Psc I-girder Bridge Design In Irc
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Structural Design of Pre Stressed Concrete (PSC) I-Girder Bridges by ASTRA Pro in IRC 112 Standard with IRC 6 Class Loadings
Launching of Pre-cast I-Girders by cranes
1
Foreword: The procedure starts with Analysis for DL, SIDL, Live Load (Multi lane vehicle moving load), then stepwise design considering temperature, creep shrinkage etc. for Flexure, Shear including Blister Blocks etc. and finally producing editable CAD drawings with relevant structural & construction details.
For PSC I-Girder the Main Long Girder is designed with applied Loading
Pre Stressed Post Tensioned Concrete I-Girder Bridge with detail step wise design calculation report and complete set of sample CAD drawings are provided convertible to design drawings.
2
Live Loads of moving vehicles by IRC-6 Class of Load combinations as per width of carriageway,
3
Design of PSC I-Girders for Bridges 1. INTRODUCTION: This design note pertains to design of Precast PSC beam and cast-in -situ RCC slab superstructure of 37.5m span C/C expansion Joint. The superstructure consists of four numbers of PSC I girders spaced at 3.0m c/c over which 200mm thick deck slab is casted. The deck width of superstructure is kept 12.0m including 0.5m of crash barrier on both sides. The construction sequence proposed for the approach span superstructure is as follows 1 2 3 4 5 6
Casting of PSC beam on casting bed. Stressing of stage I cables after 21 days of casting or when the concrete attains the strength of 45Mpa, whichever is later. Launching and placing the prestressed beams upon Permanent bearings (Pot cum PTFE) Staging & shuttering for deck slab and end cross diaphragm to be erected. Deck slab casting along with End diaphragm after 28days of casting of Girder Casting of crash barrier & laying of wearing coat at 56 days after casting of girder.
The analysis of superstructure has been carried out by grillage analogy using ASTRA software. The four span superstructure has been idealized as a mesh of longitudinal and transverse members and the loading has been applied as per the construction sequence. The analysis and design of beams has been carried out for the outer beam . Transverse analysis of deck has been done using ASTRA sofware and excell For dispersion, 65mm thick wffiring coat has been assumed but lod due to wearing coat has been assumed as 0.2 t/m2 assuming future overlay. Loading Density of Concrete (RCC) Density of Concrete (PSC) Live Load
= = =
2.5 t/m3 2.5 t/m3 2Lane/3Lane loading as per IRC 6:2010
Material Concrete Grade for Deck Slab/End Diaphragm PSC Girder Reinforcement Bars Clear cover
= = = =
M-40 M-45 HYSD Fe-500 40mm
REFERENCE CODES LIST IRC:6 IRC:112 IRC:22
2010 2011 2000
Loads & Stresses Design Criteria for PSC Road Bridges Cement Concrete(Plain & Reinforced)
4
2. Input Data 1 2 3
Distance between C/C Exp. Joint Distance between C/C Exp. Joint Effective span C/C bearing
Leff
= = =
37.50 26.52 34.30
m m m
(Skew) (Square) (Skew)
4
Effective span c/C bearing
Leff
=
24.25
m
(Square)
5
Overhang of girder off the bearing
=
1
m
6
Overhang of slab off the bearing
=
1.600
m
7
Expansion Joint
=
40
8
Deck Width
=
12.0
m
9
Deck Width (Skew)
=
16.97
m
10
Angle of skew
Ang
=
45.00
deg.
11
Clear carriage way
Bcw
=
11.00
m
12
Width of outer railing
=
0.000
m
13
Width of Footpath
=
0.000
m
14
Width of Crash Barrier
Wkerb
=
500
15
Spacing of main girder c/c
Spmg
=
3.000
m
(Square)
16
Spacing of main girder c/c
Spmg
=
4.243
m
(Skew)
17
Thk of deck slab
Df
=
200
mm
18
Thk of deck slab at overhang
=
400
mm mm
mm
mm
19
Thk of wearing coat
Wc
=
65
20
Length of cantilever
Lcan
=
1.50
m
21
Cantilever slab thk at fixed end
Dcan1
=
200
mm
22
Cantilever slab thk at free end
Dcan2
=
200
mm
23
No of main girder
Nomg
=
4
nos
24
Depth of main girder
Dmg
=
2400
mm
25
Flange width of girder
bf
=
1000
mm
26
Web thk of girder at mid span
=
0.30
m
27
Web thk of girder at Support
=
0.65
m
28
Thickness of top flange
=
150
mm
29
Thickness of top haunch
=
75
mm
30
Bottom width of flange
=
650
mm
31
Thickness of bottom flange
=
250
mm
32
Thickness of bottom haunch
Bbw
=
200
mm
33
Length of varying portion
Lwv
=
2.50
m
34
Length of solid portion
Lwu
=
2.50
m
35
No of Intermediate cross girder
Nocg
=
1.00
36
Depth of Int. cross girder
=
2350
mm
37
Depth of End. cross girder
=
2350
mm
38
Web thk of Intermediate cross girder
=
300
mm
39
Web thk of end cross girder
=
600
mm
40
Grade of concrete for precast Girder
=
M 45
Mpa
41
Grade of concrete of other componant
Cgrade
=
M 40
Mpa
42
Grade of reinforcement Shape Factor λ
Sgrade λ
=
Fe 500
Mpa
=
0.80
η
=
1.00
43 44
strength Factor η
bwcg
5
45 46
Partial factor of safety (Basic and seismic) Partial factor of safety Accidental
ɣc
=
ɣc
=
1.20 0.67
Coefficient to consider the influence of the strength Design value of concrete comp strength for Basic and seismic Design value of concrete comp strength for Accidental
α
=
fcd
=
fcd
=
43
Clear cover
cov
44
Unit weight of dry concrete
wcon
45
Unit weight of wet concrete
46
Weight of wearing course
47
Weight of Crash Barrier
48 49 50 51
47 48 49
52 53 54 55 56 57 58 59
1.50
17.87
Mpa
=
17.87 40.0
Mpa mm
=
2.50
t/m3
=
2.60
t/m3
wwc
=
0.20
t/m2
wrail
=
1.00
t/m
Weight of Railing
=
0.30
t/m
Intensity of Load for shuttering
= = =
0.50 40 500
t/m Mpa Mpa
=
1.15
= = = = =
1.00 33000 200000 6.061 1.050
= =
0.900 0.900
Stress in concrete (compression) Stress in steel (tension) Partial factor of safety for basic and seismic Partial factor of safety for Accidental
fck fyk γs γs
Ecm Es Modular ratio Anchorage from c/L of bearing Length of Girder beyond c/L of Bearing Distance of Jack from c/L of Bearing
m
IRC-112 Fig 6.3 (Note) IRC-112 Fig 6.3 (Note) Mpa Mpa m
(Min. 1/2 of end X-girder Thk.)
m m
6
Stressing and casting sequence 1st stage prestressing Casting of Deck Slab Shift of Bearing SIDL(Wearing Coat & Crash Barrier) Age of deck slab at time of SIDL Fck at 1st stage of prestressing Fck at service Modulus of Elasticity (Conc) 21th Day Modulus of Elasticity (Conc) 28th Day Modulus of Elasticity (Conc) 56th Day Modulus of Elasticity (Strands) Type of cables Breaking Load Area of 1 strand Area of one cable No of Cables stressed in 1st stage Jacking Force No of Sections to be checked Prestressing force per cable (UTS)
21 28 56 56 28 45.0 45.0 3.24E+06 3.35E+06 3.35E+06 1.95E+07
Mpa Mpa 2 t/m 2 t/m 2 t/m 2 t/m
19 183.7 9.870E-05 1.875E-03 3.737 0.765 5 349.5
T13 KN 2 m 2 m
Factors with 20% for loss calculation Elastic Shortening loss Relaxation loss Shrinkage loss Creep loss
1.0 1.2 1.2 1.2
Factors without 20% for loss calculation Elastic Shortening loss Relaxation loss Shrinkage loss Creep loss
1.0 1.0 1.0 1.0
Factor for Relaxation Loss 1000hr relaxation (for low relaxation steel) 1000hr relaxation (for normal relaxation steel) Strain due to differential shrinkage and creep Reduction factor due to differential creep (As per BS:5400)
day day day day day
*UTS
t
2.50% 5.00% 1.00E-04 0.43
7
3. PROPERTIES
8
Properties of Member
820
to
Length of slab = Thickness of slab =
Area, Ax = Iz =
0.6481 0.0022
m 4 m
815
to
819
849
m m
Area, Ax = Iz =
0.5352 0.0018
m 4 m
810
to
814
850
m m
Area, Ax = Iz =
0.4463 0.0015
m 4 m
801
to
809
855
m m
Area, Ax = Iz =
0.2635 0.0009
m 4 m
3.240 0.200
Properties of Member Length of slab = Thickness of slab =
2.676 0.200
Properties of Member Length of slab = Thickness of slab =
2.231 0.200
Properties of Member Length of slab = Thickness of slab =
1.358 0.200
m m
844 2
to
849
to
854
to
863
2
2
2
9
SECTIONS CONSIDERED IN DESIGN
34.3m
Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5
Simply Supported Span Support At end varying L/4 3L/8 L/2
= = = = =
0.000 5.000 8.575 12.863 17.150
m m m m m
10
CALCULATION OF MOMENTS AND SHEARS FOR OUTER GIRDER Analysis for dead load is done manually while analyses for SIDL and LL are done by GRILLAGE analysis using ASTRA-PRO. Only the c/c of bearing has been considered in analysis. DEAD LOAD 1. Under self weight of the precast Girder Effective Span of the girder
2.5m
=
34.3021
3.24t/m
m
2.43t/m
2.5m
4.05t/m
24.3m
34.30m 34.30m
0.001m
Support Reaction Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section At L/4 BM SF
3-3
Section At 3L/8 BM SF
4-4
Section At L/2 BM SF
5-5
=
47.80
X
= = =
0.000 -0.05 47.80
m t-m t
X
= = =
5.000 190.89 29.58
m t-m t
X
= = =
8.575 281.09 20.88
m t-m t
X
= = =
12.863 348.23 10.44
m t-m t
X
= = =
17.150 370.62 0.00
m t-m t
0.00m
t
11
2. Under Deck Slab Load
0.00t
1.56t/m
34.302m 34.300m Support Reaction
=
26.75
t
With Wet density 3 (2.6 t/m ) Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section L/4 BM SF
3-3
Section 3L/8 BM SF
4-4
Section L/2 BM SF
5-5
X
X
X
X
X
With Dry density 3 (2.5 t/m )
= = =
0.000 0.00 28.01
m t-m t
0 26.93
t-m t
= = =
5.000 120.56 20.21
m t-m t
115.92 19.43
t-m t
= = =
8.575 182.85 14.63
m t-m t
175.81 14.07
t-m t
= = =
12.863 231.25 7.95
m t-m t
222.36 7.64
t-m t
= = =
17.150 250.99 1.26
m t-m t
241.33 1.21
t-m t
12
3. Shuttering Load
0.50t/m
34.3m 34.3m Support Reaction Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section L/4 BM SF
3-3
Section 3L/8 BM SF
4-4
Section L/2 BM SF
5-5
=
8.58
t
X
= = =
0.000 0.00 8.58
m t-m t
X
= = =
5.000 36.63 6.08
m t-m t
X
= = =
8.575 55.15 4.29
m t-m t
X
= = =
12.863 68.93 2.14
m t-m t
X
= = =
17.150 73.53 0.00
m t-m t
13
LIVE LOAD BM SUMMARY FOR OUTER GIRDER OG1 AND OG2 70R WHEEL ONLY 1 LANE IRC70RWHEEL MOST ECCENTRIC Maximum BM & corrs. SF
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5) 1 LANE IRC70RWHEEL ON MEMBER Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRC70RWHEEL PLACED CONCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
14
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
1 LANE IRCCLASSA PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.39 0.39 2.19 2.23 2.38
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
0.69 0.69 0.22 0.13 0.08
t t t t t
0.39 0.39 1.47 2.18 2.19
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
0.69 0.69 0.37 0.22 0.22
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRCCLASSA PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.62 0.62 2.87 2.91 3.60
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.43 0.24 0.20
t t t t t
0.62 0.62 1.49 2.91 3.22
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.55 0.43 0.43
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
15
3 LANE IRCCLASSA PLACED MOST CONCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
3.40 3.40 3.65 3.69 4.83
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
8.57 8.57 0.40 0.17 0.08
t t t t t
1.52 3.40 3.40 3.62 4.27
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
8.57 8.57 0.74 0.64 0.64
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRCCLASSA + 1 LANE IRC70RWHEEL Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRC70RWHEEL + 1 LANE IRCCLASSA Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
16
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
1 LANE IRC70RWHEEL + 1 LANE IRCCLASSA Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRCCLASSA PLACED AFTER IRC70RTRACK Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.62 0.62 2.87 2.91 3.60
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.43 0.24 0.20
t t t t t
0.62 0.62 1.49 2.91 3.22
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.55 0.43 0.43
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
17
2 LANE IRC70RTRACK PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.16 0.81 0.42
t t t t t
1.57 2.64 6.60 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.25 1.17 1.16
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRC70RTRACK PLACED AT CENTER OF THE EACH LANE Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 15.95 15.95
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.98 14.98 1.16 0.81 0.42
t t t t t
1.57 5.40 6.87 15.95 15.95
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.98 14.98 1.19 1.16 1.16
t t t t t
14.99 14.99 1.10 0.58 0.25
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
IRC70RTRACK PLACED AT THE CENTER OF INNER GIRDER Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
3.34 3.44 4.94 15.53 15.53
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
18
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.31 1.65 4.90 15.53 15.53
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.99 14.99 1.18 1.10 1.01
t t t t t
Maximum Bending Moment due to Live load Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.16 0.81 0.42
t t t t t
5.09 5.40 6.48 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.61 1.61 1.59
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
19
OUTER GIRDER SUMMARY FOR DL ,SIDL & LIVE LOAD BM BM & SF DUE TO GIRDER LOAD ONLY Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) -0.05 -0.07 190.89 257.70 281.09 379.47 348.23 470.11 370.62 500.34
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 47.80 29.58 20.88 10.44 0.00
ULS (t) 64.53 39.93 28.19 14.10 0.01
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 28.01 20.21 14.63 7.95 1.26
ULS (t) 37.82 27.29 19.76 10.73 1.70
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.0 1.0 1.0 1.0 1.0
SLS (t) 8.58 6.08 4.29 2.14 0.00
ULS (t) 8.58 6.08 4.29 2.14 0.00
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.75 1.75 1.75 1.75 1.75
SLS (t) 8.20 7.20 4.70 2.50 1.00
ULS (t) 14.35 12.60 8.23 4.38 1.75
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 15.50 13.30 8.10 4.00 1.00
ULS (t) 20.93 17.96 10.94 5.40 1.35
BM & SF DUE TO DECK LOAD ONLY Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) 0.00 0.000 120.56 162.75 182.85 246.84 231.25 312.19 250.99 338.83
BM & SF DUE TO SHUTTERING LOAD Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.0 1.0 1.0 1.0 1.0
SLS (t-m) ULS (t-m) 0.00 0.00 36.63 36.63 55.15 55.15 68.93 68.93 73.53 73.53
BM & SF DUE TO SIDL (WEARING COAT) Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.75 1.75 1.75 1.75 1.75
SLS (t-m) ULS (t-m) 12.50 21.88 32.00 56.00 59.00 103.25 74.00 129.50 79.00 138.25
BM & SF DUE TO SIDL (CRASH BARRIER) Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) 21.50 29.03 57.00 76.95 105.80 142.83 131.30 177.26 140.00 189.00
20
BM & SF DUE TO LIVE LOAD Impact factor = 1.112 Maximum BM & Corresponding Shear force Without Impact Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.50 1.50 1.50 1.50 1.50
SLS (t-m) ULS (t-m) 5.09 7.64 5.40 8.11 7.88 11.82 17.44 26.16 17.44 26.16 16.20 16.20 1.16 0.81 0.42
24.30 24.30 1.74 1.22 0.63
Maximum Shear force & Corresponding BM Without Impact
With Impact Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 5.66 6.01 8.76 19.39 19.39
ULS (t) 8.49 9.01 13.14 29.08 29.08
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.50 1.50 1.50 1.50 1.50
18.01 18.01 1.29 0.90 0.46
27.01 27.01 1.93 1.35 0.70
With Impact
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 16.20 16.20 1.61 1.61 1.59
ULS (t) 24.30 24.30 2.42 2.42 2.39
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 18.01 18.01 1.79 1.79 1.77
ULS (t) 27.01 27.01 2.69 2.69 2.65
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.50 1.50 1.50 1.50 1.50
5.09 5.40 6.48 6.96 9.14
7.64 8.11 9.72 10.44 13.72
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.50 1.50 1.50 1.50 1.50
5.66 6.01 7.20 7.74 10.17
8.49 9.01 10.81 11.61 15.25
Comparison Between Total BM & SF of Inner and Outer Girder
Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Outer Girder ULS L.F SLS (t-m) ULS (t-m) 1.50 18.11 37.94 1.50 349.45 493.57 1.50 531.69 754.52 1.50 672.87 967.05 1.50 720.00 1032.66
Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Outer Girder ULS L.F SLS (t) 1.50 164.64 1.50 124.79 1.50 69.81 1.50 37.30 1.50 7.46
ULS (t) 164.64 124.79 69.05 35.96 5.51
21
Cable 1 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) θ L( o) θR( o) aL(per m) aR(per m)
LEGEND: a (mm)
= = = =
30700 mm 17K 13
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
HDPE 0.170 Profile in Elevation 1000 13000 13000 2700 1000 1100 1100 120 120 969 969 7.444 -7.444 5.0256E-03 -5.0256E-03
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
0.131 0.010 102.049 -0.131 -0.010 -102.049 0.130 -0.130 30700 1009 13037 2700 13037 1009 30791
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
Length of curved profile in elevation St. length of cable at mid in elevation Length of curved prfile in elevation
e(mm)
St. length of cable at left end in elevation
s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z4 (mm)
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 2 2 (d z/d x) L2 RpL2 (m) t(m)
0.000 4.2E+07 6.500 0.000 2.850 3.5E-01 6.5E+00 0.000 4.2E+07 6.500 0.000 0.000 4.2E+07
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 6500 6500 2700 6500 6500 1000 30700
Coordinate of cable at jacking end Coordinate of cable at jacking end Coordinate of cable at mid span St. length of cable at left end in plan Length of curved profile in plan Length of reverse curve in plan St. Length of cable at mid in plan Length of curved profile in plan Length of reverse curve in plan St. length of cable at left end in plan Coordinate of cable at jacking end in plan Coordinate of cable at mid span in plan Cable Profile Results in Elevation
From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm Profile in Plan 6.50 apR1 0.000 cp2 42250000.0 t1(m) 6.500 (dz/dx) R1 2 2 0.000 (d z/d x) R1 0.000 RpR1 (m) 4.23E+07 u(m) 6.50 apR2 0.000 cp2 42250000.0 u1(m) 6.500 (dz/dx) R2 0.0000 (d2z/d2x) R2 0.000 RpR2 (m) -4.2E+07 6.5
