 E +O7
.187E+05
.t06E+06 .1E5Elc6 .291E+O6
.5988+06 .105E+07 .1 65 E+o 7 .?42E+O7 .338E+07
.'186E+06 -3E2E+06 .666E+06
.619E+05
-t058+07
.3508+06
.216E+07 .377 E+07
.595E +a7
.87
1E + A7
.1 22E +08
-127E+ 06
.?2?E+0
6
.719 E+C6 .1?
6 t +O?
.1988+07 .291E+07 .4O7 E+07
.206E+06
.73EE+06
.2468+06
.239a+07
-'l16E+ 07
.388E+06 .79 6E+06
.417a+ A7
.139E+O7
.96EE+07 .135E+08 .862E+05
.323E+ o7
.237E+O6
.7 92 t+O 5 -162E1O6
4.000 4.000 14.000 'I 4.000 1 4.000
.4228+06
I
'I
4. 000
4.000
.658E+07
I 4.000
16-000 16 .000
t6-000 1 6.000 16.000
I 6.000 18.000 18 . J00
18.000 I 8 .000
.7 50
.1 558+06
.231E+06 .47 5E +06 . Ef 0Ef 06
't
16 .000
1.750
.2 49E+07
.393E+07 .5778+07 .806E+07 .56'tE+05
.147EtO6
.2 49E+o5 -686F+05
1.000 500
.113e+07
.17 5E+O6 .360E+06 .628E+06 .991E+06 .'l46E+O? -203E+07 .146E+05 .409E+05 .840E+05
.7468+05
.7 50
t.
-252E+06 .4 40E+06 .694E+06
OUTPLANT CIRCU
t4.000
16.000 16.000 't6.c00
'1.250
.365
't
14-000
't1.000 11.000 11.000 11
.750 10.750
1
.37
-3?2 -322 .32?
10
'l
.500 .625
.297E+a7
.437E+07 .6108+07 .4158+05 .1238+06
10 .-t 50
1.500
.750 2.000
.2E0
.322
10.750
.525E+ A6 .10E € +07 .1EEE+07
.280 .260 .322
-322
.500 .7 50
.280
8.625 t 0. 75r]
.3?5
TCK,IN STD LONGI 'NPLANE
.322
.250
VESSEL
NOZZLE ROT STI F IN.LB/DEG
-625
8
1-750 2.000
11.000 11
.625 8.625
.5A0
1
ULATION, CYL.
_625
.000
I .000 1 .25A t .500
'11.000
8 8
1-250
11.000 11.000 11.C00
-625
6.625
.000
r1.000
.500
E.625 8 .6?5
11 ,0 00 '| 1
6.625
-250
.000
11.000 11.000 'I1.000 11.000 11.000 11.000 11.000
OO,IN
1.750 2.000
11.000 1 I .000
LC
NO22LE
.000
1.250 't
CA
18.000
.4 87E + 06
.852E+06 - 1348+Oz
.27 6a+07
.482E+07
-375 .3?5
-
7
6OEr 07
.112E+08 .
1
56E+ 0E
.977E+05 .2 69 E+ 06
.553E+06
.9 66E +a6 .152E+ C7
.1 4'l E+O6
.219E+tl .450E+07 .287E+05
.284€+06
.4 48E+o6 .919E+06 .1618+O7 .?53E+O7 -3?2E+o7 -5?OE+07
.326E+05 .898 E+05
.184E+06 .322E+o6
. 508E +06
!
Rotational Nozzle Flexibilities for Cylindrical
Vessels
145
Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL
0DzFT
VESSEL NOZZLE TCKTIN OD,tN
NOZZLE
TCK'IN S
11.000
't.000 1.250 1.500
t l .000
2
11.000 1
.000
1
,1.000
18.000 .000 1 8 .000 't 8
1.750 .000
18.000 '18 -
000
1l.000
.2 50
20.000 20.000
.000
.500 .625
20 .000 20 .000
1't.000 11
11.000 11-000 11 .000
11.000 11.000
.750 I .000 1 .250 1 .500
.7tb
20.000 20.000 20.000 20 .000
2.000
11.000 't1.000
.250
20.000 20.000 22.000
11 .00 0
.500
22 -AOO 22 .00 0 22 .AAO
.000 11.000
11
11.000
l
.0 00
11
.000
'l
11.000
1
.7 50
1.000
22.000 22.000 22.000
t1.00c
1.250 't .5c0
0c
2.000
22 .COO
.37
Zr'.000
11.000 11 .0
11.000 11
.000
't1.000
l .000
't
11
.000
11.0CC
1't.000 't
'r
,000
11 .000 11 .0 00
5
.500 .? 50
.000 .25u .500 .7 50
2.000
.2 50
11.000 11.000
?? .ooo
22.O00
24.400 24.000 24.000 ?a.oao 24 -OOO
24.000 24.000 24 ,O00 24
-
000
26.000 26.000 26.000
'l 1
.500
'11.000
-7 50
26.000 26.000
. ?50
26.000
.000 11.000
.000
11.000 11 .00 0
11.000 1 1 .000
11.000 11.000 11.000
.500
.750 2.000
1'1
.00 0
11.000 11.000 11.000
11.000 't1.J00
28.000
.750 1 .000
23.0C0
1.250 'I
.5C0
1 -750 2 .OAO
.250
28.000 28.000 28.000 28.000 28.000
28.000 30.000 30.{.i00
11,000
,tic0
.500
11.0CC
-625
.7 50
11.000 '11.cti0
26.O00 26.000
.500
11,0C0 1'1
26.000
28.000
1'l .000
11.000
26.C00
1
,000
30.000 30.000 30,000 30.000
TD
.375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -3?5 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .375 -375 -375 .375 .375 -375 .375 -375 -375 .375 .3'?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 -375
ROT STI
F IN.L8/DEG
INPLA!,IE LONGI -313E +07
-5 46E+07 -86?E+07 .127E+oE .1 77E+08 -',|09E+06 .30',1E +06 .6'l8E +06 .108E + 07
.170E+07 .3 50 E +07 .6'11€+07 .963E+ 07
.142E+08 . 198
E+
08
.1?1E+46 .333E+06 ,683E+06
.119E+07
OUTPLANE CIRCU
Jo4E+az .182E+07 -287E+07 ,422E+07 .590E+07
.364€105 .1008+06
.206€ +06
-360€+06 .568F+06 .117E+ 07
.204E+o7
.321€+07
.472E+O7
.6598+07 .4038+05
.t11E+06 .228E+06
.398F+06
07 .387E+O7 - 67 5E +47
.628E+06 .1?98+A7
.1578+OE
.522E+07
.219E+08 .132E+06 .365E+46 .719E+06 .'131E+07 .286E+A7
,729E+O7 .141E +O5
.138
E +
.1078+C8
.225E+07 .355E+07
.1?2E+A6
.250F+06 .436E+06
424E+A7
.688E+06 .141E+o7
.7loE+o7
.247 E+07
-
.117E+08 .1 72 E | 08
.?1OEr08 .1448+06 . 397E+ 06
.814E+06
.112E+o7 .224E+07
.4608+07 .EC4E+07 .127E+O8
.
187E+ 08
.260E+06 .1 55ErC6
.42E€+06 . E79 E+ 06
.154E+O7 .? 12E+ 07 .197E +47 -E69E+A7 . 137E+08
.202E+08 .281 E+ tl8 . 'l 67 F+ 06
.460E+06
.945€+06
.3t9E+07
.5?2e+87
.799E+07 .480E+05 .'l32E +06 .2 7'l E+o 6 .47 4E+06
.718E+06 .1538+O7 .2 68E +O7 .123E+07
.62?E +07
.868€+07 .518E+C5
,143€+06 .293E +0 6
.512E+06
.803E+06 .166E+07 ,29AE+O7
.457t+C7
.672E +a7
.938E+07 .557E+05 .153E+06 .315E+06
,165E+A7
.550€+06
.2 (OE + C7
.E68F+06
.534E+07
-'178E+07
1,,
t
146
Piping Stress Handbook Table 6-1 Continued
ROI^ STIFT CALCULAIIOI,, CYL.
SS€L ICKIIN
VESSEL
11.000 11.000 11.000
1
1'l .000
2. 000
11.000 11.000 11.000 t
.250
t .500 1
.750
.500
l .000
11.000 1t .000 1t .000 1t .000
NOZZLE
VE
OO,FT
.625 .7 5s
1.0c0 1.250 1.500
OO'IN
30.c00
12. 000
32.000
32 .OOO 32 .00 0 32 .000 32 .000
36.00 0
11.000
'11.000 11 .000
I I .000
.000 1J.000 '| 1
t1.000
1.000
1r .000 11.ADO
'r1.000 t I .000
-375 .500
40 .000
.7 50
t.000
1.250
t. t00
I .750 2.000
12.000 12.000
-250 .375
'12.000
12.C00
12.000 12.000 12.000
.500
.625 -7 50
I .000 I .250
1.500 1.750 2.0c0 .250
.500
12.AOO
12.000
t2.000 | 2.000
.625 .7 50
I .000
12.000 12.000 12,000
1.250 1 .500
12.000 12.000 12.00c 't 2.000
-250
t2.000
t2.000
36.00 0 36.00 0 4
11.0C0
't2.000 12.000 12.000 12.000 12.000
.000
.750 2.000
0.000
40.000 40.000
5
.375 -375
.375 -375 -375
.375 .375
.302Er08 .179E+06 - 49ZEr06
.164Er06
.101E+ 07
.337E+06 .588E+06
.1768+07 .278E+oz ,571E +07
-333E+O7
.2028+06
.672Ero5
.556E+06
.380E{06
.664E+06 .1058+07
.375
.375 .375 -3?5
.t7
5
.t75 .375
.113E+08
.178€+06
.2 61 E +08
.365E+08 .225E+06 . 619 E+ 06
.127e+87 .222E+07
-375
.1 26E+ 08
.375 .375
.291E+08
2.375 2.375 2.375 2.3?5 2.375 2.375 2.375 ?.375 2.375 2.375
.154
3.500
.216 .216 .216 .216
.500 .500 3-500 3 3
3.500 3.500 3.500 4-500 4 .500
4.500 4. 500 4-500
.185E+06
.199E+07 .314E+07 .645E+07
.375
3. 500
.77?E+O7 .108E+08
.375
40 .00 0 40 .00 0
.r25E+O?
.1 14E+07
40.000
40.000
.19AE +A7
.998E+07 .157E+08 .231E+08 .3 23E + 08
,3508+07 .719E+07
40.000
.92E€+06
.37 5
40 .00 0
1
.37
.375 .375
36 .000
36.000 36.000
11.0C0 t 1.000
t't .000
6.000
3 3 6
1.250 1.500 1.750 2.000
11.000
.311E+07
.722e+C7 .101 E+08 .595E+05
. >UU
.625 -750
CIRCU
.216E+08
0.000 3?.000 3
.37:
't'1.000
.934Er07
OUTPLANE
30 .000
1t.000 11.000
.37 5
N INPLANE LONGI
.191E +o7
r't.000 ,l
.250
r CK,I
STD
.147E+o8
52.000 3 2.000 32.000 56.000 36.000
1.000
NOZZLE ROT SII F IN.L8/DEG
30. 000
1.750 2.000
11.000
VESSEL
.1988+08 .4078+08
.215E+O7 -376E+07
-5938+07
.E71ErO7 .12?E+oB .749E+0 5 .2068+O6
.424E+06 -7 40E+O6
.117e +O7 -240E+07
.419E+07 .661E+O7
.971E+07 .136E+08
.106E+05 .298 E+05
.3608+04
-154
-f56Er05
.6llE+05
.15 4
.'t07E+06 .1689r 06
-992E+04 .204E+05
-154 .154
.346E+06 .604E+06
-561E+05 .115E+06 .201 E+06
.154
.154 .154 .154 .216
.216
.216 .216 .216 .237 .237 .237 .237 -237
.9528+96
.11OE+07
.195E+07
. t6lE+05 .443E+05 .909E+05 .159E+06 -250E+06
.317E+O6
.467E+O6 .652e+D6
.536E+o1 .14EE+05 .303E+05
.529E+05 .835E+0 5
.5'l4E+06
.1718r06
.898E+06
.2998+O6
.112E+oz
.472E+O6
.208€r07
.694E+06
.291E+07 .212t+ 05
.970 E+0 6 .706 E+04 .195E+05 .400 E+0 5 .700E+05
.585E+05 .120E+06 .210E | 06 .
J3t E+06
.1 10E +06
Rotational Nozzle Flexibilities for Cylindrical
Vessels
147
Table 6-1 Continued ROTA VESSEL
0D,ll
,090 12.000
12
't2,000 12.000 12.000 'l2.000 12.000 12.00c 1Z
1.000
1.250 1 .500 1.750 2. 000
.375
12.00c
1
.500
.000 12.000
2. 000
't2.000
12 .00 0
12.000 't 2.000 12.000 1?.000 12,000 '12.000
12.000 12.000 12.000 12.000 12.000 12
,000
12.000 't2.000 .000 12 .000
12
6.625 6.625 6.625 6.6?5 6.625 6.625 6.625 8.625 E.625
.250 .500
8.625
-f>u 1.000 1.250 I .500 1.750
8.625
8.625
2. 000 .37
5
.500
.625 -750
1.000 1.250 1.500
1.750 2.000 .250
12.000 12.000 12.000
.500
12.00 0
0. 750
10.750 10.750 1 0. 750 1 0 .750
t0.750 10. 750 't 0
.750
10.750 10
12 1?
.750
.750 .750
1?.7 50
.000 .500
1
.000
12.O00 1 2 .000
.500 -7 50 2
1
12.750 12.750 12.750 12.750 12.750 12.750 12.750
12.000
'tz.ou0 '| 2.000 12.000 12.000 't 2 .00! 12.000 12.000 12.000
6 -625
1.750
.290
.500
4.500 6.625 6.625
1.250
12.000 12. 00 c
4
.7 50
.000
12
4.500 4.500
.625 1
t?-000
,.. 500
.500
't2.000 t 2 .000
'14.000 14-000
4.000
14. 000 -7 50
.000 12 ,000
4.000 14.000 t 4.000
.500
12 . 000
.7 50 2. 000 .2 5A
't 4 14 ,l
12
12.000 12.000 12.C00 1? -004
12.000 12.000 12
.000
VESSEL
VESSEL NOZZLE NOZZLE ROl SIIf IN.L8/DE6 TCK,IN INPLANE OUTPLANE TCX,IN OD,IN CTRCU STD LONGI
.000
12 .OOO
Sttf F CALCULAITONT CYL.
.000
.500 - 1>U
I .000
1
.000 .000
4.000 1 6.000 't 6.000
'16.000 16 .000
16.000 I 6.000
.237 .237 .237 .237 .237 .280 .280 .280 .2 80 ,280 .2 80 .280 .280 .280 .?80 .322 .322 .322 .322 -322 -322 -32? .322 .322 .322 -365 .365 .36, .36' .365 .365 .365 .365 .365 -365 .375 .375 .375 .375 -375 .375 .375 .375 -375 -375 .375 -375 .375 -375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -3?5
.680E+06 .119E+O7
.187E.07
.275E+07 .384E+07 .3?3E+05 .889 E +05 .133 E+06 .319E+06
.5038+06 .1c3F+07
.l80E+07
.2n58+O7 .418E+07
.584E +47
.426E+05 .118E+06 .241E+O6
.4218+06
.665€t06
.22'l E+ O6 .396E+06 -621ErO6 .91EE+06
.'l28E+07 .108E+05 .?96E+05 .608E+05 .106E+06 . t d8E+06 44F +o 6
,t
.601 €+06 .949E+06 .139E+07 .195E+O7 .142E+05
t
.3
.3929+05 .804E+05 .140E+06 .?22E+o6
. 136E+07
.4558r06
.238E+o7
.79 5E+ O6 .125E+A7 .184E+O7
.37 6E+O7 .553E+07
.7728+ol
.?57E+o7
.537E+05 .14EE+06 .304E+C6
.l0lE+06
.531€+06 .837E+06 .172E+07 .300E+07
.47 4E.o7
.179E+05 ,493E+05
.177E +06 -279E+O6
.573E+06
.100E+07 .1 58 F+07
.696E+07
.232E+07
.972E+O7
.324E+O? .?15E+O5
.616E+05 .17E8+06 .3 6 5€| 06 .63E Ef 06
.1o1E+07 .2o7E+O7
.361E+07
.5938+05 .122Er 06 .2'l3E+O6 .3368+0 6 .689 E+06
.t20E+07
.569E+O7
.t90Er07
.E37E+07 . 1178 + 08 .715E+05 .197E+46 .404E+06
.279E+O7
.706E+ 06
.1't1E+O7
-zz9E+07
.l90E+07
.2399+05 .656E+05
-135Ef06 .235E+06 .371E+06 .762E+06
-4OOE+07
.133E+07
.6308+07
.21OE+07
.9?6E+ 07 .'l 29Er0E
.309E+07 .431E +O7
.825E+05 .2?7E+O6
.467 E+o6 .E15€+06 .129E+07 .261E+o7
.275E+05
.758Er05 .156E+06 .272E+O6
.4?9 E+06 .880E+06
t:
'i
ir\ I
il
it;
:l
iii
148
Piping Stress Handbook Table 6-1
Continued
SIIfF CALCULATIOII' CYL. VESSEL NOZ ZLE ROI STIF II].L8/DEG VESSEL NOZ2LE T CK,I N INPLANE ICKrIN 00rIN OUIPLANE STD LONGI CIRCU ROTA
v€ssEL 0D,FT
.000 12.000
1.250
12.000 12.000 12.000
2.000 .250
12
'12.000
t .500
1.750
r2.000
.500
.625
1Z-000 '12.000
1? .00 0
12.000
1
.000
16.000 16.000 | 6.000 16.000 .000 .000 18.000 18.000 18 18
't8.000 r 8.000
r8.000
.000
-375
18 .000
1.500
12 .00 0 12 .000
2. 000
18.000
12.4O0
.250 .375
12 .00 0
.500
20.000 20.000 20.000 20.000
2.000 '| 2.000 'r2.000 12.000 12.000 1?.000 12.000 12.00c 12.000
18
.625 1.0c0
1,250 1.500 'l
.7 50
2.000
20 .000
20.000 20.000 20.000 2
0
.37 5
.000
.?50
22.000
.00 0
22 .000
22 .00 0
12.000 1?.000 12.000 12.000
.500 2. 000
.375 .500 .625
12.000
12.000 12.000
12. 000
12.000 12.000 12.000 12.000
.750 I .000
1.250 1.500
.750 2.000 .250 1
12.C00
12.000 12.000 12.000 1?.000 12.000 72.DOO
12.000
.625
24.000 24.000 24.000 24.000 2 4
-000
.500
26.000 26
.000
28 .000
.000 2E.000 28
.625 I .000
1.250
26.000 28.000 28
.000
28.000
1 49E
+08
.936E+05 .2 5E€+06 .5 29 E+06 .9 248 +06 .146E+07
-37 5
.375
.486E{06
.105E+06 .288E106 .5928+06
.961El05
. l69E+08
.275E+o7 .564E+07 -3498+05 .197
E+o 6
.103E+07 .'163E+07
.3458+06
.585Er07
.195Er07
.3358+07
.544E+06 .1',\2e+07
.9228+07
.307E+07
.136E+08
- 452E+ O7
-631E+07 .386E+05
.116E+06 .319E+06 .654E+06 .114E+07
.106€+06 .2188+06
.370E+ 07
.123Er07
.647E+07
.216E+O7 .340E+O7
. 150E+08 . ?09t + 08
.381E+06
.6018+06
.5C0 E+07
.698E+07
06
.422E+O5
.319E+ 06
.116E+06
.717E+06
.239 E+O6 .417 E+O6
+
.125E+07 .1988+07 .4A5E+07 .706E+07 .112E+08 .164E+0E
.658E+06 .135E+07 .236E+O7
.372ErO7 .548E+07
.2?9E+ 08
.7 65E +07
.138E+06
.459E+05 .127E+O6
.441E+07 .7 7 0E+ 07
-375
.12't
.375 .375
.149Ef06
.375
.308E+06
- 404E+O7
.2'l5E+ol
.375
.E59E+05 .17 6E+O6
.121 E+08
.330E+06 .779 E+06 -136E+07
.375
.312Er05
.996 E +0 6 .17 4E+07
.523E+07 .825E+07
- 127E
.375
.3578107 .49aE+07
.299ri07
.175 .375 .3?5 .375
6.0 00
2 6.00 0 2 6 .000
.
.102E+08
.000
1.?50 1 .500
.243E+O7
-375
26.000 26.000 ?
.154E+O7
.72EE+07 .107E+08
.1808+07
24.OOA
26.000 26.000
't .7 50 2 .000
.37 5
21.OOO
.000
't
12.000 't2.000
24.000
.7 50 1
.250
12 .000 12 .00 0
24.OAO
26
12 .00 0
12.000 2.000
22.000 24.000 22.000 22.000 24.000
- 461Er07
.1898+08
22.000 22.000
12 .00 0
12.000
12.000
.373 .375
2?.OOO
.500
12.000
.37 5
20 .00 0
12.00 0
r2.000 12.000 12.000
.375 .375 .375 .375 .375
12.000 12.000
't
.375 .175 .375
E+ 0E
.179E]08
.2608+06 .4548+06 .716E+O6
.147E+07
.257t+07 .405E+O7
.249E+08
.595Ef 07 .8318+0? .496E+05
.4108+06
-137E+06
-842E+06
.2El E+06
.147E+07
.490E+06
.232E+O7 .47 6E+O7
. t 59E +0 7
.a32E+07
.773E+o6
.?77E+07
Rotational Nozzle Flexibilities for Cylindrical
Vessels
149
Table 6-1 Continued ROlA STIfF CALCULATION, CYL. VESSEL
OD,'T
VESSEL NOZZLE NOZZLE ROT STIF IN.L8lDE6 ]CKTIN INPLAN€ OUTPLANE TCK,IN ODU IN CIRCU STO LONGI
12 .00 0 12 .00 0
1.500
'12.000
-7 50
't
28 .000
.375
.1318+08
-37t
.269F+08 .160€+06
28.000 28.000
12.00c
2.000
.250
30 .000
12.000 12.000 12.000 't2.000
.500
30.00 0
't
2.00r1
3 0
'l
.000
30.000 50.000 30.000
.37
52 .000
12.040
2
.00
.500
1.750 .250
0
12.000 12.000 '12
.625
.0 00
12.000 12
.00
12
.000
0
12.000 .000
12.00c 12.000
5
.500
.500 .750 2.000
12.C00
.250
12.000 't2.000
.500
.000 t 2 .000 12 .000
.? 50
'12.00c
.625
12 .000 12 .000
12.O00 '1 2 ,000
1
,000
1
.250
1
.500
1,750 2. 000 .2 5A
I2.000
. 471E+ 06
.'157
2.00 0
.967E+06
.322E+O6
.266E+A7 .5 47 E+07 .956E+07
.1828+07 .3't 9 E+O7
ri
.502E+07 .739E+o7
lls
3
't3.000
13.000 13.000 'l3 .000
.500 .750 I .0c0
1.250 1.500 1.750 2
't3,000
.000
-2 50
13.000 13 .000
.500
13.000
. a>u
'13.000
13 .0 00
.169E +o7
32-000 32.000 32.000 J2.000 32.000 32.00c 32.000 36.000
.15'lE+08 .2728+O?.
.309€+08 .193E+06
6.00 0 36.00 0
.5f2E+06
36.0C0 36 -000
.301€+07
1
.000
,109E+07 .191E+07
36.000
6.000 36.000 36.000 3
3
6.00 0
,644E+0S .177 E+06 .364E+06
.6368+06 .100F+07 .568E+07 .834E+O?
.37 5
.349E+CE
.593E106 .213E+07 .33 jE107 .689E+07
.'l
.375
2.375
.'t54 .154
2 -375
.154
.500
.103E+08
.250E+06
4C.000 r.0.000
3
.563E+06 .888E+06
.1708+08
-122E+07
2.375 2 .375 3.500 3.500 3.500 3.500
6
.375
40 .000
2.375 2.375
E+ o
.?O6E+O7
,106E+08
.215E+46
2.375
.965E+O7 .5 70 E+0 5
- 618E+07
40.000
40.000 40.000
13.000 13 .000 13.000 13 .000 1 3 ,000 13 .000
.1718+07 .298E+a7 - 691e +O7
1.750 2.000
12.000 12.000
.470E+07
58E +07
.207E+08 .289E+0E .171E+06
.?50 1 .000
'12.000
.891E+ 07 . '1418+08
1
.37 5 .3? 5
12 .00 0
1.250 I .500
.2t9E+07 .5128+07
40.000 40.000 40.000 40.000
12.000 12.000
.898E+07
.375
.500
12.000
.137E+07 .64JE+07 .147 E+O6 .301 E+06 .527E+06 .831E+06
-441E+06 .
30.00 0
.00 0
12
.193F+0E
-904Er06
3
12
12.000
.375
.000
30.000 30.000
1.250
12
30.000
.750 1 .000
12.000 12.000
12.O04
VESSEL
?0E +08
.190E+08 .2798+0E .390E+08
.t04E+05 -286€+05 .587E+05 .103E+06
.15 4
.162E+ 06 .33?E+O6
.154
.580E+06 .915E+06
-154
.15 4
.1358+07
-'l54
.188E+07 .154E+05 .425E+05 .8 73 E+ 05 .1 53E+06 .?41E+06 .494E+06
.2'l6 .216 .216 .216 .2'16
.360€+07 .116E+08
.717F +05
.'198E+06 -406E+06 .709E106 .112E+O7
.230E+07 ,4018+07 .633E+07 .9308+07 .'l30E+08
.346Er04 .9Sj€+04 .196E+05 .342E+O5 .539E+05 .111E+05 .'193E+06 _305E+06
.4438+O6 .626E+O6
.515E+04 .142E+05
.2918+05 .509E+05 .802E+05 .165E+06
lx
it:
fl
150
Piping Stress Handbook Table 5-1 Continued
R0IA sTIfr CALCULAIIOI{r CYL.
VESSEL tIO2ZLE TOZZLE ROT STIF II{.LB/DEG ODrlN TCK,IN IiIPLANE 0UTPLAI{E rc(,Itl C IRCU STD LON6I
VESSEL
OD,FT
'13.000
13.000 13.000
13.000 13.000 't3.000 13.000 13.000 13 .0 00
13.0C0
13.000 13.000
13.000 13.0C0 l3 .000 13.000
13.000 '13
.750
1.500 3.500 3.500
.250
4
.500
4
1 -250
1.500 1
2.000
.625 .750 1.000 1.250 1 1
.500
.754 2.000 .500
.0 0c
13.000 13 .0 00
11.000 13.000 13.000 13 .000 l:i
1.000
1.250 I .500 1.750 2.000 .37
13.000 15.000 13.000 t 3 .000 13.000
13.000 13.000 13.000
'tf .000 13.000 13 - 000 13 .0 00
5
.500
.625 .750
't3.000
'13.000
13.000
.500 .500
4.500 4.500 4.500 4 .500 4.500 4
.500
6.6?5
6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.62
5
4.625 a.625 8.625 a
.250
1. 500
.750 2.000
1
.375 .500
t .000
13 .000
4
1
13.C00
13.000 13.000
4.500
I .000
.625 .750 't .000 1 .250 I .500 1.750 2.000 .250 .375
13 .000 13 .00 0
.500
-625 E.625
13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 15.000 13.000 't3.000 13.000 13.000 't3.000
3. 500
6.62t
15 .00 0 [:
VESSEL
.500
.625 1.250 1.500 1.?50 2.000
.250 .37 5
.500 .675 .7 50
1.000 I .?50
8
.625
8.625 a.625 8.625 10.750 10-750 10.750 10.750 10
-750
10.750 10.750 10. 750
10.750 10.750 1?.750 12.750 1?.750 12.750 12.750 12.750 't 2.750 12.750 12.?50 '12.750
14.000 14.000 '| 4.000 14.000 14.000 14.000 14.000
.?16 .216 -216 .216 .zt7 .237 .237 .237 -237 -237 -"37 -?37 -237 .?37 .280 .280 .280 .280 .2E0 -280 .280 -280 .280 .?80 -32? .3?Z -322 .322 -3?2 .322 .t2? .3?Z .322 .322 -565 .365 .365 .365 .365 .365 .365 .365 .365 .365 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 -37' -375 .375 .375
.863€ +06 . I l6E+07 .20081 07
.?79E+07 .204€+05
.562Ef05 .115Er06 .202Er06 .l'lEE+06
.288E+06 .454E+O6 .667e+ O6
.932Er06
.680E+04 .1 87Er05 .385€+05 -672ErO5
.1 06€ r0 6
.655€ +06
-2'l8Er06 .380Er06
.180€+07
.600E+06 -8828+06 .123E+Ol
.114er07 .265E+O7
.369E+O7 .310E+05 .854E+05 .17 5E+06 .
j06E+06
.103Er05 .285E+05
.5E5Ei05 .'102E+06
.483E+06 -992 E+06 -1?3E+07 .273E+07 .402E+o? .561E+07
.t61E+06
.113E+06
.376Er05
.4108+05
.331
E+0 6 . 578 Ef06
.911F+06 .134F+O7 .187 E+O7 .137E+05
.2328+06
.7738+O5
.40 5E+ 06 .639E+06
.213Eio6
.131E+07 .229E+a7
.361E+07
.135E+06 .437 E+O6 .7 63ErO6
.120E+07
.531E+O7 .7 42E+O7
.1778+O7
,516E+05 .142E+O6 .?92E+06
-172E.05
.247E+O7
.474E+05
.97iE+05
.510E+ 06
.170E+06
.804€106 .1658+07
.268E+06
.550E+06
. ?EEE+07
.96t E+06
.455E+07 .669 E+07 .934 E +07
.152E+O7 .223E+O7
.6 20E +05
.',l718+06 .351E106
.613€+06 .967E.O6 .199E+07 .317E+o7 .5 47E+O7 .aE4E+ 07
.1128+08
.687€ +05 .189E+06
.388E+06
.Jll
E+07
-2078+05 .570E+05
.1178+06 .2048+06
.662Er06 .116ErO7 .182E+O7 .268 E+07 .374E+07 .229E+O5
.631E+05 . 1 29 E+06
.679E+O6 -107E+O7
.226E+06
.384€ +07
.128E+07
.220E+07
.357E+O6
.732Er06
Rotational Nozzle Flexibilities for Cylindrical Vessels
151
Table 6-1 Continued ROIA STIFF CALCUIATI0Ne CYL. VESSEL
OD,TT
13.000
VESSEL TIOZZLE NOZZLE ROI STIF IN.L8/DEG TCK,IN INPLARE OUTPLANE TCK,IN OD,IN CIRCU LONGI STD .500
1
13.000 13 .000 13.000
1.750
11.000
.500
,000
2
-z>u
't3.000 13.000
.62 5 .7 50
13 - 000 13 .000
.000
'13.000 13
.500
.000
1f.000
.7 50
.000 .000 '| 3 .000 13 .000 13 .000 1J .000
2. 000
13.0C0 13.0 0 0
1
13
13
13 .00 0
13.000 13.000 13 .000 13
't 3
13.000 13 .000
13.000
1.250 I-500 2. 000
.500 .625 .7 50
,000 1.?50 1.500 1
1.7r0 2.000
.500
r3,000 '13.000
I .000
13 .000
1
.000 13.000
z
13.000 13 't
't4.000 't 6.000 16.000 'l6.000 16.000 16.000 1 6.000 't 6.000 16.000 I 6.000 't6.000 18.000 ,000 1E.000 8
I
13.000 13.000 .000
.000
.000
13 .000
15
4
.7 50
.000 .000
4.000
I
18.tto0 1 8.000
.625
.000
13.000 13.000
1
1
13.000 13
1.250 .500
1.750 .000
8
.000
8.000 18.000 18.000 16.000 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000
't
20-000 20 .000
22.000 2 2.000 22.000 22.000 22 -OOO 22.OOO 22 .000
22.000 z2 -aoo
22.000
24 -OOO
3. 000
tt.000
.500
1f. 000
,625
24.000 24.000 24.000
.7 50
?4.AOO
.000
24
13.000
13.000
13.000 l3 .000 13.000 15.000 '13.000
1
't.250 I .500
1.750 2
13.000 11.000
.000 .500
t3.000 1J.000
.7 50
.000
13.0C0
1
.000 13.000
1-5C0
1.250
.000
24.000 24.000 21 .OOO
24.000 26
13.0C0
13
VESSEL
.000
26.000 26.000 26.000 26.000 26 .000
26.000 26.000
.375 .60 5E + 07 .375 .890 + 07 -375 ,124E+ 08 .375 .791E+05 .375 .218 E+06 .375 .448E+06 .375 .783E+06 .375 .1?4E +o7 .375 .?54E+O? .375 .4t 3E+07 .375 .699a+C7 .375 .103E+08 .375 . 143E]08 .375 .8998+05 .375 .? 4EE+06 -3?5 .508E+06 .375 .EE8E+06 .375 .1 40 F+ 07 .375 .288E+ 07 -375 .502E+07 .375 .793E+ 07 -375 .117E+0E .375 .1d3E+0E .375 .1008+06 .375 .?77E+06 .375 .569E+06 .375 .993€+06 .375 .157E+O7 '12?F +l\7 "7< -375 -562E+O7 .375 .8E6E+07 .375 .1 30 E+08 .375 .182E+08 .375 .1118+06 .375 .306E+06 .375 .629E +06 .375 . t 10Ei07 .375 .173E+ D7 -375 .3 56 E+07 .375 .621E+o7 .375 .980 E+0 7 .375 .',144E+08 .375 .201 E+oE .375 .122E+O6 .37t .3358+06 .375 .639Er06 .375 .120E+O7 .375 .190E+ol .375 .390E+07 ,375 .681E+07 .375 .107E+08 .375 .t 58E+08 .375 .220€+08 .375 .1328+06 .375 .3658+06 .375 .749E+O6 -375 .',131E+O7 .375 .206E+07 -375 .4248+07 .375 .7 40E+A7 .375 .117E+08 E
.?D2E+O7
.297E+Oz
.414E+Ol -2648+05
.728Er05 .149E+O6 .2 6'l E+ O6
.412E+0 6 .E46E+06 .148E+02 .233E+O7
,t
.343E+O7 .478E+O7
.300€+05 .8268+05 .169E+06 .296E+06 .467E+O6
.959E+06 .167 E+Of .2 64E+oz . f88E +07 -542E+07 .33 5E +0 5
,9 23E+o, .1 90E+06
.331E+06
.5?28.06
.107E+07 .1878+07
.295Ei07
.4348+D7
.606E+07 .370E+05 .102E+06 .210E+06 ,366E+06 .577E+06
.1 19 E +07
.?a7E+07 .3278+07 .480E+07 .67OE+07 .406E+05 -'l1?E+o6 .230E+06
.401E+06 -633E+06
.130E+07 -227E+O7
.358E+07 .526E+07 .735E+O7 -44JE+05
.122E+06 .250E+06 _436E]06 .688E+06
.141E+07 .217 E +07
.389E+07
i{
.,1
itr\
.,|\
|4
,)
itt
152
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATIOTI, CYL. VESS€L VESSEL
vE
OD,FT
TC
13
.000
13.000
ssEL
1.750 2.000
13 .0 00
13.000
.37 5
13 .0 c0
.500 .625
I
.7 50
'|
3.000
t.000
13.000
1-000
15.0C0
1.?50
13.000 13.000
1.750 2.000
13.000
t3.000
'1.500
.250
15.000 .500
13 .0 00
13.000 13.000 13.000
r3.000 13.C00
r3.000 13.000
.625
13
.000
13.000 't3.000
.5C0
.625 1.0c0
t.25D I .500 1.750 2 .000
.t75
.500
13.000
.625 .750
13.000
13.000
13.000 13.000
13.000 13.000 13.000 13.000 l3 .000 13 .0 00
13.000 13.000 13.000 13.000
13.000 13.000
I .000
1.250 1.500 1.750 2.000 .500
.625 .750 1.000 1 .250 1 .500 1.750 2-0c0 -?50 .37
13
5
.500
13.C00
.000
1.000
13 .000
'1
13.000
1t.0c0
28. 000
- 143E106
28.000 26.000 28.000 28.000
.7 50
. t00 1.750 2.000
OE
.240€+08
.t94e+O6
OUTPLA C
E
IRCU
.572E+O7
.799E+Ol .477E+05
.?238+07
.15',lE+06 .270E+O6 - 471ErO6 .743E+O6
.375 .s75
.153Ef07
.2668+O7 .4?OE+07
2E.000
.37t
.4 58E + 07 .799 E+07 .'126€+08
.00 0
-3? 5
.259E+0E
.
28 .000
28.000 28.000 2E
.375 .375
.!75
30.00 0
.375 .375 .375 .375
30.00 0
.375
30.000 30.000 30.000
.5r>
.375 .375 .375
30.00 0
32.000 32.000 32.000 32.000 32.000 32 .000
52.000
32 .00 0
32.O0D
32.000 3 6.000
36.00 0 36.00 0 36.00 0
36.000
.375 .375 .375 .375 .37 5 .37 5
.375 .37
36.000 36.000
.375
5
36.00 0 36.00 0
40.000 40.000 40.000
40 .00 0 40 - 000
40.000 40.000 40.000 40 .000
40.000
4E.00 0
4E.000
48.000 48.000 48.000 46.000 48.000 48.000 48.000
.809 Er 06
.141Er07
.lE5E+08 .
t 54E+06
.4?3E+06 .869 E r 06 .152e+O7 .239E+A7 -492E+07
.375 .375
.375
.s75 -375
.51?E+05
.141E+06 .2908+06 .506 E+06 .798E f06 .164E+O7
.286E+07
- 199 E+08
.664E+07 .927E+o?
.lf5E+08
.4 52 E+O7 .5 47E+0
5
.t5tE+06
06
.3'l0E+06
-1628+07 .?56E+07
.541E+06 .E53E+06
.9 29
E+
.5?6E +07
.91E8+07 .145E+08 .213E+08 .297 E+08 .185E+C6 .511E+06 .105E+07
.1838+07
.175Er07 .3068t07
.483E+07 .710 E+O7
.991Er07 .d18E+05 .170E+06
.350E+06 .611E+06
.289E+07
.9648+06
.591E+07 .1048+08
.t
.346Er07
- t 64E+0E .2 40E +0E
.545E+07
.336Er08
.112Er08
9EEr07
.E02€r07
.?07E+06
.6E9 E +05
.117 E+07
.190E+06 .390E+06
.570E+06 .2048+07 .3228+ 07 -662E+07 .
.375 .375
.618E+07 E63Ei07
.659E+07 .276E+08 -1648+C6 .453E+06
I6.000
4E.000
't5.000 't3.000 13.000
TCK.IN II'|PLANE STD LON6I .17?E
30.000 50.000 30.000
.375
NOZZLE ROT STl F IN.L8/DEG
6.000 26.000
1.250 1.500 1.750 2.000
1.000
N
2
30.000
13.000
15.000 13.000 15.000
OD,I
.7 50
13.0C0
13.000 13.000 13.000 13.000 13.000 15.000 13.000
0t z LE
K,I I,I
1 16
E+08
.68tE+06 .107E+07 .?21E+07 .385 E+0 7
.'l82E108
.608Er07
.268E+08 .374E+08 .249 E+ 06 .687E+06
.893E+07
.141E+07
.375
.246E+07 .389 a+07 .7988+ 07
.375
. 1J9E+08
.220E+08 .323E+ oE .451E+0E
.'l ?5E+08 .831E+0 5 .?29E+o5 .470E+06 .821E+06
.130E+07 .?668+O7 -4648107
.733E +07
.1088108 .1 508+08
Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-l Continued ROTA
0DrfT
VESSEL TC K,IN
.000
-250
VESSEL
14
4.000 14.000 14.000 't
14.0CC
14.000 14. 000
't4.000 't4.000 14.000 14.000 14.000 14.600 14.000 14,000 t 4 .000
14.000 '|
STIfF CALCULAIIOI'1, CYL.
4.O00
14.000 14.000 14.000 14.000 14.000 't4-000
.500 .625 1.000 1-258 1.5C0
1.750
z. 000
NOZZLE
0D,I
2.375
2.375 ?.375 z
.375
?.375 2.375 2.375 2.375 2.375 f.500 3
.500
.500
3.500
1
.000
3.500 1.500
't
.2 50
.625
3.500
2
3
.500
.000
14.000 't4.000 14.000 r4 14
.000 .000
14.000
.490Er05
.216 .216
.2328+O6 .176E+06 .E32€+06 .'131E+o7
.7738+05
.269
.8988+06
.216 .?16
.193€+07
E+ 07 . 'l97E+ 05
.281
E+0 5
.159E+06 .277a +O6 .437E+06 .643E+06 .655E+04
.28 0
.1678+07
.557E+06
.2638 + 07 .387E+0? .541E+07
.129 E+07
6.625
-2E0 - z6u .2E0
. I 09 E+06
.363E+05
.625
-322 -3?2
.322
.7 14 E+05 .'130E+06
8 -625
.223E+06 .390E+06 .615E106
1.250 1.500
8.625
.322
.2218+07
2.000
I .625
8.6?5 '| 0.750 10.750 10.750 1 0.750 10.750 10.750 10.750
.322 -322
.500 .500
6.625
6.625
.50b
6.6?5
6.525 6.625 6.625
1.000 1.250 1. 500 1
.750
2. 000
.375 .500
E
.62'
11
14
.117E+ 06
.9E48+05
.6?5
14-000
14.000 't4.000 14.000
. ?16
.137E+05
.27 4E+O5
4 4
4.000
.842E+05
.E23E+05 .169E+06 .295E+A6 .466E+06 .956E+06
2. 000
t
-?16
49 E+0 5
.4t08.05
.119E+O7 .996 E +04
1.750
.000 t 4 .000
I 4.000
.l
.2't6
.3568+07
14.000
14.000
-216
.?108+06
4.500
14.000 'r4.000 14.000 14.000
.181E+07
06
.629E+06 .1 10f+07 .173E+07 .255E+07
1.500
.0AA 14.0C0
.154
4E +
.237 .237 .237
4
14.000 14.000 14.000
.432E+0{i .6O3ErO6 .496E+O4
.500
.250
t4.000
.29
.130E+07
.154 .154 .154
.9888+05
.64E E +05 .102E +C6
'|
14.000 14.000 14.000
.EE?E+06
.154
.194E+06
14,C00 I 4.00 0
4.00 0
.156E+06 .320E+06 .559E+46
.9'18€+04 .189E+05 -329E+05 .5?0E+05 -107E+46 .1E6E+06
.237
4.500
'|
.15 4
.1818+05
4.500
.750
14.000 '| 4.000 14.000 14.000
.333E+04
.?76a+O5 .5668 | A5
.542F+05
1.000
14
.1 00E+05
.'t54
.237
.375 .500
14.000
.000
.154
4.500 4.500
4. 500 4 .500
14
ZLE ROT STIF IN.L8/DEG TCK,IN INPLANE OUIPLANE CIRCU STD LONGI
NOZ
-216
1.750 .000
N
VESSEL
1
.000
.250 .500 -625
t .000
1.250 1.500
1.750 2.000 .500
1
-237
.280 .280 .280 .280
.5 65 .3 65
.365
0. 750
10. 750
.306€+06
.299E+i5
.3958+05
.1268r07
.318E +07
.5'128+07 .715E+ 07
.497E+85
.'l37E+06 .281E+06 .491E+06 .7 7 5E+ A6
,365
10.750 12.750 1? .750
.1118+06
.159E+07 .?7EE+ol
.3 66E+
0
6
,5788+06 .850E106
.561Er05 .155E+06 .319Er06 .678€+06 .tE0E+07 .132E+0
5
.205E+06 .421 €+0 6 .736E+96 .116E+O7 .171E+07 .238E+07 .166E+05 .457 E+05 .937E+05 .164E+06 .258E+06 .530E+06 .926E+O6
.438E+07 .6 45E+07
.146E+07 .215E107
.596E+05 .165E+06 .336E+06
.199E+05
.9008+07
.375
.371E+Os
.300E+07 . 549€+0 5
-113E+06
154
Piping Stress Handbook Table 6-1 Continued ROTA VESSEL
OD'F1
14
.000
14.000 14.000 14.000 14.000 14.000 14.000
t4.000 14.000
14.0C0
14.000 | 4.00 0 I 4.00 0
14.000 14.000 14.000
14.000 14.000 14.000 14.000 I 1.000 t 4.000 t 4.000 14.000 14 .000
.625 .750 I .000 1.250 1
.500
1. ?50
2.000 -250 .625 .750 1.000
1.250 1.500 1.750 2.000
14
.000
| 4.000
14.000 14.000 'l4.000 I 4.000 14.000 14.000
14.000 t 4.000 14.000 14,000 14.000 14.000 't4.000 14.000 14.000 14.000 't 4.000 14.000
14.0C0
16
.625 1.000 1-?50 I .500
.000
1.250 1.500 1.750 2.000 .250 . 500
.625
.750 1.000 1
14.000 t 4.000 I 4.000 14.000 14.000 14.000
.500
.375
'1
14.000 14.000 14.000 14.000 14.000 11.000
t 4 .000
.2to
74.OOO 14 .000
12.750 12.750 12.750 12.750 12.750 12.750 1?.750 I 4.000
t 4 .000 16 .000
1.750 2.000 .250 .375 .500 .625 .750
14.000
CALCULATIOI,IT CYL. VESSEL
VESSEL NOZZ LE TCXTIN 0D,Itl
r4.000 14.000 14.000 14.000 14.000 14.000
14.000
STIfF
.250
I .500
1.750 2.000
.250
.375 .500 .625
.5918+06
.197E+O6
.932 E+06 .191E+O7
.311E+06 .638e+06
.375
.3J4€+07 .527E+07
-111E+07 .176E+O7
.375 .375 .375 .375 .t7 5
.37t
.375 -375
.375 .375 .375
.7
75E
+
07
.'l0E€+08 .662E+05 .182E+06 .3? 4E+06 .654E+06
. t 05E r07 .21?E+07
.370Ei07
.375 .375 .375
.000
.375
1E.000
.375 .375
'l 6
18.000 18.000
.608 Er05
.125E+06 -21EE+06
.3448r06 -706E+O6
.123E+O7
.194E+07 .?E6E+07
.7 558+06
.37 5
.221Ero5
.8 58 E+07 . t 20E+ 08 .764E+05
-375
.375
.258E+07 .361E+07
.583E+07
.2108+06 .432E+06
16.000 1 6.000 16.000 16.000 '| 6.000 I 6.000
IRCU
.375 .375
.37 5
.119E+07 .2 448+07
.399E+07 .255E+05 .70?E+05 -1418+46
.25?E+O 6
.397E+O6
.8'l5E+06
.427e+O7
.142E+O7
4E+07
.225E+O7
. (r7
.990E+07 .138E+08
.866Ei05
.239 t +06 .490E+06
.330Ero7
.461E+o7 .289E+05 .796 E+C 5 .163E+06 .2E5E+06
.37 5
.8t6E+06
.37 5
.135E+o? .277E+07
.16'l
18.000 18.000
.375
-484E+07 .7 64E+O7
.112€+08
16 -000 20 .000 20 .000
.37 5
.157E+08
.375
.96E
.375
.2c7a+ B6 .548E+06
.37 4E+07 .523E+O7 .3238+O5 .890E+05
IS-000 16.000 18.000 '18.000
20.000 20.000 20.000 2
0
.000
20.000 20.000 20.000 20.000
22.000 22.000
1.250 'l .50c 1-750 2.000
C
.375
.500
1.000
LON6I
000
-
2? .000 22 .000
.625
STD
16.000
-750
.37 5
I{OZZLE RO' STI F I}I.18/DEG ICK,I N INPLANE OUTPLANE
.37 5
.375 .375
E +
05
.957E+06 .151E+07 .310E+07 .5 41E+07 .854E+07 .126E | 08
.l
.375
22 - 000
22.000
.924E+O6 E+O?
.255E+07
.183E+06 .519E+06 .503E+06
-10f8+07
.180€+07 .265E+07 .41E E +0 7
?5E+08
.5848+07
107F106 .295E+06
.357E+05 .984E+05
06
.2OZE+Oa
.
