Solutions To Design Of Weldments - Blodgett

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The serviceability of a product or structure utilizing this type of Information Is and. must be the sole responsibility of the builder/user. Many variables beyond the control of The James F. Lincoln Arc Welding Foundation or The Lincoln Electric Company affect the results obtained In applying this type of Information. These variables Include, but are not limited to welding procedure, plate chemistry and temperature, weldinent design, fabrication methods and service requirements.

APPLYING THE SOLUTION GUIDE The Lincoln Electric Csmpany ,seminars offer an excellent opportunity for engineers to discuss problems that are common to many different areas of design. Orner W. Blodgett has compiled solutions to these problems and others that have been generated for companies in an attempt to share the ideas that have been gained. In order to limit this publication to a reasonable number of pages, only a portion of each design is shown and each full sheet has been reduced 75% to allow up to four problems per page. Inclusion of a design problem does not necessarily mean approval of the design, in some cases the author was asked

to estimate the capacity of thfl ·'iJJ!Idment based upon the size of existing welds. In other cases, a failure was involved and the weldment was analyzed to determine the cause and a correction was suggested. This booklet is not meant to be critical of any design. The table of contents lists problems by subject matter and the end of each problem is noted by a bold rule line. Readers desiring related information should refer to Design of Weldments published by The James F. Lincoln Arc Welding Foundation.

•

Richard S. Sabo

Manager of Educational Services

TABLE OF CONTENTS WELD ALLOWABLES- PROPERTIES OF WELD Permissible Stress on Welds Types of Welds . . . . . . . Welds Treated as a Line . . AISC Fatigue Allowables .

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CIRCULAR WELDS Moment of Inertia & Polar Moment of Inertia of Welds Weld on Trunnion . . . . . . . . . . . . . . , . . . . . . . . . . Circular Welds in Bending . . . . . . . . . . . . . . . . . . . . Coupler in Steel Mill Roll . . . . . . . . . . . . . . . . . . . . . Circumferential Welds in Bending & Torsion . . . . . . . . Butt Weld of Auger . . . . . . . . . . . . . . . . . . . . . . . . . Circumferential Welds in Torsion . . . . . . . . . . . . . . . . Circumferential Welds in Tension . . . . . . . • . . . . . . .

1 2 3 4

5 6A 6C 7 BD 9 10 11 B

WELD SIZE EXAMPLES Fillet Welds - Parallel Loading . . . . . . . . . . . . . . . . . 11 C Fillet Welds -Transverse Loading . . . . . . . . . . . . . . . 11 D Base of Signal Tower· . . . . . . . . . . . . . . . . . . . . . . . . 12A Circular and Elliptical Welds in Tension . . . . . . . . . . . 12B Fillet Welds on Gusset Plate . . . . . . . . . . . . . . . . . . . 12C Circular and Elliptical Welds in Bending . . . . . . . . . . . 12D 750 Ton Press Frame . . . . . . . . . . . . . . . . . . . . . . . 13A Lugs on Fork of Lift Truck . . . . . . . . . . . . . . . . . . . 13C 3 Dimensiona~ Welds on Storage Rack . . . . . . . . . . . . 130 Bracket$ on 400 Kip; Extrusion Press . . . . . . . . . . . . . 14A Bracket on D~iU Rig- 200 Kip Load . . . . . . . . . . . . . 14D Transferring a Moment . . . . . . . . . . . . . . . . . . . . . . 15C. Welding Attachment to Hold-Down Platten 17A (temperature difference) . . . . . . . . . . . . . . . . . . . Sign on Tension Flange of Girder (stress difference) .... 17D Bracket on a 3 High Steel Mill Roll (stress difference) ... 18A Critical Fillet Weld Size and Shape . . . . . . . . . . . . . . . 18C Welds on a 1000 Ton Press . . . . . . . • . . . . . . • . . . . • 19A Welds on a Crane Base . . . . . . . . . . . . . . . . . . . . . . . 19D Link Support Bracket of Injection Molding Press ..... 20 Links on Fork Lift Truck • . . . . • . . • . . . . . . . . . . . . 21 Attachment for Ripper Tooth on Bulldozers . . . . . . . . 23 Welds on Rail for Rollers . . . . . . . . . • . . . • . . • . . . . 24D Stresses in Shell of Pulley . . • . . . . . . • . . . . . . . . . . . 25 Welding'bf Masonry Plate on Spandrel Beam . . . . . . . . 30D Stresses in Double Discs of Roll . . . . . . . . . . . . . . . . 31 Welded Pulley Block . . . . . . . . . . . . . . . . . . . . . . . . 33D Socket and Shank of Coal Auger . . . . . . • . . . . . . . . . 35 Welds in 7,145 Kip Hold Down Box Ring . . . . . . . . . ; 38 Welds in Support Box Ring of Basic Oxygen Furnace .. 41 Flange Welds of Vibrator . . . . . . . . . . . . . . . . . . • . . 43D Welded Rock Crusher . . . . • . . . . . . . . . . . . . . . . . . 45

LONGITUDINAL SHEAR Crane Runway Girder . . . . . . . . . . . . . : . . . . . . . . . 49A Fabricated Columns with Wind Moments ........... 49D Plug Welded Cantilever Beam . . . . . . . . . . . . . . . . . . 50A Platten for Press . . . . . . . . . . . . . . . . . . . . . ...... 50B Built-Up Ends of Continuous Beam . . . . . . . . . . . . . . 50C Outrigger Beam of Mobile Crane . . . . . . . . . . . . . . . . 50D Longitudinal Shear - 6 Sided Section . . . . . . . . . . . . 51 Longitudinal Shear'- 8 Sided Section . . . . . . . . . . . . 52A Longitudinal Shear -Circular Section . . . . . . . . . . . . 52C CURVED MEMBERS Basic Curved Beam Formu Ia . . . . . . . . . . . . . . . . . . . 53 Curved Beam Problem . . . . . . . . . . . . . . . . . . . . . . . 54A Welded 2 Ton Press . . . . . . . . . . . . . . . . . . . . . . . . . 55D Transfer of Moment Into Press . . . . . . . . . . . . . . . . . 56C Weld Stress in Curved Portion of Lamp Frame . . . . . . . 58 TORSION Torsional Members . . . . . . . . . . . . . . . . . . . . . . . . . 59A Torsional Resistance- Closed Tubular Sections ...... 59B Torsional Resistance- Diagonal Bracing . . . . . . . . . . . 59C Frames Under Torsion . . . . . . . . . . . . . . . . . . . . . . . 59D Member Failing in Torsion . . . . . . . . . . . . . . . . . . . . 60

•

TUBULAR MEMBERS Welds for Tubular Structures . . . . • . . . . . . . . . . . . . 61 Tubular Structures Fatigue Allowable . . . . . . . . . . . . 63 Dihedral Angle Charts . . . . . . . . . . . . . . . . . . . . . . . 64 Example of Tubular Connection . . . . . . . . . . . . . . . . 65 SHOCK LOADING Shock Loading- Basic Information . . . . . . . . . . . . . . 67 Shock Loading- Basic Formulas . . . . . . . . . . . . . . . 68 Girder to Absorb Energy • . • . . . . . . . . . . . . . . . . . . 69A Welds on Car Bumper - 5 MPH Shock Load . . . . . . . . 69B Ore Striking Bumper Plate . . . . . . . . . . . . . . . . . . . . 69C Weld on Trailer Hitch- Shock Load . . . . . . . . . . . . . 72 Trailer Hitch - Road Conditions . . . . . . . . . . . . . . . . 74 Axle Mounting Bracket . . . . . . . . . . . . . . . . . . . . . . 75D Welded Eccentric for Vibrator . . . . . . . . . . . . . . . . . 76 DISTORTION Distortion of Spandrel Girder . . . . . . . . . . . . . . . . . . 77 A Diametrical Shrinkage of Butt Weld on Pipe . . . . . . . . 77B Angular Distortion- Single Vee Groove Butt Weld .... 77C Angular Distortion -Single Bevel Groove Butt Weld ... 77D Distortion of 90 Foot Long Bars . . . . . . . . . . . . . . . . 78A Longitudinal Shrinkage of Girder . . . . . . . . . . . . . . . 78C

•

•

Stress Allowables for Weld ·Metal

I

I

Permissible Stress

Type of Weld Stress

COMPLETE PENETRATION

~ROOVE

Required Strength Level I 1 )(2) WELDS

Tension normal to the effective throat.

Same as base metal.

Matching weld metal must be used. See Table below.

Compression normal to the effective throat.

Same as base metal.

Weld metal with a strength level equal to or one classification (1 0 ksilless than matching weld metal may be used.

Tension or compression parallel to the axis of the weld.

Same as base metal.

Shear on the effective throat.

.30 x Nominal. Tensile strength of weld metal (ksi) except stress on base metal shall not exceed .40 x yield stress of base metal.

Weld metal with a strength level equal to or less than matching weld metal may be used.

PARTIAL PENETRATION GROOVE WELDS Compression normal to' effective throat.

Designed not to bear - .50 x Nominal Tensile strength of weld metal lksi) except stress on base metal shall not exceed .60 x yield stress of base metal. Designed to bear. Same as base metal.

Tension or compression parallel to axis of the weld. 131 Shear parallel to axis of weld.

Tension normal to effective throat.

(41

Same as base metal. .30 x Nominal Tensile strength of weld metal lksil except stress on base metal shall not exceed .40 x yield stress of base metal.

Weld metal with a strength level equal to or less than matching weld metal may be used .

.30 x Nominal Tensile strength of weld metal lksil except stress on base metal shall not exceed .60 x yield stress of base metal. FILLET WELDS

13)

·stress on effective th.roat, regarle&s of direction of application of load.

.30 x Nominal Tensile strength of weld metal lksil except stress on base metal shall not exceed .40 x yield stress of base metal.

Tension or compression parallel to axis of weld.·

Same as base metal.

Weld metal with a strength level equal to or less than matching weld metal may be used.

PLUG AND SLOT WELDS Shear parallel to faying surfaces.

.30 x Nominal Tensile strength of weld metal lksil except stress on base metal shall not exceed .40 x yield stress of base metal.

Weld metal with a strength level equal to or less than matching weld metal may be used.

(1) For matching weld metal, see AISC Table 1.17.2 or AWS Table4.1.1 or table below. (2) Weld metal, one strength level ( 10 KS I) stronger than matching weld metal may be used when using alloy weld metal on A242 or A588 steel to match corrosion resistance or coloring characteristics (Note 3 of Table 4.1.4 or AWS 01.1 ). (3) Fillet welds and partial penetration groove welds joining the component elements of built up members (ex. flange to web welds) may be designed without regard to the axial tensile or compressive stress applied to them. (4) Cannot be used in tension normal to their axis under fatigue loading lAWS 2.5). AWS Bridge prohibits their use on any butt joint (9.12.1.1 ), or any splice in a tension or compression member (9. 17), or splice in beams or girders (9.21 ), however, are allowed on corner joints parallel to axial force of components of built up members ( 9.12. 1.2 ( 21. Cannot be used in girder splices (AISC 1.1 0.8).

MATCHING WELD METAL AND BASE METAL Weld Metal

BOor 70 A36; A53, Gr. B; A106, Gr. B; A131, Gr.A,B,C,CS,O,E;A139,Gr.B; A381, Gr. Y35; A600, Gr. A, B; A601; Type of A516, Gr. 55, 60; A524, Gr. I, II; Steel A529; A570, Gr. D, E; A573, Gr. 66; A709, Gr. 36; API 5L, Gr. B; API 5LX, Gr. 42; ABS, Gr. A. B. D, CS, OS, E

70 80 A131, Gr. AH32, OH32, EH32, AH36, A572, Gr. 60, DH36, EH36; A242; A441; A516, Gr. 65; A537, 65; 70; A537, Class 17; A572, Gr. 42, Class 2; A63, 45, 60, 55; A588 (4 in. and under!; Gr. E A595, Gr. A, B, C; A606; A607, Gr. 45, 60, 55; A618; A633, Gr. A, B. C, D (2·1/2 in. and under); A709, Gr. 60, 60W; API 2H; ABS Gr. AH32, DH32, EH32, AH36, DH36, EH36.

I • 1•

100 A614 [over 2·1/2 in. (63 mmi];A709, Gr. 100, 100W [2-1/2 to 4 in. (63 to 102 mmll

110 A514 [2·1/2 in. (63 mml and under]; A517; A709, Gr. 100, 100W [2·1/2 in. (63 mml and under]

J'n.LU IIBUI LOliDI!D IR .111ft' DDIIC'rlOJ!

• i ! . l l - l e - weld 1.8 the .... ae baoe metAl. llatcbi"'J -ld ....tal .....t bl lleed.

Shall not overatzeae the baae metal.

PAR'l'IAL PENB'lRATIOII G!!90VB

!!1!LDS

SREAII (pulled parallel)

TBIISIOII (pulled aomal)

Allowable ahear on weld • • 30 BXX Shall not overatreaa baae metal in

Allowable cenaioa om weld • • 30 BXX Sball DOi: overatreaa base metal 1D

shear...

• .fo 0y

tension.

AllowUle ahear 011 weld • .30 EXX om tbroat. Lover atre119t:h weld: metal may be used at ita lower allowable.

• • &0 0y

Sball DOt overat.reaa the base metal in abear.

L.ower atrength weld metal may be uaed at ita lower allowal»le.

•

'l'RIJSS JOINT - COMPLE'l'E PBIIBTRATIOII GROOVB NELliS

71\e teDaion COOipOAeftt would

SHEAR PARALLEL TO AXIS OP !!§I,D

require matahl D9 ""lei 118tal.

1.~1: ~M" '•

AllowUle on ftlcJ is the aame aa baae -tal. Ma'tahl119 weld metal 'IIU&t be ueed ..

p~n•.tnJ'tlotJ

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Allowable shear ~ veld • .30 2XX on Uroat. Lower atrenvth weld metal 11ay be u.secl at lta lower allowUle .. C9!!PI!BSSIOII IIOlUUIL TO AX.IS OP IIELD

Shall not overat.reaa the base metal in ehear.

llot reooaended uleaa

absolutely 118CBeaary blcauee of exce•'l.ive

u01111t of welcl metAl.

TBHSIOR OR COMPRBSS!O! PAJW.L!L

fO AXIS OP tmLQ

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klbe fillet welded

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but shall not exceed steady allowables

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allowable fatigue stress

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fatigue stress O.r or T., = allowable range of stress, from table K to connectton of any rolled sectKlM

Curved arrow indicates region of application of fatigue allowables - - Straight arrows indicate applied

forces Grind in the direction of stressing only (when slope is mentioned (ex. 1 in 2-1/21 this is always the maximum value. Less slope is permissable.

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set)

Omin Mmin Fmin Tmin Vmin =--=--·--·--·-"max Mmax

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S = shear T = tension R = reversal M = stress in metal W " stress in weld 1 = allowable steady shear stress

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AISC allowable fatigue stress (asr and 75 rl (kips) -also used by AWS Structural Welding Code (Sect. 8- Building) •

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Vma•

c

A

z

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nut aoment of inertia ~or the aeatton.

of a croas aectlon 1s referenced

to an axis vhlch

It ie aa though the plana or tbls sect.lcm t.eDda

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revol•e about

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·tht.a ax,s, aee figure (a)., The basic moment ot tnert18 la a un.lt area mult.lplle4 b7 the square or tho dlet.anee or this al"'!a 1.o the reterer:ace ala, see tlgure (d). Fisurea (a) and (d) reproeaent

t.he

moment ot i.nert.la about the (x-x) ax1a, and ripee

(b) aad (e) represent the moment Of ioertl.e about t.be (7-y) axle.

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oJ.' the oroos secUcm..

ot a erase sect.lco ls referenced to an axil normal to the It 11 as tbou.lh the plana ot thLs

about this axis, see figure (c). ~t~~lt.lpll.ed ~

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teads to rotate

The baaic polar J¥1msnt ot inertia is a unit area

the square of tbe rolar dlet.Gnce·

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this area (~), see tltJ"U"8 (t).

Since the SQU.Ve or tbis polar distance la equal to the SWII Of the &q\Y:res or the

y

d1atances to t.he (x•x) and (;y-7) axea 1 lt. can be shown th11t thenpoler moment ot lnertla is equal t.o the sum or the moments or tnertla taken about cny t.vo axes at 90° to ••ch

other. S!nce axea (x-x) and Cr•r) •re 90° to etch oth•1 the

or the moment ol

8WII

(r-r) axlllll 1s equal

inert.le aboat t.he (x-x) axla and the moaen.t ot lnertla about the

X

to the polar moRent or inertia about axis (s-z) 1 normal 1.o both axes (x-.a:) and ()'•7).

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bave a condttlOQ la vbit:Jb the axU ot revGlutlon neit.her Uu 11 tn tha

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plane or the section (1110ment or lDertl.a) nor 18 normal to the plrme ot the aect ion (polar

In tbe tollow1ag welcled aGMectt.on., oCOISlatlng or Wo el.ra.WI!'erentl.el velds 3o1n1n1 ~

trunnion ot a abaft

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tvo end dlsce• tbe a.ls (z-z) F&&slns thi'OUSb the center ot snvlt-7

or tbe welda 1s t.ba az1a abou:t vhich the two velds tend to rot.at.e because ot t.be beodlns act.lon or the t.runnlcD (vartloal bearlns 1"88ctlan X the moment an.).

Notice that the

IROIIMJft~

Y1r "r1)

k weldi)(z'llr) J. • C! 1t r "t 'l'lrr( ~)' • arrr\'!T"rb"-

U ve cCilSider tbe t.vo clrcumterentl•l-velds (a) ~ (b) u conoentr~Wd at t.helt aent.era or aravity, th8D lt ls seen tb3t the ret'ereaoa uls (z-•) Ls ncmu:l to the plane 01' these polar

~o~.se the·pqr«lle/ aJttr

r .. + A("A/ A~

vlthln eltber plane.

:;~ect10JI 1

First f,h,J

Iz,= (2wetcls

retarence axis {z-z) lies parallel to tbe plane of eaah veld. P'o-.ap, but does not lle

'"4&ld groups, therefore ve could. call tbls properf.J' ot the

~

a66ut tUI'S{z,-z,) t:hen -shift para lie I t!J d1ste1ncP or(%.) -ilJ eo(i~ (2-z),

theorem.

mollldlt or lnertla),

1 Jz =

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2.?(.,5' 1

ef

uertt~l component

beadmq r • !1ft. jlooorJO 1/n•I'S•nXJtn) 2'1'-S" ,;i~

:r.

rv

DLI()'> d,,.

· -,-, ,• 7111 /{) ~ /,'I •5 ,;,

"

vert iea.l 'hea.r

'"h.:t•4~<e "u..-l.re for f.'llet welrl1 a~ •-t•ID~cyoM Wid r
.~

bto),!l,C"·""'

---·

-·~-----------------

r . . • r2, + A[i)~ .r~,· {i. w~ld~{lr"'l~ A" {z we.lcls)t2'11'r)

B low • - • 'Ills tnlllnlao tllmo "' 200 IPII ond raqlllrea 100 81' to drlve 1•,

HP .. 43.oooXtco). '3/ T " c.'!lpoo RPfo\ Zoo ' pro pert'( of. weld

fi'OD

T

'ltd • 'It 'I ~

J~ = T .

~or

•

one

·

'

1 "

$

DLV p<~~e 'l,"J•I'b~
I

2

"'

Z 'lt't" ~ f

't'rtr(_j}'l.

~ liO. 27 in.., we(c{

Tz = 11"1 ( 2 r .. + b")

or

Ex&~mele

"" weld

ft • J.~ TC. /1>t,S'OO ,;, ll>s){2 in)_ /OO,fi' /h"S -

·--~·-·

"l.Z-8

!6

J.· z.(so.2'1)~ IIJO,fi'itl'(t~Jo"J•/ds) u.nit ~ore e

.,.. , .. e l)W'i> p"-'le

6. z ~. 'f

'itt;,

M ..

~ .. ; 111 • In /
i" tu:tr<:& he.au.., pipe • oD• :~.-zS'• r='f.lur

bw 11. 1rr A• /l.e I • 10~

E?Owe/d

in"

in

4

t.•.!lJin

r

~· )'!7.'!fl.r,;.

r~.·

I'IID.S t;',p

~""" ~.· '9'10. "!I,,,;, f,·

(.H..ttU.It,;

• 6

A

•

c

It: is cU.ffiCNll: ~ give a dir..,t .,...,.. on the design of thie welded coupler. Although the ral:ed of the clriving 1110~ land Ua RPHI are given, there is aome quenion in my mind aa ~ whether this ie th8 11uiJDIIDI ~rque or c:oulcl U: raverae inatant:ly? Could this be a ahoal< loed? COUld thare be any miaalig-nt in this C011pler7 If so, thia aould introdllaa very high bending 11101181\t& on tbe eo~~plar.

----...::.-.:.:::

M

__ ..... ----

I am DDt certain ao ~ the type of applioation of the load steady, fatigue, or oboe!<. U fatigue, then the life axpeoted

!..r:r ....::.~~r.' : l d"=.!~e.~~.::'"::: :r~=~o::.::~ of the wlda, Por erample, with B70 weld metal frOID a valaa going

f • u,aso v for ateady loads all the way dovn ~ F • 3180 v for a complete reversal fatigue 1oa4 over 2, DOO ,ooo cyale•.

of

On aheat l&l , I have checked the fillet - l d le9 alae for ~oion only. 'fbe aiae,variea from two 3/8• fillet• Lor a atea4y load~

t110 7/8' fillets i f complete reveral in fatigue.

r,id. ·';3,, i= ;,

On sheet IS) , I haVe aonaiclered the additiQI\81 problem of • -

as-sume

vertical llialignllant 1.010 incbesl i f the - . (discs) are a s . - to be -fectly Of c:ourae, thio aondUion would

:t:!::..~~ ~. in~

couiderat:ton •

~lf::.~:.:::a f!:"~!i:lte

•

A,.. 010 ,;,

M ~ "{3o•tc•X&&9s-){. 010),.. (71) ...

Fortl.l.nQtely

D

the end d1sc<:. arf!" not 100?, r/9/d, t!Jere

\!-Jill be ::.ome venciin~ in the dr'~s ana the moment(MJ V1ill be much lower. Two c.h-cum Ferenz'lq/ fillet wekls IAJ(Jt.ld have

of ;nertti:l of-

c:2

J.,-=2{-"ti·'): 1fi-'~. 7r(:_r.lm

zr...sso. ,;.,"

,. .. J} .,.. F.· .If:..." [o;.,oo.~X/.3) _ 't:...., •
1•1;::. "

-··--··-----------------

For steady

/()adtt?r

r.a.

~/4.~ .'Tl~rne·rrt

(treatti79 weld as a /he)

and .£ 70 -,.,efd mdttl, the ,:;,_~t.--a!A·

-11

'S

,.

~ "'(.3oY'Io.ooo'f'!"7)-=- 1'/,'ii'.SO 161,;., /,e9 517--e

"'-r,

w~ ~ ~= .17oO.''

but because of the z?./dts'c

• I

lASe

F.• f, r,ll(• f. 'Yr.

t 1-1'0

14nit force

F.·ffi

on welcled e<>nnedton

= ~d~ •1tr~ (treated as a f ~ • ~ • ::."1,. pricJ. ~~fit~Nr InCh) 'S

ltne)

5iart IAnth a ~ertrie.l dtspl~tcement Qnd um;rier ends f ,jc.,cl • c:ldermlne end momedt th

•

L

. 7.

-----:101~

tut.e

conclt'tkm

®

A

,_,. 111/A>111 end dries 'to n:~~te (~) s.. there /S nt> 1!'nd

tr10ment lh tde

r,=

---'9..1-·1 I

r~·

·~f

..., 1~ {/JJi ..!QS~ 6c1 1$ !lfptJI;?.e oncr ,~rFa':t~"i nNJm•nll rcac-t,"rr :..~-,..

Fz· '~F' (~·+~ ,. t)

-To>---;r

t>owe\IE'r

.,,., '•l

s•~n

and

A,= 6j,r;

A. r

,()(0

13.0,,; l'.S in

b•/3.5'111

t•

,;,

~~,

•

1;,

l:=

t

.

f',_ •

A r...c b" (,F t'(~ "'' 7i b + ""'

11' r;

trr.r-..

1.

"' ... • 'lrr.r. t'E 8..(:2r.t

IY~'I''tJ.

c>r

,Zbl

h.

z~/

d t".lc:

~

,---

'50

c

L~7/,;,

example

I

b)

fb•~• 2~;:

•

~. • jr;,...;if,'

/II.{()

h" F'y._,..,_,.• '3c>S

/Jyq,

fll'it>'t

305'

0 •

ZC.YO~

"'

k'l -:.ru

..uo .. !d

b..

w•

2,...

f, •

lbltn

IC,

___J_-L.:.._:

1

!ft•.(.._.,. ~~..,1([))

2.890 16/fir

~rom ~l>eet(i), fa1t'l.""' a/iowa bit',·~

her>ce

Q-=s-=s_ec_m_e_ dll'

~·1teo

1f~g.,. 9o~· or@

B

T _ l____

: :

d,,.

J. ___IIi.:-..·-----~! ··--·'

itA. be. ,tt~~

,,,.

H·;s.

~--t;i-

t?·

and

e•

e. t e.

tn••ta11t 11n:t fo.-c<." on ""ld

,.,.., Vft b' i7Y + :ii'lt:-:r.~.r.lf.""t•""E"'c"':~""r;+""b'""~

lr' jf,'• fb'• f,' • u~i>

or

E'IO

WEld

Al'SC. Fat•cjut> Allowabln life N= lfXJ. 000 l!f(Cfe~ mrtal

<11/c>wable

le1 -,,z

alt.o tnq bo.clc l.o the 1,.-j:..-~ o" o;heef@

M.. •

2

~:r.. ('~I:as)

bw.t L·

!Jt

/.n'+ z.z~·+ z.~s· cat<'qt>ry@ '!i{re-:;,

"'"''If!

1'.,.., ~ ~ • ~· = J$" 51 b.i not

~ .,f

fD

::: 1.51"''~

'"'"

k • rna. -0

P<ef"•~

21 .,,

f,'flti ....~·d

•

A.· e r;

~.0:..1 bel'<;.:; a. u.nit lei"CC-i ~ o' ""''d.-d

conneet,On

. 8.

~r~----------~l=zoo,~U--------------------------~j7

~k-------....Qa. ,,.,•::..·---------~,k!f----b

•

•

c

s'""'----~:JI

c

A

\\'A\•\1\f·"t\~' AA AA~IIAt.t.~ I l \ I I 1 1,\ ' ) \I\ \ ~ \ \ \ \ .V v If\' 1 J \· 'I 'I ~~~V V V V V V .

f

\J {\/ /!s.~t"/t·

orZ.ill"f.;,

¥1/f~

)

'Ytt or

Ze>.l

1,6&!1.;,~

,, 3.'15

Slnca tnle part ratet••• U •lght ba wall ta u•• tf'la AWl f et1Que • aftiiUlM rar tN allaweble at tllil fillet weld.

For

~n

lr/00 4J

1-

"Yz

I.U•/,,811tr••

3VOO

HH+H::oj

C(J

.IE .. 11¥. ---il

t.."lt:I0"-

1"1,•

, ...

¥ft·1<}: (I.,S~IIY)(zoo-1/
: •..j

• /2Z

baou:e .of the .• 'i~'l ml:h {h,C.( P!Re 1 AWS trG>urre a m•mmu•n o~ ~4>~b

IJJ.o..i

wo!.l.ld

lf tnla ware ahaek loading, tnla rarca could double. I believe the biliKiaat unknown load waul.d be the b6:~d1ng ar tna IIYJUrlal to be canvaved, lllhleft tPDuld rorca the ac:rBtu upward ln the central poi'Uon.

herc

e•

D

~- ~(1a ib)•(,,qs)ls~:Nz.,u4+8') = lt• 2L

2(>Da)c(

R,=r~.
/1,:

f

f

a, 3 '/ s: ,;,

'1'3.~

....,._ 12.4£):

50

,., -

'-..

tnsume an averape t!Jiiness of the tuhe and o.D. "r;,o,;, , then :r"' 3~ 7 /n-r

b-.

1!• • 4>¥8,/,

I t the sc.rew were ~reed !A.pward A." /.Chn /VT"' (iz){J)()o~lo•Y39.1)"' 3 ~7, 3oo. ,;,;6, 1

(:).Oo)'l..

8

D

th/r. would
TN only t.arque an thla cunnac:U~m waulcf be that portion eppllad to tna auacnad aacUon, hOwever we 1111111 ue• Ule full value af tnat supplied by tha ddVII unit, aesu•ln; the ather and 11 stuck,

f-------4--:r T" "'·0()() liP - fi,UJDOxlt~) RPM • '1'1

a

12,8'1:?

·;.7

f =~; .,..,

3s-?;300 ..

u •. ,

~

~

the steaclf( alhwable on a ~~ 1:::. E 70

I.? ll>

F=

//,ZOO

W

2

//,:J.OO{f16) ...

-the Fatt9tt(> a//tJwa~le on

F

, .,../,_,, • . ,.1!.9...

J..,·c.. unit torce' on b~rrdtng

~ resu.lt Qni

'f

~6h

F10

1S'

S/00 1.t.>

1-%

a

As ,a me:d't'er of 1nterest the b(!ndm9. str~ss m t-he ru.6e under tl11's tJt7nd, 'tton tS-

weld tfOO,

f = I£. (iz,a1o ')(-,,;,) =

I I

~

4

'i>;i;)

~

~ • tj • 2.2,S'?S' : b 'S., ~-' t

~

E

IS:

3'10

unit force

hv /(+ ~~.... '"(}()\tiS'

:6 /!:.,

"Jtnce

3. !;/··:·

N/

tr"'

r--.~b ~t'

=~

Rna

/if= IZ ~.._"·I

12.4 E"C.

L.._

Tn1a would lndlcat:a 'Lhat: two 5/16 inch fillet walda would prabably provide the raqubad at.rangt:h af tha tullaa far the ~ loa.da involved; hQtQe¥81' U nt:al'lal al'tould bind end fare. the BC.f'tl¥ up.rard, tor pample juJt: 1 tnch, the load on the weld as ~~~rell aa tha etraee .1n the tube wauld be varr hlgft.

aat1111

'1/6 16h_.;

• . 9.

c

A !lJ{

@

!It CtRC!JMFE!!!:NTlAb

FILLET

!!:ilo£ !!! ~

In thll next &oathodt we shall J'ACagniu the entln thi'Dilt: ea hevlng dlfferent

~

®

methode to c•lcul•ta the allawMtlle. tcorqua ldi1Lh l!llr~ be tJ'..n&fernd by a ct.rcWDhnnUal fl.llet lftld araunei • shaft,. PFi"NP51 the almpleat h to tn•t the weld aa a Una iiMd aaaume thilt U '& ncUu1 1a tha su.e

There ilr•

men~

redl1

t

bu~ we shall aaaume a uniform d1strlbut1an of ehear etre11e tnruughaut

the lllltld.