St. length of cable at left end in elevation
b(mm) c(mm) d(mm) Y1(mm) Y6(mm) Y3(mm) p (mm) q(mm) r (mm)
1000 6500 6500 2700 6500 6500 1000 0 0 0 0 0 0 0 0
= = = =
0.000 1.000 14.000 16.700 29.700 30.700 1.100 0.969
Length of Cable1
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
Cable Profile Results in Plan 0.120 0.120 0.969 1.100 0.005 -0.005 0.130 -0.130
30791mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 7.500 14.000 16.700 23.200 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(between Anchorages)
22
Cable1
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction µ Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
= = = = = = =
17K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
Area of one Strand UTS of one Strand Area of Cable UTS of Cable Length of Cable Jacking force
per m 2 t/m
A= Pu = L= Po =
= = = = = =
mm -(µθ µθ+kx) µθ
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
98.7 mm^2 18.737 t 1677.9 mm^2 319 t 30.700m 232 t
Px = P0e
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1299
0.0902
0.0545
0.0114
-0.0045
Σ∆α
(rad)
0.0000
0.0397
0.0755
0.1185
0.1345
Y
(rad)
1100
527
268
126
121
(rad)
0
0
0
0
0
Plan Angle Cumulative Change in Plan TotalAngle Change in
Z φ
(rad)
0.000
0.000
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
0.0000
0.0000
0.0000
0.0000
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 232.07
0.040 228.22
0.075 225.22
0.119 221.67
0.134 219.18
0.00
1.66
2.95
4.48
5.56
1150.718
810.512
958.118
944.951
Ordinate from C/L
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
3864.299
(t)
125.873
(mm)
45.76% 118
% Average Friction Loss Cable Extension
Cable1
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 219.66
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
16.320 m from Anchorage 219.66 t (After Friction Loss by Linear Interpolation) 98.2tm 0.000
= =
98.157tm (t) (t) (t)
0.000
5.000
8.575
12.863
17.150
-
-
-
219.660326
-
12.41
8.56
5.56
2.01
0.00
207 10.70 205.50 26.85
52.416 211 7.50 210.25 19.02
25.227 214 4.93 213.79 11.66
16.215 218 1.81 217.64 2.49
4.299 219 0.00 219.18 -0.99
23
Cable1
Drawing Data Type = 17K 13 Jacking Force = 232 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 319 t 2 Mod. of Elasticity Es = 1.95E+07 t/m Y1(mm) p (mm) 1000 = 1100 Y2(mm) q(mm) 6500 = 969 Y3(mm) r (mm) 6500 = 120 Y4(mm) s (mm) 2700 = 120 Y5(mm) t (mm) 6500 = 969 Y6(mm) u (mm) 6500 = 1100 a (mm) v (mm) 1000 = 1000 b(mm) Z1 (mm) 0 = 13000 c(mm) Z2 (mm) 0 = 2700 d(mm) Z3 (mm) 0.0005 = 13000 e(mm) Z4 (mm) 0.001 = 1000
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Elongation = 118 Exit Angle = 7.444 Length = 30791mm Wobble coeff. k = 0.0020 Area of Cable = 1677.9 UTS of One Strand = 18.737 t Z5 (mm) 0.001 Z6 (mm) 0.0005 Z7 (mm) 0 Z8 (mm) 0 rL(m) 102.049 Trans RL1 (m) Trans RL2 (m)
mm Degree per m mm^2
42250000.0 -42250000.0
Cable1 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 1100 1035 969 924 802 690 588 496 414 342 280 229 187 155 134 122 120 120
(rad) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Elevation Radius (m) inclined straight inclined straight inclined straight 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 straight straight
24
Cable2 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) θL( o) θR( o) aL(per m) aR(per m)
= = = =
30700 18K HDPE 0.170
Profile in Elevation 1000 7015 7015 14670 1000 750 750 120 120 610 610 7.957 -7.957 9.9620E-03 -9.9620E-03
mm 13
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
0.140 0.020 51.669 -0.140 -0.020 -51.669 0.139 -0.139 30700 1010 7038 14670 7038 1010 30765
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 3507.5 3507.5 14670 3507.5 3507.5 1000 0 0 90 180 180 90 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 2 2 (d z/d x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 8.015 22.685 29.700 30.700 0.750 0.610
Length of Cable2
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
= = = =
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan 3.51 apR1 cp2 0.007 68.3 t1(m) 3.509 (dz/dx) R1 2 2 (d z/d x) R1 0.051 0.015 RpR1 (m) 6.86E+01 u(m) 3.51 apR2 -0.007 cp2 68.3 u1(m) 3.509 (dz/dx) R2 2 2 -0.0513 (d z/d x) R2 -0.015 RpR2 (m) -6.9E+01 3.5
-0.007 68.3 3.509 -0.051 2.850 3.5E-01 3.5E+00 0.007 68.3 3.509 0.051 0.015 6.9E+01
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 3509 3509 14670 3509 3509 1000 30706
Cable Profile Results in Plan 0.120 0.120 0.610 0.750 0.010 -0.010 0.139 -0.139
30771mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 4.508 8.015 22.685 26.193 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.090 0.180 0.180 0.090 0.000 0.000
apL1 apL2 apR1 apR2 θp1 (rad) θp2 (rad) θp3 (rad) θp4 (rad)
0.007 -0.007 -0.007 0.007 -0.051 -0.051 -0.051 -0.051
(between Anchorages)
25
Cable2
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
= = = = = = =
18K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable A= UTS of Cable Pu = Length of Cable L= Jacking force Po =
= = = = = =
98.7 mm^2 18.737 t 1776.6 mm^2 337 t 30.700m 246 t
mm
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
Px = P0e
-(µθ µθ+kx) µθ
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1389
0.0600
0.0000
0.0000
0.0000
Σ∆α
(rad)
0.0000
0.0789
0.1389
0.1389
0.1389
Y
(rad)
750
211
120
120
120
(rad)
0
113
180
180
180
Plan Angle Cumulative Change in Plan TotalAngle Change in
Z φ
(rad)
0.000
0.044
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
-0.0585
-0.1025
-0.1025
-0.1025
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 245.72
0.098 239.25
0.173 234.56
0.173 232.56
0.173 230.57
0.00
2.63
4.54
5.36
6.17
1212.433
846.935
1001.493
992.711
Ordinate from C/L
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
4053.571
(t)
132.038
(mm)
46.27% 117
% Average Friction Loss Cable Extension
Cable2
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 231.40
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
15.350 m from Anchorage 231.40 t (After Friction Loss by Linear Interpolation) 103.9tm 17.150
= =
86.781tm (t) (t) (t)
0.000
5.000
8.575
12.863
17.150
-
-
-
231.403903
-
14.32
7.85
3.15
1.15
0.00
217 11.65 215.00 30.05
55.414 224 6.56 222.94 13.41
19.666 228 2.69 228.25 0.00
9.233 230 0.99 230.25 0.00
2.469 231 0.00 230.57 0.00
26
Cable2
Drawing Data Type = 18K Jacking Force = 246 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 337 t Mod. of Elasticity Es = 1.95E+07 Y1(mm) p (mm) = 750 Y2(mm) q(mm) = 610 Y3(mm) r (mm) = 120 Y4(mm) s (mm) = 120 Y5(mm) t (mm) = 610 Y6(mm) u (mm) = 750 a (mm) v (mm) = 1000 b(mm) Z1 (mm) = 7015 c(mm) Z2 (mm) = 14670 d(mm) Z3 (mm) = 7015 e(mm) Z4 (mm) = 1000
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
13
Elongation = Exit Angle = Length = Wobble coeff. k = Area of Cable = 2 UTS of One Strand = t/m Z5 (mm) 1000 Z6 (mm) 3507.5 Z7 (mm) 3507.5 Z8 (mm) 14670 rL(m) 3507.5 3507.5 Trans RL1 (m) 1000 Trans RL2 (m) 0 0 90 180
117 7.957 30771mm 0.002 1776.6 18.737 t 180 90 0 0 51.669
mm Degree per m mm^2
68.6 -68.6
Cable2 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 750 680 610 563 440 337 254 191 148 124 120 120 120 120 120 120 120 120
(rad) 113 0 0 1 13 40 82 128 160 177 180 180 180 180 180 180 180 180
Elevation Radius (m) inclined straight inclined straight inclined straight 51.669 51.669 51.669 51.669 51.669 51.669 51.6685128 straight straight straight straight straight straight straight straight
27
Cable3 Projected Length Cable Type Type of Duct Coeff. of Friction, µ
a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) o θL( ) o θR( ) aL(per m) aR(per m)
= = = =
30700 18K HDPE 0.170
Profile in Elevation 1000 2764 2764 23172 1000 400 400 120 120 282 282 6.704 -6.704 2.1264E-02 -2.1264E-02
mm 13
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
0.118 0.043 24.003 -0.118 -0.043 -24.003 0.117 -0.117 30700 1007 2770 23172 2770 1007 30726
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 1382 1382 23172 1382 1382 1000 0 0 -90 -180 -180 -90 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 (d2z/d2x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 3.764 26.936 29.700 30.700 0.400 0.282
Length of Cable3
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
= = = =
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan apR1 1.38 cp2 -0.047 10.6 t1(m) (dz/dx) R1 1.386 2 2 -0.130 (d z/d x) R1 -0.094 RpR1 (m) -1.09E+01 u(m) 1.38 apR2 0.047 cp2 u1(m) 10.6 (dz/dx) R2 1.386 2 2 (d z/d x) R2 0.1302 RpR2 (m) 0.094 1.1E+01 1.4
0.047 10.6 1.386 0.130 2.850 3.6E-01 1.4E+00 -0.047 10.6 1.386 -0.130 -0.094 -1.1E+01
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 1386 1386 23172 1386 1386 1000 30716
Cable Profile Results in Plan 0.120 0.120 0.282 0.400 0.021 -0.021 0.117 -0.117
30742mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 2.382 3.764 26.936 28.318 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 -0.090 -0.180 -0.180 -0.090 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
-0.047 0.047 0.047 -0.047 0.130 0.130 0.130 0.130
(between Anchorages)
28
Cable3
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
= = = = = = =
18K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable A= UTS of Cable Pu = Length of Cable L= Jacking force Po =
= = = = = =
mm µθ+kx) -(µθ µθ
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance Stressing Anchorage
98.7 mm^2 18.737 t 1776.6 mm^2 337 t 30.700m 246 t Px = P0e
from X
Elevation Angle α Cumulative Σ∆α Change in Elevation Angle Ordinate from Soffit Y Ordinate from C/L Z φ Plan Angle Cumulative ∆Σφ Change in Plan Angle Total Change in θ= Angle Force after Friction Loss Px % Loss due to Friction Area of Px diag
(m)
0.000
5.000
8.575
12.863
17.150
(rad)
0.1170
0.0000
0.0000
0.0000
0.0000
(rad)
0.0000
0.1170
0.1170
0.1170
0.1170
(rad) (rad) (rad)
400 0 0.000
120 -180 0.000
120 -180 0.000
120 -180 0.000
120 -180 0.000
(rad)
0.0000
0.2590
0.2590
0.2590
0.2590
(rad) (t)
0.000 245.72 0.00
0.284 231.80 5.67 1193.810
0.284 230.15 6.34 825.739
0.284 228.18 7.14 982.670
0.284 226.24 7.93 974.053
(tm)
Total Area of Px diag
(tm)
Average Cable Force after Friction Loss, P % Average Friction Loss Cable Extension
(t)
Estimation of Slip Losses in
(mm)
3976.272 129.520 47.29% 115
Cable3
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing X (m) Anchorage Force at Null Point (t) 227.05 Nodal Force above Null Point (t) 84.037tm Area of Force Diag above Null Point (tm) Force after Slip Loss ) P (t) % Loss due to Slip Horizontal Force after Slip Loss PH (t) Vertical Force after Slip Loss PV (t)
15.350 m from Anchorage 227.05 t (After Friction Loss by Linear Interpolation) 103.9tm 19.894
= = 0.000
5.000
8.575
12.863
17.150
18.67
4.75 58.536 222 4.10 222.31 0.00
3.10 14.018 224 2.69 223.96 0.00
227.054741 1.13 9.060 226 0.99 225.92 0.00
0.00 2.422 226 0.00 226.24 0.00
208 15.19 206.96 24.33
29
Cable3
Drawing Data Type = 18K 13 Jacking Force = 246 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 337 t 2 Mod. of Elasticity Es = 1.95E+07 t/m Y1(mm) p (mm) = 400 1000 Y2(mm) q(mm) = 282 1382 Y3(mm) r (mm) = 120 1382 Y4(mm) s (mm) = 120 23172 Y5(mm) t (mm) = 282 1382 Y6(mm) u (mm) = 400 1382 a (mm) v (mm) = 1000 1000 b(mm) Z1 (mm) = 2764 0 c(mm) Z2 (mm) = 23172 0 d(mm) Z3 (mm) = 2764 -90 e(mm) Z4 (mm) = 1000 -180
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Elongation = 115 Exit Angle = 6.704 Length = 30742mm Wobble coeff. k = 0.002 Area of Cable = 1776.6 UTS of One Strand = 18.737 t Z5 (mm) -180 Z6 (mm) -90 Z7 (mm) 0 Z8 (mm) 0 rL(m) 24.003 Trans RL1 (m) Trans RL2 (m)
mm Degree per m mm^2
-10.8818 10.9
Cable3 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 400 341 282 244 163 124 120 120 120 120 120 120 120 120 120 120 120 120
(rad) -180 0 0 -6 -86 -172 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180
Elevation Radius (m) inc. straight inc. straight inc. straight 24.003 24.003 24.003 straight straight straight straight straight straight straight straight straight straight straight straight
30
Cable4 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) o θL( ) o θR( ) aL(per m) aR(per m)
= = = =
30700 17K HDPE 0.170
Profile in Elevation 1000 13000 13000 2700 1000 1450 1450 500 500 1323 1323 7.219 -7.219 4.8718E-03 -4.8718E-03
mm 13
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
(dy/dx)L 0.127 (d2y/dx2)L 0.010 rL (m) 105.111 (dy/dx)R -0.127 (d2y/dx2)R -0.010 Rr (m) -105.111 0.126 θL( rad) -0.126 θR( rad) Length 30700 a1 (mm) 1008 b1(mm) 13035 c1(mm) 2700 d1(mm) 13035 e1(mm) 1008 Le(mm) 30785
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 1382 1382 23172 1382 1382 1000 0 0 0 0 0 0 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 (d2z/d2x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 (d2z/d2x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 14.000 16.700 29.700 30.700 1.450 1.323
0.500 0.500 1.323 1.450 0.005 -0.005 0.126 -0.126
30785mm
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan apR1 1.38 cp2 0.000 t1(m) 19099240.0 (dz/dx) R1 1.382 (d2z/d2x) R1 0.000 0.000 RpR1 (m) -1.91E+07 u(m) 1.38 apR2 0.000 cp2 19099240.0 u1(m) 1.382 (dz/dx) R2 0.0000 (d2z/d2x) R2 RpR2 (m) 0.000 1.9E+07 1.4
0.000 19099240.0 1.382 0.000 0.000 1.9E+07 1.4E+00 0.000 19099240.0 1.382 0.000 0.000 -1.9E+07
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 1382 1382 23172 1382 1382 1000 30700
Cable Profile Results in Plan
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
Length of Cable4
= = = =
= = = = = = =
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 2.382 3.764 26.936 28.318 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
0.000 0.000 0.000 0.000 0.0000 0.0000 0.0000 0.0000
(between Anchorages)
Cable4 17K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable UTS of Cable Length of Cable Jacking force
A= Pu = L= Po =
= = = = = =
98.7 mm^2 18.737 t 1677.9 mm^2 319 t 30.700m 232 t
mm
31
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
Px = P0e
-(µθ µθ+kx) µθ
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1260
0.0875
0.0528
0.0111
-0.0044
Σ∆α
(rad)
0.0000
0.0385
0.0732
0.1149
0.1304 501
Y
(rad)
1450
895
643
506
Ordinate from C/L
Z
(rad)
0
0
0
0
0
Plan Angle Cumulative Change in Plan TotalAngle Change in
φ
(rad)
0.000
0.000
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
0.0000
0.0000
0.0000
0.0000
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 232.07
0.039 228.26
0.073 225.30
0.115 221.80
0.130 219.33
0.00
1.64
2.92
4.43
5.49
1150.833
810.750
958.595
945.566
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
3865.743
(t)
125.920
(mm)
45.74% 118
% Average Friction Loss Cable Extension
Cable4
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 219.73
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
Cable4 Drawing Data Type = 17K Jacking Force = 232 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 319 t Mod. of Elasticity Es = 1.95E+07 Y1(mm) Y2(mm) Y3(mm) Y4(mm) Y5(mm) Y6(mm) a (mm) b(mm) c(mm) d(mm) e(mm)
= = = = = = = = = = =
16.448 m from Anchorage 219.73 t (After Friction Loss by Linear Interpolation) 98.2tm 0.000
= =
98.157tm (t) (t) (t)
13
t/m
2
0.000
5.000
8.575
12.863
17.150
-
-
-
219.734878
-
12.34
8.53
5.57
2.07
0.00
207 10.63 205.75 26.06
52.159 211 7.47 210.40 18.45
25.198 214 4.94 213.87 11.30
16.371 218 1.86 217.66 2.41
4.429 219 0.00 219.33 -0.96
Elongation = Exit Angle = Length = Wobble coeff. k = Area of Cable = UTS of One Strand = 1450 1323 500 500 1323 1450 1000 13000 2700 13000 1000
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm)
118 7.219 30785mm 0.002 1677.9 18.737 t
1000 1382 1382 23172 1382 1382 1000 0.0001 0.0001 0.00005 0
mm Degree per m mm^2
Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm) rL(m)
0 0.00005 0.0001 0.0001 105.111
Trans RL1 (m) -19099240.0 Trans RL2 (m) 19099240.0
32
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Cable4 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 1450 1387 1323 1280 1161 1053 954 865 785 715 656 605 565 534 513 502 500 500
(rad) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Elevation Radius (m) inclined straight inclined straight inclined straight 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 straight straight
33
Summary of Total Prestress Force at Various Sections Distance from Stressing X (m) Anchorage Horizontal Forces after Slip Loss PH (t) Cable No 1 1Nos Cable No 2 1Nos Cable No 3 1Nos Cable No 4 1Nos Sum PH Vertical Ordinates Y (m) Cable No 1 Cable No 2 Cable No 3 Cable No 4 Ph.Y (tm) Cable No 1 Cable No 2 Cable No 3 Cable No 4 Sum PH.Y Y of CG of Cables (m) Vertical Component of Prestress PV Cable No 1 Cable No 2 Cable No 3 Cable No 4 Prestress Force Cable No 1 Cable No 2 Cable No 3 Cable No 4 Area of Cables As Cable No 1 Cable No 2 Cable No 3 Cable No 4 Ultimate Force Pu Cable No 1 Cable No 2 Cable No 3 Cable No 4 Sum Total Total Total Ordinate of CG of Cables
P
(t) 1Nos 1Nos 1Nos 1Nos Sum PV (t) 1Nos 1Nos 1Nos 1Nos Sum P 2 (mm ) 1Nos 1Nos 1Nos 1Nos Sum As (t) 1Nos 1Nos 1Nos 1Nos 4
P (t) PH (t) PV (t) Pu (t) Y (m) P/Pu
0.000
5.000
8.575
12.863
17.150
205.50 215.00 206.96 205.75 833.21
210.25 222.94 222.31 210.40 865.89
213.79 228.25 223.96 213.87 879.86
217.64 230.25 225.92 217.66 891.47
219.18 230.57 226.24 219.33 895.31
1.100 0.750 0.400 1.450
0.527 0.211 0.120 0.895
0.268 0.120 0.120 0.643
0.126 0.120 0.120 0.506
0.121 0.120 0.120 0.501
226 161 83 298 768 0.922