.37 5
.450E|06
- 606E
+
.106E+07
.3538i06
.'l67E+07 .343E+07
-
5
56E+
06
.114E+07
22 -OOO
.37 5
.599Ei07
.?00Er07
22 .0C 0 22 .000
.37 5
.9 44E+ 07
.315E+O7
.375
.139E+08
.000
.375
22.000 24
24.000 2 4 2
.000
4.000
.37 5
.315
.t94E+0E .1 17 E+o6
.323€+06 .6648+e6 .116E+07
.463E+07 .616E+07 .5918+05 .108E+06 .221E+O6
.386E+06
Rotational Nozzle Flexibilities for Cylindrical
Vessels
155
Table 6-1
Conlinued ROTA STIFF CALCULATIONT OD,FT
VESSEL NOZZLE TCKrItl OD,IN
.000
.7 50
v€ssEL
14
14.000 14.0C0
4.000 14.000 14.000 14.000 I 4.000 14,000
1
1
.000
1.254 't.500 1.750 2. 000
.500
.625
14.000
14.000 14.000 14.000 14.000 't4.000 4.00 0 .000 'l 4 .000
'I
.7 50
1.000
1.250 1
.500
1.750 2. 000
14
14.000 14.000 14.000 t /, .000
14.000 't4.000 14.000 14
.500
.625 I .000 'l -?50
1 .500 1
.750
2.000
. ?50
.375
.000
14.000 '14.000
14.000 14-000 14 .000
14.000 t 4 .000
28 -000
2E.000 28 .000
28.000 28.000 28.000 28.000
30.00 0
30.000 30.000 30.000
30.000 30,000
30.00 0 30.00 0
.t75
f2.000
.500
.625
.500
1.750 2.000 .250
.375 .500 .6?5
'l
.750 .000
32.000 32.000 32.000 32.000 32.000 32.000 32.000 32.00c 32.000 36.000 36.000 3 6.000 36.000 36.00c 36 .00 0
2. 000
36.000 36.000 36.000 36.000
.500
40.000 40.000
.7 50
40.000
I .500
1.750
.000
'14,000
11.000
28.000
2. 000
1
14.000 t 4 .00c
.000
30 .00 0
14 .0 00
'l 4
28.000
1.250 1.500
I .000
'l .000 'I .2 50
14.000 14.000 14.000 14.000 14.000 14.000 't 4.000 14.0c0 t 4.000
26.U00
l0 .000
14.o00 14.000 14.000 14.000 14.000
I 4 .000
24.000 24.000 24.000 24.000 26.000 ?6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000
.7 50
t 4.000 I 4.000
14.000 14.000
24 .000
28
't4.000 't 4.000 14 .000
24.000
.64>
40 .000
40 .000
NOZZL€
TCK'IN STD
CYL.
VESSEL
ROT
STIF IN.L8/OEG
INPLANE LOTIGI
.1838+07 .37' .375 .375E+07 .375 .656E+0? .375 .'103E+08 -3?5 .152E+08 .375 .2',12E+08 .375 . 128E+06 .375 .551E+06 .375 -7?2Eta6 .375 .1?6E+O7 -375 .'1998+07 .375 .408[+07 .375 -7'l3E+O7 .375 . '1 12s+08 .3?5 -1659+08 .375 .231 E+08 .375 .13E€+06 .375 .380E+06 .375 .779E+O6 .375 .136E+07 .375 .2158ra7 .375 .4418+07 .3?5 .770E+47 .375 .1?2E+08 .3?5 .1798+08 -375 .249E+08 .375 .'l18E+06 .37t '408E+06 .375 .637E +06 .375 .146Et07 .375 .231E+O7 .375 .47 4E+A? .375 .AZ7E+Ol .3'15 .131E+08 .375 .192E+OB .3?5 .268E+0E 06 .375 .1 58E++06 .375 .4368 .3?5 .695E+06 07 .3?5 -'156E++O7 .3?5 .?47E -375 - 506Er07 .3?5 -8858t07 .375 .140E+08 .375 .205E+08 -375 .286E+08 .375 .179E+06 .375 .493E+06 .375 .101 E+07 .175 .177E+o7 .375 .279E+07 .375 .57?E+o7 .375 .999E+07 .375 .'t 5EE+ 08 .375 '232E+08 .3?5 .3 24E + 08 .375 .199€+06 .375 .549E+06 .373 .113E+07 .375 .197 s+o7 .375 .311E+07
OUTPLANE CIRCU
-610E+06
.125E +o? -219 E+07
.345E+07 .507E+07 .708E+07 .425E+05 -117E+06
.Z1j
E+O6
.420 E+0r5 .663E+06 .136E+0 7
.238€+07 .375ErO7 .551E+07 -7708+A7 .459E+05
.j27E+06
.260E +0 6 - 45 4E +O6
-7168+06
-14?E +O7
lir :t
t|j
{
ils
'{l
.ZS7E+47
.4o58+o7 .595E+07 .831E+07 .493E+05 .'1368+06
i!
.2798+06
.488E.06
.769 E +06 .
j
588 +02
-276E+O7 -435e+O7 -640E+O7
.89fE+07 .jAEE+05 .145€+06 .29EE+O6
,521F+06 .8228+06 .169E +Oz
.295E+07 .465E+07 -684E+07
.9558+07 .596E+05
.164€+06 .33?E+06 .589E+06 .929E+06 .19',l E+07 .
i33E+07
.525E+07 .772E+O7
.'t08€+08 ,664E+05 .'183E+06
.3t6E+86 .656E+06
.104E+07
,\
156
Piping Stress Handbook Table 6-1 Contlnued ROTA STTfF CALCULATION, CYL. VESSEL VESSFL
VESSEL
lcKrIN
OD,FI
1
14.000 14.000 I 4.000
1
t .500 1
2.000
14.000
.2 50 .37 5
.500
.625 .750 1.000 1.2t0 1.500
'15.000
.250
15.000 15 ir
lt 1
5.000
r5.000 15.000 1
5.000
15.000
5.000 I 5.000 't 5.000 15.000 't 5.000 15.000 15.000 1
tl
i
.500
.000
.625
I 5.000 't
F
.750
14.0C 0
14.000 't4.000 I 4.000 14.000 14.000 14.000 14.000 14.000
q;
.000
.250
15-000 t 5 .000
15.000 15.000 'l
I .000
1.250 I .500
.758 2.000 1
.375 .500 . ?50
1.000
1.250 1.500 2.000
.250 .375
5.00 0
15
.000
15.000 1 5.000 15.000 15.000 15.000 I 5.000 15.000 15.000 I 5.000 15.000 t 5.000 15.000 I 5.000 15.00 0
15.000 't5.000 I 5.000 I 5.000
15.000
.500
.625 1
.000
1.250 1.500 2.000
.250 .37 5
.500 .625 .7 50
1.000
1.250 1.500 1.750 2.000 .2 50
t 5 .000
15.000 15.000
N0zeLe
NOZZLE ROT STI F II{.LB/DEG
OD,IN
T
.638E+07
40 .000
40.000 40.000 40.000 40.000 48.000
- 11'l E+C8
48 .000
48.000 46.000 48.000
{8.000 48.000
.375
-?13E +O7
.3718+O?
.1?6E+08 .2 58Er 08
.586r+07
-21OE+06
.8 0l Er05
.662E+o5 .1f,6E+07 .237E+07
-221e+O6
.36'l E+08
.t7t
OUTPLAI{E CIRCU
.3? 4e+07 .7 69E+07
.861E107
.120Ef08
,4 53 E+0 6
.791E+O6
.125Er07 .256E+O7
.000
.375 .375
.212E+08
.706Er07
48 .00 0
.37 5
.311 E+08
.104E10E
48.000
.375
.435€+08
2.375 2.375 ?.375 2.375 2-375 2.375 2.375 ?.375 2.375 2.375 3.500
.151
.9 668+04
.3?2E+O4
3
.500 3 .500
.?16
5.500 3.500 5.500 3.500 3.500 3.500 3.500
-216
4E
4. 500 4
.500
4.500 4.500 4.500
4. 500
4.500
.500 4. 500 4-500 4
6.625
6.625 6.625 6.625 6 .625 6.625 6
-6?5
6.625 6.625 a.625 6
.625
CK,IN INPLANE STD LO}JGI
a
-62>
.625
.1 34E+08
-418E+O?
.'l
45
Fro8
.154
.?66E +05
.151
.546€r05
.887E+04 .1E28+05
.,t 54
.955E+05 .151E+06
.3t8E+05
.309E.06
.502E+05
.15 4
.154 .154
.540E+06 .8 52 E+ 06
-1808+06 .2848+06
.154
-1?5E+07
-
.154
.154 -2't6 .216
.175e+07
.479E+O4
.396€+ 05 .813E+05
.13?E+os
.1l?E+06
.473E+O5 .7 47E+05
06
.153E+06
.803E+06
.268E+06 .422E+06
.1278+ 07
.23? .237 .237 .237
. 460E
+
.1E6€+07
.8 67 E +06
. l908+05
.633E+04
-523E+05
.17 4E+A5 .358E+05
+
.107€+06 .l8EE+06 .296E+06 .60EE+06
. t06€+07 .1 67 E +O7 .2 468+07 .3 44E+ 07
.2898+05 .795r + 05
.2EO
.450 E+06
.1 63E+ 06
.285€+06 .924E+ 06
.2E0
.161E+07 .255E+07
.2 E0
.37 4E+07
.280 .322
.t22
,322 .3??
.621Er06
07
.260E
.280 .?80 .280 .280 .28 0
.271E+05
.2248+06
-716
.23? .237 .?3?
117E+O6
.583E+06
.144E+ 05
.216 .216 .216
.216 .216
.103E+06
.522e+07
.3E1€+05 .105E+06 .216E+06 .377 E+06
.626E+O5
.987E+05 .203E+06 .354E+06
,558Er06 .621E+06 .115e+O7 .9 62E+04 -265E+O5 .544E+O5
.951Er05
.150€+06 .308E+06 .538E+06 .848E+06 -125E+07 .174E+07 .127E+05 -350E+05 .719E+O5 .1?6E +06
Rotational Nozzle Flexibilities for Cylindrical Vessels
'157
Table 6-1 Continued ROTA STIFF VESSEL
OD,FT
VESSEI ICKTIN
15.000 15.000 15.000
15.000 15.000 15.000 15.000
NOZZLE
0D,IN
8
.625
8
.625
.500
a.625
8.625
.250
5.000 15.000 .000 .000 l5 .000
ALC
.750 .000
't
't 5 15
C
.7 50
.000
2
8.675 .750 10.750
.2 to
10
.500
1A.750
.62' ,7 50
10.750
'10.750
10.750
t5.000
.000 1.250 1.500 'l .750 2. 000
10
15.000
.250
'15.000
.500
.000
15
15 .000
I t .000
1
'15.000
15.000 15.000 J5.000 15.000 15.000
0 .750 I 0. 750 '1o.750
1
.750 12.750 12 .750 12.750 12 .750
.7 50
12 -750
1.500
'12.750
.0c0
1
12.750 12 .750
2. 000
12.750 12.750
15.000 15.000
.500
14.000 1/,.000
.000
.000 .250 .500
.000
15
15.000 15.008 15.000
1.750 .250
15.000 15.000 t 5.000 15.000
.7 50
.7 50
2-000
.0C0 '15.000
.250
15.000 1s-0c0
.500
15
15 't 5
.000
15.000 15.000 15
.? 50
.000
15.000
.000
1
.000
't.?50 1.500 1.750 2
'15.000
.000
.000 .000
.625 .7 50
15.000 15.000
1
.000
't5.0c0 t 5.000 15.000
1,258 1
.750
'l
2
.000
.000 1 5 .000 I 5 .000 15.000 15.000 15.000 5
'I
.500
.000
,000
14.000 I 4. 000
14.000 14.000 14.000 14.000 16
.000
16.000 16.000 I
6
.000
16.000 1 6.000 16.000 1 6.000 16.000 1 6.000
.000 18.0C0 1
15.000 15 15
4
1
'15.000 15
'14
8
t8-000 18.000 't 8.000 13 .000 16
.000
18.000 18.000 't 8.000 20.000 20 .000
.500 .750
20.000 20.o00 20 .008
ULATI0N'
CYL
VESSEL
'
NO?ZLE ROT STIf IN.LB/DEG
TCK,IN INPLANF LONGI STD
.322 .322 .322 -322 .322 .322 .365 -365 .36' .3 65 .365 .365 .365 .365 .365 .36 5 .375 .3?5 .375 .375 .375 -375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 -375 -3_tj .375 .375 .375 -375 .375 -375 .375 .375 .3?5 .375 .375 .375 .375 .375 .3?5 .375 .375 .3tj .375
.595E+06 .1228 +O7 .213E+o7 .336E+07 .494E+07 .690E+07 .4 80E + 05 .13?E+O6
.272E+A6 .475E+ 06
.7 49E+O6 .154E+O7
.268E+07
.4248+07
-623E +O7
.869E+07 .578E+05 .159E+06 .32? E+ 06 .5?1E+ 06
.900E+06 .16
5 E+
07
.323E+a7 .5C9E+07
.7198+07 .105E+08 .639E+05 .17 6E+06
OUTPLANI CIRCU
.198E+06 .407F+06 .711E+O6
.1'l
?E+O 7
.'165E+07 .238E+O7
.160E+05 - 4 41E +O5
.906€+05
.'t5EE+06
.25OElo6 .512E
+
O6
.895E+06 .'11'lE+O7
.208E+07 .290E+07 .193E+05 .530E+05
.t09E+06
.190E+06 .300E+06 .616E+06 .108E+07
.250E+07 .34EE+07 .2't 3E+0 5 -587E+05 .1?1E+O6
.632E+06 .996E+06 .205E+07 .357E+07 -564E+07
.2'l1E+O6
.116E+08 .738 € + 05 -203E+06 .417 E+o6 .7 Z9E+O6
.115F+07 .236E+O7
.4138+07
.65'l
E+D?
-957E+07
.1J4E108
.837E+05 .231E+06 .4738+ 06
.827Ei 06 .130 E +0 7 .21EE+07
.332E+0 6
.682E+06
.119E +o?
.188E+07 .27 6E+07 .386E+07 -216E+O5
.678E+05 .119 E+06 .?43e+O6
.3838+06 .787E+06
.138€+07 .217 E+07
.319E+07 .4 4tE+01 -?79E+05 .769E+05 .158E+06 .?7 6E+o6 .435E+06
.893€]06
.738E+O7
.156E+07 -216E+07
.1oEE+08
.362E+O7
.4688+07 .
1
51E108
.505E+07
.936E+05 .258E+06 .529E+06
.t1?E+O5
.146E+07
.486€+06
.925!+06
,l
i: "l
t\
.170E +A7
.3 62 Ei 06
.829E+07
:
.859E+05 .17 6a+06 .308E+06
r{
I
158
Piping Stress Handbook Table 6-1 Continued R0TA SIIFF CALCULATIOIte CYL.
vEss€L
VESSEL
TC(rIN
0DrFT
15.000
r5.000 15
.000
15.000 15.000
t -000
.?50 1.500 1
1.750 2.000
15.000
.2 50 .37 5
15.000 15.000 15.000 15.000 15 .0
00
.500
.625 .7 50 1
.000
15.000 15.000
1.254 1 .500 1.750 ?.000 .250
5.00 0
.37 . 500 '
15.000 15.000 15.C00
r5.000 1
15.000 15.000 t 5.000 I 5.000 I 5.00 0
15.000 15.000 15.000 15.000
t5.000 1 5,000 15.000 I 5.000 15.000 15.000 15.000
15.000
t5.000 15.000 15.000 15.000 | 5.000 t 5 .000
'15.000 15 .000
15.000 15.000 15.000 15.000 ,| 5.000 15 .0
00
5.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 't
I 5.00 0
15.000 15.000 '15
.000
.625 .750
1
.000
1.250 I .500 1.750 2.000 . ?50
.500 -625
.7 50
1.000
.250 I .500 1.759 2.000 .250 1
.t75
.500
.625 .7 to 't .000 1.250 1.500 1.750 2.000 .250 .375 .625 .75A 1.000 1.250
t.5c0
1.750 2.000 .250 .375 .500 .625 .750 1.000
l{oztLE 0D,IN
20.000 20.000 20.000 20.000 20.000 22.000 ??.000
.ooo 22.000 22.000 z2-ooo z2
VESSEL
OZZL€ ROT STI F II{. LB/
lcKelt{ INPLANE STD LON6I .375 .375 .375 .375 .375 .375 .375 .375
.375 .375 .375
.299€+07 .52tE+ 07 .825 E+07 .1 2l E+08 .169 E+0E .103E+06 .285E+06 .565E+06 .102E+ 07
-37 5
.134E+08
22.OOO 24 .00 0 24.OOO
-375
, I E7E+ 0E
.375 .375
.312E+06
26 -OOO
26.000 28.000 28 .000
28.000 28.000 28.000 2E.000 2E .000 ?E.000
28.000 28,000 30.000 30 .00 0
30.000 30.000
30 .000
30.00 0
.3?5 .37 5
.375 .375 .3?5
.375
.37'
.375 .375 .37 5
.3?5 -375
.175 .375 .375
.375 .375 -375
.375 .37 5
.6348.07 .999E+07
.147Er08 - ?05 E+08
. 12f,Ef 05
.340€+06 .192E+O7 .39
4E +O7
.214E+O6 .373 E+06
.5E9Ef06 .721E+O7 . zl t E+q7 .333 E +07 .490E +07 .684E +07
.4llE+05 .t13Er06
.23OE+O7 -362E+O7
.1 60E+0E .2?3E+08 .133E+06
.532E+O7
.109Er08
.367E +06 .7538+ 06
.132E+07 .20EE+0? .426E+o? 44E+0?
.t75
.141El07
.173Ef06 .241E+A8
.375
.223E+07 .4588+07 .799E+07
.37 5 -375
-624E+O7
.578 E +0 5 . t 048+06
.689E+07
.394€+06
.000
.19f,E+07 .J04E+07 .447E+07
.232e+O5
.375 .375
.375 .375
.19 5e+06
.541Er06
.406E+06 .6408+05 .131E+07
. t 43E+ 06
-375
.950E+05
.122t+O7
-375
-375
-345E+05
.697E+06
.117E+08
.375 .375 .375 .375
32.000 5 2.000
.641 E+06 .112E+O7 .17?t+ 07 . 363 8.0 7
-375 -375
30.000 30.000 30.000 30.000 3 2.000 32.000 52.000 32
.1 13E+06
.?
.t75
.275E+07 .404ErO7 .565E+07
.538E+06
.5788+07 .9'l 2 E+ 07
24.000 24.000 24.000 2 4.000 24,000 24.000 24.000 2 4.000 2 6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000
r0 6
-110E+07
-375
.375
E
.17 4E+O7
.1 61 E+07
.375
22 .000
.998
.331e+O7
?2.000
22.OOO
DEG
0UTPLANE CIRCU
.809 E+06
.126E+0E .185E+06 .2 59E+ 08
.714E+07 .444E+05 .122e+O6 -251E+06 .438 E+06 .692E+06 .1 42E +0 7
.248e+o? .391E+07 .575e+07 .803 Er 0 7 .477E+O5 .131 Eio6
.270Er06
.4718+06 .743ErO6 .153E+07 .z66ErO7 .420
E+ 0
7
.618E+07 .863
€
+0 7
.J
.510Efo5
.421E+06 'f,E+06
.140E+06
.865Er06
.'l5l€+07
.238E+07 .489E+07
.28EE+06 .504E+06 -
7948r05 65Elo7
.t
Rotational Nozzle Flexibilities for Cylindrical Vessels
159
Table 6-1 Continued ROTr STTFF CALCULATION,
VESS€L TCK,IN
v€ssEL OD,FT
5.000 15.00c 15.000
.250
't
1
't
1.500 1.750 2.000
5. 000
.000 15.000 1 5 .000 'l 5 .000
15
.500 .7 50
.000
15.000 15.000 15.000 15.000 15.000 1 5.000 'l5 .00c 15.00c 15.000
-375
.855E+07 .135E+0E
32 .00 0
.375
.'198E+08 .27 7 E+ 08
.661E+07 .923E+07
.375 .51>
.'17 3E + 06
.37 5
.977E+A6
.576E+05 .159E+06 .326E+o6
32.000 .000 I6 -000
3 2
f6.000
36.000 36.000 36 .00 0
40.000 40.000 40.000
.500
.625 '|
.000
.000
1.250
40 ,000
40 .000
1
6.00
0
6.000 16.000 16.000 1 6.000 '| 6.000 16.000 1 6.000 16.000 16.000 t
't 6
.000
't6.000 '| 6.000 16.000 16.000 16.00 0
16.000 16.000 16.000 't6.000 1 6.000
1.000 1.250 1
.500
1.750 2
.000
1
.5C0 .7 50
.10/rEr08
.530E+06
.177E+o6 .363E+06
tl'l
.634€+06
"J
.5rt
,190F+07 .3008+07 .6168+Ol
.375
.108E+08
-319e+o7 .566E+O7 .832E+47
.192Ei06 .109
E+
07
.1708+08
.612E+O5
.100Er07 .?o5E+07
.438€+06
.2?9E+a7
.7 64E+O6
48.000 46 .000
.000
4E
.000
2.375 2.375 2.375 2.375 2.375 2-375 2.375 ?.175 2.375 2.375 3.500 3.500 3
.500
3-500 3.500 3.500 4.500 4.500 4.500 4.500
.2 50
.746E+O7
.1318+07
.000
4E
.500
2.000
.32?E+07 .50E8+07
.313E+08
.37 5
48.000
3.500 3.500
1.7t0
+06
.?13E+O6
.7 50
1.000 1.250
E
.897E+06 .184E+07
06
3-500
.500 .625
. 569
.7748+O5
1E
16.000
.449Er07
.?32E+O6
2. 000
.500
.9 658+07
-285E+07
48 .000
I 5 .000
16.000
.553E+07
IRCU
.250E+08 .348E+08
48.000 48.000
16.000 16.000
.171E +07 .2 69 Er A7 .152E+CE .221E + 08
40.000
1.750
.000
5
.4768+06
C
40 .000
15.000
15
.37
40 .000
,/.8.000
.000 .000
15.000
-375
.s75
15.000 15
32 .000
.500
1.500 1.750 2.000
OUTPLANE
LONGI
40.000 40.000
1. ?50
.000
TCKTIN INPLANE
2.000
1.000
5.000 15.000 15.000
NOZZLE ROT STI F IN.L8/DEG
6.000 36.000 36.000 3 6.000
. >uu
V€SSEL
STD
3
15-000
't 5 15
OD,IN
36.000
15.000 15.000 '| 5.000 t 5,c00
15 1
NOZILE
ClL.
4. 500
-5t>
.639
.375
.315 .15 4 .15 4
.154
.154
30E +08
.43?E +07
.205E+08 .301 E+08 .420E+08
.682E+Oz
.935E+04 .258E+05 .529E+05 .924E+05 .1 46E+06
.299E+06
.15 4
.5238+06 .8258+06 .121E+07 . t 69E+07
-154
.216 -2't6
.216 .216 .216 .216 .?16 -216
.?'t6
.237 .237 .237 .237
5;
.121E+07 .24EE+o7
+
.15 4
.154 .154
5r
07 .713E+ 07
-362E
.'l
.375
E+
.1168+08
.1008+08 . t 40E+08 .3'l2E+04 .859E+0rr .1 76E+05
.308E+05 .486E+05 .998E+05 .17 4E+o6 .275E+A6
.404E+06 .5 64E.
O
6
. 1l9E +05
.16LE+04
.3E3E+05
E0€+07
.128E+05 ,262 E+0 5 .45EE+05 .7?3E+05 .14EE+06 .259E+06 .409E+06 .601 E+0 6
.252E+07 .1E48+05 .507E+05 .104E+06 .'182E+06 .287E+06
.606E+05 .956E+05
.787E+05 .13EE+06 .217E+06 . 4 45 E+06 . 778 E+ 06 . t 25 E+ 07
-l
.840E+06 -6'l3E+04 .'l 69 E+0 5 .3478+05
ft
160
Piping Stress Handbook Table eFl
Continued ROTA V ESS
EL
OD,fT
VESSEL
TCK,IN
16.000 r 6.000 16.000 16.000
1.000
I 6.00 0
2. 000
16.000 16.000 16.000 16.000 16
.000
16.000 16.000 16.000 16.000 16.000 16.000
1.250 I .500 1.750 .250 .375 .500 .7 50
1.000 1.250 'l
.500
1.750 2.000 .?50
16.0 0 0
16.0c0
.500
16.000
-625
16.000 16.000
I .000
16.000
1.250 1.500
16.000
1
I 6.00 0
16.0C0
.750
2.000
16.000 16.000 16.000
16.000 16.000 16.000 16.000 't6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000
r6.000 'l6.000 16.000 16.000 16.000 16.000 16.000 16-000
-
z)u
.500
.625 .750 I .000 't
.2 50
1.500
1.750 2. 000
.250 .37 5
.500
.750 I .000
1.250 J.500 I .750 2. 000
.500 .625 1.000 1-250 1.500
1.750
16.000
1.000
2
.000 .37
5
.500
.625
vESSEL
NOZZLE NOZ2LE ROI STIF IN.L8/DEG ODEIIi TCK'IN INPLANE OUTPLAN€ CIRCU LONCI STD 4.500 4. 500 4. 500 4. 500
4.500 6.6?5
6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.625
.?37 .237 .237 .237 .280 .280 .280 -280
.625
4.625 4.625 10.750 10 .750
10.750 10.750 10.750 10.750 10.750 10.750 10.750 10.750
-162e+07
.238r+07 .335E+07 .?79E+05 .770E+05
.145E+06 .298E+06
.280
.2 46E+ 07
.2E0
.506E+07 .369E+05
.280
.3?2
.322 .32? -322
.322
.156E +07
.362€+07
.t02E+06 .2C9
E
+06
.365E+06 .576E+06
.ll8E+07 .206E+07
.365
.3268+07 .479E+o7 -669Er07 .165E+05
.3 65
.1 28E+ 06 . 263E +06
.365
.460E+06 .7?5E+06
.3?Z
.322 .322 .365 .365 .365 .365
.36 5
.365 .365
.1 49 E+07
.37 5
.375
.179E+07 .3138+07
.3?5
-493E+Oz .7 25E +07
.000
1 4.00 0 1 1 1 1 4 .000
.339E+0 5 -696E+05
.1?2E+06
.192E}06 -394r+06
.688E +06 .109E f0 7
.160E+0? .223E+07 .155E+05 .4?7E+o5
.a77ErO5 .
l53Er06
.2128+06 .496E+O6
.316E+06 .551E+06 .8?2E+06
.13? E+07
.201E+g?
.28'lEr07 .185E+05
.291E+06 5968+06
-
.1048+07 .161E+07 -2428+O7 .337 E+O7
.375
.1018+06 .619E+05 .1 71 E+06 .350E+06
.2068+05
.175
.965E+06
.322E +o6
4.000 4.000 4.000
14.000 14.000 I 4.000 14.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000
.123E+05
.5148+05 .1058+06 . 1 84 Ef06
.559Er05 .'154Er06
12.?50 12.?50 12.750 1Z .750
.121E+O7 .1 69 E+ 07
.867E+06
.375 .375 .3?5
.37'
.521Er06 .821E|06
.260E+07 .4108 +07 .603E+07 .8 428 +07
12.75A
12.750
.257E+O5
.280
.375
12 -750
.111E+07 .932E+04 .9?1E+05
12 .7 50
12.750
.795E+O6
.4368+06 .894Er 06
?80
.t2?
8
.343E+06 .5 4l Ei06
.276F,+O6
.
a .625
4.625 I .625 8.625 4.6?5
.196E+06
.1038+07
.527Ero5
.322
I .625
.589E+06
. 158E+05
.625
8
'14
16.000 16.00c 16.00c 16.000 16.000 16.000
t6.000
STrrF CALcULATIONT CYL.
.6'l2E+06
.375 .375
. 569 E+0 5
.1 l7E +06
.2848+06
.1988+07
.660€r06
.546Er07
.182E+07
.3 46E +07
.115€+07
.6c2E+07
. ?67E +o7
.1 'l ?E+08
.7'l5E+05
.373E+07
.2f8E+05 .656E.05
,375
.197E+06 .404E+06
.375
.706e+06 .111E+07
.371E+O6
.375
.229E+07
.7 62E+06
.135E+06
.235E+06
Rotational Nozzle Flexibilities for Cylindrical Vessels
161
Table 6-1 Continued ROIA STIFT CALCULATION, CYL. VESSEL
VE
OD,FT
TC
SSEL II
16.000
1-250
16.00 0
1.5C0
6.000 16.00c 16.000 16.000 't
.750 2.000 1
.250
.500
16.0 00
16.000 16.000 16.000 16.000 1
6. C00
16.000 16.000 't6.000 I 6.000 16.000 'l6.00
0
t6.000 t 6.000 16.000 16.00
0
16.000 16.0 0 0 'I 6.00 0
16.000 16.c00 16.000 16.000
.625
J
.000
OD,I
l6 ,000 't 6.000
-153E+06 -?67E+o6
E. 000
.259E+ 07 .4538 +07
.750 1 .000
6.00 0 16.0 0 0
'| -
1-?50
1.500
.711E+07 .105Er08
r
. 147E+0E
20 . c00
.906E+05 .250F+06
20 .000
.895€+06
20,G00
-'l 4'l
20 .000
20.000 20.000 20 ,000
22.aao 22.000 22.000 ?2.000 22.000 2a.000 22.000
.500
1
.7 50
24.OOO
16.0C 0
t6-000 16.000 t 6 .000
16.000 16.000
1
.000
.250 I .500 1 .750 1
2
.000 .250
.799E
.37 5
.117E+08 .164E+08 .1C0E+06
.375
16.!00 16.000
1
.375
.302E+06
16.000
7.25A 1.500
16.00
1
.1t0E+06 .62'l
E
+
o6
.375
26-000
.37 5
.42't e+o6 .864E+06 .151E+07
.?38E+o7
.3508f07 .4898r07
-3028+05 .832E+05 .'171E+06
.298E +06 .471E+ 0 6
.966E+06 -169E+07 .266E+O7 .391E+0? .547E+07 -134E+05 .920E+05 .189E+06
.330€+06 .5209+06 .107E+07 .'l87E+07 -29 4E+07
.433E+o7
.604E.07 .366E+05 .101E+06 .207E+06
.361E+06
.35'lE+07
.'117E+07 .2018+Oz
.570E+O6
.968E+07
.3238+07
.142E+08 .199E+08
.66?E.07
.1198+06 .329E+06
.6758+o6 .1'l6E+07 -375
.431F.D7
.108E+07 .1718 + 07 .613E +07
.000
26.000
.567E+06 .990E+06 .156F+ 07 .3?18+ 07 .560E+07 .883E+07
.s75
2,6.000
26
.000
1
07
.130E +0E .1 81 E +08
26.000 ?6.000
16.000
+
.?76E +06
24.000 24.000
24.000 24.000 26.000
07
.54>
26 -AOO
16.00 0
6.00 0 '16.000
24. ilo0
E+
.290E+07 .506€+07
22.OD1
16.000 16.000
6.000
.512€r06
20.000
24.000 24.000 24.000
16.000
.375
E. 000
22.000 22.000
16-000
.458€+06
1E.000
750 2. 000
1
.1298+08 .B l0Er05
.126E+07
18.000 'l
.3098+07
.801E+C6
8
20.000
| .000
.?1OE+o7
.000
18 .000
.580
.7 50
.131E+o7
.6J0E+07
.270E +O5 .7 44E+O5
.250
.500
.399E+07
,22fE+06
18.000
1
CTRCU
-375
t 8 .000
1
OUTPLAIIE
.9 26E+ 07
8.000 20.000
1.750 2,000 .250
ICK,IN INPLANE LONGI STD
.375
2. 000
1.250 1.500
NOZZL€ ROT SIIf IN.LB/DEG
'l6.000
18.000
1.750
N
16 .000
1.250 1.500
16.00 0
16.000 1 6.000
NOZZLE
X,I
VESSEL
.186E+07 .382E+07 .667E+07
.47 4E+07 .398E+05 .110E+06 -225E+06 .393E+06 .620E+06
.127E +07
.222E+07
26.OOO
.351E+47
.750
26.000
.'l05E+0E
16.000
2. 000
26.OOO
.216E+08
16.C00 16.0 0 0
-250
-'l29
06
.375
28.000 28.000
.7208+O7 .430E+05
.500 .6?5
28 .000 2E
.000
.355E+06 .729E+06 .127E+C7
.243E+06 .425E+C6
.000
.412e+ 07
.6705+06 .137E+a7
.7218+07
.240E+07
0
16.000 16.000 16.000 16.000
16.000
.750
I .000
1.250
28.000 2E
28.000
.t55E+08 E+
.201E+07
-516E+O7
.1'18 E+06
I {
it
I .l
162
Piping Slress Handbook Table 6-1 Contlnued
VESSEL
0DeFT
16.000 16.000 16.000 16.000
t6.000
16.000 16.000 16.000 16.000 16.000 16.000 16.00
0
6.000 16.000 16.000 16.000 16.000 1
f6.000 16.000 1
6.00 0
|
6
.000
16.00 0
16.000 16.000 t 6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.C00
16.000 16.000 16.000 16.00c
r6.000 | 6.000 16.000 1 6.000 16.000 16.000 16
.00 0
16.000 16.000 16.000
t6.c0c t6-000
16.00c 16 .000
16.000 16 .00 0
16.000 17.000 17.00c 17.000 17.00n I 7.00 0
17.000
nOft STIFf CALCULATIONT CYL' VESSEL NOZ ZLE ROT STIF IN.LB/DEG NOZ Z LE VE SSEL IcKTIN It{PLAt{E 0UTPLANE 0DrIN TCk,ll{ CIRCU LONGI STD I . 500 1.750 2.000 .250 .375 .500 -625 .750 I .000 1.250 1.500 1.750 2.000 .250 .375 .500 -625 . ?50 I .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1.250 I . t00 I .750 ?.000 .250 .375 .500 .625 .750 1.000 I .2 50 I . 500 1.750 2.000 .250 -375 .500 -625 -750 '| .000 't.250 1.500 1-750 2.000
.250 .375 . 500 .625 .750 1 .000
2E.000 2E.000 2E.000 30 -00 0 50.00 0
0.000 30.000 30.000
3
30.00 0 30.00 0 30.00 0
30.000 30.000 3 2.000 32.00
0
e.000 32.000 32.000 3 2.000 32.000 3
52.00 0
2.000 52.000 3 6.000 36-000 36.000 3 6.000 3
36.00
0
6.00 0 36.00 0
3
36.000 36.000 36.000 40.000 40.000 40.000 40.000 40.000 40.000 40.000 40.00 0
40.000 40.000 46.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 2.375 2.375 2.375
2.375 2.375 ?,375
.375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -375 -375 .375 .375 .r7, -375 .375 -375 -175 -375 .375 .375 -375 .375 -375 -375 .t75 .375 .375 -375 .375 .375 .375 -315 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 .375 .37t .375 .375 .375 .375 .375 .375 .375 .154 .154 .154 .154 .151 -154
.1148+08
.3798+07
.167E+08 -235E+08
.778E+07
.138E+06 .
f,82E+06
.783E+06 .137E+07 .216E+o7 .4438+07 .774E+O? .1 22E+08
.'l80E+08 .251E+08
.1{EEr06 .408E+06
.8378+06 .1468+07 .231E+07 .47 4E+07
.828Ef07 . 131 E+06
.192Er08
.268E|08 .'l C7E+O6 .461E+06 .946E+06
.557 E+O7
.462E+05 .127E+06 .261 E+06
.4568+06 .719e+06
.148Er07 . ? 58
E+07
.407Er07 .598€+07 .636E+07 .493 E +0 5 -136E+06 .279E+O6
.488€+06 .769 E+06
.'l588+07
.27 6E+07 .435 E+0 7
.640€i07 .893Er07 .557E+05 .154E+06
.315Er06
.'l65E+07 .2618+07
.551 Er0 6
.535E+07
.17AE+07 -31?ErO7 .491E+O7
.9 35E+C7 -14?E+Oz .217E + 08
.303E+08 .186E+06 .514E+o6 . '105 E+ 07
. 1948+07
.291E+oz .596E+O7
.'l04E+08 .1648+08
.2 42 E+08 .337E+08 .225E+O6 .619E+06
.127t+O7 -22?ErO7
.350E+07
.8698f06
-7238+D7
.101E+0E .621E+05
.'l 71 E+06 .351Er06
.614E+06 .968E+06 .199E+07 .3478+O7
.548Er07 .805E+07 .112E+08
.7 498+OS .2068+06 .424E+O6 .740E+06 .117 E +07
- 291 E+08
.2408+07 .419E+07 .660F+07 .971E+07
.4078+08
.136€r0E
.907 E+04
.302E+04
.719e+O7
.1?6E+08 .'l9EE+08
.250€+05
.51fE+05 .8978+05
.1 r.1E+06 .290 E+ 06
.E338104 .171E+05
.299€+05 -471Er05
.968 E+0 5
Rotational Nozzle Flexibilities for Cylindrical
Vessels
163
Table 6-1 Continued ROTA STIf
VESS€L TCK,IN
VESSEL OD. FI
17.0
0
0
17.000 1 7.000 I 7.000 17,000 17.000 17.000 17.00c 17.000 't 7.000 17.00 c
17.000 17.000 17.000
1.250 I .500 1.750 2.000
1 1 1
0
17.000 17.000
17.000 '| 7.000 17.000 17.000 17.000 17.OOO
17.000
17.000 t 7.000 17.000 17.000 17.000 17.000 17.000 't7.000 17.000 17.000 t 7.000 .000 17.000 17.000 17.000 17
1
7.000
17.000
7.000 17.000 17.000 17.000 17.000 1
17.C00
ION,
.15 4 .15 4
.500
.675
4
.500
.500 4-500 /. .500
.1248 +05 .255E+05 .445E+05
.2'l0E+06
.701E+05
.432 €+06
.144E+O6
.,.500 4. 500
6.625 6.625 6.625 6.625
.250 .500
.6?5 .000
1.500
.375 .500 .625 .750 I .000 1.250 r.500
1
.000 .250
1.500 .250
.375 .500
.625 1.000
1.250
.33 6E +0 5 .588E+05
.27EE+ O6
.9?7E+ 05
E
+
07
.1758+07 .244E+07 .4928+05
.571E+06 .997F+ E6 .157 E+07
.231E+07
.190E+06 .332€+06 .524E+06 .771E+O6
-3?3E+07
.108E+07
.271t+05
.904E+04
.717E+05 .1538+06
.51',|E+05
.268E+06
.2 49E+05
.893E+05
.152E+07 .239E+O7
.797E+O6
6 -625
.280
.3518+07 .4918+07
- 1178+07
.625
.3?2 .3?2 -322
.625
8.625
I .625 I .625 8.625 10.750 10. 750 10 .750
750
I 0.750
,28 0
10-750 0. ?50
I 0. 750
12.750 12.750 12.750 1?.750 12.750 12 -750
12.750
.358E+05
.987Er05 .203E+06 .35 4E+O6
.164E+D7 .119E+05
.329€+05
.676e+O' .118Er06
.3?2 .3??
.5588+06
.1E6E+06
.1 15L+ 07
- 3E2E
.122
.Jt6E+07 .464E+ol
.105E+07 .1558+07
-322
.649E+07 .451E+45 .124E+06 .?55E+06
.t22 .32? .365 .365
.2oOE+ol
+06
.668E+06 .216E+07
.'l 50E+05 .414E+05
.851E.05
.1 49 E +06
.365
.4 468+06 .703€+06 .111e+07
.365
.25?E+ 07
.2348+06 .48'l E+ 06 .841E+06
.39E€+07
.133E+07
.365
.585E107 .E17E+07
.272E+A7
0. 750
'10. 750
.4236+06 .668€+06
.375
.542€+05 .149E+06
-375
.1958+07 -181Er05 .498E+05
.3078+06
.102Er06
.536E+06 .846E+06 .171E+07
.179E+06
.303€+07
1\
-t64E+05
.28 0
a
1
.101 E+ 06 .176E+06
.119
6 -625
8.625 8.625
'|
.178E+05
.252 E+06 -397E+06 .583E+06 .E15E+06 .595E+04
.755E+06
6.625
10 -
1
.280 .280 .280 .280
.133Er06
.4508+04
.'l41E+O6 .289 E+06 .505E+06
8
.375
-237
.'135E+05
.280 .?80
6.625
2.000
2.000
.237
.2EO
.7 50 1
-2't6
4
1.750 2.000
.592€+06
69 E+06 E + O6
.37 ?E + 05 .7 64e+05
-216 .?37 .237 .237 .237 .237
1.000 1.250 1.500
.1t8E+07
1
.?16
.216
4.500
.
.547 E+O6
J
.500
.507E+06
.'l64E+D7
.154
3.500
4
0UTPLANE CIRCU
.'t54 .216
.2',16
4.500
IN.LB/DEG
.267
3, q00 .500 4 .500
€L
.800E+06
.500
5.500
VE SS
ZLE ROI SIIF I NPL Allt STD LONGI
.500
.250
L.
TCXTIN
3
3.500
CY
NOZ
.000
.500 3 .500
.750
17.000 17.000 17.0C0
LCULAT
.216 .216 .2't6 .?'t6
17.OA0
t7.000 ,7.000
.500
5
2.00 0
7.00c 17.000
7.00
2.375 2.375 2.3?5
.500
1.750
r
't
OD,IN
3.500
17.000
17.000 17.000 't7.000
CA
NOZZL€
3
17.0 00
17.000
F
.?82E+O 6
.579€+06 .101E+07
!
164
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULAIION, CYL. VESSEL
v€ssEL
OD,fT
17.000 17.000 17.000 17.000 I 7.000 1
vE TC
1.500
I .750
?.000
.250
7.00 0
.625 .750
17-000
17.000 17.00c 17.000 17.000 17.000 17.000 17.O00
17.c00 17.000
I .000
1.250 I .500
1.750 2.000 .250 .37 5
17.C00
.500 .625
r7.000 17.000
I .000
17.AOO
1. 500
17.000 I,
i: "
'17.000
; I li ii
7.000 17.000 17.000 17.000 17.000
)rt
17.000 17.400 17.000 17.000
a:
l.
ssEL K,IT{
't
17-000
17 .00 0
1.250 1
.500 .625 .7 50
I .000 '| 't
17.0t/0
1
.37 5
't
14-000
14.000 14.000 14
.000
r6.000 16.000 I 6.000 1 6.000 1 6.000 16.000 16.000 16.000 16.000 16.000
.375
.375 .37 5
.375 .375
.000
.500
.625 .750
I .000
.250 1.500 1
1.750 2.000 .250
.375 . t00 .625
t7.oac
.7 50
I .000
1.250 1
1
8. 000
8.000 't8.000 18.000 18.000 1
.375 .37 5 .37 5
-375
.3 75
.375
.37 5
.5C0
.375
.000
.375 .375
20.000 20.000 20.000 2
0
.375 .37 5
?2 .000
22.000 ?2 .OOO 22 .00 0 22 .000
22.000 22.000 22.000 22.000 22 .000
.375
24
.000
24.000 24.000 21-OOO
.37 5
.192E +07
.336E+07 .529E+07
.375
24-OAO 24.OOO
.3? 5
.375
.200E+05 .552E+05 t 3E+ 06 E
+06
.312E+06 .640E+06 .112E+07
.176e+07
.7 78E+ a7 -109E+08 .693E+05 .191E+06 -39?E+06 .685E+06
.259 e+07
-222E+47 .388 E+07 .611E+A7 .E99E+07 .'125E+08
- 7t9E+O6
.362E+O7
.231
E+0 5
.6378+45 .13'lE+06 .??ae+o6 .360Er06 .1298+07 .204E+07 .300E+07 .418E+07
.786E+O' .2178+06 .445E+06
.26?E+O5 .722E+O5
.777E+06 .123E+ 07
.259E+06 .40EE+06
07
.838E+06
07 .69t8 + 07
.146e+O7
.102E+C8 .14?E+08
.340E+07 .47 4E+o?
.439E
+
.? 42E+ o6 .49?E+06 .868E+06
.137E+07 .281E+07 .491E+Oz
.l
488r06
.231E+O7
.293E+05 .607E+05 .'166E+06 .2 89
E
+06
.457 E+O6 .937f+O 6 .164E+Oz
.775E+ 07
.258E+07
.114E+08 .1 59E+0E .972E+05 .26E€+06
.380E+07
.550F+06
.5308+07
.3248+O' .895E+05
.183Ef06 .520€+06 .505E+06 . t 04 E+07
.5 4te+07
.lE1E+07
.857E+07 .'l26E+ 08 .176F+0E .106E+06
.286e+O7 .42OE+07 .586E+o7 .355E+05 .978 E+05
.2938+46 .6028+06 .105E+07
.000
24
.327E+O7
. 198
.311E+07
.37 5
.159E+07
.234E+o7
.593E+06 .936E+06
.151E+O7
21.OOO
CIRCU
.1
.960E+06
.37 5
OUTPLANE
.340€+06
.8 79E + 05
.000
20.000 20.000
.1 65 E+06
. ?5?E+
18.000 18.000 20.000 2 0.000 20.000 20
.478E+07 .703E+07 .982E+07 .6008+05
.108F+07
.37 5
1.250 1 .500 1.759 2.000 .250 .375
17.000 17.000 17.000 17.000 17.000 17.000 17.000
.375 .375
E.000
.7 50
7.000
17.000 17.000 17.000 17.000
-375
1
1
17.C00
4.000 14.000
.375 .375
.500
.525
'17.000
14 . C00 14 .000 14 -000
TCX,IN INPLANE STD LON6I
.375
,375 ,500
7.000
17.000 17.000 17.000 | 7.000 I 7.000 't 7.0c0
12.750 12.750 12.750 '| 4.000
NOZZLE ROT STI F IN.LE,/DEG
18 .000
t 7-000
t7.000
N
.2 50
1.750 2.000
I 7.000
17.O00
L E
OD,I
1E.000 .37 5
17.000 ,|
.750
2.000
t'l0zz
.166a+07 .341E+Ol .595E+07 .939E+07
-2O1E+O6
.351E+06 .553E+06
.114E+07 .'198E+Oz
.313E+O7
Rotational Nozzle Flexibilities lor Cylindrical Vessels
165
Table 6-1 Continued
SIIfF CALCULAIION, CYL. VESSEL NOZZLE ROT STIF IiI.LB/DEG VESSEL NOZZLE OUTPLANE T CK,I N INPLANE TC(,IN OD,II{ CIRCU STD LONGI ROTA
VESSEL
OD,FT
17,0 00
17.000 't
1.750 2
?.0 00
17.000
t 7.00 0
17.000 1 7.000 1 7.000
t 7-000
7.000 17.000 '| 7.000 17.000 1 7.000 17.000 17.000 17.000 17.000 17.000 17.000 1
-750
26.000
.150E+08 .2'l0E+0E
-500E+07 .698E+07
2.000
.500 1.0c0 1.?50 1-750 2.000 -z>tJ
.500 .000 .7 50 2. 000
.500 .6?5 .000
1.25O
1.500 1.750 2
.000
.500
1
.250
I .500
7.00 0
.500
17.000 t 7-000
17.000 17.000
.647
1.754 2
.000
.250 .375
I .000 't .2 59
't.500
E+
07
+06
.12ta+06
.417E+O5
28 .000
.345E+06 .7 Q7E+06
2E.000
.124E+07
.115E+06 .236E+06 .412E+06
28.000 28.000
.650E+06
28.000 28 .000
.195E+07 .400E+07
28.000 28.000 28 .000
.699E+07
.233E+o7
.375
.'110E+08 . t 62E+08
.36EE+07 .540E+07
28.000
.375
30 .00 0
-375
30.000 30.000 30.000 30.000 30.G00
30.000 30.000 30.000 30.000 .000
.375 -375
.375
.226E+08 .154E+06 , 370E+ 06
.760€+06 .133E+07 .2098+07 .430E+07 .751E+07 .'1188+06
.3?5
.375
.17
4E +
08
.243Er08 -144E+06
32.OOO
.396€+06
3 2
-E t 2E+06
.000
32.000 2.00 0
52.000 32.000 32.000 5
2.00
.375 .375
J2.000 56.000 3 6.000 36-000 56 .000 36
.000
36.000 3 6.000 J6.000 36.000 40.000
.375
40.000 40-000 40-000
40.000 40.000 40.000 40 -000
.375 -375 .375 .3?5
.375
.442t+O6 .698E+06 .1438+07 .?50E+o7 -395E+07
.5818+07 .8118+07 -479 E+05
.132€+06 .?7'l E +o6 .475E+06
.127E +08
.422E+O7
.26EE+07
.6218+07 .E67E+07 -541E+05
.4 47E+A6
.1tt9E+O6
.918E+06
.306E+06
. 160E+07
,534E+06
.253E+07
. E43E+06
.519
.'173E+07
E+
07
.907F+07 . t 43E+08 .2't0E+08 .29 4E+ 08 .181E+06
40 .000
.7518+07 .448E+05 .123E+06 .253E+06
.7 46E+06 .1538+a7
.16?E+06 -5()
.133E+O7
.142E+07 .224E+07 .460E+07 .803€+07 .'186E+08 .260E+0E
0
36.000
17.000 17.000 1 7.000 17.000 17.000 7.000
.37OE+ 07
26 ,000
3
't
.37 5
26.OBO
32
17-000
7.0C 0
- 601E
1
t . t)00
1
.1808+07 .1028+08
17.000 17.00c 17.000 17.000
1
.218E+06 .381E+06
?6 -OOO
17.OOO 17.OC0
't
.106€i06
.655E+06 .114E+07
.500
17.000 17.000 17.000 1 7.000 17.000 17.000 17.000 '17.000
.319E'06
1
7.000
7.0C 0
.37 5
.123E+07 .?16E+07 .340a+07
7.C00 17.O04 1
26 .000 26 . C00
.460E+07 .642E+o7 .386€+05
26 -OOO
'|
17.000 17.000
.193E+0E .116E+06
t .000 1-?50
17.C00 1
.138E*08
24.000
26.000 26.000 26.000
't
17.000 17.000 17.0c0 17.000
? 4 .OOO
.500
I 7.00 0
7.000 17.000
.000 -250
.302E+07 .4778+07 .7 0'l E.07 .979E+o7
-6038r05
.4988+06 .10?E+07 .179E+07
.166E+06 .341Ea06 .596E+06
.282E+07
.939
F+
C
6
07
.193€+07
.101E+08
.337E+O7
.579E
+
.1598+08 -234E+08
.551E+07 .78'lE+o7
rf
:l :
166
Piping Stross Handbook Table 6-1 Continued
R0lA STIFF CAI-CULATION, CYL. VESSEL VESSEL
OD,'T
17.000
ICK,IN
2.O00
17.000
.250 .315 . t00
I 7.00 0
-625
t 7.000 I 7.0 00
17.000 17.000 17.0 00
.7 50
1.000
1.250 I .500
48.000
18.000
.250 .375
2.375 2.375 2.375 2.375 ?.375 2.375 2.375 2.375 2 .375 2.375
.00 0
18.000 1E.000
tE.000 1
E.00 0
18.000
.500
.625 .750 1.000 1 .250 1
.250
.500
1E.000
18.000 18.000 18.0C0
16.000 18.000 't6.000 16.000 18.000
.500
1-750 2.000
I 8.0 00
iiI
4E.000 4 8 .000 48 .000
4E-000
t8.000
ir
40.000 48.000 48.000 48.000 48.000
1.750 ?.000
18.0c0 18.000 18.000
li
0zzLE OD,II{
17.000 17.000 17.000
18
i,:
vEssEL
.750 1.000 1.250 1.500 1.750 2.000 .250 .37 5
1E.C00
.500 .625
18.000 1E
.00 0
16.000 16.000 18.000 18.000 1E
.00 0
1E.000
.7 50
.000 1 -250 1
1.500 1 .?50 2.000
z>u .37 5
18.000
.