I

.l

t

®

lenqih o{ w~id • 2.1t r -lorau.e arm : r llr,it )orce c.n ·~.octd' ~101 £tJ i

1'

Torlll~
u.

obtain the Blllhl: result U'

IT~

WI'

/l1r T 1u

t•

I

r

1-.ho.H ct_

..,.td

,.,.;t AT•ZV(t+o'lll'l•)(dx)T(t+.'/D71C) , 21tT

....,,.,au

tre•t the weld lis a line lind usa at...nG .. rd

r'tr'+ Ji rr. 1.-~

T• 21TT" where

F•.7o7 wT

or

~T., = ,?()?

1.u

: 2:11"(t-t.?D'IX) :(r1.?11?1t)

-!Dr<;ue arm

o<

design farmul••·

and

•

T w l

aa that af the ahaft.

stress on aru • .,...

(rt-.'IO'JX)~(dx)

t tz.i<')dx •

rw i- ~) T· IZ 11-r"' ( r• t -r 12.

l

~

ln thh

oaet~ad, '>~e

\!;_} throot of

T

shall also recoqnln the Vilrlable ahtuilr &treH across thl

the ""'10,

w

T Fr0111 thh.we me~ salve dinctly far weld size far • glv~m tui'QUII and welD

'l.:....-t~

l

lllcwabh.

_I weld

I•M'Ifh ()I

•

21t (r-t .1o'l><)

torQue arm

rt.'IO'P'

unit stres'S at 6<) • 'T:IlL = i(r+·""'~~) ,... h_C&) D

B ln tnl' above, (A) and (B) 1 we nan 111.etde two assumptions, first we nave assumeD

that tna sneer stress 11 un1fotml~ dhtributed tnrout;~hout tne eatlre tnrollt ana, sat.and we nave use~ the rddlua or th'l anart EUI the l'ddius or tnr llna or the ..,.ld. Actually tne anear Eo tress ls sllqntly Qteehr at tne outer flLBI' of tne tnruat. Tnh meana tnP atresa is t;~reater than the average 11111 h•\o'& used, or laokirlg at it tne otner ...av, tne lnn.r pnrtlon af t.nr throat has a lower airess end thtrnfore tne torQue transferred by tne weld will be allgnUy lees tnim calculated. By ueing th• ndlu9 of the &haft far tt\a ~a~ald, wa are c:onaervatlve, ths 11'18 ar tt-e weld 111· at e sllgntly gneter radius.. Thase_ two Bfio&unptlons tend to offset eacn othl!i'r. As the redlus or the snaft incredt:l!l wltn re~pect to tne sln or the w&ld, the error ln using these two assumptions decreases. Fer the usual sln of shaft end weld, tl"lls metnad is adequate.

~

Far

11

&fllall shaft aand rat,_r.large

~~~t~ld,

u&e

@w.

4

anJ@ @

1t Dd.c,ht be will to uu • m-tnoa

....,len Qlvea a IJIDre true picture or tne prabhm.

In the next methud,

ll!f' .... 111

tetter v111lue far the radi'ua af t••• we!ld.

C4ft u&e ti'IP

®

tt•act radt.ue or tne weld,

len'lth of weld • torQue arm :

e 1T ( rt "'11.)

tu=

ill'

W'l'z''

tc,•· ra z.o''

c.u:-

w:.l''

rsz"

r-•Z"

ra

Z'"

T·IZ7rTwra.

'7~!183

18~S7J

?>73,/iJ.)

~3~:S;·

r~ (i. trTw(r+"'4)'

9'1,/(ICJ

'10,:,.).)

'1'/1.~!>0

1, '.3~.~.\)

T• ,ll11'Ti<J(r'tl:jl 1-Jt{}

T• 7f~r+~· ~.,J

0

(r ... "'/~)

!

9'l,:J40

~/0,6'10

J99.fi'IO

Lf!J ·~ "1..)1 'l,l}~,.M:)

I

"fC.SSO

I

--- ..

11nit ~tell! on weld • .'to? w r Although method (E) h

'T•21T(d~)(r + "'f.,V_.7o'l "'T)

:.:;

-·-

--·-- ---··· •n:J:;tu 9. 387,3-tl

-·#·-

•

more involved, 1t gives tne 'bBst picture ar the loading_

ar tnP weld 1 and th11 010st accurate valuaa.

-(t_ 'Shaft

ttethod (D) requires as much worll:, but 1s not quite as accur&te because we hava assumed a unlfal'ffl stnse dlstribl.lt:lan acrose tha throat ana.

or

Mtlthod (C) t..~hlch tnats the weld as a line gave al1110st the &881e nsui Ls as method (D).

but ln order tu obtain thP fillet weld elze (tD) • we mua.t be vtlll to sche the fall011·1ng cubld •aw. tlan ..

[0arw~-t-t~:>r..,- ~""0

Method (A) ar (B)

I

(;~re

really tha same method) treat

~a•

the &811111 radlua for the weld as the shttft.

tha

lart;~er

diameter shaft and ameller W!Plds.

the weld aa a line and

Tney QB1Je

vsr~

good

ra~ul

u

ror

The only problem la ln very smell

ahafte and rather hr~a welda, in this case it does nat give ~;~au tna full va.lue af thll' taraue because the smaller radius of the ahert is used rather th&n the

Although thh cau!d be Dana, .u mtght be batter ta make .. t"ble or rnalsUr•g taraue ln t•l".fll& or &hlllt racllua (r) 11nd leg al.ra ar f"ilht wPla (w).

larger radlu& ar the line of tM weld.. P

should be "ltl, 1)0 inch oaunds •

. 10.

Pfotica far tt111 2° radius shaft and the·

fillet w.ela, the result 1a a torque or l13 1 10D incn

~ounds

1 whenee tha villue

•

Circum £eren rial Weld

K,.• .L.. r.

K• ~ ' r.

•

To

C-r

1" • weld sbe:rr allowable

_., r 1>-

[i(1+ 1<, tKJ-'

T

r. =

;;r:\

r--

v

r."' =

[

Q

~

G:l

II

•

s

~ t~qx

'If' thtrJQt

T..

V')

l~t

tor~ue

OSSIUII~

c

A

It!... ""T;cs,'fJn

Jl....

--lw 1'-

tH: ] 6.{a 'IT

lrl(, +K,

K~(3t !',) + (H'...).. (z1 ~..)] ~

For minimum t::~PIDUDt of weld rneta.\ 1 do no-t

bev•l.

L

c

ell

t

~

Ill

~

"'

V)

~

i

0

0

·' ,'I

... 0

•

1.2 L\

J,q loS

.o,

,{)'I

.08

tr

.{),

~.UIO

3.£~201

188'11

~-'"!WI

'·"""

,,,.,,.,.

~.'15'!5

'l.soe'l I ,,SSOI 'f,!.S11

mn

"""'"

'1.12.~

'1-'1'16.!1.. 'f.fl(,'tl

'1."1'1~

S.Olb'?i 5.tAo6

,,,

"·"':1.

"·''"

~

~(\J

~""' 1.1);

,.,....

5,'1,8'1 :;.5'1153 r.r.~ 1~. Oo5 5.77ff~ 5;~5'/5 ,.ou.'l "'0~~ ,.17'11 '-'-5'8'- &.H'fi "-'1118 6..50~~ &.5'8'1~ "-lt'IO& '-113'12 ,,ql~l '/.OO,S 'l.O'tS'f .1818 1·'-lo&'l '1.35"1 'l.~q'IO '1633-S ~~Ob i-'111'11 '1.?/0l. ?.8005' '1.8'11{) '1.'!1111 ~.O'Ill 'a.lh~ '6.;1:1' ~ q:'1110 <J,y)'l,t 'l.'lo80 $.7~?? fl.8~33 'il.'ll"'l "1,016/ .,,,012 "'.?tm, '!.'iO&r. 'f.''IID/ IQ,OI:L IO.IIS to.'-16 /M1~ /Q.'iSt. II.Of>~ /ll
(.0

3.:>.1~'1 'l.a'ID:I. 2,'!>3.,8 ~?.85"1 2.4'1'10 2.5~ 2WD'1 2.8012 ~~?0. 2M.?.1 ~~ 'M'46o'l 3.1lX!O '1.3&.11 148'1,. ~'IH'I 3.'1'110 ~~ss-w 'j-Oq{)h '1.15"1'11 'f.~ 'li,I!J'Iq 't.Wt8 i'lo't'~&l

/.'18?'1 2.0~" 1.0'1'15 2.1Sb/

,'1 S.2YtJ3 15.'\IS'f

I.D M

OS ·'-'1.'1'1'1

• S0)88

·" 3.1'1/7 [:ll3~1S

.a

.o'f

.'l.'l~ .'M6o&>~ .~1.11'- .'fo'IU -~~~~· -"~~ ·'7'15'3 .ssDO'I .S'i'IS3 .r.'/S)~ ,r.1'U'l .'l'·llqq .'l'llli' .~1 ,e8'181 !mi' U1t.8 /,0,0 t.mr 1.186~ W11~ '1,'1'108 1-\'1~ II·~ :1~1'-S ~82.1'1 l.&'llo'l ,;q~l\ J.I.J'I'-8 /.~'t'fS I.SS2.'1 u.os'l J.lo5'12 •m-ar

.5 15',/b .'I

.01

.01/~3~

.I .tlfsqq

.z

.o~

,01

"l
:::jl")

"1.

::)

6'.1!.5~ $'1~'1

Lt..

.,.,,,

'"!

I

"'"5'1'1

~

9.5381 ID

<:: "!

q..

'1

"!

~

f·.;

B

D

I• ·•·.

I

'

Va/u""" of {_!(,)one! {K,) for minimum wo.ld m...tal (~r.') and a 9/ven w~lcl throat area ('Yr.~) F· terrsi/e force~ T.. A i.,• v.eld shau- 41/owa.b/ A· weld thrrxd area::---:olotLf:l-l--+r±Yr:H--t---±1~·8'1

~ ell

~§

~

~~ Q:

,82.~

--1----l-.81 _; ~

y.eo "

"; ~

'-

1.1)

1\J

-J -J

""'

'q VII I'<)

~

;r,

.,,

l

I

<:

"'.

<::

-.

0

!\j ~

- 11 •

-·

?~

111

"'·.

~ ----.. "! ::r:

31....

"1

"!

0

·.;::

e

~

U. tule\ velA et.ae tor tbe baae ot • alpel. tovw, aanme vtnd pressure ~~ ~\#f'~J!.":' ..ue per hOUI' Iliad, • • - tt>l.o mm-

c

A

V:2

:_.1111~ ~ !:;.:'..:.,•

---;;[5•

S'"stdl'!.

or 3..

1• . _

l

•

0'

0-

I,..•'frl"1a1T(~~~ !.tal r .. ISOO

, S...· ;;-· ~s-·J'f,.. "r

• IlL In

ta.mt actt.n.g c tower due to wind presaare M•

~.

·

,Z08~0)+ 1!ijld(z88)~~z"-)+(~'-XIC.O.SXz'l-.')+ ('\)(:lll.~o-~~.:_2oD.o:r:> "-~· ~00~ k;p

~ para/lei

r:

fp:'

(orce

F. 19.09 IT: 2.• IS =

~

3 IG

1£;1;,

tile. (zooino;p)(~~ln). 2.~ G. l<~t

a-•y

:18./'lln..

Jatlsue aUanlala for veld. )c.=-

min

1nii

·

•0

tc~ulta;.t

•

1\ISC:

r>

®

1

c&de<jor'l

@

~r"

N• 2.•10~ c.'lcfn

-f;aL- ~. r

S...4111& · - · Ln pipe

••• ~Ai@

a~ ~-:;;!t@

}J, t

fSt ~,': j(~34+z&.'l3f+ (~36.)' =-

337o 16;1;,

D

B r-da/()8°~

•

A..·~11'r•Z'II"(,'II!') •YD.Or. ,;,

r ... rrr"• rr (,¥:J' • bendit!t

Vol•m• o~ we(cl

8'13. '1'1 ,.,

f,;l'f:.l"'l:r..ft~· f.l/0 .,..

il t.Ued O>lcolate.J ~IZP

• ?.(.3DJ)'('Io.o6")• t 83'? in' IP211ze of

tt"Het weld

li?O

-kl meta./

• -12-

c

A She of tlllet nld 011

Ufi1Dc

u-• of forir -

Tba IIIIIXlOIIII copoolty lo ...-4 w a appllecl •• tho w\ar tRill of tho torlr, th1a vbole 11Dl \ tends to pbo\ abcN'\ tbe lonr ooraer vbere 1'\ been liP apW\ \lui 1 - """" bor, Tho •-1\batl horloODWl r_.
R_.

-

ot

ll.f\batl al-t.

tiJa

T l

Fj, Us·)· P(3d')

fn• 2 p • Z.(LI ~oj>)• 6,0

/5°

..

In th1e case tbe bgriscmt.al toroe (rhl la applled e\ tbe Up ot tbe bar at 808111

,

•

K\p

ec:oen\rlott¥ (e) w the o8ftter ot pvit;y ot the veld carmeatton.

•ert!.

b• .:1= 01.'1 ,:,

Tbla eubjaot.l: t.ha aODMOt.inl veld to IOJDit bend.t.na f'OI'Cel as vell as UDlfcmlJ d1stribvte4 trarmvene forces and. ver"lcal tOJ'Cel.

::r;•L' GS. 3 30 ....

~b (7S0T•n•2'{13/.9••) "'"' ~"<' 17.- • ~· · ·t~,3,5.

(••b,.t •·• ••I•)

t-ret.J t weld as o ;,;,, l>b-1

l

··o~

jo-- _n•· -----..j

r

weld

---- ---- --··---

tr;t.

BI :·.~·

S..•bc!+"• fs'•'l'+~·.

7.83 in ..

bend.lq Ioree

transverse Iaroe vert.lcal Iaroe

D

B lmtp\Udlllal · - ln tho veld clepeDdll -

tla value or tho aboar (V) ln \he sbAar Thora \a a ahoar ot V • 'ISO lr:ipo \a tho top aNI bot.toa horlsonwl portlons ot the traM, tnl'\ notice tber'e 11 no abear in ,._ two vertlcal partl.ans. 'l'b.ls lllBBQ8 1

d!.aCI'aiDo

~IHHHH I

theoreticaU,, no weldlnc b needed in these portions. Bovever t.o be practlcel 1 w will uae the mln.l111W1J weld sbe1 vblch in the c:ase ot tbe .1a· inch \hick tlance pla\e voul.cl require llL!J!eb tUlot vel!b,~.· for t.he

borll:~t.al

L='"lein--oj

(uatul O<Jrtuin") r-

port1caa...

1/.BO "lone~ t.ransverae un1'\ bearlnJ' f'orce (aseWIIB r p ISOO .:,.

I

'•'"L" ~· IZ.so "linch

I,..•l'(2o.•b){if~~\=(2AHvti.f=

f.)~: + fL '"_ jcu.ao)'"t~":_:!!:.___ ~2 ·~ 'i_'ji,

____ o!-_. d\..t

USC ta'\lpe valuea, 1bear and traAaveraa baartna use eoadU.lat (37) 1 ....11"1'7 (O), aveHp qcle ..ort S mlmlwo 12/br. " 8 ~~~ " 200 ~/year :K 20 7Bara • 384,000 cycles 01' a Ute ot l00 1 !JOO to S'001 000 ct)'ales

t.v•

/7./'f

"lti•

IZ, 1<.~ 1

-

~'ld!Xih,~l ...lciS) -

( bu:( not to e~c...e.! f,()fv or

use

~

~

each

~·de

of

zd

Q.

(z.a+b".!4)

~:e b

M

0

~--~2 ---'!..a_ Zl>

;:.1 •~i )

steod'f a lfowa~ It> , :

0

a a' za.b

-

1'",... •

f"lau• valul, condlt.1al (16) 1 ea'"&Wl' (0)

~· ~~~~ •Ill'·~•

(ht not to e;u<>d '>ie<>aq alt..,.>l• of pL>.t< of 1'16"/<':.i)

'1'tiutw (ver;tt.oall 'ertia•l •bar

• r··

-t

__ l - - - - - - - - l

-13-

:I:

J:~

0

0

a• a a.• I>

a"' 0

Z•C4+b) ~(ZCl+3b) T

·----------·--- ------·----·. ·---Qrog!e voldo AISC

weld d

I

®®

J(6o.+1b+d)

~or "X"r, ~<~e re~ere.nc:e aJli~ (z-z.)

F~

,z,.,,;• 1".,.,. .!.. ,_,. • 7=0

.

C4•~•:..(::!·!f!:!l

•/.O?m

r,• r•:r,-f·-'f
c

•

"·"""

- - . 1, "'loal.p ot ~to" pop lo.7•) k - - ... - - - - IIIZllllll beldiJic _ , ·~ - M• K,fr •(+.l"){l~t.B){t.fr.) • 10.77 ,;,11

~t.ol -.u. force ID oh8l1 ot T= K, t • (.sDDX,12.t.'l)• '-'34 k

0t - · ""' braolat u .WI'F thlok IS 1/2•) ODd tbio vi.U opnod tho farce oot •• lt l.o looo I doD't lloUon tho bolldi.Da otreoo

-\ntod,

In t.ba aheU vlU be 111 bi.ch ae ta4lcaWd abave.

.. b

"d

A /2.()

2•4"

s.s 8.0 s.s

~·

2•'1"

S'l'l

'3t:o

tot.. I

'I -~

M•AY

I.·MY

:r,

.-3-~-

_!J_Dj ___ 0

~'

+26'12

/4.7

()

0

-Ia -lD

-IVY

-

-110

+:1200

-2'f()

'1"1'17

Also tbo tblak ~... - vi.U otUten and the oholl 1a tbl.o nstaa.

-

atreu~t.m

It thNB beDdlDa otreooeo 11'11 hlch, tbea a oUttCIIDs ri.Da lfllf7 llo oddod, u.p ODd ~ttom, - d tbo obaU oad ~...-.

-

Cbe fobrion!Da probl.oa vW llo ptti.Da a . tit.-ap ID tbo 3D1Dt tho tbiok bracket oad tbo ........t . - . . . of tbo olloU. . Tile odp of the lfllf7 t.o llo ... biDod t.o prorlde • load

fit.

B

b· z .:1• ID

m•

1'-

n' 'i

x•.o) •.

..,. ,,111

P·

- -F,

.!We !!!a r.7, ~ .~

ZOOt<

9• 'fS"

06 ~

vohunc• IS,S'Ji7"

V.olume:= 8/7 ;,,

1011' cbeak ta aee 1t the tube U cwerat.reaaed: trosa the foJ'Q8:8 or t.ha supports.

p•oper h

of weld· treat,J

s., . fkl~l. s ('lll•O\+ln~( T

shell

liS

~'l.

F. ~'~·.

F,.n

s;-· F.,m f: ;.: ~ --;;;--. I

\_

nP --r..('IJ?t»~)MSYS" Sit' " CDS6

m P-sin 8

l~XztJoll)'>,;,ys•

~·

sui

a h;,e

n.H ;,..

•

in

"·"' t.; "'/,Z8 "1,;,

realotw-

Pl•

z.(~ e ~.{t +f)+t{f.)"f] • ~ (dte){d-1 :ae)_ as a '?"'de,.,,.

e=/¥

l!! l!!!! J!l!l'!! t. 'l>

t.fl. I)?.S") • IZ "8 «1,· (21a &.16){zotz•or.~) • '"

m4~im.IJI Mni~ ,.J,..I ~

M sht!ll F,.,.

•

bt~~cKer

·14-

c

A

,, -str-a.r'tthi u.p

•

b-en clrit'f J?!l""lle I

(,.Au

F,n ~f.aoo~<('f) • f).OO ~<;,;,

( ~ .!f. •

1-DO~

t,

l¥4

,.,

'5,.

A.,

t'l

.,., ";

?.'1

(, . If•• + f; . I

bend•nq

F.·

l!!!ra!/,/l,a& t_rt~mver1e i4ad

n P N~l2 <;...

m

,~,;,s

f: =s;F•• p <'Mb F4 =

"' r "'-;,;,e

.

f,,.

6.00' t

1'/,/C.

li("J.t>O K} L"O~ I'J()' ,

.

V..( ,.oo ~<}1Jilno•

•

11>0 I(

•

0

H~"

5'3.~~

.

"II.~

- c;, ",,~ "J,,.:

JJO'

- £1)-7 ~<;,,;

t< ,,;, 130'

+ .:.. 3b' 4 ~,,,;

I"IJS

she<~r applied to web pletfe. Re,.ttu;'l doaqona.l

~ /Q,OS'S Kf,,'

~DO

A..,

~4

t...., "'.ie af fjllet wt'kl !71) luL"!d 1!11!''0:il htmrf~ I.Mtl} ~ :~.c:..t.;~.s-"lm • t,'/93/, "r !~"A w f""1fl11<St) 1 '· 6 :~~-. ..,.,,; • !,Zr.,?,;. '-I K~l

or

Iff, 1i?d,

she.ar stres~ to

hold IA.nit ~orce

on w•lds

(r.. • f~ .-fh-u,a,

i~ r.M port1a/ ~,;,t penetMf--on 9r""""" weld

t~

compre~s•oil f::•1Jc, -tv h< kle '"eb P 1.l~f

-

;1.4

(welds

on

lltJth

T=.'tooy

51de:. of web plate)

•~ Z. A..

tlmJa't

I

D

TRANSFER OF MDqfNT AROUND CoRNER USING

DIAGoNAL 5T!ffNf/(

~===>r==========~~~·~ • d.

that f-e9 tmn5 ferrecl. b'f weld-s

f. • b

I - 15.

-!!!.L

d.J d.: tO:

F.

/WI d..

ore

.. db/ t!:td: D

c

A

1RANSFER OF MOMENT f1tlm ~

e

~

D

di F,

II

OA!c ,MEMBE-li W ,4.":;ru~ I<

I

I

l

Omer W 8/Dd!'J.,.ft April /tJ,I!i'/'1

•

1

•• ~(d.-:l.d,' P• d.d,-zd,d .a a, zd, . 'J (P -t d3) d 1

...i·~.

.

.

T4!tke tn<>ments

a6C>ut

pD/nt

(

•Zd d t

d;+d~

cl,) d,

®

- z f-. d, + z v ...l =o

L_ _______ f~;:===~ '•

·----- -----l~C==-:::!!::::======f.....S-.

B ~"''"'' ~illat o.ueld on bDth ~td.as e>f

weld@

weld

r • .J.L,

ra

1d1

•

"'"!>

plc..te

li.dv. ~ '-d~d, z.c1, d,

@)

l'BANS FER Qf MOMENT FROM oN£ MF~BfR To ANtJTH€1?

f4 • fb•

wel4s®ancl® we.td®

(_rb:

zero

lli-~ z d,- 4•ct,

v

MJ,.

f.,"zM•~ " d,d..d, shear 5tres'3

-16-

,;, wei> p/4te.

•

A

c

:1ft tbla .,..,.la

L= 4o''

•

,_.-- au11.me at:

,• .!o/1

~f)()·f"

T 1

J

f c £c.. • 11:1.4,1; J
1"/e

t

n~u.rrt>d

~ I

___~Pf

t,.•

f1J,'17Itffio

~,.

.'t"'i

1n

~

or~

It ea:n ba abam. 1t the burl..nc npport la eeSWDid to be ID1ltDrmJT dletrlbutad OVOJ' tblrd \he leDatll, tbat.-

IDo:roaoe 1n le,.tb of platten over laqtb (L) duo to a ~oroture dltferiiiC8 of 300"r

,.n;-•

L T

lq ps

;o. '17 K 1/n

r

In

1brD
'f.' 5"'

Tbla aJIOOI1t ot nldla& OD tile enda abODld ho adiiQuate to tranofOJ' tho for. . doe to tbo ....,..., boltlag ot tbo platt... and attaehl.nc plata, addl tlooal valcla 111117 bo nee e....,. trw other 1oadl!l.

"""" ... !.

e, •

or I q,l1 l<tps

X')

F,• I 1~1~ ••'p ('io)' + \(4)'

L.

~.-

1 'f,l70. lbs

f. ('JOo'F)(lO•m')(ltBY,"I().:j.

"ide taffa.<.hment

weld /

Fr •

or 1n tbla IIZIIIIPla

We am.st place a loqitu.dtnal u:lal eccentric force em this att.achmeat to equl t.ble maveant QX

f. j L'-+ Z, 'S w• Fr• I"/, '7 !<.,p.. -~: .. •

. s-o ,,;ch

•'a/ stress

I~ ... be ohom lt tbo boOJ'lna aupport la IHUIIad to be IDilf.....tT distributed ...r tho ontlM lanatb, tbot.-

F,.• 01'

~

j L'-+ s:?4 w•

1n tblo UOI!Iple

Fr• ao,4.l<tp's

t,.•, .. 18mch

It la • - 1n tbla •""''IPla, tbat tbo ezact botrlnl d1at~lbut1oo boo lnt1uoltce on tbo ruultlna force IDd 11814 alae,

mornent

ll~tla

dio<jrnrn

RIOf oet

F-L.

Et

tb~

~0 e, • e.,

IIQDOl to ..,;.

(j_W t3W)• t'"

Ia

l.enc\b

of tbe platten ...... tbe

l.eiiPI>

B

A alp 1a attoobad to tho tana1oo £lenp ot a plata alrdor hotoro OJ'eotion. »otarllllao tbo force on tbe OODDeotln& volda at tho OPCI ot tbe olgn, boldtna lt to tba girder tbe 111nt... 1a etreooad to zo kill,

(L)

-

(.4)

u.ni form

loo..c!

J. T &.•ttr~

Notlao tbot tblo 10118ltwllael force (J'J) ...... tbe attachlnl plate to bond . . .ord

Cesl,

F•

~

:T ....(8' I

~------x----------~

1..

', l

17)oment


-; f'e, r~

liow W8 f'lnd tbe t1'8D8Yerao !'
l

e • (z F.,.)l •

,.

~eEr

1 .5..L. z.,e-r

mp11ement' of

F

/19'9

r.,.

equq.l

or

resolve tbeae forces toaetber

I_ fr •

te..t

r b = ......>EL' ~. ~~./"' ... Yb') AI!' ,.

"'"• ~F.W' z. L.

HGV

Slfft

u"A""

jF..• + F/

- 17-

..

... ,-F_•_f_L_1_{_l=~~-=4-b'-)'9'-~

0

c

A ._unc bl'ackeloo to

It ia nOOOOIIII'J to rid -

the ...111 4

!r'"":. ~::!!!"LIIl.~m!~::..1'=: ~-~~ :.~:.. "l'here very little en the bnciiAt, t.ba elesttc 11

l.Dad

bUt

IIICJI'emaDt of tbe fl'ame vtll caue &OJDB ra"'e to enter ttae braakat tbi'Cqh tha cCIII'Iecttna vel.de. StAoe the comaect1ng welda I"WW across the tall vt.d.th of the braoket, we vtll cCID81del" cmlJ a 1 inc:h thick aecttcn. We vtll neglect 8lf7 reet.raiDiDI aat1Cil ot the bracket u.paa the main h'ame.

•

____.,..p

c.anatclar tbe eannectlng Velda to be eDt eo tbs fraM ta fTee to 1111:n1e, lt 1 e llaal.de face wtU elAstlaallJ' al.oDgat.e •

€·f tr=

Bow ·~ the IGZ'Ce ot the cOJmeottng veld to the brncket, Ptrat oona:tdar the effect or the Yertlclll torceVert.tcal llov••nt

--au. lii"iiii'""axlRl lDad·

E•f•ft

o-•}•-\:: duo

t

.

eo.e

E..Ji.!!.i_ i -- ...£:._t ~

f:"

11ormal sifrj$ {tensile)

6.·~d·;~

'iJiur stre n

It ve CGDI1del' the IIII%1Dum cCIIIblned et.Haau, t.blll becaa.e-

to bonc11D1

{:.{+

-~~·lJa E·f·* 6··'d·W total Aa •.O..""Ab•

..&...,. 'P

~fbd

}
J.[ cos 9 +j co,..9 + '{sin"B]

o;..,.,

~~ Tbe d1sUnee of point (a) or the med;Jer to the taqont of point (b) of the ...-r equals tba lllOJII8D't. or the a rea 'Wider t.he mC'Illl8llt diagrara tokan about polllt (a) dlvlded 1>7 EI. see 2,9•7 Deatp of \faldiiBDU

(!)

i

or

=-p- [ C..s 8 + 2

o-..,,

JCDs~ + ~

Sin"

al~ = Q_f. o;;...

PCos9)\ (Psip(/ = .1_ ( 2T"" t- l Zt-

j cos•e +'I si/1"6 -

ai.P

• 'f..,.

8 Rw ve vUl PQ.t all or tnt.s together-

0 • ,6,-L:Ir

h-a.-.•

e

Jib•'!:! iqs.:.'e

-0

cl.

co>& +&'eH SJn'e

2

~

000

or

bra.<.lle't

or

0

,o.-

A, =

ha.me.

.!10

......

br-A. .. krt

--

0

~

t:lt.~

•

"('>

3o' zo• 10' 6'

~~--·~+'--~.----

~c:;~~~\1-

----~~~ l

8ot"'ff --------'

I - - t(

'

-- -

t

I

f. ) -----1

! ;~)afi!::J~ .J"'l~S;-t =t, tcz~t;..:"J..t!::r=,•=:,(!:""~"';)the ohsar st.reas ( ls thln tba all
.....

T)

1f,~

ta-b

vi

tact.ore 11s\e4 in t.he above table can be proper tbroat atze.

The

'l'be thr<>st at

~~n·~l

usecl In these

e • 0 11011ld bo equal to the plate tltlclolus

For a 1/2 lnch thlck Aldil plate

Co;.. • 50 kal)

two !Ori!Dllas to arrive at ttw (t),

st..,.. to the allowable of IT• 30 klll,

the aolt force aotbl1 alon1 the edie of t.he plata (and t.he weld) would be l$ lrip:~ par linear lnoh. The all011ablA &hear on. the throat ot 110 veld 111eta.l 1a 21 kat, plate ts 20 kal. 8. 90° would be• o·

The HqUi.red 'throat at

i,• ta-b •

: t

tT= 3.1; I<.Si

Example

b• IB ,;, d. ~0 ;, -t{U 1Ui){l11~)

r

'"

7

'0

bendl.Dg

7 5 in

stras reault!Ds trom an:t eccenV1c1ty.

'

The ~entr1c1ty would probabll' increase

tba ......,.1 stress (tanolla) bnt ID the repon where tllis !!!lpt throat cwmot ~ increaaed DmCh above the tb:l.Gkneaa ot tbe plat.e.

/~)

rIr".J~. ~f' jJ'-'+32.'1' ~ 'fB.'-1 t r. •

•

fbla eBIIUIIISS a anltona dlatributtcm of atreas almg t.be tbroat and nepecta alqf aecandart

MJfr,

~' ~. (. (1~Si¥teip\'. '32,'1 ~,,;.

• -,cr-

(f) • ~2 ;~ ( ~00 ~~~) "

(aboot& • 00), tbe

For e jo!Dt In Vl>lcb tba plat.. lntereect •• en ""f!le of 67 l/2°, use tbe- date tor 700 .. """ tba rcmmuas vltll 67 1/2°, title........ e-?o' ..... qssl

e.

"'It;.

t=

e.

[f.;.

/;Jr-..'9-+~ sin•EJ • zfhl~'"h"+~slrf~'lt.· ~ .708 U.ch ~·'¥ ~·.?16.mu.

ihrot:c ~

• . 18.

c

A .J,.• L .. I,· ~''l"oO+ U,?/l't = 3~8, ~'10 m3 A.,• 'fq?."J ,;, (/e"''th o~ weld.) Fo~ ~ /000 Ton'$ • 2,000 (op's moment arm .. ~'ltn+IOin-1·q'fill" 30.tJ6 in

•

0 tr'1;

UPW V!ld at (Y TVlatla& b<ml>oatal)

•

(vertical)

~.•

Vertioal oheer

~·

Reoultoat

j

f., •

2.~~~.,

~: + ( ~- f,'j •

"i.JS >J;p

J(to.O"')•t ('f.IS-.?0)'

:

IM>t. l
fhio roaultoat unu roroe or 10,66 klpo per llaeor taoh ie based upon a atand>rd ot l bleb tbroat. !o trans1'0nl ~l.s unlt. force intO • aU, 8"t.ft8St 8~ divide tlr tbe thl'oat. abe. ill t.hls cue 1 l.nch.

llaace t.bla VOD.ld CGJTeapond. t.o a unit atreaa of 10.66 lml.

'1'ba all01111ble att. atre&8 tor the tbraa\ of • veld UDdar st.ea~tr loadl.ng 1s 2lksl. (E'IO veld neta1), T~e prea101t AISC ratlpe all..,obleo, oandUioa (16) or ()?), cate8017' (O), viti> K • iata/lm: • HrO, 1IOUld allow the tolloulaB•

lS kal U kat ? kat a kel

...,... ot ""' ~ lA o..,.i-"'1 Ule eve.. .., the \bl'aot ot o vold, oopeeioll;r rem ool.Uplo loo
....s .....l.dor

t11o uait

r-

~ veld at point

on tbio liAI,

tor 100,000 o;roleo tor SOO,ooo eyolea tor 2,000,000 070lao tar orer 2.ooo.ooo c;rala

®

Ia tllio euoq\11, Uae ald nrt.oa IJl tno ond aloe, eo t11o llao vlll alao ttrt lA NlaU..., oioa, !Ma 11 .s- b7 .-l-"'1 tllo otomlud veld to have a tllroet ot 1 laoh, md uta& tile ratio ot ao-1 tllroat to t.11o 1 tach at.andord •• tile rolatlYe alee ot tile liAI,

The :rawl:t.ant. un.l\ terce oa. the weld 1a lwer htJI'8 and vOdld. aot. cca.Vol the desiBD•

f,· '1. 15' ~,,.,

lt t.llo .U•obla alloor ... t.llroat ot ... 11'10 vold 11 ,)0 or m, or.,.. -21 kal, tllla beaoMI ... allwable 'IIDlt to:rae ot t • 21 ktpa per linear inch tor the standaJ'd lt.Da ot vol4 (1 laob tllroatl •

• __t;.

B

k"·

H~'-1

~ 'Sl2f!'

•

lolounn !wit !!._j\2_~

t-tt:+l~

•elaft ;., • l 01>1

~ relottv•. I ~ ~tz..

D

z c.blf&•Z1DO."'...;,

i

f,•'fll.11-lp

~

~"'pcrt.ft

~~tt!"' • "Z.IZ I

·•

A

II • II

8 ,8

828.

r,·z f· Wf!1~~· -~~

1.97.9

toto1

-u•

1•

I,,lv• I,t ~-

n,";h'l•,q •

'1 =I:,-tr,·C6•M.' I

C6toaW=

17,b79

'B. I"

9'f1,"30.·{3S.1'.(/~¥7'f) r 32?,"'0 iP" A

11•11

I,•ltl

~: '4~• '3."/'1''

i..,,. ly+I,- '1/• I,•:r,- CEo•M• /'f,l:l'/-~.f/'1){19''1) • 1/,J'I'I.in' noitt. lilr.d

- 19-

..,.,(d

on z !<.."

t '"

I'.' t:.

.r.3

'f4r.r.7. ,;,>

J.• r.•IY·'~l.;
14.,•2l'lo.ma;•

CG

2t I!!!!!!

i. • Z(zb) • .<(z•s.:>"l• zao.i• T.,.• 2. if'. '
c

A HIN89"er tbere U a horizontal taroa ot ZOO klps aet.tng en t.h.ll!l joint.

'fhe resulting

unlt. baarbla preaeue is -

cr=

F A"·

zoo.r
,:r·. 1''At··

1•

au"· ~ ,s,

\bia w the pr,..101UI -dlq etreoo, t.hla vlll have the effect ot sbUtlng the reference oxla \a tbe rlst>\ b7 tile ......,\ ot 1.. 8L kol,

ApplTinl

•

q

~

Air a l!llde tor the allowable tatlpe atrua, ve vl.ll ue the US: vat.uea. Uoln1 taUaue aondiUOII (16), partul pC~e\reU'"' . . - . veldo In e.oi!SI teaalao tranavene, oateaory (O), the tau ... t......W. .wid be ,-.::;r-

q_.

Tha parttcu.lar load. eycle vlU produce a etreaa raop or I • o., huce Di.u~&.oKsl Dfottee t.h.e lftd.Lcate4 \aDdle ~ e\reaa OD tbe l.aDer •urtaoe 111 7.31l kill. VbaD the azlal campresaln toroe la add.ed1 tbls tan&lle bllld.tnc atrua 1a l'ttduced. to S.SO ksl, wblcb La vltblll t.be 1'at.lpe all.ollable of B.o ksl tor a part.ial penet.ratlGD P"OOI'B

1~2~

veld.

the reeultat atreu wa ewer the fatlpa allovable• tar SUIIPle to. 0 ksi.., In t.bu partlcular problelo, ,.klntl t.ha veld (Jur lllc1'88oin1 U' • throat) vould not hel,p because t.bla would ollllp]l' oxt.oad the root ot the ..u fUrther ln\o t.be compresalcn area. fbe tensile area vhicb caratrols *be at.reaa 111 tbe teeld. la determl.ned. by the cll.atan.ea from the sbl ft.ed neo.tral uta to the surface, and Wa vlll oot ehanp •IJqplJ' by ~~aldlla the veld deeper. IA tbt.. eaae, lt vDUld be necuaary to increase t.he t.hlckneu ot the bracket so that t.be dlattmoe of tbe sbltt.ed aeutral uls to tbe Suppc~~e

In ctleclil:ln9 tP'Ie weld a he af tne above Llnlr. Suooart B.rack.et, members (A), (8), iNS. (0) fal'lll a curved besm at the (.Qrners. Thla means that the neutral Bk1& will t~nift tl\lil8rd, tharPDV lncreaatng the bending '8treas an ttle l'lner race, and ascnulng tna handing str .. a an tna outer fac:a. As the radius gr cur\lut.~o.~n or thla tnware~ earner ls increased, this candiUan becamaa lees se~o~rn ana tne bending &tress ls reduced. In thll fallowlng IIIDrk, we ha\le aaslollned ta start witn, t."at tne partial penetnhan 9roowa weld on tne lnslde corner is 2 112• dri'ap cna rsJnrorced with It 'Ulet ~o~eld which wlll pravlda a radtus of curvature of 1/211 •

1a....,..

aurtace VOiald beei:IDB c:nat.a:r. Jlot.lce tbet th.e inward. veld. axt.en.da ap tbrQucb tbe ahltt.ed: neutral axU, tbte •ana the\ u doea not tenainste In 'he ' - l l e rep.on, All of t.ha ooterlal above \hla sbtftacl IWlt.l'al u.ls la aaswaed. to be ln cGJIJpl'fiUI.ciD..

!InA systf!?ln t:~.tt«n•ri

to

mtvdiP dte plrzte

B

"'A,'( ~'t ').~·)

S.A

,.. :2,1/'f• 171dui.s of f~

fit• ~= tt.'N(I. 1• l§'.)t"Jf"O·~ ~ ~endio.9 ~~~ inQer f~~-~f.--weld-·

ab,M(r;-r(> .. /l.1"'"·1'1&"{:~.il'f.t&.") _ A(r1 - r. )r, !(, W(!u~·} (u39•-.l.ll'l'?l~·) •

J";; i,..eld

11eutr4/

uit~ bearln& (tronsvene)

7, 3 '-/

~.--t;.~:. '1.1/"fit<

k:si

in com~<>IJ

f.·f;-~.... 35'"11;.

Allowbla tetl.pe otreoo on t.hroo\ ot ""ld, ...., AlSC tonoolaa, oODclhi.Gn :rT, ~ (O), ovOl' z,ooo,ooo 070les, taUpo t......W. lo

'/'-----------.(~we\4

1: .. ~ IM.,. 1-1<.

in 'fens/1;,

,'~'-+~----------------, ['- ns14trat ll.~tti: rhifn Jinuucl a:t t:ltrVI!'

vort.laal obear (parallel)

•7.3'fl<1i

bare I • rdn/max • 0

-!.red veld tbroo\ I.e ccm
benuin3 ·~,;, '-'"'

t•

Slnoe 'he t.ho laoldo veld oxMndo ll8ylllJ;r aee the taUpo all-ble tar a •"'''le"' ponet.nUao .......,. weld.

• 20-

'1.8'l"M •.C.IIi• e>r ~1nCb 8.0 &'Sol

beDae

"tma.w

!;"

8.0

t("S. ,·

but. aot to axoeed. etoa requll'ed leg alae ls

value of 2_2.0 kat

condlttca 37

• 'f, &"'~I@ • i6o5" or '1b. ii!C b w(.?o?)(B.o ..t) ' 'r:>

•

c

A

•

p ~

;...e 't

~p 0

•..:...:.:1

refr&.c'f~d

P"~it,(m !hie tOJ"k Wt t.NCk baa a ec1aaors deYlce which aU.OW. tbe tork and ita loed. to - . . out -ioon~, flSW'fl l., fho too dlapnal ...,.ben (a) and (b), CtSW'fl 2, ore pimled togotbar at polnt (5), One [a) la pimled at lta 1 - r end to the 1lf1obla portion or the t.nck, polnt (2), lta upper 0114 elldaa vortl.QalJ¥. along the uppor 0114 of the fol'l< support, polnt (h), fha ........ (b) U pimled at lta lower ODd to tho lower 0114 or tho foJ'k oupport, point (1), lta upper end olldaa vartlcdq along t.ho upper and of the 1lttlng portl.on or t h o - · point (3), It 11 neceasaJ7 to deteralna the a1101111t of veldlDI reqm.red. ai'Oillld the pin et \be center or tho - - · polnt CSl •

•

0

8 S fXI"'II•I !,rces on member ( hj ~ - p ( ~) eo~s + r, eMf)-

0

cr F,"'Fy

JM

F. Stiff) t

zero

left skle of

PsinB- Pf coss ~ o

+ P(kf/-}-PfV/, + Pj-

:£ tn:ume~e for~es"" membet {b) •zero

+ P[~).,m8-f;etn6-l'j,51n8t}>fs,;,t9.,. 'PcosQ~o

@)or f;,= P(~)-Fv ~ r P£ + P~ noUJ ie t eA~ua 1 In the abGvo fliiOI'• ), notice that the vortloa1 load (P) ot (1) o•=ot tnnoter wt ot (l) or (k) booaooo of t.ha ellde wblob oalT tnnofon a borloonto1 fol'Oe, Ja order to

i:;!:::.,";:.:! ~8P!:"J..~!'!o (~~~ !! ::!\f!:"' pen tbl'oagla tho pin at (S),

A1oo the horiaonto1 forooo o n - (a) ot (2) and (k) oro oquol 01111 oppoalta to tba horhontal forooo on - e r (b) ot (1) 01111 (3), :fb.aa - t tronarv tllroltcb tbo pln at (S). We can aee tbat the 98Z'"oal torea on t.be piA i.e P and. the horlzoAta1 Ioree le

F,• Pi

i

P('¥)·

P(~)

In the Slime munner f.tom(j)

F. oti>61o- p(~)$08 ~If, I!!OSS + psine-

d••e)

F. = _ ~ ~ F. ~ f ,. '1. -a- 'Sih7f h 'ShoS

Pi c..oseo

p -p tiT e <'<>:>$ S'iR9

Pom! 2bh • - n1ue of 1!. eon be obtained 117 uelng the '"'""'"'"' or porollel torooo or the aumatlcm Of tile t.ruavei'IN!I tONu on e1tber MJibNt to be SBI'O.

or

• 21 .

F;,: p{ b~'e)

Ftqu.re

6.

c

_,.,

A

•

90&31!..

tt1Jt1AI

®1-r ......·~

A~

: •• 1' s• opin:·o~•

wct.l -treated as" lthe.

.::

'

/pttld (paml/el)

l.O in"

I" '1.1!i in"

(net uette>n)

1

:'

... ' __ ,.1I

~ ,

to

¥

..6... A,..

o,an.lh

/Z, 308 P''

~

IZ,S1PI

~l
res~tl1emt

- 3,0Z8

p1.1

&f>
max

tensttJ'n

{net S«t"ttPI'/)

B

D -(b)

z·!b1~......

t'tmst der f~t 1iu.e lt:Htt:l,;q

- £70 weld metQ.{ a httd euery S tninl(tes, ~hn p4r dtt'( 5" dtt9 wee/( 1 fiO wee/<~ per 'fear for lo year'

A'S~IItne

{t'-'{B'/S"Xsofzo)~ '18-0,ooo. e~alt-~ C't:d~")Df'f @ 5tres5 "'

tZ

SOO, 000 C'fc/es ~I

I='F: :-

<.SilJI.

""'

'

/{:-;;~aD

:z.

'

,.B,Il.

elJ
bcndoi!ct lottd (tRinsverse) I

•

/<5.1

A•

t,.o m... ;

I· zr.. to+

•

ft1r /O,&JZBib {lfOrh) :-

if

/t:J'f,Zf!JO p. !6

_Me .,(?o9.zec>){3) I 2'-

'='

.rTb· Q¥141 CtH'II]JferNbr'

4~ I I tenst~n

iJ

max

tenst,n

(net seetroPn)

=

OWB-234

• 22.

•

c

A mtJment- em sec"t!~'r,{c--Ja~ member

•

.Me-e.

'1"18,

F, ( 11?a.).. 39,""-'-•(;;k':)·

..

ol<

ehec.k this Me-c.:

roo."* \

Fa(Bfz)•

'(~8, oOO'* _ /

S'1 76S"(Bi)•

From ihe:,e ~or-ces, de'5Jqi1 -the rnember

0 0

. .. !

2lte··

1 :

1311

11

/

f.rotn

'/Aotlr ... ewp1•4J. dttWct;

, to <:n$1. bear-. A p.rt10n Df tiJtt I(F;-Fio) ,·fl. tntns~er-red 1nio s~o.pptirt/119 butl-do~er blade qs(FJ.), • t'lii reiiiG'tnin~ ~rt1im (Fa) " J 'tr4n'$ ~errfd 1rito the member. • rn'wttnq tn G. bendtriq moment:

!,'

J

:

<''

·"~ '•, 1 .,"'·,''~',\.,@I ,l· .. ,

,/:,,..

{ FF~()()().,..

En
'""

')·\ '\: ""j·'

,/:_.:: . .....•.••

.r··v

fore"" in e•rcle(\.~re appluod to member

uitetnAl f.,rc•";, SIIIIA,..[J 11re I"Q'ioi\tecl

•

e.. .. ntcr WISe ra'taftin C+)


:E~"'o

b., member

~-.. ... u. •. ,.,,

t- £o,a(x/{33")- Fr(7.o)

f+)

D

8

bencla~
=o

-T·

Fr'" ,o,ooo~~) .. 99,oc;o'*'~,o,ooo( t3")

a. Mb.,. o

F; ..

o

beca.u.~e

u

tlio~om)..

I~

.....-til

-- ·- --- --. ""C:>

9~ '1~ o."'

F, + F-a. t Fr = o F.. --- f;-- F, ~ -(- 'l'!,t:JeJO) -(+ t~I,U,!r} •

.®

4'~---.ll

+~~~hi

ux.ed)

-tt.o,ooo•(n")- ;:;{8~) F1

~ H~;, .. o

If"

F', appl1ed io member +~o.ooo('-t~·)- F.{B~) F,.,. ~o,ooo1¥f-J:::. ;s-~ '16 o.'*'

"-"-:.-:,CA.tttC" member

~.hl"·o

"3'1, CJod"'

}orce'!.r,F. ll

noVJ '-"9-n"ider 2'111c. ...

..

I l!(

-t~~~~~~

- F; ~o) ~ o

,po .ooo'&~)

Ct•3.9"~

- ~.z.,'l·~

of the Qepl ted force'!, the mem 6er 1i io bend ttlCf

'SIA.I> jec. ted

~ F,~ 39,000.

. 23.

c

A wei d1~9 of

max comp~s,'ve ~~~ ~~ 4Ft{c-c)

c:r=.!!!... ... .lf'{&~mi.St . S.. zt:..l?in"

~orc.e

11,2oo P"''

i.-1.1 /en9 t-!1 o ~

r:

19

~hec/{

('heck t:dltJwahle eompresst~e benrJuir; stress A l '5 C '3t> c. I. s. /,'IS"' i~ A~l. 'Steel

[;.o - &:t J. Ce" j ~aE' 2 Cc Cb

•

2.

L:.

we·b

~

7 'If 0

•

IY ~

1~;,;.,

hort zon'6:d shear 'Stress ,;, of. member-

14." fi = s-:., 7~ 'I lb ~

5'1, ?{,L/

'f"= ~ • ,_._ ~··If•... i3, !'TO

t7y

&..o

9 " '3~""

weJcl.

3ftOOO =

r

tr =

-b:.p kr- t-o web cf member- a'f@ F, = 3 -,, Ot:JO fb

p-:.i

<. . Yt' "f.,,.. ~~; ol<.

/2{..,/

zoH

y.

D

8

we I d l~"' o~ /~"•' er- brad:eis torc.e {Dtz:J

lenptll ~·

le~~ ~e

to..

weld 11;19

ft:, 2uuer- bar -

Fa. • sz, ?~S 16s ~f.

ft'//d iS :l,?j.;"

IDeJ:I

o~

or

.. 2~· •

lb/t~ uu

:zo,:,

~

.

[be=... ~ th"'" """)

&:!wer- b1'1:1Ckts t~:~ web of- member-

F,._= S2,'l's- lbs

lem,tlr of f/1/e:i weld ('. ~....

r let srz.e.

8

2. &. '-ID

1M~: "' ,~ ~10"

fcrc.e ~I

•

) 300

''

w•

/fi~g

=- •

8"~e :1." =/~,,;

ratl&ae au-blo '"' Qld - AIBC - -ti.CD (37), cate11017 (0), k • lllln/""" • aero 2 at -111 .,. ueh pau or L qc1ea per trip • 1 trl.p .._ S mlmltea or z 200 z 10 • 7681000 qcla lD 10 :rears. haDae ue a,ooo,ooo qalea.

lb;,:,

'-~~" or

11 • 12 :a:

r'

't..... • ~ " ~~

tA.ae.@

'I1-.o k\l .. 'It<~ i

'b•:t n.t t • ~

.o.ce•"'

Z-t ....)

• -24-

•

A pulley ta very .:aplp and cflff1cul t kt CDIIJil&t:ely llft&lyze. llUla lnFol'llatian an the deaign ar pulleya. In pal't

@

I ltave found very

c

A

!: ~:;:1 :~:'.~~~ :ra!:',:~~:r!,a;~~:a::: !~~.'!:r~::~~· .m1 dtecf"

I ttave chackH U.a fDKn tram tne beU: an \tie pulley and Htatnea a

::C.~~s;:.:::c..: ~= ::-:.~ toba~:. '::~. (f r) D w.ll

u

the raeultant af She

F.,"2.2,'1''i

~~

In pert

@

.-:::"

,, ,.q,-?··

~,~

In part @ I have conaldand en. pulley kt be • alalple bHJI, euppor:ted !ly UQI twa: beerlnge ihG obtalftad tu rnulttng bending IIDMftt an en. aullay,

I neve gone rurtl'lar lind conailllera th8 bllftdlng ar • pulley llll"'ich ~tea

a lll"'aft irw1H.

In part (!) I n.va trnaed the pullq Mall n Tile uU eppUee• e) radial forces b) tenoanUel force• to ttta rlng.

• 'U '4'15" fb a r.lftv. uaing a t• wlda atl'lP.

'·' "''•~"'~ "'

F,.•IF.'t2F;~ coset tFi• F;.•f(9J,'I¥F)£U('I/.'•I'Ir'/.2'1,Y6
/ei. Sop

S"2,;., ... ~e

"'

a 11 '3

+ (211 '1"}& = /I)~ 800 16

l!.;,.;.,h ,;., wrdth

Tna rln:g ie eupportad by• c) tangenUel ahaer d) a"'eer perelhl to the reaul tent Df the twa belt tanetan farces.