111 47 27 188 373 0.430
57 27 27 138 249 0.283
28 28 27 110 192 0.216
27 28 27 110 191 0.214
26.85 30.05 24.33 26.06 107.29
19.02 13.41 0.00 18.45 50.87
11.66 0.00 0.00 11.30 22.96
2.49 0.00 0.00 2.41 4.90
-0.99 0.00 0.00 -0.96 -1.95
207 217 208 207 840.12
211 224 222 211 868
214 228 224 214 880
218 230 226 218 891
219 231 226 219 895
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
840.12 833.21 107.29 1311.59 0.922 0.64
868.18 865.89 50.87 1311.59 0.430 0.66
880.48 879.86 22.96 1311.59 0.283 0.67
891.50 891.47 4.90 1311.59 0.216 0.68
895.32 895.31 -1.95 1311.59 0.214 0.68
34
6. PRESTRESS SUMMARY STAGE - 1 SECTION Support 5.00 L 8.58 L 12.86 L 17.150 L
X (m) 1.050 5.000 9.625 13.913 18.200
F (t) 840.1 868.2 880.5 891.5 895.3
CGfrom bot. (m) 0.922 0.430 0.283 0.216 0.214
Fh (t) 833.2 865.9 879.9 891.5 895.3
Fv (t) 107.3 50.9 23.0 4.9 -2.0
35
STRESS CHECK WITH 20% LOSS Item
1
2
3
4
5
Support
End Varying
L/4
3L/8
L/2
m
1.050
5.000
8.575
13.913
18.200
m2 m m m4 m3 m4
1.619 2.400 1.241 0.820 0.707 0.661
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
Area of Composite section Depth of Composite section CG from bottom Inertia of Composite section Zt Zb
m2 m m m4 m3 m4
2.201 2.600 1.574 1.501 1.462 0.954
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
Dead Load Moments 1st Stage
t-m
-55.11
152.05
259.22
344.56
385.16
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.4
640.1 -662.5
715.5 -740.5
Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
Stress at CG of Cable GR1
t/m2
83.4
-292.3
-498.3
-662.4
-740.5
Segment Length Average Stress for Each Segment
m t/m2
3.950 -104.4
3.575 -395.3
5.338 -580.4
4.288 -701.4
0.000 0.0
Average Stress at CG of Cables
t/m2
-462.4
Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
Stress at CG of Cable
t/m2
21.4
-189.2
-382.7
-545.2
-610.9
Segment Length Average Stress for Each Segment
m t/m2
3.950 -83.9
3.575 -286.0
5.338 -464.0
4.288 -578.1
0.000 0.0
Average Stress at CG of Cables
t/m2
-367.9
3.74 865.9 0.430 0.790 -0.441 2.546
3.74 879.9 0.283 0.937 -0.715 2.829
3.74 891.5 0.216 1.005 -0.839 2.959
3.74 895.3 0.214 1.007 -0.844 2.963
Chainage of Section from left support
Unit
Section Property (Beam Only) Area of beam Depth of beam CG from bottom Inertia of beam Zt Zb Section Property (Composite)
Stress due to Dead Load Top Bottom Stress after Eloss
Stress at 21 st day before 1st stage of stressing
Detail of 1st StagePrestressing after 21 days No. of Cables of 19 T 13 Prestressing Force (P2) CG of Cables from Bottom Eccentricity of Cables Prestressing Factor (Top) Prestressing Factor (Bottom)
t m m
3.74 833.2 0.922 0.318 0.167 1.100
36
Elastic Shortening Loss (ELOSS) Eloss of GR2 Cables P2-Eloss
t t
23.2 810.0
23.2 842.6
23.2 856.6
23.2 868.2
23.2 872.1
t/m2 t/m2
135.5 890.7
-371.6 2145.6
-612.1 2423.6
-728.9 2568.7
-735.8 2584.0
Stress due to P2-Eloss(2) Top Bottom
Stress after Stressing Cables Top Bottom
t/m t/m2
2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
Stress at CG of Cable
t/m2
621.9
1504.9
1682.7
1726.8
1677.6
Segment Length Average Stress for Each Segment
m t/m2
3.950 1063.4
3.575 1593.8
5.338 1704.8
4.288 1702.2
0.000 0.0
Increase in Avg. Stress at CG of Cable
t/m2
1533.3
t t
23.2 810.0
23.2 842.6
23.2 856.6
23.2 868.2
23.2 872.1
t/m2 t/m2
135.5 890.7
-371.6 2145.6
-612.1 2423.6
-728.9 2568.7
-735.8 2584.0
Top Bottom
t/m2 t/m2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
Stress at CG of Cable
t/m
2
621.9
1504.9
1682.7
1726.8
1677.6
Segment Length Average Stress for Each Segment
m t/m2
3.950 1063.4
3.575 1593.8
5.338 1704.8
4.288 1702.2
0.000 0.0
Increase in Avg. Stress at CG of Cable
t/m2
1533.3
Elastic Shortening Loss (ELOSS) Eloss of GR2 Cables P2-Eloss Stress due to P2-Eloss(2) Top Bottom
Stress after Stressing Cables
Check for Eloss for cable
t
23.7
Shuttering Load Moments
t-m
0.00
36.63
55.15
68.93
73.53
t/m2 t/m2
0.0 0.0
68.0 -70.4
102.4 -106.0
128.1 -132.5
136.6 -141.4
0.5*$C$144*(ecable/econc21)*(nocable2-1)/2*acable*ifeloss
0.5
Stress due to Shuttering (for deck slab casting) Top Bottom
37
Losses From 21st day to 28th day Creep loss of Cable Shrinkage loss of Cable =(shr21-shr28)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
Total Loss (C+S+R)
t t
11.0 0.6
11.0 0.6
11.0 0.6
11.0 0.6
11.0 0.6
t
11.1 0.618
13.4
14.4
15.3
15.5
t
22.7
25.0
26.0
26.8
27.1
t/m2 t/m2
-3.8 -24.9
11.0 -63.6
18.5 -73.4
22.5 -79.2
22.8 -80.2
2
53.7 949.2
-10.1 1719.3
-9.5 1745.8
61.8 1694.5
139.1 1622.0
Stress due to (C+S+R) Top Bottom Stress at 28 th day before casting of deck slab Top Bottom
t/m 2 t/m
Stress at CG of Cable
t/m
2
605.09
1409.15
1538.69
1547.64
1489.99
Segment Length Average Stress for Each Segment
m 2 t/m
3.950 1007.1
3.575 1473.9
5.338 1543.2
4.288 1518.8
0.000 0.0
Average Stress at CG of Cable
t/m2
1399.2
Check for Creep loss of Cable
t
11.4
t-m
0.00
120.56
182.85
231.25
250.99
t/m2 t/m2
0.0 0.0
224.0 -231.8
339.7 -351.5
429.6 -444.6
466.3 -482.5
Dead Load Moments due to Deck Slab
0.4 (creep21-creep28)*ifcreep*nocable2*acable*C190*ecable/1000
Stress due to Deck load moments Top Bottom
Stress after casting of deck slab Top Bottom
t/m2 t/m2
53.7 949.2
213.8 1487.5
330.1 1394.3
491.4 1249.9
605.4 1139.4
t/m2 t/m2 t/m2
0.0 0.0 0.0
-26.8 -20.8 50.5
-40.3 -31.3 76.0
-50.4 -39.2 95.0
-53.7 -41.8 101.3
-5.1 -4.0 9.7
-6.5 -5.1 12.3
-7.1 -5.5 13.3
Stress due to release of Shuttering Load Top of Deck Top of Girder Bottom of Girder
Stress release due to hardening of solid slab i.e density reduces from 2.6 to 2.5 t/m3 Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 2 t/m
0.0 0.0 0.0
-3.4 -2.6 6.4
38
Stress after release of Shuttering Load & hardening of deck slab t/m2 t/m2 t/m2
0.0 53.7 949.2
-30.1 190.4 1544.3
-45.4 294.8 1479.9
-56.8 447.2 1357.2
-60.8 558.1 1254.0
Creep loss of Cable Shrinkage loss of Cable =(shr28-shr56)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
t t
8.2 3.0
8.2 3.0
8.2 3.0
8.2 3.0
8.2 3.0
t
6.0 0.33
7.3
7.8
8.2
8.4
Total Loss (C+S+R)
t
17.2
18.5
19.0
19.4
19.6
0.009 1.137
-0.284 2.391
-0.392 2.594
-0.441 2.687
-0.442 2.690
t/m2 t/m2 t/m2
-0.2 -1.6 -19.6
5.2 1.4 -44.1
7.4 3.1 -49.3
8.6 3.9 -52.2
8.7 3.9 -52.7
Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
Stress at CG of Cable
t/m2
592.41
1265.60
1297.03
1228.13
1144.47
Segment Length Average Stress for Each Segment
m t/m2
3.950 929.0
3.575 1281.3
5.338 1262.6
4.288 1186.3
0.000 0.0
Top of Deck Top of Girder Bottom of Girder Losses from 28 to 56 day
Prestressing Factor (after Composite action) Cable Top Bottom
Stress due to (C+S+R) Top of Deck Top of Girder Bottom of Girder Stress at 56th day before laying SIDL
Average Stress at CG of Cable
t/m2
1170.6
Check for Creep loss of Cable
t
8.4
0.1
Stress after Shift of bearings Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
t-m
34.00
89.00
164.80
205.30
219.00
t/m2 t/m2 t/m2
23.3 18.7 -35.7
65.0 50.6 -122.6
120.4 93.6 -227.1
150.0 116.7 -282.9
160.0 124.4 -301.8
SIDL applied at 56th day Moments due to SIDL Stress due to SIDL Top of Deck Top of Girder Bottom of Girder
39
t/m2
-13.02
-88.99
-186.10
-243.96
-260.69
Creep loss of Cable Shrinkage loss of Cable =(shr56-shr_infinity)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
t t
18.9 28.2
18.9 28.2
18.9 28.2
18.9 28.2
18.9 28.2
t
36.9 2.048
44.6 47.8 =2+1-0.334-0.62
50.6
51.5
Total Loss (C+S+R)
t
84.0
91.7
94.9
97.7
98.6
t/m2 t/m2 t/m2
-0.7 -8.0 -95.5
26.0 7.2 -219.2
37.2 15.4 -246.3
43.1 19.6 -262.4
43.6 19.9 -265.2
Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
22.4 62.8 798.4
66.2 249.6 1158.4
119.6 406.9 957.3
144.7 587.3 759.6
151.5 706.3 634.4
Stress at CG of Cable
t/m2
500.21
962.53
858.45
704.30
591.44
Segment Length Average Stress for Each Segment
m t/m2
3.950 731.4
3.575 910.5
5.338 781.4
4.288 647.9
0.000 0.0
Average Stress at CG of Cable
t/m2
763.4
Stress at CG of Cable Losses from 56th day to Infinity
Stress due to (C+S+R) Top of Deck Top of Girder Bottom of Girder Stress during Service at Infinity
Check for Creep loss of Cable
t
21.2
2.4
Moment due to Live Load
t-m
6.4
169.6
306.3
376.3
400.7
Stress Due to Live Load Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
4.4 3.5 -6.7
123.9 96.4 -233.7
223.7 174.1 -422.1
274.9 213.8 -518.6
292.7 227.7 -552.1
t/m2 t/m2 t/m2
26.7 66.3 791.7
190.0 345.9 924.7
343.3 581.0 535.2
419.6 801.1 241.0
444.1 934.0 82.3
t m t/m2 t/m2 t/m2
83.95 0.93 -52.91 80.95 -43.41
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
302.1 673.1 496.5
378.4 893.3 202.4
403.0 1026.2 43.6
Stress at Service with Live Load Top of Deck Top of Girder Bottom of Girder Stress due to Differential Shrinkage & Creep Force Eccentricity Top of Deck Slab Top of Girder Bottom
Stress after Differential Shrinkage & Creep (at service condition with Live Load) Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-26.2 147.3 748.3
148.8 438.1 886.1
40
SUMMARY OF SHORT-TERM LOSSES 1st Stage Prestressing Loss due to Friction & Slip Loss due to Elastic shortening % Loss due to Friction & Slip Total Loss
t t t
159.0 23.2 15.9 182.2
130.9 23.2 13.1 154.2
118.6 23.2 11.9 141.9
107.6 23.2 10.8 130.9
103.8 23.2 10.4 127.0
SUMMARY OF LONG-TERM LOSSES 1st Stage Prestressing Loss due to Creep Loss due to Shrinkage Loss due to Relaxation of Steel Total Loss (C+S+R) % Loss in terms of applied Force (After Friction & Slip)
t t t t
38.1 31.7 54.0 123.8 14.7
38.1 31.7 65.3 135.1 15.6
38.1 31.7 70.1 139.9 15.9
38.1 31.7 74.1 143.9 16.1
38.1 31.7 75.4 145.2 16.2
Total (C+S+R)
t
123.8
135.1
139.9
143.9
145.2
14.7
15.6
15.9
16.1
16.2
% Loss in terms of applied Force (After Friction & Slip) SUMMARY OF LONG-TERM+SHORT TERM LOSSES Total Loss in 1st Stage % Loss in terms of Jacking Force
t
306.1 30.6
289.3 29.0
281.8 28.2
274.7 27.5
272.2 27.2
Total Loss % Loss in terms of Jacking Force
t
306.1 30.6
289.2 29.0
281.8 28.2
274.7 27.5
272.2 27.2
41
STRESS SUMMARY Item Section
Unit m
1
2
3
4
5
Support
End Varying
L/4
3L/8
L/2
1.050
5.000
9.625
13.913
18.200
Permissible stress t/m2
Stress at 21 st day before 1nd stage of stressing Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
> <
-229.4 2293.6
OK OK
t/m2 t/m2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
> <
-229.4 2293.6
OK OK
Stress after Stressing GR1 Cables Top Bottom
Stress at 28 th day before casting of deck slab Top Bottom
t/m2 t/m2
53.7 949.2
-10.1 1719.3
-9.5 1745.8
61.8 1694.5
139.1 1622.0
> <
-229.4 2293.6
OK OK
t/m2 t/m2
53.7 949.2
213.8 1487.5
330.1 1394.3
491.4 1249.9
605.4 1139.4
> <
-229.4 2293.6
OK OK
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
> > <
-305.4 -229.4 2293.6
OK OK OK
t/m2 t/m2 t/m2
22.4 62.8 798.4
66.2 249.6 1158.4
119.6 406.9 957.3
144.7 587.3 759.6
151.5 706.3 634.4
> > <
-305.4 0 1529.1
OK OK OK
t/m2 t/m2 t/m2
26.7 66.3 791.7
190.0 345.9 924.7
343.3 581.0 535.2
419.6 801.1 241.0
444.1 934.0 82.3
> > <
-305.4 0 1529.1
OK OK OK
403.0 1026.2 43.6
> > <
-305.4 0 1529.1
OK OK OK
Stress after casting of deck slab Top Bottom
Stress at 56th day before laying SIDL Top of Deck Top of Girder Bottom of Girder Stress during Service at Infinity Top of Deck Top of Girder Bottom of Girder Stress at Service with Live Load Top of Deck Top of Girder Bottom of Girder
Stress after Differential Shrinkage & Creep (at service condition with Live Load) Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-26.2 147.3 748.3
148.8 438.1 886.1
302.1 673.1 496.5
378.4 893.3 202.4
42
Shrinkage Model Shrinkage Model
(Microstrain)
Total shrinkage strain
(Refer Cl: 6.4.2.6 of IRC; 112-2011)
εcs
=
+
εcd
=
Drying Shrinkage Strain
εca
=
Autogenious Shrinkage strain
εcd
Basic Drying Shrinkage Strain
εca
(Refer Annexure A2.6 of IRC; 112-2011)
fcmo
=
is the mean compressive strength (Mpa)
fcm
=
12.5 Mpa
=
is the co-efficient which depends on the type of cement
=
4 for Normal cement
=
is the co-efficient which depends on the type of cement
=
0.12 for Normal cement
αds1 αds2
RH
=
is the ambient relative humidity (Percent)
RH0
=
100 percent
=
0.88627
Residual Shrinkage Strain
( upto 7 days)
0.000206
0.000203
0.000203
0.000203
0.000203
Residual Shrinkage Strain
( upto 14 days)
0.000198
0.000195
0.000195
0.000195
0.000195
Residual Shrinkage Strain
( upto 21 days)
0.000193
0.000190
0.000190
0.000190
0.000190
Residual Shrinkage Strain
( upto 28 days)
0.000190
0.000187
0.000187
0.000187
0.000187
Residual Shrinkage Strain
( upto 42 days)
0.000182
0.000176
0.000176
0.000176
0.000176
Residual Shrinkage Strain
( upto 56 days)
0.000178
0.000173
0.000173
0.000173
0.000173
Differential Shrinkage Strain
( upto 7 days)
0.000030
0.000033
0.000033
0.000033
0.000033
Differential Shrinkage Strain
( upto 14 days)
0.000038
0.000041
0.000041
0.000041
0.000041
Differential Shrinkage Strain
( upto 21 days)
0.000043
0.000046
0.000046
0.000046
0.000046
Differential Shrinkage Strain
( upto 28 days)
0.000046
0.000049
0.000049
0.000049
0.000049
Differential Shrinkage Strain
( upto 42 days)
0.000055
0.000060
0.000060
0.000060
0.000060
Differential Shrinkage Strain
( upto 56 days)
0.000058
0.000063
0.000063
0.000063
0.000063
Differential Shrinkage Strain
( upto Infinity days)
0.000236
0.000238
0.000238
0.000238
0.000238
43
Ac
Concrete cross sectional area Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At 7 days
Age of concrete in days at the time considered t End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
0.0
0.0
0.0
0.0
0.0
7.0
7.0
7.0
7.0
7.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.41089
0.41089
0.41089
0.41089
0.41089
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000027
0.000027
0.000027
0.000027
0.000027
Total shrinkage strain ε cd = ε ca+ ε cd
0.000030
0.000033
0.000033
0.000033
0.000033
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
7.0
7.0
7.0
7.0
7.0
14.0
14.0
14.0
14.0
14.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.52684
0.52684
0.52684
0.52684
0.52684
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000034
0.000034
0.000034
0.000034
0.000034
Total shrinkage strain ε cd = ε ca+ ε cd
0.000038
0.000041
0.000041
0.000041
0.000041
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
Concrete cross sectional area
from table 6.7of IRC:112-2011
Ac
kh
Age of concrete in days at the time considered t At 14 days
1.56
Autogenous shrinkage strain ε ca
Perimeter of that part of the cross-section which is exposed to drying u Notional size (mm) of the cros-section h 0 = 2A c /u
End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)] Autogenous shrinkage strain ε ca
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011 At 21 days
2.20
kh
0.70
0.70
0.70
0.70
0.70
Age of concrete in days at the time considered t
14.0
14.0
14.0
14.0
14.0
(t s )
21.0
21.0
21.0
21.0
21.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.60009
0.60009
0.60009
0.60009
0.60009
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000039
0.000039
0.000039
0.000039
0.000039
Total shrinkage strain ε cd = ε ca+ ε cd
0.000043
0.000046
0.000046
0.000046
0.000046
End of curing in days Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
44
Ac
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
Age of concrete in days at the time considered t
21.0
21.0
21.0
21.0
21.0
(t s )
28.0
28.0
28.0
28.0
28.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.65295
0.65295
0.65295
0.65295
0.65295
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000042
0.000042
0.000042
0.000042
0.000042
Total shrinkage strain ε cd = ε ca+ ε cd
0.000046
0.000049
0.000049
0.000049
0.000049
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
28.0
28.0
28.0
28.0
28.0
42.0
42.0
42.0
42.0
42.0
0.042
0.073
0.073
0.073
0.073
7.312E-06
1.28E-05
1.28E-05
1.28E-05
1.28E-05
0.72642
0.72642
0.72642
0.72642
0.72642
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000047
0.000047
0.000047
0.000047
0.000047
Total shrinkage strain ε cd = ε ca+ ε cd
0.000055
0.000060
0.000060
0.000060
0.000060
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
Notional size (mm) of the cros-section h 0 = 2A c /u
400.9
269.5
269.5
269.5
269.5
from table 6.7of IRC:112-2011
0.70
0.70
0.70
0.70
0.70
42.0
42.0
42.0
42.0
42.0
56.0
56.0
56.0
56.0
56.0
0.042
0.073
0.073
0.073
0.073
7.312E-06
1.28E-05
1.28E-05
1.28E-05
1.28E-05
0.77612
0.77612
0.77612
0.77612
0.77612
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000050
0.000050
0.000050
0.000050
0.000050
Total shrinkage strain ε cd = ε ca+ ε cd
0.000058
0.000063
0.000063
0.000063
0.000063
Concrete cross sectional area Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u
At 28 days
from table 6.7of IRC:112-2011
End of curing in days
kh
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At 42days
Age of concrete in days at the time considered t End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)] Autogenous shrinkage strain ε ca
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
kh
At 56 days
Age of concrete in days at the time considered t End of curing in days
(t s )
Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
45
Ac
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
56.0
56.0
56.0
56.0
56.0
14056.0
14056.0
14056.0
14056.0
14056.0
0.978
0.988
0.988
0.988
0.988
0.0001711
0.000173
0.000173
0.000173
0.000173
1.00000
1.00000
1.00000
1.00000
1.00000
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Total shrinkage strain ε cd = ε ca+ ε cd
0.000236
0.000238
0.000238
0.000238
0.000238
Concrete cross sectional area