'tE.000 18.000 18 .0 18 .0
.500
.625
00 00
-7 50
18.000 't6.000
1
16.00 0
't
16.000 18.000 '16.000 18.0 0 0
'| 1
.000
3
.500
3.500 3.500 3. 500 3 .500 3 .500
3.500 3. 500 3.500 3.500 4. 500 4. 500
4. 500
4.500
4. 500 4 .500
4.500 4. 500
4.500 4.500 6-62> 6 .6?5
6.625 6-625 6.625 6-625
.250
6.625 6-625 6.6?5 6.625 4.625
500
8.625
.250
.500
.750
2. 000
I E.000
48.000
-
.625 .7 to
18.000 18.000 18.000
1
.000
18 .00 0 18 .00 0
1
.500
1.250
.6?5 8 .625
8
a
.625
a.625 4.625
NOZ2LE ROT SII f II{.LB/DEG OTJTPLANE T CK,I N IIIPLA E
SID
LOIIGT
CIRCU
.3278+08 .218E+06
.109E+08
.601E+06
.200E+06
.123E+ 07
.411E+O6
.3? 5 .37 5
.215e+07 .540E+07
.718E+06
-375
- 698E+07
-375
.'192E+08
.375 .375
.375
.375 .375
.'l22E+08 .283E+ 0E .395 E +08
.7?7e+Oj
.1138+07 .2t3E+O7 .406E+0? -641e+O7 .942E+D7 -'13
2
E
+08
-88?E+04
.2948+O4
54
.2438+05
.81 08 +0 4
-154 .154 .154
.499E+05 .871E+a5 .157E+06 .282E+06
-166Er05
.493E+06
-164E+06 .2 59 E+06 .381 €+06
.154
.t
.'154
.154 .154 .154 .154
.216 .216 .216 .216 .216 .216 .216 .216 .216 .216 .237 .237 .237 .237 .?37 .237 .217 .237 .280 .280 .28 0
.280 .280 .280 .280 .280 .280 .280
.322 .322
.778E+06 .111E+A7
.372 .322
.9418+05
60Er07
.sf,?E+06
.131E+05 .362E+05 .742E+05
.437E+O4
.130E+06
-43?E+O5
.t
.205E+06 .420E+06 .733E+06 .1 168+07 .170E+07 .237E+07 . l73E +05 .478 € + 05
.121E+05 .247E+O5 .682 €+0 5 .'140E+06 .z 44E+O6
.386E+06 -567Er06 .792E+O6 .
5 78E
+04
.159E+05
.9818+05 .1718+06 .2708+o6
.327E+O5
.555E+06 .969F+06
.22tE+97
-185E+06 .321E+06 .510E+06 .7 49E+06
.311E+07 .263E+05 -726e+Os ,|
.1 05E +07 .8 78 E+04
.2428+O5
49E+06
.497Er05
60E+ 06
.868E+05 .137 e +O6 - 2El E+06 .491E+06
.153E+07
. .
2
.411E+06
.843€+06 .147E+O7
.232e+07
. 571 E+0 5
.901E+05
.477E+Ol .348Er05
.774E+06 .114E+07 .159E+07 .1 l6E+05
.9 59E + 05
.320E+05
.342E+07
.197E+06
.322 .322 .3?2
.?90E105 .4 58 E+0 5
.314E +06
.543E+06 -111E+07
.195E+07 .307E+07
.657E +05
.1158+06 .18'l E+06 .371 E +06 .6 49 E +06
.102F+07
Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-1 Continued ROTA STIFF CAICULATION, CYL. VESSEL
vEssEL TC K,I I'I
VESSEL
00,fT
0zzLE OD,I N
NOZZLE
TCK,IN STD
0
1.750
18 .00 0
2,0 00
1E.00
18.000 1E.000 18.000
18.0
't
't
I C. 750
-ol>
10
.000
18 .00 0
'1
18.C00
1.750 2.000
. 500
1E . C00
18.00c
.375 .500
1E.000 1E.000 18 .000
18.000 '16.000
't8-000 1E.000
18.000 16.000
.750 1 1
18
16.000 1E.000 .000
18
?8.000 't8.000 1E.000 18-000
18.000 't I .000
.375 .500 .625 .750 .000
2. 000
.250 .37
5
.500 -750
1.000 1.250
t.500
-250
.7 50
r .000 't -250
?-000
-
000
18.000 18.0 00 18.0 0 0 1E.0 00 18 ,000 18 .0 00
18.000
12 -750
. 169F+07
12 .750 12 .7 50
11-OOO
.750
16 .00 0 18
.'l45E+06 .2968+06
14.000 1 4 .000 14 .000 1 4 .000
.500 .62
5
.750
1 .000 1.250 1.500 1,750
14
1
6
.375
.295E+07
.9E2E+06
1E
.000
1E .000 1E.000 1E .000 I E.000
18,000 20.000 20.000 20.000 20.000 20.000 20.000 20 .000
20.o00 20.000
+06
E
+
07
-515E+a7 .7 56E+ 07 .106E+08
-5ft
-375
.37 5
6
.155E+07 .22EE+Ol .318€+07 -195E+05 .536E+05 .110E+06 .192E+O6
.303E+06 .622E+O6 .1098+O? -1?2E+07 .?52E+O7
.352E+07 .619E+05
.666E+ A6 . 105E+07
.8738+07 .J?2E+08 .7 64E+05
.127E +O6 .222E +06
.350E+06 .719 E+O6 .126E+07
.'f98E+07 .291E+07 .106E+07 .2558+05
. 210E+ 06
.702E+O5
.432E+06
.144E+o6
,755€+06
.375
+O
.225E+O5
-594E+E7
-375
-5 62E
.186E+06 .3E1E+06
.377 E+07
.375
-27 4E+o6
.67 4E+05
.2168+07
18 ,000
18.000
.577t
.326E+07
.000
18.000 1 6.000
05
.3108+06 .1P'7
.000
t6-000 '| 6.000
+
.910E+06
.375
.9948+05 .'17 4E +0 6
.161E+06
16.000 16
-129E +07
.189E+07 -265E+07 .17 6E+Os .4E4E+05
.521E+06 -E22E+o6
.9 5 4E+07
.000
16.000 1 6.000 1 6.000 1 6.000 16.000
-468E+06 .817E+06
.527Er05
.750 12.750 12 .750 12.750 12
1
tE.000
1E.000
.79LE+07
12 -750
1.5C0
1.?50
1.500 1.?50
16 .00 0
I 0. 750
14.000 't 4.000 't 4.000
1
1E.000
18-000
.568E+07
12.750
-2288+06
.387E+ 07
10 . 750
- 5648
2. 000
t 6 .000
.245E+07
.375
1E.00 0
18.000 16.000
.365
I 4 .000
1-750
'18.000
10 .750
-114E+O6
.140r+07
.000 .250
2
.403€r05 ,827Er05
.24E8+06 .433E+06
.4658+07 .683E+07
18.0C0 1E.000
.146E+05
.375
.000 .000
.000
.438 E +05 .121E+06
.683 E+06
.750
-150E+07
.210E+0?
.365
0
CIRCU
.6J08+07
.750 10.750 't 0.750
I
OUTPLAT.IE
.1512+A?
'12.750
t8.000 r8.000 18.000 18.000
.000
F IN.L8/DE6
INPLANE LONGI
.250 1.500 1.750
1E.000
tE 't 8
0.750
.500
00
18.000
.322
10 . 750
18.000 18.000 1E.000
a.ol>
ROT STI
.119 E + O? .? 44E+07 .427E+07
-252E+06 .397E+06
.8'l5E+06 -142E+O?
-674t+e7
.225E+07
-99oE+07 .'138E+08
.330E+07
.235E+06 .483 E+06 .844E+06
.785E+05 .161E+06
. 1 33E +07
- 4 44E+06
.854€+05
.?738+A7 .477?+07 .753E+07
.11tE+08
- 461E+O7
.2858+05 .
z
8'l E+06
.9t'lE+06
.159E+07 .251E+o7
.369E+07
167
168
Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULATI0NT CYL' 0DufT
VESSEL TI(TIN
3.00 0
2.000
VESSEL
1
2? -OOO
18.0 00
13.000
.500
18.000 1E,000
.750
18.C)00
18.000 18.00c 18 ,000
18.000 1b.000 18.000
OD,IN
20 .000 22 .00 0
.250
18.000
NOZ2LE
r.0c0 1.250
22.000 22.000 22.000 22.OOO
22.000
1.500 1.750
22 -000
.000
22 -OOO
2
22
.000
24.000 24.000 24.000 24.000
18.C00 18.0 00
.500
1E.000 1E.000
-750
24.DAO
1.000
1.2t0
18.000 18.00c
1.500 1.750
24.000 24.000 24.000 2/..000 2 6.000
'tE.0G0
18.000
2. 000
24 .000
1E.0 00
.250
18.000 1E.000 1E.000
5
?6.OAO
.500
26.000
- 750
I .000
26-000 26 ,000
18.000 18.00c 't8-000
1.250
.500 1.750
26.000 26.000 26.000
.000
2-000
1E-000
1E.000
1E
't3.000 18.000 18 .000 1E.000 18 .000 16.000 13.000 16.C0C
18.000 't8.000 18.C00 18.0U 0
16.000 18.000
.37
.625
1
.?50
28 .000
.500
E.000 28.000
.625
2E-000
.750
28 .000
.000 1 .250
28.000 2E.000
'I
1.500 'l ,7 50
?.000
.250
.375 .500
28.000 28.000 28.000 30.000 30.000 30.000 30-000
.750 .000 .250
50.000 30.000 30.000 30.000 30.000
2.000 .250
30.00 0
.500
32.000
18.000 18.000 16.000
18.000
18.000 18.00c 18.000 1E.000 18 .000
1
16 .00 0 18.00 0
1
t6.000
26.000 2
18.000
18.000 18.00c 16.000
26.OOO
1
.000 32 .000 3 2
.625
3? .OOO
.000
32 .000
.250
.500 1-750 2 .000
32.000
3 2.00 0 3 2 .00 i:J 3 2 .000
32 .000
VESSEL
f IN.L8'/DEG TCX,IN TNPLANE OUTPLANI CIRCU LONGI SID
NOZ2LE ROT STt
.375 .15 5E + 08 -375 -944E+05 -375 . ?60E+06 .375 .5348+06 .375 .933 +0 6 .375 .1478+O7 .3ZS .3OZE+07 .3?5 .528E+07 .3?5 .8 33E + 07 .375 .122E+08 .375 .171E+08 .375 .103Er06 .375 . 285 E+ 06 .375 .585E+06 .375 . 102E+07 .375 .161E+Ol .3?5 .331E+07 .375 - 578E+07 .375 .91?E +07 .375 .134E+08 0E -375 . 1872 E+ -375 .1t E+06 .375 .3',10E+06 .375 .636F+06 .375 -'l11Eto7 .375 -115E +O7 .3?5 -3608+07 .3?5 .629E+07 .375 -992a+O7 .375 .146€+08 .3?5 .204E+0E 06 .375 .122E++06 .375 .33 5E -375 .667E+06 .3?5 -12o8+oz .375 .139E+07 .375 .5898+07 -375 .1C7E+08 .375 '679E+Q7 .375 .1 58E +08 .375 .220E+03 .3?5 ' l31E+06 .375 .360E+06 6 .3?5 .7 3E Elo .375 .1298 +o7 -3?5 .204e +A7 .375 .4'l8 €+ 07 -375 .730 E+ 07 .3?5 .1 1 5E+08 .375 .169E+08 .375 .236E+08 .375 .1169 + 06 .375 .3R5€+06 .3?5 .790€+06 -375 - 133 5+0 7 .375 -?18E+O7 .375 -4t ?E+O7 .375 .760E+07 .37, .123E+08 .375 .181E+08 -375 .253E+o8 F
.515€+02 .3'l5E+05 .867E+05 .178E+06
.311Fr06 .491E+06 .101E+07 .17 6E+07
.2788+07 .408E+07 .570E+07
.345€+05 .950E+05
.'t95E+06 .3418+06 .53EE+06
.1'l0Ei07
.1938+07 .304E+07
.447E+07 .624E+O7
.3758+05 .103E+06 -212E+O6
.371E+06 .585E+06 -120E+07
.2'l0E+07 ,331E+o7
.486E+07 .679t+O7 .405E+05 .1128+O6 .229 E+06 .400E+06 .631E+06
.'l30 .22
E+0 7
6E + O7
.357E+07 .5?5e +o7 .733e+O7 .435E+05
.120E.06 -246E+06 .430E+06 .678E+06 , tJ9E+07 .243E+O7
.3E4Er07
.564Er07 .788e+07
.465E+05 .'128E+06 .263E+06
.460E+06 .7?5E+o6
.149Er07 .260E+D7
.4'l0E+07 .603€+07 .E12E+07
Vessels Rotational Nozzle Flexibilities for Cylindrical Table 6-1
Continued ROTA VESSEL
0D,rT 'tE.000 18.000 't
8
.000
18.0CC
1E.00c
tE.00ri 18.006 't 8.000 18.000 1E.000
18.000 18.000 18.000 1 8.000 18.000 18.000 16.000 't8.000 18 .00 0
15.C00
16.0c0 16.000
16.000 18,000 16.000 18.000 18 .000
18.000 16.000 18.000
STIf'
NO2ZLF
VE SSEL
OD,IN
TCK,IN
.250 .375 .500 .625 .? 50 1 .000 1 .250 1-500 1.750 2.000 .?50 .375 .500 .625 .75O 1.000 1.250 I .5OO 1 .7 50 2.000 .250 .375 . 500 .625 .750 't .000 1 .250 1.500 1 .750 2.000
CALCULATION'
36.000 36.000 36.00 0 36 - 000
6.000 6.000 36.000 36.000
3 3
36. ooo
6.000 40.000 /.0.000 40.000 40.000 40.00o 40.000 40.000 40.o0o
3
40 .000 40 -000
4E.ooo
48.000 48.000 48.000 48.000 48.000 48 .000
48.000 4E.000
48.000
CY
L.
VESSEL
NOZZLE
ROT STI
TCK,IN
INPTANE LONGI
slD
-375 -375 .375 -175 .375 .3?5 -375 -375 .375 .375 .37t .3?5 .375 .375 -375 -375 .375 -375 .3?5 -375 .375 .375 -3?5 .3?5 .375 -375 -375 .375 .3?5 .375
f
It{.LB/DEG
.158Er06 .434t+06 .892E+06 .156E+O7
.2468+07 .504E+07
.8El€+07 . 1f9 E+ 08
.204€+08 .285E+08
OUTPLANE
CIRCU
.525E+05
.115E+o6 _297E+O6 . 519 E+06 .819 E+06 . 168€ +07
-2948+07 .463E+07 .681E+O7 .951E r07
.176E+06
.586t+05
.484E+06 .99481 06 .17 4E+07
.f31E+06
.271E+07 -562E+O?
.9a2E+o7 .155E+08 .?28E+0E
.3135+08 .212E+06 .584E+06 "120E+07
.16',| E+06
.579F+06
.9.13E]06 -187E+o7
-327E+A7 .5168+O? -759'-+o7 .106E+08 .706E+05 -195E+O6
.209E+07
.399E+06 .698E+06 .'110E+07
.678E+07 .118E+08 .187E+08
.395Ef07
.330€i07
-226E+O7
-623E+O7
.383E+08
.9'l5E+07 .128€+06
.858E+04
.286E+04
.4t6Et05
.1628+05 .283F+05
.275€+08
rt,
2 -375
19.000
2 -375
19-CC0
19.000 19.000 't9.000 19 .000
19.000 19 .0
00
19.000 19.000 19.000 19.000 19.000 19.000 19.000 19
-
000
19.000
'19.000
19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000
.500 .625
2.375
.000 1.250 1.500
.500
2.375 ?.375 2.375 2.375 2.375 3.500 3.500 3.500
1.0c0
3.500
't
1.750 2.000
'l .250
.5c0 1-750 z-000
't
.250 - 500
3. 500
f.
500
3.500 3.500 3.500 4-500 4 .500 4. 500 4
.500
4.500 1
.000
1.250 1.500 1.750
4. 500
4.500 4. 500 4
.500
-154 -151 .'t54 .154 -154 .154 .154 -151 -154 -154 -216 -216 -216 -216 -z'16 .216 -216 -216 -216 -216 -23? -237 .237 -237 .237 .237 .237 .237 .237
-237E +o5
.78E E+04
.848E+05 .134 E + 06
-446E+0j
-275e+o6 .4808+06
.757E+ 06 - 1'l1E+o7
-155ErO7 . 128 E+05
-3528+05 -722E+O5
.915E+05 .160 E +06 -ZSZE+O6
-371E+O6
.5'188+06 .426F+O4
.117€+05
.241E+O5
.126E+06 .199E+06 -409E+06 -714E+o6
_42.1E+O5
- 166E+07
-5528+O6 -771E+o6 .563E+04
.113E+07 .231E+Oz
' 169E+05 .465E+05
.9 55 E+05
.167E+06
-2638r06
-6648+O5
.136E+06
.2388+06 .375E+O6
.155E+05
.318 E +0 5 .556E+05 -8778+O5
-
.180E+06
-119E+O7 -219E+O7
.196ErO6 .7292+o6
540€+06 -94f, E+ 06
.31 4E+06
Table 6-1 Continued RO]A STIFF CALCULATION, CYL.
VESSEL TCK,IN
vEss€L OD,FT
NOZZLE
NOIZLE
OD,!N
TCK,IN STD
19.000 19.00 0
19.000 19.000 19.000 19.000 19.000 't9.000 19.000 19.000 19 .00 0
19.000 19.00c 19.000 19.000 19.00 0
19-000
:l
2. 000
.250 .37
n
.750
19.000
19
10 .7 50 10 .750
5
1
.7 50 'l
1.750
2.000
.000
19.000 t 9 .000 19 . C00
19.000 19.000 19.000 19.000 9.00
.625 1 '1
19.000 19.000 19.000 19.000 19.ai00
.500
z. 000
.500 ,7 50 '|
.000
1.250 1.500
.3?2
.322 -3??
10.750 10.?50 12.750
12.750 12.750 12 .750 't2-750 12.750
.365
1
.5538+07 .5138+05
-375
.5i7E+o6 .800Ei06
.1648+ A7 .247E+07 .452E +07
.665E+C7
.9298+07 .568E+05 .157E+06
14
.32'l €+06 .561E+06 .885E+06 .132E+07 .317 E + A7 ,501E+07
.000
14.000
1
6.000
't
6. c00
16.000 6.000 1 6.000
t
.7 36e+07
.5 r>
.000
16.000
2. 000
.111E+A6 .290E+06
4.000 14.000 14.000 14.000 1 4.000 14.000
.7 50
1.500 1.750
.422E+06 .665E+06 .137 E+07 .?39E+07 .3768 +07
1
16.000 16.000
1.25A
t t8E+06
12 -750
c25
.000
.108E+07 .189E+07 .299E+07 -4398+07 .6118+07 .427E+05
-772t+Ol
12.750
16 .
.52EE+06
.241E +06
12 -750
.?50 .500
.934 E+05
.
0.750 10.750
t4-000
'l9.00 0 19 .000
.332E+07 .464E+07 .339E+05 .192E+06 . 3f5 E+06
't
1 4.00 0 1 6 .0C0
19.C00
.400E+06
.'143E+D7 .2 26E+ 07
10 .7 50
10 . 750
-855E+04 .236E+O5
.2E0
.322
.375
-375
.
NE
.1O?E+O7
.821Ei06
.322
A
CIRCU
.256E+Os
260
.280 .280 .280 .322
OUTPL
.3068+07 .7olE+C5 .145E+06 .253E+06
.280 .?80
0. 750
't -750
2. 000
9.000
19.000 19.000 19.000 19.000 19.000
.000
1.750
0
19.00 c
.280
'12.750 .500
19.0c c
1
.500
.600
19.000 19.000
'|
.000
1.250
19.000 19
8.625 8.625
.37
19
1
.6?5
3.625 'l0.750
.500
.000 't 9 .000
a
SII F IN.LB/DEG
INPLANE LOt./ GI
8.625
.000
.250
ROT
8 -625
t .0c0
.000
19 ,000
_
8.625
2
19.000 19.000
-625
6.625 6.625 6.625 a .625
.?50
19-C00
t9.0cc
.28 0
6
1.250 1.500 1.750 2.000
't.250 1.500 1.758
19.000 19.000
-625
6.625 6.6?5
.000
19.000 19.000 19.000 '19
-2E0
6
.75A 1
'19.000 'l
5
.500
4.500 6.625 6.625
VESSEL
tC3t+08
.484€+05 .845E+05 .133E+06 .27 4E+O6 .47EE+06 .7 51E +O 6 .111E +07 . 155E+07
.1t3E+05
.3'l l E+05 -
639E+0 5
-112F+06
.1 76E+06
.561E+06 -631E+06
.996E+06 .146E+C7 -204E+C7
.142ErO5
. 392 E+0 5
.805E+05 -141E+O6
.222E+06
.455E+06 .79
5 E+o 6 - 125E+O?
.'184E+oz
.257€+07 .17'l E +Os .171E+O5
.968Er05 -t69E+06 -267ErO6
.5 47 E+O6
.956E+06
.15t E+07
. ?22E+A7
.310E+07
.'189E+05 .522E+O5
.1078+06 .'l t 7E+o6 .295E+06 .606E+06
.106E+07 .1678tO7 .245E+07 .313E+07
.656E+05 .1E1E+06 .371E+06
.219E+05 -602E+05
6IEE + C6
.216E+O6
.102E+07 .21OE+07 .367 E+07
.341E+06
.850E+07
-2838+07
-
.578F107
.'l
19E+ 08
,'12
4 8+O
6
-699€+06 .122E+a7 .193E+O7 .39 6E+Ol
Rotational Nozzle Flexibilities for Cylindrical
Vessels
171
Table 6-1 Continued ROTA STtFF VESSEL
OD,fT
VESSEL I€KTIN
.375
19.C0C
1
.750 ,0c0
19.C00
'1
.?50
19.000 19.00c
1.750 2.0c0
19.000 19.000 19.000 19.000
.375
19 ,000
19. 000
E,000
18.000
-3?1E+07
.7 648+O5
20 .000
.229 g +O6 .470E+06
.25U
20.co0 20.000
.82'l E+06
.5O2E+07 .306E+05
19 .000
.500
22.000 ?2.000
.000
22 .OOO 24 .000
.520€+06 .9cBE+06
.173E +O6
.3038+06 -980E+06
2+ O7
.1718+87 -270E+O7
.3978+A7 .555E+07 .336E+05 .925s+05 .190E+06
.532E+06 -523E+06
.322E+07
.107E+07
.250 .500
24 -000 24 .000 2/, -000
.8E8E+02 .131E+08
.?9 6E 107
.7 50 2. 000
.500 -625
19.000 19.000 19.000
1
19 .00 0
't
.000
21 .OOO
26 .000
26.000 26.000 26.000 26.000 26.000 26
1.500 2
'19.000 19 .00 0
26.000 26.000
.608E+07
.109E+06 .302E+06 .619 E+ 06
.365Er05
.101 E+06
.'17'l E+o7
.569 E+06
.108Er07 .
j508+07
.6'l2E+O7
.965E+07
.206E+06 .3 61 E+06
J17E+A7
.204E +07
.322E+A7
.198E+08
.118Er06
.473E+07 .6618+o7 .394t+O5
.500
2E.000 28 .000
-326E+06 .669 E +06
.223E+06
.7 50
28.000
.0c0
28.000
.1 42€+08
28.O00
.117E+O7
2E.000 2E .000 28 .000
. 184€+07
1.750
28.600
.?50
30.00 0
.127E +06
'1
.435E+07
.'tE2€+08
-378E+07 .6 6'l € +07 - J 04 Er08 .1 53E+0E
1
.188E+07
26-000
.7 50
-250 .375
r9.000 19.000
.000
.563€+07
.000 .250
I .500
28.900
.2'l4E+08
I
.844E+05
.478Er06
-157
I I
.155E+07 .2448+07 .359E+07
-?94E+07 -514E+07 .811E+07 .119E+08 .'t 66E+08
?4.OOO 24 .000
*'l
E+06
. 143E+07
.10'l E+06 -ZtZE+46 .5708+06 .995E+06
24.000
7
24.O00
19 .00 B 19 .00 0
19.0 00
't
24.000
.000
19 .0C0
19.000 19.000 19.000 19.000 19.000
.
.7 50
19.000 19.000
19.000 19.000
22 -00 0 22 .000
1
0
19.000 19.000
.27qE+o6 ,432E+06
.108E+08 .150E+0E .919 E r 05 .253E+06
.2 50
19 .000
19.00
.157ErA6
20.000 2 0.000 22.000 22.000
20 .000
'I
.500
.449E +07 .277E+O5
.465E+ 07 .733E +07
-000
19.000 19.000 19.000
.219E+O7
20.0c0
22.000
250
.1 39E+0 7
.88
-?50 1 .000
-
.;93 E +06
30E+07 -2668+07
.625
2
.248E+05 .683E+05 .140E+06 .245e+O6
.9 61E+07
.ll5E+08 .831E'05
1.750
CIRCU
18.000
.000
19.O00
.421E+O6 .735E+O6
OUlPLANF
1t.000
.500
t9 -00c 19.000 19.000 19.000
.205Er 86
l8 .000 20.000 20.000
19.000
.0c0
.743E+05
.6568+07
.000
19.000
TCK,IN TNPLANE LONGI STD
.lE6E+06
t 8 .000
22 .000 22 .000
C
NOZZLE ROT STI T IN.LB/DEG
t 8 .800
-75n
19.000 19.000 19.000
VESSEL
.116e+D7 ,238E+07 .416E+Qz
18.000
20 .000
19 .0C
'| 9
1
1.000 J.250 1.500 1 .750 2.000
9.000
19
OD,III
ION' CYL'
'l .500
.500
.000
9
't
19
NOZ?LE
1E.000
19 .00 0
't
LCULAT
l8 .000
19.006 't9.000 19.000 'r9.000
19
CA
.109E+06 .390E+06 .615E+06 .126E+O7
.220F+07 .348 F+07
.5119+07 .714s+C7 .424E+Ot
It/
172
Piping Stress Handbook Table 6-1 Continued ROIA
VESSEL OD,FT
TCK,IN
00
19.000 19-000
19,000
r9.000 19.000 19.000 r9.000 19.000 19.000 19.000 19.000 t 9 .000
'19.00c
19.000 19.0c0
'19.000
19.000
t { il
'19.000
.500
30.000 30.000
.6?5
30.00 0
.750
I .000
1.25C
1,500
1.750 2.000 .250 .375 .500 .625 .750 1 .000 1.250 1-500
1.750 2.000 .2so
19.000 19.000 19.000 'r9.000 19.00c 19.000
't
19 .00 0
I .500
19.0C0 19 .00 0
19.000 19.000 J9.000 19.000 19.000
.37 5
.500 1
.000
.250
1.750 2.000 .3?5 .500 .6?5
19. 00 0
.000
J
-
9.C00
19.000 19.000 19 -000
19.000 19.000
.500
.750 2.000
19 .0 00
r9.000 19.000
.625 .7 50
'19.000
.000 .250 .500
19.000
t9.000 19.000 19.000 20.000 20.000 20.000 20.000 20.o00 20.000 29.000 20.0c0 ?0.000 20.000
250
.75A
2.000
.250
.375 .500
.625 . 750
I .0c0 1 -250
.750 2.000 1
.37 5
.375 -375
30 .00 0
.375
30 .00 0
-375
30.000 3
0.00 0
30-000
30.000 3?.000 32 .000
32.000
32 .00 0
32.000 32.000
52.00 0
f2 .0c0
52.00 0 32 .000
36.000 36.000
36.00 0 36 .00 0
.750
CtL. VESSEL NOZ ZLE ROT S'I' IN.L8/DEG TCK,I N I NE OUTPLAiIE '{PLA STD LONGI CIRCU
CAI-CULATl0lrlr
VESS€L
19.00c 19 .0
STIff
36.000 36.000
56 - 000
6.000 36-000 36.000 40.000 40.000 40.000 40.000 40.000 3
40
.000
40.000 40.000 4
0
.000
.375 .37 5
.375 .375 .375 .375 .375 .375 -375
.375 .375 .375 .375 .37 5
.375 .375 .375 -375 -375 .37 5
.375
.375 .375
40.000 4E.000 4E.000 48 .000
_37 5
4E.000
.5t>
48.000
48.000 4 8 .000 48 .000 4E -OOO 48 .000
2.375 2.375 ?.375 2.375 ?.375 2.375 2.375 2.3?5 2.375 2
.3?5
.350E+06 .7198+06 .1268+07 .198 E+07 .4O7E+07 .71Oa+07 . I 12E+08 .165E+08
.117E +O6 -24OE+06
./,19€+06 .660E+06 -136E+o7
.237E+07 .373E+07
.230E+08
.549E+O7 .767E+O7
-136E+O6
.453E+05
.374E+06 .7 69E+ 06
.134E+07 .21?E+07 .435E+07 .7598+ 07 .1 208+08 .17 6E+OE .2468+0E . t 55E+06
.42tE+O6 .66E
E+
06
-152E+07 -239E+07 .491e+ 07 .8 58 E +07 -135E+08 .'199E+0E .2?8E +08
-125E+06
.256E+06 .448E+06
.7068r06
.115E+O7
.253E+07 -399E+O7
.587E+O?
.820E+07
.5t1Er05
.141E+O6 .289 E+06
-505E+06
.797E+O6 -1648+O7 -Za6E+07 .451E+O7
.171E+06
.663e+07 .926E+07 .570E+05 .157E+o6
-967e+O6
-322E+O6
-267 E+O7 .5 47 a107
.889 E+06 .1828+O7
-171E+06
.169E+07 .956a+07 . 151E+08
.222E+08 .310€+08 .206E+06 .5688+06 -117E+Ol .204E+07 .321E+07 .660E+07 .115E+08
.5638+06
.3198ro7 .5038+07 .7398+O7 .103E +08
.687E+05 .1 89 E+06
.369 E+06 .679 ar06 -1O7E+07
.?67E+08
.220E+07 .384e+A7 .606E+07 .891E+07
-3?3e+DB
.124F-rOE
.1 54
. 837 E+ 04
.279E+O4
-154
.231e+O5 .473p+O5
. 768 €+04
.s75
.154 .154
.182E+08
.8278+05
.1 54
.130E+06
.154 .154 .154 .154 .154
.268€+06 .468 E+06 . 73E
E
.'108
E
+06 r 07
.1 5l E+07
.1 5E E+05 -276E+O5
.435E+05 .892E+05 - I 56E+06 -246E106
.362E+06 . 50 5Ef06
Rotatlonal Nozzle Flexibilities for Cylindrical Vessels
'173
Table 6-1
Continued ROTA STI f VESSEL
OO,FT
20. c0c
NOZZLE ODZIN
V€SSEL ICK,IN
.500
3.500
20-000
,500
3. 500
2C.000
-7 50
5. 500 3-500
20-000
.500 1-750
2C.000
.250
4.500
2C,000
.500 .6?5
4.500 4.500 4.500 4.500
?0.000 20.000 20.000 20.000 20.000
.000
20,000 20.000 2C-000 2C.000 2C
.000
2A.O00
20.000 20.000 20.000 20,000
4. 500
1
,000
't.250 .500 1-750
't
.500 4-500 4 .500 4
2.000
4.500
.500
6.6?5 6.6?5
,250
6 -625
-750 .000 .500
2C.000
2.000
26.000 20.000 20.000 20.000 u 0.000 20.000
.500 .500
3 3
.375
20 -0 00
20.060
3.500
3 -5AO
20.000 2C.000
3.500
2. 000
20,000 20.0c0
.7 50
6.6?5
6.625 6.625 6.625 6.625 8.625
.500 .750
E.625 I .625 E.625
- 000
.625
2C.C00
.250
20 .000
1.750 2.000 .250
10 . 750
- 500
'1o.750
20.000
20.000 20.000 20.0c0
8 8
- 500
20.c0i.J
20.000
a
.625 .625
8.625
'to.?50 1
0. 750
10 .750
20.000 20.000
.000
1
20.00iJ
.5C0 .7 50
19.750
20,000 20.000
20.000
2
.000
2C.000
.254
20 .000
.500
20.000 20.000 20.000 2C.000
20.000 ?0.000 20.000 2C.000
0.750
10 .750
1A.750 0. ?50
1
12.750
12 -750
.7 50
.000
't?.750 12 -750 12 -750
.500
12 ,750 12.750 12 .750
.2-50
14
.750 2-0c0
NOZZL€
TCK'IN STD
3
20.000
CALCULATION,
F
.000
CYL.
VESSEL
F IN.LB / DEG OUTPLANE INPLAN€ CIRCU LONGI ROT STI
.216 .1246+o5 .2'16 -3438+05 .2'16 .791'5+05 .?16 -123t+o6 .216 .19/+E+06 -216 .398E+06 .2'16 .696E+06 07 .216 - 'l 10 E++O7 .216 .161E .216 -?z5E+O7 .23? . 164E+05 .237 .153E+A5 -237 .9f l E+05 .237 .163E+06 ,237 .256E+06 .?37 .526t+O6 .237 .920€+06 -237 .145E+07 .?37 -?138+07 07 .237 .298 € ++C5 .25OE .?ttl .2E0 .689E+05 .280 .14'1E+O6 .280 -?47E+06 .280 .390E+o6 .280 .800E+06 -2E0 .140E+07 -280 -220E+07 .280 .3216+A7 .2EO .152E+07 -322 . j30E+05 .32? .910 E+ 05 .322 . t87E+06 .3ZZ .326E+06 _3ZZ .515 +06 .32? .106€+07 .32? . 185F+C7 .322 -291 E+o7 -3zZ .4288+C7 .3?z .598 E+07 .365 .416F-+O5 .36t .1 155+06 .365 .Zj5E+06 .365 .411E+06 .365 .643E+06 .365 -133E+Q7 .365 .233E+O7 .365 .367E+D7 .365 ,.539€+02 .365 .753E+07 .375 .,DgE+05 .325 ..t 38 E+06 .375 .?83Ef06 .375 .4E4E+O6 .375 .7S0E +06 -375 . 160E+07 .37, .280E+07 .375 -41'lE+O? .375 .648E+07 -375 .9 05 E+07 .375 .5 54 E+ 05 E
.4
15E+O4
.114E+05 .235E+05 .410E+05 .647E+05 .'133E+06 .23?E+O6
.366E+06 .538E+06 .751E+06 .548E+04
.'l5'l E+05 .f10E+05
i,i
.542E+05 .855E+05 _1ZSE+O6
.307E+06 .484E+06 -7118+O6
.993E+06
.6 33E +0 4
.230E+o, .171E+A5
.3239+05 .1 30E+0 6
.267 E+O6
.4666+O6 -735E+O6 . 108E+07
.1519+07 .110E+05 .303E+05
.62jE+05 .'l 09 E+06 .17 2E+o6
.3SZE+46 .616E+06 .971E+06
.143t+Oz
.199E+07
.139E+05 .3E2 E+0 5
-784E+05 .1378+O6 .216E+O6 .4 44E+o6 .7?SE+O6 -122E+O7
.180E+07 .251E+O7 .161E+D5 .459E+05 .943E+05
-1658+06 .260F+06 .533€+06 .932E+06 -147E+O7 -?16E+O7
.302E+O7 .185E+05
u
174
Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCUIATION, CYL. VESSEL V ESS
VESSEL ICK,II{
EL
OD,FT
20.000 20.000
.375 .500
20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
.7 50
2C.000
20 -000
20.000 20.000 20.000 20.000 20.000 2
0.00
-625
t.000
1. ?50 'l .500 1
"750 2.000
.750 1 .000 1-250 1.500 1
-750
2. 000
.500
-750 2.08O
20.000
1.250 1.500
.625 .000 .25A
.500
- 500
.7SO 't
2C.000
20.000 20.000 2U.000
20.000 20.000 20.000 20.000 ?0.0c0 20.000 20.000 20.000 20.000 2C.000
20.000
.000
1.750 2.000 .250
2ri.00G
?0.000 20.000 20.000
NOZZLE ROT STIF IN.LB/DEG
TCK,IN IfuPLANE STD LONGI
14.000 14 .000 14 - 000
14.000 1 4.000 .000 14.C00 14
14.000 t 4 .000 16 .000
16.000 16.000 16.000 16.000 t 6 .000
16.000 1 6.000 16 -
.663E+06
-375
.309E+07 .4888+07
.375 .375 .375 .375
.37 5
.375
.500 .7 50
.000 1-250 1.500 1-750 2.000 't
.250 .500 .7 50
.000
18 1
.375
20.000
.587E+05 -121E+O6
.632E+06
.211e+06
.205E+07
.332€ +0 6 .6E2E+06
.357 E+07 .5 64 E+ 07
-137E+O6 .239 Et0 6 .377 E+06
.l'13€+07 .2328+O7
.405E.07 .639Er07 . 131€+08 .Et0€+05
4E
+
07
.'ltJ5E+08
.5078+06 .885E+c6 .140€+07
.'t 62F+08
.9t2E+C5
?4.LOO
.27OE+A6
24.OOO
.555F+06
24.000
.500
2. 000
24 ,000
24.000
26.000 z6.ooo
.37
5
.970E+06 .153E+07 .314E+07 .519E+Oz .E66E+07
,127Er08
.375
-313E+Cz -
437E+O7
.270E+05
,864€+06
-79OE+07
24 .000 24 -LAO
.135E+07 .213E+o7
.259E+ o?
.'116Fr08
24-000
.773E+O 6
.7 41E+ 05
.237E+07 .501E+07
22.000 22.000
.666F+05
-223E+06 .45E€+06 .601E+06
.247E+ A5
22 .000 ?2 -OCO
.386E+07
.410E+06
.E96E+05
22.000
-276E+O7
.242E+O5
.147€+08
22.OOO
.119E+07 .188E+07
.725E+05 .200E+06
.71
.375
E+0 7
.213€r05
6E + A6
.453:+07
?2.000 22.000 22.AOO 22.AOO
.17
.334
-3628rD6
.126E+07
.3-t5
.t03E+07
.100E+08 .639E105
-9 39E+47
.37 5
20 .000
20.000 20.000
z4 .ooo 24 -OOQ
.750
375
.000
20,000 ?0.800 20.000 20.000 20.000 20.000
-718E +07
.163E+07 .239e+07
. 716 E+06
.000
I .000
.590E+06
.ll6E+0E
-
.182Er06 .288E+06
07
7 E+
.629E+07
.000
I 6.000
.17
.996Er06
t 8 .000 1E
.547E+06
.375 .375
000
t 8 .000
. 508 €+0 5 . l04E+06
.313€+06
18.000 16.000 18
OUTPLANI CIRCU
.153E+06
I E.000
?0.000 20.000 20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000
20.0c0 20,000 20.000
OD,IN
'16.000 . 500
0
20.jco
NOZZL€
. 1 78E+ 0E .1o7E+A6 .291E+06
.153E+06 .2 6?E+06
-421E+o6
.1j'lE+07 .238E+07 .350€+07 4g9E+07 .299E+05 .323E+05
"
.169E+O6 - 295E+o6
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.9t6E+06 -167E+o7 -263E+07
.387E+07 .5 4'l E+o7 .3?7E +o5 .902E+05 .'t 85E+06 .321E+06 .510E+06
.105E+07 .1E38+0 7 .289 E +O7
.424E+07 .592E+07 -356E+05
.980€+05
Rotational Nozzle Flexibilities for Cylindrical 'liable 6-1
Continued
SIITF CALCULATION, CYL. VESS€L NOZ ZLE ROT SlI f IN.L8/DEG VESSEL NOZZLE OUTPLANI TCK,IN INPLA}JE TCK,II'I OD,]N CINCU LONGI SID ROTA
VESSEL
0DrFT
2C.000
20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20 .00c 20.000 20.00c 20.000 20.0c0 20.000 20.0c0 20.000 20.000 20.000 ?0.000 20.000 20.0c0 20,0c0 20.000 20.c60 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000 20.000 20.000 20.c00 20.000 2C.000
20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 2C.000
20.000 20.000 20.000 20.c00 20.000 20.00c 20-000
20.0!0
20.000 ? 0.000 20.000
26.000
.500
26.0C0
26.000 26-000
1-000
26.000 26.000 26.000 26.000
1.250 1- 500
1.750 2. 000
2E.000 2E.000
.375 .500
28.000 28-000 2E.000
.7 50
28.000
.000
28 .000
28.000 28.000 2E.000
2.000 .?50
10.000
.625 .750
30.000 30.000 30.000 30.000
30. 000 30.00 0
t .000
1.250 I .500 1.?50 2.000 .500 .6?5
1.000 1.250 1.?50 2.000 .250
50 .000 30. 000 30
.000
32.000 3 2 3
.000
2.000
32 .00 0
32 .00 0 32 .000
2.000 32.000 32.000 3
r2.000 56.000 36-000 6.
.500
3
.7 50
36-000
't.500 I .750
3 6 -000 36. 00 0 36 -000 3 6 .000
.625 1.000 I .250
2. 000
.250
.500 I .000
1.500 1 .750 2.000 .250 .37
5
.500
COo
56.000 36.000
40.000 40.000 40.000 40.000 40 .00 0 40 .000
40.000 40.c00 40.000 40.000 4E.000
48.000 48.000
.375 -375 .375 -375 -375 .375 .375 .375 .375 .375 .375 -375 -375 .375 -375 -375 .375 .375 .375 .375 .3?5 -375 .375 -3?5 .3?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .3?3 .375 .375 .375 -375 .375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375
.604E+06
-201€+06
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.1658+07 .341E+07 .597 E+o7 .941E+O7 . 'l38E+08 -'t sf E+06 - 115
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.318E+06 .652E+06
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.314E+O7 .461E+O7 .644E+O7
.384E+05 .'106Et06
.1148+o7
.217E+06 .380 E +0 6
.',|E0E+07
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.2152+07 .339E+07
.1 49E+08 .209€ +08
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lOAc.a\7 -6928+07
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.?3'l
E+O7
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.8 46 E+ 06
.118E+07 -233E+07 .479E+07 .E36E
r07
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.'l948+0E .271E+O8 .1 67 E+ 06
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.943E+06 .165E+O7
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.282E+06 .4938+O6 .777s+O6 . t 608r07 .279 E+a7
.44OEr07 -646Er07 .90?€+07 .556E+05 .153E+06
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.101€.0E
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.185€+05 .379 E+06
Vessels
175
176
Piping Stress Handbook Table &1
Continued ROTA STIFF CALCULATION, VESSEL
OD, FT
20.000 20.0c0 20.000
20.0cc
20.000 20.0c0 20.000
vEssEL TCK,ll{ .625
ilozzLE
OD,Ill
48.000 .000 48 .000 48 .000 4E.000 4E.000 48
I .000 1
.250
1
.500
I .759
2.0c0
48.000
CYL.
VESSEL
ZLE RO' STIF IN.LB/D€G T{ INPLA'.IE OUIPLA}IE SID LOI{GI CIRCU
NOZ T
CK,I
.375 -375
- 199E+07
.313Er07 -643E+07
.1128+08
.177Er08 - 261
E
+08
.364E+08
-662E+O6
.1C4E+07 -214E+07
.3748+o7 .591E+07 .868 E+07 . 12t E+08
Pressure and Stress Ratios
By merely multiplying or dividing, P/S ratios may be used to readily determine: Ferritic Smls Temperature (Carbon and AlloYs
l.
Allowable working pressure 2. Working stress 3. Wall thickness required
900 950 1,000 1,050 1,100
This extreme simplicity arises because in the formulas devised to predict the stresses in a pipe under internal pressure, the P/S ratio may be equated to a quantity that is dependent only on the diameter and thickness of the pipe and the applicable allowance for threading, mechanical
D-2y(t -A)
.4 is known as the "modified lame" formula. In Sections 4 and 8 of ANSI 831 the Barlow formula is used, which is a special case of the general formula in which y 0. kr addition, Section 8 is based on nominal thickness rather than minimum thickness; the tabulated P/S ratios for y = 6 tut 6" placed on a nominal wall basis by mul-
:
as:
2(t.
:
tiplying by 8/7. Tables 7-1 through 7-4 give the precalculated values
=
t : A: D: y :
for
the right-hand side of the preceding general equation for each pipe size and weight based on a wall thickness 87Uz% of nominal and for values ofC varying from 0.0 to 100 in. in increments of .005 in. For any pipe size, wall thickness, and corrosion allowance the allowable working pressure is found merely by multiplying the P/S ratio by the allowable stress. Obviously, this relieves the designer from making annoying multiple arithmetical manipulations which might be subject to error.
lbs/
in.2
Ss
0.7
=
- A) D-2y(t.-A) where P : Maximum internal service pressure, P/S
o.7
The y value in the general formula reflects the effect of creep at high temperatures. In some ANSI Code sections that do not cover temperatures over 900'F, the y value of .4 is directly inserted in the formula; the formula with y
2SE(t--A)
This formula may be written
u.) 0.'l 0.7
strength, and/or corrosion. The general formula, adopted by the ASME Boiler Code in the section on power boilers and the ANSI Code for Pressure Piping is:
D_
0.4
Austenitic Steels (Cr-Ni stainless, such as Types 304, 316, and 347) 0.4 o.4 0.4 0.4 0.5 0.7
Allowable stress in material due to internal pressure Minimum pipe wall thickness, in. Allowance for threading, mechanical strengih. and/or corrosion, in. Outside diameter of pipe, in. Coefficient having values, as follows:
(Text continued on page 250.)