~~~&)•

.:!Jl:: ::.~:.:d;. :~l:!,.t:.~==~~.!~=d1~·~=-o:.:~:tn~S:~tng

aamanta.

1 ...auld augoeat you Check 'the warJc end the 11ethod Far accurac:w.

1 cauld neve •ada

a mletske, I have not rechecked t.he work.

I

0

B Wa wUl nat~~ treat the ehell es a ring and find t.he tJending atrueu on a 1 in~

The ""alumn Analogy 118thad 111111 be used ta detesina the banding atreesu wl thin tne

alice or tha ahell. The ring will be dlvliHid ln'ta l8 parts, avery 20 d&QJ'UB.

t~~ia

ring.

------------------------------------·-----

1)

1ha Shear on t.ha ring cauaed tJy t;he torelan fi'DID t.he llel t t.ansiona-

·-·-·-----·-. -- .. ·------·----this farce camaa fralll thll belt. and ac:t.a in • counter-.claekwlae dlrect.ton.

The ring ia cut at. aame aoint ea that. it beCDIIIte ataUciSlly datennlnant ..

2)

The forces are applied to tna ring enc1 the tlanding mament determined.

3)

lhla mament diagram naw bec:amea the load an an analogous column. lhta anlllogaus calumn has the same aut...ard dlmenelane as t.ne real ring, ttawaver Ua thlekneas ia equal ta liEl of the real ring.

&. )

Thla loiHI (bending moment of the reel 1'1ng) naw ia treated aa a) en adlll. force b) a bendtnQ moment abaut h-•l axle c) e bending ~~Ga&nt about h-y) ada

S)

The thraa •stresses• on the analcgaus columna) Pial G 8

The HBhtlng shaer from tha a!'jacent. snell, act.a around tha entire circumference or 18 segment&• in a clack w1Ba direction

b) bending stress a~t b•d

c) bandln9 atresa about

.. -I~!'/ !~_.:_ ___________ 'I "j, '/ 1';/-;e9ment



a;• §Y

nDIII Dacoma ttut corrective mamanta wt\ieh -.111 bri"9 t.ha at.attcallv dataminent ring back t.a the initial staUclll.ly inaeterminant ring. Their eigne will ba chqed and then added diractlv t.o tha lniUIIl. bending moment.

This meane there is a net ahear force undar tne belt. or-

.,(i\ .. ·.

Each mD11811t. 1& found by muUiPlving t"'a particular force Dy tna distance Hblun a Una through this fDrce and tna POint in quast.19n on the rlng. Mrment.a are considllrad to be poslthe if thev are in a clackwiae direcUQII. rnaaa diatencaa are ecaled orr of tne drawing. To get. the IIICYB8nta on aecl'l segment. cauaed bv the rorces, U ia necaasarv to di'I!IW a great. dlltiDBt.er t.hrougl'l the paint Of eppl1cat1an Of tl'le fo.rce 1n thll ring and measure tne anarteat dietance rroa thie to thll center of the ugmant ln queat1an. Un t.hls figure paint. a).

!I!!!!!

..... ~ I& I?

'"'

I bYr: F..

"'-

f.ot

,~·

1'18

50'

so•

~

"'$

?D"

~D'l I~•

1'/

<Jo•

3Sl lb<

/2

no· no·

li

/50"

13 /0

"'

8

no•

no·

?to•

-~"16

!(.,s Ta get the momenta an asctt &&QIIlBnt caused by the 1t is necesserv to d1'11W e tangent t.hs'ough the paint or aPP).icetian of the farc;e 1n tne r1nt llftCI measure thll ahort.eat alatance frOfll th1& ta the canter of the BI!Qm&nt in question (in ttale i'igure &eQAJeRt a).

'I'S" 1&. '18'1 lb• Sl'(

'i'rO 6> I~

.

::::

\'

:12l :1" /bs

If

tt"""t

!!!!!!: farcn,

{~· .:,: :~s

-25.

A to gat the

IIQmllflt&

an

ncn

(o) J £!!I.U1

16 15 14 ll

-26& •

aei)Dll!n't caused by- the

!!!!II.

-1.6.9. 37.,5.- 1,7&D""' -46.9 • 45.6 ... 2,1..0:::: •ltf.,.9 X 52,.0 a • 2,1eltCJ I

10 -521 • 21.6 • -11,•00 'tiJ +5'JO • 14.0 • • 7' liS

8 +614 "

24 178 '59

-•6.9 • 1e.o • • e•6 ... ·•6.9 • 26.0 • • 1,222"'

28.0 • -12,190

11 ......... 26,.4 •. ·12,800

QUB&tlon (hera paint a), at an engle of 32 Clegreaa ( tnil 1a the angle of the reaul tant farce of the twa belt tenelon fDI'cn). The attona,.t distance b&tldllen each paint of B121211Ci1Uon of farce to thla tine h maa&~Jred and 111 tha moment ar11,.

l!!!S!!2!!

·46.9 a .s • -4&.9 • .s • -4.6.9 " 10.0 • -

..., .• - l,lOl 14.0 ... 4,325 21.6 • - 7,600 H .. lt • -1D,470

·309.• -352 • ·396 x 12 .., •

~ faJ'cea, U 1e ftllceaaary ta draw a alngla Iliii"'tiiiough the canter af the B&Qmant tn

: :: ::::-

~:; 51,.0 ~==~ • • 3,755

... 9 • + 3,012

+73.7. +73. 7 • +73. 7 Jl +7),. 7 • +73 .. 7 • +73 .. 7 • ·•9,091 +6,1'7? fatal Me: • +15,61el inch pounda tM

45.6 37.5 26,.0 18 ... 0 10,.0

... •• •• •• • •

3,355 .. 2, 7&0 ' 1,917 • ... 1,327 !:" 737 ...

lie •J52 x lle.O • • 4 1 9lD ll ·39& " 21 .. 6 • • 8,560 12 26,.4 • •11,500 11 . . . . . 28.0 •. •ll,580

-46.9 •

),.8 • ..

178

::::: : t~:g : :

-le» •

:~: ~

-46,9 • 26.0 .. - 1,222"' ·46.9. l7.5.- 1,760~ •46,.9 X 45,.6 a - 2 1 140 I

10 ·527 • 26 ••• •ll,920

: :II.:

9 .,70 • 21.6 • +12,320 8 +614 x U.O • + B,&DD

~:; 55.] ~=~ • • 4,065 ~:~:-)

- 'l'l, o£1)

+71 .. 7 . ...73.7. +71.7. +71.7. .+7l. 7. +7l. 7 •

Sl.O 45.6 37,.5 26.0 18.0

3,755). 3,355 ~.. 2,7&0 I'll 1,917 ... 1,327

•• .. + •• ••

18 •178

17 16 15 lit ll 12 11 10 9

a

le.9 • •

81)

-.9.

t•.o • • a,&DO

_.,,, •

,5 • • l.l.. ....... 10.0 • -46.9 x 11.0 • •

Itt&

::.::: : ~~:g : : ~:~t -46.9 • 4!1.6 • - l,lltQti::

-.9 •

52.0 • • 2,"0 ~ ·•6.9 • 55.l • • 2,600 I -"'·' .. 55.] .... 2,60D

~:: : ~~:2 : : ~:~}-

+7]., 7 • +7),.7 X +7l. 7 • +7l. 7 x •''·'. +7l,.7. -6,l06

·•5,1!10

2• 118 ,.,,

37.5 26.,0 18.0 10.,0 ].8 .5

• • 2, 760 • + 1 1 9J7 ~ • + 1,327 ~ • + 7J7 , ... • • 280 .. • + 37

•117,) ·117.) -117,) •117.l

+117,.]

+li7.l +117,) +l17.l +117,)

+117,) +117.l

+117,) +117.3 +117,)

+l17.l

2.5 .; • •• , • • J,O • • 1,7 • + •••• + 18.0 • + 27.6 • + 36.7 • + ""·' ~ .. .9 •• 51,4 •.•

"+

u

l!I!U!

.,lUI

,Jl2 ,2J2

l.D • +

l52

l& •266. 15 lie 1l 12 11 10 9 8

t•.o ...

J,7tl

·l09 lC 21,6 ... 6,675 •.JS2 X 26, .. c • IJ 1 JQD -JH • 28.0 • -11,100 -435 • 26 .... -11,500 21.6 • -1o,•so •527 x llt,D • .. 7,!90 •570 X lt,9 a + 2, 790 .&lit X 4,9 • + l,D12

-•a. •

z• 178

+7), 7 X 26.0 a + 1,917 ~ +73, 7 x 18,0 • + 1,327 f" +7l,7ll 10.0 • + 7)7.,. +7),7. ).8 * + 280

•117,) • .7.82 +117.l • ·'. + 82 +117.l s.z • + 610 +117,) 12.5 • + 1,467 +117,.) 21.7. + 2,51t5 +117.l l1,2 • + l,66U +117.l ItO.) • + ... 7.30 +117.l ltB.D • + 5,637 +117.l 53.1 • + 6,210 +117,tl 55.1 • + 6,'-60: +117,3 53.1 • • 6,310 +117.l 49,.4 • + 5 1 8DO +117,) 42.1 • + .. ,835 +117.l 33.2 • + l,IOD +117.J 23 .... + 2, 745 +117.) lle,.2 • + 1 1 667 +117,) 6.7 • + '716

-ne

+57,)82 ""

-.9 •

-46.9 • lD.D liKD ..6.9 • 26.0 -'-'·'. l7.5

• • U9 • • eu • - 1,222 ... ... 1,760""

=:::: : ~~:~ : : =:~ ~

-1.6.9 • 55.3 • - 2,600' _,.,,, • ·55.] • - 8,680

.,,,,. st.o .. • J,7ss+7l.7 ...5.6 .. + J,J55 +7), 7 X )7 ,5 • + 2,. 760 ..,

-55,454

Total

"aJ •

2• 178

• .,

18,.0 • -

8le6:

leS.6 • - 2,140 ,

+7],.7 +73.7 +73 .. 7 +7],.7 +73.7

~:~=N::~ .,5JO ,,.75

,5 • • ],.8. ..