Perimeter of that part of the cross-section which is exposed to drying u Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At Infinity
Age of concrete in days at the time considered t End of curing in days
(t s )
Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
46
Creep Strain Creep strain of concrete where φ σc Ec
= = = =
φ x σc/Ec creep coefficient (calculated as per IRC-112) constant Compressive stress applied to the concrete at time t Modulus of Elasticity of concrete
Compressive stress at CG of the tendons at transfer stage Compressive stress at CG of the tendons after application of SIDL Comp stress at CG of the tendons after application of LL (losses upto infinity) Modulus of Elasticity of Concrete
= = = =
7.073 5.888 3.846 34000
N/mm2 N/mm2 N/mm2 N/mm2
Calculation of Creep Coefficient The development of creep with time may be taken as β (t,to) x φ (inf,to) φ (t,to) = where β (t,to) ((t - to)/(β H+(t-to)))^0.3 = t is the age of the concrete in days at the time considered to is the age of the concrete in days at time of loading=21 days (t - to) is the actual duration of loading in days βH is a coefficient depending on the relative humidity ( RH in percent) and the notional member size (ho in mm). βH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 <= 1500 for fcm <=45 βH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 α<= 1500α for fcm >=45 fcm = 55 α = SQRT(45/fcm) =0.904534034 Grade of concrete β H f (inf,to) b (t,to)
=
f (t,to)
=
Creep Creep Creep Creep
Strain Strain Strain Strain
for
at at at at
21 28 56 infinity
21 28 56 90 28 56 90
days days days days days days days
= = = = = = = = = = = =
1.500 0.0000 0.2386 0.3589 0.3796 0.3579 0.5384 0.5695 0.000000 0.000050 0.000093 0.000170
47
Check For Ultimate Moment b
ηfcd
εcu3 εcsu1 x
Fc
λx
h d2 d1
As2 As1
Fs2
εs2 εs1
Section Schematic
Strain
Stress-Strain Relationship of concrete at ULS:
Fs1 Stress
Considering Rectangular stress block
εc3
0.0018
0.0018
Compression strain at peak stress for rectangular Stress distribution
εcu3
0.0035
0.0035
Ultimate compression strsin for rectangular stress distribution
η
1.00
1.00
Co-efficient to convert to rectangular stress block
λ
0.80
0.80
Co-efficient to convert to rectangular stress block
0.67
0.67
Co-efficient to convert the strength in the test to strength in structural member
1.00
1.00
αc
fcd
Co-efficient to convert to rectangular stress block 2
20.1
20.1
N/mm
Co-efficient to convert to rectangular stress block
25.125
25.125
N/mm2
Co-efficient to convert to rectangular stress block
48
Section under considaration
Sec 1-1
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
1. Ultimate Applied Moment, Mu (KNm)
-343
9072
15728
19791
21387
2. Overall Depth, D (m)
2.600
2.600
2.600
2.600
2.600
3. Cg of Cable from sofit, Yord (m)
0.922
0.430
0.283
0.216
0.214
71
71
71
71
71
9.9E-05
9.9E-05
9.9E-05
9.9E-05
9.9E-05
6. Area of Section (m )
2.20
1.56
1.56
1.56
1.56
7. Effective depth , d
1.678
2.170
2.317
2.384
2.386
8.Effective flange width , Bf (m)
3.00
3.00
3.00
3.00
3.00
9.Effective Flange thickness, t (m)
0.200
0.200
0.200
0.200
0.200
10.Width of web, b (m)
0.650
0.300
0.300
0.300
0.300
11.Ultimate force per Cable (KN)
183.9
183.9
183.9
183.9
183.9
12.Ultimate tensile strength of steel , fpu (Mpa)
1863.7
1863.7
1863.7
1863.7
1863.7
13.Prestressing Force after all Loss (Kn)
6930.56
7098.63
7173.54
7243.80
7268.74
175.26
175.26
175.26
175.26
175.26
16.Total Compression, C (KN)
11357
11357
11357
11357
11357
17. Initial Prestress, fpe (Mpa)
989
1013
1024
1034
1037
18. Initial strain in tendon
0.0051
0.0052
0.0052
0.0053
0.0053
19. Strain due to bending in tendon
0.030
0.040
0.043
0.044
0.044
20. Total strain in tendon
0.0351
0.0450
0.0480
0.0494
0.0495
21. fpu/1.15 (MPa)
1620.6
1620.6
1620.6
1620.6
1620.6
22.Corresponding Strain
0.013
0.013
0.013
0.013
0.013
23. 0.9*fpu/1.15 (MPa)
1458.5
1458.5
1458.5
1458.5
1458.5
24.Corresponding Strain
0.007
0.007
0.007
0.007
0.007
Ultimate Design Flexural Moment MEd
4. No of Cable Strands 2
5. Area of each Strand (m ) 2
14.Ultimate Flexural Capacity 15. Assume neutral axis from compression flange, X (mm)
1620.6
1620.6
1620.6
1620.6
1620.6
2
26. Area of Steel , As (m )
0.007
0.007
0.007
0.007
0.007
27. Total Tension, T (KN)
11357
11357
11357
11357
11357
28. T-C
0
0
0
0
0
29. CG of Compression Zone from compressive flange (mm)
88
88
88
88
88
30. Z (mm)
1590
2082.0
2229.2
2296.5
2298.8
31. Flexural Capacity, Mu =T*Z (KNm)
18059
23645
25317
26080
26107
OK
OK
OK
OK
OK
25. Fb (Mpa)
Status
49
Check for Ultimate Shear Shear Corresponding to Maximum Moment Grade of Concrete
45
Mpa
Grade of Steel
500
Mpa
fcd
45.00
Mpa
fyk
435
Mpa
fywd
348
Mpa
Section COMPONENT
Sec 1-1
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
UNIT
Ultimate Shear Capacity of Section uncracked in Flexure (Cl. 10.3.2 of IRC 112-2011) Ult. Applied Shear Force, Vult
KN
2046.9
1567.0
1290.8
653.5
319.8
Overall Width, bw
m
0.650
0.300
0.300
0.300
0.300
Overall Depth, h
m
2.600
2.600
2.600
2.600
2.600
0.513
0.513
0.513
0.513
0.513
19503
9001
9001
9001
9001
OK
OK
OK
OK
OK
v =0.6[1-(fck/310)] Max Shear Check VEd <=0.5bw d ν fcd
KN
Area of Section
m2
2.201
1.556
1.556
1.556
1.556
Horizontal Component of prestress after all losses
KN
6930.6
7098.6
7173.5
7243.8
7268.7
Cg of cable from sofit, Yord
m
0.922
0.430
0.283
0.216
0.214
Comp. Stress due to prestress, σcp
Mpa
3.148
4.563
4.611
4.656
4.672
Effect of Vertical Prestress, Vpr
KN
-1072.9
-508.7
-229.6
-49.0
19.5
Second Moment of Area, I
m4
1.501
1.233
1.233
1.233
1.233
First Moment of Area b/w Centroidal and Extreme Comression fibre about centroidal axis, S
m
3
1.462
1.369
1.369
1.369
1.369
Vrdc = SQRT((fctd)^2+fctd.σcp).I.bw/s
KN
31051
12762
12768
12774
12776
50
51
Provision of Shear Reinforcement (Cl. 10.3.3.2 of IRC 112-2011) Ultimate Applied Shear, VEd
kN
2047
1567
1291
653
320
Design Shear Capacity, Vc
kN
1011
786
834
858
861
Vertical component of Prestress
kN
-1073
-509
-230
-49
20
Net VEd
kN
3120
2076
1520
702
300
No
No
No
Yes
Yes
Shear R/f Required
Shear R/f Required
Shear R/f Required
Minimum R/f
Minimum R/f
3119.8
2075.8
1520.4
0.0
0.0
αcw
1.070
1.101
1.102
1.103
1.104
ν1
0.60
0.60
0.60
0.60
0.60
Is VEd less than Vc ? Reqirement of shear reinforcement VEd
KN
Shear Reinforcement :-
2
i) Aswmax / S = 0.5*bw*αcw*ν1*fcd/(fywd)
mm /m
27.0
12.8
12.8
12.8
12.9
ii) 0.072 x (SQRT(fck))/fyk
mm2/m
25.3
15.1
16.1
16.6
16.6
Governing Shear reinforcement
mm /m
2
27.0
15.1
16.1
16.6
16.6
Shear RF Due to ultimate loads, Asv/Sv = VEd/(z*fywd)
mm /m
2
5346
2751
1887
0
0
Design Shear Reinforcement/web
mm /m
2
2673
1375
943
8
8
Spacing
125
125
150
200
200
Bar Dia
16
12
12
12
12
1608
905
754
565
565
OK
OK
OK
OK
OK
Reinforcement provided
52
Check for Ultimate Shear 2 Maximum Shear & Corresponding Moment Grade of Concrete
45
Mpa
Grade of Steel
500
Mpa
fcd
45.00
Mpa
fyk
435
Mpa
fywd
348
Mpa
Section
Sec 1-1
COMPONENT
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
UNIT
Ultimate Shear Capacity of Section uncracked in Flexure (Cl. 10.3.2 of IRC 112-2011) Ult. Applied Shear Force, Vult
KN
2112.0
1659.3
1237.1
774.9
367.5
Overall Width, bw
m
0.650
0.300
0.300
0.300
0.300
Overall Depth, h
m
2.600
2.600
2.600
2.600
2.600
0.513
0.513
0.513
0.513
0.513
19503
9001
9001
9001
9001
OK
OK
OK
OK
OK
2.201
1.556
1.556
1.556
1.556
v =0.6[1-(fck/310)] Max Shear Check VEd <=0.5bw d ν fcd
KN
2
Area of Section
m
Horizontal Component of prestress after all losses
KN
6930.6
7098.6
7173.5
7243.8
7268.7
Cg of cable from sofit, Yord
m
0.922
0.430
0.283
0.216
0.214
Mpa
3.148
4.563
4.611
4.656
4.672
KN
Comp. Stress due to prestress, σcp Effect of Vertical Prestress, Vpr
-1072.9
-508.7
-229.6
-49.0
19.5
1.501
1.233
1.233
1.233
1.233
Second Moment of Area, I
m
4
First Moment of Area b/w Centroidal and Extreme Comression fibre about centroidal axis, S
m
3
1.462
1.369
1.369
1.369
1.369
KN
31051
12762
12768
12774
12776
^2
Vrdc = SQRT((fctd) +fctd.σcp).I.bw/s
53
Provision of Shear Reinforcement (Cl. 10.3.3.2 of IRC 112-2011) Ultimate Applied Shear, VEd
kN
2112
1659
1237
775
367
Design Shear Capacity, Vc
kN
1011
786
834
858
861
Vertical component of Prestress
kN
-1073
-509
-230
-49
20
Net VEd
kN
3185
2168
1467
824
348
No
No
No
Yes
Yes
Shear R/f Required
Shear R/f Required
Shear R/f Required
Minimum R/f
Minimum R/f
3184.9
2168.1
1466.7
0.0
0.0
αcw
1.070
1.101
1.102
1.103
1.104
ν1
0.60
0.60
0.60
0.60
0.60
2
27.0
12.8
12.8
12.8
12.9
2
25.3
15.1
16.1
16.6
16.6
2
27.0
15.1
16.1
16.6
16.6
2
5458
2873
1820
0
0
2
2729
1436
910
8
8
Spacing
125
125
125
200
200
Bar Dia
16
12
10
10
10
1608
905
628
393
393
OK
OK
OK
OK
OK
Is VEd less than Vc ? Reqirement of shear reinforcement VEd
KN
Shear Reinforcement :-
i) Aswmax / S = 0.5*bw*αcw*ν1*fcd/(fywd)
mm /m
ii) 0.072 x (SQRT(fck))/fyk
mm /m
Governing Shear reinforcement
mm /m
Shear RF Due to ultimate loads, Asv/Sv = VEd/(z*fywd)
mm /m
Design Shear Reinforcement/web
mm /m
Reinforcement provided
54
10. TEMPERATURE As per sec. Fig.10 of IRC : 6 - 2010, for the combination of loads with diffferential temperature gradient effects, maximum 50% live load shall be considered . Effect of Temperature Rise F
=
EC α ∆t A
= = = =
EC α ∆t Α 2
3.35E+06 t/m 0 1.20E-05 / C Temperature differential X - sectional Area Where temp. differential is ∆t
TEMPERATURE GRADIENT ( FOR CONCRETE SUPERSTRUCTURE ) ( Refer IRC : 6 - 2010 ; clause 218.3 )
AT MID-SPAN POSITIVE TEMP. DIFFERENCES
17.8 8.60
1 150
1.61
2
4.0
250
3
0
150 0
4 2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
4
2.910 0.200 0.582 0.100 0.058 0.006 8.600 5.006 0.501
1.000 0.199 0.199 0.299 0.060 0.018 1.61 0.320 0.096
0.300 1.805 0.542 1.301 0.705 0.917 0.000 0.000 0.000
0.650 0.396 0.258 2.402 0.618 1.486 0.000 0.000 0.000
TOTAL
1.580 1.441 2.426 5.326 0.596
55
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
12.922 0.859 3.833 2.076
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000824
=
0.0000460
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 17.800 2.1E-04 -440.1
0.200 9.2E-06 3.200 3.8E-05 116.7
0.399 1.8E-05 0.000 0.0E+00 214.8
2.204 1.0E-04 0.000 0.0E+00 -63.5
2.600 1.2E-04 2.100 2.5E-05 -209.2
m m 0 c t/m2
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
151.5 706.3 634.4
+ + +
146.3 113.8 -276.1
-440.1
+ + +
-440.1 116.7 -209.2
= = =
297.8
-142.3 936.9 149.2
t/m2 t/m2 t/m2
-142.3 0.026 Point of zero stress
116.7
214.8
820.2
+
936.9
=
-63.5
-209.2
358.4
Consider 1 mt strip Area of steel required
=
1/2 x
= Provide
10
φ
@
149.2
250
0.7 mm/m
0.026 2.4 2 cm /m =
x
142.279 1.15
3.1
cm /m
x
2
OK
56
AT SUPPORT POSITIVE TEMP. DIFFERENCES
17.8 8.60
1 150
1.22
2
4.0
250
3
0
150
2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
2.910 0.200 0.582 0.100 0.058 0.0058 8.60 5.006 0.501
1.000 0.247 0.247 0.324 0.080 0.0259 1.22 0.302 0.098
0.650 2.153 1.399 1.524 2.132 3.2483 0.00 0.000 0.000
TOTAL
2.229 2.270 3.280 5.308 0.598
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
17.411 1.358 7.310 5.154
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000893
=
0.0000597
Calculation of Eigen Stress
Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 17.800 2.1E-04 -416.8
0.200 1.2E-05 3.200 3.8E-05 130.9
0.447 2.7E-05 0.000 0.0E+00 210.2
2.600 m 1.6E-04 m 2.100 0c 2.5E-05 2 -305.0 t/m
57
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
22.4 62.8 798.4
+ + +
2.2 1.8 -3.4
-416.8
+ + +
-416.8 130.9 -305.0
24.6
= = =
-392.2 195.4 490.0
t/m2 t/m2 t/m2
-392.2 Point of zero stress 64.6
0.133 195.4
130.9 210.2
+
=
-305.0
795.1
Consider 1 mt strip Area of steel required
=
1/2 x
= Provide
16 φ
@
490.0
150
0.133 x 392.201 2.4 x 1.15 2 9.5 cm /m 2 mm/m = 13.4 cm /m OK
58
TEMPERATURE As per sec. Fig.10 of IRC : 6 - 2010, for the combination of loads with diffferential temperature gradient effects, maximum 50% live load shall be considered . Effect of Temperature Fall F
=
EC α ∆t A
= = = =
EC α ∆t Α 2
3.35E+06 t/m 0 1.20E-05 / C Temperature differential X - sectional Area Where temp. differential is ∆t
TEMPERATURE GRADIENT ( FOR CONCRETE SUPERSTRUCTURE ) ( Refer IRC : 6 - 2000 ; clause 218.3 )
AT MID-SPAN REVERSE TEMP. DIFFERENCES
10.6 6.64
1 250 0.7
2
0.53
3
0
200
h
200 0.8 250
1.07
4 2.1
Temperature Fall case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
4
2.910 0.200 0.582 0.100 0.058 0.0058 6.64 3.865 0.387
1.000 0.199 0.199 0.299 0.060 0.0178 0.53 0.105 0.031
0.300 1.805 0.542 1.301 0.705 0.9170 0.00 0.000 0.000
0.650 0.396 0.258 2.402 0.618 1.4856 1.07 0.276 0.662
TOTAL
1.580 1.441 2.426 4.245 1.080
59
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T)
P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
10.300 1.556 3.833 2.076
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000597
=
0.0000301
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 10.600 1.3E-04 -226.3
0.200 6.0E-06 2.680 3.2E-05 72.2
0.399 1.2E-05 0.179 2.2E-06 152.8
2.204 6.6E-05 0.215 2.6E-06 -31.1
m m 0 c
2.600 7.8E-05 2.100 2.5E-05 -147.0
t/m2
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top of Deck = Top of Girder = Bottom =
151.5 706.3 634.4
+ + +
146.3 113.8 -276.1
-226.3
+ + +
-226.3 72.2 -147.0
= = =
297.8
71.5 892.4 211.4
t/m2 t/m2 t/m2
71.5 0.000 Point of zero stress
72.2
152.8
820.2
892.4
+
=
-31.1 -147.0 358.4
Consider 1 mt strip Area of steel required
Provide
10
φ
@
211.4
=
1/2 x
=
0.0 mm/m
250
0.000 2.4 2 cm /m =
x x 3.1
71.503 1.15 2
cm /m
OK
60
AT SUPPORT
REVERSE TEMP. DIFFERENCES
10.6 6.64
1 250
0.44
2
0.7
200
3
0
200 0.8 250 2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
TOTAL
1
2
3
2.910 0.200 0.582 0.100 0.058 0.0058 6.64 3.865 0.387
1.000 0.247 0.247 0.324 0.080 0.0259 0.44 0.109 0.035
0.650 2.153 1.399 1.524 2.132 3.2483 0.00 0.000 0.000
2.229 2.270 3.280 3.974 0.422
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
13.036 0.958 7.310 5.154
12.078 2.156
=
0.0000672
=
0.0000450
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 10.600 1.3E-04 -275.7
0.200 9.0E-06 2.680 3.2E-05 12.8
0.447 2.0E-05 0.000 0.0E+00 83.4
2.600 m 1.2E-04 m 2.100 0c 2.5E-05 2 -326.0 t/m
61
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
22.4 62.8 798.4
+ + +
-275.7
2.2 1.8 -3.4
+ + +
-275.7 12.8 -326.0
24.6
= = =
83.4
64.6
=
-326.0
795.1
=
16
φ
@
469.1
1/2 x
= Provide
0.153 77.4
+
Consider 1 mt strip Area of steel required
t/m2 t/m2 t/m2
-251.2 Point of zero stress
12.8
-251.2 77.4 469.1
150
7.0 mm/m
0.153 2.4 2 cm /m =
x x 13.4
251.2 1.15 2
cm /m
OK
62
11. END CROSS GIRDER B.0 Design of End Cross Girder at Temporary Lifting Condition / Jack up condition The end cross girder is designed as a continuous deep beam for bearing replacement condition, continuous over knife supports at the jack locations. The CL of jacks are taken to be 1061 mm from the CL of main girder. The reaction of main girder due to (DL+SIDL) are applied as load at the girder location as shown below.
-120.00 Mton
-110.00 Mton
-105.00 Mton
1.06m
2.12m
127.32 MTon-m
0 MTon-m
-120.00 Mton
127.32 MTon-m 20.83 MTon-m
14.41 MTon-m
-38.08 MTon-m
15.00 MTon-m
21.45 MTon-m
0 MTon-m
-40.13 MTon-m
63
BASIC DESIGN DATA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Distance between C/C Exp. Joint Effective span Overhang of girder off the bearing Overhang of slab off the bearing Expansion Joint Deck Width Angle of skew Clear carriage way Width of outer railing Width of Footpath Width of Crash Barrier Spacing of main girder c/c Spacing of cross girder c/c Thk of deck slab Thk of deck slab at overhang Length of cantilever Cantilever slab thk at fixed end Cantilever slab thk at free end Thk of wearing coat No of main girder Width of footh path Width of raillings Top Flange width of girder No of Intermediate cross girder Grade of concrete Grade of reinforcement Shape Factor λ strength Factor η
Leff
Ang Bcw
Wkerb Spmg Spcg Df Lcan Dcan1 Dcan2 Wc Nomg
bf Nocg Cgrade Sgrade
26.52 23.32 1.050 1.600 40.0 12.0 45.00 11.50 0.30 0.00 0.50 3.00 11.66 0.20 0.40 1.50 0.21 0.21 0.075 4 0.00 0.00 1.000 1.00 M35 Fe 500
m m m m mm m deg. m m m m m m m m m m m Nos
m Mpa Mpa
λ
0.80
IRC-112-Anexure A2- A2.9(2)
η
1.00
IRC-112-Anexure A2- A2.9(2)
28
Partial factor of safety (Basic and seismic)
ɣc
1.50
IRC-112-Cl 6.4.2.8
29
Partial factor of safety Accidental Coefficient to consider the influence of the strength
ɣc
1.20
IRC-112-Cl 6.4.2.8
α
0.67
fcd
40.00
Mpa
fcd
15.63 40.0 2.40 2.60 2.200 1.00 0.30 0.50 35 500 1.15 1 32000
Mpa mm t/m3 t/m3 t/m^3 t/m t/m t/m2 Mpa Mpa
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Design value of concrete comp strength for Basic and seismic Design value of concrete comp strength for Accidental Clear cover Unit weight of dry concrete Unit weight of wet concrete Unit Weight of wearing course Weight of Crash Barrier Weight of Railing Intensity of Load for shuttering Stress in concrete (compression) Stress in steel (tension) Partial factor of safety for basic and seismic
Partial factor of safety for Accidental
cov wcon wwc wrail
fck fyk γs γs
Ecm Es Modular ratio
200000.00
m
IRC-112 Fig 6.3 (Note) IRC-112 Fig 6.3 (Note) Mpa Mpa
6.250
64
Live Load calculations as per Effective Width Method The live load intensity on deck slab is calculated based on effective width method as given in Annexure-B.3 of IRC-112. The dispersion along span of deck slab is ignored, this is a safer side assumption as concentrated load produce worst effect than udl. C/C Spacing of Girder
=
3.000
m
Total Width of Deck
=
12.00
m
Cantilever length
=
1.500
m
Number of support
=
4.000
m
b/lo
=
3.887
α (Constant)
=
2.600
(Cont.)