177
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250
Piping Stress Handbook
Tbbles are presented
y y y y
for four values of y:
: 0 @arlow) : 0.4 (Modified lame) = 0.5 (Average diameter) : 0.7 (Creep)
3. The following two solutions can be used to determine the maximum allowable working pressure perCtable
7-l)
(lable 7-2\ Clable 7-3)
missible.
r
(table 74)
Ushg the design formula from the ASME Code, Section VItr, Division 1, 1983, and the symbol definitions contained therein:
SEt
P: Instructions and Examples
Example 1: Determining Allowable Working Pressure Determine the maximum allowable working pressure in accordance with the ASME Boiler and Pressure Vessel Code, Section VIII Division |, 197'7 , for a 10-in. , schedule 80 steam line, A106 Grade B materials, operating at
750'F.
R + 0.6t
S
=
E
:
12,900 psi 1 .00 (See the 1983 ASME Code on joint efficiencies) t"r,, .518 in.
lnsloe
D-
(12,900) (1) (.518)
4.8s7 6 69.)
).lo/
Solulion.'
r 1. List known information about the pipe. Size:
Weight (or schedule no.): riy'all thickness
:Ze t
".:
Material: Code section:
Operating temperature: Corrosion allowance:
l0-in. nom. (10.750 o.D.) Schedule 80 .593 nom. (.518 rnin.) ,{106 Grade B ASME, Section VIII
Division 1, 1983 750'F 0 (The 1983 ASME Code formula does not include allowance for corrosion, therefore, it is the responsibility of the designer to adjust the wall thickness where corrosive conditions exrst.)
2.
=
12,900 psi
raOrUS
+
tnri "-'
(.6) (.s18)
: l.lv:
osl
A simplet quicker method is to obtain the applicable P/S ratio from the pressure/stress ratio table listing Y = 0.4 (Table 7-2). Nore: In the ASME Code, Section mula:
*:?-,* thus
P:
P/S
:
SEt R + 0.6r
Et R + 0.6t
E:1.0 P/S
: D" 2
Obtain from 1983 ASME Code the allowable stress:
S
.. OrD" 2-
R:
P/S
:
-r+0.6t 2t
D"-2r+1.2t
VItr,
1983, for-
-w Pressure and Stress
pE:
D"
2t
Design factor (F) for Type
-
consrucuon
0.81
C
:
Ratios
251
0.5
thus, y in the basic ASME formula The foliowing two solutions can be used to find the stress or required yield strength.
P/S: 2(t -A) D-2y(t--A)
.
must equal 0.4
With the allowable stress(s) obtained from the ASME Code, Section VItr, Division 1, 1983,
therein:
(12,900 psi) and the P/S ratio obtained from Table
7-2
P: P:
?ST
P:---XFXEXT
(.r0M)
D
PD
^
SXP/S 12,900
Using the design formula from the ANSI Code 831.8, 1982, and the symbol definitions contained
2tFET
x.1004
=
l.295psi
Example 2t Determining Stress or Required Yield Strength
P
=
1,100
T1
-
1't 7<
11""*;
:
.562
F:.5 E:1.0 T : 1.0
Determine the stress or required yieid strength in accordance with the ANSI Code 831.8, 1982, on gas sion and distribution piping systems for a 12-in., schedule
transmis-
60, gas line, A106 Grade B materials, operating at 1,100 psi at 250"F.
s=
Solut'ons.'
s-
(1,100) (12.7s)
Q) (s62) (.5) (1) (1) 14'025 .562
=
24.955 psi
1. List known information about the pipe:
Size: 12 in. nom. Weight (or schedule
no.):
831.8,
t982 Operating temperature: 250"F
P:
1,100 psi
.
A simpler, quicker method is to obtain from Thble 7-1 where y = 0, the applicable P/S ratio, and then multiply to determine the stress or required yield strength.
Corrosion allowance: 0 P/S
2.
or required yield strength of
24,955 psi is less than the minimum yield strength of35,000 psi for A106 Grade B pipe, the pipe correctly meets Code requirements.
Schedule 60
section: ANSI Code
Operating pressure,
Since the stress
o.D.)
Wall thickness: .562 nom. Material: 4'106 Grade B Code
(12,750
ratio
:
.0771
Obtain from the Code section on gas transmission:
Minimum yield Y factor
strength : 35,000 psi =0
Because we are using a construction factor of .5 from the ANSI Code 83l .8 and because this Code is based on nominal wall, we must use the .5 fac-
Piping Stress Handbook
v:.4
tor and an 817 factor in the following formula along with our P/S ratio.
S: S:
A:0
P-P/S(8/7)(.s) 1,100
-
.0771 (8t7)
(.s)
:
(e00) (6.62s)
24,967 psj
2 tl3.000
<06?<
Example 3: Determining Wall Thickness Required
t^:'""-"
26,720
(900) (.4)]
.223
The nominal wall, T".-, is equal to .223 817 : .254. Because the ANSI
In accordance with the ANSI Code B31.1.0, 19g3, for power?iping, determine the pipe wall thickness required for a 6-in. steam line, A106 Grade B pipe, operating at 900 psi at 750'F at maximum allowable stress, with a iorrosion allowance of .050 in.
87lz% .223 x
Code B31 . 1 .0 design formula makes no allowance for corrosion and/or erosion, the corrosion allowance determined by the designer must be added to the nominal wall calculated. Therefore Tnon,,:
.254+.05O: .3M.
Sorutions.'
Then, refer to Chapter 10 "properties of pipe,' to determine the next thicker commercially available pipe. which is schedule 60, having a nominal
1. List known information about the pipe:
Size: Material: Code
wall thickness of .375.
6 in. (6.625 O.D.) A106 Grade B
.
section: ANSI Code B3l. 1.0, 1983
P: C:
:
Using Table 7-2 (where y 0.4) across from the 6-in. nominal pipe size under the column for .050 in. corrosion allowance, pick the pipe wall thickness having a P/S ratio equal to or greater than that just calculated. This value is .0869. Therefore, tno,o = .375 based on a P/S ratio of.0869 as
Obtain from the ANSI Code section on power piping (1983) the allowable srress:
S
=
=
y factor
A simpler, quicker method is to calculate the minimum required P/S ratio by dividing P by S:
P/S:900=13.000:.0692
Operating tempetature: 750.F Operating pressure, 900 psi Corrosion allowance, .050
2.
:
+
13,000 psi
0.4
shown in the table should be used.
The following two solutions can be used to find the
required wall thickness.
Note: Interpolation For values ofC and y intermediate to those shown in the tables, linear interpolation may be used.
.
Using the design formula from ANSI Code 831.1.0 and the symbol definitions contained therein:
PD^" 2(SE + Py)
L: ''' P
=900
D"
:
6.625
S = 13,000 E:1.0
+A
Note: Special calculations: Only the lhree most important uses for the P/S values have been illustrated. Those who would like to examine all of the uses are reminded that the tables may be employed to indicate the effect of operatmg temperature, corrosion allowance, material, and pipe size.
Branch Reinforcement The various ANSI piping codes give formulae for the reinforcement of nozzle openings in two respects:
Pressure and Stress Ratios 1.
The pressure area cut by the opening must be replaced by reinforcing the area within a prescribed
T = t :
zone around the opening.
which attach the reinforcement to the pipe must meet certain (essentialiy shear strenglh) requirements. The Petroleum Refinery Piping Code
2. The welds
831.3 (1980) gives detailed requirements in Section 304.3.3. The Power Piping Code B31.1 (1983) refers to Section 1O4.3.1 for a detailed description of this nozzle reinforcement design and calculation. For convenience, reprinted here is ANSI Code 831.3, Section 304.3.3 in Figure 7-1.
Nominal thickness of pipe, in. Pressure design thickness of pipe according to the appropriate wall thickness equation or procedure in 304.1 in. When the branch does not intersect the longitudinal weld of the run, the stress value for seamless pipe, of comparable grade, may be used in determining t for the purpose of reinforcement calculation only. When the branch does intersect the longitudinal weld of the run, the weld joint factor of the run shall enter the calculation. When the branch contains a weld, the weld joint factor of the branch shall enter the calculation.
Section 304.3.3 of the ANSI Code 831 .3-Reinforcement of Welded-Branch Connections Additional reinforcement is required when it is not provided inherendy in the components of the branch connection. This paragraph gives rules governing the pressure design of such branch connections for cases where the angle between the axes of the branch and of the run is between 45 and 90 degrees, inclusi.ve.
Required Area
-
The quantity (trdr) (2 sin B) is known as the required area; in the case of right-angle nozzles, the required area becomes t5d1 square inches. The branch connection must
be designed so that the reinforcement area defined in 304.3.3 (c) is not less than the required area.
Reinforcement Arca The reinforcement area shall be the sum of the followrng two areas.
Notation The notations described below are used in the pressure
design of branch connections. The notations are illustrated in Figure 7-2. Note the use of subscripts b for branch and h for run. Note also that Figure 7-1 does not indicate details for construction or weldins. B : Angle between axes of branch and run, degrees b = Subscript referring to branch : Corrosion allowance. in. c D" : Outside diameter of pipe, in. ,l : Actual corroded length removed from run pipe, in. : [D.o - 2(Tr - c)]/sin B : d1 or [T6 - c) + (Th - c) * dr/z] whichever is greater, but in any case not more than Dol : h Subscript referring to run or header L+ : Altitude of reinforcement zone outside of run pipe,1n. : 2.5 (Tr, - c) or 2.5 (Tb - c) + L, whichever is lesser : L Nominal thickness of reinforcing ring or saddle, in. T : Actual thickness ofpipe, in. @y actual measurement, or minimum thickness permissible under purchase specification)
1. The area lying within the reinforcement zone [defined in 304.3.3 (d)l resulting from any excess thickness available in the main run pipe wall and branch pipe wall over that required by the proper wall thickness equations, i.e., the thicknesses Tr - tn - c and T6 - to - c multiplied by appropriate lengths. Any line having a thickness greater than
2.
that required for corrosion allowance and for pressure and other loading considerations will occasionally be in service until the excess thickness is also corroded away. If this is the basis of the design, the excess thickness cannot be used for reinforcement of pipe+o-pipe branch connections. The area ofall other metal within the reinforcement zone (defined in Section 304.3.3 (d) provided by
weld and other reinforcement metal properly attached to the run of branch. In computing areas of weld metal deposits, the minimum dimensions required shall be used unless a definite procedure is employed to instruct the welder to provide specific larger dimensions, in which case lhe latter dimensions may be used in calculations. Fortions of the reinforcement area may be composed of materials other than those of the main run pipe, but if the allowable stress of these materials is less than that for the
254
Piping Stress Handbook
BRANCH REINFORCEMENT
DESIGNCONO|IONS:....... psig.......'F
Sfaigfn Pipo Und€r lr{om€l Pr€aslrg (a) For motallic pip6, thg inlornal prgssrro d6ign thicknoss 0) shall bs not legs than calculat€d by the lollowing Equalion 3, itt is loss han Do/4: 3O4.1 .2
HEADES
BRANCH
Nominal Siz6 Outside Oiameler
PY)
Dotr
Dob
T6
T6
S6
NominalWall Tabl6 304. t .l Values ot Y for Fenous Mato.ials
rempsraure
O€gr6o"F
Actual or min. Wall Matorial Spgc. ASTM
900&
115{, &
Below 950 lO00 1050 1100 Abovo
Ferritic
St€€ls Auslonidc
Sle€k
0.4 0.5 0.7 0.7 O.7
O-?
0.4 0.4 0.4 0.4 0.5
0.7
Allowabig Str€99
sh
Joint Elficiency
E6
Co€fliciont
Y6
Y6
Me
C6
eb
lhtorssc,iion Angl€
p
Y
REQUIREO THICKNESS OF HEAOEB AND BRANCHI PDoh
th=-= '' 2S6E6
2t.......x..,
+ 2YhP
2r.......x.. ..x....... . t 2x.,.....x..
.. +
PDcb
t 2Y6P 2t.......x...
2S6Ep
LIMITS OF REINFORCEMENT: Oqb
- 2(T6.C6)
... ...
.
-
2
r
(.......
-
.......)
sin P
(....... -.......) + (....... -.......) + 0.sx....... Sefecf farger ol lhe values, but not lo Exceed Ooh dZ = . .. ... , L4=2.5(th.Ch)=2.5(.......-.......)ot=2.5(lu-Co)+te=2.5(.......-.......)+.......
d2=d1
or
=
{Tb -
Cb) + Oh- Ch) + 0.S1 =
S€l€ct lossor of the valu69 (te = 0 if pad oi saddlg i9 not used) L4 = . . .
.
=
...
REOUIRED ANO AVAILABLE REINFORCEMENT AREA:
Ar€a =
...... . sq. in. required. (2x....... -....... ) (....... -.......
thdi = .... ... x... .... =
Ai =
(2d2 -
A2 =
214(Tb-tb.Cd =
A3 =
tf
dt)
(Th - th - Ch) =
= 1.......12
2r....... (....... -.....
-.......
- A3 =....... r....... +....... i..... AreaA-(At-Aa-Ad At + A2
A4 + 2 = sq. in. ol pad on €ach side ot nozzle =
sq. in. available. . . sq. in. ol area in pad requrred -
A4
+2-.......
Ac-2=L=.......* OEDusopadts
=.......
xL
=......,
Figure 7-1. Reproduction of ANSUASME Code 831.3, Section 304.3.3 giving detailed requirements for branch reinlorcemenl.
.
Pressure and Stress Ratios main run pipe, the corresponding calculated area must be reduced in the ratio of the allowable stress values before being counted toward the reinforcement area. No additional credit shall be taken for materials having higher allowable stress values than for the main run pipe.
Sample Calculations for Branch Reinforcement Example 7-l
Reinforcement Zone
The reinforcement zone is a parallelogram whose
length shall extend a distance d2 on each side of the centerline of the branch pipe and whose width shall start at the inside surface of the main run pipe (in its corroded condition) and extend to the distance La from the outside surface of the main run pipe measured perpendicular to this outside surface. (See Section 3M.3.3(c) (1)).
An NPS 8 run (header) in an oil piping system has an NPS 5 branch at right angles (Figure 7-3). Both pipes are Schedule 40 API 5L Grade A seamless. The design conditions are 300 psig at 400'F. The fillet welds at the crotch are minimum size in accordance with Section 327 .4'4. A corrosion allowance of 0.10 in. is specified. Is additional
reinforcement necessarv?
Figure 7-2. This figure illustrates the nomenclalure used in ANSI Code 831.3, Seciion 304.3.3, 1980. ll does not
inJicate complete w;lding details or a preferred melhod of construction. (Reprinted courtesy of the American Society of Mechanical Engineers.)
REINFORCEMENT ZON E
10.,*,".1 c=o'roin'
L4 = 0.268 in.
C
= 0.10 in.
4,286 in.
4.286-
Figure 7-3. Figure of branch reinforcement for use in Example
8.625 in. OO 7-1 '
7-
256
Piping Stress Handbook
t" : O.7 (0.237) = 0.166 in., or = 0.25, whichever is less : 0.166 in. t
Solution
SE:
Tr, =
Tr:
16.0 ksi. (0.322) (0.87t =,A.2{2
:
n.
(0.23? (0.87s) O.2U7 m. L'4 = 2.5(0.282-0.1) = 0.455 in., or 2.5(0.207 -O.l) + 0 0.268 in., whichever
:
t4 : dr: dz=
d,: tr, =
b:
is less 0.268 in.
I4.s -2(0.2s7 (0.207 2.432 4.286
-
in n.
-
0.l)l/sin (90') = 4.286 in.
0.1) + (0.282
-
o.D
+4':'6 z
or d1, whichever is grex er
+ (2) (0.4)
(300)
(300) (4.5m) (2) (16,000) + (2) (0.4) (300)
: :
0.080 in.
0.042 in.
:
0.166
o.1ut 0.235 in.
Thus, the required area, A1 (90)l 0.343 sq. in.
:
= (0.080) (4.28O t2 -
The rcinforcement area:
- I1l*o wall;
A.z
0.437 sq in.
:
In branch wall,
:
(300) (8.625) (2) (16,000)
Minimurn leg dimension of fillet weld
@.286) (0.282
A3
-0.08 -0.10)
sin
:
: (2) (0.268) l(0.207 -
0.042) - 0.101 0.035 sq in. In branch welds, Q) Q/2) (0.235)2 .
&:
ln. The total reinforc€ment area
:
:0.055
sq
0.527 sq in.
This is more than 0.343 sq in. so that no additional reinforcement is required to sustain the internal prcssure.
Design Criteria for Allowable Loads' Moments, and Stresses
Design Criteria for Pumps with Steel Nozzles and Casings
larger reactions. The vendor must submit comparable cri-
teria for pump cases constructed of cast hon. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expansion or contraction of prping. Piping reactions should be computed in conformance with ANSI Code B31 . or
API Code 610: Steel Pump Force, Moment, and Stress Limitations
I
The following criteria apply for pumps with 12-in. discharge nozzles or smaller. The forces contained herein are
considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting
ANSI Code 831.3 for pressure piping and should be designed within the limiting criteria set by this standard. The modulus of elasticity must be adjusted for the operating temperature condition. Each nozzle should be capable of withstanding double the forces and amounts listed in Table 8-1 applied simulta-
Table 8-1 Nozzle Loadings
Fotce/
oment
Nomlnal Size ot Nozzle Flange (in.)
<
Each top nozzle E
160
F, (compression)
200
Fy (tension)
100
F,
130
Each side nozzle
R Fy
160 130
F,
200
Each end nozzle F" F
F,
200 130 160
Each nozzle
Mr
340 260 170
My
M" M= x=
Moneu Axis
Reprcduced
ft-h
parolzl to shaft
6810
2
240 300 150 200 240 2W 300 300 2W 240 700 530 350
320 400 2W 260 320 260 400 400 260 320 980 740 500
12
14b
'| 6D
530 700
1,000
1,500 1,800 920 1,200
560
850
1,200
1,500
4ffi
1,000 1,500
1,zffi
700
7W I,100
I ,800
1,600 1,900 2,000 2,3w 1,000 1,200 1,300 1,500 1,600 1,900 1,300 1,500 2,000 2,300
700
1,100
1,500
1,800
2,000
2,300
4@
700 850
1,000 1,200
r,2w
1,300 1,600
1,500
2,6N
3,700 2,800 1,800
4,500 3,400
4,7N 3,500
5,400 4,000
2,2W
2,300
2,7W
560 700 350 460
850 1,100
560 1,700 1,300
1,900 1,300
870
t,2N 1,500
750
1,500
I,900
J = Verticalgo" to shaft z = Hoizontalgo' to shaJt
from Centritugal Pumps for ceneral Refinery Services, Suth Edition,
Institute.
257
1981
, Standad 610 Table 2. Repinted courtes, of the Ameican Petroleum
25A
Piping Stress Handbook
neously to the pump through each nozzle, in addition to internal pressure, without causing an hternal rub or adversely affecting the operation of the pumps or seal. The baseplate and pedestal support assembly should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when subjected to the loads shown in Table 8-1. These loads represent the total effect of all external mechanical forces that may be applied to a fully grouted pump base. They are to be applied to the pump through the suction and/or discharge nozzle (see Figure 8-1): For purposes of evaluating computed piping-imposed external moments and forces, these forces be transferred from both suction and discharge flanges to the intersection of the X, Y, and Z axes. An algebraic surffnation should then be made for comparison with the moment limitation just given. The vendor should submit alternative criteria for pumps larger than 12 in. Because a particular nozzle on a pump will not always be subjected to the maximum allowable resultant force and moment simultaneously, an increase in either the resultant applied force or the resultant applied moment may be made if the following limitations can be satisfied at that nozzle:.
(F"iF.) + (M^/M.)
where C M"
: = =
<
2, F"/F,
<
2, and M"/M.
(
C
M. F, D
=
: :
=
forces and moments from Table 8-2 on both nozzles simultaneously, taken about a point defined by the intersection of the axis of the shaft and the centerline of the pedestals. For heavy-duty baseplates the total applied resultant forces and moments on the suction and discharge nozzles should not be more than twice the eouivalent of those given in Thble 8-1. For applied resultant forces and moments that are greater than these, allowable values shall be mutually agreed upon by the purchaser and the vendor.
Design Criteria for Pumps with Cast lron or Aluminum Nozzles and Casings
Aluminum Pump Force, Moment, and Stress Limitations
2, for nozzles 6 in. and smaller (D + 6)/D, for nozzles 8 in. and larger resultant applied moment at the nozzle, ft-
lb E
The resultant applied force or moment may be increased up to double the values in Table 8-2 if the maximum combined limit on the installed equipment is not exceeded. This limit is determined by the summation of the
resultant applied force at the nozzle, lb resultant moment (from Table 8-2), ft-lb resultant force (from Table 8-2) lb nominal diameter of nozzle flange. in.
The following criteria apply for pumps with 4-in. or smaller discharge nozzles (suction nozzles may be larger). The forces contained herein are considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting larger reactions. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expan-
sion or contraction of piping. Piping reactions shall be computed in conformance with the petroleum refinery piping code for pressure piping ANSI Code 831.3, Section 319, and should be designed within the limiting criteria set by this standard. The modulus of elasticity should be adjusted for the operating temperature condition.
Table 8-2 Suggested Allowable Resullant Forces and Momenis (For Vendor's Standard Baseplates) E io^
-de..
Resultant Force/Moment F
Figure 8-1. Pump coordinate system.
M.
Nominal Size of Nozzle Flange (in.)
23
4
640
6
810
124
860 1,500 2,300 2,',700 2,900 690 1,400 2,000 3,500 5,200 6,600 8,200 430
Design Criteria for Allowable Loads, Moments, and Stresses Each nozde should be capable of withstanding forces from external piping determined by the following formuIas:
.
Limit tension and comDression forces to 500 lb
where F r X
Suction nozzles:
v z
F"(1.6w(50D r
w D d
Discharge nozzles:
F,6
(
S
(2w
F.,)
-
<
259
Force, lb Resultant of forces Axis parallel to shaft Vertical 90' to shaft Horizontal 90' to shaft Weight of pump only, lb Diameter, nominal diameter Discharge or exhaust Suction or intake
50D
o Top suction and top discharge nozzles are further limited by:
F. is the resultant shear force in the plane of any specific flange face.
and for suction nozzles
Each suction and discharge nozzle should be designed to withstand the forces described for the specific configuration. Unit stresses in each nozzle should be limited to: 4 one-third of the allowable hot stresses for pipe sizes
F*(1.3w(40D
in.; one-half of the allowable hot stresses for pipe sizes > 4 in.; as shown in ANSI Codes B31.1 and 831.3.
F.. and F,.a
:
(Fx2
+
Fz2)L/'z
(
(
1.2w Fr" (in compression) 25D Fr, (in tension)
( F",(w(35D
(
50D
The baseplate and pedestal support assembly on pumps
having a discharge nozzle of 4 in. should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when
and for discharge nozzles
F*a
(
(1.8w
r
F*) <
(
40D
t
(2w Fr") Fra (in compression) Fra (in tension) 0.5w < 25D
(
subjected to the following loads. These loads represent the forces tliat may be applied to a ful1y grouted pump base. They are to be ap-
tot;l effect of all externil mechanical
<
50D
nozzle.
F,a((wtF,,)<35D
o End suction and top discharge pumps are further limited by:
F":
G^'?+Fy.)-
and
F,6: (Fl and
+
M, :
3.0 W*
ftlb
: 2.0 wx ftlb = 1.5 W+ ft-lb M* : Moment in Y-Z plane My : Moment in X-Z Plane M, : Moment in X-Y plane W : Weight of pump only, lb Mv Mz
F"a'?)"'
For purpose of evaluating computed piping-imposed
for suction nozzles
external moments and forces, they should be transferred from both suction and discharge flanges to the intersection of the X, Y and Z axes. An algebraic summation should then be made for comparison with the moment limitation just given. The vendor must submit alternative criteria for pumps having a discharge flange of 4 in. NPS. It is suggested that these criteria be developed as a result of tests'
F".(1.2w(50D Fr.(0.6w(35D F.,< w(40D and
plied to the pump through the suction andior discharge
for discharge nozzles
F"a((1.8wtF*)<40D
(
Fra (in compression) 2w + Fy. Fra (in tension) 0.5w 25D
(
F.a((w1F".)935D
(
<
50D * Minimum W is 500 lb in tlpse
computations.
260
Piping Stress Handbook
D. :
Design Criteria for Turbine Drivers with Steel Nozzles and Casings Steel Turbines Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus "E," resultant bending moments are permissible up to a value that would cause a bending stress of S5/4 in a connection having a section modulus equal to the connecting piping for the same size where the comection is 4 in. IpS or larger. On smaller size connections a stress of S"/3 is permitted. (56 is as defined by ANSI Code 83l . I or ANSI Code B31.3 (current issue) for the material of construcnon. ) The resultant shear force at the face of the flanee and any individual component may not exceed 2,000 lb. The resultant forces and individual components are limited
The combined resultants of the forces and moments
the centerlines of the exhaust connection and shaft must not exceed the following two conditions: (2s0 D.
F.
where
F, : M, : D. :
F(
F,<
( ( w(
F."
F
160D
'vr
F
Algebraic summation of F." Algebraic surnmation of Fo Algebraic summation of F,'
( ( (
F-r)'"
w
l.6w
(
2w
Use up to 100% cold spring and satisfl the operaring condition only. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:
(s0oD"
where
F : M:
-
Combined resultant
of inlet.
extraction.
and exhaust forces, lb
Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ftJb Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction and exhaust openings up to a value of 9 in. in diameter. For values beyond this, use D. (i8 * equivalent diameter)/3 ln.
<
< <
50 D., 125 D., 100 D.,
M_
<250D, My. < 125D. M., < 125D.
1.6w
Combined resultant:
(F.*), + F.y, +
M.)
Components of these resultants should not exceed:
160D 130D
o Resultant components:
r
-
:
o Individual comDonents:
1.3w .6w
of
the inlets, extraction, and exlaust connections, resolved at
further as follows:
F-<
Pipe size of the connection (IpS) up to g in. in diameter. For sizes greater than this use Dc : (16 + IpS)/3 in.
M)
(lb), including pressure forces where unrestrained exoansion joints are used at the connection. except Resultant force
on vertical exhausts Resultant moment, ftlb
Vertical Exhaust Connection For installation of turbines with a vertical exhaust and an umestrained expansion joint at the exhaust, an additional amount of force caused by pressure loading is allowed. (The additional force referred to is perpendicular to the face of the exhaust flange and central.) For this type ofapplication, calculate the vertical force component on the exhaust connection, excluding pressure loading, and compare with the value of t/o the pressure loading on the exlaust. Use the larger of these two numbers for a vertical force component on exhaust connections in making the calculations just outlined. The force caused by the pressure loading on the exhaust is allowed in addition to the values established bv the Dreceding up to a maximum value of vertical force (ib) o; the exhaust connection (including pressure loading) of 151/: times the exhaust area (in.2). These values of allowable force and moment Dertain to
the turbine structure only. They do not pertain to the forces and moments in the cormecting piping, flange, and
Design Criteria for Allowable Loads, Moments, and Stresses flange bolting that should not exceed the allowable stress as defined by applicable codes and regulatory bodies. (See
Figure 8-2.)
261
resultant forces and individual components will be limited
further as follows: o Individual components:
F"(1.3w(40D Design Criteria for Turbine Drivers with Cast lron or Aluminum Nozzles and Casings Cast lron or Aluminum Turbine Force, Moment and Stress Limitations
Fr(.6w(35D F"< w(40D .
Resultant components:
Algebraic summation of F,* Algebraic summation of Fo Algebraic summation of F'"
.
( ( (
1.6w w 1.6w
Combined resultant:
At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a
(F*2+F,r2+F''?),n<2w
value which would cause a bending stress of 56/4 in a connection having a section modulus equal to the connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller size connections a stress of Sr,/3 is permitted. (56 is as defined by ANSI Code B3l. 1 or ANSI
Use cold spring, but comply to these limitations in both
Code 831.3 (current issue) for the material of constructlon.) The resultant shear force at the face of the flange and anv individual component should not exceed 500 lb. The
operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:
F< where
(s00D.
F
/
M)
= Resultant force (lb), including pressure forces where unrestrained expansion joints are used at the comection, except
RIGHT ANGLE TO
TURBINE SHAFT-
-
M: D":
on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to an S-in. diameter. For sizes greater than this (16 + IPS)/3 in. use a D"
:
The combined resultants of the forces and moments of the inlet. extraction, and exhaust connections, resolved at the centerlines of the exhaust connections must not exceed the following two conditions.
l.F.<
(2s0
where F.
D.
:
M,: Figure 8-2. Turbine coordinate system.
-
M)
Combined resultant of inlet, extraction, and exhaust forces, lb Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ft-lb
262
Piping Stress Handbook
D.
:
Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction, and exhaust openings up to a value of 9 in. in diameter. For
values beyond this, use D. (18 + equivalent diameter)/3 in. 2. Components
F*
o Combined resultant:
(F*2+Fry2+F.z;rnE2* Use 100% cold spring and satisf the operating condi tion only.
of these resultants should not exceed:
D., < M* < Fy. 125 D., < My. < F". 100 D,, < M". < 50
250 D. 125 D, 125 D,
The total resultant force ald total resultant moment imposed on the compressor at any comection must not exceed the following:
F< Design Criteria for Compressors with Steel Nozzles and Casings
where
F
= Resultant force (lb), including pressure forces where unrestrained expanston
M:
Centrifugal Steel Compressor Force, Moment, and Stress Limitations
value that would cause a bending stress of $,/4 in a connection having a section modulus equal to the comecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size comections a stress of S1/3 is permitted. (S1 is as defined by ANSI Code B31.1 or ANSI Code 831.3 (current issue) for the material of construc-
1.F.<
(463
where
D.
F. : MI:
( ( F" ( F,
1.3w .6w 1.0w
< < <
160D
l30D 160D
Resultant components:
Algebraic summation of Fo Algebraic summation of Fo Algebraic summation of F-
2. l.6w 1.6w
-
M.)
Combined resultant of suction, interstage and discharge forces, lb Combined resultant of suction, interstage and discharge moments result-
ing from forces, ftlb Diameter (in.) of a circular opening equal to the total areas of the suction, interstage, and discharge openings up to a value of 9 in. in diameter. For values beyond this, use D, = (18 + equivalent diamerer)/3 in.
Individual components:
F*
.
joints are used at the connection. Resultant moment, ftlb Pipe size of the connection (IPS) up to 8 inches in diameter. For sizes greater than this use D" : (16 + IPS)/3 in.
The combined resultants of the forces and moments of the suction interstage and discharge connections, resolved at the centerlines of the discharge comection must not exceed the followins two conditions.
tion.) The resultant shear force at the face of the flanee and any individual component should not exceed 2,60 lb. The resultant forces and individual components will be limited further as follows:
r
M)
J
D:
At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a
-
(925D.
Components of these resultants should not exceed:
F," Fy.
F,,
< <
<
92 D.,
M_ <
230 D,, My.
460 D, 230 D,
r85 D,.
230 D,
< M. <
Design Criteria for Allowable Loads, Moments, and Stresses
Design Criteria for Compressors with Cast lron or Aluminum Nozzles and Casings
where
F :
(lb), including pressure forces where unrestrained e xpansion joints are used at the connection. except Resultant force
M= D"
:
Cast lron Compressor Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus, "E," resultant bending moments are permissible up to a value that would cause a bending stress of S;/4 in a connection having a section modulus equal to tle connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size connections a stress of 56/3 is permitted. (Sr is defined by ANSI Code 831.1 or ANSI Code 831.3 (current issue) for the material of construc-
:
The combined resultants of the forces and moments of the inlet, extraction, and exhaust connections, resoived at the centerlines of the exhaust connection must not exceed the followine two conditions.
1.F.<
(250
where
hon.) The resultant shear force at the face of the flange and any individual component shall not exceed 500 lb. The re-
.
-
MJ
Combined resultant
of suction, in-
terstage and discharge forces, lb
Combined resultant
of
suction, in-
terstage, and discharge forces, lb Diameter (in.) of a circular opening
eoual to the total areas of the suction, interstage, and discharge openings up to a vaiue of 9 in. in diameter. For values beyond this use D, = (18 + equivalent diameter)/3 in.
2.
ComDonents of these resultants should not exceed:
<
< 460 D. < 230 D, < F. < 185 D., M- < 230 D,
F."
F.y
Resultant components:
Algebraic summation of F* Algebraic summation of Fo Algebraic summation of F,"
F. : D, :
o Individual comDonents:
Fr(.6w(35D F"< w(40D
D.
M. =
sultant forces and individual components are limited further as follows :
F.(1.3w(40D
on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to 8 in. in diameter. For sizes greater than this (16 + IPS)/3 in. use a D"
( ( <
92 D., M,230 D., M.y
1.6w 1.0w 1.6w
o Combined resultant:
(F*2+F.y2+F-'?)'n<2w
API Code 661 Design Criteria for Air-Cooled Heat Exchangers
Use cold spring, but comply to these limitations in both
operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the followins:
F<
(s00D"
-
M)
Each nozzle in the corroded condition must be capable of withstanding the moments and forces defined in Table 8-3. The design of each fixed header, of the fixed header to sideframe connection, and of other support members should be such that no damage will occur due to the simul-
264
Piping Stress Handbook
taneous application of the following design iotal nozzle loadings on a single header:
For the direction of loads see Figure 8-3. The total of all nozzle loads on one multibundle bav should not exceed three times that allowed for a singli header.
Moments.
ftlb
Forces.
The maxirrum allowable moments and forces for floatirlg headers are a matter of agre€ment between the pur-
lb
F,FyF"
MM, IvI, 3,000 4,000 2,000
r,500 3,000
chaser and the vendor.
2,500
This recogrrizes that the application of th€s€ moments and forces will cause movement and that this movement will tend to reduce the actual lmds. Tabte
&3
Allowable External Forces and iloments tor Air-Cooled Heat Exchangers Nozzle
NPS Moments ft-lb Inches ilr lily M:
Slze,
lth 2
6 8 10
t2 14
50 70 50 70 120 70 200 300 2N 400 600 400
1,050 1,500 800 1,500 3,000 1,100
2,W0 2,5W
3,000
3,m0
1,250
3,000 1,500 3,500 1,750
Forces, lb
F,
F,,
F2
100 150 100 150 2ffi 150 300 250 300 500 400 500 600 750 750
850 2,000 1,000 2,000
1,200
1,500
1,250 2,W 2,000 1,500 2,500 2,500
Figure 8-3, The direction of the loads defined in Table & Exchangers for General Refinery Se/.v,bes, Second Edition, i978, Standard 661, Figure L Reprinted courtesy of the American Petroleum Instilute.
3. Reproduced lrcm Air-Cooled Heat
Simptified Solutions for Pipe Stress
These tables are developed as a tool for the piping stress
can readily be seen that the smaller expansion
engineer or the piping designer by which he can quickly evaluate a proposed layout before he proceeds with his deslgn worK. It is important for the reader to understand that the tables presented herein do not compose a rigorous solution to the pipe stress problem. Computer calculations must be made for borderline cases. The tables are approximate values onlv for two-anchor oroblems.
Example Problem 9-1 Consider the piping arrangement in Figure 9-1.
Size: 8 in. Schedule: Sch 40 Material:
O.D.:
=
F:
A-53 Grade B 8.625 in.
where
Temperature: 600'F Coefficient of thermal expansion: .046 in./ft
:
The expansion for the 20-ft leg is X .92 in., and the expansion for the 10-ft is X = .46 in. By inspection, it
will deflect
the longer leg more easily than the larger expansion will the shorter leg. To develop Tables 9-1 and 9-2, a guided cantilever formula has been used to calculate stresses. If we observe our Example Problem 9-1 for an expansion ofX -92 in., the required offset is about 13 ft for a stress of 15,000 psi (See Thble 9-1) and 23 ft for a stress of 5,000 psi (See Table 9-2). If Point A is attached to a piece of rotating equipment, you will need to have about 23 ft to make the system more flexible. If the system is attached to a piece of nonrotating equipment, a 13-ft offset will be sufficient. To find the thermal forces Table 9-3 is to be used, which shows forces for a unit reflection with various leneths of offset. Note that in identifuing pipe sizes the tables show wall thickness and moment of inertia as well as O.D. All forces are calculated from the formula:
6 Ell1728 L3 (guided cantilever)
F: E=
{:
Force, lb E O-.ton, t tn., Young's modulus of elasticity, (30 psi) Moment of inertia of pipe, in.a Length of the shorter leg, ft
I : L: I
I
Fys
=
F.B
x
106
434lb
=
Figure 9-1. Diagram for Example Problem
6,949lb.
9-1
.
(Text continued on page 291.)
265
256
Piping Stress Handbook
Table 9-1
Lengths ot Offset Required to Safely Absorb Various Expansions tor Piping Between Two Solld Anchors (Stress Limit is 15,000 pst)
Pipe O.D.
(in.) ol
1.3 1.9 2.3 4.5 6.6 l'.D
rs .7 74.9
16,S 18 .0
.g 24.5 2g
30 .s 36 .g
42,9
4A.S
54.9
1.5 2,6 3.5 3.3 4.2 5.1 5.3 5.7 5.1 6.4 7.9 7.8 9.3 tg .5
tength (ft)
Bequired to Absorb Expansion A (in.)
o.2
0.3
2.3
.8
3.4
3.0 5.2 5.9 6.6
l1,l
t4.l
I4.9
8.4
ro ,4
11.8 L3 .g
IS .1
14.3 16.3 L8 ,2
74.0
19 ,9 2g .8
L6 .O
l8 .0 26,0 24,9
3g .g 36 .S 42 .0
48,9
54.5
22.3 23.6
24.9
u.d
9.7
12.o 13.6 15.1 15 .5
l8 .9
2I.0
22.9 24 .T 27 .3
29.8
Jt.5
8.1 8.9 9.9 .5 11.1 10
tJ.o l4 .9
r6.l u.3
18.3
36.1 38,5
4r,s
9.9 10.9 13.4 L5.2 l5 .9 l8 .5 21.1 23 .5 25.6 26 .9 28.8 30.5 32.2 9.4 .2 .7 .9 a2.9
3
38.6 44.6 47 .3
5.1 6.7 7.4 8.4 9,4
5.il
tength (ft) Pipe O.D. (in.) -r-:3 2.9 2.5 1.3 1.9 2.3
3.9 4,3
4.6 5.2
4.3
7.6 8.1 8.5 9.1 9.9
0.4
43 a6 49
rg .2 16 .7
t2 ,2 12.a
t4.l
IE ?
17.3 18 .5
2L.I
0.5 3.6 4.4 4.8 6.5 5.8
9.4
10.5
IL.4 12 .g t2.a l4 .4
!7,6 2g ,8
0.6 4. 4.8 6.6 7.4 8.2 9.0 l0 .3 12,5
13.2 14
.l
14 .9
15.7 17 .3
l9 .3 2t .7
22.A
o.7 .3
5,2 ?1
8.5 8.9 11.1 L2.4 IJ.5
14.2 15.1 L7 .S
t8.5 2g
22
.8 .8
.4 28.0 26
23 .6
0.8 4.6
0.9 4.9
6.1 8.6 rs .4
lr.:t
l4 .5 .2 16.3 17.3 t8 .2 15
8.9 9.1 tg ,r
.3
1.1
1.2
6.2 5.9
5,4 6.5 7.2 8.9
6,8
t0.6
.l
9.3 10.5
12.2
I2 .8
7S
Lt.2
tl.l
lt.7
l4 .1
14.9 16.2
15.6
L7 .g
12,6 16.1
27 22 24 26 28 29
1.0
.r
23,6 .9 28.9
.4
25
.4 .2 .9
29 .9
18.2 l9 .3 26 .3 22 .3
24.9
29
,s
1',t t
14,9
14 .5
r7 .0
17.8
17.8 l8 .6
,2
2L .T
2S
23.4
22,3 24.4
26 .7
27 .3
33.1
34.5
28.6 39,9
JJ.5
Required to Absorb Expansion A (in.) 3,0 9.9 l0 .8 11.9 o.5 20 .2 .l
.r .l
23 za .6 28
29.5
38.6 43 .2 47 .3
51.1 54.7 5A.g
4.5 9,7 12.9 15.9
I8 .g 26 .g 2L .9 25 .0 27 .9
35,4 31.9 34.1
tg ,4
11.0
13.8
14 .6
17 ,g
2I.3 23
.4
29 .8 36 .4
36.1
38,5
JO.I
4g .7
4r .7 46 .7
51.1 55.2
59,1 62.6
5.9
44.6
49.9 54.7 53.1 67 .S
t3.3 78,5
26.5 24
.8
3r,5 34.4 36.1
ll.5
!4 .6 15 .4 t9 .6 2I .6 23 ,9 29 ,9
36,3 JU.I 4S
43.2
,'l
47 .3
45.6 49.9
58,6
51.1
67 .S
70.6 7 4,9
6.6 L2, 2g 22 25 27 31
23 ,6 26
.L
.3
4I.7
45.3
47 .3 49 .9
47.8
52 ,3
5 8.6 64.1 7
4.I
I7 .6
24.6
54.7
61.t
67,9
16.5 .2 22.5
18
39.9 41.4
43.5 46.5 49,3 52 ,S s5 .9
63.6
39 .4 43
.s
45,1 48.2
sl.1 53 .9
55,0 ?a I
8S
a2.6
7,0
28 ,2 34 .6 38 .S
4S
.6 42 .1
13 ,2 L6 .g
28 .6
34.9
66 ,O
7t.s
.0 .6 .g .4
16.9 29.8
6.5
,5
88.5
267
Simolified Solutions for Pipe Stress
Table 9-2 Lengths of Oftset Required to Safely Absorb Various Expansions tor Piping Connected to Rotating Equipment (Stress Limit is 5,000 psi)
Pipe O.D.
(in.) -6:i t.9 3,5
3.4
6,6 8.6
5.4 7.3
4.6
ro.7 8.r r2.7 8.9 74.s 9.3 L6.0 9,9 t8,0 I0,5 1t.r 28 .0 24 ,O 12.2 13,5 30 .o 36.s L4.9 42.A 15.1 48.0 L7 .3 54,6 18.3 Pipe O.D.
(in.) i.s 1.3 rl .0 1.9 13.3 2.3 14,6 3.5 18.0 4.5 29.5
8.6 24,3 ls.7 31.6 L2.7 34.4 14.0 36,L L6.0 3 8.5 18.0 4L.O 26.9 43.2 24.6 47 .3 30 ,0 52.9 5a.S 36 .0 42.O 62.6 48.5 67.0 54.9 7 r.g
Required to Absorb Expansion A (in')
Length (ft) o.2
4.9 4.8 6,6 7 .4 8.2 9,9 r0.3 12.5 t3,2 14.9 r7.3 19.3 21.1 22.8 24.4 25 ,9
0.3 4.9 5.9 8,9
9,r
t0.r
1r.1
12.6
15.4
16.r 18.3
27,r
23.6 25,9 28.9 29.9 31.7
Length (ft) 2.O
2.5
0.4
0.5
0.6 6.9 8.4
9,3 .5 11.7 12.8 14 .6 16.3 L7.8 18.6 19.9 2r ,r 22.3 24.4 27.3 29 .9 34.6 36 ,7 L6
70,4 1r .8 13.0
11 .4
14.3
15 .7
L2.9 14 .3
16 ,3
L8.2 19.9 2q .8
20 .0
2r .8
22.3
24.4
23.6 24.9
25 .9 27 ,3
27 ,3
0.5 33 .5
29.9
3
38.6 4L.0
36 .7
39.6 42 .3
44.9
o.7 7.5
0.8
rg .0
10 .7
74,0
8.0
r5,4
l6 .5
lo I
20
16.9
2r.6 24,7
r8.t
.7
26 .4
0., 8.t
76.1
1t .3
1.0 9.0 l0 .8 11,9 14.7
29.5
39.6
45 .7
48.5
11 .9
47 .A
43.2
44,9 48,5
47 ,3
55 ,g
58.0
6.q
7.9
17 .5
19.2
26.2 23
24.5 28 .g
.r
28,1 29.5
38.6
34,6 38.6
9,4
tr .4
1.2 9.8
.4 16 .1 r 9.4 29.2 24.2 25,3 29.5 36,8 32.3 30 .9 34.6 33 .l 3 8,5 37 .6 40.5 42,3 49.7 sl .9 56 .0 53 .6 57.3 59 .9 60,8 6 3.5
r4.0 t5 .8
28 .0 32 ,3
1.1
48.9
5I
.I
15
Required to Absorb Expansion A (in.) 3.0
15.6 16 .8 18.8 26 .3 15.9 18 .9 20 ,7 22,4 20.8 23.3 25,5 27 .6 23.6 26,4 29.s 31.3 29.2 32.0 3 4 .6 26 .L 28.6 32,0 4g.r 43.3 36,5 4q.8 44 .'t 48.3 44.5 48.'t 52.6 3 9,8 4r,7 46 .7 Fl I q( ' 44,6 49 ,9 54.7 59 .r 47.3 52.9 58 .0 62.6 49,9 5s.8 61, t 66.0 54.7 61.r 67 .0 72.3 61..1 68.4 74,9 8q.9 67.9 7 4.9 82 .S 88.6 72.3 89.9 88.6 95.7 77 .3 85.5 94 .7 r02.3 82.O 91.7 109.5 rsg.5
4,9 18 .0
29.5
4.5 23,g 25 ,4
5.0 20.L 33.0 37 ,4
37.9 49,5 46 .3
43,5
49.r 54,8 62.6 67 .0
61 ,0
70.6 86.5 L02.3
L09.4 116.0
77.0 74,9
4t .4 45.3
51.7
74.9 7 8.9 85,5
L00.5
ro5 .9
108.5
114 .4
rt6,g
123.1
28 .g
34.6 39.2
r22 .3 L29 .7
22,9 26.6
35,r 4t,0
43 .4 41 ,5
45.3
66 ,5
63.2 68.9 72.3
66.9 65.0
82 .0
9r.7
21.1
24.3
74.L 78,5 82,8
90.7
49 .7 56 ,7
22.9 27 .7
3t ,5 39.6
42 .7 49 .0
59.0
65.8
78.r
77 .3
80.5
85,5
96.0
94 ,7
98 .6
a2.g
23 .8 28 .8
88.6 93 .4
IO2 .3
I6L,4
10s.9
110 .3
]f
r2g ,o
125,3 134,0
130.5
135.4 L44.7
ItL.r
r36.1
1r5.0
I42.I
I2A .a 139 .5
L4't,9
4.4
r25.3
Piping Stress Handbook Table 9.3 Force (lb/ln.) ot Expansion tor L-Shaped pipe (No Etbow)
?.375
{IFF-
l. J/J
,,t65
FI i J 5 6
t I 7 LE
t.3ls 190 l,!li 5t3 :6? i52 9$ 5{ 45 J3 ?5
4!
19
l3
IE
t,
15 !l rfl
J.lt0 !.SS3
!,3sc
t6!94: 5,5?t :!rtB t!98{ ,i2? 3t5 165
t8s 136
t9i ?n 6?
{t 45
E 31 7 t9 6 ?l 5 ts, 4t7
i0 12.;5 i .
4,5S9 5.563 ii,6:5 !.6?5 lS.;Ss l3,ig$ g,gs3 0.1t9 g.lr9 0,lg? Lt3{ 9.156 ?.8tt 6.?4t ll.84t ?6,{{t 6?.?6S t22.iAF Ig!586 99t457 t5{!!3? 344!?74 8l?r9fi9 l$.849 ?iigg? tf,7r5 tEi,BE1, ?4t,t3E i?f.lgg 1.573 l!!td7 t9,t8g 4Jtt34 19?,486 199:?t l
:!3,11 5!789 ?,87! ?!rfi{ 52,4?3 lS!!991 I.353 3,35t 5!7lz 1?!751 3g!5i6 t9,62? 853 ?! ltg .3,19i 9,F35 l9! t23 37,169 57? lr,ll3 7,418 :!17? lt,gu Z4Jrg {9t 993 l,i9l 3,778 8!997 17,{8F ftJ 724 l,?3{ :,;5,1 6!3:l l2r?{9 275 5{1 121 ?,989 {!9?8 9,578 169 4t9 714 11594 J.?96 7,378 t33 32t 55t I,I5{ 2!985 5,803 tE? ?64 45t l!fs{ ?!399 {.i{6 s7 4 3AA 816 l!t{t 3t717
7r i7 3gr 672 r.6tt 69 147 tst 561 t!t35 5i t?4 2l? 47i I,tIs 43
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sc!.i. 5s PIPE
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lll 19M9
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Simplitied Solutions for Pipe Stress Table 9-3 Contlnued
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Piping Stress Handbook Tbble 9-3 Continued
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Simplified Solutions for Pipe Stress Table 9.3
Contlnued
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4r
THICrjI/ESS, AND MOMENT OF INERTI,A-
Piping Stress Handbook Table 9-3 Continued
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Simplified Solutions for pipe Stsesg TEible 9-3 Contlnued
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Piping Stress Handbook Tbble 9-3 Continued
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3 UNFS ARE AD., WAIT TIIICKNESS, AND MOMENT OF NERTU.