10.0 • -

.s

-.9

ll.6 • 29.6 •

19.7 • + 10.5 • +

52.0 • +

l,llld'"

55.,3 • + lt,D&5

to-

55.l. + •• 0651:

:~:~

: : ~::: :·

3'7,.5 • + 2, '760 .,. 2'6.0 • + 1,117

+117.3. +117.]. +117.3 •117.1 +117.3 ·117.3 +117.3 +117.] +117.1 +117.3 +117.. 3 +117,.]

l29 1,17] 2,262 3,380 4,460 5,!150 5,930 6,190 6,020 5,510 4,660 3,600 2,455 1,374 ft69

+117,) •ll7.J

l.8. • ....6 13.2 • • 1,550 22.7 • • 2,663 n .. e •• l, 7lo ll.t. • • t.,620 4'-.6 - + 5,225 1..6.6 • + 5,t.60 45.2 • • 5,310 ~eo.a ·•• t., 790 3t..t. • • t.,040 2t..4 • • 2,862 lle.8 • • 1, 737

5.6 • + 2.2 • •

~ ~z,e.\il.

Total M

lealnt

.,...4,037 lnch paunda

•

13 12 11 10 9 8

•

.l'.esl!!l!l_ +117.] • . 2r.8 • + +117,]. 10.0 • • +117.]. 19.] • • +117.] • 28.8 • • +117.3 • li,.O • + +117.] • 45.6 • + +11?.] • 50.6 .... +117.3. 52.7. + +117.] • 51,.] • + +117.. ] • 46,9 • • +117.]. 39.7 • + +117.3. lD.7. + +117 .. ] • 20,9 .•• +117.] • 11.7 • + +117.3 x ~e.o • •

W5!!!m

26,0 • - 1,222 .. l7.5 • - 1,760

..6.9

+7),7

•

657 258

....

CltL

cr>l

US!!l

.s • ... ],8.-

........,, +73 .. 7

!!!!II.

-"'·' • -46.9 •

-•6.9 •U.9 •U,9

10 -527. 28,.0 • •llt,'78D 9 +5-?0 • 26.4 • +15,Di0 8 +&lie • 21.6 • +13,280 -JS,'D3

(b)j

17 •222 . . . . , • - 1,0&1

··l5 •

!!WI

4.9 • - 1,723 a.o •• 5,5411

12 21,6 • • 9,~ 11 . . . . . 26 ••• -12,800

Total M8 • •1,519 inch paunda .a,;

!paint

•l52. -J!16 •

5,200 5,800 6,DWJ

+117,)

+117..,)

u

29. 505 l52 200 ll0l2 2UI5 l,21t0

+ll7.l

l!U 6&1 1,5)8 2,500 l, 730 4,810 :i,700 6,310 6,540 6,400 5,860 5,015 3,955 2,817 1,725 821

D

£!!I.U1

l!ll!t

U,O • - J,107 21.6 • - 5, 7!10 26, ........110 28.,0 • - 9,150 26.6 • •10 1 070 21,6 • ~ I,.UO 14.0 ... 6,785 • •••• 2,51111 " · ' . + 2,790

s.e • •

ltaaint (e)!

8

X

•222 a -266 • -:1119 • -l52 • •HI x ··l5 • ........ •527 • •570. +61" x

1,.3 • •

ll.l .. + 21.3 • + 31,.8 • + 40.9 • • 48,.6 • • 5].7. + ss. 7 • • 54.5 .. + 49.9 • + u. 7 • • ]),7 • • 24.,0 ID + 14.7 • • 7,.D .. +

• Sl,Uol. "'

Ta till Md • +l2, 21e2 lndl pounds """

£!!I.U1

+117.3 • +117 .. 3 a +117.3 • +117,.) • +117.3 x +117 .. ) • +117.]. •117.]. +117.] • +117 .. ] • +117.3 • +117.] • +117,.]. +117,.) X •117,.]. +117,.] x

.sa,ss5'*"

-.9 • .s.- 2•

15 •J09 • ••"'·•--U•JI/5

lpaint (a)l

c

lpolnt

-396 .... )5 -r.e4 •527 +527 +614

!!WI

.... 9 • 14.0 • • 21,.6 • x 26,.t. • x 28.0 • • 26 ••• •

-

- 1,960 - 6,090 -10,1t8D •13,ft0 +15,960 +16,220

,J ')t).

=:::: : 3:: : :

-U.9 x -46.9 x -'-6 .. 9 • -46.9 A •73. 7 • +73. 7 • +73,.7.

10.0 • • 18.0 • ... 26.0 • 37,.5 • 45.,6 ... 52.0 • • 55.].+

~~: :

469 :..

8'-6 ~ 1,222 • 1,"0 l,J55l,llD ... 4,065 CQ

: ::

:~~:~ :~:~

~:= 2

+7). 7 • 45 .. 6 • • l,l55 : +73.7. 37 .. 5 • • 2.760

.Ell!li.!!9!l +117.3 • +117.3. +117.3 • +117.3 • +117,.3 x •112iJ • +117,.] II •117.] • +117.3 • +117.3 • +117,.] Jl •117,.3 x

...a . •

lle.l 23.5 ]1,1 36.2

• + • + ... • •

l8.2 • + )6.,!1 c +

32.6 25.2 16.2 6.5 2,9

S6t. 1,678 2, 760 3,650 ft,25D 4,485 4 1 3]5 3,826 2,957

.... •• • + 1,900 • • 763 e. ... litO

-117,). 10.5 • - 1,2J2

~ 'l'i I~"'" ... >i"T,:at=•=l=";lrr.;,"-..so.;:...:.•OJ~Z~lnch.;:.....;_..;__.,. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ )paint (glj radial 12 _,.,, • 11 10 9 8

+1,780 tn.:h pauna1 or..

~

..., ... 2,1l0

-484 x 14,.0 • .. 6, 78! -527 • 21.6 ....u,r.oo +570 X 26,.1e • +15 1 060 +614 • 28.0 • +17,220

..

"·""~

-•6.9 ·46,.9 ·46 .. 9 -46.9

a!£!!!!!! •

.5 3,8 x 10.0 • 18,.0

x

.. ,,S" ~~

. 26.

... -

'tilt ....

178 .. t.69 eo._ 846 N

: : : ~:~=~-·

:;~:; ~~:~

•73.7 X le5.6 a + ) 1 ]55 1, •7l. 7 • 52,.0 • + 3,8JQ Cb

:: ::::::= ~',.

=~~: ~ :~:~

Total M • +49,9)6 tncn pounde 9

• • • •

=~~: ~ :~::

~:~~

•117.3 +117,.] +117.) +117 .. ) +117.3 +117,.3 •117.] +117.3 +117.]

• X

• • • x • • •

lt .. 9 13,.8 21,.6 26.6 28.,7 27 .. 3 22.9 15 .. 6 6.6

• + • + •• - + • + • + •• "' + • +

564 1 1 620 2,536 ),120 1,370 l,2DD 2,687 1,8JO 775

-117.) • l.2 • • l76 -117.) • 12•••• 1 •• 56 ·117.J • 20,0 • • 2,JU

+ f~,Sl."'.,..

•

A

fpotn& (a)

lpalnt (h)l ahea:r

I!l!!ll 11 _,..., •

-4&.9

"·' • - 2,)75

::::: 1~:~::

10 ·527 • 14,.0 • - '1,JB5

•

9 +510 .. 21.6 • +12,)20 8 +614

26,.ft • +16,220

X

.5. -

ll

-46.9 " 18.0 - +?l, 7 +7l.7 +7l. 7 +?l. 7 +7),. 7 +7).7

reaction

=•.. ,...

+117.) • ...) • + +117,.) X 12.0 • + +117.) X 17.,2 a+ +117.l 1111 19.2 • + +117.l. 17,8. + +117.) • l:J.l • • +117.) .. 6.0 • + •117.1 • l .. O • •117.) • 12.1 • -

~=t

~

• 26.0 • + 1.915 • l7.S • + 2,76Dc,. • c.s.& • + l,l~5 > " !2.0 • + l,8l0 M 55,.) • + 4,065..., X 55,.) a+ 4,065:

c:

1\ •

.... , . , JC

.5 • .. J,8 • 10.0 • -

+9).7 X li.Q • + 1,)2'7 +7). 7 • 2& .. 0 • • 1,915 +7l. 7 X l?.S • + 2,7&0,..... +7),. 7 X 45,.6 a + J,J55 ;;;; +7l. 7 x 52.0 • + l,B)Q _.. +7),. 7 X ~5.) • + &.,06" "" +73,7 X 55,) • + &.,065 ?"

•l.~ ··~

8 +&14

111

IE!!!£ -46.9

Ill

552

i,t1~

lpa1nc !ell D!l&!l

one

!!IW

.E!!IS.Usll

+7l,7. .s. + +7), 7 II J.8 • + +?l.7 x lO.D • +

•ll7.l a 5.0 ., ... 585 -117,) • 14.2 • - 1,667

•117.]

X

21., • • 2,560

potnt.

+7l.7. +7l.7 X

...

)7~

.5. + J.8 a+

zao,

.E!!IS.Usll •ll7.J X 4,& • • 5.40 •117.J. 11.8 .... 1,4)2

-1'1,"1 Total M • •1,655 ...

ii4!biil

,

l!l!!E +7l.7.

.s -

.E!!IS.Usll +

l7

.EI!!Sll9!l

2&.:

+117,3 +117.) +117.J

+7l.7 Ill l7.5 • • 2,760 .... •''· 7 )( 1!1.& 0 + l,l55 ~..

:~~=~: ~~:~

•

•

+117.) • l.& .. + 1.11 +U7.l x a.a •• l,Oll +117.,) X 10,9 • + 1,280 +117.J X 9,6 • + 1,128 •117.l x s..o • • 586 •ll?.J X 2,2 • • 258 -117,) X U.l • - l,l2& •117,) X 21,0 • • 2,ft65 -117,) X XJ,.2 • • J,51t2 -117.) Ill 37 .. 9 • - 4,450

N

.s • ...

=~:;: l~:g : : ~~}! +7l. 7 X 18.,0 • + 1,327 ... .·u. 7 . H.D ... 1,915 •

1&..,.0 • + 8,61l0

.. ,,,,q,

(j,atnt

•• 7 o •

X

-117.l •

J.a • ..

446

(JJJ

radial 9 +5?0- ... 9 • + 2,792

Total

•ll7,J

•ll7,J. "·7 •.• 1,562 •ll7.l Ill 2l.5.- 2,760 •117,) • ll,2 ... l,660

TaHl M • -6,1Sl lncb paunda ""

1,562 70ft l52 1,50)

.£!!!£!.&!!!!

2ft;. 178 • 46t,..

-~r.o~

Joa1nt

)7 _

210•

·'i,U1

.....,_, • •lo6,9 •

..., .... 2,582

9 +5?0 X 14,.0 a + 7,980 e •&lit • 21.6 • +lJ,zao -t

.5 • + l.8 • +

•"l,6'64 lm:n paunda

l!l!!E 10 -527 •

.E!!IS.Usll

=~~=~: ~~:::: l,j~~=

2,25S 2,090

+<~,'-'"""

of'f'l,~~·

Total

l!l!!E +7J. 7 a +7l.7 x

505 l,ftlO 2 1 020

-117.J • 22.0 • - 2,580 •117.] • 29.6 - - J,•75

+7l.7. 51.0 • + l,?55

c

I

DIU!1

"J .. •ll,977 inch paunda

8 +&14 x

4,9 • + l 1 D10

-ll7.J.

1.9.-

X

.. ao 1, SZ../0

2)4 &.9)

J05 22J

+I"JZ,SZf

-117.,)" 9.2 • - 1,080 -117,) " 18 .. 2 • - 2,ll&

·117,3 • 28.0 • - J,28S •117.,)

3&.,2 • • 4,250

X

•ll'J..,) X 4r..,8 • - 5,260 -1 s,to:r...-

Dt:.

-

I

!k)

l!!!!!1

:: !:~:,.

X

2,0 • + 4.2 • + 2,6 • +

X

.s - -

.... 6.9 • +73.,7

2\,..

l.8 • +

280

+7l. 7 • 10.0 - +

7]7

II

+7). 7 .. +7), 7 • +7),7 X +7).,7. +7l. 7 x

11.0 26.0 37,5 lt5,6 52,0

D

B .EI!!Sll9!l • • • • •

+ 1,327 )> + 1,915 • + 2,760 AI + + l,8l0 1'

'·'"'l;.

•117,) •

·' • •

-ll7.J.

1.5- -

,,

176

•117.) • s ••• ,,.. -117.,.) • 12.8 • - l,SD2

•117.3 x U.l •117.3 x Jl.S •117 1 l x WI.? -117.3 " •8.J

., ...,.

• • • •

1::.: .·

• ~,!llill • 1,700 ... lt 1 785 - s,&&s

: :·!:·::

,~

•

t•

•

. . ...:..l :.:.:.... -.

'!:

.EI!!Sll9!l -117.] • -117.] "

,.

L: .. 1 .........•

1.0 - 5.5 - -

: .. !

117

6~6

-117.) • 12.8 • - 1,502

-117.] • 21.8 - - 2,560

-u?,l • n.& • - J,no •117.l. ItO.& • - 1t,76D •117.) • lt8.2 ... 5,6&0

·t&,'U'S"

I pa1nt

(m)

I

!!!!!!!

l!l!!E +7l .. 7

Jl

.s •

=~~:~: l~:g

.EI!!Sll9!l +

::

l7

~~~ ~

+7), 7 • 18,0 • + 1,)27: +7),7 • 2&.0. + 1,915.,. +7),7. l7.5. + 2,760

•117.] • .., - 528 •117.] • 11.8 - - 1,J85 •117.J • 21.0 - - 2,.6J •117.) • lO, 7 • - J,600 •117 .. ) • )9,8 • - 4,&65

-,,,,q,

•117.J •

~7.2

·-~-·

..•. : !'

- - 51550

.;

Total Mm • •11,135 inCh p.ounde ,ur

lpa1nt (n)l

···-·~

.E!!!!!l

.EI!!Sll9!l +7l. 7 • .5 • + l7 ~ +7l.7. l.& • + 280 00: +7J,7 • 10.0 • • 7l7 ~ +7),? Jic 18,0 • + l,l27 :t' +7),7. 2&.0. + 1,915 ...

•

•

... .,.

...

.

'

I

<:·: . . :.·!·i.

-117,3 a 4.2 • • 49l •117.J • 13.2 • - 1,550 X 23.0 .... 2,7Dd -117.] • J2,0 - - l,756 •117.1 • " · 7 ..... ,&60

•ll7.l

- ,,, 1$'1

u

Total M • •I,B£J Pit

"\":. l \·,.

. 27.

I

"'""" - • • an ouUcollv - • ring (.,..\ riiiQ) ... """"" In tno flgun Oft page 11. Since ,,.•• ...,.,. an ftDIII gal.ng to tr8 cant~SII•ru aa a lad an u.. maJ.aeau• alu.t, 1 t will hi IIDH ccarrqnl•c to nsrl~~e~~ tnn ..1en

c

A

corrcant:l'eUd V8luu. Thla can be dane by aal.UplylRQ tha val-.e by tne ere langtn _ , ar 10,1 tnBa. Tho naulCIIIQ ...n.:onua\od •ol- an . - In

ar -

-

talllllollng

r~g,...,

• I /

I

/

y

•

•15,190 +17,800 +156,410 +l22, .. 20 .....0,)'10

b

" •,

d

+SOO,:J20

g

...99,350

h

....... 3, .. 80 +317,210 +139,770 ·17,730

I j k

. •

-85,1t4D

1

•111,)50 -aa,6lD -61,5lD -37,590 •1&,550

a

•" q

... ,090

Total·~

D

8 bDS!!!s !ii!l!!1 .!1!!1!!1 i!=!!l !.!!! i! !!!!1.siliU S!l!!!l • 15,190 + 17,800 +156,'-lD +l22, ..2D .41tD,l7D +510,)20 .....99,350

,. (+28 .. 0) • (+2&.3) • (+21 ... ) 1111 (+1 ... 0) 1111 (",B&) M (-t..,Bii)

+lt4ll,.ltl0 +31'7,210

(-21 ... , (-26.3)

(-28,0) t-26,3) t-21 •• )

, ... ,86) • (+14.D) • t.Zl •• ) • •

299,030 S26,lDD

•

+1J9, 770 - 17,730 • 85, ••0 -111,350 • 88,630 - 61,530 • 37,590 - 16,550 ...

(+ft.3) • -

107,560

•b

- 15,190

c d

•

~

g

"JI

k

. 1

n

a

1\

- /

/

p q

..

4,090

(Ml ... Q)

• • • • • •

425,JOO + •&B,l5D •),l ..7,DDQ +4,51 .. ,000 +2 1 1 .. 0,000 -2, .. ll,SOO • --6 1 991 1000 ...,, .. ,1,000 • -8,)4.3,000 • •3,913,500 • • •&&,JDD • +l,B83,DDD

c-t•.o> • t-•.a6l •

-

•

•1,559,000 +

U0,15fl

35.,110

--~26 /

c d

,• 'I

g h I

/

J

k

1 II

a p q

•

( 0

+!IDD,l2D

) 0 (-9.57) .... 17D,lldJ (-11 .. 0) • -1,815,200 c-z•.2> • -7,883,000 (-2'7.6) • -12,153,000 t-27.6) • •U,B09,DDD

+.ltlt3,.8D +317,210 +1J9,77D - 17,730

(-18,.0) (-9.57) ( 0 ) (+9,51)

- as,••o •111,350 - 18,&30

(+2~.2)

• 17,8CO +156,410 •322,420 .....0,370

••99,350

• • •

c-z•.z> • -12,aa3,ooo

• ... 7 1 98) 1 000 • - 3,0J5,'JOD • 0 • 169,680

t+U,Ol • - 1,5JB,DDD • - 2,69~,8DD

(+27 .. &) 61,5)0 (+21,6) 31,590 (+2 •• 2) 16,550 x (+18.0) lt,D9D 111 '(+9,.57)

.... 2,1t46.2DD

• • • •

- 1,6511,200 909,100 .. Z97,9£JO .. H,lltO

• . 28.

•

•

•

c

A

Tne reaul Ung •atreaaaa• an the analogous column tlecorq th8 carrecUng 11011111nta, :ln other woJ"da Cf'lange thel r etQna and add dlhi:Ur ta tha 1n1 tiel mamanta of the CUI' ring.

c

•

"'·· -r. • ?,JIG ln

.Z8,0

b

+26.3 +21 ...

• •,

+

.... 86 -~.86

g

-21.~

1

-26.3 •26,3 -21 •• -14,0 -•.86

. 1

n

a

+4 .. 86 +14.0 +21 ...

p

q

-2~.2

·24,420 -27,850

·27.6 •27,6

- ),6111

-2~.2

• lti1D

•18,0 -9,57 0 .,.5, •18.0

-27,850 •24,UO ·11,170 - 1,660 0 + 9,660 +18,110

~ ,,

i. !

+24 1 C.2D

+24.2 +27.6

+21,850 +27,850 +21t,UD +11,1'70 • 9,6MI

•''·' +24,2

• 1,110 + 6,1DD

+26,]

0

~ 9,6&0 •18,170

•18,0

• I,IGD •7,DD ... 6,900 - 5,6111 - 3,680 ... 1,270 + 1,210 • ),680

-za.o

J

k

6,900

... 1,1711

·14.0

It

0

+ 5,&10 + l,&ID + 1,270

•t~.a

d

111y• • try

c:.

.,,,

lil

+18.0

+9.57

~-!-!-:

.

··••t•·l . : ; ~ :::;

OWB 20'1 Tl'te L1ncall"' Electric

~any

Omar bJ Bladgett

Nav,8,1%8

D

B

"• M

•

c

d

•1l,&2D

•ll,620

•13,620

• 7,)50

.. &,900

.. 5.&10

-27,850 +41t 1 0l7

-27,850

0

... 9,660

"1

.. 1,519

+ 1,780

-18,170. +15.61tl

·ll,61!11 ... 3,689 -2~, .. 20 +32,242

"r

- 7,789

•llt,IDD

•1D,Il8

•IUN

• J,ll7

• 7,292.

"'•

-13,61!11

-13,620

•ll,62D

"·

- 3,680

M

y

-14~420

Ml

"r

X

"v

.

'

·U,&ZO • 1,270

h

+419,935

- 6,900 - 9,&60 +ll ''J2l

·13,620 ... 7,350 0 +1),977

•ll,620 - &,900 + 9,660 ... 1, 77)

- 5,610 +18,170 • I,S44

+ 8,215

.. 6,9r.e

+ 1,51t1

- 6,993

-12,533

- ,,604

a •ll,61!11 .. 1,270 +2"1,,850

•ll,&ZO + :S,680 .z~.~211

-ll,620 + 5,610 +18,170

-11,&20 + &,900 + 9,&00

---

"

p

• M

•ll,620 • 3 0 680

M

>2~.420

•ll,61!11 ... 1,210 +2?,850

M1

•ll,U5

- 8,863

- 6,153

- ), 759

- 1,655

"r

- ~.Dlt

+ ... ..,

+ ,,,.,

+10,721

+ 8,505

ldharet

+5D,OJI

•ll,620 ... 5,&10 -18,170 ..... ,148

M

v

·U,620 - 1,270

~D'J

• 2,5Jl

•atr-•

"• • ._..., r~ the laia1 laed d the .alopua column II• • IRQIIII1nt rram tha bendlng •etl"aae• about b-x) orthe enelagaua ~:aluM. "v • mamant from the bancUng •a:treaa• about ar tha analCJQOLI.a colUIIUI. Mi • inlt1al moment or tne at.aUcally d•terminant (cut) rlng, "r • final moment ar tha atatlcallv ltN:Ietermlnant rtng. IIDII.nt an rtng-

M•

Section Udulue or 1• wide l"ing

s~

MB•im~o~~~

- 1¥,6~ (1'~111.)'" =

,;, lk

.2"

~;,"

Bending atre•a in ring

tr=

~~

~ ... o{.. oZ.4

z.oo ps

1

t:."'mpres:u#n ~n &J~"t5Jd6' t etr:Jtdn 11111 ln'Sir:ie

-29.

c

A Ac\ually ,.,. ....u .... 1• lly 1.7!1• aurr...1ag ~lnp, on 1~· ...,ttou. Til• tnuUing bonding """"" an U.la 1~• Ofilia _ , _ la ~- a1ow•

Ha&-llanhl Clangl\udlne1) lhoar atJ.doan Uoo onall and ,.,. aUffonlng ring.

}!:-a::-=::,--::d ':n:!~;•.!:!:a:a;::,.!• ~":!:-~'=•~.:;-~:r::,~:r!n":.~=11

1 tna .,.._ lld'llcl'l ia

r-

1~ 0

fu thtl

•lila ...,uon, Uola HcaNa

UB,91DlC1~)

2.0 3,,

8

t.r~~n.teerlld

•

\hnugh t.ne lfltlde.

TD Qllt the ...a.. ahur, we laak t'ar two pairrte 411ftlch llaue t.l'la tp'eetee\ ci'W'lga ln &landing _,.,_ FI'IUI llhlld: 19 U.le 8PCIBBI"I m bB palnte (c) and (d) , 10.1 lncnaa

in...

·-··

• 1SO,DDD ln lila

The bllndlnQ a&rnsea ua-

-io,:&.

tr= Me JlfAIJIXi'btl"t) ., -y»S$1'

tM/cie

\ I?"= ~Jip.aro'trfi!J

:r.

:I03.'t

Tile ...'-- ttqaUva IIGUn&

_ 1, '9b pJ;

""·.f.

7. '18"4 q, lk yl'(,,;) - -1()'1, 200 ,;, ,~. .M,.• {+ 2,n1 ni lkY 1¥ml • ... 'D, ~~)() in 16s _ JI'IC: (-JDUIK>TI.,7) = - 89'1 fl$/

• + 5', ,70 p-si

0,.-y 11ft

For &N 11,• wlda IAUan, Utle

be~

UI,UII)(l4) •

ZDJ,'t

f.·(- B'l'lf>tiXJtl'\t'l,? •

the 1• 1111lda ucU.an af &lla rl.ng le 11,&110 ln lba. 101,000 1n lH

- /S,H'o AS,

~ (•ltilti'IOYI.6?)

y• z.oi+ "' +Z.'IOp-a," F;. • fz'IOpt.IXN""IAt'j" .... !r,oe o 1~'5

Tna blinding e&ranu are•

tr,.=

Ttta dlffH811ca ln \haea twa bending farcn auat &renefer out ea ehear wlthln a 10.1 lneh lenoth•

r .. -16i";fo-(!6ioeo) ., /P•/

l"o

or

TMI auUlda eurrace ar the lft811 hb • tang..,Ual ltl'au _,.1ah varlae fi'GII a tene1an ar 2 1 180 pel to a CIDIIPI". .1Dn ar 1,~ pel.

103()

lb;,;, per

~hnch (t~<Jt> wetrls}

Z07t::J C,'l/et we.lcl

Tha lnalR edge ar &he atlft'enlng rlng hila • etnlla wblc:n verlea rru a tanalon ar 1,170 Pill "' o - - l a n af 1,110 Pill•

B

D

Now ... will c::onat.ur the 14• wlfti Hctlan or tN 111'11111 with ltll aurr.nlng rlng H a curve be• .nd 111 lf thla lncr•-- V.. bending a\naBD to any IJI'IIt extent .. Baa O.aign af IRlc:rm.rtte, IICtlan 1.1

~

~-----

I

\

\

I A

I

\

ZZ'\<.!?it ..i"'tLS':t.-7/i(

I

\ \/

•. , ... !Itt' total

e~F

c•nte.r

-f:.-c..---.,..,,..,..t-u.re

Z S, 7

radt~

0

7

or

.

;, ...- csntar of ,,... t'l 1

1!.1~

y

M~AY

0

-tZ-bi~S

MS

t

21.'1~0

/1.08125

5,4JZ" ~D1~~ ~z.l'l$"0

Y·~· ~ ~ I. A

zz.·· _____...,

D

3.'1'1

at"4'IO

•

•

s-oo

T.•Jt\Y

Ia

0

31./l.l.

/IB.bS'-

l.!i/t.a

/j'f.798

m•

r.,.' T.•J:i~... T.'X, -{'l'f~)~ II,<{, '7'1[3- {t.!itJof.33.1'/S)•/f.!l.'7'/&- '18.'-FJS• J/{,.513ti{~-

bendoil<j -sire-s<;

mSiae

M( r:- r;.)

111 (zs-.1ss--18.) _ • o'l'l'- ft-1 g; = A Us"- r~) rt" z,.n(tr.?o7-ZS:S6"s:X~stre ..,. ,...:to/Jt> M(r.-rn) /1'1[?..8.-U.3H) ,. tr, • A {r~- r.) r.: 21..UC U,7"7-2S".iiij'211)

bendtn'l

.o;oz M

.Tn tlu"s PKRmple-

m-;u Itant .. nit ;orce

~ • . 0'1'12 .111 = {.O<J'I2.){2o'I.OOcJtn//;) •

'f,OOO.p-s./

~= .o,oz ..,_ = (.rHoa){zo'i.ooo,;,/6) •

.Z,oao.

Fr:i.J.~-~ (,)'+

post'

r: ·/~o/tl.t.7·n8S)+("'s,:.~j

~

i!'-/':l9.? tL,.;

lr'l -:;,;., £70 weld rrei::z ·• "e;,. 11 ."~'"·-'~'"s Z~'l.q,t tty,;,

r.o; {~I.OfJo,... 1 )~'''7}

. 30.

~. 11>3¢>" a,..

bea:l:J"t' ::Jf

n

!1;7l, use~

•

c

A

Moment In dtic at"@ /14

•

•

Ms +-

Q

+ M,

M.,

--------------e.rt•

lri.L Ft'

..,

!1.!1'. !!.• (Lt' +'1\ I{ r o f }

Fd=}(-t-M,•~..,."'Ot""""~+fif"'"'.''~YXGI. 'I FJ. M,= ~+'{

Lt' FJ "'N" £.., :t:ol +-?

F

L--iot~

~o~e.

nee. J

M _ B.Et ,.

M.,

'IFd

(~)a. &H

"

" M. t 1

= '1 Fd

we need

~~~:,t

. 31.

""' 'IFI

+ Ms

/1'1 (Lt> x;;;

•

And .a. M.L

""'

M~ • 14?

B

1

t-

M,"'fo\.: M-{1+ ~)~ Mr -rrr-y;:t'l t { Lt'

L-t

'"1

#))

'I

.M,,

we mu~t f,~d M,.

~

)

0

c

A

• ~>r

M."

f1()W

uns/der the

M11 •

1imer

dtic

a"t CGJ

B

D

Example.:

M,_ +Mn + MNJ

•

1

S Fd

56 /1, =jl.tl )L Lx;. +'I

tt' l{LJ.

•

Z.Fd ~ ~~ {L t' + I( )L

-+-L

xa.

F• 2 2,000

I .. ~\

/b

'!!.f/2•.

---Jj d· zs'J¥u.

2ol

in,

r.

--------------·---------vve nef'd M,

If

• /'!.,()()0 lb wt -atu.l • 2.'1,178 I~ wt Lva:ter • lb ., ,0 ~~ o~ -a-z,ooo 1\. em

q,'tO?S

Qt:at:-h

r; ='f ,;., J:. = 1'/ • 3•.s-

F-..

r • 14 in Deso
beo.r-1'11'3

?.'l-B

17

erlrje SIA('PIN"ted Cll = .s"(

11

= 2.06

• . 32-

•

A

ht vert AI shec:u- CU1d bendtnq. are -su/Jfec't to. q et:Jmp/e.te rever-saf 1 we CtJu.ld use tim Far tne fct t '
,;tnce

IJufr!r

beno1n9 i /e stret>S

a.llo tNQ ble et"' d. ir:to'n

Z7

'l,ZOO. p-o 1

c

t

-

RP~

or ~'ttl6){ '1so){2o) = 15!> x./IP6 e9cle.s

w:/1

"!>0 1./.Jt!

't,_• 1~k

u.se

..

oulllr

~~-o •

Z~a,aoo cqc/O''S

'/,ooo ps,

1.21,;,

,%111 iF

we were te~ a:>nsti:ler tlte ~ILter ecl9"'s of

li...

:r....

partt4.f pe.ae trn.fta·a '/fPD!Je weld

1::::.

(l"s-Yts>' = .s1

(2&>/)(,S'f

M.4 .(zz,ODoXls';y){.st){l+ .L 1 t - L ('lSI)

('Mi/)

t- .. •) ..

f'l.stJI

1?f" ~

f.",.

dt's c to be st'mp/y '1>1Appt>t"ted, {ht~ l.ck:JUid cbt:~rqe tc. ffle fo 1/f) IAIIn"f 3 •

or

3 'f zo llwi ,. • 85so/MO p$l

1;,

.?§" deep .

0 ,_

79.'100 ,~ IJ.

Th~ ac..t"ttal edqe C!dndt't;ptrS of. tl;e drs.'c w,'/1 he SIJme wh.sre be'tu;een t1;ed and s(mp/4 S1A.pf>ort9J,

fience ,the f'Q.dJa.l 'tenstle stress r th• :r:·~-· .::r: ~fe hu. 1:. wr II bE> ~ome wherC' 1h betl{)e{'n th("'.;e two sets of ~Jetf«e'3. ..

D

B

Welded

hl!et weld befltlecn tAe outer cliic an'lr the 5/vJft at' t»hf @ must be aJ/Je to trr~nsFer tl!ri mtJment {1<4) ffl)m the sktft llito the d~ •

71le ciratm Fert?lltlal

5,.,~ ~d'& 'ft'~B/m sa. 3 in.., ./01....

r

1/Z,?OO

ro • --s;- •

S'O. '3

qfso 11111st

z, z -.c.; u,.,

_

-

rmnsfer

a

/~'/':..