Thickness of wearing coat
=
75.00
mm
Thickness of deck slab
=
200.00
mm
1Lane Class - A
TRANSVERSE ANALYSIS 1 FOR LIVE LOAD
Load on Wheel-1
=
57
kN
Load on Wheel-2
=
57
kN
Contact width across span
=
250
mm
Contact width along span
=
500
mm
Distance between two vehicle c/c of wheels (Traffic Direction)
=
1.200
m
Distance between two Wheels C/C (Transverse direction)
=
1.800
m
Minimum edge distance upto c/l of wheel
=
0.400
m
b1
=
0.400
m
initial position of first wheel
=
0.900
m
Final position of first wheel
=
9.300
m
Number of load generation
=
58
Transverse increament of Wheels
=
0.1448
Impact factor
=
1.5
Nos m
65
Wheel-1 Load Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Dist. of Position Nearest (X) Support 0.9 1.0448 1.1897 1.3345 1.4793 1.6241 1.769 1.9138 2.0586 2.2034 2.3483 2.4931 2.6379 2.7828 2.9276 3.0724 3.2172 3.3621 3.5069 3.6517 3.7966 3.9414 4.0862 4.231 4.3759 4.5207 4.6655 4.8103 4.9552 5.1 5.2448 5.3897 5.5345 5.6793 5.8241 5.969 6.1138 6.2586 6.4034 6.5483 6.6931 6.8379 6.9828 7.1276 7.2724 7.4172 7.5621 7.7069 7.8517 7.9966 8.1414 8.2862 8.431 8.5759 8.7207 8.8655 9.0103 9.1552 9.3
0.60 0.46 0.31 0.17 0.02 0.12 0.27 0.41 0.56 0.70 0.85 0.99 1.14 1.28 1.43 1.43 1.28 1.14 0.99 0.85 0.70 0.56 0.41 0.27 0.12 0.02 0.17 0.31 0.46 0.60 0.74 0.89 1.03 1.18 1.32 1.47 1.39 1.24 1.10 0.95 0.81 0.66 0.52 0.37 0.23 0.08 0.06 0.21 0.35 0.50 0.64 0.79 0.93 1.08 1.22 1.37 1.49 1.34 1.20
Wheel-2
beff
beff (mod)
P with Impact (kN)
1.12 0.95 0.77 0.60 0.42 0.71 1.04 1.33 1.58 1.80 1.98 2.13 2.24 2.31 2.35 2.35 2.31 2.24 2.13 1.98 1.80 1.58 1.33 1.04 0.71 0.45 0.81 1.12 1.40 1.65 1.86 2.03 2.16 2.26 2.32 2.35 2.34 2.29 2.21 2.09 1.93 1.74 1.51 1.25 0.95 0.61 0.56 0.90 1.21 1.48 1.71 1.91 2.07 2.19 2.28 2.33 2.35 2.33 2.27
1.12 0.95 0.77 0.60 0.42 0.71 1.04 1.26 1.39 1.50 1.59 1.66 1.72 1.75 1.77 1.77 1.75 1.72 1.66 1.59 1.50 1.39 1.26 1.04 0.71 0.45 0.81 1.12 1.30 1.42 1.53 1.61 1.68 1.73 1.76 1.77 1.77 1.75 1.70 1.64 1.57 1.47 1.36 1.22 0.95 0.61 0.56 0.90 1.20 1.34 1.46 1.55 1.63 1.70 1.74 1.77 1.77 1.76 1.74
76.34 90.36 110.69 142.83 201.26 120.52 82.48 67.66 61.47 57.00 53.74 51.39 49.76 48.73 48.23 48.23 48.73 49.76 51.39 53.74 57.00 61.47 67.66 82.48 120.52 188.57 106.00 76.11 65.67 60.04 55.96 52.99 50.86 49.41 48.54 48.18 48.32 48.97 50.16 51.98 54.57 58.13 63.03 69.85 90.30 140.34 153.21 94.91 71.03 63.87 58.74 55.01 52.30 50.38 49.10 48.38 48.17 48.45 49.25
Dist. of Position Nearest (X) Support 2.70 2.84 2.99 3.13 3.28 3.42 3.57 3.71 3.86 4.00 4.15 4.29 4.44 4.58 4.73 4.87 5.02 5.16 5.31 5.45 5.60 5.74 5.89 6.03 6.18 6.32 6.47 6.61 6.76 6.90 7.04 7.19 7.33 7.48 7.62 7.77 7.91 8.06 8.20 8.35 8.49 8.64 8.78 8.93 9.07 9.22 9.36 9.51 9.65 9.80 9.94 10.09 10.23 10.38 10.52 10.67 10.81 10.96 11.10
1.20 1.34 1.49 1.37 1.22 1.08 0.93 0.79 0.64 0.50 0.35 0.21 0.06 0.08 0.23 0.37 0.52 0.66 0.81 0.95 1.10 1.24 1.39 1.47 1.32 1.18 1.03 0.89 0.74 0.60 0.46 0.31 0.17 0.02 0.12 0.27 0.41 0.56 0.70 0.85 0.99 1.14 1.28 1.43 1.43 1.28 1.14 0.99 0.85 0.70 0.56 0.41 0.27 0.12 0.02 0.17 0.31 0.46 0.60
beff
beff (mod)
P with Impact (kN)
2.27 2.33 2.35 2.33 2.28 2.19 2.07 1.91 1.71 1.48 1.21 0.90 0.56 0.61 0.95 1.25 1.51 1.74 1.93 2.09 2.21 2.29 2.34 2.35 2.32 2.26 2.16 2.03 1.86 1.65 1.40 1.12 0.81 0.45 0.71 1.04 1.33 1.58 1.80 1.98 2.13 2.24 2.31 2.35 2.35 2.31 2.24 2.13 1.98 1.80 1.58 1.33 1.04 0.71 0.42 0.60 0.77 0.95 1.12
1.74 1.76 1.77 1.77 1.74 1.70 1.63 1.55 1.46 1.34 1.20 0.90 0.56 0.61 0.95 1.22 1.36 1.47 1.57 1.64 1.70 1.75 1.77 1.77 1.76 1.73 1.68 1.61 1.53 1.42 1.30 1.12 0.81 0.45 0.71 1.04 1.26 1.39 1.50 1.59 1.66 1.72 1.75 1.77 1.77 1.75 1.72 1.66 1.59 1.50 1.39 1.26 1.04 0.71 0.42 0.60 0.77 0.95 1.12
49.3 48.5 48.2 48.4 49.1 50.4 52.3 55.0 58.7 63.9 71.0 94.9 153.2 140.3 90.3 69.9 63.0 58.1 54.6 52.0 50.2 49.0 48.3 48.2 48.5 49.4 50.9 53.0 56.0 60.0 65.7 76.1 106.0 188.6 120.5 82.5 67.7 61.5 57.0 53.7 51.4 49.8 48.7 48.2 48.2 48.7 49.8 51.4 53.7 57.0 61.5 67.7 82.5 120.5 201.3 142.8 110.7 90.4 76.3
66
2Lane Class - A
TRANSVERSE ANALYSIS 2 FOR LIVE LOAD
Load on Wheel-1
=
57.000
kN
Load on Wheel-2
=
57.000
kN
Load on Wheel-3
=
57.000
kN
Load on Wheel-4
=
57.000
kN
Distance Between Two vehicle C/C of wheel (Traffic direction)
=
1.700
m
Distance between two Wheels C/C (Transverse direction)
=
1.800
m
initial position of first wheel( Wheel 1)
=
0.900
m
Final position of first wheel( Wheel 1)
=
5.800
m
Number of load generation
=
40
Transverse increament of Wheels
=
0.1225
nos m
67
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 38 39 40 41
0.9 1.0225 1.145 1.2675 1.39 1.5125 1.635 1.7575 1.88 2.0025 2.125 2.2475 2.37 2.4925 2.615 2.7375 2.86 2.9825 3.105 3.2275 3.35 3.4725 3.595 3.7175 3.84 3.9625 4.085 4.4525 4.575 4.6975 4.82 4.9425 5.065 5.1875 5.31 5.4325 5.555 5.6775 5.8
Dist. of Nearest Support 0.60 0.48 0.36 0.23 0.11 0.01 0.14 0.26 0.38 0.50 0.63 0.75 0.87 0.99 1.12 1.24 1.36 1.48 1.40 1.27 1.15 1.03 0.90 0.78 0.66 0.54 0.41 0.05 0.07 0.20 0.32 0.44 0.56 0.69 0.81 0.93 1.06 1.18 1.30
Wheel-2
beff
beff (mod)
1.12 0.97 0.83 0.68 0.53 0.43 0.74 1.01 1.26 1.49 1.69 1.86 2.01 2.13 2.22 2.29 2.33 2.35 2.34 2.31 2.24 2.16 2.04 1.90 1.74 1.55 1.33 0.52 0.59 0.88 1.14 1.38 1.59 1.78 1.94 2.07 2.18 2.26 2.32
1.12 0.97 0.83 0.68 0.53 0.43 0.74 1.01 1.23 1.34 1.44 1.53 1.60 1.66 1.71 1.75 1.77 1.77 1.77 1.75 1.72 1.68 1.62 1.55 1.47 1.37 1.26 0.52 0.59 0.88 1.14 1.29 1.40 1.49 1.57 1.64 1.69 1.73 1.76
P with Dist. of Impact Position Nearest (kN) Support 76.34 2.700 1.20 87.87 2.823 1.32 103.51 2.945 1.45 125.92 3.068 1.43 160.71 3.190 1.31 197.75 3.313 1.19 116.29 3.435 1.07 84.48 3.558 0.94 69.43 3.680 0.82 63.62 3.803 0.70 59.24 3.925 0.57 55.90 4.048 0.45 53.34 4.170 0.33 51.40 4.293 0.21 49.98 4.415 0.08 48.99 4.538 0.04 48.40 4.660 0.16 48.17 4.783 0.28 48.30 4.905 0.41 48.79 5.028 0.53 49.65 5.150 0.65 50.95 5.273 0.77 52.73 5.395 0.90 55.09 5.518 1.02 58.19 5.640 1.14 62.25 5.763 1.26 67.60 5.885 1.39 163.94 6.253 1.25 144.88 6.375 1.13 97.19 6.498 1.00 74.79 6.620 0.88 66.26 6.743 0.76 61.24 6.865 0.64 57.42 6.988 0.51 54.50 7.110 0.39 52.28 7.233 0.27 50.62 7.355 0.15 49.42 7.478 0.02 48.64 7.600 0.10
Wheel-3
beff
beff (mod)
2.27 2.32 2.35 2.35 2.32 2.27 2.19 2.08 1.95 1.79 1.61 1.40 1.16 0.90 0.61 0.50 0.79 1.07 1.31 1.53 1.72 1.89 2.03 2.15 2.24 2.30 2.34 2.29 2.23 2.14 2.02 1.87 1.70 1.50 1.28 1.03 0.76 0.46 0.65
1.74 1.76 1.77 1.77 1.76 1.73 1.69 1.64 1.57 1.50 1.40 1.30 1.16 0.90 0.61 0.50 0.79 1.07 1.26 1.37 1.46 1.55 1.62 1.67 1.72 1.75 1.77 1.75 1.71 1.67 1.61 1.54 1.45 1.35 1.24 1.03 0.76 0.46 0.65
P with Dist. of Impact Position Nearest (kN) Support 49.25 4.400 0.10 48.54 4.523 0.02 48.20 4.645 0.15 48.22 4.768 0.27 48.60 4.890 0.39 49.35 5.013 0.51 50.50 5.135 0.64 52.12 5.258 0.76 54.30 5.380 0.88 57.16 5.503 1.00 60.89 5.625 1.13 65.79 5.748 1.25 73.48 5.870 1.37 94.77 5.993 1.49 139.08 6.115 1.39 172.28 6.238 1.26 107.71 6.360 1.14 80.26 6.483 1.02 68.10 6.605 0.89 62.63 6.728 0.77 58.48 6.850 0.65 55.32 6.973 0.53 52.90 7.095 0.40 51.07 7.218 0.28 49.74 7.340 0.16 48.84 7.463 0.04 48.33 7.585 0.09 48.93 7.953 0.45 49.88 8.075 0.57 51.27 8.198 0.70 53.16 8.320 0.82 55.66 8.443 0.94 58.93 8.565 1.07 63.22 8.688 1.19 68.89 8.810 1.31 82.73 8.933 1.43 112.68 9.055 1.45 186.66 9.177 1.32 131.27 9.300 1.20
Wheel-4
beff
beff (mod)
0.65 0.46 0.76 1.03 1.28 1.50 1.70 1.87 2.02 2.14 2.23 2.29 2.34 2.35 2.34 2.30 2.24 2.15 2.03 1.89 1.72 1.53 1.31 1.07 0.79 0.50 0.61 1.40 1.61 1.79 1.95 2.08 2.19 2.27 2.32 2.35 2.35 2.32 2.27
0.65 0.46 0.76 1.03 1.24 1.35 1.45 1.54 1.61 1.67 1.71 1.75 1.77 1.77 1.77 1.75 1.72 1.67 1.62 1.55 1.46 1.37 1.26 1.07 0.79 0.50 0.61 1.30 1.40 1.50 1.57 1.64 1.69 1.73 1.76 1.77 1.77 1.76 1.74
P with Dist. of Impact Position Nearest (kN) Support 131.27 6.200 1.30 186.66 6.323 1.18 112.68 6.445 1.06 82.73 6.568 0.93 68.89 6.690 0.81 63.22 6.813 0.69 58.93 6.935 0.57 55.66 7.058 0.44 53.16 7.180 0.32 51.27 7.303 0.20 49.88 7.425 0.07 48.93 7.548 0.05 48.37 7.670 0.17 48.17 7.793 0.29 48.33 7.915 0.42 48.84 8.038 0.54 49.74 8.160 0.66 51.07 8.283 0.78 52.90 8.405 0.91 55.32 8.528 1.03 58.48 8.650 1.15 62.63 8.773 1.27 68.10 8.895 1.40 80.26 9.018 1.48 107.71 9.140 1.36 172.28 9.263 1.24 139.08 9.385 1.12 65.79 9.753 0.75 60.89 9.875 0.63 57.16 9.998 0.50 54.30 10.120 0.38 52.12 10.243 0.26 50.50 10.365 0.14 49.35 10.488 0.01 48.60 10.610 0.11 48.22 10.733 0.23 48.20 10.855 0.35 48.54 10.978 0.48 49.25 11.100 0.60
beff
beff (mod)
2.32 2.26 2.18 2.07 1.94 1.78 1.59 1.38 1.14 0.88 0.59 0.52 0.82 1.09 1.33 1.55 1.74 1.90 2.04 2.16 2.24 2.31 2.34 2.35 2.33 2.29 2.22 1.86 1.69 1.49 1.26 1.01 0.74 0.43 0.53 0.68 0.83 0.97 1.12
1.76 1.73 1.69 1.64 1.57 1.49 1.40 1.29 1.14 0.88 0.59 0.52 0.82 1.09 1.26 1.37 1.47 1.55 1.62 1.68 1.72 1.75 1.77 1.77 1.77 1.75 1.71 1.53 1.44 1.34 1.23 1.01 0.74 0.43 0.53 0.68 0.83 0.97 1.12
P with Impact (kN) 48.64 49.42 50.62 52.28 54.50 57.42 61.24 66.26 74.79 97.19 144.88 163.94 104.66 78.70 67.60 62.25 58.19 55.09 52.73 50.95 49.65 48.79 48.30 48.17 48.40 48.99 49.98 55.90 59.24 63.62 69.43 84.48 116.29 197.75 160.71 125.92 103.51 87.87 76.34
68
1Lane 40T Boggie (L-Type)
TRANSVERSE ANALYSIS 3 FOR LIVE LOAD
Load on Wheel-1
=
100
kN kN
Max. load on a wheel
=
100
Max. tyre pressure
=
5.273
Contact width along span
=
810
Distance between two loads across span = Distances between C/C of wheel Across the traffic Impact factor
1.22 5.273
Load on Wheel-2
=
100
kg/cm2
Contact area
=
1896.5
cm2
mm
Contact width across span
=
234.1
mm
m
1.93
=
0.384
m
=
1.93
=
1.25
Initial position of first wheel
=
2.13
m
Final Position of first wheel
=
7.940
m
Transverse increament
=
0.1162
m
kN
m
69
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
2.13 2.2462 2.3624 2.4786 2.5948 2.711 2.8272 2.9434 3.0596 3.1758 3.292 3.4082 3.5244 3.6406 3.7568 3.873 3.9892 4.1054 4.2216 4.3378 4.454 4.5702 4.6864 4.8026 4.9188 5.035 5.1512 5.2674 5.3836 5.4998 5.616 5.7322 5.8484 5.9646 6.0808 6.197 6.3132 6.4294 6.5456 6.6618 6.778 6.8942 7.0104 7.1266 7.2428 7.359 7.4752 7.5914 7.7076 7.8238 7.94
Dist. of Nearest Support 0.63 0.75 0.86 0.98 1.09 1.21 1.33 1.44 1.44 1.32 1.21 1.09 0.98 0.86 0.74 0.63 0.51 0.39 0.28 0.16 0.05 0.07 0.19 0.30 0.42 0.54 0.65 0.77 0.88 1.00 1.12 1.23 1.35 1.46 1.42 1.30 1.19 1.07 0.95 0.84 0.72 0.61 0.49 0.37 0.26 0.14 0.02 0.09 0.21 0.32 0.44
Wheel-2
beff
beff (mod)
1.68 1.84 1.98 2.10 2.19 2.26 2.31 2.33 2.33 2.31 2.26 2.19 2.10 1.98 1.84 1.67 1.49 1.28 1.04 0.78 0.50 0.56 0.84 1.09 1.32 1.53 1.71 1.87 2.00 2.12 2.21 2.27 2.31 2.33 2.33 2.30 2.25 2.17 2.08 1.95 1.81 1.64 1.45 1.23 1.00 0.73 0.45 0.61 0.89 1.14 1.36
1.45 1.53 1.60 1.66 1.71 1.74 1.76 1.78 1.78 1.76 1.74 1.70 1.66 1.60 1.53 1.45 1.35 1.25 1.04 0.78 0.50 0.56 0.84 1.09 1.27 1.37 1.46 1.54 1.61 1.67 1.71 1.75 1.77 1.78 1.77 1.76 1.73 1.70 1.65 1.59 1.51 1.43 1.33 1.23 1.00 0.73 0.45 0.61 0.89 1.14 1.29
P with Dist. of Impact Position Nearest (kN) Support 86.26 4.06 0.44 81.65 4.1762 0.32 78.08 4.2924 0.21 75.33 4.4086 0.09 73.27 4.5248 0.02 71.80 4.641 0.14 70.86 4.7572 0.26 70.40 4.8734 0.37 70.40 4.9896 0.49 70.87 5.1058 0.61 71.83 5.222 0.72 73.32 5.3382 0.84 75.40 5.4544 0.95 78.16 5.5706 1.07 81.76 5.6868 1.19 86.40 5.803 1.30 92.38 5.9192 1.42 100.19 6.0354 1.46 120.10 6.1516 1.35 159.63 6.2678 1.23 249.06 6.384 1.12 222.27 6.5002 1.00 149.05 6.6164 0.88 114.52 6.7326 0.77 98.39 6.8488 0.65 91.01 6.965 0.53 85.33 7.0812 0.42 80.93 7.1974 0.30 77.52 7.3136 0.19 74.91 7.4298 0.07 72.96 7.546 0.05 71.59 7.6622 0.16 70.74 7.7784 0.28 70.36 7.8946 0.39 70.45 8.0108 0.51 71.01 8.127 0.63 72.06 8.2432 0.74 73.65 8.3594 0.86 75.85 8.4756 0.98 78.75 8.5918 1.09 82.52 8.708 1.21 87.38 8.8242 1.32 93.66 8.9404 1.44 101.87 9.0566 1.44 125.56 9.1728 1.33 170.42 9.289 1.21 278.97 9.4052 1.09 203.41 9.5214 0.98 141.00 9.6376 0.86 110.12 9.7538 0.75 96.89 9.87 0.63
beff
beff (mod)
1.36 1.14 0.89 0.61 0.45 0.73 1.00 1.23 1.45 1.64 1.81 1.95 2.08 2.17 2.25 2.30 2.33 2.33 2.31 2.27 2.21 2.12 2.00 1.87 1.71 1.53 1.32 1.09 0.84 0.56 0.50 0.78 1.04 1.28 1.49 1.67 1.84 1.98 2.10 2.19 2.26 2.31 2.33 2.33 2.31 2.26 2.19 2.10 1.98 1.84 1.68
1.29 1.14 0.89 0.61 0.45 0.73 1.00 1.23 1.33 1.43 1.51 1.59 1.65 1.70 1.73 1.76 1.77 1.78 1.77 1.75 1.71 1.67 1.61 1.54 1.46 1.37 1.27 1.09 0.84 0.56 0.50 0.78 1.04 1.25 1.35 1.45 1.53 1.60 1.66 1.70 1.74 1.76 1.78 1.78 1.76 1.74 1.71 1.66 1.60 1.53 1.45
P with Impact (kN) 96.89 110.12 141.00 203.41 278.97 170.42 125.56 101.87 93.66 87.38 82.52 78.75 75.85 73.65 72.06 71.01 70.45 70.36 70.74 71.59 72.96 74.91 77.52 80.93 85.33 91.01 98.39 114.52 149.05 222.27 249.06 159.63 120.10 100.19 92.38 86.40 81.76 78.16 75.40 73.32 71.83 70.87 70.40 70.40 70.86 71.80 73.27 75.33 78.08 81.65 86.26
70
1Lane 40T Boggie (M-Type)
TRANSVERSE ANALYSIS 4 FOR LIVE LOAD
Load on Wheel-1
=
50
kN
Load on Wheel-2
=
50
kN
Load on Wheel-3
=
50
kN
Load on Wheel-4
=
50
kN
kg/cm2
Contact area
=
948.2
cm2
mm
Contact width across span
=
263
mm
m
b1
=
0.413
Max. load on a wheel
=
50
Max. tyre pressure
=
5.273
kN
Contact width along span
=
360
Distance between two loads across span
=
0.79
Impact factor
=
1.25
Initial Position of first wheel
=
1.905
m
Final position of first wheel
=
7.715
m
No of Load generation
=
50
Transverse increament
=
0.1162
m
m
71
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Wheel-2
beff
beff (mod)
1.905 2.0212 2.1374 2.2536 2.3698 2.486 2.6022 2.7184 2.8346 2.9508 3.067 3.1832 3.2994 3.4156 3.5318 3.648 3.7642 3.8804 3.9966 4.1128 4.229 4.3452 4.4614 4.5776 4.6938 4.81 4.9262 5.0424 5.1586
Dist. of Nearest Support 0.41 0.52 0.64 0.75 0.87 0.99 1.10 1.22 1.33 1.45 1.43 1.32 1.20 1.08 0.97 0.85 0.74 0.62 0.50 0.39 0.27 0.15 0.04 0.08 0.19 0.31 0.43 0.54 0.66
1.32 1.53 1.72 1.88 2.02 2.13 2.23 2.29 2.34 2.36 2.36 2.33 2.29 2.21 2.12 2.00 1.86 1.69 1.50 1.29 1.05 0.80 0.51 0.61 0.88 1.14 1.36 1.57 1.75
1.06 1.16 1.25 1.34 1.40 1.46 1.51 1.54 1.56 1.58 1.57 1.56 1.54 1.50 1.45 1.39 1.32 1.24 1.15 1.04 0.92 0.79 0.51 0.61 0.84 0.96 1.08 1.18 1.27
30 31
5.2748 5.391
0.77 0.89
1.91 2.04
1.35 1.42
46.34 44.14
6.0698 6.186
32
5.5072
1.01
2.15
1.47
42.47
33
5.6234
1.12
2.24
1.52
41.25
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
5.7396 5.8558 5.972 6.0882 6.2044 6.3206 6.4368 6.553 6.6692 6.7854 6.9016 7.0178 7.134 7.2502 7.3664 7.4826 7.5988 7.715
1.24 1.36 1.47 1.41 1.30 1.18 1.06 0.95 0.83 0.71 0.60 0.48 0.37 0.25 0.13 0.02 0.10 0.22
2.30 2.35 2.36 2.36 2.33 2.27 2.20 2.10 1.98 1.83 1.66 1.47 1.25 1.01 0.75 0.46 0.66 0.93
1.55 1.57 1.58 1.57 1.56 1.53 1.49 1.44 1.38 1.31 1.22 1.13 1.02 0.90 0.75 0.46 0.66 0.86
40.39 39.87 39.65 39.72 40.10 40.79 41.83 43.28 45.20 47.73 51.04 55.42 61.31 69.49 83.86 136.35 94.44 72.58
P with Dist. of Impact Position Nearest (kN) Support 59.12 2.7 1.20 53.81 2.8162 1.32 49.83 2.9324 1.43 46.81 3.0486 1.45 44.50 3.1648 1.34 42.74 3.281 1.22 41.44 3.3972 1.10 40.52 3.5134 0.99 39.94 3.6296 0.87 39.67 3.7458 0.75 39.69 3.862 0.64 40.01 3.9782 0.52 40.64 4.0944 0.41 41.62 4.2106 0.29 42.98 4.3268 0.17 44.81 4.443 0.06 47.22 4.5592 0.06 50.37 4.6754 0.18 54.52 4.7916 0.29 60.09 4.9078 0.41 67.77 5.024 0.52 78.86 5.1402 0.64 121.96 5.2564 0.76 102.47 5.3726 0.87 74.64 5.4888 0.99 64.90 5.605 1.11 58.03 5.7212 1.22 53.00 5.8374 1.34 49.22 5.9536 1.45
Wheel-3 P with Dist. of Impact Position Nearest (kN) Support 40.65 3.49 1.01 40.01 3.6062 0.89 39.69 3.7224 0.78 39.67 3.8386 0.66 39.94 3.9548 0.55 40.52 4.071 0.43 41.44 4.1872 0.31 42.74 4.3034 0.20 44.49 4.4196 0.08 46.79 4.5358 0.04 49.81 4.652 0.15 53.78 4.7682 0.27 59.09 4.8844 0.38 66.37 5.0006 0.50 76.79 5.1168 0.62 111.85 5.233 0.73 110.76 5.3492 0.85 76.56 5.4654 0.97 66.21 5.5816 1.08 58.97 5.6978 1.20 53.70 5.814 1.31 49.75 5.9302 1.43 46.74 6.0464 1.45 44.45 6.1626 1.34 42.71 6.2788 1.22 41.42 6.395 1.11 40.51 6.5112 0.99 39.93 6.6274 0.87 39.66 6.7436 0.76
beff
beff (mod)