Simplified Solutions for Pipe Stress Table 9-3
Continued
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UNES ANE O.D.
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TEICKNESS. AND MOMENT OF
NERTU.
276
Piping Stress Handbook Table
$3
Contlnued
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WAIL TH]CKNESS, AND MOMENT OF INERNA.
16,864
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Simplified Solutions for Pipe Stress Table 9-3 Continued
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Piping Stress Handbook Table 9-3 Continued
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3 UNES ARE AD., WAIL T'IIICKNESS, AND MOMENT OF NERNA,
Simplified Solutions for Pipe Stress Table 9-3
Continued
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FIRST 3 I.]NES ARE
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WAIL TIIICKNESS, AND MOMENT OF INERTU.
113,:94
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Piping Stress Handbook Table 9-3 Continued
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3 UNES ARE O.D.. WAIL MICKNESS, AND MOMENT OF INERTA.
Simplified Solutions for Pip€ Str€ss Table $3 Contlnued
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FIRST 3 UNES ARE
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11
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75i i,6tg 3, t69 8,:74 1?,16? 37, 183 :;9 1,?4& ?r4{l n!371 14.76S ?8,$4S 456 9St 1!9?S i,gi2 11.69t ?!:5;$ 7f,5 l!51; 4!0ll 9!:91 1s'g3i I6i t97 639 l,?5F 5!?63 ?!53; l4,Si4
4n il
17 !5 14 34 lI ll 2t lt ig 15 :i t s28 7lB 717 5
6
O.D.,IULL
16
ti
5:6 l.$:t 1!659 6,11i ll!;83 439 S5S ?,:41 5, 191 t9,871
169 7It 6l:' tl{ 5:7 ri? 131 4i5 ?A2 3!! 34i ll7 15i 3t5 17fi lls 74s l:3 lF9 !!4 197 tgi 8E li..j
sd 7: ir &6 35 tl, 4i 4:
l3t l4r i:9 ir7
36
;i
I'i
YiJ 'ts A3
gSE 4,373 !.'186 l.d6t l,7lE 7,?l: t.3i; 3,1s8 6,196 1.189 2ti'u4 i!144 lttl4 i.3t5 4,6{g 991 ?,t96 4,9&g 7l? 1,345 3.58t 7i3 1! 61? 3,167 h27 l!451 :,S16 559 1;:t6 ?,514 ifiz I,i6? :,;5,1 45? I 940 I' f?t 4ts ' 913 1,!ll 378 Ssi 1!66[ ll& t'il 1.Il$ iEh 7Li |,377 849 1!:5-q :uB lil 5t5 I, i34 :47 i, tsi :3i 564 li7 iL7 I 1!3 si4 4li iii 17? 3!? iii l'i 3;0 ilg I,
:.q
:4
3l
io bl
TTIICKNESE, AND MOMENT OF INERTU.
Piping Stress Handbook Table 9-3 Continued
1q
EFi-
!Ei i-T
3
'i
il 1?
tl !4
l5 l6 l7
lc 1?
?i 22
:3 ?5 ?6
7i ]B
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34
if,
lif a7
]B
It tiv
+l t4 45
,ln 41 FIRST
ic
?4
Iii, :c!. !B iIFE
t60 lS.6ril 9.759 S,S43 L9-i7
11.90S 697,31t
1,9.
115d.
:s.{{g !. iili
:4. gs!
l.
i:e
?9S 1833.46t ?771.61S :67t.839
1i9.ii5 ?35!t4t 173,0:i t!, ?il 165.::l :6t, ?84 71,5t6 l:6,44i t9$,9S6
tt6, !t6 gl0,4i: :88.71F 5t0,tli
51,ifl 90.494 143.491 : l,l, 9l: {43, sgs 4l,4lJ tt,TrtJ l lS.5:4 167, I S.il.9gi 3?,tgg 54! 924 86.939 l ,4ll 169.9ii :$, $l! 43,5t5 6t,6fl lr5, 5 r15,ll I !l !It4 35, $St 5i.:S? 85.544 175, S:6 17,479 l9!4f6 46,6i8 ;g!496 !44,141 l4t57l ?4,316 38!t74 58t 764 l!6.15= n! ?76 ?t!6i3 3?t 748 49,504 lfl.t66. tg,43E t7. t6' :7.t45 4?! 99? 56,137 8,t49 t5!S:6 ?i,8?3 36.tgl ;3,8:: t73l l3,fi6 :9,6!3 ll, 175 il,796 6, ii4 rJl! 17.9J6 ?;, i14 55.,tS! 5.ESi 9tlqg 15,6t7 !-:! 7:9 49,559 7
:.1i9
s,713
t3.sls
4,591 7!;99 12,2?i 4,S7i 6,953 tS.!64 l,617 6,llt 9! 793 l,:61 5!4i7 F,7FS ?! 936 4,9t9 i, E3t :. s"? 4,4il 7,17 4 2,4i3- 4!S4l S,li l :.165 3.6i$ 5, 1,iE2 3,:5? 5!:t4 t!g?; 3!d,i5 4.85t S?B
1,67C ?.SS?
1,5i5 :.38? 1,4!l ?,37S l9 l,s3t 9b6 939 !,i0 7St 736 699
3t1ifr
!r rTJ
.j,'tcr
l.8Br t, i4g !!i!& 1,515 1,414 1,3:t l!:37 l. t6u
i.954 :! 771
t,287 r,Srt
l,l
4!4:4 ,1. $93
t,::o !.5i8 1,402
?.:4: :,596
lttS? 1,94t
?r,sg5
4?.73A
tE!,t77
37.
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ill:
4?6
14,,158
36, d16
l3t
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1S.613 :t,88:
itl el1 s, t34 i.t4i t,
,
6,7J4
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16.,14f
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t]!
7Et
lss l?t ii3 :r 7fg i l, i64 5.?i? ig,i|i {,t67 9.969 4,511 9.? 4,139 g!3i:i l! 997 7,1i 3,631 ,411 l.lst i! 936 Ir 1ig 6!494 i! 966 6117g 6!
l
4
1
1 lrtl
q ,igl
3 UNES ARE O.D., WAIL THICKNESS, AND MOMENT OF INERTA.
Simplified Solutions for Pipe Stress Table 9-3 Contlnued
:.3;5 rS 1?,i5 li,l, slil. Bts PIFE
IFF-
t.375
:.59t
iEl
t. ?lg t,8rF
F.389
:t
ll,tsl :s,?0i 1i9,ll7 ;6!!i4? 5?7,::? 1.34i 15,0?{ 3i,t?s i9,149 l:6,?14 4t7!856 8lt.716? l,4ll i.3lr li,i4: li!i44 63,?SI i7t.f64 314.971 5tB.45S i?3 3,?4i 8,tfi9 l:,!?6 3l'74I 88!597 176,6;t 301,?8t ,119 1,S78 4!&35 l!968 19.5?; 5i!182 it?r?14 1t{.:56 3i{ l.iBl ?,9t9 6,!7i l?!ig7 3i!lt5 64!JrE id9'79t i77 79? l!955 4,?{5 8,239 ?1.5S8 43,1?l l3!i56 t:{ 55$ t!37J ?,954 3!7lA 13,ld6 39,?s6 5iii61 496 1,8c1 :!153 4,:18 llrFlz 2ztg18 $.661 tg 69 3t5 i5! 1,618 3' 161 8,174 16,58S !8'295 5?. ?35 579 1!?46 t,,141 6.3i3 l2t77i 11,794 4t Ig5 45S 9lt 1,9?6 l!91? 19!649 17t14? J63 ?85 1,537 4.gll 8!646 13,72: 13 l{8 ?97 618 l!t5t 3,:&3 t.542 1!,1:9 27 tln q9 :44 li6 1!g3i :,58? lrllt t.lts 72 l8 83 2$4 438 8t8 ?,:41 4.41{ ir6i6 76 1;2 3i9 i73 1!8Eg J!79! 6'{i8 16 lI 5? 146 3i4 6i5 1,6i3 3r?19 i,491 ;69 5?? 1,3?7 ltltr 4.;0u fl 51 l:5 ig 44 ls8 ?33 455 l.l8t itSg{ 41967 ,4 767 3l$ 1.s34 1,613 3,537 s 3r a2 177 34i 9S5 1,815 3!S95 7 ll 717 1,5?7 2,i24 71 156 lt5 7 it ri ?6 64 lJE 27* ;t5 l'4ll l!{ifl it7 l!!55 :, i4l 1f3 2$ it i 13 5 ?l 51 169 ?14 559 1,1:: t,9il t8 19? 35: !,St6 i!716 46 4 l8 452 955 1,144 88 lis 4 t7 4l lsa 40t Slg l'195 *t 3 15 J7 175 741 1ri64 7r t4l 3 l{ 34 j: lJ6 t7{ 1! 149 l:f 3l si i2 3s6 614 lrg4s 6E tl7 I 1l :8 s5 Li7 ?SS 562 ti8 15 : 10 515 u7t 95 ::7 5S r I t3 ,fl :J6 471 E7 4i 2 I :t g3 2t7 436 114 43 ? i 7fr 281 4t? 686 i7 i It 7 1S 3i2 6i5 71 ii6 36 2 7 t7 34 5g 112 145 383I 6 16 gt 169 3rg t46 Jl 1 6 15
; 4
5 6 7
t t LU
l? l3 l1 :s 1l
l9
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4t FIRST
3. EtS
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3
LTNES
ARE O.D.
,
WAIL TTIICKNESS, AND MOMEITT OF NETN'1.
Piping Stress Handbook Table 9-3 Contlnued
?,3;5
i;5
rFF.
?.
3iT
9.436
9T
i,ili:
2
T0
J,sSt 4.".J9fl 5,:63 6.6?5 !.61I S.itS0 9.b74 ,.73t 0.S64 9 giS 5.ttg i5.iEg lJ.6Jt i6.3t0 i6t.9git
UiY
78,921 ?l 1!q
4
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it4
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4! 994
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4
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;
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t?
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I! gts l, g?o
:67
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lE7
95i
lt7
6?4
?35.9F
r:1,911
1t7!
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174
5d ,tg
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tl ll ti
La
'l
l?i
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17
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rq
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f,l 45
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:
:0 !3
$4 173 ?t: r11 tIz l5u I3I I l! lEi El it 65 59 !l 4t
qqE
1!
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lrd38
Etl 713
6fi 5t I 43S
378
l:t
:EE
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ts7 78,I l8
11,495
32,95i
:9,145 9!478
c6!i
l??
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i:l
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iti
l.V
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lt
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6ll
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1, gE8
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Y,l
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ii?
5l
l'i
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ils :t3
i/'
it
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49.194
6, t 16,871 5! 191 17,{17 J.9t9 !t i65 3.1{5 7,6gi ?,518 d.l{t 2,847 5.106 t,687 4, tit l!416 3!{34 1, 1.35 :! 893 |,'tgi ?r,i6g F64 ?,!89 ;46 t,8?; r49 1.:85 5{8 I,3S7
It
t7
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:
ittY
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4i
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:t 4
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199 6,843 ?! 184 4, tr6 1.5?? J,5d4 1! 196 ?t 6li 9!l ?, i?B
?t4 i85 l5?
5i,?77 l:{!
4,642 lg!ill
6:
t63
iB,i?9
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FIRST
gt3,;t6
l?1,7b1 34,7{4
t6l
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li3 li? ]?T itl ,ti
4Jt.95l
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?77 L6 ?li :r' t:4 i1
556
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199!
103
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B.i!5 IR, Sti{. i:is FIFt
i35 1:6 ii6 lfit Lli'
iit
566
3:5 4,19
42' 3?4
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?84 261
:,i3
3 UNES ARE OD., WAIL T'HICKNESS, AND MOMENT OF INERNA.
Simplified Solutions for Pipe Stress Table $3 Contlnued
d.6i5 Tl ?4 iH.
,itt:!T
:;
s.6:5
g,5
i,J.
i5S
S.1r8
i2,75S S.443
iit.3?s :86.139 16l.65g
sCH. lEg PIFE
14.u6g 16,99t 13',Jrio 2g'fr88 :4'oti
r.937 l.g3t 1.156 l.:81
S?4.41{ lJ64.,l3t ?179'6SS
l3l5'ttS
1.5:l
e€:1.i?..
3
+
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tfr
ll l? l3 l{ l5 t7 i9
i: :3 :,1
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7i :1
3i :4
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:i 3i
157.467 46i,7t9 914 t 144 tgl. tt3 ?38,441 4S8,i4? 58.559 1:;,9BS ?7,J!854 16!t45 86,896 179'569
6g7r63g 397.5S7
659!99?
?59!375
41{,36t
?,157 :,111 !g! jil2 l{!?:5 I, B4l 4,145 S,:3f 1!,::l !,:it t!7?6 7.3iI lt!i35 I,lt3 1.3i3 ;. a i,:li IttgT ;,799 3!494 8,0i5 1,639 ?,43fi 4!!i9 ir S5l 914 :, rs6 4,?t: 6,?12 Edr l.lsg 3! i44 5!4?6 it? i,69i 3,3:9 4,SS6 64? I,514 2,?77 {:363 5?6 1,35t ?.s6: 3r !!? 3ts l!::? t,ltt 3,3?1 45S 1.164 z,lhi l! !8! 4?4 1! 6!if i,9ri4 ?,lu; 380 919 lt 795 2,ill st9 !!i!a ?,l9t ;i? 7iB I,,t89 ?! lg5 ;;? it5 095 i,365 :,,i93 lii iri i,::4 1tS41 :,i9 584 1,155 l,6ti :;f 341 1.,,6u l!5$5 :13 :8? 986 lr44g 191 ,i6, tl4 i 3,1? 1fl3 4t? 849 tli,li t
il FIFST
t$l.955
:4!693 58, 4 114.2i8 l!7!73? 277,513 445!{5S rzi.+lr -: 17,tJ6 4t,E!5 St! ?54 ll?:gg4 t94,?i4 3ll!455 473!6Bt 9it.Sl7 t?,63s :t.8s5 5S,5t5 gi,g7f r42.1?8 r?7. S5l 343rJl5 i13.7tB 9,495 ?!.393 43,956 64!322 196,?93 l7t,5B7 259,44S 5lg.??; 7!It1 i7,?4S Il!E5t 4?.699 93t ?59 lll!195 ll ?. aJs 413!t51 5!75? 13.166 ?4.619 39,SBl 64! S9t 103,146 l5?! 175 3:4! 969 4!656 ig! 8&? :1!lil il!?97 5lt7i6 BI!iq4 t?5,S41 169.lgl 1,745 8,83t 17,335 ?5,446 4?,1l? h7 t274 1g?,315 ztr,47t J,585 7,?7,1 14,:E4 :g! 946 i4.699 55,,11: s4.rt5 174.?18 ?!3?t 6,967 11,9dS 17.,lso ?8.939 4i! !14 7g,2g| 145, i7l
:1,17t
38,51?
zg,72t !7t766 t5,347
?St
13t348
?1,l?3
lt!69!
33,19; !4,51?
is!281 9,dr6 a,da7
7r:?l $,4i5
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lg!661 16.{?4 14,5
164
,Zli 5l,4lS ?8,iBl :{.t79 37
?:,1SS
,l5g
1$4,956
g!t
?15
i71467 n7!
tlg
:8,i69
il,,r:9 4!r e7g
l9!64;
40.
11.515 16,343
17,144.
3s, ?6i
t!
319
t64 8.469 7!6!l 4,ii | {.:3t 6.1:9 3.953 6! 319 1,616 iri'ii 1,315 :t:96 It {;16 ,i, Ai6 ?.896 4,1g: 2!77t !, s6:
4J.
l
t?,!lg
5,
;,i9s i,;t6
5?! 6 3S.3{r
4.1:r
3,9!t 1,518
J,:94
3 UNES INN O.D., WAIL THICKNESS, AND MOMENT OF INERNA.
6t8
13,;3i !i! l:?
3?!:13
12,73?
:6.41,i :i! t5g
ll,igl
iq!164
Ig,33X:' ;1r;dl 9,&S9 l9,i6f
iu6 l8! i59 8,t54 i6,6,io i,4tt 1:,;t7 6!El? 14, ttF 6,t9-r !l,tt7 5.8?l l:,il: 5! 196 llr l:]
f,
5,019 li! l:6
Piping Stress Handbook Table 9-g
Continued
4.i i0 l:.i5 I{. UiFSET
F1
2
;
I
1 a
I It l? i3
l5 l,: 17
ts
it 2g
?l :? :3 t5 ;b ?; !$
:t ]l 3?
tl i5
li
31
ti ;9 4t
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lit
FIPE
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l:1,
s4t
t4g
115!
14,99? ?9!?7!
igl 7ig
a4t! 9tl 191,3!9
5,1:,lBt
I s9,746 ?is, i36 5?i.7ll ?t 443 4i!J4? lli,lll ??f. tEg 3t4, i?s 5!g?4 t!,4t9 23t 9?5 67,77{ 156,t59 3i?,445 i! 54t 7!9t3 15.SS6 4?,S8t 9S.465 l?4, Eit ?.371 5,t35 l0.tt3 ig! 59? 65, ?$4 lt$,547 l, &$i 1ttt77 7,989 ?fi!081 46,3?? 91rgE7 t,?15 :,6S6 5.16S 14,639 il,7;3 6,5,541' 3 t,014 3rg8l t0! 999 ?5,375 59,118 ;0J 1.551 t!t9t c.47? 19.545 lB,rdl
lg!
9J
h
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441 t6g 2?7 247 ?gE 171 l5r l3l I t4 lsg EB r8 il 6? 55 IS 45
4t 17 34 31 ?i ?6 i,i t: 1fi 11 iu
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srt s? 75 6S 63 57 53 49 4i 1t lY
rr
J.JL
1! gg3
l!531 1, ?6?
I
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i74 331
294 ?S3
n5 ?1?
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6,66J 15,3?3 5,115 l?.1t8 4!338 l$!997
1,374 It ?8t 2.:10 ?, ii4 I,EJd i,:Br
3S.4?3
:4, t59 19,8i,i
8.t45 16.JiA 6!87{ ll,6Fi 7!1 i1,461 4!9?4 9! 745 51
4r7ZZ
1,647 11175 3.17: 1, ?S3 2,17& 1.f59 ?! 443 937 3! 16! i44 661 6SS 54? 491 447 487 37: 141 il1 7AS t67 217 ?2i ?l?
8!l:5 7,;i? 6, i7; 5,494 1.435 4, ?79
t!71d 3,196 1.53? I,945 f! 355 I! i,li l!:31 :1476 1,134 ?,244 1,031 I,E4B 94S l!96g S5? i.;91 789 1,55t j74 i!43r 6i7 1,l2j; &!5 l!?18 ;,)t 1,1:i 5:g I,944 ,ifr 4t,
3 UNES ARE AD,, WAIL THICKNESS, AND MOMENT OF NERru.
Simplified Solutions for Pipe Stress Table 9-3 Contlnued
I,t 10 !4 il{. scll, 1i0
cFt-
iEI
l4.E9t ri.g00 lE'tlgg ig'g$n :4.d0, l.gt3 l.tlg l.3lt 1.-5Eg i.sl! 9ir.5:r' l:55.419
lsr.11: Il$,441
'J
,i It t2
i3 t.l
249S.irgt 3;5{.13S 568,!34
l]?,819 !22,i32 :36!tsl 96,s:5 16?,S?? :oS! ?lB 7:,746 l?l 710 195t3{5 56,933 93!761 159,589 r
4{![7] 73,]{7 tl8!4{? J5!?96 59,i{6 94.83?
15
l6
76
1
gl5,t57
?93.gsl 6ii.l65
:?6.36i
4il
t77t996
379t987
!61?
l{?!514 ?i7,933 lt3!8A9 ?4t.49d
l2!978
5?,965
27,182
44t6i9
6i,p54
37,9J8
57,914 I lB! 839 48,8S? lSl!88?
?1,$ll !g!::3
J?,5?7
19,455 17.495
?s,69S
15t
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7!958 13,3t7
:3
539,43S
lil,g58
95,473 ltg.9g9 79!597 155!S9g.
9!i9l
22
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77,19? 63!539
16!
t9
78?1'53S
28,6t9 48,967 ?3!619 3Yr33&
l9,7rg 6t? l4,tt7 t?,1f5
t7
lo
?4.418 ?1,187
l3?! 756
4?!2?6 3&.7?6 3?! 141 :8.r8€ 2:,0:8
83.01S 76.546 66! 999
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!5
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45
47
FIRST
PIFE
3
LINES ARE O.D.,
WAII TIIICriI{ESS,
5t,?6s
AND MOMENT OF NERNA.
Piping Stress Handbook Table 9-3 Continued
E,iir5 T0 iS. r'55 l:.75d d.El: L.t1g l. ltS
S,6?5
iiFF5EI
ci
193.i:t 167.dtt ?9t.:SS
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198
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7
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1.9
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lt :i :7 !u
i9
lt
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Btt
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l
LNES ARE OD., WAIL THICKNESS. AND MOMENT OF INERTA.
l?
408,93t t?7.,1l9 i66, !S4
?09 t1t,i45
89.381
tB7,97A
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Simplilied Solutions for Pipe Stress Table 9-3 Continued
r.;i5 i0 1:.;5 I}{ Stii. !i-F-
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l,iY) i! /tJ r r c..o
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Piping Stress Handbook Table 9-3 Continued
14
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Simplified Solutions lor Pipe For the example shown in Figure 9-1, it will take 7,552 lb for a l-in. expansion for a 10-ft offset for Ax '9214 ex' oansion the force F- = 6,949 lb' For a 20-ft offset the iorce will tr-g44lb for a l-in. expansion. for Ay 46 in' 434 Ib. the force Fv
:
The nomograph in Figure 9-2 is used to size piping loops, depending on the size of the pipe and the thermal exoansion between anchors. This nomograph is conserva-
tivi for a refined design' An exact
calculation by com-
puter should be required.
What size piping loop will be required for a 300-ft straight pipeline under the following conditions: TbmDerature: 400"F O.D.: 12,750 Schedule: Sch 140 Materials: A-53 Grade B C.S. Use the nomograph in Figure 9-2, and join points A' B, and C. This will ihow a need of a 70-ft loop (L = 70 ft).
11
A
J&
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L = 2A+B
100
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Example Problem 9'2
B
l-t -]JL
Stress
o1000
IJJ
Flgure 9-2. Stress nomograph'
0)
10 Properties of Pipe
: Fifth power ofd, in.5 = DrlL2: outside pipe surface, ftrlft (ength) : dtr/12 : inside pipe surface, ff/ft Qength) : @2 - &)n 14 : metal area, in.2 : d'z rl4 : flow area, in.2 : 3.4A. = weight of pipe, lb/ft W* : 0.433 Ar : weight of water in pipe, lb/ft Rg : (UA)', : (V + &1*4 : radius of gyration. m. I : A.Rl : 0.0491 (Da - 6+; : moment of inertia, in.a Z : 2llD : 0.0982 (D4 - d4yD = section modulus : in.3 ds A" Ai A. & W
The following are the definitions of the tefms used in the table.
Definitions
D = Outside diameter of pipe, in. Sch : Pipe schedule, nondimensional t : tl6ll thickness, in. d : lnside diameter of pipe. in.
Table 10-1 Properties ot Pipe
T
Sch
D
losi
V8
40
sT 40s
D'.40S
80
xs
80s
Y4
40
sT {0si
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80 )
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r87
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160
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Properties of Pipe Table 10-1
Continued
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3.49 3.32 3.20
1.186
2.t94
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3.018
t.724
l.8so
1.080
294
Piping Stress Handbook Table 10-1 Continued
t
Sch
D
(continuod)
3 D -3.500
.241 .254 80
xs
80s
160
55
-4.000
t oot t ot, 2.900
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40 80
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3.834
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1.04? 1.047
t.021 1.4&l
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1.047 1.04?
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r.047
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10.94 10.78 r0.31
562 480
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2.680
t.04?
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1.047
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8.89
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1.004 .984 .980
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3.732
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3.548
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alt .r.t,
t20
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t.04? 269
4.334
1.04? 1.047 1.178
4.244
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1.178
t.1l
I.t?8
4.2t6
1358 1332
1.108 1.104
4.t24 4.090 4.026
1193 1144 1058
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3.900
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3.152
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5,34S
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1.080
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1.178 4363
1.399
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1.250
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l.38ri r.321
l.n7 l.l9{ I l2q
1.064
1.349
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6.09 6.04
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t.542
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5.44
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1.416
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t4.61
11.34
12.97
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2.81 J.JO 4.ZL
t.2{8
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2.054
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2-64 2.84
1.262 1.869
i.949
7.88
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4.27 10.42
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8.€
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8.66 8.03
41Cr
t.928 1.920
9.70
4,925
4.02
1.464
27.04 32.9?
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8.?8 9.05
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23.95
3.33t
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4.78
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8.08 q i,t
19.00
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16.52
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1.461
1.534
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1.88 2.?S 4.30
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1.368
1.549
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2.78
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1.455 1.4s6 1.456
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Pipe
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Table 10-1 Continued
D
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d"
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10.80
1.734 1.734
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10.38
9.82
I.734 r.?34
6.249
6.071 4{,
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9.lol
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5.O25
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5.501
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8.407
4.897
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1.640 l. qlo 1.620
3.80
1.604 1.589
r.?34
t.588
I t.?34
t.440
4.41
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2.?'58
36.8
8.149 20
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D-8.625 60
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34.2
2.248
7.93?
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7.875 7.813
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7.439
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10.482 10.420 10.374
2.2€8 2.258
10,020
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2.143
t9.66
2.133
2t.32 2237
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30.43
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47.9
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46.4 45.?
55.2 22.45
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1.800
21.30
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23.25 24.52
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14.98 11.81
6.13
23.44
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4.42
45.4
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2.246 2.248
10.29
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10.192 10.136 10.0s4
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9.91 13.40 14.25
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54.5 54.2
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2.Al
t8.gtl
3.94
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2.86 c.a
8.16
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10.344 10.310 10.250
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1.996 1.944
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v.o2
7
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2.304 2.295
n.64
18.8
2.089 2.O78
15.4
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29.5
2.t52
2.2,58
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14.99
15.64
2,180
2.045
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2.?58
32.4
80s
120 140
35.4
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30.1
4€t.30
2.160
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9.29
13.28
2.201
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10.70
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8.40
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8.249
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12.39
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2.82
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1.664 1.646
1.734 1.734
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18.78
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2.81 2.81
10.07
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80.7 79.4 ?8.9
34.2
34.9 34.4
J.b9 3.68
I54-0
lAt
160.8
4.6
296
Piping Stress Handbook Table 10-1 Continued
n
?
Sch
(continurd)
..JYC
60
to D
-
10.750
xs
80s
80
l0o
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12.85
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9.564
80.0
85.3
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2.81
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9.064 q ?q/t
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2.81
2.4
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30.63
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2-26
t.t2s
8,500
44.4
2.81
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12.390
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t?^344
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12.312
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8.625
40st
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t,J
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tt.2
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3.60 J.50 3.stt
244.9 ?€.8.2
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109.9
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3.52 3.4? 3.4It
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399.4
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3.34 3.34 3.34
3.25 3.24
6.17
12t,5
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120.6
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4.45 4,44 4.44
1?9'4 140.5
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8.62 9.36 9.82
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13.3?5 13.2s0
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389 380
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13.0@ t2.814 t2.?50
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2.98 2.90
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118.3
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2.81
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9.960 9.?!t0 9.68?
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3.53 3.50 3.47
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3.6? 3.67 3.67
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136.6
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3.6? 3.6? 3.67
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84.9 89.3
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84.1
Properties of
Pipe
297
Table 10-1
Continued
I
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D
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t
d
Ao
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Am
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(contiaucd)
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80
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1.093 1.250 1.344
120 140
14.000 160
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262
u.814 .t.ot
I1.500
1.406
I1.188
,I88
t5.624 I5.524
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4.19
902
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15.438
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4.19 4.19 4.19 4.19 4.19
126.4 12,,.7
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4.69
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50.0
4.63
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98.2 117.9
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t3.124 13.000
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16.876
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16.750 16.562 16.500
1247 1?23
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80 100
t5.066
120
15.250
t40
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1.688
14.625
t4.438
4.?l
3.44 3.40
azl
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13.94 17.36
?3.4 72.7
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64.8
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1550
194.5
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5.t2
1815 1894
236.7
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61.0
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14.688 14.625
459
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294.0 308.5
103.6
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1
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5.84 5.80
L
2908 3020
8I-A $!!.5 323.1
als.6
298
Piping Stress Handbook Table 10-1 Continued
Sch
D
t0
20 D
-
20
sT
30
xs
l9.s@
.sls
t9.3?5 r9.250 t9.124
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40
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18.814
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.8tz
I8.?50
6{'
tSIt
1.99
1.500
17.000
1.42
140
l.?50
16.500
l60
1.844 1.968
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st
:
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sT
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a.ps
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23.000
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22.876
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4.750 4.626 22.064
80
t.2r8
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t0o
t.531
l.oall
I.812
140
2.0t2
160
2.188 ?-3+3
sa
xl;
20
ST
xll
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20.938 20.376
r9.8?6 19.52s
r9.3t4
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2.9.t25
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29.000
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42 42.000
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n.w
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-
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17.€8
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30
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5.24 5.24 3.24 5.24 5.24 5.24
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34
2.82 2.73 2.64 2.56 2.48
18.250
20
D-30.000
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xli
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r.86 1.64
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5.24 5.24 5.24 5.24 5.24 5.24 5.24
5.Zt
5.0? 5.04
(nt
4.9? 4.94 4.93 4.91
4.8t 4.?8 4.?6 4.70 4.58
4.'r 4.4{t
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5.24 5.24
1.07
4.9 4.n
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4.21
4.59 4.3it 4.08
o.to
5.dl
c.,t0
7.r7
6.8
t.oo
o-15
Am
!9.36
ta t,
26.9 30.6 34.3 36.2 38.0 48.9 52.€ 54,3 61.4 J!t.o
?5.3 87.2
Af 298.6 294.8 291.0
?at.z 283.5
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209.0
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135.8 161.9
2249 2550
212.5
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129.5 140.7
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5.92 5.89 5.78 5.74
50.3 54.8 70.0
442 398
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102.5 136.2
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293.5 291.0
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L1 Weight and Dimensions o{ Pipe and ComPonents
Weight of PiPe and ComPonents
c
lhbight of iwulntion of the PiPe
I = Insulation density, 1b/ft3 T : Irsulation thiclness, in.
qnd compoWhen determining the weight of the pipe nents, several factois must be taken into consideration:
D=
Outside diameter of PiPe' in.
Weight of insulation Weipht of pipe : lJse the values for properties for carbon steej pipe as a standard. These values can be found in
o
Values
Chapiei tO. The relative weight factors for other mate-
Aluminum Brass Cast ircn Copper
Thermobestos
=
0'35
: l.l2 : 0'91 = l,l4 Fefrtic stainless steel : 0'95 Austenitic stainless steel = 1.@
{arbon
Depleted uanium
(D+f; = 67n
ll
lb/ft3
10
to 11 1b/ft3
11.53 lb/ft3
KAIJO
r9-2rlbltr
Super-X Foly-Urethane
?5tbltr 2.3rbltr
Amosite asbestos
16 lb/ft3 9 rb/ff 91b/ft3
Foamglas
Cellular glass
0.98
,
IT
Diatomaceous earth = 2rrbltr ?AIbItr High temperature
!
Wrbught
.0218
for insulati.on densitY:
Calcium silicate 85% magnesium
rials are:
:
,r)
Mineral wool
8lb/ff
Tables 11-1 Orough 11-10 give the weiglt of insulation and various pipe componens by size.
t
Wigtrt of water in pipe: See the proper.ties of pipe in Chapter 10.
The following pages are tables and figures showing fittings' valves, anct ptpe
standard dimensions of flanges, bends.
299
Piping Stress Handbook Table 11-l Weight of Insulation (lb/linear ft) Plpe Slze
Thickness of Insulation
21h" I
.72 .84
1.35
3
1.01 1.25
4 6
2.tl
t.62
3112"
1.94
2.',|6
| .71
2.52 2.53
3.47 3.48
2.08
3.01
4.O',l
2.5s
J.Ol 4.5'7
4.66 6.09
5.64
7.8s
t2 t4
3.28 4.13 5.20 6.04
.07
6.r6
16
6.90
8.38 9.33 10.4
8.45
11.6
8.93 10.5 10.7 12.0 13.3 14.6
t3.4
r7 .0
21.0
21.1 24.8
14.1
18.0 19.2
2r.9
26.0
23.4 25.0 26.5
27 .8
28.O
JJ. I
29.s
34.8 40.1
40.3
45.9
46.4
52.2
1.5
2
8
10
l8 20 24 26 28 30 J2
7
8.
10.0 10.4 11.2 I 1.9 12.7 13.4
36 42 * me tublc
15.
l3
I
16.1 t7
.l
t4.2
18.2 19.2
16.5
22.2
is based on calcium silicate at
I
20.5 21.7 23.0
t tb/ff
28.0
3.70 4.52 4.42 5.24 6.07 7 .60 9.48
5.59 6.65 7
11.5
t3.2 15. I
11.0 12.7 13.
l
15.8 t7 .5 19.3
14.6 16.3 l7 .7
29.5 31.3
34.0
and nust be adjutt"d 1o,
olnt
^ot"riol".
Table 11-2 Weight of Flanged Gate Valves (tb) Size
(inJ I 1.5
150# 300# JI
55
3
95
4
140
6
240
8
/100
t0 t2 t4 16
l8 20 24
900#
68 75 t4s 215 420 700
1500# 2500#
1,050 1,530 1,490 2,0w 1,150 2,170 2,410 1,580 2,800 3,500 630 830
1,910 3,720
136
115
194 270 530 940
330 720
256 460 610 1,410
1,220 |,560 2,600 1,880 2,350 2,630 35W
3,2W 4,680 4,230 6,500 7,2W
2,350
4,90
9,800
3,900
7
,380
I 1,800
CourEsy of Crane Co.
314 430 900
.4
20.4
1'7
18.
I
18.5
2t.3
20.5 22.6 24.6 28.7 30.2 32.2 JZ+. J
23.6 25.9
39.r
36.3
41.1
38.3
43.'7
rn" tort"
28.1
32.9 34.6 36.9
41.6 44.1 46.6
51.4
54.4 57 .5
49.1 51.7 59.2
iiuaiionaig *d-o*rin.
60.5
bJ-) 72.6 ."ighr.
(tb) Size
(in.) I
9l
16.0
Table 11-3
35
45
2
600#
9.10 11.5 13.8 15.5
weight ot wetd End cate valves
Rating 400#
.48
9.82
150# 300# 20
Ratlng 400#
1.5 29 55 245 60 380 120 4 120 170 220 6 210 360 460 8 340 590 830 l0 550 9r0 r,250 12 730 1,220 1,800 14 990 |,960 2,210 16 1,460 2,550 3,100 18 |,730 33N 3,76s 20 2,200 4,350 24 3,350 6,700 Courtesy of Crane Co.
600#
900#
25
80
70
125
80
155 270 &0
190
260 350 750
410 520 1,250
1,080 1,300 1,610 1,970 2,240 3,2N 3,000 4,350 4,030 6,000
1,910
6,760 8,950 10,500
. Weight and Dimensions of Pipe and Gomponents 301 Table 11-4 Welgtrt of Flanged Check (Swing) valves (tb)
Size
weight of wdd
3OO# 4OO# 600# 900# 1500# 2500#
160 70 23462 280 180 140 120 3 65 630 4 100 180 2W 260 3401,360 6 2N 330 395 530 640 8 390 620 680 900 1,180 2'100 l0 510 9m 9N 1,440 2'170 t2 775 r,2n 1,250 |,970 t4 1,200 1,650 16 1,450 2,050 2,420 18
.t
J
80
t40
6
250
8
a0
l0
598
t2
824
139 214 396
a8 686
14 16 18
20 24 Councst oI craie co.
zto
155
190 210 240 310 420 500 580 740 890 820 880
390 780 1,320
Counesy of Crane Co.
150# 300# 400#
4
100
2500#
130
18
Co.
79
900# 1500#
55
20 24
Table 11'7 End Globe \ralves weld tlreight of (tb)
slze
Ratlng
2
600#
1,015 1,150 r,200
t2 t4 t6
Table 1 1-6 vrteight of Flanged Globe \hlves (lb) Slze
47 80 130 zffi 510 760
1<
10
a^
Ctaw
Ratlng 400#
350 4 100 6 160 8 360
20
Courtesy of
(lb)
Size
Ratlng
(ln.) 150#
Table I l'5 End Check (Swing) l/alves
90 160
600# 115 191
233 476
318
820
1,2:U.
782
900# 1500#
2t5 46 4fi 490 65 920 1,890 215
2500#
Ratlng
(in.) 150# 3OO# 4OO# 600# 900# 1500# 2500#
234757897 3 75 115 130 L6 170 185 + 120 179 206 272 2N 285 6 220 332 401 656 630 680 8 363 530 900 1,100 1'1'+0 l'370
10 12
1,056 1,160
535
794
L4
l6 18
20 24 Courtesy of Cratv
C'a.
r,730
2,7N
3,850
2,400 3,024 4,lm0
Piping Stress Handbook
Table 11-B Wbight of Flanged Angle \hlves 0b) Ratng 150# 300# 400# 600# 900#
238 130 160 230 4 110 2N 235 280 370 6 zl0 370 385 675 1,000 8 360 634 685 985 10 552 1,130 1,950 12 r,720 3,100 2,350
14
lo 18
20
Counes! of Crune
Co.
Table 11-9 Weight of Weld End Angte Valves (tb) Rating
(inJ
r50# 300# 400# 600# 900# 15oo# 2soo#
2
70
3
8l
r70
4
155
490
o 8 10
530
330 880
t2
t4 16 18
20 24 Courtesy
ol Crane
Co.
r30
Table 11-10 Wbights ot Flanges (tnctuding Botts)
2WN 6 10 13 13 31 31 48 2SO 6 9 11 tl 32 32 48 2 BLD 5 10 12 12 31 31 49 3 WN 11 19 27 27 38 61 113 3SO 9 17 19 19 36 60 gg 3 BLD 10 20 24 24 38 61 105 4WN t7 29 4t 48 g 90 r77 4SO 15 26 32 43 6 90 158 4 BLD 19 31 39 47 67 90 164 6 WN 27 48 67 96 130 202 451 6 SO 22 45 54 95 r28 2U 396 6 BLD 29 56 71 101 133 197 418 8 WN 42 76 104 137 222 334 692 8 SO 33 67 82 135 207 3t9 60i 8 BLD 48 90 115 159 232 363 gg l0 wN 60 110 152 225 316 546 1,291 10 so 51 100 117 213 293 528 1.148 r0 BLD 78 146 t8l 267 338 5gg t.245 f2 wN 88 163 212 272 434 843 1.919 12 SO 72 140 1& 261 388 820 1,611 t2 BLD 118 209 26t 341 475 928 1,775 14 WN 11,3 217 277 406 642 1,241 14 SO 96 195 235 318 4@ 1,016 14 BLD r42 267 354 437 s74 16 WN 108 288 351 577 785 1,597 16 SO t85 262 310 42 559 1,297 16 BLD 160 349 455 @3 719 18 wN 140 355 430 652 1.074 2.069 l8 so 229 33t 380 s73 797 t,694 18 BLD 196 440 572 762 1,030 20 wN 43r 535 8lt 1.344 2.614 20 so 181 378 468 733 972 2,114 20 BLD 298 545 7tt 976 r,287 24 WN 295 632 777 1,157 2,450 4,153 24 SO 245 577 676 1,056 1,823 3,378 24 BLD 446 Ur 1.355 2.442 Courte\) of Crane Co.
303
Weight and Dimensions of Pipe and Components
Steel Butt-Welding Fittings (in.)
,."n a/rf-/..'t( '(tiiJ t!ng t.dlu.
t ilt
9Oo
llbow
on
aA T/f 4 LJJRodlu.
9Oo Shorr
:tbov,
on. lnd
.N -A/ > lons Rodlut Elbow "1.-J
45o
1 | | tl F\ i /i -t-:-L
I
5l..l9hl Cror!
r-l-T Ill t*tl _n Ll
/--*\-T / ,--\ \J
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tg":J-t l*G--!
c"P
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/ \ /ini\l \#l l+, l.-H- +l
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3 4
3Ve
1r/z 2
6
x
33/t
4Y8
9 l0s/a
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47/E
6
3.4
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E
8
133/t
l0
15
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t7
6U
t2
1t
t2
20rh
t '/2
8r/2 10
9
2l 16
24
t8 20
30 36
18 20 24
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2Yz
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6
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8r/rs
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t?/s 1r/z
113/t
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4th
L'/16
5Vz 8 18
16 24
6r/t
\r/a
73/t
l0t/ta
95/te
12r/
9
40 4E
t
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93/s
80
40 40 40
80 80 80 80
40 40 40 40
80 80 80
40 40
80
4
80 80 80
80
i
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8
2
t43/a
6
zoYs
tx|/a
2rh
t77/s
7
18%
248h
l5 t6ta tath
10 10
23/t
201/.
8
3r/t
22YB
13
l0
3r/z
24r/6 26yE 30r/a 34r/E
L4
JO
40
20
20 20
t0
28
60
8
6/re
44 4t) 40 4n
153/e
48 s4
toth
81/z
1Yt
Stror
l2E/rs 165/re
28
6
e
63/rs I -/L6
4r/s 43/t 51
Extr
S 2
4
L-/r6
7r/z 9
lrr/re 2 2r/z
lVs
30
6 6r/z
15'
2r/z
rt
t
llr/t t3rh.
lr
3 33/t
10
ll.
12r/2
M
J
2Y1
r1h.
t'/2
t'/a
tL____J)
---r
H
I tta
6t/t
3r/z
s
lr6/ts
rYL
2Vz
[\
tl
F
D
s/t
lr/z
[_-\ l!--/-l k-
k
long Rodlur R.lurn B.nd
R.lnfor.lns
lYz
Shap!d Nlppl.!
20xlE'
w.ldlnr 5!ddl.
Yz
Dincnrion "T" it rhown in tobl. beloe; r.f.r lo lors. loblc for diln€nrion "E".
9oo Typ.
Stub End
R.turn a.nd
Size
R.ducinr Crott
ml url
t-M+l
Shorl Rodlur
M
R.du.lns T..
therein, to lhe American Standard, B r 6.q- r qi8; see page 2gr. Thickness: Stendard Fittings r z-inch and smaller ate made for use with Standard pipe (heaviest weight on 8, ro, and r zjinch sizes);sizes r4-inch and larger are made for use with O.D. pipe fu-inch thick, Exrra Strong Fittings rz-inch and smaller are made for use wilh Exlra Strong pipe; larger sizes are made for use with O.D. pipe \/2-inch Lhick. Schedule r60 Fittings are r''"'le for use with Schedule r6o pipe. Double Extra Strong Fittjngs are made for use with Double Extra Slrong pipe
Iong Tang.6t
Stroighl or
lll
l._E-*Ei
Arnerican Standard: These fittings conform, in sizes and types included
Lonr Rodl'rr
i
--r-'llf ill" T U- b .--ul
160,
ad Doubl. Exrro Strcns FitrinE. trov. tr|. ro,n. outdd. din.ttiott.
L__-r-'
1
T-/:
S.cndad, Exrrc st'ots. S.rrcduL
1
n
9oo
Courtesy of Crane Co.
F-c.---
F--A---l
30 36
40 48
x3 17r/t
20
304
Piping Stress Handbook
Forged Steel Flanges (in.) Courtesy of Crane Co.
150 ond 3oO-Pound
Slip-On W6lding Flqn!. 150 ond 30O-Pound
Class
Pipe Vz 3/t
3Vz
1/ts
31/8
I lr/t
4Y.
Yz e/rs
45/^
3A
2W
6 7
7r/t 3Y2 150
Pound E
8Vz 9
l3/s
2YE
r/-
lrr/ra
13/t
Y2
2 2y2
3Yg
I Vre
2TB
3A
35/e
%
rtl" I B/ts
l0
r,/rs
T1
I
l3Y2
lyE l3/rs
l6
150 ond 3O0-Pound
lyg
Tta
8
5/z
7Yz
E
5/e
t-/lB
8r/z
E
x/t
17/rs
9Vt
8
ll3/t
E
l3Aa 23/t
l6
27r/^
xqr/,
20 20
l3/e
Ls/e
11h
'rr
45/e
I
4YB
rr/ra
lr/z
6YA
t3/--
'/a
2
6th
2U
7V2
I
3
8Ut
lYs
%
l6
lrr/ra 3r/t 2 2,r/t
3W
27/8
4rh
37/e
4Y8
'/1
t3/t
f6 %
1rs/re 2r/r,
1
2Y2
4Y2
ru
lTAc 6.63 8.63
14.00 16.00
lr/t
3U,
6
24.O0
Y2
7/s
2r/ra
5/s
1
0.84 1.05
'/a
lr/rs
2r/e 27Aa
3/t
l3/ra 2rt/ta
4
rllc
3/t
6./e
8 8
ts/rel 3
,i\i,"l
3Ve 33/rs
1.90 2.38 2.88 3.50 4.00 4.50
5Y2
7V
E
"/a
7TE
8
lTg
33/s
l1
l3/s
75Ae 8r/z
9Y1
8
'/1 '/l
2
37/g
105/n
t2
3/"
2rAa
37/a
TE
27/te
43/s
I
x'/s
45/e
lr/s
27h
5Y8
3
55/e
6.63 8.63 10.75 12.75 14.00
l0
17Y2
t2
20Yz
2Vt
lo3/e
12t/t
1sY1
16
t7t/t
l5/rs
lY2
lrr/r, Lfa
77As
33/t
4
20
lVa
22W
20
lY.
3Y4
53/t
r6.00
4t/r
24t/e 27
x4
lr/e
3W
6r/t
1E.00
t'/a
24 24
lYa
33/t
6t/a 6./a
5V2
2
3Y2
20.00 24.00 4.50
l6
25W
xY1
l8
2E
23/e
21
20
30rh
2Yz
36
23/r,
27tA
l0
l3/e
6sAs t -/16
77/a
8
9ra
E
% %
to6/^
t2
7h
t2
I IYB lY4
ll
tr/z
12r/z
1s/*
8!z
17r/z
l1/B xYE
lo'/a l2t/e
loYz
2Yt
t73/a
l6 20 20 24 24
l5Y1
2s/p.
r6Yt 20r/t
16 18
25Yz 2a
2r/z
tgt/z
25/c
21
x0
3or/z
2r/t
36
3
77r/^
l3As
20r/a
16r/, lEYz
E
r3a
I
r.66 )
63/ts
l5/a l7/a 2
3Y" 37/re
lrAa
lr/t
t4c
l3/t
lYa 2rYre 5r/2 r E.00 lr3/rt lYe 27/8 5rr/te 20.00 4r/ra
l3/rs
t2r/,
te/,"
to-75 lr5/rt 2t/re
9
6 8
l0
xl/rs
I
s/e
s%
3 3Y2
3r/z
E
3./a
rY1 2r3/rs
0.84 '/e 1.05 "/a 1.32 rr/re txt 1.66 1.90 % 2.38 1 2.88 lY8 3.50 13/,, 4.00 4.50 t -/16
l0
l4
40O, 600, 9O0, 1500, ond 2soo-Pound
5/s
6 7
223/t
33/e
l,
W.ldins No
5lz
5 5r/z 6sAs / -/16 ar/z los/a
2T
u
5
Pound
4Yg
lrr/ra
t4
400
21/re 2Y2
27Yz
lrh
W!ldlng N.Gk Flans.
I
l8Y2
18 20 24
Pound
%
l7/re le/ra
l6
3Y2 4
^/2
x3r/z
lr/r
21
tL/-^ 23/re
-/a
18./t 2lY4
19
l4
2r/ra
4r/.
t6rL
17,
l7/e
'/a
37/8
13/,
150 ond 3oo-Pound
H
|3/.-
4
l4Yt t7
10
300
Yz
E
r/
3t/c
123/t
C.oh.l.p Flong.