"'

torque af

- 1f3,ooo HP • 63,ooo{oroo). T• RP.., Z.'7 a

c:lo u

biC' sc t

of

we Ids

rc>~ht-.r/r:l 'J..•11'~-s.'fl':>'·

f+• {~v {'fr,if~:'D"I)

fo {ir,,S) • ZZ,OOO ( '12, ?S)

t.· 21.ooof"t2.~~):

sr..'I(:O

lb1

n /Js

Yi>Z.x>o 1

=

LfOZ.m-,

z, H-5'". lb,,/,

t

27.,0il>O If>

t,F( C

..

A..,, 1td .. 'Ita· zs-,2. ,;,

-...,-- ..

(. l: Is 'l A..,

~

I

S"f.,'IOO .. c. ( z s)

1.,1 30, 11>;,,;

Allllllllllllllffih: -~~~::;~~~

•

bead ,.; 9 stress f:eao.i/e

COII"DreS$t•e

-33-

_(7.1SO.;,"'•X3t~,;,).

Me ~·r-

~s.sr>t.

.e/

t.•

'1.05 "'";

ltfc /SO.. ";P){2.o\~.,. 2 [gl D;"r· 1ss.sst.l~ •

Mi

c Route 4th £d. PIIQII 220, CBU lit

• 1

1

~::a: :n-: ::r;:.: !~ ::U::r!::r:::~:f =~:,.:W"•

axle plu. any vertlcal portlon ar t"- weld, ... below.

:r ~ ·::1:!~..: ~r::::::!~ 1

Total lltllgth or alngla wld aaaU~&U to ba erractlve 111 tranarenlng the vertical ah. .r ..

L~2.(21'H~\").,.

701-'ftP

Unl t ehaar rarca DR wela.

3'1"Z"'" r, ..Y... L • ~

L•

~

1/,;8

y,,.

~ •

Lag alza or ru1at weld (£70 we-ld 118tal) ateadv lolld !..)

'f.

HI "fln

=(.7D7X'-' "'~ ~ •

ZCfS" •

""

but bacau&e or the 1 1/2 lnch thiCk plata, mlnl•um weld elza 11 5/16 lnch. Ir 11111 . .uaa t"- rauawlftG retlgUII load condltlana: z,onotooo cyclea atraaa range K • mtnJ•u • o, thle bec:amae AISC Fatigue catega.rv (F) and

1

'i""' • =- ..::!i!:._: II1-D 1t. i 1-K

=

Ill<'-'

but

_ 3F(m'!.t) .(); 'ftrlti'Ft'

not to exc:aed ataady value or 21 kal 6

a:, til.: ~~."!;-:. ::..101~!...""::"..-;;:.~

r

'

[r"'-t'-1- zmr.'lr:-r."l-Bmr;r,•~ft+'fr.'r.Yifltl){l"'kft-f"] r: {m-1) + r.'" (m tt) •

'

1C~.f")~).._1] [ "'-s' ~ 2!~'(11~s'l-Bt\Ji'6'{s}~J.,. 'f +'1Wfsffkl'{i>te'ftJ" o. I ?I ~le

Y'ltf.;'i)'fiGoJD'b'l.l'

ll1)'(;\-1) +

(s)'t~.. l)

&t<6tlfer) ·

B

D

!:rrt!.~":; ~~..:·~~~...

Thta Mlll produce • horizontal rarce or lll 111,... Jr we • .._. bn&lel ar ttt. natuft ar the burlAp or the ahll.ve ahairt, that thla rarce le eurlad aqually bv the outal' alde pl-'- end the lrtnBI' aldll plate, thla 1111111 ndu.n tne eppll.ad ron:a tia aiiCh Plata to 56.5 111,..

0, 2 Z

•

/1/C/tt!S

(•t <e11ter)

F•&SO" Treattno Chs outer atde plate

Roan ~&h Ed, ·PBu• 218~ """" 1

a circular pJ.ete* wlth IINI wltftaut e arrtnl hOle, almpla iiUPPDrte or rbad at tha autar adQe, w get a aallect1.Dn or valuee uelng 1111

ronuJ.u rram Aoartt•a FaNUlaa rar Straaa I Streln, ltth Edltlan. Dut-er

~J~e~

s/mplot •"P~r eJ

@ . ciro./4r

P!"tl'

..lth -ttt/11 f»(fo

o;= '" 8 /(s; t;;xmtMI ot

traf hilt

A 1:dJ, 37 melle:~ Rt center

Df~":j t>"'feS

8;• 3"1.6

a-,•

G

eir&A{ar pMtt' solid

',.4t&& w ~ent:fAI .tt -~ter r;

4,. o. :1. :l /fteMs _.t: t!mtter

Iii, {t 1<si

::.1J:r~e

c.,:' 1!), 1'3 ~ .at center

a:,. 1 tJ:: 32.$"/<Si

(<.,;

~f-'IH1:

711ts

wo~l<

follows on

5/Jee6®<111ti®

~o.q ~t~i

or :!-fent.i.t •f cBIIt4r r,

""'"'

(f..•

•

li,'J K';i

='fr•:t...

IT.• l.fn~,; ot

.

~.~

A,• ~'f.::t"i:

• 34-

Traa fgllacdlng aaclr:et and &hlll'lk for a large ba 1nvaat1gatad ln ragard to weld &118 and stresses an the unit.

~:oupJ.er

c

A

1a to

These •atreeeae• . .aceme carrrctlvB momenta whlel'l must be •ddaa tD the ar1g1n•l mamente of the st•Ucflly determlnent frame. Since they ere corrective, their algna IWet be changed.

•

•

The reaultlng moment.a tnan became t.he final mamente an the statlcelly :lndeteJ'rdnent.

frame.

·

='::.

Tnere lo one do the roaleUng shear farcaa occur only ln twa oojocent aldea, figure h), el' ua t.hey 1n ell faur alGae, figure (b) 1

-

21,'1{,8 ..

a._,..

The resulting banding mamants era

]

shm.~n

...

811C8UBU Of t.na lGDBIII f 1 t 1 we will aaeuma that the shank cantaeta the &aekat at just tw oppaa1te pglnta •

bdaw-

+ll.'l5'd'"'

+6o,fil7r~lJl;,JIILIIII!miiii[J]]IllJIIII![I\t
D

B The socket ra~lll be traat.ed sa a at.ruct.urel frame. It 1e etatically lndatermlnant. Th• •calU!Uft analooy• msthod utill be ueurd. Thh nthod la c.av•r.S ln Rmra d111taU in the book •oeaign ar Welded Struct.una•, Section 6.1.

T= /,

The calUIIll"' enalagy method involves finding t.ha propartlaa af the •aeaUon•. Tnat the fra11a H the c~mtla section of a column. The dlmwneiana of t.ha •aacuan• are the same as tha soCket, BJICapt that the wldt.h af· th& •section• bacamaa l/£1 of th8 socket.. The fallowing three prapert.in of t.he section 81'8 founda) b) c)

an axial laed (P) e bantling moment about pia (x-x) a .bendl_ng l'lloment about ads (y-y)

Zl?, '80.

atatically determinant, Md

Tha resul Ung aoment.s an than t.reated as s lDad on tna •analvQG&e column• These •1oade• will causa-

f)

.... =I= J,9",ZOQ,. 28'-~N. r; d, ,,.,.,~

area 1110ment of inertia about the <•·•> neutrllll ada RIGIII80t of inertia about the (y-y) neutral elllla

The fnN ie then cut at aoma paint, thh •ekes u the IDDRtanta are found using tne appUad loads,.

d) e)

BJiiel strne

On a I"

h)

banding streaa

l)

banding stress

th.CI<. -r.I!Ce ol th•'s fn:ane,

t~ for<:•~ ,!>~me -

.L

T "!fs''-

(M ) (foJ:)

l

p

"•. i M

1£

CPc>lurnn

aecUan~

Using t.hua •load&• and •ma!Mnte• with tha propartlal!l af the •analogous column• aactlan, the resultlrtQ •etrasaas 111 on thie uection ar• found,. g)

184 ZOO 11 tr

"r

'--

c

•.-;;M C

(J

y

=+ y

The ero~?. secfti:>n 1$ treated as .::~ Fr-4me{ , Tf t"s now t:""t so it become'S -statlcclfy cle ermmate ~%

0

•

·

~ 1.'14& IIUr

-35.

..-c:c..o.t here

c

A ·I!J,?I.>

-1!{11(;

O

-B,?Iii

f(ll~

•

,.._ '

,.

ilf".588

(IJQ)

--·

(/TyJ

......

... c.u. t

"---~,v--f -r;

-stmph'f~

the

wDr

I<- the f.,/,4,.,,,.;., wlll be u.sed-

A~tt.;,l Ea~ne on &:~nt:l/d'!OU'S

B

13end 1~ moment a~~u t

~,.f<M-o

•

i:;;;;J

.!IO,,ooo

E"I .

Bendrry moment

0

~

I'X-J<) QJU"J

l Jl.l?'tlGta't"'i·$:1S)-tl6.(31,1'1'1l'l.s'2!}i-3.tliU'/)ti(-31,J'I'tt'l.r6~- ~. IJ
,J ;,.:

\Jue v,',tl eomider t~ 10 mch /e.J19th 0~ StJC/<e'f io earrtt the two ~86.1 000 lb ~orces,

aolttmn

P• ;a(taX~j." YJ,.,'I) + (!tl;,_~:¥9~ .::

M...

~rom th1~, """ 9et the f1;.21 rvl'!!=fl?i'-: :.~-;tgtlcall'f li?deter,'Tl/,'nate frame

"i"'.U81b

abo~t.t IY~Y) axt'S

f!1y=-O

(,,871

Oi

=

.Att.c .,

.:z:;, .

''~A>o 14,c d;.... .r;.

{1_73D.'@/af'l.5"~'- 5) .:: OCt; d)/e-..r

,t2'139+0<)

stJ,,

s

l~..r'(3.o'1!'1) ~ In:

....

./If,? PI')

/S", rBB

c

I.J I,

200

J"··

/ 1,8'.3

tlyz zero

• . 36.

A lt m1ght be erguad that the torque 119 tronsferrsa tr•rouqh t~-11 fDLir plorte!l liB

co,ecl

fallCIIolll"'

• \!.1r· · ·

•

'·-·l

resij,ftr~') •o;tte:us" or correcir'ue /lloment'S

tr:L:: qo.e, ?JBO 3.l.S'

A

_Pl. c.

e

-t

c

2'1d 320 . I

_6;:, ?~,Boo F'IS":Js). r2 vd, 32CJ

o;, - .:r. ·

so.l. s-

Za6Q::>6

/~88'1 11>

ln thb CIIISB we cen trem·fer the two outside farces in tna 1st ~:notvels tc tnesu ·four farces Dy ad~1no the rall['b•lng ta the prPsent Bl'li:llysls-

·r:.cse roncr·' •; •ts 41C llo<•.· 4/.-t·.'·i- .J. t~ t ht' /716f!l€'rrf: of !i,.. ~,lafrr:>llr1 :1,...-/.',./mrrbnt ·frame ((-ut frQmP} o~ <:.hr:-e( 'I

Ll&.int. the colwtn ~alagy matttad. we CL.rt one leg of"ll:' calcuh.te tne aht1cdlly aetern.lnent fr-BILs •

ll:m.tnt~

B

D

- ~9.330

rr:,I:?••J '' 1>acl'

e,, a .,e.tc1.~!,"" ·""r '~~ "'"

had'

p~ 2·~( 9'03o)'91ta)~ ''/'l<:"ilt .P~6Uf

9o~ 380

tJ · C'

or tr.ie

+ 9~.330

a)l. t'al

/e.

In

/.Y· /)

11.- M'1'1,33oJ9%/1'f,S6jj)1 Ye('19,33tl)''17sY+ /.n 1)= +2,?S,,BOC)

/f;J

m"mud t?!oiit l'r-Y) , ' ;111 , fz/9''l310,l'9tef·'I.S$:.S)-t~(91,31o}9iaY-t.s::u) .. -~1S'-B.oa. !r.L

• • 37-

c

A

.

AX• .-...- )(

T y

moHment raJiiltl'l mi...rd •ses co tn preu tOn or "'"ll'lt•ve (-f:}

CQ.

•

rtM•n

L· /(

:t~;,(tHo<) e

:ui. (sM)•

,;,

ees ot

t

eos !!> s,;,..,

ll,.

cr

ll,.

set

e&v.a.l

JL).[s•nte•«L} ll--x sms ~ sin8'.:

eo~B·f -

·-.L!_-)· (•d

£ ~-r~•~

coso~.

sr~ ) .

. + :t.. d smo~...t cl

o-= e:

E

x(ech<-J) 1 '( sirr<JI.

r-}(. t!M"'f~ ,,n~

fo.- pcsiitof' :rl r•u;,

"""' pt'f;~.p st~/km.ln)

no,.,

+

t:lrtd-

!IIJ'l '"

Stqn

11

t enSflilt1 a.mptft11Dtl

D

B Notloo oo oheet (3) tbot tbo Jan lloJol .,.... HCtl.cm of tbe rtaa t.o1lda t.o alodarl.llo, !bLII will c111111e • - portl.ooo of tbo l'lDa -tlaa t.o - · radia~ l.mrard; placiD& tbeo Ulldor ol.rcaatereatlol c_...,.l.oD, eed ot.bor portl.ano Hdia~ Ollt'IIUd, placiD& - . ODder ~ormtlal toael..,

•

<•>•

Ql oboot tlfe l'edlt.l.q c._orootllll otnooeo tbrout~J>oot tho HOtlca ora detoft11De4, At tho bcttoa of tbla oboot I.e 111 _ . l e u tor tbo I.DterDal potootl.lll energ oboorbad bjr tbLII atraoeed oocu... , !be - 1 nhloo 01'0 " " - em oboot (S), oooumi.Da tbot tbe mu ooctl.cm (1 !.Deb thlck) rototeo - a b m BD8lo of 1°, !bLII I.Dtonuol _ . , la oot ~ to tbe -mal BDV/11 of tbo oppllod. torque rotot!JI& tbi~ tba oamo ana10 .of 1 , Prom tbla lt 1e f011Dd tbet tbo mu t.orquo far o ...-... or 1 1.11 )201,7 !.nab ll1pa !.Doh of looatb of rtaa, - · • tbo ootaol lllllt t.arqae oppll,S bjr tho rp 1.11 602,1 lllcb ll1pa por Inch; tblo tbot tllo octaol roto\1.<11 u ~ot.oe! !~1:!,; ~~~~:-~ !~5 aUOCWitertmtUl atrease.a are .188 of

4

:::.:::1

•aluu•

tbe nerap olrcumfenntlal teDIIUe et.ra•• 1n t.ba bo\t.om plate ot tbo •IDa 1lo fOOIIIII to bo 11,17 bl. em ahaot (6) ood an obeot(7) tbLII u r-.1 to...,.. o radial fcru of U26,J. tipo, Tbl.a foroo 1.11 n...sad to ot.roao tbLII ploto to bbo e._onDtLIIl toael101 olroe4v f-d, !be o.,..oopood!JI& Talno for tbo top plato of tbo rtaa 1e fOUIId to be 829.9 kt.po on · - (8),

U1ln1 tbeee nw

b

c d

t

lf•. ?J'3 -1/,,.719 -1(••1111

(9) ot tbo top, oanol.dora 1 al.aUor raollltonoo otfarod bjr tbo l lCI>al.todi.Dal web platoo, All of tbl.a l.o .,._~d ot tbo l011v portion of obeot (9) and 1t 1.11 Dotl.cod tbat- U.aa fGN:u balance oa.t Vff17 QU.

Shoof;

the vertlc•l •'-ar 'Lran1111fer ehCMJ at t.be top of ebee\ (10) ..... to be t.abn 081'11 of tol.rq nU. At tho bottom of ohoot (10) l.t • - tbot tbo .....,.t \nnofor lll.pt 01111110 o problalll, •-u~ at tllo bott.oo plato of tho liq, !be top of ohoot (11) bettor Ulliatratoo tbe problell boo- of the loci< of -t.tnc oold1l to tbo pbto of tbo ri.Dc 011d tho tnnnoroo web plotoo, fie leoor fl .... 1.8 a -tl.cm vMeb 1tOilld prool.de o bettor t.ronator of foroo,

f"--

.s\1" ·~··11 ...

;...""'~

-----------

_..tn.er

,..,.,2. 11

""'"""~'" rtr-..• .~,ft .~ pate~ """''

• -38-

c

A pto.te..

.!J c'f.:r~~'.r> k+11/i'l}.+(1:1.'1"1 x: .,'" ,, )+(""' ?.l}i ~

"/. 711.8

® . Ct.~%~;~{~9 [(-"12.J~j\~q"'''-,t..33,,1)t(• m~j ~ © '·'~n:!!\P [~u,.flt+C-:'"'"~·"'·06Jt(.,.,..,,~.

.B~/1

C'IB~Yj,.f83) f~m.l'f-:tf-13?,1'fvif2,8l)t{iOJ.Bif~. 1

j.86l

f'i\\

,fb

L

M3D•Io')

J

J.."

(each cJrcum Fe rerrtta I weld) or

the'~ t~J"

S"'t

eQoAQ(

7anfcl'lfl,f.t (emile fence ,;, rtt~

or lerqtb of rinq

-l ('-?.9'1o) =- ·"~'ls'1{27.'11fo)" ~tQioon of "','•)

i'KQIA.f

!lowc•llr Mt •c.i UAI "nit Ur&ue ,, •.

l = 6t'I.S'"'~ X'43..l'8 irl) S"/.3'{ in

a

10

• "oz.

I'

3

at

3'().t,7'l ~ (tor"'-"')

of T~

t!I'Jd

F.'

•

'·

/12.~.'/J /flf~

>,

fl.,r·.:>~e at~41 mrmol -stre:.s ,;,

(IIUSt

b~ frQnT ferred D« t

b~ ~ .. itat.le

weLd'l.

[

hon~nta I ra.duil ~orce (F.) ,r, th( •·~to'f' piA'te. of the rin9 rna~ abo be fz>u nd b'l the fDUo wn1'1 Mel !?~a.

The

PIJ.?~'

............

. ·,',,~~ ...... '~~~~ 8.'110~ ~<.'....: -~'\. -loo, ~-.

~/3.t.Z'r"''

fJ•.'·""' ('J"<JI!' iJI~ic ~~

rul!'f;auo ~ //. u,'fiiSJ

Now i/?e fRVt:'"J~Itin ,; ,; wfwt rod·.:i.l fore~ {t>dh~r un;te>rm or concenirafecl) t$ relflLIIrecl to str~s'S tlus ruiq !o the alxne Pircqm(ererd/a.t (l{oop) stress ! /111~ Foru m,~t be tranJnred throv 9 n the circum fer entta f welds t!onnect thq t hts ~tt"f71

phde

/.539 F

the

B

.......

force<;

~~"~ ~<•p

tht: actual vq/11.e of th~ :streo:>I!''S '"1 ITI"Ii ,[>lopirt:t the vreVIDlt~ value'S bl.j U"'o; foetor .1880'1

'

?P!f l""'l ~tweer>

f.:>r::<>

~r ./BBD'/&>f tho~e va/u~'S alread4 used,

,,

forces

•f"'C•cl sl.3'1m •p<~rt

fto~o now 011 ~,,. o,_;/1 ~•.,

tT

..,..p/t'c.at,~n

f'/•10

4Ntt '" 'fl, '65 ,;·,

,...,.tNt•)

tAere rore thF oc~··e>l t:~f19ular {7;)t,;;trt>ni'.J) eorre-::.pondr.n<"1 :;tre-~"''S wit/ 1-e

~/."~

£?D w~ld meta I -:.tead'l /oad

D...

li;

Fi,

~ .. ,.;t tDr•rAeJ ,,~h ~~P~ of torQ\lO per {nch o( ctrCL\mfercnce

(t...ced kyon"

~

to eacb otltt'r {t)/,

t·

., •

top

The auerl'l'le

eircto(mfercflf

the t"p prate ,,:

to the rtnCJ.

. 39·

p~te

t!"n1ider the

;n a -s/mi/tu m.:>•mer

,;,f

eompressive stress ,.,

~?./3Si/8.2_1/,. :t~./0?~

XSI

A

These are the ferce~ 4ffllecJ tt:J s~tton

The ~ t.veb jlfQtes r.uitl also d>(fer -:.ome ff";,•:t::tnC'e to mo11e rneh t".

d

c

I the n;,9. 'II'IS"

f ll ....

+

~~·

~"" port,on :J e. 'l.(rms'fn.unY.•·IDZ)sin•a•• ~(01.DM(n.tf3t,e3)•mt8'+Mu. 7'1ifl7,f81t.. 18'1)~mtd'J • Jo'f't'l"

I

boffonr pt:>ttuin

fbere 1.o o reoe-blo voaotor ot taroo (Ia!? .L klpa) hom \he IIPP01' tlonp ot the rea bnokot tlorWp tbo 3 tro-.... web ploioo l.oto Ulo U j l - plot.e ot tile rill&. ol111o tho web ploko oro ,.ldod dlftctlT to Ulo l'llla plato. I dCilt belieVe tbt8 Ia troo In* oeee ot tllo 1o1m' ploto ot tile rlq. It tlooo DO\ oppoor tbat the 3 web plot.eo oro nldod to tllo - - plot.e, I boo t11o rodlal , _ , ot 1126,S kl.po J'ell'llzed to poll - - l'llla 011\wonl ooa bo devolapod bT tbo n• brookot throulh tblo orlUC81 comer,

_,

zf'h('·"""YPl'/.1.1tTJ.)$ir,lfJ'+ M~.l11BX"V){.'-')SiniB''f- f.('f.m 'f"i''/..98'1)r,,lf'l' 'l!.oa~

*

g...f.....-4 ...bt

i tntsttnq momeqt M..(B)9.21.~,.,.7'C{u~)?)+(ll2f.H")(",'2o) <~ppl1eJ mo1116flt M• fll't,!>'ftt3.~l>8)

'31,~:t'll

111111

... 3o,96'"1ft

p

JtP

B

l waulcl 11Uq08•t eome a~ethad of W8ld1r'lg the 3 trii!1Mv_..e W~lb platu tD tne bQUDG plate of the ring rnu:Uon ae wdl as to tha tap plate. Parhapa tnla caula be done before the central and 1nward wllll plat .. are put tn The central c.reb plllte could tie welde£1 by uetng • single bavll groove IUI!IIld.

plac:•l

. --,.-~~= .

I

• I

I

r

t,aJ

F•1t'I.S~

I

I

1 :~

•

I I

I

I

I

I I

I I

L __:_.:_--:._-

ll·~·~.f~

1~

""11'l.Sil

·---·:-:--

t 1

'

I

'. ' '' ''

I

I'

.. __ ·- --'' ''

'II

,_._:

'--

·------------· I

I

I

I'

_

I I

I

I

l_~~=

msK

h'l"'-' e 1

U 11110Uld nelo to add same harhantd briiCk.ta lnllde the rtng secUan to help ln transferrinG the horbontal

r11d1ll farce dF C.2?., k lps from the flanglt of ttle nm bracket into the trBI'averae r11eb pletl!la, both tnp

LI :

j

...

-

I I I I

loaJ

. ' .. ..' . I

I

I

I

I

I I I

I

and bntt.am •

:J

l

.: I

I I

I

L ___

II 1

. I

moment. 7lte llfper /lprtiDntal mclt.;_l pus/res the -t11p plate .r;F tfte rtt1f tit~ o ~1174/ler­

'TransFer .,f {,acJ as

eom~nent

t!irde. The ~wer honiorrtllt rar/ta/ tompon~nr. ent~ tlte b"ttom plate-:. oF tht: rin9 qnd p
. 40.

D

~

A

c

Tht's .re-s;~tinq moment- ez"t 0 re.prneqtecl bq h,r-ce-s (~~ ac.ttnq o:t a di•t.qrrce (e), wilt CO~
M., • F., The

SQme

FoJ/~twing

Pr cos 6

z.]Z:e

cos S 11..,·- Pr 2.{1:

..

-.

re~u·stin9 mtJment < (}) ""ill co<~~o<se the t•r•ILe 4i!' point @

a

~

-

e."

--_A_

Pr sine

''

f., • ~b ">in 6• · 2. ~ e \

\

_L_

T,;1 "

t., e. .. -aPrs/ns /2. e. e

~

~

or

)

c.o«~~ter-t::./ocJcwtse (+)

-.t 111

torQ~.<e

Pr sinS •+ Z.{Z

cros.s sectr"n of. rin'l

B

- -- D

4A~ ~eded a.:. iheJ.e IS M reslstt~

0

.S -tor~ue, ,/u::;t rett3t'"1 ~17'(

same "l>u.pport reacttDn at (j) will cause tl>e tDI/Dwins torQu.e at pDtnt @

The

M, •

t ({i:-) or

also

~. •

=

f.

e

Pr

2.JZ • 41 •

e- o

-t#}

c

A

Up to the point. ® o'" the Jrrst lo• d

'(,s• 8• 0 it. '($" 0

8 • 415'·~ fa•

t-[d s~ns+r(,mB-W)]

M.·-ls•ne( d +,21lZ9or)

T.•!-[d CDS9+r(~tcM-t)]

T.•l ccse(d+•.zllZ'1or)

,-v••

•rt>

"•

To

• l&SJ!"OIP

--

--

-1192

+ 1811./UP

I

v. ]0111

429.

••z.

j_ j_

.

7

+

+

5

?

+

+

0

8 From po•nt® of. the fr.:St load

e

= '1~·

to 9.?

D

to P"'ht ®

0

.M8 ~~[(1-i}}sinc9. +htt- 4-)cos~ orjM... ?f(2.-./2.)sJn9 +{is,;,(;)

+

'fJ

sin 9

I

To "'~ [tlf- :lf) 51;,h ~- ~)12»e]t .r;C~J&e~ P,f~-li)cosQ

or\ 7;. ~(.?. --Ia)

el5 D

lfle•O"" .. ''~in, KtP

t

mrnrJeJ'lt dta9/12m

.fl ~a

fJ

f rlnfJ

~ !'j ro~ B-1

l

• •

.

•

•

•

.

-:. heo.~ d rQ.'I tQJn

on rtnq

. 42.

c

A ••lllc.a banding amnent

...... Ui5J. ln. kl.pa

=

Oft abeet fZ) , I have considered the foraes to be traneferl'ed tbl'cu.gh tbe two cil'aamferential fillet welds. If we aasume t.he flanges to 1 1

~~0~ ~ ~1~0n:!..!:f!."i!i

appear to be relatively low.

'• . . . . ln. klp

1

!"S.:sett!"i":~o~~o~..::: :o!:"'~:;.,.

~hls

work. should be checked.

Bowever, when. ve t.reat the flange as we abould, in that: it deflects somewhat and 1nUoduoea momut int.o the ad of the shell, tbeD the . atreaaea ill the shell and, of aourse, tbe connecting welds could be IIIQCb blghar. On sheets Ill and It I, l have used fomulas from Roark •a 11 Fozmulas for Stress au4 Strain• Fourth Edition, page 307, aaae 32. This would indicate a l<mgUudinal bending st:resa ln the shell adjacent to the fillet weld of 11,310. pal. On sheet lSI, I have used similar fonaulas fl'om Harvey • a 11 PI'eaaure Vessel De&itJn", page 14& and arX"ived at: a bandiDg st.resa of 18,400 psi, 1110 there is naaoft&ble atJI'eemeftt.

\ • lO kip

GoiAg' back to sheet: (!) , t.here is an axial stress in the shell of i50 pal. Consl.derlng that the unit luis an applied l<>&d of 4000 lbs.

- 11,500 lba., this would indicate a range in cambined·longitud1nal stress ())end.intJ and axial) of +18,720 psi t:o -9,055 psi, or a range of 27,755 pal.

"'mer:zn dimen:w®s DF-

se~t;t<.n

If t:heae fiCJUres are correct, I believe this would inclicat:e the .possibility of fatiCJUe ~l'acking 1n tbe shell just: adjacent to the circumferential fillet weld.

'l'he.ae calculations are on the basis that the ahell, with it:s axial load of 4000 lbs. :t 11,500 lba., is 11upported only by the flange. IUIOthe.- Jmpoztant question ill fatigue loading is the proper stress allowable to use. If rc!JU were to use AISC fatique allovablea as a

igU1de, the allowable fOX' the &bell (center tu.be) plate because of t:he attached fillet weld would oome under condition 30 1 catagory (B) , and. fOI' 2,000,000 cycles, t:he alloWable stress wou.ld be ,

o- a

I

•.!·

where K• ruqe of stress In t:bis example applied :::

and X -

;U~3oo

a

7~~:

:= • ;:!: P max • 4,000 + 11,500 • +15,500 lbs. J' min .. 4,000 - 11,500 • -7500 lbs.

-.484

eo the allcWable fat:ique stress would be -

•

U' • i~1~.484l 4720 pal however, ve found the maximum oalculated atzess t:o be 18,720 pal. Sheet Ull sbowa """"' possible methods of BUPPMt of the bolts to t:he shell wbicb will qrea.Uy decrease t:he bending stress in the shell.

D

B E70

i~ the amverler IS charyed ever'!

• 3'-o dars • 30 ~n

2x 2.'1 h4u~ or

..V~

U$t!

weld

h.t~IF

met-a/

h,u.r

szs;''OO

c.~

S'C4 ooo"" t» 2.~01 0t:Jtt:)"""

Pari11:i/ per>e~ra,tt,;n ~ove weld in siJeqrFati9Ut> cDn d r t16n @ CJr o::d:e9or'( ® 1"

~

=

1/,"oo,.,;

/e'l! ~... '!/::,~ ~~~

=:

0

lienee 141!!

7"= '"()()()psi !""rita I pcrrtt r.f,,·,,

*when -the rinq

9n'"' e wrtd 'I • ' 37u f: i/,000 7 'll' I

h:J.~ r.~t /f~S

;~

'I

't/,;,'7

-B-

CrDs:s ~ec

tu/n

~o

l!n<~f711P5

-[E]-

and there ,;. 11" lr~fl?it.'!:'1'1'ql shear Dn Hie weld ff"'m ,..,r:un.,, hence use J<· ~·~ = 0

:If". 35'1

beco"se of

"the

from

is tlite~- 90:

W~

hence u::.e ~· +Ye' Dr f.'2." de-ep 9roove .. ,.,

____________._____________

IJ.n &~nal'l<.i!S

:shot.t!d te 1114de wr'th the

;n other /'0:;/ttdn-s,

to pour.

for e.xQrnf>le

t/lt'~<>'

rm9

"7'hts ass~mes ~ n.9/d fla119.e 1 170 d;llecf.-~n,..., hence ;«s't an tfUtqf 'elnc/ ~pqq/ ,..~rce.

over

flpwe~er

flam.;f! d61M del!t?ct' and places behd//19 HffJil!lfn't on rne ede;e tPf t-he she//.

·&I

tm flte /1f'J(f 5/teefS /(;e ~vi// C'"n-;/der- (he 'Sfrf!,~IPS on 1/le shell eke to the ·mpvement ~F file f!e~n9e -

-43-

c

A Use ~ • F"rmu.la1

T~-n l~li r· P

=Jc~(:£~)

a~

at.''