2.29 2.33 2.36 2.36 2.34 2.29 2.23 2.13 2.02 1.88 1.72 1.53 1.33 1.09 0.84 0.56 0.56 0.84 1.10 1.33 1.54 1.72 1.88 2.02 2.14 2.23 2.30 2.34 2.36
1.54 1.56 1.57 1.58 1.56 1.54 1.51 1.46 1.40 1.34 1.25 1.16 1.06 0.94 0.81 0.56 0.56 0.82 0.94 1.06 1.16 1.26 1.34 1.41 1.46 1.51 1.54 1.57 1.58
1.43 1.31
2.36 2.33
1.57 1.56
39.69 40.02
6.8598 6.976
6.3022
1.20
2.28
1.54
40.66
6.4184
1.08
2.21
1.50
41.64
6.5346 6.6508 6.767 6.8832 6.9994 7.1156 7.2318 7.348 7.4642 7.5804 7.6966 7.8128 7.929 8.0452 8.1614 8.2776 8.3938 8.51
0.97 0.85 0.73 0.62 0.50 0.38 0.27 0.15 0.04 0.08 0.20 0.31 0.43 0.55 0.66 0.78 0.89 1.01
2.12 2.00 1.85 1.69 1.50 1.28 1.05 0.79 0.51 0.62 0.89 1.14 1.37 1.57 1.75 1.91 2.04 2.16
1.45 1.39 1.32 1.24 1.14 1.04 0.92 0.79 0.51 0.62 0.84 0.97 1.08 1.18 1.27 1.35 1.42 1.47
43.02 44.86 47.28 50.46 54.64 60.25 67.99 79.26 123.67 101.32 74.36 64.70 57.89 52.89 49.14 46.28 44.09 42.44
Wheel-4 P with Dist. of Impact Position Nearest (kN) Support 42.44 4.285 0.22 44.09 4.4012 0.10 46.28 4.5174 0.02 49.14 4.6336 0.13 52.89 4.7498 0.25 57.89 4.866 0.37 64.70 4.9822 0.48 74.36 5.0984 0.60 101.32 5.2146 0.71 123.67 5.3308 0.83 79.26 5.447 0.95 67.99 5.5632 1.06 60.25 5.6794 1.18 54.64 5.7956 1.30 50.46 5.9118 1.41 47.28 6.028 1.47 44.86 6.1442 1.36 43.02 6.2604 1.24 41.64 6.3766 1.12 40.66 6.4928 1.01 40.02 6.609 0.89 39.69 6.7252 0.77 39.66 6.8414 0.66 39.93 6.9576 0.54 40.51 7.0738 0.43 41.42 7.19 0.31 42.71 7.3062 0.19 44.45 7.4224 0.08 46.74 7.5386 0.04
beff
beff (mod)
0.93 0.66 0.46 0.75 1.01 1.25 1.47 1.66 1.83 1.98 2.10 2.20 2.27 2.33 2.36 2.36 2.35 2.30 2.24 2.15 2.04 1.91 1.75 1.57 1.36 1.14 0.88 0.61 0.51
0.86 0.66 0.46 0.75 0.90 1.02 1.13 1.22 1.31 1.38 1.44 1.49 1.53 1.56 1.57 1.58 1.57 1.55 1.52 1.47 1.42 1.35 1.27 1.18 1.08 0.96 0.84 0.61 0.51
P with Impact (kN) 72.58 94.44 136.35 83.86 69.49 61.31 55.42 51.04 47.73 45.20 43.28 41.83 40.79 40.10 39.72 39.65 39.87 40.39 41.25 42.47 44.14 46.34 49.22 53.00 58.03 64.90 74.64 102.47 121.96
0.15 0.27
0.80 1.05
0.79 0.92
78.86 67.77
7.8872
0.39
1.29
1.04
60.09
8.0034
0.50
1.50
1.15
54.52
8.1196 8.2358 8.352 8.4682 8.5844 8.7006 8.8168 8.933 9.0492 9.1654 9.2816 9.3978 9.514 9.6302 9.7464 9.8626 9.9788 10.095
0.62 0.74 0.85 0.97 1.08 1.20 1.32 1.43 1.45 1.33 1.22 1.10 0.99 0.87 0.75 0.64 0.52 0.40
1.69 1.86 2.00 2.12 2.21 2.29 2.33 2.36 2.36 2.34 2.29 2.23 2.13 2.02 1.88 1.72 1.53 1.32
1.24 1.32 1.39 1.45 1.50 1.54 1.56 1.57 1.58 1.56 1.54 1.51 1.46 1.40 1.34 1.25 1.16 1.06
50.37 47.22 44.81 42.98 41.62 40.64 40.01 39.69 39.67 39.94 40.52 41.44 42.74 44.50 46.81 49.83 53.81 59.12
beff
beff (mod)
2.16 2.04 1.91 1.75 1.57 1.37 1.14 0.89 0.62 0.51 0.79 1.05 1.28 1.50 1.69 1.85 2.00 2.12 2.21 2.28 2.33 2.36 2.36 2.34 2.30 2.23 2.14 2.02 1.88
1.47 1.42 1.35 1.27 1.18 1.08 0.97 0.84 0.62 0.51 0.79 0.92 1.04 1.14 1.24 1.32 1.39 1.45 1.50 1.54 1.56 1.57 1.58 1.57 1.54 1.51 1.46 1.41 1.34
0.64 0.52
1.72 1.54
1.26 1.16
49.75 53.70
7.6548 7.771
7.0922
0.41
1.33
1.06
58.97
7.2084
0.29
1.10
0.94
66.21
7.3246 7.4408 7.557 7.6732 7.7894 7.9056 8.0218 8.138 8.2542 8.3704 8.4866 8.6028 8.719 8.8352 8.9514 9.0676 9.1838 9.3
0.18 0.06 0.06 0.17 0.29 0.41 0.52 0.64 0.75 0.87 0.99 1.10 1.22 1.34 1.45 1.43 1.32 1.20
0.84 0.56 0.56 0.84 1.09 1.33 1.53 1.72 1.88 2.02 2.13 2.23 2.29 2.34 2.36 2.36 2.33 2.29
0.82 0.56 0.56 0.81 0.94 1.06 1.16 1.25 1.34 1.40 1.46 1.51 1.54 1.56 1.58 1.57 1.56 1.54
76.56 110.76 111.85 76.79 66.37 59.09 53.78 49.81 46.79 44.49 42.74 41.44 40.52 39.94 39.67 39.69 40.01 40.65
72
1Lane 70R Track
TRANSVERSE ANALYSIS 5 FOR LIVE LOAD
Load on Wheel-1
=
350
kN
Load on Wheel-2
=
350
kN
Contact width along span
=
4570
mm
Contact width across span
=
840
mm
Distance between two loads across span
=
2.06
m
b1
=
0.99
Impact factor
=
1.25
Initial Position of first wheel
=
3.985
Final position of first wheel
=
7.82
No of Load generation
=
50
Transverse increament
=
0.0767
m
73
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
3.985 4.0617 4.1384 4.2151 4.2918 4.3685 4.4452 4.5219 4.5986 4.6753 4.752 4.8287 4.9054 4.9821 5.0588 5.1355 5.2122 5.2889 5.3656 5.4423 5.519 5.5957 5.6724 5.7491 5.8258 5.9025 5.9792 6.0559 6.1326 6.2093 6.286 6.3627 6.4394 6.5161 6.5928 6.6695 6.7462 6.8229 6.8996 6.9763 7.053 7.1297 7.2064 7.2831 7.3598 7.4365 7.5132 7.5899 7.6666 7.7433 7.82
Dist. of Nearest Support 0.52 0.44 0.36 0.28 0.21 0.13 0.05 0.02 0.10 0.18 0.25 0.33 0.41 0.48 0.56 0.64 0.71 0.79 0.87 0.94 1.02 1.10 1.17 1.25 1.33 1.40 1.48 1.44 1.37 1.29 1.21 1.14 1.06 0.98 0.91 0.83 0.75 0.68 0.60 0.52 0.45 0.37 0.29 0.22 0.14 0.06 0.01 0.09 0.17 0.243 0.32
Wheel-2
beff
beff (mod)
2.10 1.96 1.82 1.66 1.49 1.32 1.13 1.05 1.24 1.42 1.59 1.75 1.90 2.04 2.17 2.29 2.40 2.50 2.59 2.67 2.74 2.80 2.85 2.89 2.91 2.93 2.94 2.94 2.92 2.90 2.87 2.83 2.77 2.71 2.64 2.55 2.46 2.35 2.24 2.11 1.98 1.83 1.68 1.51 1.34 1.15 1.02 1.22 1.40 1.57 1.73
2.08 1.96 1.82 1.66 1.49 1.32 1.13 1.05 1.24 1.42 1.59 1.75 1.90 2.04 2.12 2.18 2.23 2.28 2.33 2.37 2.40 2.43 2.45 2.47 2.49 2.50 2.50 2.50 2.49 2.48 2.46 2.44 2.42 2.38 2.35 2.31 2.26 2.21 2.15 2.09 1.98 1.83 1.68 1.51 1.34 1.15 1.02 1.22 1.40 1.57 1.73
P with Dist. of Impact Position Nearest (kN) Support 210.38 6.045 1.46 222.86 6.1217 1.38 240.80 6.1984 1.30 263.49 6.2751 1.22 292.89 6.3518 1.15 332.22 6.4285 1.07 387.21 6.5052 0.99 418.05 6.5819 0.92 353.41 6.6586 0.84 308.28 6.7353 0.76 275.13 6.812 0.69 249.86 6.8887 0.61 230.07 6.9654 0.53 214.25 7.0421 0.46 206.75 7.1188 0.38 201.04 7.1955 0.30 196.10 7.2722 0.23 191.81 7.3489 0.15 188.12 7.4256 0.07 184.97 7.5023 0.00 182.31 7.579 0.08 180.10 7.6557 0.16 178.32 7.7324 0.23 176.93 7.8091 0.31 175.93 7.8858 0.39 175.29 7.9625 0.46 175.01 8.0392 0.54 175.09 8.1159 0.62 175.53 8.1926 0.69 176.34 8.2693 0.77 177.52 8.346 0.85 179.08 8.4227 0.92 181.06 8.4994 1.00 183.47 8.5761 1.08 186.35 8.6528 1.15 189.74 8.7295 1.23 193.69 8.8062 1.31 198.27 8.8829 1.38 203.55 8.9596 1.46 209.63 9.0363 1.46 221.07 9.113 1.39 238.56 9.1897 1.31 260.63 9.2664 1.23 289.13 9.3431 1.16 327.11 9.4198 1.08 379.90 9.4965 1.00 427.18 9.5732 0.93 359.57 9.6499 0.85 312.70 9.7266 0.77 278.44 9.8033 0.70 252.42 9.88 0.62
beff
beff (mod)
2.94 2.93 2.91 2.87 2.83 2.78 2.72 2.65 2.56 2.47 2.37 2.26 2.13 2.00 1.86 1.70 1.54 1.36 1.18 1.00 1.19 1.37 1.55 1.71 1.86 2.01 2.14 2.26 2.38 2.48 2.57 2.65 2.72 2.78 2.84 2.88 2.91 2.93 2.94 2.94 2.93 2.91 2.88 2.84 2.79 2.73 2.66 2.57 2.48 2.38 2.27
2.50 2.49 2.48 2.47 2.45 2.42 2.39 2.35 2.31 2.27 2.21 2.16 2.10 2.00 1.86 1.70 1.54 1.36 1.18 1.00 1.19 1.37 1.55 1.71 1.86 2.01 2.10 2.16 2.22 2.27 2.31 2.36 2.39 2.42 2.45 2.47 2.48 2.49 2.50 2.50 2.49 2.48 2.47 2.45 2.42 2.39 2.36 2.32 2.27 2.22 2.16
P with Impact (kN) 175.06 175.45 176.20 177.33 178.84 180.75 183.10 185.91 189.23 193.10 197.58 202.76 208.72 218.88 235.83 257.15 284.59 320.97 371.19 439.27 367.65 318.46 282.73 255.72 234.70 217.97 208.34 202.43 197.29 192.85 189.01 185.73 182.95 180.63 178.73 177.25 176.15 175.42 175.05 175.04 175.39 176.10 177.18 178.65 180.51 182.81 185.57 188.82 192.63 197.04 202.13
74
70Rw+1lca
TRANSVERSE ANALYSIS 6 FOR LIVE LOAD
70RW Load on Wheel-1
=
85
Max. tyre pressure
=
5.273
Contact width along span
=
810
Distance between two loads across span
=
1.93
Impact factor
=
1.25
kN
Load on Wheel-2
=
85
Contact area for 70RW
=
1612.0
cm2
mm
Contact width across span
=
199.0
mm
m
b1
=
0.349
m
kg/cm
2
kN
1Lane Class - A Load on Wheel-1
=
57
kN
Load on Wheel-2
=
57
kN
Contact width across span
=
250
mm
Contact width along span
=
500
mm
Distance between two loads across span
=
1.200
m
Minimum edge distance upto c/l of wheel
=
0.400
m
b1
=
0.400
m
Load on Wheel-3
=
57.000
kN
Load on Wheel-4
=
57
kN
Impact factor
=
1.5
initial position of first wheel(70Rw)
=
2.130
initial position of 2nd wheel(1LCA)
=
7.740
Final position of 2nd wheel of 1LCA
=
11.100
m
Total movement of train
=
3.360
m
Number of load generation
=
20
Transverse increament of Wheels
=
0.168
m
m
75
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
2.13 2.298 2.466 2.634 2.802 2.97 3.138 3.306 3.474 3.642 3.81 3.978 4.146 4.314 4.482 4.65 4.818 4.986 5.154 5.322 5.49
Dist. of Nearest Support 0.63 0.80 0.97 1.13 1.30 1.47 1.36 1.19 1.03 0.86 0.69 0.52 0.35 0.19 0.02 0.15 0.32 0.49 0.65 0.82 0.99
beff 1.64 1.87 2.05 2.18 2.27 2.30 2.28 2.22 2.10 1.94 1.73 1.47 1.16 0.80 0.40 0.72 1.09 1.41 1.68 1.90 2.07
Wheel-2 P with beff Impact (mod) (kN) 1.64 64.67 1.87 56.76 1.99 53.37 2.06 51.67 2.10 50.66 2.11 50.26 2.11 50.45 2.07 51.23 2.02 52.67 1.94 54.88 1.73 61.40 1.47 72.28 1.16 91.53 0.80 132.38 0.40 268.63 0.72 147.67 1.09 97.64 1.41 75.47 1.68 63.29 1.90 55.90 2.00 53.08
Position 4.06 4.228 4.396 4.564 4.732 4.9 5.068 5.236 5.404 5.572 5.74 5.908 6.076 6.244 6.412 6.58 6.748 6.916 7.084 7.252 7.42
Dist. of Nearest Support 0.44 0.27 0.10 0.06 0.23 0.40 0.57 0.74 0.90 1.07 1.24 1.41 1.42 1.26 1.09 0.92 0.75 0.58 0.42 0.25 0.08
beff 1.33 0.99 0.61 0.51 0.91 1.25 1.55 1.79 1.99 2.14 2.24 2.29 2.29 2.25 2.15 2.01 1.81 1.57 1.28 0.94 0.55
Wheel-3 P with beff Impact (mod) (kN) 1.26 84.15 0.99 107.10 0.61 174.17 0.51 207.58 0.91 117.33 1.23 86.72 1.37 77.38 1.50 71.00 1.60 66.59 1.67 63.62 1.72 61.77 1.75 60.86 1.75 60.82 1.72 61.64 1.68 63.40 1.60 66.25 1.51 70.50 1.39 76.66 1.24 85.66 0.94 112.97 0.55 192.67
Position 6.12 6.288 6.456 6.624 6.792 6.96 7.128 7.296 7.464 7.632 7.8 7.968 8.136 8.304 8.472 8.64 8.808 8.976 9.144 9.312 9.48
Dist. of Nearest Support 1.38 1.21 1.04 0.88 0.71 0.54 0.37 0.20 0.04 0.13 0.30 0.47 0.64 0.80 0.97 1.14 1.31 1.48 1.36 1.19 1.02
beff 2.34 2.28 2.17 2.01 1.81 1.55 1.25 0.89 0.49 0.73 1.10 1.43 1.70 1.93 2.11 2.24 2.32 2.35 2.33 2.27 2.15
Wheel-4 P with beff Impact (mod) (kN) 1.77 48.34 1.74 49.16 1.68 50.75 1.61 53.23 1.50 56.88 1.38 62.15 1.22 69.87 0.89 95.60 0.49 173.61 0.73 117.43 1.10 77.59 1.31 65.09 1.45 58.90 1.57 54.63 1.65 51.69 1.72 49.74 1.76 48.61 1.77 48.18 1.77 48.41 1.73 49.34 1.68 51.04
Position 7.92 8.088 8.256 8.424 8.592 8.76 8.928 9.096 9.264 9.432 9.6 9.768 9.936 10.104 10.272 10.44 10.608 10.776 10.944 11.112 11.28
Dist. of Nearest Support 0.42 0.59 0.76 0.92 1.09 1.26 1.43 1.40 1.24 1.07 0.90 0.73 0.56 0.40 0.23 0.06 0.11 0.28 0.44 0.61 0.78
beff 1.34 1.63 1.87 2.06 2.21 2.30 2.35 2.34 2.29 2.19 2.04 1.84 1.59 1.29 0.95 0.55 0.53 0.73 0.93 1.13 1.34
P with beff Impact (mod) (kN) 1.27 67.35 1.41 60.44 1.54 55.70 1.63 52.41 1.70 50.21 1.75 48.86 1.77 48.23 1.77 48.28 1.74 49.00 1.69 50.47 1.62 52.81 1.52 56.27 1.40 61.27 1.25 68.57 0.95 90.21 0.55 154.64 0.53 161.44 0.73 116.93 0.93 91.66 1.13 75.37 1.27 67.43
76
DESIGN FORCES FOR DECK SLAB INTRODUCTION : The RCC deck slab is analysed as 2-Dimensional frame considering 1m width of slab. The slab is supported over longitudinal girders. The concentrated live load for 1m width of deck slab is calculated as per effective width method given in AnnexureB-3 of IRC-112. The analysis of deck slab is carried out for Transverse Live Load. Analysis Models
Analysis Model with Member Numbering
Analysis Model with Node Numbering
77
Node 7
Node 8
Node 9
N ode 10
N ode 11
N ode 12
N ode 13
N ode 14
N ode 15
N ode 16
Node 6
Node 5
Node 4
DL SIDL (Except surfacing) SIDL (Surfacing) FPLL 1CLA (Max. Hog) TRANSVERSE ANALYSIS 1 FOR LIVE LOAD 1CLA (Max. Sag) TRANSVERSE ANALYSIS 1 FOR LIVE LOAD 2CLA (Max. Hog) TRANSVERSE ANALYSIS 2 FOR LIVE LOAD 2CLA (Max. Sag) TRANSVERSE ANALYSIS 2 FOR LIVE LOAD 1L 40T-L (Max. Hog) TRANSVERSE ANALYSIS 3 FOR LIVE LOAD 1L 40T-L (Max. Sag) TRANSVERSE ANALYSIS 3 FOR LIVE LOAD 1L 40T-M (Max. Hog) TRANSVERSE ANALYSIS 4 FOR LIVE LOAD 1L 40T-M (Max. Sag) TRANSVERSE ANALYSIS 4 FOR LIVE LOAD 1L 70R TR (Max. Hog) TRANSVERSE ANALYSIS 5 FOR LIVE LOAD 1L 70R TR (Max. Sag) TRANSVERSE ANALYSIS 5 FOR LIVE LOAD 1L70RW+1LCA(Max Hog) TRANSVERSE ANALYSIS 6 FOR LIVE LOAD 1L70RW+1LCA(Max Sag) TRANSVERSE ANALYSIS 6 FOR LIVE LOAD LL (Max. Hog) LL (Max. Sag)
11.12 3.01 5.28 0.01 16.9 -16.9 16.9 -16.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21.8 -21.8
25.04 7.99 11.10 3.77 18.44 6.76 2.16 2.99 1.02 4.98 11.88 3.78 5.27 1.79 8.76 0.01 0.00 0.00 0.00 0.01 33.8 22.1 7.4 3.4 6.8 -33.8 -22.1 -7.4 -3.4 -6.8 33.8 22.7 7.3 2.9 6.6 -33.8 -22.7 -7.3 -2.9 -6.6 7.6 7.8 11.1 4.7 10.5 -7.6 -7.8 -11.1 -4.7 -10.5 0.0 5.2 9.5 4.6 6.6 0.0 -5.2 -9.5 -4.6 -6.6 0.0 10.7 14.5 6.0 15.1 0.0 -10.7 -14.5 -6.0 -15.1 0.0 5.6 7.6 3.5 7.3 0.0 -5.6 -7.6 -3.5 -7.3 21.8 16.0 9.8 3.1 6.4 -21.8 -16.0 -9.8 -3.1 -6.4 Combination for ULS as per IRC-6
1.87 0.50 0.89 0.00 4.5 -4.5 5.5 -5.5 5.7 -5.7 4.7 -4.7 6.7 -6.7 4.3 -4.3 4.4 -4.4
16.25 4.39 7.71 0.01 6.2 -6.2 5.9 -5.9 9.1 -9.1 8.9 -8.9 11.8 -11.8 6.9 -6.9 2.6 -2.6
3.20 0.86 1.52 0.00 4.1 -4.1 5.4 -5.4 5.7 -5.7 5.7 -5.7 7.4 -7.4 2.8 -2.8 2.4 -2.4
14.73 3.98 6.99 0.01 6.9 -6.9 6.6 -6.6 10.5 -10.5 7.8 -7.8 15.5 -15.5 6.6 -6.6 1.8 -1.8
2.35 0.63 1.11 0.00 3.2 -3.2 3.2 -3.2 4.4 -4.4 4.4 -4.4 5.3 -5.3 3.0 -3.0 1.3 -1.3
7.39 1.99 3.51 0.00 7.3 -7.3 7.3 -7.3 10.7 -10.7 10.6 -10.6 13.8 -13.8 5.2 -5.2 0.9 -0.9
16.83 4.54 7.99 0.00 17.4 -17.4 18.2 -18.2 7.8 -7.8 6.9 -6.9 9.8 -9.8 10.6 -10.6 0.5 -0.5
36.17 9.76 17.17 0.01 25.6 -25.6 25.6 -25.6 11.4 -11.4 0.0 0.0 0.0 0.0 17.3 -17.3 0.0 0.0
18.36 4.96 8.72 0.01 12.8 -12.8 12.8 -12.8 0.0 0.0 0.0 0.0 0.0 0.0 8.6 -8.6 0.0 0.0
1.35*(DL+SIDL)+1.75*SIDL 1.35*(DL+SIDL)+1.75*SIDL+1.5*FPLL 1.35*(DL+SIDL)+1.75*SIDL+1.5*LL1 1.35*(DL+SIDL)+1.75*SIDL+1.5*LL2 1.35*(DL+SIDL)+1.75*SIDL+1.5*(FPLL+LL1) 1.35*(DL+SIDL)+1.75*SIDL+1.5*(FPLL+LL2) DESIGN HOG. DESIGN SAG
28.3 28.3 60.9 -4.3 60.9 -4.3 60.9 -4.33
46.9 46.9 56.6 37.3 56.6 37.3 56.6 0.0
4.8 4.8 11.4 -1.9 11.4 -1.9 11.4 -1.9
41.3 41.4 45.2 37.5 45.2 37.5 45.2 0.0
8.1 8.1 11.7 4.6 11.7 4.6 11.7 0.0
37.5 37.5 40.2 34.8 40.2 34.8 40.2 0.0
6.0 6.0 8.0 4.0 8.0 4.0 8.0 0.0
18.8 18.8 20.1 17.5 20.1 17.5 20.1 0.0
42.8 42.8 43.5 42.2 43.5 42.2 43.5 0.0
92.1 92.1 92.1 92.0 92.1 92.1 92.1 0.0
46.7 46.7 46.7 46.7 46.7 46.7 46.7 0.0
1.0*(DL+SIDL)+1.0*SIDL 1.0*(DL+SIDL)+1.0*SIDL+1.0*FPLL 1.0*(DL+SIDL)+1.0*SIDL+1.0*LL1 1.0*(DL+SIDL)+1.0*SIDL+1.0*LL2 1.0*(DL+SIDL)+1.0*SIDL+1.0*(FPLL+LL1) 1.0*(DL+SIDL)+1.0*SIDL+1.0*(FPLL+LL2) DESIGN HOG. DESIGN SAG
19.40 19.41 41.15 -2.35 41.16 -2.35 41.16 -2.350
63.7 20.3 28.2 9.6 63.7 20.3 28.2 9.6 96.3 44.3 43.0 14.3 31.1 -3.7 13.5 4.9 96.4 44.3 43.0 14.3 31.1 -3.7 13.5 4.9 96.4 44.3 43.0 14.3 0.00 -3.7 0.0 0.0 Combination for SLS as per IRC-6 43.68 13.93 19.36 6.58 43.69 13.93 19.36 6.58 65.43 29.92 29.19 9.70 21.93 -2.07 9.53 3.45 65.44 29.92 29.19 9.71 21.94 -2.06 9.54 3.46 65.44 29.9 29.2 9.7 0.000 -2.07 0.00 0.00
32.17 32.18 38.60 25.74 38.61 25.74 38.6 0.00
3.26 3.26 7.69 -1.17 7.69 -1.17 7.7 -1.17
28.35 28.35 30.90 25.79 30.91 25.80 30.9 0.00
5.58 5.58 7.95 3.22 7.95 3.22 8.0 0.00
25.70 25.70 27.50 23.90 27.51 23.90 27.5 0.00
4.10 4.10 5.45 2.75 5.45 2.75 5.4 0.00
12.89 12.89 13.78 11.99 13.78 11.99 13.8 0.00
29.36 29.36 29.81 28.91 29.81 28.91 29.8 0.00
63.10 63.11 63.11 63.1 63.12 63.1 63.1 0.0
32.03 32.04 32.03 32.0 32.04 32.0 32.0 0.0
SECTION
Node 3
Node 2
Summarry of unfactored B.M (KN-m)
78
Design for ULS condition Design Design Design Design Design Design Design Design
Hogging Moment at Cantilever Face at node 2,16 (end of haunch) Hogging Moment at Outer Support Node 4, 14 Hogging Moment at Outer Support 6,12 Hogging Moment at intermediate support Node 8,10 Hogging Moment at Intermediate Span at mid node 9 Hogging Moment atouter span at mid node 5,13 Sagging Moment at End Span(at node 5,13) Sagging Moment at mid of mid span( at node 9)
= = = = = = =
60.9 44.3 14.3 11.7 45.2 43.0 0.0 0.0
= = = = = = = = = = = =
35.0 32.0 500 40.0 200 32 1.000 0.800 0.400 1.150 40.0 16.0
KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m
DESIGN OF DECK SLAB fck fav fyk fcd Es Ec.eff
IRC-112-6.4.2.8
η λ β γs Clear Cover Bar dia to be used
Cantilever Face
SECTION
Mpa Mpa Mpa Mpa Gpa Gpa IRC-112 -A2.9
IRC-112 -6.2.2 mm mm
Outer Span (Face Outer Span (e Mid spans (Face Mid-End Span of outer Girder) of inner girder) of girders)
Midspan-Int. Span
DESIGN HOG.