Cron.lop Fl.nso 4OO, 600, 900, | 500, o.d 250o-Poqnd
Bolts
D
Siie
1r/z 2
Scr6v.d Flon9. 400, 600, 9O0, 1500, ond 2500-Pou.e
5lip-On !Y.ldi.s Fldns! 400. 600, 9O0, ond l5o0-Pound
21Yz 2434 27
lr/" z\g
6 2
zrh
2r/t 4t/," 2rrAe
6.63
2V,
E.63
rr/rs
27/B
47/B
r0.75
4
3YB
53/e
lr/t 3sle
12.75
4V.
57/a
l3/s 3rr/rs t./E 31h
6 6Y2
lr/z
6E/a
14.00 16.00 18.00 20.00 24.00
t3a
4r/,
67/*
53/s
5t/t
Weight and Dimensions of Pipe and
Forged Steel Flanges (in.) Continued. Courtesy of Crane Co. Class
Pipe Size
rY1
5r/t
r3/,"
2 2r/2
lYz
6Yg
7/e
x7/8
2
z\z
6Y2 7r/z
IYB
3
81/^
lYt
lo3/t
lr/z
63/ra
13
l3/e lr/p.
t -/16
I
Y2
'/e '/a
31h.
'/L
0.84
xr/t
1.05
1r/rs rYa
21/ra
l|/t
23/t 27h 3Y8 3r/^
L5/e
8
-/B
t/t
6s/e,
3A
lr3/rc
8r/z
8 8 8
11/ta l5/e
1/B
2r/B
loYz
I
gYz
rrv
8 11
I
1,5/^
45/e
lo5/s
t33A
t2
lYg
J
5Y1
33/s
6 6Yg 6Vz
Lr/^
l4
10
20
2r/,
123/a
t7
l6
lr/t
20
lY4
233/L
2r/e X3/t
19Y1
l4
16r/a
X03/a
z0
3rr/ts
l8Y2
233/e
20
l3/t lr/z
18
29Yt
2.53/t
20
l5/e
46/a
7 7\/a 7Yz
l7/a
$t/z
E
3Yz 9Yz 133/t 15
900
t
23/e
ll
lra
8rh
11,y,
t2
rVa
33/e
5r/z
12
l3/e l3/e l3/e
4Yz
4V
7Yt
6.63 8.63 10.75
4V8
77/a
12.7 5
5s/s
83/a
14.00
6Va
24
3YB
t6rh
22
l6
X73/t
33/t 3r/z
lSYz
2Ar/q
27Vt
l6 20 20
3Y6 63/e
11/z
r'/a
t'/a
81/z
r6.00
6Y2
l7/s 2
6
9
6V
93/t
35r/z
xo
ZYz
E
llr/z
18.00 20.00 24.00
/ '/2
29U
20 20 20
x7
l3/s
3Y4
lY1
23/e
9r/e
I
"/a
'/1
lrr/rs
3Y2
-/A
l3/e
23/a
I
57/g
lr/s
2
7/E
lt/e
27/B
lY1
6r/r,
rVR
2r/z
43/z
4
1/"
F/a
27/e
lYz
7 8r/z
lr/n lYz
x7/e
47/s
I
lr/a
3V
35/e
6r/,
E
%
2V
96/e
l5/s l7/e
4YB
7r/z
d
I
21/z
4Y8
t0rh
E
E
rYa
lxr/t
zYB
9Y2
8
143/t
27/B
63Aa TsAs
llYz
rv
27h.
E
lr/z
6
t5y,
3r/^
8r/,
12r/2
tz
8
19
35/a
t05/B 123/t
tx l4
4r/t 47h
3e/ts
47/e
4.50
3e/re
4Y8
6Ys
l3/a
4rr/ts
63/t
4rrA,
rsYz
l6/t
5'/a
83/s
6.63 8.63
l9
6V
16
l7/8 2
l6
'),r/^
22\/2
5Y4
lB/ra
l3/e
3Y2
ta
sw 6V
Ita
lrr/te
33/t
3/a
I
13/e
7r/
lV2
4r/a 5Va
%
lr,
2 2r/z
8
ls/t
27/s
534
4
2
33/e
63/t
E
I
23/e
zYl
4r/s
734 9
8
IYB
E
8
ev
2Y2
lor/z
3
tt
l5/a
4s/a
l6r/t
lYz
lx/s
2Yt
5r/t
2
0.84 1.05
8r/t
t0v lYl
1.66 1.90 2.38 2.88 3.50
26Yz 29r/2
Yz t/a
5r/z 6 6Yz 2Ys
25r/^
l0
4s/s
14.00 16.00 18.00 20.00 24.00 3.50
t4
3
3
4.50
l5t/2 l8Y2
2W
43/a
4Yz
lx"/o
2
6.63 8.63 10.75
2e/t 3Yg
1o7s
%
zY8 L"/e
lYa
73/t
4t/t
--)
8 8
2Y2
5r/z
lr3/r'
9r/t
23Ae
4l
rv
lTAa ls/e
2Y8
75/ra
4Ya
tv"
7/B
2
133/t
1.66 1.90 7.38 2.88 3.50 4.50
8
5 63/ra
t8t/z 2lYz
18 20 24 r/z
1
lr/ra
'/2
lY2 t3/t
l0
E
43Ae
L'/A
28r/z
27r/t
I/s
2Yra
l6t/z
3 3r/a
H
I
5 4YE
G 7h
E
llY2
Pound
rt/ts
lr
Dia.
6
3
2500
4Y2
47h
20 24
1500
3r/z
I
27
Pound
t./a 3r/t
41/s
t2
Pound
l3/e Yre
3x/e
-/1
600
Pound
D
lz
116 '/a
Bolts
c
B
t4 l6Yz
3
63/ra
lo3/t
35/e
123/t
t
l9
41A
l4r/,
E
r/t
t2
13/t
IYz
4YB
t0.75 lrYB t2.75 10
55/a
7
8%
tt3/a
14.00
9r/"
27/8
0.84 1.05
lsAe
r'/t6 lLYra
3Ys
I
1I/s 2rAa
3r/z 3t/^
lYs
23/s
1r%o
t.32
tlA 2rAa
43/e
1.66 1.90 2.3E
2./t
3Y8
5'/e
2.88
3Y8
lVt
35/e
6r/e
lVz
4V
7Yz
4.50
4Yl
5VE
9
6
tosa
5th
8
2lt/t
5
t -/t5 8Yz lo5/s
10
26y.
6rh
123/t
2trh
2r/z
9
l6Yz
1o.75
9
t2
30
7Yt
t5
243/e
2.4
t0
l8r/t
12.75
l0
5 6
17
2
l1Y2
2
6.63 8.63
Components
305
Piping Stress Handbook
Cast Steel Wedge Gate Valves 150- to 1500-Pound Dimensions Courtesy of Crane Co.
E-T FEh ltf JIK D
E-T l-E$r--l ,-t
|tI
I
I
JIL D fltt ory" ./-i\ |
I
Ylf i*
I
_5=a r- I
T-
/- i\
I I I
T--T--T -=] fi=-l='il1 r-i--l l-c----l
I
-1 I -t- -l-
f---r-l F-A----l
Bun-W.lding
Dimensions, in Incher Cless
Size of
B
Valve
6r/t
t'/2
zrh 3r/z 4 5 6
1S0-Pound
734
8
8
8Y2 9
c
D
E
Er/z
Lt'/l 16Yz
8 8
201/.
9
grh
llVt
25.4
l0
3r/z 4
B
c
D
E
\rYz
llYz
l3
l3
l8r/+ 22r/t
6 9
t4
l4
253/a
10
32
l5 t7
t7
20 22
20
6 8
26
3l
363/t
14 14 16
423/t
20
52Y1
24 27
3lr/z
10
l5
30%
157/e
JnYa
t4
8
tlr/z
t6r/z
4
l6
10
13 14
18 193/t
52Yz
IE
l0
ffir/z
l8
t2
70
7or/t
27
14
77r/t
30 30
l4 l6
79s/t
l8
97Y1
27 30
20
trh
z0
32
ll23/t
30
163/t
8
7
IE
8
2r/z
l9
3 5
7r/z 8Y2
E9
15
27r/t 3tr/2
4
18
t2
t2
28r/t
l0
15
15 t57/e
33r/z
t7
l0
38r/z
14
t2
3E
l6 16
4oY2 44r/z
30
30
7s%
l6 IE
33 36
9lr/z
30
20
39
993/t
45
36 39 45
t2oy2
36 36
l6
16
303/a
18 19r/z 23r/z
1E
26Y2 30 32Y2
1E
22
900-Pound
20
6
24
E
29
I lr/t
20
38 40Y2
44r/z
10
l0
ll
11
l6
423/t
20
52\h
24 27 30 30
62V1 73r/z
77r/t
a5t/t
l6t/z
t2
11
10
9
l4r/z
22YB
l0
263/E
12
16r/z
l6Y2
Itrh
l8Y2
11
4
2lY2
ttr/z
5
26Yz
3t3/t
6 8
273/a
26rh 27%
323/t
323/t
i'5
t9r/z
40r/t 5or/z
20
26r/z 30 32r/z J5'/2
593/t
67./t
74
74t/.
27
8 8
l4r/2
L'/2
73Yz
t4
363/t
3
1500-Pound
t2
2
1t./-
8l
14 16
36
126
11
t4
l4 l6
t04r/z
23r/t
l9t/t
10
47
llr/z
IE
t
20
llYE
t9./t
6
43
8 9
47 56Y2 64Y1
39
62V
l8
9th
l6Yz
31
833/t 933/t
8Yz 9Y2
r6Yz IE
l0
39
7 8 9
Ls% 8
600-Pound
l6
24 26 28
18
400-Pound
Valve 2rh
9
t2
Size of
l0Y2
t2
300-Pound
Class
'A
l4 16
20
Weight and Dimensions of Pipe and Components
Cast Steel Globe and Angle Valves Courtesy of Crane Co.
Claes
Butt-Welding
Flanged
2
z\z 150
Pou
r
t500
Pound
E
16r/2
11Y2
t93/a
rrlh
t9t/t
53/a
173/e
14
23
l6
2ot/e 7.134 X3r/z
E
8 9 9
lTYt
10 10
x4Y2 26
l9t/z
24r/z 26
7 8 93/t
loYz
173/t
Sr/a
173/e
t9
53/a
19
2oY2
6Y4
xo\2
9 10 10
65/s
22r/z
tx
7
24t/t
t4
7Ye
x6v
l6
293/e
36lz
IE x4
12Y2
xoYz 22r/z
121/2
14
l2Y2
l3x/t
91h
ttth
l3t/r.
HIK
4t/t 4t/t
t9
3r/z
Flaneed or
All alves
Butt-W€ldingt
t4t/2 t6r/z
173/t
243/t
14
243/.
11
16
5 6
t53/t t7r/2
26rh 293/.
t7r/z
293/t
E
22
36U
L2
36y2
834 l1
l6
25Y1
16
8
xSYa
l4
28Y2
It
x1t/r
18
28Y2 3lV1
9
28Y2
1E
93/a
31r/n
20
38r/a
ll3/a
38t/t
x7
23Yz
6Yz 7 7Y2
2tr/1 23rh
z7r/z
8Yz
27rh
r8
l0
303/a
x0
191/z
3lr/t
191/z
E
23r/z
3ara
23r/z
2 zYz
llY2 l3 l4
l9
1lY2
21r/e
t7
27r/2
20 22
303/t
x3Yz
t4
20
l5 18
29Y2
IE
37t/a
6
303/e
22
3
2
l4lrz
25V8
l4Y2
2r/2 3
r6yz
28r/s
18r/z
33Y2
t6t/z l8t/2
10
t9
2lr/t
3Y2
b
900
133/t
$Yz
rrrh
Pound
Pound
I
l4Y2
t0r/2
400
Pound
t33/t
8 8V2 9Yz 10r/z
2U Pound
600
JJ
2 +J
300
K
K
19rh
8
Screwed
HH
HH
l4 l6
5 6
Angle Valves
Globe Valves
Size
t2
l4
II
24
24 29r/2
7Y2
9
24 791/z
373/t
t2
37 3/a
20
l4 28r/a 331/2
IE
308
Piping Stress Handbook
Cast Steel Swing Check Valves Courtesy of Crane Co. Weighlr cnd Dimension:
Js I P F+ T'---'-'T t--N
Prea-
Size
Class
Pounds, Each Valves
,r.l
2V2
3rh r50
5
Pound
5
50
30
Flanged or Butt-Welding
P
E
l0
100
100
140 200
120
390 510
360
5
8
slz
!
$rh 9r/t roYz
1rh
5
rlYz
300
Pound
400
Pound
80
100
120
l2YE
27Yz
133/a
on 39 60 80
9rh lo3/t
63/t
torh
6t/t
E
ll3/t
llr/z
E
EYl
l2Yz
130
l4
g3/t
153/t
t03/t
6
260
lTVz
t\3/"
8
620
510
2l
t4
l0
920
760
12
1290
1015
24t/z 2a
200 270
190
16
l0
IE
t2
6
310
19r/z
8
6E0
l0
900
580 820
13Yz 26r/z
t2S0
I150
30
38
32 40 70
l3
100
14
4
260 400 530
17 20
6
170 300 420
E
900
l0
1440
740 880
t2
1970
1200
180
6
340 640
t
I lE0
l4Yz
t$r/t
63/t
llY2
70
J
l5 I
6V 9Yz
140
900
500
t0r/t
240
2r/z
t
lgYz 24th
180
2
Pound
8 9
250 330
lr/t
Pound
13
160
4
1Y2
600
6 6Yz
ltr/z
1200 1450
40 70
P
8
12
2 zYz
M
$rh 9rh
94 96
M
N
u 40 50
Screwed
Valves Weldinp Valves
FD&SF
Inches 2
Dimeneions, in Inches
Butt-
$r/t
I
tor/r 123/.
tir/t 31
t8t/t 2lr/z
15
Ith ll
240
l8
500 890
29
t6r/, EY1
t0r/z
t33/t
trh
ll0
EO
2 2r/z
160
130
t2 t4rh
245
t70
l6V2
2E0
210
l8Vz
ttut
630 950
Ltr/z
l3r/t
1360
390 480 780
26r/2 273/t
t51/t
2100
1320
3
Pound 6 8
93/t
rsv
Weight and Dimensions ot Pipe and Compononts
Miter Welding
30"
Siz.
6o'
45"
+v2
3/4 15/r 6
5ta
7la
6
I
c
R
r-3/8
r- r
5/16
3/4 15t16
6
1-5l16
I 1-0
t3/a 1-13/16
1-1/8
I,13/r 6
2-1t2
10
1.1t16
2.114
3rl8
12
r
2.5la
3-11/16
l-6
+1n6
1-9
2-1lA
+5la
2-O
35/16
11/16
11la
lA
2.7
2.11A
35/16
18
2.7 t16
r3l4
20
2.11t16
+1ta
t6
22 26
71116
i6
4 13^6
1-7 7-7
| 16
3a
t1l16
.t0
5.3/8
t2
5-An
8,11/16
6,7/16 1.1/4
9,15/
"q 1)
5/8
lA
1r
-3/16
'|
-
o-1/16
1
-
2.r5/16
7 15t16
t
911/16
8-1t/16 s 15/r6 11,Vt6
r-05/16 1
,2.1116
1-
3-r3/16 5'9/r 6 7 5/16
-
3-O
5
1
-
2-15/16
9-1t4 9- | 3/16
103/8 1l I t -9/',t6
l6
1,G7t16
8,3/16
63/8
&5/8
4-5116
4-t5l16
1-7t16
1r-91/16
8-1/16
+9/r6
r
r
tr3/r6
34
3/16 1G9/16
r-11/16
5,3/8
- 0-t/8 1- r7ta
1-
+1tA
'|
-
5-318
2
7.1ft 8 5/r6
1I2
7.7t4 9-1/a
8-lt/16
2,2.1t4
6-0 6-9 7-6
915/16 113/16
2
9-O
1
3-6 3-9 40 4-3 4-6 4-9 5-0
r
r ,3-9/16 r
-
8-13/16
Source: Tclas Pipe Bending Co., btc., Houston' Texas'
5,3/8 5-13/16
1
6-3/16
6-5/8
1
1-v16
1
1.7 | 16
1
-
0-7/16
2-15t16
10-3/8 11,5/8
GT/A
8-3/4
-
-
22-
to.tla o-S/A 2.31a 4-1/A
2-5714
2 7-5tA 2 - 9-3ft 2- 11-1tA 3-O.7lA
43
- 9-S/16 3- 1-1t4
3
6-5/t6
5
0-7116
!t/2
4.r
9-15/16
1-9/ 16
r
6-r5/16 1.1/2
1-7/16
1
I-
5
3 r/8
10-3/ 16
I
+1lA 4.5t16
6
2.114
5
5.1t4 8- r
2.5rc
3.3t4
3-314
2-9
+9/r
32
v2
3.
2-
3-3/16
4
2-5la
t8
5-3t4
2-15lr6
6
E
5-1t4 6-7 lA
2-1t2
2.t14
3-3t4
63/r6 6sta
30
't-7
3
6-3/16 11-7/A
4.314
5-3114
11-
2 2
11,1/8 2-1t2
5.7la
2-9-1/A
- 2-15lt6 r - 5-3/8 1-7 7/a I - 10.3/8
2
0.1t4
r/t6
11.5/8
1,
t-14
1-
21ta 45tA
1
- 0-7116 2 3-5t16 1 - 6,3/16 2 5-13t16 1-1.13116 3 - 3-13/16 1 - I,S/16 3-7.1 6 2 8-5/16 1- 11.3/t6 2 - 10-13/16 3 - 10-7lr6 2- O-1ta 3 - 1-114 4,1-5/8 4-5 2 - 4-1/a 3 6-114 4 - 8-3/8 2 - 5-1ta 3 a-3t4 4 - 11,5/8 2- 7-1t2 3 - 11.1/4 5-3 4- 1-11/16 2 - 9.r/16 5 - 6-5/16 2 - tor3/16 4 - 4.3116 5 - 9-9/16 3 - 3-314 4 - r I,5/8 3 - 8'3/4 5 -7.11A 7 - 5-1t2 a, 3.7t16 6 - 2,9/16 4- 1-11/16 4,11.94 I - 1t-3/8 3
309
310
Piping Stress Handbook
Miter Welding Dimensions
K
H
13/r6
3.5/16
3.1n6
2-1116
1-7 /16
1-5/8
+Aa
4.1116
3-3/16
1t8
2-1/16
6 9/16
69/ l6
4-13/16
r.l5/ r 6 3-rlr6
l/8
33/r
8,13/t 6
8.11/',r6
6-7lr6
ll
lG15/16
8-1/16
9.58
6 t/4
1t2
l-
6
1.7116
I
M
11/16 +13/ t6
t7 la 2-1/a 2.7
/16
5.5/8 6.7
/16
1.1/4
1-
1-3/16
1
1
3-3/8
r
5-9/16 7-314
211/t6 81/r6 2.15/16
8, t
3/16
3-3/16
$5/8 10.7
t16
3.3/4
11-114
4
1
+5/16
1-O.7la
+gfi6
1
-
1-
5.51A
- 4.7t4 - 7.5t16 1 - 9-1r/16 2 - O.1lA
6.7116
7.1t4
8-1/r6
1
'|
Source: Texas
G3/16 2.3t4
r
2
+9t16
2
2-
6.3t4
2 -
2
-
11.1|a
1.11/16
5 3/8
4-1116
-
2
0-1/16
413/16 1-2-7/16 5.r/16 1 - 3.114
l-3 t-51/8 1 - 7.5/16 - 9.1t16
3,9/t6
3 7.15/t 6 3 - 1(}t/8 4- +t1t16 4- t1-5/16 5-5-7tA
6-7
'|
3 7tA
t1-9/16
1
-
1C1t2
-
a.1la
2
-
O.1/8
2
-
rG5/r6
2
-
1,
3 3 -
3
0-7116
29/16 4- 1tlt 6 6-7tA
3-9 4- 3.1t16 4-9.7lA
5 4,3/8 6-51/4
PW Bending Co., Inc., Houston, Tlxas
22 2 22 3 3-
4
7la
23tA
l1l16
3
1-114
3 9/16
r0 1rlr6
-
Gr5/16 t-7 /8
-
+1/A
t1t16
3-5/16
+15t16 6.9/16 4.1/a S-3t4
2-9t16
73ta 0-1t4
4-10
- 8-7/16 - 9-3/8 1- 1O1/? 2- 1-111t6 2- 4-7 tA 2- 8-1/8 3 - 2.3t4 1
r
4.13/
5 3/16
11-13/16
1
t-3116
4 3/16
9-9/16
1
&5la
1- r
7-1/2
1
7ta
3/a
1ll16
8-5/8
2-1t16
- 4-ll16 r - 5lr/16 1 - 7.5t16 1 A-7 la
2 3
3
1t-114
1-O7lA
s
N
3/16
l6
7.3/16 9-5/A
I -O
T
29/16
t
3-114
4-15/16 6-1/2
8-1/16
3
-13/ 16
23t8 9/r6 43/4 515/16 7 3t16
11/16 1-.1/2
2.3/1C 3
3.13/16
q.iirrc 9.1rl16 - 2-1t16 t.3/8 4,3/16 1 - 4.13t16 11.1t8 8 3/8 s.slu '| 7-114 t.s/16 4-3t4 r - 0-r1/16 I9/',t6 6.7/ 16 l.r3lr6 5-3/8 1 I5/8 1 - 2 3t4 10-3/4 7,rta 2 515/16 2- 0-1/16 r 1-15/r6 t.'ts,1c 2-3t16 6-3/t6 2 - 2-7t16 1- 5.112 1,11t4 q 914 2.3/a 7-3/t6 2 - 4.13/16 1 ,7.1t16 \- 2:9t16 , e:9/16 2.9t16 7.3/4 2 - 7.1t4 | 8,5/8 1 - 3.112 lo 3,/8 2.13n6 8.3/8 2 S-a/a I 10,5/16 t 1:1/l6 3 8-15/16 3 - Or/16 1- 11-1t8 1 - 5.1t4 11.7tB 3,3/16 I9/16 3 - 2-1116 2 - 1-112 1 - 7.1/a 1 0.3/4 1G r/8 1- 1.9/1C 3-3/8 3 - 4-7/a 1 8,5/16 1G3/4 1 9- 12 3-9/16 3- 7 1t4 2 - 4-5/A 1-23!a I t-5116 3-3t4 I - 10.11/r6 1 - 3.3/1€ 11- 15/16 4, G1/16 2 7.71A 4 1- 11-l ta r - 3.7/6 4 3/16 1 -O.112 4 2.1/2 2 - g-7 t16 2- 1-11t6 1 1111. 4.3/4 4- 9,11/16 2 - 4-5ta l-71l',8 1 - 4-1/8 5 - 4-7la 5-3/8 3-7 2 A 1t4 1-9.1/2 6.15/16 1 - 5-718 6 - 0-1/8 3 - 11-5/8 2 - 11.3t4 I - I1.7,t 7.3/16 1 -9.1/2 7 -2-1/2 4 - 9-3/8 2, 45ie 3-1 1
a_
Weight and Dimensions of Pipe and Components
L€ngth of Pipe in Bends Courtesy of Crane Co.
Radius of Pip€ Bends
-'l
f*.9\ |
90" Bends
|
180' Bends
the length of prpe in d bend having a radius not qiven above. add together the Iength of pipe in bends whose combined radii equal the required radius.
ro nna
270' B€nds
540' Bends
length of pipe in 90'bend of 5'9'radius. Ersmolcr ' Find Lenetli of prpA r; o0" bend of 5 radius = o+ra' Lengrh of prpc rn 90'beno of a' ,adius = W Then, l€ngth of pipe in 90" bend of 5' 9' radius
=
109rl'
311
312
Piping Stress Handbook
Calculation ot Pipe Bends Courtesy of Crane Co.
4i'
Eromple No.
8-Given A,
9o
:
sin
B, C, D,
R
tH : lllc K:tanlH L:A-K P: B _K N:F*2K
E : D -A _B F :YE'+ E
zc
x
R
Exornple No. I
B:
3.414
2.828 0.828
t+A--E
,
l.-s1
Eromple No.
E:D_A-B F:2N_C e :11o"+
$:
tan
r'
zH
K:14c
Exomple No.
E=D-A-B e -tVl-lT" " =
=
stn
ltJ
z,
tso
x x
x
^R
R
l--€ivcn R ond 45o Angler T = T ans.ent
Length oipipe in bend
R
9.425
x R +27
:
-
9-Given A,
M
B, C' D,
R
:llK'-n,
{:sinzN lP :90" *
to:r4tP
ZH
- tN
S:tanlOxR
lO-Givan A, B, C, D,
otf
l2-Given A,
P:2D C:A-2R n _tl,op,, r--, E:D-n F :2E
R
tH:tltc K=rantHxR v =A-K \. _ R .K ':-"-
Erornple No.
Exomple No.
C:%B
D=R+C
E = A -2R F =l/D'+E'
R
C/2R:
sin
tG
lH:90'+ lG lK = 180'-2 tG
l3-Given A,
EiF = sin lG H =%F x = 1ln-' K/H : sin lL
n'
B,
R
tJ[:tG-tL
lN = r80'+2lM t?==s2o; +
trI
Weight and Dimensions of Pipe and Components
313
Galculation of PiPe Bends Courtesy of Crane Co.
Exomple No.
D:B-C F =ll I
Ii = H: --l
aA
Sln
Exomole No.
l--Given A, B, C, R
zr F lS: tP * tG tK : 9O" - tS tL : t4 tS_ M = rar] lL xt( N:H+M O:B_C-M = stn
E,
Zu
llr;-
n'
4-Givsn A,
E:V a'+ D'
€xonple No.
2--Given A, B, C, N fxomple No.
D: B -C E:A -R F
:lo,
+ o'
E
F=s:nz\l H
:
lr'- n'
D:B -C
E:la'+a A
E --'-'
-A
c
:y
S-Given A,
(2R)"
R (1
- B'
lp:
sin
tD
R
7:sinlP t8:zP+tG lS lK:9O' lL : 1/2 lSM=tanlLY,R N:H+M _M O :B -C
Exomole No. 3---Given
R
LU:sinzF H:tanlG Xft tG:y2tF P:C -H
D:B-C
B =2R
B, C'
A, B, C,
fxomole No.
C:thB D: t4A
tG:%tF H:tanlGxR P :C -H
D
E --'--
E:IC'+ U
G
Exomple No.
R
E
=D
6-Given A,
=%E
B
lH:90" - tF A, + R1 -' 4A | _ rtl
Z-Given A, B, C, D,
G/H:sinlK
-A-B F:R-C t':lzH G:n+F H=lE+ G" rI:V L'-R'
R
IIlL=sintN to :90' - tK , t\ 7p =/2 tO S:tan IPXR
12 Allowable Pipe Span trlormulas and Tables
Pipe-Span Stress Limits
^M -Z
5
WL' 42
In order to have a workable set ofpipe-span tables or to
find an allowable span that will require a minimum of manual calculations, the limit for dead load stresses is set at S1/2. This eliminates the need for checkins the sum of
'=!@
the longitudinal pressure stresses plus dead load stress. (Sr, allowable stress at maximum temperature. ASA
:
Code 831.1 and 831.3.) The formula used to determine the maximum soans in the tables (Thbles 12-l through l2-9) is a mean berween a uniformly loaded beam simply supported at both ends and a uniformly loaded beam with both ends fixed. This mean formula most nearly depicts the conditions actually existing in a refinery. (See Figure 12-1.) By inspection, if the two moment diagrams in Figure 12-1 are superimposed, the point of the maximum bending moment will still be at mid-span.
Mean=
M:vz(Y.y-)
A safety factor of 1.25 is required because of the discrepancy between theoretical assumption ald the actual field situation.
M:wL'xl 124
Pipe-Span Deflection Limits Maximum allowable pipe deflection between supports must not exceed 1 in. or ll2 the nominal pipe diameter. whichever is the smaller. This is the basic piping practice: however,.it is subject to compliance with the customer,s specfrcanon. The formula used to determine the deflections in Thbles 12-1 through 12-9 is a mean between a uniformly loaded beam simply supported at both ends and a uniforn r loaded beam with both ends fixed. (See Figure l2-2.) In order to maintain homogeneous units, "Lt' must be in in. and "W" must be in lbs/in. , however, for ease of handling we wish to have "L" in ft and "W" in lb/ft, whicL we must now convert to inch units. The preceding equation becomes:
5 WL2 48
In order to maintain homogeneous units, "L" must be in lb/in.; however, for ease of handling we wish to have "L" in feet and 'W" in lb/ft, which we musr now converr to
.
wL4 I28EI
^
13.5WL4
inch units. Thus the preceding equation becomes:
M =-
5WI
-
48
2
60
wL,
5 WL2
48
l3.5WL4 EI
EI (Text continued on Dase 3:0
314
a Allowable Pipe Span Formulas and
Tables
Fixed Ends
simply Supported
frrnT 1_,-N
Load
I Shear
t uoment
2-l
z-l--
uJf Fixed Ends
Simply Supporled WL ., V =-
., "-
"'-=Y
rvrl -
2
,., -
WL 2
WL, ;;
by figuring the and a uniformly both ends at supported mean between a uniformly loaded beam loaded beam with both ends {ixed.
Figure 12-1. Diagram showing how stress limits are determined
!
r,
Fixed Ends
Simply Supported 5WL4
WL4
384E1
384E1
Mean: =
A1 +A2
3WL4 384E1
WL4 128E1
by figuring and a uniboth ends al supported the mean between a unitormly loaded beam fixed. formlv loaded beam with both ends
Figure 12-2, Diagram showing how deflection limits are determined
t
315
316
Piping Stress Handbook Table 12-1 Piping Spans Based on the Following carbon steel Materials: seamless A53 Gr. A, A106 Gr. A, Apt 5L Gr. A; Wetded A53 cr. B, Apt 5L Gr. B, A155 C55 Ctass 2 >200.F wilh Water,
(L =
No Insulation
7,650 psi)
201'F-600.F wilh Commodity
(f. =
6,175 psi)
=
Wetghi ot Waler, Minimum Insutation
Maximum
'
Exceeds maximum dettecrion. Courtesy of Po$,er Piping Company.
Tabte 12-2 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A312 Tp316, Ag12 TP317, 4430 FP316H, A376 TP317 >200"F with Warer, No Insutarion
(L =
Pipe
Size
'
SCH.
9,375 psi)
Maximum Span
Exce€ds maxiftum deflection,
Co nesy of Power Piping Conpany.
201'F-600oF with Commodity
(L =
8,550 psi)
Maximum Span
=
Weight ot Water, Minimum tnsularion
Recommended
Allowable Pipe Span Formulas and
Tables
Table 12-3
TP304L' A312 Piping spans Based on the Following stainless steel Pipe Materials: seamless A213 FP304H A430 TP304, A376 TP3o4L, 201.F-600.F with commodity
>2OO'F with Waler, No Insulation (1, = 7,550 psi)
(r3
=
5'800 ps4
weight ol water, Minihum Insulation
Becommended
Maximum
'
=
Exceeds ma)(imum dellection. Courtesy of Power Piping ConPanY.
Table 12-4
piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A213 TP304L' A312 TP3O4L >2Oo"F with W.ler, No Insulaiion (1, = 7,650 Psi)
Maximum Span
'
Exceeds maximum delleclion. Courtesy of Power PiPing Compan
Becommended
201.F-600.F wirh commodity
{L =
a,500 Psi)
Maximum Span
=
weigh! ol water, Minimum Insulallon
Recommended
317
318
Piping Stress Handbook Table 12-5 Piping Spans Based on the Following Nickel pipe Material: Seamless 8161 Annealed >200'F with Water,
(L =
No Insulation
4,ooo psi)
Maximum
201dF-450cF wlth Codmodity 1,000 psl)
[. =
Recommended
=
Weight of Waier, Mtnlmum Insutation
Maximum
Courtesy of Po,,er Piping Company.
Table 12-6 Piping spans Based on the Following Aluminum pipe Material: seamless B24l Gr.3oo3 H112 >200'F wlth Wbter, No Insutation (1. = 4,000 psi) Maximum
Cowteq of Power Piping Compaat
Recommended
201'F-400.F wilh Commodity
(r. =
1,7s0 psl)
Maximum
=
Wetght ot Warer, Mtnimuh tnsstation
Recommended
Allowable Pipe Span Formulas and
Tables
319
Table 12-7
PipingspansBasedontheFo||owingA|uminumPip"M"tg'iM >2oooF with water, No Insulation (1. = 3,000 Psi)
Pipe Size
'
scH,
201.F-4O0dF with Commoclily d- 2.ooo Dsi)
=
=
Weight ol Waier, Minimum lnsutalion
Recommended SPan
Maximum Span
Maximum Span
Exc€eds maximum dell€ction. CourresJ of Power PiPing Comqany
Table 12-8 8235 Piping spans Based on the Following Aluminum Pipe Materials: seamless B21O' 9'234' and H18 Gr. 3003 Gr. 6061 T4, 8241 >200'F with Waler, No Insulatlon (1. = 4,500 psi) Maximum
'
Exceeds maxlmum dellectlon.
CouneE of Power Piping ComPant
Recommenaled
201.F-6OO.F with Commodity (t! 9s0 psi)
=
Maximum
=
welght o, water, Minimum Insulation
Becommended
320
Piping Stress Handbook Table 12-9 Piping spans Based on the Following Red Brass pipe Materiar: seamress B43 >200"F wilh Waler, No Insulatton
(l =
tot
1,500 psi)
Maximum
u:o'o:offn
il.
=
weisht ot warer' Minimum Insuration
""""oditv
Fecommended
Courkq of Power Piping Conpany.
: : W:
where SB
L E I Z f
=
: : : :
Longitudinal bending stress, psi Maximum deflection, in. Weight of pipe, including commodity and insulation if any, lb/ft Length of span, ft Hot modulus of elasticity of pipe, psi Moment of inertia of pipe, in.t Section modulus of pipe, in.3 Unit stress = Sr/2, psi. 56 per ASA Code 831.3
To solve for an allowable pipe span with a known __ llectlon, use the foliowing lormula:
.
4i EIA Y 13.5W
de_
Piping Wind Loads Wind Loads Tables 12-10 through 12-12 can be used to calculate wind loads. The wind pressure (P) in lb/ff on a flat surface normal to the direction the wind for any given velocity (V) in miles/hr is given quite accurately by the formuli
P
:
0.004v,
Table 12-11 gives the pressure per square foot on a flat surface normal to the direction of the wind for different velocities as calculated by the preceding formula. The design wind pressure at the location of a given pipeline should be applied ro the projected area ofthiout-
I
l
Allowable Pipe Span Formulas and Tables side of the pipe (or insulation) to determine a uniformly distributed load as follows:
w_ where
(P) (c") (D)
The design wind pressure depends on the location of the vessel or stack. The U.S.A. Standard Building Code Requirements for Minimum Design Loads, in Buildings and Other Structures, A58.1-1972, and the Uniform Building
Code include a table showirg wind pressure at various
t44
P: C": D: W:
I
heights, and a map where these values apply.
Design wind pressure, 1b/ft2 Shape factor (See T};ble 12-12)
Outside diameter of pipe (or insulation)' in. Wind load 0b/in) pounds per linear foot of plpe
More tables have been developed according to wind velocity in miles/hr, wind pressure lb/ft2, wilh reference to a pipe outside diameter. These tables are very usefirl for computer data input to model uniform wind load on pip-
ins.
Table 12-12 Shape Factors
Table 12-10
Ofticial Designations of Winds
Shape Less than
Calm
Ito
Light wind
1
Cylinder
/
8to12
Gentle wind Moderate wind Fresh wind Strong wind Gale Whole gale Hurricane
Factor
General Use
13 to 18 19 to 24 zf, to J6
Octagon Sphere
Flat
39 ts 54 55 to 75 Above 75
* Beoufon Wind kole, U.S. Weather Burca-.
Towers, stacks, drums, tanks, exchangers, prping, etc. Piers for towers and drums
0.6
Tbnks
0.60
Open signs Solid signs Closed buildings, framing, and com. parts Frames, open-type structure
1.60
0.80
1.40 1.30
1.60 Open plan
0.80 Sec. plan 0.00 other Plan
Table 12-11 Pressure per Sq Ft on a Flat Surface Normal to the Direction of the Wlnd Corespondlng Pressule Velocity
(miles/hr)
(lbflrl
To
10
0.4
Gende wind
20
1.6
30
3.6
Fresh wind Strong wind
40
6.4
)U
10.0
60
t4.4
80 100
25.6 40.0
Gale Gale
Whole gale Hurricane Violent hurricanes
322
Piping Stress Handbook Table 12- l3 Wind Load (lb/in.)
t5
rb/tt2 lil
il
0
40
45
50
55
9l
to0
105
lt2
117
85
.r4 .2t
.19
.24
.29
,29
.35
.43
.51
.25
.31
.41
.50
.58
.37
.,t5
.56
.65
.75
.69
.81
.68
.42
.89
.
.4r
rl5
.55
8.625
r0.750
.67
.89
12.7 50
,79
t.06
I4
35
80
4.500
5.525
30
7! es,/ti R
2.375
4.0
20
l.tl
.39
.49
.58
.55 .83
.84
.93
.92
1.04
1 t5
L.27
.96
1.10
1.23
1,38
1.51
r.0?
1.25
I.44
I.61
1.34
1.56
2,r2
t.38
1.32
2.01
.47 r -15
1.45
1.75
2.04
2.3
3
2.61
1.00 r.33
1.66
2.00
2.3
3
2.67
2,99
l8
t.r2
1.87
3.35
20
t.25
22
r,37 1.83
24
1.50 1.99
t,62
1.4
9
2a
r.7
30
r.87 2.49
5
2.62
3.00
2,50
2,9I
3.34
2.75
3.20
2.49
3.00
3.45
4.00
2.70
3.25
1.79
4,34
4.85
2.9t
3.50
4.0
8
4.61
.12
4.75
4.31
s.01 5.3
2.08
2.13
3
2.00 2.56
3.32
4.00
4.66
34
2.t2 2,83
3.53
4.25
4.95
35
2.25
2,99
3.7
4
'1.50
5.21
38
2.17
3.r6
3.95
4.75
40
2.50
3.33
4.16
5.00
12
2.62
3.49
{.35
5.25
44
2,75
3.56
4
46
2.al 3.83
t ,74
48
3.0 0
3.99
4.99
50
3.r2
4
.16
5.20 5.40
I.9l 2.39
1.46 2,92
2.9r 4 -1,2
a,16
4.58
rt
4.58
5.0r1
4.48
4.99
5.45
5.45
5.9S
4.
6.41 5.51
5.8?
5.9 8
6.65
7.33
6.35
7 -08
7 .7A
5.0I
6.?3
7,49
8,24
-34
7.10
7.91
8.?0
6.68
7,48
8.3 3
9.15
8.?4
9.62
6
5.83
.9t
4
.01
7.85
6.4I
7.34
8.22
9.r5 10.0I
5,75
6.70
7.68
8.60
9.58 10.s3
6.0
0
6.99
8.01
s.97
9.99 l0 .99
6.25
7 .29
8,35
9.35
10.41 I1.45
8.68
9.t2
10.83
,57
4.33
.80
.71
7
rl.9I
5{
3.37
4.49
s.6t
6.75
55
3,50
4.66
5.82
?.00
8.
58
3,52
4.83
1.25
60
3,75
4
6.24
7.50
4.14
10.02 Ll.22
t2.49
1.3
3.87
5.16
6
.44
7.75
9.03
10.35
tr.59
12.9t
14.20
.99
54
4.00
5.33
6.5
56
4.12
5.49
5.
9.01 10.09
1t.24 \2.X7
r5
9.3 5 10.47
1r.66 !2.42
4.45
9.58 10.84
12.08 13.28
7
.87
5
.008
10.68 1r.95
g5
8.25
1I.02 12,34
.7 4
14.66 13.74
15.12
Table 12'13 Uniform Wind Loads (lb/ln.)
.59
1.02
.9{ 4.00 /t.500 5
1.00
l.l2
8.625
r0.750
I4 18 20
1.08
2.15 2.58
1.3r
1.2r t,?
"525
.79
.84
1.09
l.16
r.23
r..25
1.33
r.
.54
1.40
9
2.69
2.33
2.34
2,47
3.05
2.91 3.45
1.33
/t.50
4.8?
5.00
5.41
1.3I
r./15
2.14
1.78
r.87
2.62
2.76
3.41
3,59
4.03
t.25
t.17
4.78
5.02
3.99
1.21
l.5r
1.37
.4.56
{.95
1.65
5.00
5.33
5.83
6.25
?.08 8,25
8.?0
9.00
9.49
9.20
9.7 5
10.29
9.91
10.50
r1.08
t.08
4.00
.98
1.66
1.49 2.20
.94
r.50
!11
3.80
3.50
.89
5.54 5.00
5.99
22
5.50
5.95
6.41
6
.87
7.79
21
6.00
5.49
7 .OO
?.50
8.49
25
6.50
8.56
?.54 7.58
8.15
?.91
10.83
2S
7.00
30
?.50
32
8.00
r0.00
r0.56
11.33
8,50
r0.62
11.33
12.03
13.45
r4.16
L2.7 4
L1.24
15.0
15.04
15.83
34 36
40
9.00
10.0
9.99
9.20 4
10.50
r0.29
II.OE
9.7
10.83 L2.23
a2
ta
II.O 12.45
45 !t5
14.00
r2.0 12.5
13.54
13,0
t{.08
5a
r3.tl
L4.62
15.75
15.70
16.9t
54
t5,0
12.00
13.45
14.25
13.3
1{.1
rt.00
13.12
13.99
14.87
13.75
t{.66
15.00
16.5
17.4I r8.20
19.16
16,99
r 8.00
18.99
20,00
17.?0
18.?
5
19.79
20.83
16.25
17.33
t8.al r9.50
20.58
16.87
17.99
19.12
20.25
2!.37
17.50
18.56
r9.82
21.00
r 8,75
15.78
19.37
20.55
17.33
20.00 20.52
2L.21
2a.!.6
22,50
23 .7 4
25.00
23.25
24.53
25.83 25.66
24.00 23.27
22.50 23.22
2L.75
18.12
\5.24
0
17.50
15.28
14.37
19.99
!7 .A7
rt .8?
2
12,50
r1.87
14.58
14.0
50
11.99
10.5
24.75
25.L2
27.50
13 Pipe Support Selection and Design
Pipe Supports
t Because piping is aflected by thermal expansion. supports in a piping system move thermally in different directions. Weight is supported by two kinds of supports-rigid
tions are critical (very expensive). They have been use
and flexible.
c Rigid supports are supports in a piping system which stay fixed. They generally move thermally in two directions-horizontally and laterally, but not vertically. The weight at this point is usually supported by shoe supports, bracket supports, dummy legs, or a rigid hanger. There are hundreds of ways these supports can be designed and every company seems to have its own way. (See Figure 13- 1.)
c Flexible supports move in all three directions. Weight is supported in this application by use of spring supports.
Spring Supports The types of springs offered for industrial support applications can be segregated into three classifications: are the springs most commonly used in the petrochemical industry for supporting loads. They are used almost exclusively in the construction of pre-engineered and calibrated variable- and constant-support spring hangers. They are also used in less expensrve forms in the construction of hold downs, field supports, and vibration dampeners. c Disc spings (BeIlviIIe springs) are seldom used in the construction of variable- or constant-support spring hansers, but are available if desired when space limita-
o CoiI spings
Variable Spring SuPPorts The word "variable" in this description refers to the fact that the load-carrying capacity of the spring varies considerably as the spring is compressed or extended from a fixed reference point. In other words, as the pipe moves up, the spring is extended and the load that it exerts is decreased. The opposite effect is experienced when the pipe moves down. In either case, the force exerted must not vary when extended or compressed by more than 25 % (maximum) from the calculated load. Manufacturers offer a large variety of variable-load spring hangers with standard and nonstandard scales. (See Figure 13-2.) The scale is attached to the spring support
frame and indicates the vendor's recommendation for range of load. Normally, a safety scale is provided above and below the scale. Beyond these points the unit either loses all load carrying capacity or it reaches its fully compressed position, therefore prohibiting frrther displacement. In every case, an attempt should be made to select a spring so that the calculated load falls in the center of the spring-scale range. The maximum deflection, which will compute to be not more than a 25% variability, can be found by dividing the full range of the spring scale, in inches, by a factor of 2.5. Where the equipment loading is sensitive or critical, larger-range scales may be beneficial in reducing the variability percentage. Typical applications are shown in the next pages along with an explanation on how to size and how to determine the type of spring to be used. Dimensions for variable {Texl conlinued on Page 327
324
E
\
"'l
J
.,|
",1
\tf\ET
" , 'S+
I
x
;
e
!4
t
E
F.l
t6 t
HI
I
1
g
o.l
FI
|
-.ll
tlsstA
trTli |t /
ill $
tl
E
Ie
ol
;l
ll.l tl
u_!J
lP
l+
Pipe Support Selection and
I _l
r.
fl
J
o RI
c)l
.{l
.i
a
Design
o
f
oo-
6 o l
o (9
o
.9 lt
325
326
Piping Stress Handbook
Type A
Typr A
Typo B
!t
T=
I
m
T
,t
Special variable spring hangers can be fabricated for
.d\ V
i|fr
l|\ Typc C
fi
lo D.Lrnio. Type: The type of variable sorine hanger to be used depends upon the physical ihari acteristic-s_ reqlired by the suspension problem; i,e., amount,9f head room, whether pipe is to be supported above the spring or below the spring, etc. Conslderation _should be given to the seven standard types of-
Typr
How
fered (see line cuts of types ,,A', througlr',,6"r, unusual conditions.
How io Dctcrminc Sire: Conplete sizing infornation is given above the hanger selection chart This information is applicable to sizing hangers of all series.
It will be noted
on the hanger selection charts that
the total spring deflection in the casing leaves a leserve above and below the recommended working
D
load mnge.
Trovol Stop: lrrtr-l PICCEI
lrnev:L
f
i LrIrTl
sroP
PtEqg
Typr F
Typc
F
Wirh Roller
L--,1 rH
The functional design of the pre-compressed variable spring hanger pereits the incorpo.ation of a two-piece travel stop that locks the hanger spring against up-
Type E
Typr
G
ward or downward movement for temporary conditions of underload or overload, The complete travel stop, the up litnit stop only for cold set purposes or the down limit stop only which rnay be ernployed during erection, hydrostatic test or chenical cleanout will be fumished only when specified. The travel stop is painted red and is installed at the fsctory with a red ..cautio!,' tag attached calling attention that the device rnust be removed before the pipe line is put in service.
Figu.e 13-2. variable supports. (courtesy support rechnology and piping Technology products,
Inc_)
Pipe Support Selection and springs are generally the same for all the malufacturers. That is why loading tables and dimensions that can be used for application in supporting piping have been included.
Constant Spring SuPPorts The word "constant" in this description implies that the spring will exert the same lifting effort as the pipe moves up and down. Actually, the spring rate in most cases rs minimized by transferring the load through a series of levers so that the elongation or compression of the spring is
negligible. Constant-support spring hangers are considerably more expensive than variables and are therefore used sparingly. They are used in conjunction with large deflections where variability becomes a problem, large loads where erren small variabilities are a problem, and at strain-sensitive equipment. (See Figure 13-3.) Manufacturers offer a wide variety of load ranges, deflection ranges, and frames for their constant-support springs. Loading tables given in Thbles 13-1 through 13-5 and in Figures 13-3 through 13-6, generally are the same for all the manufacturers, but dimensions are different and should be obtained from each manufacturer. (See Figure 13-7 for typical arangements of constant supports.)'
Travel Stops
All hangers have built-in stops to limit the travel at the top and bottom to a small percentage beyond the specified range. In addition, temporary stop pins are provided at the initial travel position for the purpose of hydrostatic testing and to facilitate erection. All stops are of rugged construction to withstand appreciable overloads. It should be remembered, however, that hangers will function only when temporary stops are removed and the hangers load-rods are adjusted properly to enable the hanger to operate within the specified range oftravel. An arrow traveling on a scale readily indicates the travel posi-
tion at all times. Load Ad justment
All
hangers are equipped with a load-adjusting nut that permits up to a 10Vo increase or a 10% decrease in loadcarrying capacity. However, since all hangers are carefully tested ald preset in the factory to specified loads, it is recommended that no field load adjusfinent be made until it is accurately determined that a change is necessary.
Otherwise, the proper distribution of pipe stresses in the system may be disturbed.
Design
327
Standard Hangets Load-travel data, physical design features, and dimensions are shown on the following pages, for convenience in selecting the proper type and size hangers for any specific requirement. Since the load-supporting capacity of a given size is inversely proportional to the travel function, excessive overfavel when specified may require a larger and more costly hanger size than actually needed.