•

b = 3'1~· d • 'IZW,"

t. t,•·

II~

~z.·

p=o

P = ;s;soolk

..

3

r

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lf thl• 1a breaking beciiUH at the lndlcatltd bandlnQ et.HeBIIa ln thtl ahell acJjacent

H t.ha flUe\ wald• parh.- eaN af thll fallowing ldne might tla helpful.

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• A t.hnldad round atack, wlt.h an offaat. could b8 1118lded dlractly tia the ahall and t.ha flange. lt-la ldOUld t.n:nafar the ulal forca aon dlrect.ly t.a the shall wlt.hDut aa rauc:h banding acuan.

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A at.ralQt-t thrallded I'DUJ1d atock could be walc18d dll'tlctly t.a t.l'te shall and thll tlenga. Trtle also would tiranafar the a:aclal foi'D8 mara dlNcUy to t.hll ehllll wlt.haut u CDUCh btlndlng act.lon.

~= + IBI70{-J,'f:6)= ; 6'li:J0pa/

A thicker shell aecUan adjacent to the flange, Trtle would grntly reduce tihl banding atraaaea in \lila raglan. Far PUtPle, wl tn 1 112• thldc aact1Dn next. to t.fta 1/2• flange,_ tne bandlng at.nas &J&OUlq reduce to about lt760 pel (calc...lat.lld). Thlt!l 11 lllhV moat rlangea uaad ln PliPlftQ and pnaaun vnaala have a hpand aacUan. and tna ahllll could ba uaad.

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If 'the crusher ia a\opp8CII ln one n\lal1.1Uan or e etrak• af 1 1/lt j.nch, end we ..."" thia la tne IIDIDUnt of 1110veant of the pitman where lt atrllcea the na1at1ng flarce af a atnl objact accidently di'OtJtJI!Id inta the crusher, th.na

Work • F d

Crank le S/8 inch off center .. Mu:lmum t.hrcw of Cl'llf'dl: 1a

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Ill !Wet Velda1 porallel to tile azlo of tho welda

f.~ v~~·•a,v.). t'7o•('IO•Z'I.~'/tl'l.l~·ze,'ll) •

r...l.

c

2. I2.S' r ,,.,

1

'l'l,f.'I8(Zwof4c)

••leo

'fblo oroJ oUFtl¥ Ill.,... tar the la>aitladblal olloor oo tba nllot wold lA \bl.o _ l e , 1ll.ll oot obmp tllo ronltont lllllt toroo •817 lllDb. rile lea ol.oe ot tllo tlllet veld. wCillld not ln01'88H.

D

8

T

h'l'f'

1 Tbo les ol.oe ot tho !Wet wold u """ 117 dlvl.diq t111o N811ltont ..,l\ f - ot b,67 lr:lpa ,P81' lbloor lllcll 117 tile wold aU-ble, Far ataaciJ loadbls aDd 170 •ld metll1 tbo au-llle

'f.&7"t.td._

ar

tu•(.101){11k~l)''

~15'

cr

u

"'

but bocaU8o at tho 2 lllcb tblok tlanp plato, """' uo FOr

(,30)(70 kal) •

n

kal

o/i •

@

tatliue load&• uaa tbB "'al.UII prod.d&4 "1 the AISC. • • • - 1000 000 oreleo, tlllot wold aOlldiUOII (JS) parallel oboar, oatoFJ7 (F) llld • fWot veld conditlan (37) tooolan tnnavene, oet1FJ7 (0) wW oGDVel. 1 1;,.• 15'~1

Ct...t not tD e~J

Z.l

I

I'""''-". a= ..,,.1..-

"'I)

@ veld on oolli:ID vitbbl beam oaaneotlm ~aaM!,{U2"}'&~'1\.Io) rn. {,.,.,. ..... • to

tbu .,., be

e.o'f .,Ill k,.

.-blod tba - · ...u

tor-

A pDI'tlcu at tho tleop tone ....t be trmofOJTocl -all t;b1o wold wltbbl tile dUtoooo d............q,.,

or U5e@

•-bldor

of thlo rarao u - - dlroot!J' Into tbe bartaGDt.ll atWeaere. f. • F ~ 0 dfo• li&.!.'l•z\ ..,~(p ""' A...,• .....H "" (1849 ...Z.)fZflO... J) • l 'I I

Tba

.. baaed -

""

averaae ot

3 eyoleo

pv hoar, 8 boDzoo, 200 dQU, ODd 20 roora.

t.bt8 1a a ualt. 1'oroe Cll tbe veld. of

Z~'l• ' " .... Jm ~·~~(, .....

~~·II'

tho roolll\orlt Wilt tone on tho Weld lo

~.·)f:+ ~:. Jr..o''+ r..C.l1

•

10.'1{, "'1,;.

tho les aloe ot tho nllet wld lo

. 49.

c

I b If

,

..

d

1./)0

:17,.

s.oo S.oo

~U..I

z

A

If(

Jlf•AZ 0

c. J~

I .r,

I•MZ

I

0

B.IZSO tl.lZSO.

/3.:1031

.J'{()i. ~~0112.

~.rid f'l"pert,es of ,;ect,;m

WT 8•3'- k= 9.41 inz :I;"' 'I 8. 3ln4 y=- 1.13 ill

/$"."1'17'1

c,• 1.011..~ lfl• /,?>"'I •n Co' '.ZS-1.~'11' l.iS"f in ~dlf1 f

/lever 6e.a,

t.r"' ~ ,.

M# PL

1¥--

"r

p:

r:;

{oi.d mo.qrnrun Jo,d en beam

e:~//e>w&~.6te ost~-s

,-=.ti.'

ASI'I Steel (f!Jenciii!CIK ftmpereJ) ~r· [.r,,){toox~l)" tJ.(, xsi

P.. .a_. ~ Kst)(~<.'1tO Jiif) J.. G. "6.0 in)(/. 8~ i~

" '1.55'"

•

2

W II.•"" Ar 18. 8 /p I,~ 83!.. ln4

A

d;•totJ!rSI

Y
Wllo•"'~

18.9

WT8•32.

'/.Ill

/'1. 3 S'

l.:t<

I..Z:.•i'IY

83(,.

Z4"l."76 3B1l31j

0

I

0

Z.8 .Z I

"TDtttJ

M•.AY

U'l-7 .. I

1,..~ '1'15'£!."/

0

.Ale> V· lf.ss"

Alloo.u... ble -sheQr orr J~in ch4nrett'r p/a9 weld F = {l~"qV1r po•IIOO<'Oi): 2"1. 2S' I<•P~

l/!0 WFiri

hortaqnf:-a{

l!'e!o:~'

lot!f SIZ, ,.f

smr ~Wet

Vo.Y ll'o"X"·'IIIo'l'I.S4in) 6 f . rn. l'-'':s·~""'•)li-1....)" s. '1

weld

w ·~.!;}17!c)·

~<.'

'"/liMtr tnelt

.2.~'i or 'At Inch

@

Bot. hooao.. or tho , 71$ !Deb t.bl.clr tlaop, aoat -

D

B

•

I,..= 'lfJOO, in'~-

At ceMe1"llaao tbON · - t . he ........ vel,d to t.r...fer 72,67 kip, there u a vold at. tho top •• v.U •• at tile bottom at t11a bozo, h811Ce ...h veld baa )6,]4 kip.

Aoouoll! • leacth at

s lnchea

34.l4 r ~ (·707){11 ~1)". ye
At. - b 811111 tho reaoUon bot.t.cm, md oOilld uoe

u

Clleck bend triq :!tre s ~ in bea lfJ • M" (~o in'f.7S t
or veld,

• II'/•

- M

e>r

c _('15'00 in ~tX s1Et ...~

r- ""':-

36'1.~ tnor

<>

"

"'·

0

• "''

Thti t'.l Above the yietJ 5iren1 th () f A 'II.( I steo~l, hence · ac.counts Ft:ir the hell!ltn f'tt'lti? a/ermcment /Jend occa<;;/on.:rllr. Thtr wou.ld no h&~ppen /f the

hoU or ti!U, or 18,17 ldp on oaob veld, tcp md

beam were marie o" t () F A S/1/ -:,tee I lif_u.enc/111d and tempered) since tlu"s ht.l:t a /(){) ;<SI ttield stren'jtQ•

• 50-

•

c

t!!D~tld also treo:t as a ltne

't= ~ ~

~-'f"t ..

¥

li>t

Treat 1t?9 tilts sectton crs a t?;e IJ,.,)..~1d (t) a .. 3 t bm y-:f(.&.603)b,:: .S'J7'JS L.'t1

T:;;-

r!,SD

t

f.b= Vra.

where

C. •

Dm

J= 2.

r • f).O r 6!.,

l

colu.mn 1n bencla~

Check.

b; Y,..

2

.J>Jf'{.&,a3}'~-~')•Ji(,U603.XIZ.z
(.8660~) V_ • 3 lf~ll 1 Y

2.6"bm

bm

-

M·(~«
/o, zoo

tr= .t!Lc,.fJ.BOt::!.oooYtz.29). I 2,172.

pru'

D

8 chec.J IPnr/tudtital sheor from !Jend/;,_, -

~ _ 8(. B~)V(b!-b,') • B(.8,(,03'f.Str~:~'f1Z.Z't!ll.11') b-

15 ( 1>:-

ch~c/t

r lj, ..

Tlle unit -sheor foi"C.e

1.. it:

where t{b..-b,).~o3

b;•)

I!J ( ll.Z'f"-1/.11")

hnp/t-udrnal ';fht!!4r fmm • 'f 'T b~ + b," "

• 't(~DOO., 60)

t~rS/i:Jn-

~

n.ztt'+J/.11'

rep~"t, trecdl;.,fj sec'tton as a

;,;,e

' " l..fio t:b:.· z..so(ft)~t)'"" 21'-D ~= (!.sea. ""o :(tz.zq) = /P, ?oops,·

,;,

...

:1 16C)

hn9;t'11o'tn¢1 shtu2r from

or cou.ld trea.t

f. •

cthe ...... d

b

.

sec.t:/6n a.s a

on .. he- flcow)

T

,' I

·,

,,--- ---,

L

\ '

\

.

T

l'l 0

CF%o3)(.rooo) " 2.~( IZ.)

Sl>OIJ• 60

q' II! • (1.191. )( rz-)"

li • s: 1

\

I \

l.fi

IDnf/~~tdtnal ,h_r ff'l:Jrn

/me1--b,.--!f

where A = area t.ui thn1 med1on = z.sqa ~

lB'~ 3) Y.

Jt!!/Kitt?<;-

:

tof:s,;,njf Ol

\

,)

,'

,/

'b;,;,

~-----J

-51 •

lA;,;,

c

A Cl-= tr(r..'- r,·)

a" Z.'II'IO (b:.-h.')

y =•S"/DZ, ( b;-1!') (d,stance between C6

t:~f tll!'s (l~U

and Mil. of w/,p/e sec ttlfJn)

:C= /.B602

(b:-b.')

~

{d,\Uince betiAJeen c.c:; ,( t!lr., an1:1 and A/.A. of. LVht:~le sect1~n)

"'"-

!TII)ment of

I=

1nertiR D{ whofe sec:tl(;n

•

V• shear appluid tl> member/pnep"tttdtOal shear force on .Weld .------, dt.te "to bendto/,

~ !Drce D.!J. welt!- fn:~m benrhrlty

weh'

;rcr. ~-r."~).

( /lii)ITietrl- o~ lll~rita o( ~·;!,,k, :·1';·l.~)

V = shet:tr df'plterJ to member I~ per hnear inch of

~rea held !J'{ we/Js)

~~~~ ;-r;') _tt{r,...+r,r. tr.•) _ / Y =-,'IT(r...·-r.· - 31T(r.:r,)

.. (b~-~'")

(each wefci)

I

F= Vr 'l2..Y

I

Jl,.s pjr lm'enr tnch of we lei (2 welds)

..1....------'-

Tre4 t ~~ this sec. tto'n as a hne

(bm)

a., 'It A,

I= 6.11./8 b~ t

yc. ?BBSJ b,

ami(t)

• 25'5"<;7 f.b· ..__ ___v

b.,.

~ ~

L.emyita d11ia/

where

7ira...ea

B

c ·.H"3" O .. t b.) t• I.Z.t:J71 (6.-P.) J= s.?~"'~" ox-b.')

T

Uar.)

The u.nit ~hEttr f-orce ,.,

c. T(r-..t-r.)t 't 1r(~;.4-re"')

Treed ,,;9 f/le -s,u "tt~n 111s

f • 'T'"t = If..! i

f~"'

J

T 1.'30€.5"?

"· 31 3"'

1ft

ltne where

where

c

c

1. so,s?

l"t

where

t· r..-r;

T(r;1-r,)l"-r.) 1t

Zr.;•- r.¥

or

c.• r.,

b,

b, t b! t ( :

v

T "t

ft #1'". 1:"

Tt2:tv r:,

or .,...-£--t-.-~-T-r-:r--.

• /lfJ60 T"

b·.,

er bcase d upon shear- ~low

•.•/dl 'let the '5a.me result

. 52.

U.'i111'l

•

c

A

lA

+

....-----"\

\

~

~~-tl.ltS

"=:: .. ,._-: __

center "~ Clir~at.irE' -..1

Ths banding atraaa at env polnt (r) tn a sacUon af a curvad memttar ta:

center o~ 1...3rv4tull!' ---ol

r.· ~(1.Z.Alocj.li)·~ r;

T.i b

I .

.C==~~-r,..D

l

r.-

r, • radluB to inner f'aea Df IDBIIIbBr (and GU'tBI' fibBJ' Df inner plata)

ax/a/ stress

®

d.ii=-

.10 • radlua tg outer face af member

·r..._ ... radius to tnnar fiber af inner plata
F

A=

ANMJ00/1.

.2'/.tr,;,..

/

=+

3,;j,90 pt•.t-fensmn}

(!) (!}

I

B

D

I

lcmterol

.~

4

I

an bac.k 'S ,.cle

5tre:;:.o;:,

o; .. M(t;-r..) ~ {MtwJo•Pf.'i8s'JI'I•'IS'- 3-4/.L

1-r---l r·r01

benduiq

ll(f3·rn}

il--l

r.

('.9,2.!lJ.'-'·3.(,1Y.IV.1S)

Tot-41::

Force F=

1n

t

n.. !i?O •

3:190-

-

/Z,S'70ps•(t!1Jmprl:3SIM)

-

- 9,'J.BO ps/

fcomprPSsron)

inner flo.n9e diA.e io bend inq

A7r,"-r•} ~ ltt~,e ~: - (r,;r.)J

or

Tna radius
rF·

F ...

Z(arb dr) r :E .r~b c:lr

center of 9rtll'l.t'l

The Clanaminator is the total forr:a (F) SJtd h88 bean celc:ulatad above, BD 1 t ls anlv necusary to calculata 'the nuaaret.ar, and 1t la-

•

_f:!1k_ A{I;- ra)

~r

P~

{_n.-r) r

dt r

~n

fi~~ r~ • ...!::!..!_) (r,.-r) dr .~ (r.r-ra\ 2 A£r,- rn A!!i•rn) /r•rt

r..(r...-n)J~i ,.... )

... ' \

'"'G r, 1.,.5l..cr.~~-n)

~~

rt

...A(r;-rn) ~ [r.( r~- r;)- r"';z.-r,J so r,'

-ri)·(¥/

r;,(r...

r. lo 1

*-

{t'frt, ~00 x. 71Z)"'

or

{r,..- n)

- 63.

/t/)~1 zoo lb

oj:

1,,, (

tl11's

force

)

~.2S'•I.S •

·?lz.

(2.2f"' -J..rL) ~ /, 30/ --e.--

-:vz:.

/.827"

c

A

• r.,

Y•

c:os

e

F =- P(4 + r;. rl)ss)

d F• PZ (n• r;,

lu.t

c = hnF ~

t9) c:/!)

e

dF c r,.dD

a a

18

S/n

z ar~d

dn= !;dB

.B = _ .fZ... t; '5111

PZf- Stn!J) d6

r,.

de

F

B

-then

p,.. ..:.F...;.A.:..(~r..J..,-"r.;;.=)'---=-----=(
rn '·~e ~-

D Moment •r•• diatanca l:l•tw••n nautrel

-''II."- r. e.:o,,g ..

(r.llt- rt~

Bending

IMHnlftt ~~pplhd

H

sub si:itu ti!: tlu$ Into the Formula tor (f"s)

4 ·-9.1,3'~:i5'f• .. fi!/,'B6<.t"

to thla

M .. q~(n8'~in) ..

•d• end appUcat1an of laad

1

~::rau

a.cttan, uaumlng • 9

k.l.~

•

loM

?so,7e inch t
~,.

F Sth8 s {at r,) r.

mqximum (f,) occur:!> this hec.ome<5-

$/nee

when

(b<~ th welda)

r,• r. (r,-fi)- ~(r;!-r.'). '1£3{4\-,t..)- ~ t~'-("'1.), = ra IDfc ~- (r.t.-li) 't"3'"-k- (c.~-~~) Thla unit ahaar farce ta figured along the axta ar the cantral afhct or the farce (r, ). It rtq:JI'IIB&nta the dlfferanca ·tn the rtanga ron:a (F) whiCh awat out as anaar (" ). tr the conn-.ct1ng WBld 1a nat located exactly an tnla axle Cr, ), than tn1a value nwat be adjusted because of the difference 1n the length the weld. If (r•) rapreaanta tha af tna connecting wld, than thla un1 t anaar farca IW&t be lrlUl t1pl1ad by t;. )

lnw.rd radial untt rer.:a an walda (2 flllat wdds)

t:Gia8

or

f.• .L.13.00t r. '·'-'-'llu~ ----·-··-

l'Blu•

r., •

Thia unt t r1dhl farca would CIIUae tha these flll•t waldl'

fall;~wtng

;(8.:1.~ JB.fj(,

(both wslds)

and

'l'f'l"''

• nn ------------

a Una an 'lha throat

ar

liSt

l'i.l'i II. '32 lfow check tha longltudinel shear on th . . . fillat welda.

This value wound tnan ba divided bY the n~r or welda.

£"&1.111p/e~

F • 106,2.00 lb.

__E_.. f..-£cttl'h)r.,

/0&,,2.00 /b"S ,.

(l()'t'at3.,t)z.2&

or

f~,. 1,630. ll>n;,

r;.•z.u• {~ld a.t ( oF Flo.nge)

•

tt2(oO ~· (l.oth welds) -. • "'

ea.ch weld

. 54.

c

A Tho - - longl\udlnol ollou

....,., aa \ha

£1'1111

uc\lan

.F,·. ~0 •r..(tJ) ..

tho OIOldo W1ll DC- 0'

chana•• ura l'arl1dlv t'lua. Dn

6

o

'llfi'

olnco tho 111 figure Ill , ,.. -.t.ce ~~ tile applied -ill!l -~ 1111

aau... a U..olle fane IPI l.D ""' lowu' f1U19e •

'1.2.0 ../ill

tn11 111111 lncn... VII pnutc.,. atran••

by

Beoauoe ~ flange 1e ouzved ltlle - i o o 1e cuzved), tbio U..oile fOJtce ...,.... an 1mlud J:adlel 11J1U f - If.,) dine~ · - u d tile -~ of """"tva ·m be ~ed m any oecUoD of tile fleDge,. He figareo 121 and IJ).

zr.s.

The tallawlno la..,. uw appll.c! an ttl• given era•• ucUan:. F t • 5.29 kltl8 fiiS'DI tl'8n8VII'. . ta UCtlan F1 • 1.28 tlp '••co PVOllol to oocUon N ... 250.8 ln k lpa _.nt ebaut n.utr11 u11 ar uctlan

'l'hh 11J1U redial fOJtoe applied m a DDi~ width of tile fl8119• 11• vide), figure 141, . .,.... U to defleol: deOIDwud lndiaUy l.D-l ao a be... 111 oo doiii!J, i u rodiua to tile oeo~u of can>a~uu will cbaoge al01>11 tile width of tile flU19e -.l1II!J to tile deflectloo """"".

Aalal litr••• an MC-t.ilm-

'l'lle canual pc>J:t:ioo -111!1 ll.Dwudl will ...,... tile ndlu ·~ tbla pol.D.~ to decnopa by tile -~ of tile deflacUoo. IU radial oual.D will be E • ;r-.

_.

""'

0

Ft- _ 6",z<'ll< I..C Jr" - '1.5"1111•" .. ...

~a 1'

IU oual.D ill the auaa.f- OJ: UDge~~Ual dluotlOR will aloo be ~ to thla -~. By ll\llUpli,.iii!J tbla valu by tile ~....

~~

:~!:·~~. 1:1.!;!.·~~,.:: :t': .~~~!:i~

:-"'..!!!"u...

cbaDgo iD oUaoo 1-reUiOD) will CIOCJUJ tllenfou, tile l.Dl~ial uoalle ·~·· iD tile fleDge iD tbio h!lioD will daoru-.

to tbla ..,uple, tile oot;ar edge of tile fleDge dofleol:o _...s l o a - ) , and iu J:..U.ae g tile aeabJ: of OIIZ9&mu wUl l.DOitaOH, pJ:odocio9 • paaUhe auaio eod a paaUiYO ~·• cbeDga l~ile). 'l'lleufOJ:a, tile ioiUal UDelle ~- l.D ~be fleDge •~ tblo h!lioD will 11110raa... Ae a renlt of thia auip of ~ fleoge beadiDg ae a beea, then will be a uaa-ae ~-11• ouaao 1-111!11 ac:roaa the faeo of the fleDge, being -~.oua •~· the of the fleDge ju~ aa l.D a olaileJ: - · Aloo, tble ouip of fleo9e acUOil u a wUl J:OUb ltll a~ ""' pol.D~ of euppoJ:t:, tile fille~ wold m tile web. I t 1o tblo J:OUU011 nleb u tile wold. 'l'be followlDg will belpa

Ill

If tile fleDge could be made thloku, tlleoe ~·-• eod

-~wuld-. 121 n - l d be po. .il>le to ..~ tile web plebe iD oli9bUr to • paiD~ - " • thb _.al.u rouUoa •~ tile tl8ld VD\1ld be ouo.

, We/Jed 2. '"Tiin Prets F~me

8

lfoOO

Jb<. 2~

®-------------

2...,

-t

~--m~q-~tr,rtl"T-~ I'

\.,.1.:..

L~Lw-·1~4l ~ett• of

chect v~rtte41 seetmn (i-i)

r, • .,, 'A/'• r.· .:r(I>J..r.#-)"' z·:..·~ 'Hf= ~"

cu.rwd'"'rl!

Z~t

£A

benda01

~~ 'moment" di<>
at"

ntm- IDMr

~

M(r.,-r.) • 2000 lb"Zllt'):''I.Z,!.z,n1

A 0;- r,)

-55-

3~''

re

'·'~ ~s--~z&) z.1s

D

c

A

r,·

?.$" £A

1"""£11(~~)"

&Jil

li - '·

.;!ll.t.,n~ z,.,..ZfO ~ -

37"

U!:!.u

F ZCJoo lh DO.& A= .,,7f;- /p'L

"

.Y~o.

P'/

ehecl<. buck/1~9 aF back. Stdf'~ 'fdresa- /S'-/0

+ '120 "!Dial

ps/ $mp) . /

- 1/:J.Opsi(t'tJmP)

D

B

~.,\w'n ~I. 3{.., &.~mprnsum

ol..=

~1 ~a·?"~

i

CJ>mp/'Y!IJS,;,n

'-i

•

I<-

"

'Yb" .%ra= z.

0

. IT .ac. =,. tr,.

$t11Ce

® ~nsert tr~

..

Dj.

./8%

11alue CJf.

we 90 -to step (l)

ff

/nt-o Formulct ®

• r~3·,o'X3.3z,.,., 4t ,., t(ff}'- .1836(s.3'Vo~)~+('-3Z.wto")z.

(f!f-rayz.

33 '

aoq ; ps

Shear dt'octrom

and cr/tJC.a/ 6uckl1i9 'S'trc!'S3 r.,: &cr- ,.. try

Fr-om f/11~ 1 we wou..ld e.xpect no

•

anws ua./ 6uci hn9 proi$/em-s

Since tlct"~<~al aompnesston 1~ a/Jout s;8"8'0.ps,' a/sCJ the tank w/11 st,f{eo thr; t-e9/on.

. 56.

c

A

I ® ru 1 ~""'

'·l~

'h

~.~r

~~" encl pfo.tt> ... nit ~=e en weld ( • '13'/,l ~ c

l" iMid
"

F• ~:\~:

'I Kt . • m

r '1•1?in leq st3e o~ f<"U..t weld (E10)

/.75 "lm

•tw. .. ••ns.~ .7o?{:lt~<~o)

w= t:..'?>t or

...:~e

=

I.'Jfl«tin 'l'be vvt1aal - " ' force ot 417,1 kipo "" the left, eater a tile web - 1 41recUy f,_ tile 3-1/2" tllld: plate tllrough tile ot l/2' verUaal fillet -ua.

pair

leq s,-2 e of frlld weld W

= .70'1{:1.1 K~l)

c

.

•

II B on

bu.t becQu.~e of l" 1

Y~' ~

•

=:=J:-!t

'l'be 2" l:biclo: :Lnll14e plate appl1ee a vertical alleer foroe of 129.1

:!f:.~

1.1~e $)r.,' 1:1,

~~~!.Cirtoo~':f;ll~~:f.f~!!:!.. of 337.5 kipa (oae-Mlf of 675 k:Lpel. toOau 417.1 kipo.

already 11110 a verttaal 7.'beae boc! va1uea a44

B

D

TT

v_. 1&6".'1!'

I

n!

------- f t

F,• ,3'1.2"

Yli'

1

F•.2S't.2"

L,

~

v·t:.?sk

I

a·va· ____,.,

";:a

.., '1•

=

186: G•

• .

~

.t;

;:: ~

•

~

t... ...

~

web plAt~

"""' a SJ!I9~ po.nef

.......

-

~

~

II"

... •

N

...

3~<.' ,~1·· )'Ill,' '""''

wep

?.•:~.'f•11'4'

"'in

~r U)e

ll,'•l:l"te".

a

I" tluC.!< V.

we6

J8tio'i~

r

fiii•AY

r._•MY

SS'.I1S"

'IS.ll't

:t31'f.~'lS"

•nrnsct

,.,.,'J,qi.!

4o..:lS"

5"'1,5"0

Hor;:.ontal shegr

I ··'-0 K'\1

f

oil•?"',../ cDMptrn_, mtVbf <»ucr t-./ti""'DF- ..,..f>. pfa.te w~ ... td d" thts

"i"=~= ~· 1~,<(0 11

-

30~,,.'t8

3867.
ra /&•..0'18 Ul'f.'i S'