60.9
44.3
14.3
11.7
43.0
45.2
DESIGN SAG
-4.3
-3.7
0.0
-1.9
0.0
0.0
b
1000
1000
1000
1000
1000
1000
145
145
145
145
145
145
Kav = M/bd f av (for Top)
0.0906
0.0658
0.0212
0.0174
0.0639
0.0672
Kav = M/bd2f av (for Bottom)
0.0064
0.0055
0.0000
0.0028
0.0000
0.0000
x= ((1+sqrt(1-4βKav))/(2*β))∗d (mm)
13.646
9.814
3.106
2.538
9.515
10.016
x= ((1+sqrt(1-4bKav))/(2*b))*d (mm)
0.9345
0.7934
0.0000
0.4072
0.0000
0.0000
Z for Top (mm)
131.4
135.2
141.9
142.5
135.5
135.0
Z for bottom (mm)
144.1
144.2
145.0
144.6
145.0
145.0
As required for Top (mm2)
1066.9
753.7
231.6
188.8
729.8
770.0
69.0
58.6
0.0
30.0
0.0
0.0
As provided at Top (mm2)
1398.0
1398.0
1398.0
1398.0
1398.0
1398.0
As provided at Bottom (mm2)
1398.0
1398.0
1398.0
1398.0
1398.0
1398.0
As
OK
OK
OK
OK
OK
OK
Remarks for Bottom As
OK
OK
OK
OK
OK
OK
d 2
As required for Bottom (mm2)
Remarks for Top
79
Min Ast Required min of ((0.26*fctm/fyk bt*d),(0.0013*bt*d)) Ast Required at top 1066.92 mm^2 16
Provide Ast provided qat Top
1398.01
Ast required at bottom
188.5 16
Provide Ast provided at top
1398.01
dia @
200
2
mm /m
c/c +
188.5
mm^2
10
dia @
200
c/c at bottom.
10
dia @
200
c/c
ok
mm^2 dia @
200
2
mm /m
c/c + ok
N ode 4
N ode 5
N ode 6
N ode 8
N ode 9
N ode 10
N ode 12
N ode 13
N ode 14
N ode 16
N ode 2
Calculation of`Longitudinal Reinforcement: Design BM for Longitudinal Reinforcement BM ARE IN KNm
0.2*(DL + SIDL)
5.7
4.1
5.6
1.9
1.0
8.3
1.6
1.2
3.8
8.6
9.3
0.2*(LL+ FPLL (Max. Hog))
4.4
3.2
2.0
0.6
0.9
0.5
0.5
0.3
0.2
0.1
0.0
0.2*(LL+ FPLL (Max. Sag))
-4.4
-3.2
-2.0
-0.6
-0.9
-0.5
-0.5
-0.3
-0.2
-0.1
0.0
Design Hogging BM
10.0
7.3
7.6
2.5
1.8
8.8
2.1
1.5
3.9
8.7
9.3
Design Sagging BM
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Provided Depth (mm)
SECTION
210
210
210
210
210
210
210
210
210
210
210
2
Reqd Ast (cm /m) (Top)
1.4
1.0
1.1
0.4
0.3
1.2
0.3
0.2
0.5
1.2
1.3
Reqd Ast (cm2/m) (Bottom)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Required longitudinal top reinforcement at cantilever support = 10
Provide Ast provided =
200
dia @ 3.9
cm2/m
c/c at top for cantilever support
2
cm /m
>
1.4
cm2/m
OK
2
Required longitudinal bottom reinforcement =
0.0
cm /m
Provide
10
dia @
Ast provided =
1.394
3.9
200
c/c at bottom except cantilever
2
cm /m
>
0.0
cm2/m
OK
Design for SLS condition Design Design Design Design Design Design Design Design
Hogging Moment at Cantilever Face at node 2,16 Hogging Moment at Outer Support Node 4, 14 Hogging Moment at Outer Support 6,12 Hogging Moment at intermediate support Node 8,10 Hogging Moment at Intermediate Span at mid node 9 Hogging Moment atouter span at mid node 5,13 Sagging Moment at End Span node 5, 13 Sagging Moment at Intermediate Span node no9
= = = = = = =
41.2 29.9 9.7 8.0 30.9 29.2 0.0 0.0
KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m
80
SECTION
Cantilever Face
Outer Span (Face Outer Span (e Mid spans (Face Mid-End Span of outer Girder) of inner girder) of girders)
Midspan-Int. Span
DESIGN HOG.
41.2
29.9
9.7
8.0
29.2
30.9
DESIGN SAG
-2.35
0.0
-2.1
-1.2
0.0
0.0
b
1000
1000
1000
1000
1000
1000
d
145
145
145
145
145
145
dc= (-As Es + sqrt((AsEs)^2+2bAsEsEc.effd))bEc.eff (mm) (Top)
42.35
42.35
42.35
42.35
42.35
42.35
dc= (-As Es + sqrt((AsEs)^2+2bAsEsEc.effd))bEc.eff (mm) (bottom)
33.20
33.20
33.20
33.20
33.20
33.20
18781818.9
18781818.9
18781818.9
18781818.9
18781818.9
18781818.9
σc (Top) (Mpa)
14.8
10.8
3.5
2.9
10.5
11.2
σs (Top) (Mpa)
224.9
163.5
53.0
43.4
159.5
168.9
Check concrete
OK
OK
OK
OK
OK
OK
Check Steel
Ok
Ok
Ok
Ok
Ok
Ok
19425126.5
19425126.5
19425126.5
19425126.5
19425126.5
19425126.5
σc (Bottom) (Mpa)
0.6427
0.0000
0.5648
0.3197
0.0000
0.0000
σs (Bottom) (Mpa)
13.525
0.000
11.884
6.728
0.000
0.000
Check concrete
OK
OK
OK
OK
OK
OK
Check Steel
Ok
Ok
Ok
Ok
Ok
Ok
I (Hog) cracked M.I
I (Sag)
81
Check for crack width for maximum moments at node no 3. =
0.059 Hence OK
0.425k 1k 2ϕ is applicable ρ ρ .eff where spacing of bonded reinforcement with in the tension zone <=5*(C+ ϕ /2)
=
244.7 mm
=
240 mm
Wk
=
S r,max ( ε sm - ε cm )
S r,max
=
Maximum crack spacing
3.4c +
ϕ
=
is the bar diameter.Where different diameters are used in section an equivalent diameter canbe used ϕ eq
=
16.0 mm
C
=
Clear cover to longitudinal reinforcement
=
40.0 mm
K1
=
is the co-efficient which takes account of the bond properties of the bonded reinforcement
=
0.8
K2
=
is a co-fficient which takes into account of the distribution of strain
=
0.5
( ε sm - ε cm )
=
σ sc - k 1 f ct.eff / ρ ρ. eff (1+α e ρ ρ .eff ) Es
=
0.00024
σ sc
=
is the stress in the tension reinforcement assuming a cracked section
=
αe
=
is the ratio Es/Ec
=
6.250
ρ ρ. eff
=
A s /A c.eff
=
0.0250
A c.eff
=
is the effective area of concrete in tension surrounding the reinforcement of depth h c.eff , where h c.eff is the lesser of following
=
55882.36 mm2
= = = =
1000 210 145 42
>=0.6 σ sc / Es
1 One third of the tension zone depth of the cracked section,(h-x)/3, with x negative when whole section is in tension
b h d x
159.54 Mpa
mm mm mm mm
2 half of section depth,h/2, or 3 2.5*(h-d)
As
=
Area of tension reinforcement
=
1398 mm2
f ct.eff
=
is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur f ct.eff = f ctm
=
3.000 Mpa
82
Design of Transverse Cantilever of Slab A) Loads & Moments at Crash Barrier Side: 0 450
0 200
200
0
Water pipe
1000 Load due to self-weight of slab Cg of self-weight of slab Load due to RCC Railing Cg of RCC railing from edge of cantilever Cg from cantilever face Load due to wearing coat Cg from cantilever face Load due to Crash barrier Cg of crash barrier from edge of cantilever Intensity of FPLL CG of FPLL Intensity of Water Pipe C.G of Pipe Moment due to rcc railing Moment due to wearing coat Moment due to crash barrier Moment due to FPLL Moment due to selfwt of slab Moment due to pipe Load due to Class A wheel Wheel Contact Width Wheel Contact Length Clear distance from kerb face Effective width, beff 1st Wheel a b1 beff Concentrated maximum wheel load Spacing between consecutive , nearest axle Net beff Hence Load acting on the 1m width slab LL with Impact IF= Moment at the cantilever face due to LL
= = = = = = = = = = = = = = = = = = = = = = =
1.5
= = = = = = = = =
0.500 0.500 0.000 775 0.775 0.110 0.275 1.000 0.775 0.000 0.275 0.000 0.600 0.000 0.030 0.775 0.000 0.250 0.000
t m t mm m t m t mm t/m m t/m t/m t-m t-m t-m t-m t-m t-m
500 mm 250 mm 150 mm 1.2 a + b1 0.15 0.38 1.00 5.70 1.20 1.00 5.70 8.55 1.28
m m m t m m t t tm
83
2nd Wheel(it will not lie on the cantilever part) a b1 beff Concentrated maximum wheel load Spacing between consecutive , nearest axle Net beff Hence Load acting on the 1m width slab LL with Impact IF= 1.5 Moment at the cantilever face due to LL
= = = = = = = = =
Total desigm moment as ULS = 1.35*(DL+SIDL1)+1.75*SIDL+1.5*LL Total design moment at cantilever face = 3.360438 Total desigm moment as SLS = 1*(DL+SIDL1)+1*SIDL+1*LL Total design moment at cantilever face = 3.62
Total Design Moment due to DL+SIDL+LL
=
0.15 0.38 1.00 5.70 1.20 1.00 5.70 8.55 1.28
m m m t m m t t tm
3.62
tm
tm tm
END OF DESIGN REPORT
84
Launching of Pre-cast I-Girders by cranes
1
Foreword: The procedure starts with Analysis for DL, SIDL, Live Load (Multi lane vehicle moving load), then stepwise design considering temperature, creep shrinkage etc. for Flexure, Shear including Blister Blocks etc. and finally producing editable CAD drawings with relevant structural & construction details.
For PSC I-Girder the Main Long Girder is designed with applied Loading
Pre Stressed Post Tensioned Concrete I-Girder Bridge with detail step wise design calculation report and complete set of sample CAD drawings are provided convertible to design drawings.
2
Live Loads of moving vehicles by IRC-6 Class of Load combinations as per width of carriageway,
3
Design of PSC I-Girders for Bridges 1. INTRODUCTION: This design note pertains to design of Precast PSC beam and cast-in -situ RCC slab superstructure of 37.5m span C/C expansion Joint. The superstructure consists of four numbers of PSC I girders spaced at 3.0m c/c over which 200mm thick deck slab is casted. The deck width of superstructure is kept 12.0m including 0.5m of crash barrier on both sides. The construction sequence proposed for the approach span superstructure is as follows 1 2 3 4 5 6
Casting of PSC beam on casting bed. Stressing of stage I cables after 21 days of casting or when the concrete attains the strength of 45Mpa, whichever is later. Launching and placing the prestressed beams upon Permanent bearings (Pot cum PTFE) Staging & shuttering for deck slab and end cross diaphragm to be erected. Deck slab casting along with End diaphragm after 28days of casting of Girder Casting of crash barrier & laying of wearing coat at 56 days after casting of girder.
The analysis of superstructure has been carried out by grillage analogy using ASTRA software. The four span superstructure has been idealized as a mesh of longitudinal and transverse members and the loading has been applied as per the construction sequence. The analysis and design of beams has been carried out for the outer beam . Transverse analysis of deck has been done using ASTRA sofware and excell For dispersion, 65mm thick wffiring coat has been assumed but lod due to wearing coat has been assumed as 0.2 t/m2 assuming future overlay. Loading Density of Concrete (RCC) Density of Concrete (PSC) Live Load
= = =
2.5 t/m3 2.5 t/m3 2Lane/3Lane loading as per IRC 6:2010
Material Concrete Grade for Deck Slab/End Diaphragm PSC Girder Reinforcement Bars Clear cover
= = = =
M-40 M-45 HYSD Fe-500 40mm
REFERENCE CODES LIST IRC:6 IRC:112 IRC:22
2010 2011 2000
Loads & Stresses Design Criteria for PSC Road Bridges Cement Concrete(Plain & Reinforced)
4
2. Input Data 1 2 3
Distance between C/C Exp. Joint Distance between C/C Exp. Joint Effective span C/C bearing
Leff
= = =
37.50 26.52 34.30
m m m
(Skew) (Square) (Skew)
4
Effective span c/C bearing
Leff
=
24.25
m
(Square)
5
Overhang of girder off the bearing
=
1
m
6
Overhang of slab off the bearing
=
1.600
m
7
Expansion Joint
=
40
8
Deck Width
=
12.0
m
9
Deck Width (Skew)
=
16.97
m
10
Angle of skew
Ang
=
45.00
deg.
11
Clear carriage way
Bcw
=
11.00
m
12
Width of outer railing
=
0.000
m
13
Width of Footpath
=
0.000
m
14
Width of Crash Barrier
Wkerb
=
500
15
Spacing of main girder c/c
Spmg
=
3.000
m
(Square)
16
Spacing of main girder c/c
Spmg
=
4.243
m
(Skew)
17
Thk of deck slab
Df
=
200
mm
18
Thk of deck slab at overhang
=
400
mm mm
mm
mm
19
Thk of wearing coat
Wc
=
65
20
Length of cantilever
Lcan
=
1.50
m
21
Cantilever slab thk at fixed end
Dcan1
=
200
mm
22
Cantilever slab thk at free end
Dcan2
=
200
mm
23
No of main girder
Nomg
=
4
nos
24
Depth of main girder
Dmg
=
2400
mm
25
Flange width of girder
bf
=
1000
mm
26
Web thk of girder at mid span
=
0.30
m
27
Web thk of girder at Support
=
0.65
m
28
Thickness of top flange
=
150
mm
29
Thickness of top haunch
=
75
mm
30
Bottom width of flange
=
650
mm
31
Thickness of bottom flange
=
250
mm
32
Thickness of bottom haunch
Bbw
=
200
mm
33
Length of varying portion
Lwv
=
2.50
m
34
Length of solid portion
Lwu
=
2.50
m
35
No of Intermediate cross girder
Nocg
=
1.00
36
Depth of Int. cross girder
=
2350
mm
37
Depth of End. cross girder
=
2350
mm
38
Web thk of Intermediate cross girder
=
300
mm
39
Web thk of end cross girder
=
600
mm
40
Grade of concrete for precast Girder
=
M 45
Mpa
41
Grade of concrete of other componant
Cgrade
=
M 40
Mpa
42
Grade of reinforcement Shape Factor λ
Sgrade λ
=
Fe 500
Mpa
=
0.80
η
=
1.00
43 44
strength Factor η
bwcg
5
45 46
Partial factor of safety (Basic and seismic) Partial factor of safety Accidental
ɣc
=
ɣc
=
1.20 0.67
Coefficient to consider the influence of the strength Design value of concrete comp strength for Basic and seismic Design value of concrete comp strength for Accidental
α
=
fcd
=
fcd
=
43
Clear cover
cov
44
Unit weight of dry concrete
wcon
45
Unit weight of wet concrete
46
Weight of wearing course
47
Weight of Crash Barrier
48 49 50 51
47 48 49
52 53 54 55 56 57 58 59
1.50
17.87
Mpa
=
17.87 40.0
Mpa mm
=
2.50
t/m3
=
2.60
t/m3
wwc
=
0.20
t/m2
wrail
=
1.00
t/m
Weight of Railing
=
0.30
t/m
Intensity of Load for shuttering
= = =
0.50 40 500
t/m Mpa Mpa
=
1.15
= = = = =
1.00 33000 200000 6.061 1.050
= =
0.900 0.900
Stress in concrete (compression) Stress in steel (tension) Partial factor of safety for basic and seismic Partial factor of safety for Accidental
fck fyk γs γs
Ecm Es Modular ratio Anchorage from c/L of bearing Length of Girder beyond c/L of Bearing Distance of Jack from c/L of Bearing
m
IRC-112 Fig 6.3 (Note) IRC-112 Fig 6.3 (Note) Mpa Mpa m
(Min. 1/2 of end X-girder Thk.)