Sway Brace Support This type of support is also a spring, but is not used to take care of the weight effect. It is recommended for controlling vibration, absorbing shock loading, guiding or re-
straining thermal expansion, and bracing a pipe line against sway. Figure 13-8 shows different sway braces and tables for loading and sizes.
Insulated Pipe Supports and Anchors for Cryogenic Service Gryogenic Pipe Supports and Hangers The design of supports for piping used in cryogenic service diffbrs from those designs used for standard piping. In this application the support is designed to avoid metal-to-metal contact of the support with the pipe. Such contact would create a heat sink whereby heat would be transferred from the ambient environmental conditions to the cold pipe through the metai support. To avoid this metal-to-metal contact, a support is manufactured from rigid polyurethane foam. Polyurethane offers both the insulating properties necessary to maintain the cryogenic temperature, and also the high strength necessary to support the pipe. Figure 13-9 illustrates a typical cryogenic support. The insulated support is normally furnished with the foam, vapor barrier, protection shield, and a galvanized cradle. These components are all adhered together into a unit that is easily installed. The saddle as ihown in this figure may be removed and replaced with other types of supports such as a pipe clamp for use with rigid and spring hangers, or with graphite teflon slide Dlates.
The design of the polyurethane support includes the following considerations: . Required insulation property (K-factor). o Thickness ofthe insulation on the remainder ofthe pip(Text conlinued ofl page 3,15.)
324
Piping Stress Handbook Table 13-1 Load Table for Variable Spring Supports for Selection ot Hanger Size
Lood Toblc in Poundrr lor Sclection of llonger
site
0
3
3
1
6
I 6
2
hir
I
21/.
sp.in, S.dl.
- lb, p.r i.,
Courtes! of Support Technolog, Products, Inc., and Piping Technolog)t Products, Inc.
il'
Pipe Support Selection and Design
Figure 2680
TY PE -8.
TYPE-A
329
TYPE-C
-
Type B and C opringe are furnished with one ot two luge ae ehown, welded to tlre toP cap of epring'
Typc A rpringc are furnirhed with r threedcrl buchirg in the toP Platc, providing for a rimplc rod attachment for the upper connection. ugt naiad
ha|t9al !12a
load
tb
20 3'o
00 124
v, c
713
tu9
cadn0
crdng
thd lgth
holc
lengtn
dlan
c
3l2a
v2
th
813/rs gqa
5 27 29
Vr
950
6
1Ol/s
1235
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6
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t/.
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1
79
1Vs
7
th
a4 100 124
11h
7
1
lU!
7
1V2
154
14t
5130
16o 7125 170 q5fl0 18o 12645 19o 1680s 200 22325
21o 29688 19591
l.ngth
6
lt
x
R
s
T
tht
1Y2
101/rs 1013/re
1Ua
7h
1V2
301
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3,18
2U1
456 528 684
21/,
2!e
I
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a
I I
t0 10 11
2% 27/a
3Ys
9154e 1oe/r o
85/6
8% 8%
131/ro 131316
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1U4
t/s
V4
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121/^
11/a
7/e
V4
125h
1313/,e 14s/ro 1sYa
11/2
1Ua
121/B
15
11/2
12 13%
1Ua
1st/g
16%
11/2
137/s
14rh
167/a
'|
11/2
14V2
11/4
1U4
1
1V2
1Sla
1U4
11/^
16la
17Y2 18Ya
''|
2
147/a
1Ya
15%
177e
15%s
11/2
187/rs
1V2
2171rc
187ls
11/2
1515he 1815/rs 181s/rs
qa
2131le 2471rc
23111le 261s/ro
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2811rc
3 3 4
41/2
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nelS
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4
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Ya
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tb
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le
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3811/,4
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395/15
4113/r o
37/a
1
463/rs
48rr/16
Figure 13€, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products, Inc')
330
Piping Stress Handbook
TYPE-D
Figure 2680
TYPT-T
EJ
TY PE-F
--,
c=_: .-- rl
Type D spring permits adjustment from the top, by lurning lhe nuls on the hanger rod against a piece ot tubing. The tubing is securely welded to the spring cap. Type D spring is set above the supporting steet_ Type E permits rod adjustment from either above or below the spring. Type F spring assembly is designed to suppofi piping lrom below, direclly lrom the tloor Adjustment is made by inserting a bar into holes in the load column. and turning the load column as a jack screw The base plate is welded to the case and has lour holes for fastening.
type F csBlng
Lnglh a
0o
6r1/,0
cr3lng
!hipplng l.ngth K
4
10
M
9'3/,6
3Vs
8s/,a
50
8%
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3Ys
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5s/,6
60
%
80
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tto
7h
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11/2
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1O1/a
67a
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101h
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9'si,^
150 160
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181/6
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201h 235h
124b
5
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123/4
61/t
295/,6
32
1211$ 137/,0
16th
2
3
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21Vs
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3 3
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a%
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1orh
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+t
107 101
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13//s
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I 1(F/16
16}t
3
161{
10'
13Y2
131/.
121/B
14Ya
1@/16
18%
14rr/16
16!r^
13U. 13U. 13U.
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16V2
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19%
13Y. 13Y.
25%
197/,n
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25r1/,5
191^6 2151'6
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2gqe 3231,a 35e/i
6
295116
127e
lG6
17U.
15,1/.
17U.
159t 15Y.
l7U. 17U.
Figure 13-3. Continued.
10'/!6
1g/.
6,a 161, r
6V16
Y. U2
8U.
a%
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aU. Y.
Y2
AY.
%
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%
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td
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15r3/,6 183/a
tt
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71h
3
21h
21/a
121/a
111/e
18o 190
21/2
101/a
1431a
2
fian96
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131k 151h
bolta
7Y2
131/a
170
200 21o 220
10'5/,6
9s/16
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8%
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7 7
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8%
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7
7Vz
123/a
10,/15 131/4
1251o 13
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L
ranglh
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20 3o
120 130 140
lenglh
h.ighl
tt
12\t
6
Pipe Support Selection and Design
i80
Figure 2680
ROO
SrZ€ A',
--
l
L
z
N\
-c Type G trapeze type spring assemb,y is formed by welding lwo standard spring assemblies to the ends of
a pair ot channels. Type G assembly is especially adaptable tor use where headroom is limited, lo avoid interference, or lo accommodate unusually heavy loads. The assembly can be furnished wiih center to center dimensions, as specified by purchaser. When ordering Type G, divlde the total pipe load in half to select the proper spring size. Ihe travel range of the springs remain unchanged-
r F
hanger
.alod load
(appror)
!tza
tb
each, lb
0o
138
1o
200
20 3o 40 5o 6o
256
70
8o 9o 10o 110
12o 130 140 150 160
170 18o 190
200
21o 22o
rod
caslng
lenglh
79142
min thread cngegornonr
channtla
V2
6rr/re
1/z
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38 39 63
8s/'"
4 4 4
,b
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3/a
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sh 5k
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th
1
2
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la
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137
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125 't37 175
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10,/re
1Ya
131/s
183
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13Y4
224 270 326 630
1U4
13/a
8% 8%
11/g
11/z
161/re
gVa
231rc
2Va
13/a
lAYs
Bsh
271rc
21/e
91s/rs
2
18Y.
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at6
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1
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%
lt 1
6% 6%
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1V2
2
Ya
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1V2 1Y2
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1/a
1b
933 1137 1436
z
P
28 29 30
v2
446 598 798 1064 1426 1900 2470 3230 4276 5700 7600 '| 0260 14250 19000 25290 33610 44650
caslng dlamater
1Ya
11/a
11/4
1
1Y2
t/a
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4
3s/rs
27/a
3e/'a
3rr/ro
3Vs
4
Figure 13-3, Continued.
31t
4
3il
l
332
Piping Stress Handbook
Figure 980 TY PE-B
TYPE-C
--I-
RiS
rElh r
rll
I
stzE'A'
Type A springs are furnished with a threaded bushing in the top plate, providing for a sjmple rod attachment for the uDoer connection. Type B and C springs are unfurnished with one or two iugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached direc y to building steel by a pair of angles, eye rod or a single plate.
rypr
B Aa,c o,Ec oo
lo
20 30 40
].t
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tt +t
170
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4
lu.
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150 160
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A.h.
yr 2631rr 315/r6
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67 't(B
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h
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is3
(rppror) lb,
tP.
a,c
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l1
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th th th
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hg a
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n7
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936 I
l7t
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51l,t
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015
842
196
64
210
t1t0
1154
2506
Figure 13-4, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
Figure 980
***-ffj
___l_
T-ffi-r I FC-t I
xllE
llrll Ll-l-L---i TYPE-D
TY
T YPE -G
TYPE-F
PE-I
!
0o 'lo 20 30 10
50 80 70
19%
2.Y.
1Y. 1U. 1Y.
2OY.
1U.
22 23v.
1Y.
21lt
23\'tr th 25Y.
80
5h 5\t 5\t
1Y.
5h
29h
O
25Y.
120
27Y. 32Y.
130 140 150
1.900
AYa
tl
1.9m 1.9m
7V2
8Y.
Y.
vh
a%
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AY.
7Vr
7
1\'
90 100
th
Yr
7 7
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8
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13U
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stt
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16Y. 16v, 16v,
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70
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5v,
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160 190
48tl
l5Y.
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'|
200 210 220
35'1. m+t
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ti li
3.50 3.50 3.50
53/r. 9Vt
8U. 8u.
v.
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h
4.50 4.50
aU.
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h h
th th
4.50
AV.
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a%
2Vr
al
12/t
17v.
l5V.
llUa
r
5?r
22
2
U.
*
It
Figure 13-4. Continued.
2h
8Vt
5.563 5.56:]
51{
h
2\l
5.563
6Y.
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2
l2v.
{ 4
lVa
AY.
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h
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12v. 12v. 12v,
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4.50 4.50
qt
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Y.
Y.
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th
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15Y.
17Y. 17U. 17U.
6n
lt lt
16v, 16v.
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2.875 2.475 2.475
'16Y7
13U.
2Y.
AY.
2'h
3}t
3ti
1
{ a 1
a 1
333
334
Piping Stress Handbook
Figure 820
TYPE-A III' ROD S|ZE
"A"
TYPE-C
TYPE-B
r-l-t
- --_<,1
__JH
I
B
__t
ROD SIZE
"A"
Type A springs are lurnished wilh a threaded bushing in the top plate, providing lor a simple rod attachmenl for the uooer connection. Type B and C springs qre unlurnished with one or two lugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached directly lo building steel by a pair of angles, eye rod or a single plate.
S
r.rqhl {lp9ror)
lug in9
c
\E,C o,E
f
00 20
10 10
25
6
'
27
17
29
t8
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19
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8
17
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m
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8%
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m
45
12
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r
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80 9o r00
91/,6
8
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r90 16 1T
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2
16
16% 18Y. 2O1t$
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23
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ro
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488 539
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it13
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460
$
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m2
Figure 13-5. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
Figure 820
ROD & NUT NOT
FURNISI]ED LENGTH TO SUIT CUSTOMER
TYPE-E
TYPE.t) r-r--
--
ROD SIZE
.
LOAO FLANGE NOT FUFNISHED
\\\ INDICATOF
00 10
20 30 40
7v,
7 7 7
AYa
7Ya
9Yt
ala
1 900
2.475 2.875 2 475
AYa
50 70 80 90
9
I
9
8
1Ot/r
I I
1oth 1O7/.
13Y. 13%
16v2
13%
161/,
120
13V.
16V.
130
13%
16V,
13U.
16Y2 16Y2
't6Vz
100 110
2
13% 13V. 5
25
%
h
16V,
3
3i3/,e 3r3^6
1
I
1.9m 8%
50
140 150 160 170 180 190 200 210 2.O
1.9m YB
16v2
l5Y.
22
17U
15Y. 15V.
22 22
17Y. 17Y.
157. t 5Y.
22 22
v,
3.50 3.50 3.50
5% 5%
I
5Va
1
1
I
65/,6
1
4.50 4.50 4.50
41.,a
2 2 2 2
S1/.
1Y. 1V.
2 2
4.5!o
8%
1V,
4.50
1V. 3
4.fi
8V. a%
1Y2
3
450
aV.
21h
1
4.50 4.50
8% 8th
2v.
2 2
5.563 5 563 5.563
Figure 1&5. Continued.
8Va
v,
214
12V2
2%
121h
2rt
121h
27/.
12V, 12V.
3th 3%
v,
1
335
336
Piping Stress Handbook
2Il2"8H
SERVICE: Recommended for light loads where vertiCal movement does not exceed 1% inches. APPROVALS: Compties with Federal Soecification WW-H-171D (Type a9) and Manufacturers Standardization Society SP-69 (Type 4B). INSTALLATION: Designed tor attachment to its supporting member by screwing a rod into the top cap of the hanger the full depth of the caD.
THO,
4'FN. TIiD
LIGHT DUTY SPRING HANGER Corbon Steel Spring Coil ond Coge The Light Duiy Spring Honger is used for the support of rniscelloneous lield run piping systems subiect to slight (up to l,/4") verticol displocement. lt is designed for incorporotion in rod hongers with o lood coupling provided for spring Iooding. lhe unit does not hove o lood scole ond trovel indicotor. Amount of spring looding con be opproximoied by reloting "8" dimension with spring deflecfron role.
Selection of correcl spring size is normolly done by opproximoie methods toking into occount weight o{ pipe, covering, contents ond mojor fittings. Ordering: Order by port number ond spring size nurnber,
DIMENSION5 IN INCHES Sl1in e
a
c
No. %
l)
D
E
Def
6/,
2
6'/.
l'/1
7)/.
t1
81"
6'/^
I0'/s
Lood
1,/, 2
V/"
Spr in o
Defle
oio
w n
sighr Lbs.
per 100
52
26
160
266
66 87 152
00
200
238 287 350 680
600
210
982
5 3',/,
6t/,
6
ledion
,4
Figure 1$6. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,
Inc.)
Pipe Support Selection and Design
I
f
L. T +
T
----'l
.[w7-.,
-es.;-
Figure 13-7. Typical arrangements oi constant supports. (Courtesy of Elcen Metal Products Company.)
Piping Stress Handbook Table 13-2 Load Table for Constant Spring Supports (lb for total fuavel in in.) hango. 3lzo
load in oounda for lolal truvel in lnche3
Pipe Support Selection and Design Table 13-3 Load Table for Constant Spring Supports (lb tor total travel in in.) losds in Dound3 lor lotal trevel in inchas
340
Piping Stress Handbook Table 13-4 Load Table for Constant Spring Supports (lb for total travel in in.) load In pound! lor total lraval In Inchca
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21B2
61331
56617
52572
4965
4600
43295
46aA
67164 73500
62m2
57573
53732
5G75
47413
44777
3g/36 424m
33otx) 3€800 10300
6784 8
58799
55125
51884
49O0
&20
44100
4ts5
80830
74617
63@ I 6S287
33451 36633 40087
4t665
80625
57060
53848
51051
4€500
46187
4467
58848
56788
53000
48177
61344 63888
58156 60525
50472 52615
fi222
42t71 4€G4 4@r0 50000
47315
628q|
54313
5't 953
49700
7?943
68888
65261
9757 56$0 5943
52m8
66388
56358
53909
51666
75884
71666 74444
57500 59750 620@ 64500
61423
58G31
56003
5374t
67000 6S500
63804
m96 ws1
720m
64566
87500
81540
75716 78930
70665 73665
66250
6q)53
96
a2145
71a75
97
&5360
74688
875m
82665 85998
875&
77500 80625 8i]750 86875
875m
6235s 66@2 67649 70296
78826 81767 84708
87500
110
1$m
12641
18350
44665
107
11939
13244 13940
19573
i5819 600m
i06
12508
20@3
53091
94
11nO
2172
61400
s
I
0756 103(n
25a5 m972
584m
9.
921
!t611 10179 10747
a5m0
1
8o1l
10042 11235
11149
52500
5111
/u,
9043
3299
57500
tt
aaTa
231f7
s8
91
9808
t2
13907 14680
87
90
1769
'fl 1{
v21
70524
38378
[email protected]
cx30
Stgla
71351
62604 65430 68250
6ta1,l
743t 1 77265
71c62
dJ122
80946
739€
70831
84469
80628
v125
73914
875m
83992
80342
a7446
s3646
770m m183
875m
86050
830
8@@
73156 75787
83610 47221
79210
75250
71661
43176 65444 68402
82629
785m
74756
67500
86050
81750
n851
87500
850@ 87500
66185
64708
Pipe Support Selection and
Design
Table 13-5 Load Table for Constant Spting Supports (lb for total travel in in.) load In pound3 ior
nangJ aLa no.
l2V.
13v2
14
14Ya
't5
5696
5492
5303
5126
4961
4a06
42
5544
5359
518 7
5025
1SV2
16
64
6152
5915
65
6432
6184
66
7062
67$
6538
6304
6087
5884
5694
5617
67
7@0
7394
7120
6966
6629
6408
620 r
m0a
6a
8320
sm
7m3
7428
7172
6933
6709
65@
8843
8503
8188
7895
7623
7365)
7131
6909
9005
8671
8361
8073
7804
7552
7317
a m
57
lotll tievol 15Y2
In
inchc
17
llth
t8
1AV2
le
19h
m
71
9888
9507
9155
8428
8523
8239
7973
n25
72
10507
10103
9724
cts
9057
8755
4473
82G
73
11126
10697
10301
9932
9590
9270
8971
8692
74
11714
1
t292
r0873
10484
10123
9786
9470
9175
12416
1r
ct8
11496
11084
10703
10346
10012
9700
76
1$88
12544
12118
11584
11282
10906
10554
10225
77
!3760
13230
12740
122€4
11861
1
1466
11096
10750
78
14507
1399
13432
12951
12505
12088
11698
|l34
79
15254
r4666
t
4123
13618
13149
12710
12300
11917
&)
16000
153€4
14814
fi2€4
13792
12902
125.O
81
16m0
r6153
15555
14S8
14482
14m0
1354 7
13125
8it
't7€o0
'16922
16295
15712
15171
1465s
14r92
13750
83
18400
17602
17(B6
16427
15861
15332
14lX)7
14375
19680
18522
142.1
1756S
16364
16398
15859
r5375
20960
20153
19406
1A712
18068
17465
16902
16375
86
22160
213o7
m517
19783
19102
18465
17869
173r3
87
23:t60
?2461
21628
20855
20't36
19465
18A37
18250
88
24560
23614
2739
21C26
21171
20465
't9805
19188
89
25384
2757
219e8
21288
20625
2€3o7
24413 2725a
23569
m
26400 29440
26283
25377
24331
23740
23000
g1
3?210
31@0
29&50
a7a2
27791
26864
25998
25188
g2
35280
as22
32665
31496
301r I
29397
28449
27563
3aan0
37g)E
35944
34639
33446
32330
31247
3)313
12!00 40788
39257
37853
$549
3530
34t90
33125 321 19
31175
3@45
29442
2fl647
27494
27179
26500
442@
42494
40g24
39460
381m
36830
35642
34531
33482
32498
31570
30691
29863
29078
28332
27625
4amo
44ZiO
42590
41067
39652
38330
370€3
35938
34445
32856
31941
31080
30262
29486
?€750
47800
,r5960
44257
42873
41204
39829
39545
37344
35209
43822 35r 45
3r'141
3l}191
32295
31448
30640
?3875
4SOO
47690
45023
4428[
42755
41329
4m00
38750
37572
36468
35/27
34441
33511
32631
31794
310m
99
51600
49613
47n5
46066
44479
429S6
41609
40313
39087
37939
36855
3584t0
3/,862
3:}946
33076
32250
tm
$6m
51536
49627
47451
46203
44662
43221
41A75
406m
39r09
38284
37219
36214
35a62
34358
335m
u
s 91
95
98
tol
55800
53459
51479
49637
47927
46329
44434
43434
42117
40880
39712
34607
37565
36578
35640
34750
102
57600
56382
5330
5142 4S51
47995
4&47
450m
4S32
42350
41141
39996
38916
37894
36922
38000
1(x,
802m
5788e
55738
53744
51892
50r 62
44544
47031
456(P
44262
429S
41801
40673
39604
385€8
37625
104
62800
60382
58
54r 34
52324
50640
49063
47571
$174
44455
43607
42429
41315
&255
39250
105
65400
62882
m552
58346
56375
54495
5e737
51094
49541
4€085
46712
45412
44196
€025
11921
40875
106
68000
65382
62960
60707
58616
56661
54834
53125
51510
5mm
48569
47214
45943
44736
435€8
42500
107
700m
6€228
657m
63350
5116€
59127
572m
55438
53752
52r 73
506a3
49273
47942
46683
454 85
44350
t0a
7"3920
68441
65992
63719
61594
59607
57750
55994
54350
52797
51328
49942
€6i]0
47343
a6200
109
70960
7to14 74m0
71255
6530
u127
62059
60125
58297
5459
53439
5200
50€30
49331
48rm
1t0
80000
76920
74070
68706 71120
64960
66€60
64510
62500
60600
57140
55550
54050
52630
51280
5m00
r45
58820
341
342
Piping Stress Handbook
Figure 550
VIBRATION COIIIROl AND SWAY BRACT
The FIG 550 vibrotion conlrol ond swoy broce presents o neol, conpoci oppeqronce
Sire Ronge: For pipe sizes 2 through 24 inch. Service: Recommended for conttolling vibration; absorbing shock loadings; guidittg or restraining the movement of pipe resulting from thermal expansioni bracing a pipe line against sway. Instollotion: Shipped ready foi installation
Adiustment The sway brace should be in the neutral position when the system is Hot and operating, a: which time the tension test collar should be hani tight, If it is not, the sway brace should be adjusted to the neutral position by use of the loai coupling. The screws in the tension test colla: need not be loosened, since they serve o[ly to secure it to the load coupling. Feotures:
rVibration is opposed with an ilstantaneous counter foice bringing the pipe back to normal position. rA single energr-absorbing pre-loaded spring provides two way action.
Cut.owoy section shows simplicity
of exclusive .single spring
design
o
One spring saves space and simplifies design.
o
Spting has 3-inch travel in either direction.
r Accurate neutral adjustment assured.
oEnclosed spring excludes ditt and gives a clear. compact aPpeaaance.
Speci{icotions: Fulfills the requirements of the ASi Code for Pressure Piping as to fabrication details and materials.
Deflection of single spring occurs when thrust exceeds pre.compress ion
Tension couses dellection of sin. glo spring in opposite direction
Figure 13-8, Vibration control and sway braces. (Courtesy Support Technology and Piping Technology
Produc:-.
Inc.) Fi
Pipe Support Selection and Design
lmportont: Rod lengths should be cut and final tension adjustments made for the hot or operating position of the pipe. If, with the pipe in its hot position, the
Siue Selection: The vibration control and sway btace
gives full deflection forces from 200 to 1800
pounds
initial precomptessed spring forces from 50 to 450 pounds to dampen vibrations, oppose pipe sway and has
tension test collar can not be turned by hand or if it tums very freely, loosen the jam nut adjacent to the rod coupling and rotate the coupling until the coliar
and absorb shock forces.
The exact amount of energy needed to control piping should be in proportion to the 6ass, amplitude of movement, and nature of disturbing forces acting on the pipe. When it is possible to calculate the exact restraining force required, the size of the vibration control and sway brace capable of providing this force
can just be turned by hand. Retighten the jam nut.
When correct tension adjustments are completed, the btace exerts no force on the pipe in its operating
position. Undei shut-down conditions, the brace allows the pipe to assume its cold position. It exerts a nominal cold strain force equal to the pre.load force plus the amount of travel from the hot to cold position, times the spring scale of the particular size of the vjbratron control €nd sway brace.
should be selected.
To simplify the selection of size, engineets have designed the vibration control and sway brace in three sizes that are readily related to nominal pipe size. For pipe sizes 3%-inch and smaller, the small size is recommended; for 4 to 8-ioch, the medium size; and for 10-inch and larger, the large srze. Instollotion: The vibration control and sway brace is shipped ready for installation. The rod coupling rotates with slight resistance and the tension test collar can be rotated by hand while holding the rod coupling statiorla!y,
vibrqtion control crnd sway brrrce END
El'lD
PLATE
PLATE
SPR]NG PLATE
rN SIO
343
-.
SPRING PLATE
,-ROD
COUPLTNG
STD. JAIV NUTT
JAM NIJT,'
E E
loads
.
L
FtG 550
weights
o
FtG 555
dimensions (inches)
FtG.550 preload
1
2 3
21o
spring
weight
to
(approx) each. lb
4to I
50 150
10 to 16 18 to 24
450 900
31/,
5 6
1350
1800
ID
200 600 1800 3600 5400 7200
rod size,
trkeoul
3ize,
E '11/z
22 1
36
plpe
1
11/a
2 2 2
79 95
212
41/z
135/o 14TB
41,'
1 1
3/a
1
11/2
'|
1Yz
11/2
'lrz
Y2
11/z
6tb
15/B
177/s 185/s
173/4
15/s
22
17
21/a
141.h
21/a
2011
2lt
13/B
23r3/ro
6Ys
1 ,1
87/a
1
13
63/q
lYz
111i2
63/a
112 112
13 15
63/a
11/a
95/a 11/a
1
r3i, o
FrG. 555 spfing ror pipe size
l 2 3
4 5
6
2lo 4lo
tb 31/2
8 16
10 to 18 to 24
50
150 450 900 1350 1800
A As specified by customer.
Figure 13-8. Continued.
pipe size,
weight (3ppror,
rod M,
each, lb
E
200 600
23 26
11/?
1
1
2
1
1800
38
1
2
1
3600 5400 7200
1v2
2 2vz
'| Y2
a2
11/2
6s/s
98
1t'2
21/2
1\',2
65/s
3/a
11/a
41i2 3/a
1Y2
65/e
20
24Va
77/a
I
2O3/a
25
77/a
1
241/s
283/B
7?/3
1
2451.o 6s/rs 2513/, o 6'g/,s 2713 rc 6'g/,s
31Ya 33Ls
295/B
g'/a 91/a
11,, 11.,
9Ya
1)ta
93i r6 91si, e
135/,s 12
13lz 15Yz
11/a
1l/a
344
Piping Stress Handbook
FIG 550 A **il:"1iu *ll *
FIG 555 A dimension
i! 2It 0 in
recornmended when W dimension is
or les!
2
lt
0
in, o! lo38,
-
FIG 555
FIG 55OB recommended when W dim€nson is 2
Il I in.
B
recomm€nded when W dimeBion is 2 lt
or rnot€
I in.
or more
-r.
_
PIPE
olAp
-
tl!alqace
corior oI plpa noDLnol plpa
drs
rwoy broce
!l:e
2
2% 3
I
6% 2
I
l4 l8 20 24
7 8,,16
sX" r0%
l0 t2
s% s% sr\e 8Xe
3% 4 5 6
lo olltlld6 stud ol ptD6 cloEp
3
rr%
t2tlft r3,\"
I4tXc rs% r7%
Dimenaions lor ssgemblies lor lsrger pip€ sizes dvdilobl€ on opplicalion. psrogroph "How lo sir6 qsBemblios" obove.
S€€
Figu.e 13-8, Continued.
t
-a-
\
Pipe Support Selection and
Design
Molded rigid polyurethane foam supports may also be to support other types of piping systems where the medium being transferred in the pipe is to be maintained at a high temperature and protected from a cold environment. This type of application is typical of a pipeline pumping oil at a design temperature of 180'F through a cold environment at approximately -50"F. The insulating properties of the polyurethane foam are necessary to keep oil in a low viscous state for pumping over long distances. The supports for this type of application are designed in the same manner as those for cryogenic appli-
ing system. The thickness of the polyurethane support should match that of the line pipe. . Support load, o Environmental conditions-The exposed cradle may require special coatings or galvanizing. From these design conditions, a suitable foam density is selected for the supports. Thbles 13-6 through 13-11 include some typical properties of molded rigid polyurethane foam used to fabricate supports. Examining these tables, it is apparent that as the foam density at ambient temperature is increased, both the thermal conductivity factor and the compressive strength also increase. At cryogenic temperatures, however, higher density rigid polyurethane foam has approximately the same thermal conductivity factor as lower density foam. This results from the fluorocarbon within the foam cells becorning a liquid at the cryogenic temperature, thus creating a partial vacuum. Thus the normal support design procedure involves first determining the required K factor to insulate the piping based upon the thickness of the matching pipe insulation. Secondly, the foam density needed to produce the required K factor is selected. Lastly, the length of the support needed to
used
cations.
lnsulated Anchors For special designs where it is necessary to anchor the piping system, it is also necessary to avoid the metal-tometal contact for the conditions already stated. Anchors are fabricated for this application by foaming between an actual piece ofthe line pipe and an outerjacket. See Figure 13- 10.
support the pipe is determined using the selected density.
P0WERFoAM/P0WEBSLIDE Beference Guide
POLYUBETNANE FOAM
sEcTloN "B.s'
AOLTEO PLATE TO STR1JCTUBE
l-g-
*..o.o
"*r.
ro
"t"r"tu".
Al ligure numbers ir lhis section
are ava lable in any POWEFFOAM thickness, sin91e, double
or lriple layefing lo conform to the line
Figure 13-9. POWERFOAM/POWERSLIDE"
345
reference guides. (Courtesy of Power Piping Company.)
346
Piping Stress Handbook
POWERF0AM lnsulated Pipe Anchor Stainless, copper and alumanum pipe can be made
into PowERFoAM anchors.
ULTRA HIGH DENSITY POWERFOAM STEEL PIPE EXACT DUPLICATE OF LINE PIPE TO BE WELDEO TO LINE PIPE
ON/CONTRACTION
Figure 13-10. POWERFOAM" insulated pipe anchor. (Courtesy of Power Piping Company.)
Pipe Support Selection and Design
347
Table 13-6 POWERFOAM- Thermal Properties
oella "T"/2 ll. lb./cu.ll. 10 10 14 14
160.0
20 20
320.0 320.0
Cou
Hol Face
Kq./cu. m,
+43 5 +42.9 +41.6 +42.4 +44.3 138.7
160.0 224.O 224.O
esy of Power
cold
Hol Face
Cold Face 1S3 7
I
162 193.4 159 6 193.4 157 6
l.
''K" Faclor Blu. ln. Hr. Fl.2
264
88.7
0 0213
o 141
0.0219 0.0241 o.0244 0.0297
0.r52 0167 0169
110 3 109 2 106
-3I6.7
103.2
-261 2
760
232
792
-316.1
104 6
-58 4
109
986 860
-746
111 7
102.2
357
-59 4
101 7
-255.3 ,316.1 251 7
24.9 25.2
750
31 8
121 7 108 6
1
Conduclivity
Blu/Hr.
Face
-15 1 -60 0 -75 9
I
Apparent Thermal
Power Input amount ol Energy Pow€r Loss To Malntain
TemDeralure in Fahrenheil
Temperalurein Cenligraale
Powerloam Den3ilier
"F
0.206 o.223
0 0321
PipW ConpanJ.
Table 13-7 POWERFOAM* Physical Properties Engineering Oata Slrenglh Compressive
At Yield with a Safety Faclor
Ske.glh
Srrenglh
Or 5:1
Densilies Kq.
t0
160 0 160.0
10
224.0 224.O
320.0
20 20
320 0
-256 -318 -256 -318 -256
160 194.5 160
60
194.5
,318
194 5
6.0 6.0 6.0
r60
60 60
152 152 152 152
152 152
5900 4500 9200 9200 r 4600 18000
2625
I191
2550
3575
1157 1667
2800
1270
4204 3900
1905 1315
PSI
PSI
PSI
PSI
2676 2441 4173 4173 6522 8165
534 408 833 833 1322
38 29 59 59 93
1630
115
234 231 333
17
2.8 1.9
23
3.1
3.2
254 380 354
PSI
27
32
25
4.8
19500 22104 27200 27004 40000 34900
1371 1483 1912
1898
2812 2453
106.8 81.6 166.6 166.6 264.4 326.0
5.74 11.71 11.71 1€.59
22.92
ar Yrerd
Courtesy of Power Piping Conpan!.
"o*',l'-?;ly ST?31'.':Tf;",:"':$f3$'j1".'#ij::l'.'h Table 13-8 POWERFOAM" Temperature Range
lrsrimum (Hol)
Temperalure
Temperelure
Den3illes lb./cu.
Kg./cu. m.
10 14
160 0 224 0 320 0
20
Minlmum (cryogenic) seflice
Servace
'c +275
135
425
+275
r35
-425
-245 ,254
,275
135
-425
-254
Data is all based on tests performed on POWERFOAIiI made with our tormula and molding techniques. Independent testing laboratory corroborating iesl data available upon request.
Courtesy of Power Piping Compant
SUPPORT CONTACT 30" each side of vertical center line.
60"
-
SUSTAINABLE LOAD FORMULA:
/n'D'L I lc\ Sustainaute Loao \ 6 l\ t = C = Compressive strength with safety lactor O = Ouier diameter in inches L = Length in inches
Piping Stress Handbook Table 13-9 Engineering Data
IEIGHI
OF PIPE, WATEi {PEe Footl
r'rl|sutaTtol{ 1J2
22 2.052
i5 192.01
I 5
402.n
'u
f .375 t "r^"",1 PIPE I
t7912 39.59 23
1323.,15
'.62
257.&A 751"O
r3233 9
i
"Are
nol regular p pe
sz6
*"SUSTAINABLE
LOADS OF INSULATED PIPE SUPPORTS
2 fb./cu. tl. 32 Kg./cu. n. COMPaESSIVE STRENGTH = 5.8 pst (.40774 Ks./Cm.t W|TH 5:1 SAFETY FACTOR
-
'rrBased on ioam .c,mpresston (with
a S:1 salery
Courtes! of Power Pipin| Company.
tacroi,
tengrh ot slpports and pipe sizes.
FOAM BY AMBIENT TEMP
-it
Pipe Support Selection and Design Table 13-10 Engineering Data
*-SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS 4 lb./cu. tt. - & Kg./cu. d. 13 PSI ( 9139 KS /Cm, WITH 5:1 SAFETY FACTOR
COMPAESSIVE STRENGTH =
*rBased on loam compression (with
a
AMBIENT TEMP,
5l
saietv laclor) length ol supporb and pipe srzes
96 Kg./cu. m' 6 lb./cu. fi. COMPBESSIVE STRENGTH ='I6 PSI (1.1248 KS./CM.4 WITH 5:1 SAFETY FACTOB (NON-MOLDEO FOAM AY OTHEFS AMBIENT TEMP
-
"'Based
on road compression (wnh a 5:1 salely lacior). length oi supports and pipe s[es
Courtesy of Power Piping Conpany.
Piping Stress Handbook Table 13-1 1 Engineering Data
-*SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS t tbJcu. fi. - 128 Kg./cu. m. COiIPRESSIVE STRENGIII = ZI PSt (1.5466 Kg./Cm.,) WITHi:1 SAFETY FACTOR lt{ON-MoLDEo
FoAM ay
OTHERS AMBIEXT TEMP.
ot supporrs and pipe si:es.
fi'8as.d
on foam densirios (wnh a
""Comprossive strength ol
5r
salety lacto4, iength ot supporls and pip€ sizos.
POWERFOAM onty.
Counesy of Power Piping Conpan!.
J
t4 Fundamentals of ExPansion Joints
Thermal movements in pipelines and ducting result from variations in temperature of the flowing medium or from variations in ambient temperature where piping is exposed to weather. If not compensated for in system design, these movements may cause high stresses, possibly resulting in failure of the piping or connected equipment. Compensation for thermal movement in a piping system . can be achieved by three basic methods:
Nomenclature and SYmbols Standard nomenclature used in discussing expansion joints and the symbols used in applications drawings are presented in Figure 14-2.
Types of Expansion Joints
1. Designing a flexible piping system that utilizes
2. 3.
-
changes of direction to absorb movement. Using pipe loops or bends to absorb the movement. Using expansion devices, such as expansion joints, swivel joints, ball joints, ard flexible hose.
There are two general categories of expansion jointsthe slip type and packless (or bellows) type. The packless, corrugated metal expansion joint is most frequently used in modern piping applications. It does not require maintenance, and its hherent flexibility to absorb thermal movements in several planes permits greater freedom in piping design. The slip joint, a pair of telescoping sleeves made pressure tight by a packing gland, can absorb a greater amount of axial movement than a comparable bellowstype joint. However, it requires periodic maintenance and is restricted to axial movement only.
Types of Joint Movements
The type of expansion joint used depends on the qpe movement to which it will be subiected.
of
Single Expansion Joint This is the simplest type of expansion joint . As its name
implies, it is constructed with one bellows and is used mostly to absorb axial movements. A single joint can also be used to absorb angular ald lateral movements, as well as a combination of these three basic movements. Figure 14-3 typifies good practice in the use of a single expansion joint to absorb axial movement. Note that the expansion joint is placed between two main anchors (MA) and that it is located near one of the anchors. Q'{otice also that the first alignment guide (GD is placed close to the joint. The second guide (G2) is close to the frst, and intermediate alignment guides (G) are provided along the balance of the line.
Expansion joints installed in piping systems are subject to thee types of movement-axial movement, angular rotation, and lateral deflection. These movements can occur individually or in combinations. The four examples in Figure l4-1 show how single and universal expansion ioints absorb these movements.
Double Expansion Joint This consists of two single joints joined by a common connector that is anchored to a rigid part of the structure by means of an anchor support base. Double expansion
351
Piping Stress Handbook
I r*F AESORPTION
OF AXTAL
I
MOVEMEIiT
(SINGLE JOTNT)
ABSORPTION
OF ANGULAR ROTATION (SINGLE.'OINT)
--I -t-' 1+
-
-li rl
L EGEND
- X: +X: 9: Y:
ABSORPTION OF LATERAL DEFLECTION AND AXIAL MOVEMENT (UNIVERSAL.JOINT)
COMPRESSION
EXTENSION ANGLE OF ROTATTON L
ATERAL DEFLEcTIoN
Figure 14-1. Expansion joint movements. (Courtesy of Badger Expansion Joint Company.) joints are supplied with or without an anchor support base depending on the customer's preference. See Figure 14-4. A double joint is used when the axial movement to be absorbed is too large to be handled by a single joint. The intermediate anchor on the center nipple divides this movement so that each bellows of the double joint is usually located in the center of a pipe run: so both ends are subjected to the same movements and have the same num-
ber of corrusations.
Universal Expansion Joint This consists of two bellows joined by a common connector which is not anchored to the structure. This per-
mits the universal expansion joint to absorb any combinaand angular-where these movements are too sreat to be handled by a single joint. Universal joints usually have tie rods with stops that distribute the movement between the bellows and siabilize the corrunon connector. The joints find increasing use in steam and hot-water distribution systems because there
tion of three basic movements-axial, lateral.
are impressive cost savings for the large amounts of movement they can absorb with a minimum of guiding and anchoring.
Figure 14-5 illustrates a universal expansion joint used to absorb lateral deflection in a single plan Z bend. Both anchors are intermediate anchors because the pressure loading is absorbed by the tie rods. Only directional guid-
Fundamentals of ExDansion
T
MAIN ANcHoR
Xf--f
T
Ft DMA l2\-------------1
mmr
F__x--? IA
.
-ffi-
Joints
353
sTNGLE E*PANSToN JorNT
DTREcnoNAL
DOUBLE EXPANSION JOINT
MA|N ANcHoR
WITH INTERI\4EDIATE ANCHOR
INTERMEDIATE ANCHOR PRESSURE BALANCEO
T
EXPANSION JOINT
I
t
\DIRECTIONAL INTERMEDIATE
m7f DIA
'ANcHoR wtrH
GUTDE
SINGLE EXPANSION JOINT
l----
PrPE ALTGNMENT GUTDE
WITH TIE RODS
rr---r l
'" lfi:11 tEt mmm sroE vrEw
UNIVERSAL EXPANSION JOINT
END VIEW
WITH OVERALL TIE RODS
PLANAR PIPE ALIGNMENT GUIOE
ra*/L 't
t
c-------E-------
)
sPRrNc suPPoRr
UNIV€RSAL EXPANSION IOINT WITH SHORT TIE RODS
+
P,PE REDU.ER
GUSSET
UNIVERSAL PRESSURE EALANCED EXPANSION JOINT
l--'-4
-Ff
HTNGED EXPANSToN
rorNr
GIIvIBAL EXPANSION JOINT
Figure 1'l-2. Expansion loint symbols. (Courtosy ol Badger Expansion Joint Company.)
Piping Stress Handbook
di
'1il-
l|l Figure 14-3. Single expansion joint. (Courtesy of Badger Expansion Joint Company.)
Figure 14-4. Double expansion joint. (Courtesy ot Badger Expansion Joint Company.)
fI
-LATERAL
MOVEMENT HOT
Figure 14-5. Universal expansion joint. (Courtesy of Badger Expansion Joint Company.) ing, if any, is required because the compressive load on the pipe consiss onJy of the force necessary to deflect the expansion joint.
Where dimensionally feasible, the expansion joint
should be designed to fill the entire offset les so th;t its expansion is absorbed within the tie rods as ixial movement.
Pressure Balanced Expansion Joint This is a combination of single joints that oppose each other in the same way the internal pressure loads oppose the other. This prevents excessive loading due to presiure thrust from being transmitted to pipe anchors, turbines, or
Figure 14-6. Pressure balance expansion joint. (Courtesy of Badger Expansion Joint Company.) process equipment. The compressive forces of the two bellows are additive, but these are usually negligible in comparison with the pressure forces. This type ofjoint is used where a pipeline changes direction. It absorbs axial or a combination of axial and lateral movements. _ Figure 14-6 shows a tlpical application of a pressurebalanced expansion joint for combined axial movement and lateral deflection. The anchor on the piping run and that on the turbine are intermediate anchors, and onlv directional guiding is required. By proper design. the guide directly above the turbine can be made to absorb the axial movement forces of the expansion joint without transmitting these to the turbine. The only force imposed on the turbine is that which is required to deflect the expansion ioint laterallv.
Fundamentals of Expansion Joints Hor
Hinged Expansion Joint This is a single expansionjoint designed to permit angular rotation in one plane only by use of a pair of pins through hinge plates attached to the expansion joint ends. Hinged jo-ints are used in sets of two or three to absorb pipe movement in one or more directions in a single plane piping system. Each individual joint in the system is restricted to pure angular rotation by its hinges. However, each pair of hinged joints, separated by a section of piping, will act together to absorb lateral deflection in much the same manner as a universal expansionjoint in a singleplane - application. Expaniion joint hinges are designed to transmit the fu1l pressure thrust of the expansion joint and, in addition' may be designed to support the weight of piping and
----------.1
rA(:
HEJ:
Hings Expansion Joint
PG:
Planar Guide
equipment, and absorb thermal loads, wind loads, and other external forces. A hinged system permits large movements to be absorbed with the minimal anchor forces.
Figure 14-7 illustrates a two-hinge expansion joint system. In this application the expansion joints absorb only the differential vertical growth between the vessel and pipe riser. Any horizontal movement due to piping elpqiion, vibration, wind loads, etc. will be absorbed by bending of the vertical pipe leg. A planar guide may be installed near the top of the vessel to protect the hinged joints from wind loads at right angles to the plane of the piping.
Figure 14-7. Hinged expansion joint. (Courtesy Badger Expansion Joint ComPanY.)
Gimbal Expansion Joint This is a single expaqsion joint designed to permit angular rotation in any plane by the use of two pairs of hinges affixed to a cornmon floating gimbal ring' Unlike the hinged joint which can absorb angular rotation in a single plane ofun the gimbal joint can absorb angular rotation in any plane. The ability of the gimbal expansion joint to atsorb angular rotation in any plane is most often applied by
using two gimbal joints which act together to absorb movement. Gimbals, like hinges, are designed to transmit the pressure thrust and are used in pairs, or in conjunction with a hinged joint. Figure 14-8 illustrates a gimbal-joint application. Because pressure loading is absorbed by the gimbal structure, only intermediate anchors are required. Planar zuides are provided to restrict the movement of each piping leg. Ai in a hinged-joint installation, the location of pipe suppo.t. is simplified by the load-carrying ability of the simbal.
Figure 14-8. Gimbal expansion joint. (Courtesy Badger Expansion Joint Company.)
of
Piping Stress Handbook
Anchors, Guides and Supports Pipe Anchors The.function of pipe anchors is to divide a pipeline into individual expanding sections. Since thermaj movement cannot be restrained, it is the function of pipe anchors to limit and control the movement that expansion joints, lo_ cated in the line between the anchors, must abiorb. In some applications, major pieces of connected equip_
ment such as turbines, pumps, compressors. and reaciors, lI desrgned to wlthstand the forces acting upon them. can
function as anchors. Additional pipe ichors are com_ monly located at valves, at changeJ in pipe direction, at blind ends of pipe and, at major branchionnections. ix_ pansion devices must be installed in each of the pipe sec_ tions to provide flexibility.
Pipe Guides A pipe guide is a sleeve or frame fastened to a risid structure that permits the pipeline to move onJy along-its 9wn lxls: The guide is needed to prevent the pipeline from buckling due to the pressure thiust or ftelbiiity of
the expansion joint-or both. planar pipe guide is a pipe guide modified to permit .. A limited movement in one direction other than loneitudi_
nal. It is used in
"L" or "2"
Cold Springing of Expansion Joints "Cold springing" means prestraining the elements of a piping system at the time of installation so that thermal stresses occun'ing when the piping is hot are appreciably reduced. The purposes of cold-springing expaniion joints may be considerably different, although the mechanics are basically the same. Cold springing is generally applied to expansionjoints absorbing only lateral deflection or angular rotation. Cold springing should not be confused with ..orecompressing" or "presetting" an expansion joint. Tire laner terms apply to adjusting an expansion joint in an axial direction to allow for specified amounts of axial compression or extension without physical interference between the corrugations or overextending the corrugations, yhich mighl damage them. If deshed, cold springing can be done at the factory before shipment to facilitate installation. The endurance or cyclic life of an expansion joint is dependent on the maximum mnge of stress to which the bellows is subjected, the numerical maximum stress value being a far less significant factor. Cold springing an expansion joint to reduce the maximum numerical stress would not result in any great improvement in cyclic life. There are, however, a number of other reasons for coldspringing exparsion joints as foliows:
piping configurations (see
figurg J+j) where rhe expansion idints ar6 subiected to lateral deflection or angular rotatton. Pipe guides should be located and spaced carefullv in a piping system. (See Figure l4-9.) A pipe support carries the dead weight ofthe insulation, . piping. and its contents. Pipe supports are not pipe guides. supports do not lim.it the free movement of piping or con_ tribute to guiding it in any way. The recommendations for pipe anchors and guides given in this chapter represent the mlrxmum requrements tor controlling pipelines contain_ ing expansiotr joints. However, standard piping practice usually requires additional pipe supports b;twe;n guides.
Forces and Moments To calculate the loads on piping, supports, and equipment, the forces and moments to move an expansion joint must be known. The expansion joint manufacturer will provide axial, lateral, and angular spring rates.
Force Reduction
Il
a wide range of applications, the force required to deflect an expansion joint is significant. Where the expansion joint is used to relieve the loading on sensitive equip-
ment, where anchor structures are limited to extremely small loads, and in other similar cases, cold-springing the expansion joint at installation can cut the maximum deflection force in half. In some cases, a 100% cold spring will reduce deflection forces to a minimum at extremely high operating temperatures.
Stability Figure l4-1 shows the movements ofbellows due to angular rotation and/or lateral deflection. In both cases, one side of the bellows is extended and the other compressed. so the bellows may become distorted when subjected to
Fundamentals of ExPansion Joints MAXll,4UM RECOMMENDED SPACING FOR TNTERMEDIATE PIPE GUIDES AXIAL MOVEMENT ONLY (VALUES BASED ON STANDARD WEIGHT CAREON STEEL PIPE
400
357
)
400
350
350
300
300 250
200
200 r80
t80
r60
t60
r40
r40 r20
6
roo
=a^
feo r..r 70
e lao
(9 -k--
6
>40 CE
F
z-30
toL
400
250 MAXIMUM PRESSURE-PSIG NOTE: I.ADOIIIONAL PIPE SUPPORTS ARE USUAILY iEOUIREO A€TW€EI'I GIIIDES II{ ACCORDANCE WITH STANOARO PRACTIC€. 2 ARROWS REF€R TO EXAMPLE GIVE^I IN TEXI
Figure 14-9. Spacing for guides with expansion joint. (courtesy of Badger Expansion Joint company.) internal pressure. Reducing either the internal pressure or the displacement of the corrugations will improve the stability of the expansion joint. By cold springing the expansion joint 50% at installation, the maximum displacement per corrugation is cut in half and the exparsion joint is far more stable. For this reason, where expansion joints are subjected to large lateral deflections, or where operating pressures are high, it is good practice to install the joint in a 50% cold-sprung condition.