'.IA."\'18

~~~'I~0."-8

.. .. ~, 1 r••-

J;.A• l:t:r"i-(rVA)M• n~;J'IO.:l8-~'f.'i'&.(3f387.'138)" ss;'J."'/,~7 in+

d WO';Lid be we(/ t~ keep flu$ w.•'tlu~ '1'•,'10G, -.'lo{'!t~)· l"f,'-/K1i <>tlrt:rw,.e i{le reo.oltlll?

~o.~?>

'ILl ..,

M _ '!S67.'1l6 Nfi•A"'/"ffi,OO

Yz" 1:::..

c.h
y 815"

A G.3.00

/'jS,OO

fitfd ,.,,.JrJ

?.20 L18f!i' IV= .101 (2.1 ••I) "" .-,

.....

~·

~· 1.~0 ftro

.,.,;.e of

,. ...;

~

..

we/J heiMu::en flaage A

-----

+

"'

"

v . 18(

t TT

hom.potAI shear ferce on {.,'1/et

, v, r,•-r

l£9

..,.,

i::}

~«--•

"'"'t

..:::.

'(.

: 'Y:r.. y (No..,woool>)

/~"' ~tie 7

'

b~
. 57.

pf fitlst

"'"14

befwetll tti!l (/sOfe t11nJ we6

J~3~.l•Y:l•?.lo.'•n""'J'ao.'!J') • .,,"' '3~ {n, 'l.'ll,ldt'J.'I .,etch)

0 3 w= ,1D1(11KS1}. "·"' "of., • .ll'J.

bec:,.u,;e

~~

:l~"

t m~<st

u.se

Jz'

~

lltm

c

A

,,.I

oendJn9 stress

~nner s~rhtce -

(Jh

/~6GOps/ I

/f.

thts were a

.,.. =

_,111_ ,. N>t:i I( 96

S

/,J2.7

st-rru91Jt =

hee~m

z 2 .n::> rw -,.

The. re~d~1is IJf. the ~nt/ffl/ ef.fect of fh1s force t;

,S= r;,(r.,t-lj·)-~(,_.~-li'): /,033fS"Z-,'IIJ)-~{.5"Z\Y•) ","lot." t;, lo'/a ~ -( r.~e·Ji)

F

~o---- 3. o•

8

.~· leI

fore e on t-he two Sl'cle:J. H'/0. • ) 73 u7~ 1J'!117• (;t,.,o stde" r., ~

I

trl d1a/

I I I

F.. •

F

m

fr =

or

•

3'70 ~'1,;, {1Jpe :uCie)

t'Ats res~.~tts ;n 11 17!1dllil shet:~r st-,_3 of!?1¥11~ .....I "' ~~~ 30, 6oo ps/ ~ "t- '• .IZ

I I

..

fvce

I

1.--

./$'}

""'~

chec:;

l~n'fltud/nal

ass um~

s/tf!!4,..

r.; • ,.d,/is

t~F ~

oF mner fla'19e •. Y''"

r _ F ,. 33'f0 ,.. 7 S. r-,.(a+t;,) r.. (9'1"/.~nY,•i') or I,=- 37.s- lbJin (one s,.'de) this res11lfs

Iii 11

..,.. = it. -t =

L

center

o~ ro.duis

J~· (1:.WI

de)

s1

:s

late~~:~/ skt:lr sfms of -

a?,S" --:;z::

,.

3/0 p•,. ..

•

of ao.rvot11.re

. 58.

TORSIONAL MEMBERS

A

c

{jf .s

Dl'f

~~... J

a "o"-.J

~~S"

; o....

rJ

oil

·E-J.-

J.i

~ ..r·-1 ...~o__, :!r

7:= a lLl

-~ ~

T.· D!. b L

~

4,.-l;a+~'td)+ !jet

T. _-T, a -{latb) - ia+b4Cl L

d-

e-T•bH..a ,.- E,R

e' ,E £.R

D

8 ·A

• ena enclosed. vlt.h.lD. MaD di_..lCII tbi- ot oectlCII at ·poW (a)

\8 •

=•

~ • shear 1tzoe.. at potnt. (a)

a •

eL

t.orelcwael rui.lltuaa,

sJI

~:-=~':.~ ••lon&Q ....,wr llrlot, n4lua or-..

1• •

n...&

aheer

n,.• PIJ.IIlbcr o~ ltnq,h:dialll

a ttant..erte mem••ra

T ·d· d R=~

l.

b+d

.~r~l:,.(T.
A, !DE,J;[

or A" ~ ~[.:!!._+ 4,- 1,SJl E, I,

~r,t.+JII,I>,U,+il<) ]

~·>or, f~ l~.sz, + R,)

~1 Jd

1

l u:,(n:r,.a..)+~ild(I01.~i;lj

._ If nBQlact d8fbct1on due ta bending af elda end end memb•r•• ::t'• cD «-.tr naglect. at.lrtn••• dYe t.o \.Qnlonal nelatllf'ce ar aide and end Ulllbar•• 1.,•0

-59-

A

SullaUtutllog

t•>

c

into fai'IIIUla (6) we get

G)

+ F2 sin (/) •o

- F; ian B- F sin cc:

Taka foi'IIUlae (5) and (7). solva for (F2 ) and sat these tlllll equal to aach other -

F

L"OS o(.

®

cos;

r3

Fit sin tP "

Fa=

+

-F-. (!05

tfJ

+

tQn I!)

t~ sln¢

~tan 61

'Sin~

F t!.OS

b(

•

®

tan& sin¢

F,

::::

cos ¢

F'>ino<

f

sind-

F

sin¢

h{- c~¢> - ~'f: $)

This is the tall g~~te of a trtJck. Aa the 1111terial is dumpeo into the tall and or the truCk, this oate ls pulled forward by No hydraulic cyUndan and forc:n the material into the truck under prea Sure. Occaaianall y a solid DbJsct b8CD111118 Janned into the f'rllllll 1 8118 left hand elde, Blld holds thia end of the frame fi"'OA I!Dving further while the other end conUntJas ta be pulled forward. The h""raulic cvUndera are capable or exerting a force or about lO,DOO pound&. This subjects the frame to a twisting action. The rnme la rather fluible ln regard to toraion because of 1t 1 a open J tleam .sections and flat plate, hDWJver 1t does have Iii 6 inch diameter tube llllong it's length &nd thl& contributes almost entirely to \he torsional resistance of the friiiDa. Thls torque therefore will be reeiated almos\ entirely by this tube, vet 1t alone doea not have aufflclent atren;th to do this.

_J~:

F,•

Leost; and

o•

F {

F,

tan~- s;no(]

l'osrA.

/j

tan tP + tan t9

F coosa(- F3

~

~OS

F, s/n

Fs-

d=60"

E)t.arnple

!- =

9

30. 00-:J

::>tn

I!)

s 'S

¢. , . ~IWd

';_l•t:;'l

•

.t736

tafl6

• 19'1'/

t!os¢•

CO'i.r).• , 8660

rp

/tJ.

0

:; in a.. • .S"4?

tan&

f3

icw~· S.6713

/'/;)6

B Po1nte (a) end (tl) •r• rallara mounted on the end mambar of tha frama in tracka flhown aa daehad lines in flDIJI"I 1, A force (F) is applied to \ha lower IIO:rtUn of' \he and

ll:aaba~

llftD

rids

roller (b).

u

!::la~=r;~~=·~:a:i~BCI!~!i:~ ~r:!u~:r:; ~~i) t:!~::!l t::.~!!:~;.

.SM,O•S.'-'113- ,S()OO) .1'1'1'1+ S:t;713

•

30,()00

!.'!!1:22,${>.)/1 • ........

® "so lb ® ·~~.&SO •

!: :::::..

~~ ~=::::;.a~~!~: ~~) d:,::.,rats!!!::'~h!n..!, d!~::!o~n::a:!::'.:'i~' =!::~ i:n~~!edroti.!:. the left, \here 1B an axial tensile farce

fi" 30,000 (

:.2 2,

\a

(F' 2 • F ")

./Cf'{l{=

1

~~= ::a~O::~r!:.:.=!: o;rt=~::.;.:a;::r~~!i~ ;:;!:•~r t~ai:~s r:!~~:r (~.a dirac\ ion a\ righ\ angles \a \he mSIDbar and 1n \he appalua dirac\ ion of (F ;),.

fr\

3

I(!:) •

30,000• '8,60 - l '17 3~

,,,so

AMlal fOf'ce 1n end aulbar ( t.analan) la the aame •' 00\h enda-

(!)

F,=-F'y ~t

roller

'-f,O/&

./908

(a) -

Fr sin B F.s- cos $ ,..,.. thio we gat

=-

~

= - F. tan 6) ~

• F1 Fs

g

® ®·

Sin~:a

\he 6 inch plQ& cantribu'ties the graatas\ 'ta the torsional reeia\enca of \hll frBM, lt will wUhtl\and moat or thia torque. Ita polar moment or lna.rtta la -

J"' 2.r= 2.(2a.JII,;,~) ..

+ Fa. eos ¢> taking the \he and

F

C!O$ o(, e

~H~~~~~Btlan

~~~HJ~bar

0

't- Tc _(I, 35'3,,ooX3.3~)

-

0

eo

J'" -

j"G, !!8

ao,ooops.i

Thla would 8CE:OUnt far \ha plpa tearing au\ of \he wllba of \he friiiD8.

of for1:11a a\ fight angles to the &Mia of

\a bl!l zero ...

- F, - Fs/nol. + ~ sin ~

6,.:2a ,:r."

and will raaul' in a al'lur a\raaa of •

At tollal' (b) .. taking \he summatlan at forcaa in lina of \tte u.ia of the and m~r to be zara -

F~

-i J,o~ o.ib

@ . 60.

•

Stepped box

/,,')it.

Punching Shear 10.5.1 10.8

·(3

<------'

CljJ ..

.30

1.0

~I

> 0.6

ifll

Of

~

= 1.22

ifll " 0.6 1.0

- 0.5U

~

~

OjJ= 0(1

= ___!!_y__all Of

0.9 ,0.7

I'

, .. tb

[a a sin 8

tc

Ka

+

!!t] Kb

r

Kb=1+3sin8 4 sin 2 8

@ ,, P

ifll c;; 0.5

· ab =

r

a;of]

a$

but not to exceed 0.40 ay

~;~n of plane bending

J aby + ab.z

K = a + b sin 8 a (a + bl sin 8 ..

1

..!2 tc

40 =...!Q_sin 2 11 (~ b ] tc · 1 + sin 8 + l + 3 sin 8

=

K b

a + 3b sin 8 (a + 3b) sin' o

[a a Kasin ° + ..'Kb !..b...] if out of plane bending use· ~----,-V

• Ob =

Oby

+ ObZ

actual punching shear stress

For circular sections in which JL> 3600 local tc ay buckling at IIXial compressive stresses less than yield strength shall be investigated 10.3.1.

a-. o,:v

1

_ lb . , fla + b) a a (a + 3b) Ob] - tc sm 9 + b sin tJ + a + 3b sin e

La

fillet welds limited to jJ .;; .8

If sufficient thickness (tel of main member is used a distance of

~

1.0 ____..,__. ~....--. if u .;;; 0.44 if u > 0.44 allowable punching shear stress

actual punching shear stress

®

1.0

(J)

Ot = 1.22- 0.5U

;

but not to exceed 0.40oy K .. 1 + sin 8 a 2 sin 8 ·

-

iTO>"Q.5

allowable punching shear stress

CD I; rp

.25

10.13.1.3

%beyond each weld, general

collapse need not be checked 10.5.2.2. The use of fillet welds limited to ll c;; ~

10.13.1.3.

Optional Yield Line Analysis Box Section 10.5.1.4 from Commentary) ( Table C1 0.5.1.4b

!11 < .s 1

axial load allowable shear stress

@

0.5T

'---------1

. f a1 = ut1.1.IZatlon actor

~

=

.!L + ..!1....:!.1..

n. ..a < 0625 . -,

vltlmafe

shear

Me

0/'1

.brace member of yie/o' stren~th

tz

=1.8

Ta i: t:

J..L----

tb ( in. (14a)

9

~j weld)

~ 1111/1 kf1.9llt ,{weN

(14b)

- 61 -

~

,

,,' ,,

• ----~~---- n fw •

Z.il7 (.7o7w){.so exx) ~

(fillet weld)

--4 1"1-

sine

, ,,

_fa_

weld_

fs., I.e Tat

ultimate .strength or welded COIInectlon ,

lb.jin.

~;sine

1,'

(lnif rorce on weld ,!rom /JrQC8 111~m1Jer of yteld stren,ptll

= Uy

,'

~J_j ___ T

I

----- ---- ------

F,

...

,.,

-----~--r---t .R

,,' ,' ----!.,·1

,,

1 -ll

4111 + JJ)

/

at f'qillll"e , ' _L:~

2

=

moill mem/Ju

shear area ,

_____

Ojl =

II> 0.625

.

for suggested values) K = reserve strength factor see commentary SF sef~ty factor Table C1 0.5.1.4& U = rat1o actual to allowable stress - main member

'·

+--21 -II v'1=j 4111 +/ir-

_!!__

OjJ = shape factor

r = SKF OIJ.-!L_

1111 ,','

in plane bending

lb. ) ( in. of weld

~w =*z.,7 (twH.3o

Exx) partial joint penetration ) (. groove weld (14c)

__.61.1-

_ll ~t,)­

Stepped box- 10.5.1.3

Matched Box

10.5.1.1

• If

I

.81 or I

>

(J

1.25 (1 + 11) ~· if T/ < 1.0

O(J =

I

(J > 11 or a < b sin 6

=

~

if u > 0.44 allowable capacity

@

I= F

(J

0.8 tc

ay

(J

= 1.o

I

O(J and Of as in Fig. 11

2.5

~

if

1.22 - 0.5U =

I

both

T/ ;;>

1.0

allowable capacity

1.0

(j)

~

u~

if

0.44

rLS'iil8 a + fJtc .Op a, J 0 12

I

F = 1.2 tc Oy ay

[ins + ~]

10.5.1.2

Full static load capacity of branch allowed if:

= ~

D

Complete joint penetration groove weld and matching weld metal.

D

'Y =~

n=aox=

~<

2

a D sin 8

22 or 'Y < 11

3

av of main not less than that of branch. tb 4 "t; ~ 0.72 or

-- 1.0

!~ "" 5

FATIGUE STRESS ALLOWABLES

11

>

1.0

~~~~ f'_l I I'

,

......:

"

-

~

c•-

u

E F ......_6 ~':.l-:: :"...,;:!

K

T

~

'

14- 1-

~

...

~

~ ~

~ :""!.. ~:-.... ,...

-.

~

.... .....

"""

r-.. l

...... I"

....

....

II:

~

:::::: ~

...

t;;::

--

~

...

T

10

10

5

10

·c-;;

if'

-t-.

~

s,.,. 2

iiiii;;

::'Iii:. .... _

!'ooi"'!o;;;: 8;

4

z

Ill

D 5..'-

""'

4000

30005

- zooo'

....

-

•

----5000

X

,.._ E'.... o'

an d U .s;;; 0.44 (main ·member)

1

N- CYCLES OF LOAD

. 62-

1--

t-

-: :

-I -X-

lr =

~~ ~ i'I;

!

r..:..

'!;:

t:=

K- I--

&i~ 600 500

Ill

4oo I

300

~

z

::iii 200 ~

Ill ..I

:!

100 ~ I

.... Q:

Ill

•

~


ctb

For Tubular Structures AWS 01.1-Rav. 1-73- Section 10

inspected TCBR

® ~ @ { reinforcement Butt weld- complete jointoff @

K-~ max stress

no radiographic nor ultrasonic

©{

T

= tension

C = compression

~~~~rcement on

•but not to exceed steady stress allowable

·

Stiffened connection - bela- joint Force is transferred through joint by additional -tarial

® ®

Mernbers with continuously welded longitudinally otiffeners TCB R

~@

B = bending

inspection TCBR Butt weld -complete joint -

Pipe with longitudinal weld TCBR

Stress distribution in lnnch is essurned to be unlforrn

R =

r~rsal

Slrnple T, Y, or K connections - no additional stiffening Stress distribution in branch rnemiJer is not uniform 10• 1a• N • CYCLE& OF LOAD

Check main member by ®or ®

CompleK tubular connections where load is transferred by:

®

Members with transverse or short attachmerm TCBR

@

eccentricity

Cornplete joint Partial joint Partial joint penetration penetration penetration groove weld groove weld or groove weld or fillet weld. fillet weld Welds checked bV @ TCBR Welds checked by @> lit (uniformly loaded) @@@ (nono<Jniformly In branch member loaded)

Stiffening rings

Gusset plates

Complete joint penetration groove weld

traduction in fatigue strength is caused by uneven distribution of stress in lnnch - . I Main member checked by @or® welds checked by @')

TCBR

shear in overlapped

TCBR

Here the attechrnent is long enough so It will load up. Hence a force rnust transfer out of the end, through the notch or change in section, causing a stress raiser in the 111e111ber at this point. Welds checked by @ (unlforrnlv loaded)

FatigUe Stress Allowable Categories

ALLOWABLE FATIGUE RANGE OF STRESS

Lap joint

Tee joint in tenaion·or bending

Also check punching TCBR

portion of branch member

in branch member

~..;;24

Simple T, Y, or K connections with fillet or partial penetration groove weld

I

® Simple K Simple T SlmpleY connection conneCtion connection Allowable punching lhaar otrass on shear eree of main At termination of double wrap

TCBR At termination of cover plate

Por R/t At termination of longitudinal stiffeners or gusset

(does not apply at simple tubular connectoons)

@

®'

Shear in weld

@@

@@

Shear in weld

Shear ·in weld

Uniform load on weld

Nono<Jniform load on weld

> 24, raduce allowable stress in proportion to

Allowable fatigue stress Stressfromcurve ®or®

-bar.

=( 24)

0 7 •

R/t

Where actual stresa concentration factors or hot spot strains are known* use curve

®

CURVES FOR DETERMINING DIHEDRAL ANGLE 9·35"

.... + t:JG-

•---.--•

t....

...,f-f-Y-/4-/'V''-V"'J.
uo ..

!:__ 0

:

10-

~

70:·-

•

..... ---------k./-l-?/-J/-,4~~~

..r'o

. l

"--~~----~---

. . ·······-------t>•....

'-/-'/-/~/-v--/-1

-;too- ~ , . -·······-·---Jl)!f..r.'/__,~V-,L­

~ta­

'6

~,. -----W#'~~

i -1-i..lW

ID-·-·--·

. ,Ii j

10--"

------4---1 tao

1W t40

tsa

110

t70 110

9=40" 110---

..

'ii-1'H ·-

rHO·•

OUIG

j

10-·--· ...

Ci

10 --···

'"

. .. 9=55" no-···- ---- ----- ----··

....~

110---- - · -

---

1 4 0 - -.. ·--~-----

r,., ____

----+/-b4--!-,---4:~~ ..

··--·--J-r-/·t-/'1-c.b-+-'..

j.lO---------J-1-'f-,/,_• -;,<--_;-<;-;._..=.,_.. 1

:~~~~=t

1ino-----·

uo----·

•£' •------i-

_______

1•00·----· ;;,.

•

•

0

1-i'-V'-/f'AY~""--

j u-- ------ ----'--/fi~A/-vi;A,/--1-.

!

,

j

tOO

li I. L.L .., ...... . 1

no

:

110

'

~~

uoo no

;

'10 t10

l.

110

9=6fJ

1t0---

tTO- ••

1==~-

:110 ___ ----·-r:;;

Juo___ ,. . . . tIDO~

90-----l

0

-64-

•

c

&n$ider us""l a fl!ld weld tlte

bra ne h mcrn ~~ t

oo· z<1.o,;,

II .~{¥,;

Il}• 2 "l,t)Jnt.• /.!),',

A •

?Z. Z' ;,•

I • '178~00i•

"' •

3 '18.'1:1

"1<1Yi!J1'.1171

Mnit [,rce on tile t"dnnf'ct'~

tfJe!d frettt:trdff"::J'3

.,f t'fpe. of vJe!d ) fll4'1 be 'o .. '1d by mult,iJ/tfiPJ fhe p<•nc l1·~"l o;kar :trp-;1. ;orm~la (T) b'f the fhtcl
fmct.

4

iP

L"

'h'.'QI"'

+

i;J I

-;frC~)

{tnoa. j,l.nlt fore~ on weJ:d.)

3

f'IO weto· mefQ/

f>OO ro
l<•i>s

A/5o

checf<

r. - ,,.o,;,. 57 -x- ' 1.~ ;,, •

11i71:-e t t,,s raf:o 0 r tt:>::lii t'"•ceed ~ J'& fhP /;ranrh merne.-n,e• 'll·t:t ~,.. tl'veiJri al~n9 tl,f' s1de p:ut1on of -!~r r:;rJ"er:'•of7 -seF.-'It.tJS Fi'f~.t9.1.'3

D

8

Un euen p,·s tri bt< t1i:m A•Z1rr-f•211'Cus;.)Cu, )• t2,2,,.•

/11

Pbr S

!)00 ,;.,

..-

39B,Z ln'

•

U(t!inate 5/iearDfl main member 5h_earqr«t qt fqil~
= /, 25 /CSI

f.,'> If),

3b r<si

o. 9 ( "/.() '")"' 7 IY>tn

10.5'.1

Bntt:e member "" vielrl stt~tlf(/7

S• l'll'r"-,•(/..}ll(u..f•~IS..S·' X• ~1rr' -o(IJ¥1rlu.G),'"'II4.' s· !·'!:!:J!f.·· '~e.z ;.,t

bend '~'1 ~tress in branch member

d L(J(J,J "n Connect r~t} Weld:.

s. I

/.B.t"~l· 68('-31KSoYJ~.;,) =

jl.f,O"f Kiln

5in 'tS"

'S1n

()Jtimate strell!fth of weldecl c.qanection

~..

~ ~. 3/ J<S/

:

z.~~>'1/.•Y2.t KlOI)

=

Mo'(,'lff•-IIP){:~.I 11~) ~ 3'Uo t(

"'ltn

I f " eoJip/stf> pen,tn~t!M <JnJtJ~I! wdJ were used, /t wou.ld not be JH!C~11t:lr'f to e/lec.l. the ab:JtJe unell41l d•stributtDn of /QQ.d

'T'~ iL{.£ + ...ei).. to,;, "'

)(,.

Kb

tft ,;,

(r:J.s' f• t.?s

51

.:>n

+ ~··) .. .s: so xsi

s.ao

t,re I

< ~. 3 I

the connect1nq weld

m

s-.

/0. 't -rn~ ,...;fiKIII 11Jdra/ ()£ frtlnSVt!""' /8t"'k 'IJttns "fPili"~ to flu surk.a• 6f tM IIIDin member '~»V be fo~~J 6v /110/tlplvmq tilt! form• r.,; !foe llltl,;,..,.. jler [t> ancl clivlclrivf b't tlte It:~~ srie
Lamellae (ettr

IJI'r>:e. or<

V o' J(.•/.75 tmJ rb•I.S8 Foon d horr c IIQr 1

'i f'!'Ove w elcl

Qrt

{t.,).

a(io=~(~+~\"Y' t..(§...tA.\ w t:,., "'•) t;; K., K, ) in

thic

er
tr='if. eot,om "'''t II'. In)

"'

a. 70 ""';
. 65-

,V.,..,

c

consider the ':lame CCJr~nectttin 1
,o

/1), 7. 'f

c!l;r

o-._.•

t-K •

(assufllr (illel LOe/ds mn9e OOr• z.B "~;

read

_

z.s~s,

1-

?v = 3 73

,.,.;

B.. t act Wlf -5trr..s ,5 ~ )'/ xsi ~ 3.'13 xsi hence f.ill~t we !ti-s or padtaf icnetrw.ttdtt 9rt»V€' welds ~

•

use<~,

Pe

Tn~re{ore use t>tJmplcfc penefttJtiM :;re-ove wefd-s <4nd ~~ io;

f·'<j~ cat e9ory ®

f i~~tr~

( ronr

o-...-••

so

to.'{, 'I

read

(Cbmplefe

~netro:t.,Dr, 'jrtJO•e we(ds)

~trt!'SS ranqe

u-.,.

'I ~s,· ~. ~,

b",. •

? ""

-r.a 3 "''.

t:
ts

'3,nce

f!:''et r~ (,o·n rrOt:Jv 'i! welcJ~

CDmplete

?.3'11<'>1

< ~3Jx~t'

hef/Ce OJ< are (o

uo;ed 1 it. wi II flot bt" nra-;.:;ars to ft~fet wefclf; Ql,c:/ l>e

tr"oue wetd-:..

par-tialrperyetrott<'fl

lamt'//qr I ear~'?<]

/tJ.

s; lf

tr".!! .~ •••XJ%tn). lf.lo~" tw

8 ~' itl 6rttneh

aJti4/

11&•

F.

A.

s~•

< zo J<S•

(IIi>)

The followill<j wou.ld be one of o;ev~rul method"> uled to oHa•n suitable jol'nt details around th~ l>l"'och mem""r- for the welded CDnnection

member ·

·

7~.2.& In\ = &,qa, Kll

y

3o'io 50'

~endin'i st~' tn bmncl! member 0.• ~ = ZSO ••t ., &. 2. IC-, 1• • .. J98.Z. •

tr:

t()tal

ht!nC.~ OIC.

so·

t. B''

n'l' to IJS"

o·

&,92 +.&."-.~ ?,S'( ICSi

qo• '37' u, '15'

A/lowo.bl;..., .,hear in mai~J,...mcmbcr (fatt{Jile 164d) . IA'l ~.·'l~e~ C«t&ttO"''W N~ , .. ofc/e$ K·~· +lit

,o•

h·om ~•1u.re to,?. '"I reAd st~ess mnlfe 'l>o

1':: • .-!it_. 1114 •

t-1<.

•!;t

2

1

= '3. S ~

KS•

Cafc..!ated puncht'n'f 'SheAr :rtrn'5

_.!t(r.K.,

'1' - f

t

~., ~Din 1:~ .J

I fr it>

T,.. • 2,S' n•'

{tn.t

n.t fo e•ue<J 5'1-;Jv af/•waiJit l>f '·" ~~•)

tJfl

("•z. + ·1>2),. T.'ff t.S8

main member z."'o ,,,.

<J,,;

h~r~ce ()/<

Y·

t

anf{le art>utK! ao\r< of bn>n
dihedrAl an'lle t::~nf/e removed frDm S.Or.to.re edqe remttin1nq antj{e ()f edqe of branch mem/H'r ind~<decJ

rp., ~

• 66-

an9te

+w •

()~

joint

~ +'10-c(

•

c

A

LOADING

SHOCK

W • .atlflllcar vcloc.d.yJ rddlliii'S/:Sec..qd

F • fr•" ..."""• ~~ln/ssund

Ril'l• re .. lv.toontmtiuoJe V • veloc.it't, tiKk•!•ec...nd

@ ~L

2

t • rQd ,,... ,

d,es /t l11t ft'll (rom ou.'t

m=ma-n. • W.• u.e19hf,

D(

nowhere when

'li!JtJ

5.

dt;,n-1. e, piF'ct it

tnc.lle~

'-1. IS pou.od'l

!J~C.t"/er•t,O,, olqnawof~' ~&&.. itlf•ec. ..

F. • centrifu'f"'l forc.e, f"'"-Rd "> r • d.;.t, bet""'~"'""t""'..r 'l"'"i"f ~rotattoir,1hch.,,

£.·¥

~~ndi< enl'rQu

h • h""!ht ol k~>uid , ioc ~es

Q'"

.5•den-.lf~oll•v•'d ,!V./i~ 1 ---...,.,--_;;-=:..Y.__ p• umt ~rnwr# tJt LDtl•"" 1 p>t -~:te:.t·o! ~x~-F_ _". t• ttme,H: tR"'t r "k..' lb. per inc.h

,..0""

, . t/1tJdlfht ,,. llle-rt>

nsr""

•

ft>r '" 1 b.rtf mtr.sC'I

F"ffl'l

P• power, on-lbf•ec.

Yf- • FV

P•

1 HP• ~50 ft·l!yt«• ~~JDOft·l~l,.i•• i>6tJOJi>·l6/>«"l'"·:JDOdlllrmin •'l'fl• watts V.Jo~ · ooot' on A)

D t.odl:f

~~ IPtOIA.41 to:


/n />{netic

w. m(v:-v,')

""'r:$<1

2-

In-pufte Mom en tum

~

mV

D

B ld1th thh almpla •thad, ona ahrta with ttte farmula far the mavuant af thl

11181Dbar, .. elano•11ian far tanslh ar CDIDPr.a&lva load1ng 1nd dafllt;Uan hr b8tld1ng. &..lvlda the applhd farce by thh mavam~nt (A) ta abtaln tha aprlng canaunt (K). The patantlal anargy atared h then-

hlghar fore:• from applied 1 aad

aame atrangth

From the abava, lt 1e aeen Ln &hoek loadlng, that. the fDJ'CB rasulting from the load Ia greater than lf l t ware appllad in e steady manner. Tha atrenoth of the material (member and welds) f'or all p:ractlc:al purposes la the aama aa when undel' steady laacUng.

FoJ'mulas are avallabla for cllllculating tha raaul tlng a trees and daflectlon far shaCk loadtng, but tbay a:r11 nat alwaya varv sccurate, thera Ill'S too many r'Bctara whlch wlll change the rasul t, Haa.a\1&1' 1 tnaae eua farmulu cen ba uaad ta batter understand tt'!a problem and • • 1n what dlnctlan one waulel go ta lmprove the problem. Far example, ccneldar a almply auppDrtad beam wl\lc.h muet support a shoCk load aL mlda•an, case (1) of Table l. We could Lake tne foJ'IIIUla

pt.J 1).::

'IBeX

far the energy absorbed-

F

I<=?;; ,..

E~."Z and cnange 1 t around ta g lve the

~:saul tlng

streaa-

• .jr..H..sz

.,,..

Although thls formula may nat glve a vary eccurat!' value far the stress (a) 1 nev.ertheleas lt daea shaw us that the atreas c&n be nduced by lncreaelng tne lenQth (L).

In regard t.a Lha Prapartv of' tna crass sBCtlan of the millibar, the

atnaa can be rKiucad by l~reaalng tha value af (1/~.

Notlce that we~ cannot

separate the moment of lnertla (I) from tha dhtence Co the outer flbar td, Lhasa IDUSt be consldar•d together.

- 67-

'18FI -rr-

c

A

·~k L..

m.

v

-"·

~

~instAnt

b~fore tinpq.ci

F,.•••

__...,

I

n• munber ol t~
mometrtu.rn ---~1

v... v.(m,!'~)

L

(bod~

£.· ,:. _,ins)

T

~

L.

"'

¥-

Kine~i

. e.tlu
SoM Y•lue• ot IPI'IDs coartanW are lbted belw.

i

"f

- - ""''1~!'f'=:.:..\ hotn thl~ I.Ue 'let

v,.{Ki

•

J:

7[

A

l

LU

-1M sum oF kitlmc .1. PotutMI t!l1er'f'es is undtl.t-+

F._=m,v,~

D• IJle<~n

dr4met<'r ol cod £,• rmd•l•:; tli- eiD-:.t.Crl:~ (~~.... ~)

x:_

~ -r~er~-,l r.~

V."lll'

z l111•.,;.•l + 2ii, From tho's w~ 'l"t

= ""'2T. + ~u.. f.."'rJ,V,~

or

8

r

1-ro---d:X:.

~d

~~;.,P'"'

T

~u.pports

l

ol \118

ends

bI

I

(•1 "'•

/ ~ •.ied

-1dll bo -~

Th

r*MJ;Jl!J;l r@:;llvir1

l

• ., llntut

.Not loehorc ornpoct

-~ct

-·

~

171, "·

~

'I COIIS
J(tfteTW:: enet
(m,+me) "·

D

hom tho's ~><e~

... 1. ~--~;;-d"~ t ~~~.....:;:..~....T

lv~·v.6n.rma} I c.·~v· IC 2. \

c,..·~

.. ~ . -6. :a. •

""'""'- .. ~~tilt. •r-

-

- - \118 ol ""' !lo,) I.e evenl¥ distl'tbuted. '!lie laltl.al fOI'CO ol I.Dpot (1'1) 1lill Dot be U creat, bea&UH tl8 I008a ol tile (Joe) I.e Dot --~reel aU at ..,.., but.l.a epraad aut .,.., • perl.o4 ot u..o.

-

..., (Pz) vi.U ........,. baoa- 1ua -

I.e aboorbed Ill

-jiGJ'ti.JOiol (liz) ottl8o_.,rto-not .....

-sac ....

<-.>

!bl.a prai>loll- bo ...... ldencii>J' """" .. oquival-· ..... ~"" tile 4apaDil1aa liP'"' bw U I.e . _ w aDd bw lt u loacled, for ezilopl.o0

Pufttoi/41

ener1'f

~ ~

or

I

~

and

tp • m.!!Jh

Ep•

Ejo•

(llz~l

fr.L£ +

2. a -/11, 'a 6

r.• F.' F. or ell;+ ~-Pt.9jt 2.

(liz)

lK,

I

'L

--71o~ suar .f IUMioU Pt::ft:'J...ff'""'"- is um'btnt ~

.

-[ -I

cr

,. f"c

-68-

+-lf:-. lI 'iir.F. ... +JL. -m.!J .!i. K..

~--~~~....

~

I

2.1(,

'

J; - 'm•'l F,.-

m,[~tN+~J

\S ~m.;:, 111,1-

Dr

"

=- o

F~1•i•~sfw!~~~

•

c ®

~11M' ....

of--

@

Y~Opllao

MH

Iron Dn dropa fram a Cl'lute 1ncl1ned at lt5° with 'the varUcel at an 1nlt1al velac.Uy af v1 = lDO lncnea par aecana .. The raUlng are etrlkea a bUIRPIIr .,.:a.ta, l.2&l 1nchea belaw. whl~h h inclined at

of..-

lfl'' with

tn.1 WBI'ticel.

Find th• raacUan an the plate ®• to tna fal:.lng an.

k-j<--ld"----.1

H-4

~

~

1'--Ji'

w-..•I'IS'.IS"

®

16

T 5"

1--}lz·

l

r. • 1~8,1 io4

® _ ..._•.;.l\1.::,_,

....l!t..[

f

plate

F=v.Jif

F·W.~/w.•+-~a.

F•W,~

F=~~ 2 n.u.~

F= '!>:l,I3Z.Ih f7""' z1,1en~i

fP

a•

6• (J./'1'1 '"

2'f, 87~. !"•' (),/fiO in

F•

N{•

--"'-

':l(W,~Wo)

:>.~. 0 l

3. lb•

r•

t.r• ~ •• '"'· p•l 4•0.to7,;,

~~.1 'l. 3.

F•

ll.s

z 1, 'I 's, p•i

4• o./0?#1

D

B a 11000 pGOII4

at S laabu • opria..

-•llllc "'

o~Uo S ldlell - .._. IJI to be otappod Ia • .u.u..,. ~ l.lnO o wU. !be ' - " ' IJI to be oluUoolll" m....- lor

veloc.it"t

llhat tono ... , tbe -tiDe 1111ldo be doolpo4 tor7

c:l,',tc:tnce

'm

fc.l!en

K

~

:'::""""

~

+ v"

(i)

v_,

/z)

'Y'"-r+V~t

t:

=

9t 9t ..

From (I) we 'let F/J.