Component Clearances Where an expansion joint is furnished with internal sleeves, external covers, or tie devices spanning the be1-
lows, these components must have enough clearance to accornrnodate the lateral deflection or angular rotation of the joint. The required clearance can be reduced to a minimum if the joint is cold sprung 50%. By this means, hter-
358
Piping Stress Handbook
nal sleeves of maximum diameter can be furnished, the overall diameter of an expansion joint incorporating external covers or tie devices minimized, and the desien of external structures simplffi ed.
Use of Internal Sleeves in Expansion
Joints
. I?"r:lJ
sleeves should be specified in expansion joints
ln me Iollowlnq cases:
l.
transmitted through the flange bolts to the mating ange and then to the connecting pipe.
In some instances cold springing is recommended to keep tie rods closer to the bellows. thereby minimizing moments. When ordering, advise if joints are to be insul lated. If so, speci$ the insulation thickness, because this will affect the hardware desien. . Consideration must also be-given to the crushing of piping. Attachments must be designed to distribute -the l-oid as much as possible.
to
When smooth flow and/or minimum friction losses are desired.
2. Where flow velocities are hish. 3. Where there is a danger of pitting or erosion. 4. In high-temperature applications. 5. When copper bellows are used and the application
is
for high-pressure drip, super-heated steam, hot water^or condensate, or where there is any possibility of flashins.
In some
increase the thickness
cases
it becomes necessary
of the pipe wall and/or
the lengths of the pipe nipples in orderlo distribute the load. Proper design of attachments is extremely important. parJicularly for critical applications with high piessures and temperatures. In such cases, hardware-cai cost as much as or mrcre than the expansion joints. For greater systgm rgliab_ilrry, it is important that emphasis be put on engineerirg design rather than price. Upon receipt of per_ unent apptlcatron data. sp€cial requirements can be deter_ mlneo,
Internal sleeves should not be used where tars or other
il;;;;;t-";;;;
Calculation of Forces and Loads highly viscous fluids are nowing. 'jplcking up," "coking," or "caking" and result in joint failure..If purging will prwent these conditions, sleeves The forces or loads to be calculated for tie rods, hinges should be used in conjunction with purging
comections.
Tie Rods, Hinges, and Similar Accessories In a piping system with expansion joints, it is often impractical to provide main anchors to absorb pressure thrusts. In these cases. tie rods. hinges, or gimbals may solve the problem as long as their attachments are designed to transmit the forces imposed by pressure in the expansion joint.
Method of Attachment
and attachments are: 1. Pressure thrust. 2. Force to extend or compress the expansion joint due to thermal growth within its tied lensth. .'- Weight of joint. 4. Unsupported weight of prptng and insulation between a pair of bellows. 5. Weight of fluid carried in the joint and unsupported piping. In large joints, consideration should be eiven to the weight o[ water used in hydro testing.
6. Wind loading effects, if
present.
In addition, effects of temperature and flow conditions must be accounted for.
Tie rods, hinges, and gimbals are attached in two basic ways:
1. By a structure whose function is to transmit the loads to the pipe or equipment. This concentrated loading may introduce high localized stresses into the prping in addition to the stresses due to internal pressufe.
2. By direct attachment to
flanges, which then carry the loads on the rods or hinges in addition to their normal flange load. In this method the total load is
Cycle Life Expectancy The cycle life expectancy of an expansion joint is affected by various factors in physical Construction. These are:
1. Operating
pressure.
2. Operating temperature. 3. Bellows material.
Fundamentals of Expansion
4. 5. 6. 7.
The movement per corrugation. The thickness of the bellows. The center-to-center distance of the corrugations. Depth and shape of the corrugation.
Any change in these factors will result in a change in the life of the expansion joht. The life expectancy is defined as the total number of complete cycles that can be expected from the expansion joint based on data tabulated from tests performed at room temperature under simulated operating conditions. A cycle is one complete movement from the full-open to the fi.rll-closed to the full-open position. It should be noted, however, that laboratory tests rarely if ever duplicate actual service conditions. Cycle life is only one factor in the design of an expansion joint and may be tle least important. Many life cycle tests have been conducted and expansion joints can be manufactured to meet any specification. However, experience has shown that few applications have a real need for high cycle-life design, which adds unnecessary costs to the expansion joint.
Joints
359
prevented by covering the bellows and using an antispatter compound when welding. External conditions should also be considered. External corrosion can result from fumes or sprays that may contact the bellows or in tunnel and manhole installations where water is allowed to collect. Direct application of insulation to the expansion-joint bellows and direct burial in the ground are not recommended. Many corrosion problems encountered in the field can be reduced, if not completely eliminated. Where corrosion problems are complex, consult a qualified corrosion engineer.
Erosion This is the mechanical wearing away of the metal surfaces in a joint. It usually results from the irnpact of solid particles entrained in the flowing medium. Where there is a possibility of severe erosion, such as in lines carrying abrasive media, heavy liners should be used to protect the bellows of the expansion joint.
Corrosion Corrosion can significantly reduce the service life of an expansion joint. The design and operating characteristics of expansion joints are such that they may be exposed to corrosive attack under conditions that do not affect piping and fittings of similar materials. Types of corrosion most frequendy experienced in expansion-joint applications are as follows:
1. Stress-corrosion (a cracking of the material as the
2. 3. 4. 5. 6.
result of a combination of stress and corrosive environment). Intergranular-corrosion, characterized by a preferential attack along the grain boundaries in metals. Pitting, which is a localized attack on metals. General corrosion or the gradual eating away of the metals in a system. Impingement and corrosion erosion, associated with the impact of a liquid or gas medium on the surface of the material under attack. Elevated temperature oxidation, most comrnonly encountered in hot ak and exhaust lines.
Calculating Thermal Expansion Metallic, packless expansion joints are normally designed to move in axial compression only, and unless otherwise specified, the minimum and installation temp€ratures are assumed to be 60'F. Here is how to determine the amount of thermal expansion in a piping system:
Example Assume a 10-in. steam line fabricated from carbon steel is carrying superheated steam at 300 psig and the distance
between pipeanchors is 1,10 ft-O in. The minimum ambi ent temperature is 70"F and the maximum operating temperature is 460'F.
Sorution The corrosion resistance of stainless steel depends on the formation of a thin, unbroken, chromic oxide surface, which will form slowly in the atmosphere on clean stainless steel. Particles of steel from welding spatter should be
From Chapter 2, Table 2-1, we find that the expansion of carbon steel pipe at 460'F is 3.25 in. per l0O ft, and at 70'F the expansion per 100 ft is 0 in.
Piping Stress Handbook Total expansion:
(r4O ft) (3.2s
in.)
-
100
0 in.
Example
:
4.55 in.
Therefore, we find that we should select an exDansion joint that will absorb ar least 4.55 in. of axial
"o*o."._
slon.
Assume that the installation temperature will be 70"F. The required precompression is then calculated as follows:
6(70.F P_ (460"F
Precompression
- 0.F) _ - 0.F)
0.913 in.
Note: If the amount of precompression is very small (Va in. per corrugation or less), it may be neglected. When precompression is required, remember to deduct the amount of this precompression from the normal overall length dimensions.
If the minimum operating temperature is lower than the qggput d installation temperature, the expansion joint will be subjected to both enension and compression-dur_ ing^operation. Because most expansion jointjare designed to runcuon rn compression only. any expansion joint used rn lyclr an apphcatlon must be precompressed (prior to in_ stallatton) to prevent extension of the expansion joint beyond its original. overall length. If advised of the minimum. maximum, and installation temperalures when the order is placed. the expansionjoint wlll be tactory precompressed and may be installed as re_ ceived. In the case of expansion joints specified for low-temperature service only, the installation and maximum temoeratures are normally the same. so thejoints function eniirely in extension. Where such service conditions are clearly specified, the expansion joint will always be factory precompressed, ready for installation.
Where it is not possible to anticipate the installation temlerature, the expansion joint may be precompressed in the field. The amount of precompression is determined as follows:
-4(Tz-Tr) (Ts - Tr) D-
Application Pipe Anchors The first step is to determine the tentative locations of pipe anchors. By proper location, any piping system can be reduced to a number of individual eipanding pipe sections having relatively simple configurations. The number and location of pipe anchors will depend upon piping configuration, amount of thermal expansion, the proximiry of structural members suitable for-use as anchors, and-the location ofpipe fittings, connected equipment, and branch connections.
. Start out with the assumption that single expansion joints in straight axial compression will provide the simplest and most economical layout. Wherever possible, the distance between anchors and amount ofexpansion should be kept uniform so rhat the expansion joinis used will be interchangeable. Ib minimize the number of exDansion joints adjust the distance between alchors so thai exoansion joints having a maximum number of corrugations in each bellows (consistent with stabilitv) can be ised.
Total amount of precompression, in. Total rated axial movement of the expan-
Galculation of Forces Acting on Main Pipe Anchors
Installation temperature determined by actual temperatue reading of adjacent piping. Do not use the ambient atmospheric temperature for this purpose.
A main pipe anchor must be designed to withstand the forces and moments imposed upon it by each of the pipe sections to which it is attached. In the case of the installation illustrated in Figure 14-10, the force acting on the main anchor consists of the full line thrust due to pressure , -the the force required to deflect the expansion joint, rated
sion joint, in. Minimum temperature
Maximum temDerature
Fundamentals of Exoansion Joints
'1 0z
I
Figure 14-10, Diagram illustrating the forces that act upon the main
anchor.
Figure 14-11. Diagram illustrating the forces that act upon the main anchor in applications involving straight pipe selections and in applications involving anchors at pipe bends and elbows.
movement, and the frictional force due to the pipe align-
where
ment guides. Formulas for calculating anchor forces in various applications follow. The steps for calculating the main anchor forces for applications involving straight pipe sections (see the center anchor in Figure
14-ll)
are:
: F, : F. : F,nn
Fg :
I 2.
t
Static thrust due to internal pressure' lb Force (ftom data sheet) required to extend or compress the expansion joint, lb Frictional force due to pipe alignment guides. Note: This can be obtained from the manufacturer of the
1. Calculate the firll line thrust:
F":AP where F, : A: P:
Force on main ancho! lb
guides. Static thrust due to internal pressure,
lb Effective pressure thrust area (in.2) taken from data she€t Maximum pressure (p6i) based on the most severe conditions whether design, operational or test
Assuming that the weight of the pipeline and its contents are carried by supports. To calculate the total by any one force imposed on the main anchor pipe section use the following equation:
(F)
F':F"+F.+F"
To determine the net load on the anchor, it is necessary to add vectorially the forces imposed upon it by
each
of the three pipe
sections
to which it is at-
tached.
To calculate the main anchor forces for applications involving straight pipe sections containing expansion joints ofdifferent diameters (see center anchor in Figure 14-12), use the following equation:
4:(Ar-&)P
Piping Stress Handbook
Figure 14-12. Diagram illustrating the torces that act upon the main anchor in applications involving straight pipe selections containing expansion joints of ditferent diameters.
where
A1 :
Effective area, corresponding to the mean diameter of the corrugations of the expansion joint in the larger pipe section,
,q.2
:
P :
m.' Effective area, corresponding to the mean diameter of the expansion joint in the smaller pipe section, in.2 Maximum pressure (psi), based on the most severe conditions, whether design, operational, or test.
Here again, it is necessary to consider the differences in the forces required to extend or compress the expansion joints and the differences in the frictional forces due to pipe alignment guides and supports. Thus, the total force on the center anchor
will
be:
F,":F"+F-r+Fgr-Fgz where F.1
=
F- : Fr1 Fez
: :
Force (from data sheet) required to extend or compress the expaniion joint in the larger pipe section, lb Force (from data sheet) required to extend or compress the expansion joint in the small pipe section, lb
Frictional force (from guide manufacturer) due to pipe alignment guides in the larger pipe section, lb
Frictional force (from guide manufacturer) due to pipe alignment guides in the smaller pipe section, lb
To calculation the main anchor forces for applications involving anchors at pipe bends and elbows (see Figure 14-10) the following calculation must be used. In the case of an anchor located at a pipe bend or elbow, it is necessary to consider the forces imposed by the pipe sections on both sides of the anchor. Thus, assuming that each section contains an expansion joint, the line thrust due to pressure (F" : AP) and the forces F- and F", explained previously, become biaxial components and-must be added vectorially. In addition, the effect at the elbow of
the centrifugal thrust (Fo) due to flow, must be considered. Fo may be calculated as follows:
rp:
2ADV2
0
: Internal where A-slnD e
o
: : : :
ff
area of pipe, DensiU of fluid, lb/ft3 Velocity of flow, ft/sec Acceleration due to gravity, 32.2 fllsec2 Angle of pipe bend
Calculation of Intermediate Pipe Anchor Forces An intermediate pipe anchor must be designed to withstand the force and moments imposed upon it by each of the pipe sections attached to it. However, an intermediate anchor does not have to be designed to withstand the full line pressure thrust, because this force is always absorbed by main anchors or by devices on the expansion joint. such as limit rods, tie rods, gimbals, or hinges. Assuming that the weight of the pipeline and its contents is caffied by supports, the following calculation will determine the forces acting on an intermediate pipe anchor in a pipe section containing expansion joints (see Figure 14-13):
Fre : F.r * where F^1
Frr
Fno
=
: :
Fr1
*
Fn2
*
Fgz
The force (ftom the data sheet) required to extend or compress expansion joinr
EIl
shown in Figure 14-13.
The total force due to friction of all the
pipe alignment guides installed on the pipe section to the right of the intermediate anchor in Figure 14-13. The force required to extend or compress expansion joint EI2 shown in Figure 14-
tJ-
-Fundamentals of Expansion Joints
363
Figure 14-13. Diagram illustrating theJorcesthat act upon an intermediate pipe anchor in a pipe section containing expansion joints.
Fgz
=
The total force due to friction of all tlte pipe alignment guides installed on the pipe section to the left of the intermediate anchor in Figure l4-13.
Nore: The frictional force due to pipe alignment guides can be obtained from the manufacturer of the guides.
If the pipe is the same diameter on both sides of the intermediate anchor, and if the guides on both pipe sections are similar in number and design to F,,z and Fgr, respectively, but opposite in sign, F1a will be equal to zero. However, it is possible that the pipeline may heat up gradually from one end, thereby causing one of the pipe sgctions to expand before the other. It is therefore considered good practice to design the htermediate anchor to resist the forces exerted by one of the two pipe sections (i.e., F1a : F*1 *Fgr).
used only in applications involving lateral deflection or angular rotation resulting from L- or Z-shaped pipe configurations . Proper alignment is very important in the installation of all expansion joints. Expansion joints will not function properly unless the pipeline in which they are installed is securely anchored and guided.
Spacing of Pipe Guides Where an expansion joint is located close to an anchor, the first pipe guide should be located no more than four pipe diameters ftom the moving end. The second should be located no more than fourteen pipe diameters from the first. The recommended spacing for intermediate guides along the balance of the pipeline can be determined from Figure 14-9. For any known pressure and pipe size, the guide spacing can be determined by locating the pressure on the scale at the bottom of Figue 14-9. Follow the pressure line vertically until it intersects the diagonal line for
Pipe Guides and Guiding A pipe alignment guide is a sleeve or frame fastened to some rigid structure that permits the pipeline to move freely along its own axis and limits it to this type of motion. A roller support, U bolt, or pipe hanger, which orily supports the weight ofthe pipe, cannot be substituted for a pipe guide. Pipe guides are required to prevent buckling ofthe pipeline. Buckling is caused by compressive loading on the pipe due to the internal pressure thrust and the flexibility of the expansion joint which causes the pipe to act like a column with end loading. In axial movement applications, avoid using a single pipe-alignment guide because such a guide may act as a fulcrum, which might impose lateral deflection or angular rotation on the expansion joint due to movement of the piping in a dhection other than axial. Planar pipe guides are modified to permit limited movement and/or bending of the piping in one plane. These are
pipe size. From this intersection, follow across horizontally to the guide spacing column (left to right) and read the recommended spacing. For example, the recommended intermediate guide spacing for a 6-in. pipeline containing an expansion joint under a pressure of 125 psig is 43 feet. The first guide should be no more than 24 in. from the expansion joint, and the second pipe guide 84 in.
from the first.
Location of Expansion Joints Wherever possible, an exparsion
joint should be lo-
cated irnmediately adjacent to a pipe anchor. If it is not possible to locate the expansion joint near a pipe anchol pipe guides should be used on both sides of the expansion joint ir accordance with the instructions given in the precedhg paragraphs under "Spacing of Pipe Guides."
Piping Stress Handbook
Figure 14-10 shows the preferred practice in the use of a single expansion joint (EI) to absorb axial pipeline expansion. Note the use of one expansion joint between two main anchors (MA) , the nearness of the expansion joint to an anchor, the closeness of the fimt alignment guide (G1), the spacing between the fint alignment guide and the second alignment guide (Gr), and the spacing of intermediate guides (G) along the balance of the line. Expansion joints should not be located immediately
downstream from turbulence-pnrducing devices (such as butterfly valves). plug valveJ, and su-dden increases in pipe size, mitered elbows, etc. If it is impossible to locate
joint an adequate distanceiway from tubulence producers. the joint slould be equipped with a heavy sleeve. Figures 14-14 and 14-15 show the information required for standard and special expansion joints specification sheets. the expansion
End Connections The type of end connections selected depends upon the operating conditions and the customer's re.guirements. See Figure l4-16 for illustrations. The following is a briefdescription of the various g?es available.
Fixed Flanges (Type SF) The flanges are welded directly to the bellows material without the use of intermediate pipe nipples. In this construction the flanges are in direct contact with the flowins medium.
Fixed Flanges (Type F) The flanges are welded to pipe nipples, thereby provid-
ing greater overall length. In this construction bbth the pipe nipple,s and flanges are in direct contact with the flowing medium.
Combination Ends Expansion joints can be supplied with one weld end and one flanged end to meet installation requirements.
Covers Covers protect expansion joints from mechanical damage and serve as a base for insulation.
Van Stoned Flanges (Type V) The flanges are slipped over the ends ofthe bellows and the bellows material is flared out or "Van Stoned" over the faces of the flanges. The \r'an Stones are roughly equivalent to the raised faces on standard forged steel flanges. The flanges are loose and free to rotate, thus permitting easy alignment with the mating pipeline flanges. This construction is generally used in applications involving product purity or corrosion, because the only material in contact with the flowing medium is the corrosionresistant bellows matefial.
Sleeves Sleeves minimize pressure drop and also streamline the
flow of gas or fluid through an expansion joint, thereby reducing friction losses and turbulence. They are recommended for all expansion joints, except in applications
where high-viscosity fluids such as tar are involved. Sleeves are required whenever the velocity of flow exceeds the following values:
Welding Ends (Type W) The ends of the expansion joint are supplied with pipe suitably beveled for welding to connecting equipment or piping. Standard joints are supplied with carbon steel weld ends. See individual data sheets for grade and type. Other thicknesses, lengths, and grades of carbon steel weld ends are available on order. Where alloy pipe is used, it may be advantageous to use weld ends that are shorter and thinner than carbon steel standards. Consult the factory for recommendations when alloy pipe is used.
Nominal
Size 3 to 6 in. ) 6 in. 3 to 6 in. > 6 in. Pipe
Medium in Pipe
Steam Steam Air (other gases) Air (other gases)
Velocity
of trlow 1,000 ft/min/in. dia 6,000 ff:/min 250 ft/min/in. dia 1,500 fl:/min
Fundamentals ol Exoansion
For additional data use the sheet for supplemental information for special expansion joints. Customer
Inquiry/Job No.
Project
1. Item No.
2. Quantrty 3. Size 4. Flowing Medium+ 5. Flow Velocity 6. Int. Design Pressure, psig 7. Int. Text Pressure, psig 8. Maximum Temperature, "F 9. Minimum Temperature, oF
10. Installation Temperature, oF 11. Axial compression, in.
12. Axial
extension, in.
13. Lateral deflection, in. 14. Angular rotation, deg. 15. Pipe specification 16. Weld end specification 17. Flange specification 18. Type or catalog number 19. Internal sleeves 20. External covers 21. Anchor base 22. Limit rods Use manufacturer's standard unless otherwise specified by purchaser.
23. Bellows material 24. Equalizing ring material 25. Total corrugations 26. Lenglh limitation
If flowing medium is corrosive,
erosive, or viscous explain in detail.
Figure 14-14. Standard expansion joint specification sheet.
Joints
365
366
Piping Stress Handbook
Customer
Project
hquiry/Job No.
1. Item No.
2. External design pressure, psig 3. External test pressure, psig 4. Pipe purge, instr. connection 5. Vibration amplitude 6. Vibration frequency Special Flange Design
7. Material 8. Facing 9. O.D. 10. I.D.
ll.
12. 13. 14. 15.
Thiclness
B.C. diameter No. holes Size holes
Hole orientation
Design Restrictions
16. 17. 18. 19.
Length Maximum O.D. Minimum I.D. Axial force 2O. LatercJ force (Shear) 21. End moment 22. Cychc design life 23. ASME Code partial Data forms required 24. Applicable codes and specifications
Figure 14-15. Supplemental information for special expansion joints, to be used with the standard expansion ioint specitication sheet.
Fundamentals of Expansion Joints
Figure 14-16. End connections.
15 Glossarv .,/
Aging-The term originally applied to the process or sometimes to the effects of allowing a metal to remain at ordinary temperatures. H;at treatment ar temperatures above room temperature for the purpose of accelerating changes of the type that might take place during aging at ordinary temperature is called artificial aging. The changes taking place
during artificial aging are due to the precipitation treatment. Aging is an approach to the attaitment of equilibrium from an unstable condition induced by a prior operation. The fundamental reaction involved is generally one of precipitation, sometimes submicroscopic. The method employed to bring about aging consists of exposure to a favorable temperature subsequent to (1) a relatively rapid cooling from some elevated temperature (quench aging) or (2) a limited degree of cold work (strain aging). Alclad-The common name for a type of clad-wrought aluminum product with coatings of high purity aluminum; or an aluminum alloy different from the core alloy in composition. Alloy-A metallic substance consisting of two or more elements, of which at least one is metal, and in which all elements are miscible in the molten state and do not separate when solid. Alloying elements-Chemical elements constitutins an alloy. In steel. usually rhe elements added to mo?ify the properties of the steel. Annealing-A heating and controlled operation to impart specific desirable properties generally concerned with subsequent fabrication of the alloy, such as softness and ductility. When annealing follows cold working for the purposes of stress removal, it is called stress annealing. Arc welding-Welding accomplished by using an electric arc formed between a metallic or carbon electrode and the metal being welded, between two separate electrodes, or between two separate pieces being welded (also called fusion welding). 368
Austenite-A solid solution in which
gamma iron is the
solvent, having a face-centered cubic crystal structure. Austenitic steel-Steel, which due to its comoosition has a stable structure at normal lroom) timperatures; as for example: the 18-8 types. It is not hardened by thermal treatrnent. Bend test-A test commonly used to determine relativ! ductility of a sample by bending it over a given radius and through a given angle. BilIet-A semi-finished rolled ingot of rectangular or nearly rectangular cross section. Brass-A copper-base alloy in which zinc is the principal added element. Brazing-Joining metals by fusion of nonferrous alloys with melting points above 800"F but below the melring point of the metals being joined. Brinell hardness-A hardness number determined br applying a known load to the surface of the mareriil to be tested through a hardened steel ball of known diameter. Note: Not suitable for measurins the hardness of strip and sheet because of insulfic-ient thick. ness.
Brittleness-A tendency to fracture without appreciable deformation. Carbon steel-Steel in which carbon provides the properties without substantial amounts of other alloyins elements.
Carburizing-Diffusing carbon into the surface of ironbase alloys by heating in the presence of carbonaceous materials.
Case hardening-Carburizing, nitriding, or cyanidinr
and subsequent hardening by suitable heat trearment, if necessary, all or part ofthe surface portion: of a section of iron-base alloy. Casting-Fouring molten metal into a mold or a meta. object so produced.
Cementite-An iron-carbon compound with the chem;cal formula Fe3C often called iron carbide.
--
Glossary Charpy test-A pendulum-q pe impact tesr in which
a
notched specimen, supported ar both ends as a simple beam, is broken by the impact of the falling pendulum. The energy absorbed in breaking the specimen, as determined by the deireased rise of the pendulum, is a measure of the impacr strength of the
metal. Chemical analysis-Separating an allor. into its component elements and identi! in-e them. In quantitative analysis, the proportion of each element is determined. Chromium-A hard crystalline metal used as an alloying element to give resistalce to heat. corrosion, and wear and increase strength and hardenability. Cold working-Permanent deformadon of a metal below its recrystallization temperature. Also defined as plastic deformation of a metal at a temperature low enough to ensure strain hardening. Mechanical properties, such as tensile strength, hardness, and ductility, are also altered. Compressive strength-The ability to withstand compressrve stresses.
, Compressive stress-Stress caused by a compressive load or in fibers compressed by a bending. Cooling stresses-Stresses caused by uneven contraction, external restraint, or localized plastic deformation during cooling. Corrosion-Gradual chemical or electrochemical attack on a metal by atmosphere, moisture, or other elements.
Corrosion embrittlement-Embrittlement in certain al- loys caused by exposure to a corrosive environment. Corrosion fatigue-Combined action of corrosion and fatigue in which local corroded areas act as stress concentrators, causing failure at the point of stress concentration and exposing new metal surfaces to corrosion. The failure is progressive and rapid. Creep-Plastic flow of metal, usually occurring at high temperatures, subject to stress appreciably less than its yield strength. It progresses through first, second, and third stages to fracture or results in stress relaxation. Cyaniding-A process of case hardening a ferrous alloy by heating in a molten cyanide salt bath, thus causing the alloy to absorb carbon and nitrogen simultaneously. Cyaniding is usually followed by quenching to produce a hard case. Ductility-That property of metal which allows the metal to be permanently deformed before final rupture. Elastic limit (limit of elasticity)-Maximum stress to which a metal can be subjected without permanent deformation at the point of stress. Electrochemical corrosion-Localized corrosion that results from exposure of an assembly of dissimilar
349
metals in contact with or coupled with one aa'drc: or of a metal containing microscopic areas di-isr::-
lar in composition or structure. The dissimilar er:ments form short-circuited electrodes. The corr.--
sive medium is the electrolyte, and an electrlc current is induced. which results in the disolution of the electrode that has the more anodic solution potential, while the other is unattacked.
Elongation-The amount of permanent extension in
the
tensile test, usualll' expressed as a percentage of the original gage lengrh. (e.g. , 25 percent in 2 inches). It may also refer to the amount of extension at any stage in any process which continuously elongates a
body, as in rolling. Endurance limit-A limir of stress below which metal will withstand stress without fracture; a specified large number of applications of such stress. Eutectoid steel-A carbon steel containine 0.80% carbon that becomes a solid solution ar anitemoerature in the austenite temperarure range between i ,333.F and 2,500"F.
Fatigue-The tendency of a metal to fracture under conditions of repeated cyclic stressing below the ultimate tensile strength but above the yield strength. Ferrite-A solid solution in which alphas iron is the solvent and having a body-cenrered iubic crystal structure.
Ferritic steel-Steel which, due to its composition, is not hardenable by heat trearmenr. Such stainless types as 405, 430, and 448 are essentially ferritic steels.
Free machining-The property of steel imparted by additions of sulphur, selenium, or phosphorus which promote chip breakage and permit increased ma-
chining speeds. Additions of sulphur or selenium also help to decrease friction between the chips and the tool face.
Galling-The damaging ofone or both rnetallic
surfaces
by removal of particles from localized areas during sliding friction. Galvanic corrosion-Corrosive action occurrins when two dissimilar metals are in contact and arJioined by a solution capable of conducting an electric current, a condition which causes a flow of electric current and corrosion of the more anodic of the f$.o metals. (Also see Electrochemical Conosion.) Gas welding-Welding in which heat is supplied b1' a manually or automatically controlled torch flame of oxyacetylene or oxyhydrogen (also called fusion welding). Grains-Individual crystals in metal. Hardenability-In a ferrous alloy, the propern that determines the depth and distribution of hardness ilduced by heat treating and quenching.
37O
Piping Stress HandbooK
Hardness-Resistance to indentation by standard balls. diamonds, etc.. under standard loais. Also, the degree of cold working. Heading-An upsetting process used to form rivet, screw, and bolt heads in making these products from wire or rod. Heat treatable-Refers to an alloy that may be hardened by heat treatment. Heat treatment-A combination of heating and cooling operations timed and applied to metal or alloy to produce desired properties. Homogenizing-A process of heat treatment at high temperature to eliminate or decrease chemical segregation by diffusion. Attainment of austenite that has a uniform distribution of carbon. Hooke's Law-Stress is proportional to strain in the elastic region. Hot forming-Working operations performed on metals heated to temperatures above room temperature. Hot working-Hot forming above the recrystallization rcmperature.
Hydrogen embrittlement-A brittleness sometimes engendered by contact with plating and pickling solution acid due to absorption of hydrogen by the
metal. The embrittlement is more evident in hardened parts, and can be removed by aging or heating the steel for a prescribed period. Hypereutectoid steels-Steels containing from 0.80% to above 2.0% carbon. Hypoeutectoid steels-Carbon steels containing less than 0.80% carbon. Impact test-A test designed to determine the energy absorbed in fracturing a test bar at high velocity. The usual impact test specimen is a standard size square bar with a V or keyhole type notch. (See Charpy test and Izod test.) Intergranular corrosion-Corrosion that tends to localize at grain boundaries, usually under conditions of prolonged stress and certain environments, and in association with poor heat reating or welding practice that has caused the precipitation of a more easily attacked constituent at these boundaries. Izod test-A pendulum-type of notched-bar impact test in which the specimen is supported at one end as a cantilever beam and the energy required to break off the free end is used as a measure of impact strength. Machinability-The rate and ease with which a metal can be machined. Magnetic particle testing-This method of inspection consists in suitably magnetizing the material and applying a prepared magnetic powder which adheres along lines of flux leakage. On properly magnetized material, flux leakage develops along surface nonuniformities. This method is not applicable to high
manganese or austenitic stainless steels and nonfer-
rous alloys, which are nonmagnetic.
Martensite-An unstable constituent in quenched steel, the hardest of the transformation products of austenite.
Martensitic steel-Steel which, due to its composition, has martensite as its chief constituent after cooling.
The hardenable stainless types are all martensite ste€ls.
Mechanical prop€rties-Those pfoperties that reveal the reaction, elastic or plastic, ofa material to an applied stress or that involves the relationship between stress and strain; for example, Young's modulus, tensile strength, fatigue limit. These properties have often been designated as physical properties, but the term mechanical properties is technically more accurate and therefore preferred. Modulus of rigidity-The ratio of the unit shear stress to the unit angular strain in the elastic range.
Nitriding-A
process of surface hardening in which a ferrous alloy is heated in an atmosphere of cracked ammonia gas or other suitable nitrogenous material thus allowing nitrogen to diffuse into the surfaca metal. Nitriding is conducted at temperatures below the critical temperature range and produces surface hardening of the metal without quenching.
Normalizing-A
process in which steel is heated to a suitable temperature above the transformation range and is subsequently cooled in still air at room teiperature. This operation is used for grain refining or to develop specified mechanical properties.
Notch sensitivity-The reduction caused in nominal strength, impact or static, by the presence of a stress concentration, usually expressed as the ratio of the notched to the unnotched strength.
Permeability-Magnetic permeability is the ratio of the magnetic induction to the intensity of the magnetizing field. Physical properties-Those properties familiarly discussed in physics, exclusive of those described under Mechanical Properties; for example, density, electrical conductivity; coefficient for thermal expansion. The term has often been used to describe mechanical properties, but such usage is not recommended. Pickling-Immersion in dilute acid or other suitable media for the removal of oxide scale from hot-rolled or otherwise sealed surfaces. Plasticity-The ability of a metal to be deformed exten-
sively without rupture. Plating-Deposition of a thin film of a metal or alloy on a different base metal from a solution containins ions of the plating metal.
G Glossary Poisson's ratio-Ratio expressing the relation of strain normal to the applied load as a proportion of direct strain within the elastic limit. Also relates moduli of elasticity ard rigidity. hecipitation hardening-Hardening of metallic alloys, by aging, which results from the precipitation of a constituent from a supersaturated solid solution, usually nonferrous alloys. Also termed as hardening. (See ,{grng.) Process annealing-An annealing operation carried out at a constant temperature just below the critical transformation temperature (also referred to as sub-
critical annealing) . Proof stress-In a test, stress that will cause a specified permanent set in a material, usually 17o or less. Proportional limit-The highest stress at which the material still follows Hooke's Law, similar to elastic
limit. Quenching-A process of rapid cooling from an
ele-
vated temperature.
Radiography-The use of X-rays or gamma radiation to detect internal structural defects in metal objects. . Reduction of area-In a tensile test, the difference between the original cross-sectional area and that of the smallest area ofthe point ofrupture. It is usually stated as a percentage of the original area. Also called contraction of area, it is not applicable to the mechanical testing of sheet and strip. It is also a measure of cold work. Refractory metals-Metals such as tungsten, columbium, tantalum, and molybdenum, which have rela- tively high melting temperatures. Residual stress-Stresses locked in a metal after the completion of nonuniform heating or cooling, working, etc. due to expansion, contraction, phase changes, and other phenomena.
Resistance
welding-A welding
process
in which the
work pieces are heated by the passage of an electric current through the contact area, combined with pressure causing joining by fusion. Rockwell hardness test-This test consists of forcins a cone shaped diamond or hardened steel ball int6 a metal specimen to determine the degree of penetration and. hence. the hardness. Rupture stress-The true stress given by dividing the load at the moment of incipient fracture by the area supporting that load. Salt spray tesl-An accelerated corrosion test in which the metal specimens are exposed to a fine mist of salt water solution. Scaling-Surface oxidation caused by heating in an oxidizing atmosphere. Seam welding-Resistance welding that consists of a series of overlapping spots forming a continuous weld .
37'l
Shear-Plastic deformation in which parallel planes of metal crystals slide so as to retain their parallel relationship. Also called angular elastic strain. Shear stress-Stress acting on a shear plane. Solution treating-A condition of complete solubility resulting in a single phase for compositions of two or more alloying elements at temperatures lower than the solids. Solid solutions may be limited in extent with respect to range of alloy composition or can be continuous, extending throughout an alloy series.
Specific gravity-A numerical value representing rhe weight of a given substance compared with the weight of an equal volume of water. Spot welding-A resistance-welding process in which the fusion is limited to a small circular or oval area. Stabilization-Prevention of the formation of carbides at the grain boundaries of austenitic stainless steels. Dimensional control of nonferrous castines. Strain-Deformation expressed in units pe-r unit of length produced by strain. Strain aging-Load per unit of area. Stress concentrator or stress raiser-Any notch, scratch, sharp change of contour, slot groove, hole, defect, or other discontinuity in an engineering material that has the effect of concentratins the stresses applied to the material or generated in-it by heating or cooling. Stress corrosion-Corrosive action induced and accelerated by the presence of stresses.
rupture-A test to destruction at elevated temperature, by which it is possible to determine the stress that causes failure at a given temperature and with the lapse of a given period of time.
Stress
Temper-A condition produced in a metal or alloy by mechanical or thermal treatment and havins chancteristic structure and mechanical propertiei. Temper brittleness-Brittleness that results when certain steels are held within or slowly cooled throug! a certain range of temperature below the transformation range. The brittleness is revealed by a notchedbar impact test at room temperature or lower temperatufes. Tempering-The process of reheating quench hardened or normalized steel lo a temperature belo*. t}le rars-
formation range and then coolhg at an) rare desired. This operation is frequently called sress relieving. "Drawing" is synonymous xith temperhg. but the latter is the preferred usage. Tensile strength-The maximum load il pou_n& ger square inch, based on the origiml cro=.-^.e.-tibn. which may be developed in rensile resrilg. isee a.L:o Uhimate Strength.)
372
Piping Stress Handbook
Thermal stresses-Stresses in metal, resulting from nonuniform temperature distribution.
Through-hardening-Thermal description of alloys that harden completely, so the center of a hardened section exhibits hardness similar to the surface. Torsion-Strain created in an object by a twisting action or the stresses created by such an action. Toughnesl-Ability to absorb considerable energy before fracture, usually represented by the area under a stress-strain curve and therefore involvins both ductility and strength. [Jltimate strength-The maximum strength or stress before complete failure or fracture occurs.
Vacuum melting-A process by which alloys are melted rn a near pertect vacuum to prevent contamination
by atmospheric elements. Vickers hardness test-An indentation hardness test utilizing a diamond pyrarnid and useful over the entire range of common metals.
process of joining metals whereby partial melting of the parent metals occurs except in the case of pressure welding when heating is only sufficient to cause recrystallization across the interface.
Welding-A
Yield point-The load per unit or original cross section at which a marked increase in deformation occurs without increase in load. In stainless and heat-resisting steels, this occurs only in the martensitic and ferritic chromium types. In the austenitic stainless and heat-resisting steels, the yield point is the stress corresponding to some definite and arbitrary total deformation, permanent deformation, or slope of the load deformation curve; this is more properly termed the yield strength.
Yield strength-Stress corresponding to some fixed permanent deformation such as 0.1 or 0.2% offset from the modulus slooe.
aa
Index
Air-cooled heat ex changerc, 263-264 Allowable expansion stress range, 2, 8-9, 11, 13 Allowable external forces and moments (tables), 264
Allowable internal pressure stress,
1l Allowable loads, 257 -264 Allowable longitudinal stress, 9 Allowable momenlq 257 -264 Allowable pipe deflection, 314 Alowable pipe span, 314 Allowable resultant forces and moments (table), 258 Allowable shear stress, 11
Disffibution Piping), 11, 13, 15, 251
ANSI/ASME Code 831.9 (Building Services Piping), 15 ANSI/ASME Code 831.10 (Cryogenic Piping), 16
ANSI/ASME Code B31.11 (Slurry Piping), 16 ANSI/ASME Code for Pressure Piping, 177 API Code 610, (steel pump force, moment, and stress limitations), 257 -258 API Code 661 (design criteria for
air-cooled heat exchangers),
263-2&
Allowable span, 314 Allowable stress(es), 8-11, 257 -264
ASME Boiler Code, 177
-
Barlow formula, 177 Baseplate support, 258-259 Bellows, 356
range (tables), 38-111 Allowable working pressure, 177,
250-251 Anchor(s), 122, 345, 356, 360-363 forces and moments, 3 intermediate, 362-363
main, 360-362 Angle valves cast steel, 307
flanged,302 ANSI/ASME Code 816.9, 120 ANSI/ASME Code B31.1 (Power Piping), 3-6, 14, 257 , 260 allowable stress range (tables),
38-'72 ANSI/ASME Code 831.2 (Fuel Gas
Piping),
14
ANSI/ASME Code 831.3 (Chemical Plant and ktroleum Refinery Piping), 6-7, 14, 25'l -260 allowable stress range (tables),
73-111 ANSI/ASME Code 831.4 (Liquid Petroleum Transportation Piping
, 9, 11, 14-15 ANSI/ASME Code 831.5 (Refrigeration Piping), 15 ANSI/ASME (DOT) 831.8 Code Systems),
7
(Gas Transmission and
Bellville (disc) springs, 324 Bending, 123 maximum, 314 stress, 1, 260 Bends, 120, 3ll-323, 350 Boiler external piping, ,14 Bracket supports, 324 Branch connections , ll4, 253-255 Branch reinforcement, 252-256 Buckling, 356, 363
Building Services Piping Code (ANSr/ASME 831.9), 15
Coil springs, 324 Cold springing, 2-3, 356-358 Combination ends, 364 Compliance codes, 3- l6 Components of pipe, 299-313
clearances,357 Compressors, 262-263 Connections
branch, 114, 253-254 end,364 purging, 358 vertical exhaust, 260-261 Cons^TLlt sprjng supports. 327,
load table, 338-341 Corrosion,359 Covers, of expansion joints, 364 Creep, 2, 177 Cryogenic hargers, 327 , 345, 349 Cryogenic Piping Code
(ANSr/ASME 831.10), 16 Cycle life expectancy, 2, 358-359 Cylindrical vessels, 122- 176
Deflection, 324, 329 lirnits of, 314-315 Design criteria air-cooled heat exchansers.
263-264 compressors, 262-263
pipe suPports, 324-350
pumps,257-259 turbine drivers, 260-262
Butt-welded fittings, 303
Design factor
Caking,358 Centrifugal steel compressor, 262
Direct longitudinal sness. I Direct shear stress, 2 Disc (Bellville) springs. 3?4
Chemical Plant and Petroleum Refinery Piping Code (ANSI 831 .3) , 6-7 , 14 , 257 -258 allowable stress range (tables),
73-111 Circumferential bendhg, 123 Circumferential stress, 2 Coefficients of thermal expansion
(tables),2-32
373
F,
13
Discharge nozzles. 257 -259 Distortion energy (von Mis€sl theory, 2 DOT Code B31.8. 13. 15. 51 Double expansion joim- 15l-351 Dummy legs, 324
ll.
Elbows, 112, 118-lll Electric generadng pla s. l-t
374
Piping Stress Handbook
End connections, 364 Ends, 121, 364
i
loops, 351
Erosion,359
factor (table), 120 Industrial plants, 14 Insulated anchors, 345 Insulated pipe supports, 348-350 Insulation of pipe, 299-300 Intermediate pipe anchor, 362-363
spans,314-320 rypes of, 325-329
Expansion devices, 351 Expansion forces, (tables), 278-290 Expansion joints, 351-367
anchors,356 application, 360-363 cold springing, 356 corrosion, 359
Internal sleeve, 358
k factor (table), 120, 327
erosion,359
Load adjustment, 327
265-291
't2
specified rninimum yield strength,
forces and moments, 356 guides, 356, 363-364 precompression, 360 thermal expansion calculations,
Loading, sustained external, Loads,257-2&, 326,357 Leaf springs, 324
359-360 types,351-355
Piping Systems Code (ANSUASME 831.4), 7-1r Longitudinal joint factor t, 13 Longitudinal stress, 1-3, 5,7,9,
Factors, k, h, i (table), 120 Flanged elbows, 118 Flanged valves, weight of (tables)
angle,302 check (swing), 301 gate,300
globe,30l Flanges
fixed, 364 forged steel, 303-305 weight (tabl€), 302
Flexibility, 122 Flexibility factors,
1
12
flanged elbows, 118- 119 miter elbows, 120-121
Flexible piping, 351 Flexible support, 324 Force reduction, 356 Forces and moments,3, 122,
257,26/.,356,358 Fuel Gas Piping Code (ANSI/ASME
83r.2),
14
Gas Transmission and Distribution
Piping Code (ANSI/ASME (DOT) 831.8), 11- 15, 2s1 Gimbals, 355, 358 Globe valves, 307 Guides, 356, 363
stress, l-2, 5-7 compliance codes, 3-16 simplified solutions (tables),
Joint movements, 351
cycle life expectancy, 358-359 end connections, 364-367
Expansions, offset lensths reouired (tables), 266-267' Expansion stresses, 2-3, 6, 13 range, 8-9, 11 External mechanical forces, 258 External pressure, 5
materials, properties (tables), 33 properties (table), 292 -298
3
Liquid ktroleum Transportation
tl,
13
Machining, 112 Main pipe anchors, 360-362 Maximum allowed wall thickness, 6 Maximum allowable resultant forces
supports. See a/so Supports. tor cryogenic service, 329, 345 design and selection, 324-350 flexible, 324, 356 insulated, 348-350 nsid, 324 Piping restrained, 11 three-dimension, 2 two-anchor, 3
unrestrained,9 Piping codes, 3-16 Piping wind loads, 320-323
(tzble),324-325
Planar piDe euide. 356. 363 POWER,FOAMTM, 345-347
and moments, 258 Maximum bending, 314 Maximum def lection, 324
Fower Piping Code (ANSI/ASME 831.1), 3-6, 14, 257 , 260 Precompression, 356, 360
Maximum radius, 112 Maximum shear (Tresca) theory, 2 Mechanical forces, 258-259 Minimum radius, 112 Minimum thickness, 177 Miter(s)
Pressure
bends, 120 elbows, 120-121 spactng, 112, 120-121
welding,308-309 "Modified lame" formula, 177 Modulus of elasticity (table), 33,257
external, 5
working, 176, 250-251 Pressure-balance expansion, 354 Pressure design, 5 Pressure stress, 6-7, 11
rutios,
177
, 250-256
(tables), 178-249 Prestressing,3 Pumps, 256-258 Purging connections, 358
Moments. See Forces and moments
Nominal wall thickness, 11, 111, 177
Nozzles, 122-123
flexibilities, 122-
176
loadings (table), 257 snction, 257 -259 Occasional longitudinal stress, 6 Offset lengths required (tables),
266-267
Oil piping,
14
Radial flexibility, 122 Radial stress, 2 Refrigeration Piping Code
(ANSr/ASME 831.5),
15
Reinforcement area, 253, 255 Reinforcement zone, 255 Required area for branch connections,253 Required yield strength, 350-351 Restrained piping, 1l Resultant applied forces and
moments, 258 Pedestal support, 258-259 Pipe(s)
Hangers, 324, 327, 345, 349 Heat exchangers, 263-264 Heating plants, 14 h factor (table), 120 Hinged expansion joint, 355, 358
anchors, 356, 360-363
Hot \pater piping, 14
insulation, 299-300
Resultant bending stress, 6-7 Resultant shear force, 259
deflection, 314
Right Rigid Rigid Rigid
guides,356,363
Rotational nozzle flexibilities
bends,311-323,351 components, 299 -313, 357
angle nozzles, 253 ends, 122 hanger, 324 support, 324
(tzbles), 122-176
-
{d ---r
Index {Is Saturated sream. properties
(tables). 3-l-36 -
Self sprineins.
l
Shaft displaciment
of
. 258-259
Shape factors. 321 Shoe suppon. 3!-1 Shear strissSingle expansion ioint, 351
l
Sleeve.356.358,364
Slurry Piping Code (ANSt/ASME 831.11). t6 Spans, allouable, 313. See also ptpe sPans.
Specified rninimum yield stren eth (SMYS.,, 9, Spring rate of nozzles, 122 spnng suppons, 324_341
ll
Stabiliry,356
Standard hangers, 327
standard terms, 3_4
Stress(es). .te€ aho piDe stress.
allowable. 8-l l. 38--l I t, 257_264 deadload, 314 intensificarion factors, l. I12. I L4-121
limits,314-315 pressure/stress r atios,
prtmary, 2
lj 7 _256
range, 2 shear,
ll
Structuraj supports, 325
suctron nozzles, 257_259 Supports. 324-325, 327, 342. 356. Slee a/so Pip€(s) supports. baseplare. 258-259 pedasral, 258-259
-'
Support load, 345 Sustained longitudinal stress. 5 )usralned-pIus_thermal expansion stress, 6 Sway brace support, 327. 342 Swing check v-aives, 30gTemperature derating factor terms, standard. 3_4
Thermaf expansion, 2-3,
359-360
f,
l.]
5-6. 324,
_.coefficienrs of (tabtes), 2_32 r nerma movements, 351 Three-dimension pipine. 2 Three-weld-miter elbo;s. 12 I tte roos, JJ6 Torsional stress, 2 Travel stops, 327 Tresca (miximum shear) theory, 2 rwo-anchor Ptplng systems, 3
turbines,260-267
Thrbulence-producing device, 364
Uni{orm Building Code, J2l unrtorm wind loads, 323
U.S.A. Standard Buildins Code R^equirements for Deiign Loads. Universal expansion joint, 352_J54 unrestratned ptplng, g
rtical exhaust connecrion. 160_16 l vrbratron control, 342_ J4.t Von Mises (distortion energr r l.betrrVe.
2-'
Wall thickness pressure stress, 7. 251
wall thlckness
maxrmum allowable. 6
nominal, l l, l12, required, 177 Weather,35l
177
Wedge gate valves. 306 Weld elbows, l12 Weld-end valves (tables)
angle,302 check (swing), gate,300 globe,301
301
Welding ends, 363 Weld joint factor E,
l0
Wind loads, 320-321 (table),322-323 Wind pressure, 320
Working stress, 172
y values (tables), 177_250 y : Q Garlowy, 178-195, 250
y=
Van Stoned flanges. 3& Variable spring iupports, 324_327 load tabte, 328
y
U.4 (modified lame). 196_214,250 = 0.5 (average diameter).
y
:
2t4_231, t50
0.7 (creep), 232_250
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