E!.J-'

F'"

2 ·:~.11: p11tentl•l

trlnet/c, enllf9'f

~. m

set eQIA.a/

«'

2

.,..,.,'I

cr {~)

v.~- v., t " 9-

v,'

IF~¥'1 1'-,oso. Dr

A(JUJSO)•

/his

t'O .. fd

'80 :l.S lbs

pe tlarr-/eJ

lbs

or ('1)

on e41!1t '"PPDrt

b't

.Tr. th•5 n am p le

4

:l~l;w,IS Df ~'1 r,Uef wtl
v.. ~

~Ia,;..) (~ ln){.'1o?)(~I.OOOp-..j"" ...J1S 90• .IJ,s

.

J

V,

CO :I

lfS" ~ (/tJO y. 70710'/) "' '/0. 1/0'1 Rr/:~ec

Jz. 9 Y +'1,.z. =j z.{3~.t/tY.IZOln) d'IO.'ltfJ'I)'"

f'i)

Vv..=

(•'

t~

= 'o'(. 'lOS~

£?()1\oual:i

metal

'.j

V..gV., -_30Y.'IDS'10.'1107 3a&.o't

horriootAI d,:,tance

X"

t

:

• id:H>3. se.CJ:>nc/S

~

V,= V,

sin 'tS 0 •1DD(.70?II/J) :::-7~7107 ~ ..

Jl.~{~os3Y71.),7/0'I) = 'l:l.go ,;;~bn

-69·

c

A Tllo ..locUy •' &110 Uti I!!E.!l1!! &o tho - , . . lll•~o (V') will no& _,PlW any '•rca unleu tn.re le .... nii~.~C:Uen ln val.. tty lllwt te fri.ctt.n lllltd.,. tne 111111ng are _,.. t"- plata. Jr than ahaulct lr• 8\lf ra~n tn thill ..11'KU1m, U: would ba parellal ta the plat. . .., woullf nat c:auu u u Dend.

•

\

\ \ \ \ \ \ I I

\

The valaclty af the are !!S£!!1 to tha bumper plata 1a raducael to ••ra bac•u.• the an atrtkaa tha plata ~d anaota aut P•nllll t.a the plata.

I

I I \

\ \

\ \ \

\ I

\

\ (f.)

Xn.wwiq ""~.-1 /

t!An

Un

qet 8_,.nd

Tnis change in the narmal velocity of tha are caua.a • forcatta ba applied !!!B!!!lta tha platat and in the a~~Qaalte directian t.a the appUIId valocit'l vect.ar. Tnia farce may ba faunell in the fallawin~ ftUIRitar.

we

V,

\1." Jll,G/0 10hc • /!.07"

D

8 .l!!f!&U.

18 the applhd fare:• (F0 ) 11Ult1p11all by l.ha tncrnant af time (AT) fUr1nQ whiCh the fan:• acta ..

CH!NGf

li'C MOMENTUM i l the lilna ar tNI Ntutal invalvd aurtng t.ha tlmo ~T) DW11:illl1111 by ib cl'l.nga in velocity (Vn • D) ..

•

naw.

Th.tl of 11'1 will bl CDnltant 1:hrDUQhau1. it.& mtln fllll, tnat h thl flaw in IHM'Idl par minute will ba canatant.. Jr the m1tarlal bahevld •• a liquid, tlla erne aactlanal araa would vary lnvanaly 1111th 11:1 valacity, Tho fa•t•r 11: travel•, the .malllr would be ito craaa aacUonal area.. S1nca thll ara canaiata ar 11111111 aolid Jt.arttc:laa, there cttuld be ai:JIDII aproading aut during the fall, with air vl1da praaant 1n tn. intariar, a that ito craaa aactianal .rae ay app.~~ar to ba greater then it octuolly 1&. We ciiN\Cit mo1a~o~r1 tne craaa aacUanal ar•• af the ar• flaw juat •• 11:i atrlkaa tna plata, and if we could, it prabllbly would nat bl • true walua bae.uaa ar tna air voida. Sine• tha rna ar flaw at tho plata. ia tna auo 11 tha nu of flaw fram tho cnuta, we w1ll uu thl latter linea U can ba muaurad.

The 10111 of t.h1 ara in.,alv.U during tn. u ... interval at

rna valacity

J!I!I!!ll.el.

to the bl,..mper

pla1.~~r

h

V,•v,a..~(I1.0.,i30)"31,.Sl41S'13,1J'/• Tne valocUy

.22£!!1.

":l-:!.5.:1~

,;,n,.c

rnQ.n (m) =

(4T)

ia

A V, .5 tAT)

9

to the bumper Plate 1a

Yn·U...~'n{I).O?t3o)=312.S/ smY3.47'- 313.'1/ "Yser:

• -70·

t

A

If

we wue to ne'll~t. tlte dfeet DF tilt

hmper pl11te 4.5Semlll'f

ii..tA ol fit•

c

mv'

a

FlAT)

=

m

(v.-o)

I:HANGE IN 104£NTIM

IIIPULSE

F::::

B

'i1 we consider the effect of p/fA..te assembly

.

t/Jt! mert1a of tht' hu.mper

Suppaaa • 111 pound piec:a ar ll'an ar• ahaW.II DC.Ceaionall y fall out or tha chub and •tr1k• tha pl ta. whai. wa.uld be tha :naul Ung banding atr... on tha plata aaaMbly 1

~·zo•

~W

~~

pl...te

n•t.Ce tire r-ed~~.c.t/im ,;, ~rce w-ht~n Me Jnertti:t DF the bumper plate assem611.1 1~ ~~ns/d•retl

1.• zS" t.-ms

Ao7-~5",n' I• S3.5" in"~

d • ,,S1on Lr ItO in W,•z.~q.,

eQ

Jb,

w.•\}(wt")~IH.B lb., d.e.flec.tro'n

A• ~,'/let Proper t'( of bumper pla.fe t.·~l!O·

t ... W6•2S' N.-1 ......

A

lfi•AY

zo.oo

,26' T.·fl!l5"

z.s

.1'1.'10 2'1.'70

r·~ ~~!"

S'f,II>'IS $"(..(, '1

r•~t~Y

,,zs

19'1.1!.11(,

.:rs

IV

lf71> 6

welds b...tween

IAnit ~orce

- IL..e rekren<e •••;, £z.-z)

y

t "' lf.OI,WiD

"

00

wetJ

• •08

f)

Jnt:.hes

6" p/a..te and ~ea.m v~

%. = ?01 730. ~'

'l....:.l'~~=:..,.;:;:.A..:~.u. =- .:1.0 ~b. t~.y;nc.'!.,

2ll.t'Jt()'f 10 'f,()

,O'l,-1'1

z.a't ,;,

I=-l;-t.r,-f'=J;i'.:xHy){/>4) • Jo7.'f'[email protected]'lX6C..6'1 }..- /77.,7 fr,4-

. 71 -

D

c

A kriletic eneuty of moving frudc

E. /('f:.

tn..v~z

WL'41.

z.

Pot.entttif ener9'1 abst:Jrbetd b., Fa.

Ep•

Y11

set these _Fl ZK

•

29

Ftl

"'"""

ffJn9ue.

er

etr~~a.l

= m, -y-

v, '

ar

IF v.JK =

m.

h!J .1.•euer 1

-~ ·~

\ f.

\

B canal"er naw tnat. thl! trallar t.a atuck in tns earul.,

NM~

The t:ruck i& backe" up

allghtly unUl U ill. tight: agalnat: tl'le hUcn, figure (b) irld tnen

maiU!IB

wa auat .gat en BKIWeaalan for the velocUv af t.M truck at the t.n&tant ar

'"""u cv2l.

8

run far U, aU.empt:lng. to jal'k thl trailer aack ont:a thl!l roadway, flgura (c)~ Tna truck atart:lnQ st nat wlll eceoalarata to a velaclty ar (U ) wUhln the 2 111et:.-n.:a (S).. ale rlllll •••ume tb8 traUar ln thla CBill doltlil nat mava lllld tha ttnaU.:. anargy of tha n·uCIC k.!lll be abR:rb:ed by the c.ongue af tne t:rall~ar ..

A •vlnt tlady atart:lnQ •t rnt: and aut.jact to a conetant ~~ecel•rat1an (a), hence Iii eoaat.n' fare• (f)Jwlll prgduce the fallawlng vllac;ltle& F': ~

Q)v

®<J hence®

~·a·~

z.

2m. 2 FS

y~ .. 24':l

--,;r;-

lila wlll •••..,.. • c:arhtn pawer •v•U•bla at thta f1nel ·v•lacl ty Just befof'a lmpocl (P).

Ct-ud pulls a/Jcad hq c:

® /"'preunt t I!IDVIi.c,

"

Ft

m. FtL

a.t!!La

P"FV

Sull1t.lt.utlng ttlla lntD

(!}

lid

gat

irw;J:.

~

__

.,__ ·F

tr•A

:...

----··~

FL

£A

• . 72.

c

A Sl.H or rw.t. nl4. to

••1'17 u:ota obaot -

~~ co:

II lo-'1"-1

Slaee ve bo.. -...011 Ula -.,.. t.o U1e

Ia

tbio ooaldu\ol obaot lGid, - - l l d l -

t..-

7lel4 Rnllo ('f) 1 ""v1U laorouo U.. veld ..U..ble 1Q' Uae . _

Unit to- ... tWet. veld

=-LF

F

=

1/1,8,3 1!.~ IZ. 1h "

las ol.H or tul8t nl4 , 1'10 ...u -

9322 • lb;,,;

-

3"

'13ZZ

w::{U.?Xzt.ooo)(.7o?) "' o. J?G, e~r 7e b..

B E•IIDPll:

The truck walgha ~tODD 11111&, thete ie 1/2 1nc.n

11

play

11

ln the hitch,

Ia _ ...... - -.. -Ia....__...

we will aaaume thet the pewer af the truCk buUda up to 25 HP at thl lnat•nt "' impact when tha maximum.. valaclty at (V 2 ) ta relehelll. The tgngua ia mGe af twa Chlll\nela, hav1ng • tatal craaa aacUanal area af 3 .. 18 1n2 11rut a length at 50 tnchBI.

P=ZSHP"

m~-= 0:, "'

A=

Wa

T

D tt. _.... . . - af tlae \HUor -

tlae H04 0114

OD

1~\ap\ la •de t.o

3uk "

n 1 7SD r.t-~., /.t,fiJ
3&-o'~..

=

m,• mau of trU:ekV,. ve.loc.it'i .,f tt"-~" be~ore . im P.act m.• mo.ss .of trailer =DO (stw.c.k in E!<1~tll) ~· v. • 0 (eo.rth d.. es n.ot move)

k. 1~c.fr ~.18

in ...

To avotct the Pl'Db!em cf mulUplylng t.~nrtnUy by zera squared 1n \he case ar

t:= SO /n

<mz>
and

('"2)(Ul)e, u wUl be boUu to do the roliawlng-

SiiJce

Z.( /,(,~A./()r)( fa.)

V..... V,• 0

F-j K(m, v.~ r¢...'l- m, v:- ry/;) I I< m. (V.'-v;) orl F=

if""'o;;~..,~

t-

a

v,{K:J

Th.i.'" ia abaut tha vtela strength af ttw BiBel.

here

f= .L

5>~'SS

-73-

z.fi,Jt..jdqoaoxto'Y.'!JfS:t) "

F 111.8'-~ lh_ -:or-177 tr= A.. 3• 18 fn... - .,,,,

JJI,Br..3. lbs

/ P'". c.or at

.

y1e

td)

c

A, TM tl"'ltler langue muet tnn~~rer Ute rorcae stu. ta the deld laM blaldllr) an ~· tnUer. Hawavar, thue farcu ere not v•J'V gnat etnce it ,..., ill paaelille fol" ana ..,.. to pick up th• taneua lll1d CDMact it ta hta truck. lf ~·•• war• t1ta rmly fal'cee involved, then wuld be 1t0 pralll• 1n daelgning 1 aut\Ule \Piller t.angw. The prabl• li11 1n ahack laedll encauntered ·in pulling tbll tr1ller •lang the. ned. Thaae fare•• 1r1 rattler hiQh be.ceuee any bUIIP ln the roed will nave an e•tr...ly .nart u .. lntervel, pruduclng hlgh accelnattone and thereran la.rp ro.raee. Foll..awing •r• aau typo of attack laede lmpoeiHI upan the treller tangua. Jn flfJura (e)

111111

•••wu

the center or ntetlan ar thtl unit ie the hitch.

•

®

Any

up and dawn 1111tlan ar the nH a.Ul apply 1 \lerttc:el force an the treller through If the wheeh an located at 1 point known •• the S!!!l!£ !! tUn will be no varttcd eccalentian at point (a) ( tn. hi tDh) lnd th11nfon na vertlcel fare. would be applied ta the hit.dt or the tengua Coute1ct. or thaee c:eueed by th1 deH lpad).

it 'e whll1l1.

.I!!J:S!!II!.!!•

. f CG

,___T""__.....___--:0 (p) F

po•nt of.

l"'int oF rot o.t/Dn

p~ld,lon

Tha point or percueeian wlll lie allgnUy b•yand the trailer Un ~il figure, to tha left) ..

c~~nter

ar gravltv ar the

Sim:e the whe1l1 an ueuallv placed alightlv ~M-van&t th8 e-nter or gravity Un thlil figun, ta the lett) 10 that thtl taneue would ard1nerUv rest on the ground, I would ...... tnat tn practiCe, thl lllheele en verv cloaa to the canter of pen:uaa1an (altnaugh ther• was no 1ntentlon of •otnv th1al. Far th1a r•••an 1 dan•t baliava thara will ba much up and dawn •at1an ar th• hitch dUll to the .1E!!1!£ itself 110ving avar a rough ron. I don't belteve thla will pne~Mtt cnuch or • problp. Th1a 1a 1llustrat:ad ln figure (a).

8 Hawever. then 1tl • prabl• with the truck mavlng up and dawn, flgura (b). in thia cue a rapid vartic•l 11111vU~ant or tM hitch due ta the trUCk gaing av•r 8 bump 1dll cauee a twiating action ta \ha trailer and w•ldu. B•c::•u•• ar the !1!!1 !!1!121 .a! ..l!ll.!:1!! af thia unit nalaUng t:hia rotation, there will 1M' 11at: up a ra•i•Ung tarqua equal ta

T=-IC(

(For tor.oo.e) F=

liar ..,. nee• tM .... -•nt ar lnartla ar th• w.ldar and t:raller. Th• actual value ia rather •itricul t ta find, but lll8 ahell ••• .... that the wa1ght ia unifU8l.y •tetrlbutall avar • langth ef 60 lncnaa (5 flat).

lOa

m a. (for 1-Qrce)

I[]

A

I

t =

vs .

IJ~ m•3•

181() ""

~··

"7 J6(al'

,, --,;,-"'

dista.n~~

Vei'i<7lii

so

T= Fd

h

Q

•

z.,t.ches "'·"7fee't

S ~ IIJ ~3

•, illl Feet

d • 7 feet V .. 30 mph

. 74.

c

A

ca..-

Mam.nt an tangu• af treUer

M= Fe:: ~lzo 16XY~m)

or

:12,'1~0

tn

lh

• 'io/, 8tJO;i, /6

~n eacb

2!t'•ZI'z'•~· 981( in""

.r,. ••

1 believe tna ;rntaat: rar-cn 1n the tengVI' emf tNllar- en "'... 11¥ "'hitch (truck) moving var, rapidly up 1111• Uwn •v• te &I~ 1ft the ..... , Ill flgura (b). lha valuaa af thaae ·rar-cn era •itflcult H . .tanlnl IIKeYII • ' the uncertainUu ar1) actual aiza or tr. bump ar hale in the ~"•••• 2) .BIIlDUnt af 'an.rgy ebul'bld by tha Uraa and aprlnp af tna trucJc, 3) velocity af the ti'U:IOir., It) NBI IIID!IIef1t of inartle af the welder and trailer •

'1/de

an9/e'

A~ I.'J':Iin'

Hawavar, I ballave t:ttaaa are real forcn, tNt they caulll be vary high uftCier unusual road candi Uana and therefan 1 batter ta"9U1 ahttuld be uan. far IK&mpla, that·mada af tRI 11• Channel.

17, 3oO psl

compressHJn

l bdiave no patnta af weakneaa enauld be allawuf, far ....ple,. c:ut auta, II' carnera 1 cut, bllllt, and then welded, with poor quality welda, the quality 111hict'l may vary wl'daly from ana tangua ta the na.t. It aha bat.hara ID8 that 1111 muat rely uPlift ~~Mae cuatalllr t:a llllkl thll iq~~~rt.,t carvt.ctlng welda ta tn. trailer, aaM \n ttte avarhaad paaUlan. Thil . .Y be tha f1rat aut af paaUian 1111lding thl cuetomar 111a ever mellla in hh life.

D

What }or.ld (P) can tlte'iie ws.ld'S trfJIIS

?

fer

p

rrelcl a

~-

-

P

~-~·~ f--2.'1Z"4

8 Of caure• tn•B• atrUeaa •r• calCiulated on the bi!IBh af the truak (ar hitch) gain; over a certain aiza bi.Dp ( · i.nct., ''lut',) at 30 •Uaa ptlr huur. ate don't knN wMt apeer:la and ain af bumpa shauld be uaad. Never the leu, U a 11• 5.,1t lb cha•nal .,." uead, the aPia driving conditione would reSult 1n a r.OUC:ad b11ndlng atnaa af 11 1 600 pal. And thia tong..,. wuuld nDt hav• anv cut awaV ucUan whllfh wauld we~en it.

••r.h

.:emn~tlln

t.

S.,· Y+J'{,,.t~.a~¥· 'M•?in'"

~or two ~nnf!d'ums

'S.,.,. •.,,r.'? = 't.3¥in'

----------...., .. F,;.n,;,

----- ------- ---

F,;· Pees a •· 'IBS" P

.,.

F.• PtinB •,1'1'/P

(o-me 8

Nllllffr d.t:-Wtlf'

-[

• 10:)

M".ifB5PC88•n)-t.!7'1P(2.~11o) ~ 1.2s~ P(inJ

I.· 3,8E>m" A ~ 1. set irF

.41 r--;<~>r

f.b • .t1 S... •

1.288 P{lll)

.,,,., ,.,,

or

f6' ·l'i?'t .L. m

Thle brlnga out thll advantega af tha four wt'teal traUar, Jn thil cue till tangua 1a hinglld and anY vertical movement at the hitch will Jua.t move U up and down wlthaut introducing anv moment ar banding atreaa. ln rtgura (c) tha uial farce 1a epplhd to the trai••r by m:.calaraUng and braking the truck. These farces could be cauaed bv the truck ar trailer hitting chuck halaa in the ~ad. figure (d) lllustrataa the tranaverae force ceuead bv aide matla11 af either the truck ar traller etriking ruta in thll raad.

Rr,.. lt4'1t ,.,;,t r.., ..

btl

f,..=/(~... f.)'+

weld

f.'

~r -j(.mt-l;+.ot.~f,)'i-{.ot'J.If,;)" "'. z.o~ <; 16,

The ring tvpe tratlar hitch hils a loaaa fit and 111ill praduce mor• of·a jerking action 1n caaae (b) 1 (c). and (d). A batter fitting hitch, fo.r I)I.B~SJPll a ball and aockat typs ad:OUld reduce t:ha P88lr:l an thne loada.

b.._-t

~.· .707

W '-I,ODO

Jt..

, lO''t-#;" .'/O?w '-1,0()0 ~U."

The tangua lllUat have aama tlorizantal atltfnaaa and atrangth ta prevent tt tram binding if the tralln ehould •jack knife• IMhtle backt.ng 1f the rear whaala or the truck ahauld be PIJ'Bhed inta the tongue, see ftgu.re (a).

p..(.?o7Y&X~·ot)o) ' .~6

th•s

,~

for

st~dct

e?D we lcl tneta.f

. 75.

/d4d

10

4/le

'Set et~~U.O.I "to . ZDcS'r ~,; a •

II, m) 2.j,(J()0 ~,;,• P= n.ooo lbs

'70?{

or

A

'1.'1~

bend•"'=t

\be

c

''hr.

t11a booo 1.8 troo to _., \ID ...trlpotal tano h
'b••• vll1 var,.

•

.

y I

u

'bclq (a,)-•1-, - . , 1.8 r, • •••• w ""' ca acooloroUca ot t11a - bOd1lo to aocoloro\o 11J1Vud (o1.), :r.

• t01'08 ot

OD lmb torvoo ot on em tho ODd to - . l \ ~ o.,..ID11\ (B), torvoo at occolordlca ot \ID - bodiu aa\

<•.>·

·=..e:,

:... T.J!" =~· t!W, dou.:",.;.:",:_~ot\o:;.••·~= - • l o r • - ot t11a to
«r.(Uitn'c wei 'ht '~" 2. lbs

IK"

(booo)

rt&>\6

e~-r"'

s• a•ZI'el'

r.oo

•u.s

(z.'fS)(.90U1)

u'""~'

.,1'17

'-2'10" u.~ IS.'t'l to;fr.l

M•AY

~·l'.'f_

.. 2"

+S,DOO

• S.Dtll)

-.Dt.25

, 2.1 '1?

','"·

ts>' Iy•tr

t

(;~;7{/ =-

•

al-.o

111

lh

itt

1--·""

v.,

v

t>n

and

a .. •

=

ml:;,•

w"r(~m,"!: m..)

!be 1'00111~ - 1 t l l p l tone oo\l.q ca t11a 'bclq 1ll t11a

•muol - - u

~ F,•m.(a.-a~) • 2.m,+llla fb1ll 1.8 looo - t h o ...trl.fllpl

f'b=

m,a. •

t..._o oo\l.q ca tlla

'bclq ID tho borlson\ol 41rac\loa

w... rm,

!be ronp ID t - oo\IDc ca t11a 'bclq 1.8

k.. S. ... !!.("'~rm.tn. \/_1_\ ... --.!!!!__

F,... r., uvm• ]\i..,~rm.J Ill,• m, •

bodot bos,.

F• W. ir'-rlii.P~,. 'fU. u,, .._zltoiriJliOOD § "J(JD '"" • '100 b&or&i>'l reA<'ttt;n {alSIJ s.lrear lfn welcl}

w'r-al

$1>

j,ljljq

1&.180

..,

T
: Z.B 71/J..J/n,•

l8.11

"~"2.

a m,-t-mz.

~·.oaela.,.trolto of Y"'"~~

32. z ~~.... 38G. ..,_.

lhfj

$l'DD ILJ_,

• l<1f1'S

• Po\!IU o~lo ca vo14 USC o..r t,ooo,ooo 07"108, aa11 1;.• a bi

1c1p•

e. l

w41J

!'Is&'{,)" kip){'l~ip)•

a,• w"r-

{!:;t•) = w..r

(le"'ltb .~ welcl)

bend,n.; 111•ment

u.z.e an two tonu. haae

0

'~'fBO m

!t•V·~.. (:eB.7f)• 14.3'

vlll.ab • - t11a boao \o occolon\o

,,,0()

J..• r., t r,· '2.~80 .._ s2."o 7 • B s: s-6? in' Frm:es. en wel4 centrlf~
tano

r • ...l

B

· .. /S.,28 • 6'::t.,07 m •" ll{Zlfs){z,S)+

Aw• l!i.'i
toroe h
(o,• .._)

S1Doe t.beJoe are two bodiu•

r._

07

·13.?6'1 -8.'11$'

HA•~• ~· -,S?'9ito

J;..·r.•J;·.f• 38.180-

"' ""

.2m1 (Q,·¢a) • ~a.. (a•••• o) ( 1 buo)

r 1... t1~-liaf!)•(z".1,)(,.JJ~'II.-·¥}·1S.fi 28

y +LOO

oL ,

tlf'l .,. ;.'

A~z.r(J • 2£z.7rXI.I)~'Ib)o 4.2'10 in

A

r • ••

aad tbl.o _ , bo - 1 \o t11a

r.,•r1(~+·~)· L$'~•Mt¥-·~~~{]

1 .....-~ S"-----1

~

~

,S,J'f 1irk1p

bo\ -

w-

....u. ot

:r

..... tulo\ 101ldl1 oon41.\1CIII ()7) 1 ooi.ocao7 (0)

""0 " 1<~/.

o\oo
tulo\ vol4

<~.s-
. 76-

Dr

~.... 71(,

b.

~~- of tho S IDob tbt.ak nilb\o tlla mn1am tUlo\ w14 oloo 1.8

@

•

c PJogparUn af Craaa sacuan - Glrl:l•r

tan

.20 tan

l- j

act uRI

Vertti:al Up

= II"

'-' pa.s.'!>sS

~e

Thla work. would lndicata tn.t tha ada 1.1111uld mava har1zantall\f to the right about :J lnchaa. lt waul 1:1 be batter in thh parUoular example, ta weld tha twa Tea aactiona, each n a ••parata aubaaaelllbly. 1t 1a aatl.oatad t.hay will each bDIII about 7 lnchea, haw8VI1' thaaa aa&.~Jd be etnlghhned .in a bull-dazer, ar thay could ba weldad 1n • pra•bent paa1t1an 10 11 to be atraight •ftar w.ld1ng. The atra1ght TN ncUonil would than ba aa&amblad lnta tha final glrdal'. flllat1ca tMt; thh nnal waldlng wlll not ba lDcatad on tha wttb, alanv Uta neutral Pia or tne lllhDh aacUan. Th1a llnould aauaa no ~aawlng aaUan and wlll raaul t ln an .J.mnt; atra1Qht glrdar.

actual

/,-

~4/c"/t!lted

=

/3D

Vert/cat Down 39 ptuses

B 'deal ~

D

!! .! 1!!1! !! ! !!!!!!! I! !.lll!!l .._,

•

KA~o Tha 11111ld along with ••• lldjacant plpe t~ r•:llal rurca (fr) along VIa clrcumt'ertme:a ar

=~••:~!:';t

:!•~:::u .. 1nwarll

..L-

The clrcumferantlal t ...alh raaldual etrna ln tfte wld

F "" A K rl

•

v

A111

1 ..... I eQUal ta• craaa aactlanal un ·ar t;ha ldld

•

a(

ralatl¥a ••wnt at •Jaaent ,..,. -inglna lllong wUn ...ld •v • rnldual ~tnn in waJ.ct .uaa

K

•

!~ 1 ~:·;~~!' 1 ~0 ;~: :~:•:n-: !;:•rd radial fore• Bltl'llU

T

U the GirGUafarana•

.20 tan

r •!

• •

where

(Pooi-~ -· "V•·'nat-•o)

Puttlng thla tagatnar, wa gat-

Ar•

~If;

Thle biCOmtiS•

/.Z81>

K ..

actll.4/

0

~tuai

12•

"" '/ ct~/cula:f.eci = 11.3 °

lQ

O'y • 70 kil

r - - - - - - - - - - - _ ; 1 • JD • 10' kol

Ad =3.0>
ualng:

e ,.,

r • U 5/8 ln

A..,J1i l(r..r "'''~-steel)

t • 1 1/2 lft

A" •

A, ... lOA/O'A..}!; • lO•If{" (1.1'~)

Jlttii

<:~;.:.~)" know tha v•lua or K,

calcu.latec/

1.n 1n2

..--.......--~or At- a • 0 'f

lf lt war• luger, tn• Miirl"lllftl!!ll"l::::':i'::"'"

. 77.

=

/1.3•

c

A $htJrtemn9

ruo 1/1' t.hlak btn 1 80 te 90 teat l•a •n liJI veld&4 t~ vUk S/W tlll.et. welda. !be t•brioa\or tlada ibQ" briDd aboat the strorlf: nb (I..X) eMI:Qt I to L teet.• bat; ....-u, do an baed abatlli tile vuk a:l.a CT·T),

~ D... e ~ k"'f/tqdtlW .~ ( - ..t .;.w. wU.k"''• eHct <>I tr....u••• ofiff-.)

ol

X

ff-1

.!...

.,.

,.,.

~ ~

'It' y - · -

-y .l.. I ,I

T

---·--------------------Ptopertt
x,-

• A.. • ..,....

.,.td (ill')

~.1' • <1/PSS sect_!_._ cl 91ider (tit? 1'\ • relo.trtie GIDSS ...~t,iJnill Qf't!!;f;f tt~f 9,ra., aJj•c,,.r t~ ""'lei W~tc/1

-Hi{,;;;; z.o'f~'l in

r•-1•

ud""'" llrd# "f """ f/lkt

s6nnts tl{""f ..,,til wetd. IT • eo.ucr"'f" rllst'dual fl!lrst{t' sfress ,,,; ....ld and acl;aeePt ..,... (i • '-"'"fre9'Sttie ~tra ,_;, til~ /Mp t/1 of ~ 91rder (

r,.. r-(ttM)• !rB-'1~6 -(-z_.,X-IhU) • + as; 'f8 in"

"'"'?'1

liV'1

~b

.O"t 8 /n

A,. • Z. " l'z(lif6)' • A,.• Z • .., l\111' •

\fj'!..

L\m .oo~A,d

1.•.

./'f I

'-=eo' • 'lr.t>'

2

dr

ina

/emile shait&,qr

~.()4(.5''

b!!r«

{tbs)

F• fA..IC (}"

.oos(.o
rss.¥8)

lhti 4'""'er

ts

onl'f as 'i"'>d as fhe '""""'""' 114111•1 o ~ ®and®.

!k-h~ beHer va.l~~.es "~ ®ano® c..... td be abt4tne& I>~ ~eci
D

B Properttc!l abt>ut IY-Y)

Ex,.tnple;

L • le11'1th .,f 'lirdcr = liO

'(_ 't'.&lllrillmzllliilfj.JIL~i!!hi'.. " _y_~[A'

Aa. z(t"•IO")t(.la"•lli)

+.uW

r

1

'lfi,(; m'

A,.• ~(~,·· i.1)" • .o6. irl

(.,r;.

Y·

~ • ··~~~

~ /0 .,f adjacent pW« shn'ntmq al6n
.nu.··

•

~ >~ooo fKi {r-Hr'du.af

I.: I{vt,.t)•.'f58}}-(,11"X.•'s) • • J'f~'7 in oJ . A.d L• A.·""~

'-'

J:

~,t.M

"'

•

.

.oosGo,sX.II.,.J.'U.t>) • · t!r ?J. • . ,~~,

tabl'ieatm' aald the _..... dld aot.

t en,t'lt"

••

st-res:~)

'? ~?

bell.- ill th1a directlca,

In tbb aue Lhe ~~~DWn' or lner\.la (.U.lttDese) ot the Ulllber t.a YU7 lCN (t•.3la4S s.nl&> tnd altltwah t.he def"'1.Mt1Cin ronula doel I.DdicaM • larp cletlact1tz, the valght. at the lll8l'lber t~OIIld w4ou,b\clllll' keep 1t 1¥tDs flat. Cl1 tbe fiOCO' ot t.be tabrlcetlns: sbcl:p.

It Use 111911ber

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to at.ut. 1\Rlng \IP off at the tl00:1'1 lt VOQ14 reqnlre " bend\a&

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® ..,.-11 '""ve Ji, ~war-d the cente-r hrie o d,Hance ~6/ 1 wheu Q) ,S th~ ,;,itu:i{ dtstance of the pomt {D the cent.er-ltne.

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actual p/Qft' ftTders

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THE JAMES EUNCOLN ARC WELDING FOUNDATION CLEVELAND, OHIO

0810.17 Printed Sept. '85 5M

Litho in U.S.A.