m m
6
Stressing and casting sequence 1st stage prestressing Casting of Deck Slab Shift of Bearing SIDL(Wearing Coat & Crash Barrier) Age of deck slab at time of SIDL Fck at 1st stage of prestressing Fck at service Modulus of Elasticity (Conc) 21th Day Modulus of Elasticity (Conc) 28th Day Modulus of Elasticity (Conc) 56th Day Modulus of Elasticity (Strands) Type of cables Breaking Load Area of 1 strand Area of one cable No of Cables stressed in 1st stage Jacking Force No of Sections to be checked Prestressing force per cable (UTS)
21 28 56 56 28 45.0 45.0 3.24E+06 3.35E+06 3.35E+06 1.95E+07
Mpa Mpa 2 t/m 2 t/m 2 t/m 2 t/m
19 183.7 9.870E-05 1.875E-03 3.737 0.765 5 349.5
T13 KN 2 m 2 m
Factors with 20% for loss calculation Elastic Shortening loss Relaxation loss Shrinkage loss Creep loss
1.0 1.2 1.2 1.2
Factors without 20% for loss calculation Elastic Shortening loss Relaxation loss Shrinkage loss Creep loss
1.0 1.0 1.0 1.0
Factor for Relaxation Loss 1000hr relaxation (for low relaxation steel) 1000hr relaxation (for normal relaxation steel) Strain due to differential shrinkage and creep Reduction factor due to differential creep (As per BS:5400)
day day day day day
*UTS
t
2.50% 5.00% 1.00E-04 0.43
7
3. PROPERTIES
8
Properties of Member
820
to
Length of slab = Thickness of slab =
Area, Ax = Iz =
0.6481 0.0022
m 4 m
815
to
819
849
m m
Area, Ax = Iz =
0.5352 0.0018
m 4 m
810
to
814
850
m m
Area, Ax = Iz =
0.4463 0.0015
m 4 m
801
to
809
855
m m
Area, Ax = Iz =
0.2635 0.0009
m 4 m
3.240 0.200
Properties of Member Length of slab = Thickness of slab =
2.676 0.200
Properties of Member Length of slab = Thickness of slab =
2.231 0.200
Properties of Member Length of slab = Thickness of slab =
1.358 0.200
m m
844 2
to
849
to
854
to
863
2
2
2
9
SECTIONS CONSIDERED IN DESIGN
34.3m
Sec 1-1 Sec 2-2 Sec 3-3 Sec 4-4 Sec 5-5
Simply Supported Span Support At end varying L/4 3L/8 L/2
= = = = =
0.000 5.000 8.575 12.863 17.150
m m m m m
10
CALCULATION OF MOMENTS AND SHEARS FOR OUTER GIRDER Analysis for dead load is done manually while analyses for SIDL and LL are done by GRILLAGE analysis using ASTRA-PRO. Only the c/c of bearing has been considered in analysis. DEAD LOAD 1. Under self weight of the precast Girder Effective Span of the girder
2.5m
=
34.3021
3.24t/m
m
2.43t/m
2.5m
4.05t/m
24.3m
34.30m 34.30m
0.001m
Support Reaction Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section At L/4 BM SF
3-3
Section At 3L/8 BM SF
4-4
Section At L/2 BM SF
5-5
=
47.80
X
= = =
0.000 -0.05 47.80
m t-m t
X
= = =
5.000 190.89 29.58
m t-m t
X
= = =
8.575 281.09 20.88
m t-m t
X
= = =
12.863 348.23 10.44
m t-m t
X
= = =
17.150 370.62 0.00
m t-m t
0.00m
t
11
2. Under Deck Slab Load
0.00t
1.56t/m
34.302m 34.300m Support Reaction
=
26.75
t
With Wet density 3 (2.6 t/m ) Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section L/4 BM SF
3-3
Section 3L/8 BM SF
4-4
Section L/2 BM SF
5-5
X
X
X
X
X
With Dry density 3 (2.5 t/m )
= = =
0.000 0.00 28.01
m t-m t
0 26.93
t-m t
= = =
5.000 120.56 20.21
m t-m t
115.92 19.43
t-m t
= = =
8.575 182.85 14.63
m t-m t
175.81 14.07
t-m t
= = =
12.863 231.25 7.95
m t-m t
222.36 7.64
t-m t
= = =
17.150 250.99 1.26
m t-m t
241.33 1.21
t-m t
12
3. Shuttering Load
0.50t/m
34.3m 34.3m Support Reaction Section 1-1 Support BM SF Section 2-2 At End varying BM SF Section L/4 BM SF
3-3
Section 3L/8 BM SF
4-4
Section L/2 BM SF
5-5
=
8.58
t
X
= = =
0.000 0.00 8.58
m t-m t
X
= = =
5.000 36.63 6.08
m t-m t
X
= = =
8.575 55.15 4.29
m t-m t
X
= = =
12.863 68.93 2.14
m t-m t
X
= = =
17.150 73.53 0.00
m t-m t
13
LIVE LOAD BM SUMMARY FOR OUTER GIRDER OG1 AND OG2 70R WHEEL ONLY 1 LANE IRC70RWHEEL MOST ECCENTRIC Maximum BM & corrs. SF
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.40 1.00 0.49
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5) 1 LANE IRC70RWHEEL ON MEMBER Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRC70RWHEEL PLACED CONCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.72 1.72 5.84 6.25 9.32
tm tm tm tm tm
14
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.59 1.72 1.72 6.25 8.10
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
2.65 2.65 1.41 1.40 1.40
t t t t t
1 LANE IRCCLASSA PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.39 0.39 2.19 2.23 2.38
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
0.69 0.69 0.22 0.13 0.08
t t t t t
0.39 0.39 1.47 2.18 2.19
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
0.69 0.69 0.37 0.22 0.22
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRCCLASSA PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.62 0.62 2.87 2.91 3.60
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.43 0.24 0.20
t t t t t
0.62 0.62 1.49 2.91 3.22
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.55 0.43 0.43
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
15
3 LANE IRCCLASSA PLACED MOST CONCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
3.40 3.40 3.65 3.69 4.83
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
8.57 8.57 0.40 0.17 0.08
t t t t t
1.52 3.40 3.40 3.62 4.27
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
8.57 8.57 0.74 0.64 0.64
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRCCLASSA + 1 LANE IRC70RWHEEL Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1 LANE IRC70RWHEEL + 1 LANE IRCCLASSA Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
16
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
1 LANE IRC70RWHEEL + 1 LANE IRCCLASSA Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.95 1.95 6.48 6.96 10.55
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.17 0.56
t t t t t
1.62 1.95 1.95 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
3.00 3.00 1.61 1.61 1.59
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRCCLASSA PLACED AFTER IRC70RTRACK Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
0.62 0.62 2.87 2.91 3.60
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.43 0.24 0.20
t t t t t
0.62 0.62 1.49 2.91 3.22
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.04 1.04 0.55 0.43 0.43
t t t t t
Maximum SF & corrs. BM
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
17
2 LANE IRC70RTRACK PLACED MOST ECCENTRICALLY Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.16 0.81 0.42
t t t t t
1.57 2.64 6.60 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.25 1.17 1.16
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
2 LANE IRC70RTRACK PLACED AT CENTER OF THE EACH LANE Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 15.95 15.95
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.98 14.98 1.16 0.81 0.42
t t t t t
1.57 5.40 6.87 15.95 15.95
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.98 14.98 1.19 1.16 1.16
t t t t t
14.99 14.99 1.10 0.58 0.25
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
IRC70RTRACK PLACED AT THE CENTER OF INNER GIRDER Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
3.34 3.44 4.94 15.53 15.53
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
18
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.31 1.65 4.90 15.53 15.53
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
14.99 14.99 1.18 1.10 1.01
t t t t t
Maximum Bending Moment due to Live load Maximum BM & corrs. SF BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
5.09 5.40 7.88 17.44 17.44
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.16 0.81 0.42
t t t t t
5.09 5.40 6.48 6.96 9.14
tm tm tm tm tm
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
16.20 16.20 1.61 1.61 1.59
t t t t t
Maximum SF & corrs. BM BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
19
OUTER GIRDER SUMMARY FOR DL ,SIDL & LIVE LOAD BM BM & SF DUE TO GIRDER LOAD ONLY Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) -0.05 -0.07 190.89 257.70 281.09 379.47 348.23 470.11 370.62 500.34
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 47.80 29.58 20.88 10.44 0.00
ULS (t) 64.53 39.93 28.19 14.10 0.01
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 28.01 20.21 14.63 7.95 1.26
ULS (t) 37.82 27.29 19.76 10.73 1.70
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.0 1.0 1.0 1.0 1.0
SLS (t) 8.58 6.08 4.29 2.14 0.00
ULS (t) 8.58 6.08 4.29 2.14 0.00
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.75 1.75 1.75 1.75 1.75
SLS (t) 8.20 7.20 4.70 2.50 1.00
ULS (t) 14.35 12.60 8.23 4.38 1.75
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t) 15.50 13.30 8.10 4.00 1.00
ULS (t) 20.93 17.96 10.94 5.40 1.35
BM & SF DUE TO DECK LOAD ONLY Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) 0.00 0.000 120.56 162.75 182.85 246.84 231.25 312.19 250.99 338.83
BM & SF DUE TO SHUTTERING LOAD Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.0 1.0 1.0 1.0 1.0
SLS (t-m) ULS (t-m) 0.00 0.00 36.63 36.63 55.15 55.15 68.93 68.93 73.53 73.53
BM & SF DUE TO SIDL (WEARING COAT) Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.75 1.75 1.75 1.75 1.75
SLS (t-m) ULS (t-m) 12.50 21.88 32.00 56.00 59.00 103.25 74.00 129.50 79.00 138.25
BM & SF DUE TO SIDL (CRASH BARRIER) Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.35 1.35 1.35 1.35 1.35
SLS (t-m) ULS (t-m) 21.50 29.03 57.00 76.95 105.80 142.83 131.30 177.26 140.00 189.00
20
BM & SF DUE TO LIVE LOAD Impact factor = 1.112 Maximum BM & Corresponding Shear force Without Impact Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.50 1.50 1.50 1.50 1.50
SLS (t-m) ULS (t-m) 5.09 7.64 5.40 8.11 7.88 11.82 17.44 26.16 17.44 26.16 16.20 16.20 1.16 0.81 0.42
24.30 24.30 1.74 1.22 0.63
Maximum Shear force & Corresponding BM Without Impact
With Impact Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 5.66 6.01 8.76 19.39 19.39
ULS (t) 8.49 9.01 13.14 29.08 29.08
SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
1.50 1.50 1.50 1.50 1.50
18.01 18.01 1.29 0.90 0.46
27.01 27.01 1.93 1.35 0.70
With Impact
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 16.20 16.20 1.61 1.61 1.59
ULS (t) 24.30 24.30 2.42 2.42 2.39
Section Mark SF(SEC. 1-1) SF(SEC. 2-2) SF(SEC. 3-3) SF(SEC. 4-4) SF(SEC. 5-5)
ULS L.F 1.50 1.50 1.50 1.50 1.50
SLS (t) 18.01 18.01 1.79 1.79 1.77
ULS (t) 27.01 27.01 2.69 2.69 2.65
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.50 1.50 1.50 1.50 1.50
5.09 5.40 6.48 6.96 9.14
7.64 8.11 9.72 10.44 13.72
BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
1.50 1.50 1.50 1.50 1.50
5.66 6.01 7.20 7.74 10.17
8.49 9.01 10.81 11.61 15.25
Comparison Between Total BM & SF of Inner and Outer Girder
Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Outer Girder ULS L.F SLS (t-m) ULS (t-m) 1.50 18.11 37.94 1.50 349.45 493.57 1.50 531.69 754.52 1.50 672.87 967.05 1.50 720.00 1032.66
Section Mark BM SEC. (1-1) BM SEC. (2-2) BM SEC. (3-3) BM SEC. (4-4) BM SEC. (5-5)
Outer Girder ULS L.F SLS (t) 1.50 164.64 1.50 124.79 1.50 69.81 1.50 37.30 1.50 7.46
ULS (t) 164.64 124.79 69.05 35.96 5.51
21
Cable 1 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) θ L( o) θR( o) aL(per m) aR(per m)
LEGEND: a (mm)
= = = =
30700 mm 17K 13
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
HDPE 0.170 Profile in Elevation 1000 13000 13000 2700 1000 1100 1100 120 120 969 969 7.444 -7.444 5.0256E-03 -5.0256E-03
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
0.131 0.010 102.049 -0.131 -0.010 -102.049 0.130 -0.130 30700 1009 13037 2700 13037 1009 30791
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
Length of curved profile in elevation St. length of cable at mid in elevation Length of curved prfile in elevation
e(mm)
St. length of cable at left end in elevation
s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z4 (mm)
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 2 2 (d z/d x) L2 RpL2 (m) t(m)
0.000 4.2E+07 6.500 0.000 2.850 3.5E-01 6.5E+00 0.000 4.2E+07 6.500 0.000 0.000 4.2E+07
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 6500 6500 2700 6500 6500 1000 30700
Coordinate of cable at jacking end Coordinate of cable at jacking end Coordinate of cable at mid span St. length of cable at left end in plan Length of curved profile in plan Length of reverse curve in plan St. Length of cable at mid in plan Length of curved profile in plan Length of reverse curve in plan St. length of cable at left end in plan Coordinate of cable at jacking end in plan Coordinate of cable at mid span in plan Cable Profile Results in Elevation
From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm Profile in Plan 6.50 apR1 0.000 cp2 42250000.0 t1(m) 6.500 (dz/dx) R1 2 2 0.000 (d z/d x) R1 0.000 RpR1 (m) 4.23E+07 u(m) 6.50 apR2 0.000 cp2 42250000.0 u1(m) 6.500 (dz/dx) R2 0.0000 (d2z/d2x) R2 0.000 RpR2 (m) -4.2E+07 6.5
St. length of cable at left end in elevation
b(mm) c(mm) d(mm) Y1(mm) Y6(mm) Y3(mm) p (mm) q(mm) r (mm)
1000 6500 6500 2700 6500 6500 1000 0 0 0 0 0 0 0 0
= = = =
0.000 1.000 14.000 16.700 29.700 30.700 1.100 0.969
Length of Cable1
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
Cable Profile Results in Plan 0.120 0.120 0.969 1.100 0.005 -0.005 0.130 -0.130
30791mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 7.500 14.000 16.700 23.200 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(between Anchorages)
22
Cable1
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction µ Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
= = = = = = =
17K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
Area of one Strand UTS of one Strand Area of Cable UTS of Cable Length of Cable Jacking force
per m 2 t/m
A= Pu = L= Po =
= = = = = =
mm -(µθ µθ+kx) µθ
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
98.7 mm^2 18.737 t 1677.9 mm^2 319 t 30.700m 232 t
Px = P0e
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1299
0.0902
0.0545
0.0114
-0.0045
Σ∆α
(rad)
0.0000
0.0397
0.0755
0.1185
0.1345
Y
(rad)
1100
527
268
126
121
(rad)
0
0
0
0
0
Plan Angle Cumulative Change in Plan TotalAngle Change in
Z φ
(rad)
0.000
0.000
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
0.0000
0.0000
0.0000
0.0000
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 232.07
0.040 228.22
0.075 225.22
0.119 221.67
0.134 219.18
0.00
1.66
2.95
4.48
5.56
1150.718
810.512
958.118
944.951
Ordinate from C/L
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
3864.299
(t)
125.873
(mm)
45.76% 118
% Average Friction Loss Cable Extension
Cable1
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 219.66
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
16.320 m from Anchorage 219.66 t (After Friction Loss by Linear Interpolation) 98.2tm 0.000
= =
98.157tm (t) (t) (t)
0.000
5.000
8.575
12.863
17.150
-
-
-
219.660326
-
12.41
8.56
5.56
2.01
0.00
207 10.70 205.50 26.85
52.416 211 7.50 210.25 19.02
25.227 214 4.93 213.79 11.66
16.215 218 1.81 217.64 2.49
4.299 219 0.00 219.18 -0.99
23
Cable1
Drawing Data Type = 17K 13 Jacking Force = 232 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 319 t 2 Mod. of Elasticity Es = 1.95E+07 t/m Y1(mm) p (mm) 1000 = 1100 Y2(mm) q(mm) 6500 = 969 Y3(mm) r (mm) 6500 = 120 Y4(mm) s (mm) 2700 = 120 Y5(mm) t (mm) 6500 = 969 Y6(mm) u (mm) 6500 = 1100 a (mm) v (mm) 1000 = 1000 b(mm) Z1 (mm) 0 = 13000 c(mm) Z2 (mm) 0 = 2700 d(mm) Z3 (mm) 0.0005 = 13000 e(mm) Z4 (mm) 0.001 = 1000
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Elongation = 118 Exit Angle = 7.444 Length = 30791mm Wobble coeff. k = 0.0020 Area of Cable = 1677.9 UTS of One Strand = 18.737 t Z5 (mm) 0.001 Z6 (mm) 0.0005 Z7 (mm) 0 Z8 (mm) 0 rL(m) 102.049 Trans RL1 (m) Trans RL2 (m)
mm Degree per m mm^2
42250000.0 -42250000.0
Cable1 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 1100 1035 969 924 802 690 588 496 414 342 280 229 187 155 134 122 120 120
(rad) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Elevation Radius (m) inclined straight inclined straight inclined straight 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 102.049 straight straight
24
Cable2 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) θL( o) θR( o) aL(per m) aR(per m)
= = = =
30700 18K HDPE 0.170
Profile in Elevation 1000 7015 7015 14670 1000 750 750 120 120 610 610 7.957 -7.957 9.9620E-03 -9.9620E-03
mm 13
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
0.140 0.020 51.669 -0.140 -0.020 -51.669 0.139 -0.139 30700 1010 7038 14670 7038 1010 30765
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 3507.5 3507.5 14670 3507.5 3507.5 1000 0 0 90 180 180 90 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 2 2 (d z/d x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 8.015 22.685 29.700 30.700 0.750 0.610
Length of Cable2
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
= = = =
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan 3.51 apR1 cp2 0.007 68.3 t1(m) 3.509 (dz/dx) R1 2 2 (d z/d x) R1 0.051 0.015 RpR1 (m) 6.86E+01 u(m) 3.51 apR2 -0.007 cp2 68.3 u1(m) 3.509 (dz/dx) R2 2 2 -0.0513 (d z/d x) R2 -0.015 RpR2 (m) -6.9E+01 3.5
-0.007 68.3 3.509 -0.051 2.850 3.5E-01 3.5E+00 0.007 68.3 3.509 0.051 0.015 6.9E+01
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 3509 3509 14670 3509 3509 1000 30706
Cable Profile Results in Plan 0.120 0.120 0.610 0.750 0.010 -0.010 0.139 -0.139
30771mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 4.508 8.015 22.685 26.193 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.090 0.180 0.180 0.090 0.000 0.000
apL1 apL2 apR1 apR2 θp1 (rad) θp2 (rad) θp3 (rad) θp4 (rad)
0.007 -0.007 -0.007 0.007 -0.051 -0.051 -0.051 -0.051
(between Anchorages)
25
Cable2
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
= = = = = = =
18K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable A= UTS of Cable Pu = Length of Cable L= Jacking force Po =
= = = = = =
98.7 mm^2 18.737 t 1776.6 mm^2 337 t 30.700m 246 t
mm
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
Px = P0e
-(µθ µθ+kx) µθ
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1389
0.0600
0.0000
0.0000
0.0000
Σ∆α
(rad)
0.0000
0.0789
0.1389
0.1389
0.1389
Y
(rad)
750
211
120
120
120
(rad)
0
113
180
180
180
Plan Angle Cumulative Change in Plan TotalAngle Change in
Z φ
(rad)
0.000
0.044
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
-0.0585
-0.1025
-0.1025
-0.1025
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 245.72
0.098 239.25
0.173 234.56
0.173 232.56
0.173 230.57
0.00
2.63
4.54
5.36
6.17
1212.433
846.935
1001.493
992.711
Ordinate from C/L
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
4053.571
(t)
132.038
(mm)
46.27% 117
% Average Friction Loss Cable Extension
Cable2
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 231.40
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
15.350 m from Anchorage 231.40 t (After Friction Loss by Linear Interpolation) 103.9tm 17.150
= =
86.781tm (t) (t) (t)
0.000
5.000
8.575
12.863
17.150
-
-
-
231.403903
-
14.32
7.85
3.15
1.15
0.00
217 11.65 215.00 30.05
55.414 224 6.56 222.94 13.41
19.666 228 2.69 228.25 0.00
9.233 230 0.99 230.25 0.00
2.469 231 0.00 230.57 0.00
26
Cable2
Drawing Data Type = 18K Jacking Force = 246 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 337 t Mod. of Elasticity Es = 1.95E+07 Y1(mm) p (mm) = 750 Y2(mm) q(mm) = 610 Y3(mm) r (mm) = 120 Y4(mm) s (mm) = 120 Y5(mm) t (mm) = 610 Y6(mm) u (mm) = 750 a (mm) v (mm) = 1000 b(mm) Z1 (mm) = 7015 c(mm) Z2 (mm) = 14670 d(mm) Z3 (mm) = 7015 e(mm) Z4 (mm) = 1000
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
13
Elongation = Exit Angle = Length = Wobble coeff. k = Area of Cable = 2 UTS of One Strand = t/m Z5 (mm) 1000 Z6 (mm) 3507.5 Z7 (mm) 3507.5 Z8 (mm) 14670 rL(m) 3507.5 3507.5 Trans RL1 (m) 1000 Trans RL2 (m) 0 0 90 180
117 7.957 30771mm 0.002 1776.6 18.737 t 180 90 0 0 51.669
mm Degree per m mm^2
68.6 -68.6
Cable2 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 750 680 610 563 440 337 254 191 148 124 120 120 120 120 120 120 120 120
(rad) 113 0 0 1 13 40 82 128 160 177 180 180 180 180 180 180 180 180
Elevation Radius (m) inclined straight inclined straight inclined straight 51.669 51.669 51.669 51.669 51.669 51.669 51.6685128 straight straight straight straight straight straight straight straight
27
Cable3 Projected Length Cable Type Type of Duct Coeff. of Friction, µ
a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) o θL( ) o θR( ) aL(per m) aR(per m)
= = = =
30700 18K HDPE 0.170
Profile in Elevation 1000 2764 2764 23172 1000 400 400 120 120 282 282 6.704 -6.704 2.1264E-02 -2.1264E-02
mm 13
(dy/dx)L 2 2 (d y/dx )L rL (m) (dy/dx)R 2 2 (d y/dx )R Rr (m) θL( rad) θR( rad) Length a1 (mm) b1(mm) c1(mm) d1(mm) e1(mm) Le(mm)
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
0.118 0.043 24.003 -0.118 -0.043 -24.003 0.117 -0.117 30700 1007 2770 23172 2770 1007 30726
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 1382 1382 23172 1382 1382 1000 0 0 -90 -180 -180 -90 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 2 2 (d z/d x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 (d2z/d2x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 3.764 26.936 29.700 30.700 0.400 0.282
Length of Cable3
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
= = = =
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan apR1 1.38 cp2 -0.047 10.6 t1(m) (dz/dx) R1 1.386 2 2 -0.130 (d z/d x) R1 -0.094 RpR1 (m) -1.09E+01 u(m) 1.38 apR2 0.047 cp2 u1(m) 10.6 (dz/dx) R2 1.386 2 2 (d z/d x) R2 0.1302 RpR2 (m) 0.094 1.1E+01 1.4
0.047 10.6 1.386 0.130 2.850 3.6E-01 1.4E+00 -0.047 10.6 1.386 -0.130 -0.094 -1.1E+01
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 1386 1386 23172 1386 1386 1000 30716
Cable Profile Results in Plan 0.120 0.120 0.282 0.400 0.021 -0.021 0.117 -0.117
30742mm
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 2.382 3.764 26.936 28.318 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 -0.090 -0.180 -0.180 -0.090 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
-0.047 0.047 0.047 -0.047 0.130 0.130 0.130 0.130
(between Anchorages)
28
Cable3
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
= = = = = = =
18K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable A= UTS of Cable Pu = Length of Cable L= Jacking force Po =
= = = = = =
mm µθ+kx) -(µθ µθ
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance Stressing Anchorage
98.7 mm^2 18.737 t 1776.6 mm^2 337 t 30.700m 246 t Px = P0e
from X
Elevation Angle α Cumulative Σ∆α Change in Elevation Angle Ordinate from Soffit Y Ordinate from C/L Z φ Plan Angle Cumulative ∆Σφ Change in Plan Angle Total Change in θ= Angle Force after Friction Loss Px % Loss due to Friction Area of Px diag
(m)
0.000
5.000
8.575
12.863
17.150
(rad)
0.1170
0.0000
0.0000
0.0000
0.0000
(rad)
0.0000
0.1170
0.1170
0.1170
0.1170
(rad) (rad) (rad)
400 0 0.000
120 -180 0.000
120 -180 0.000
120 -180 0.000
120 -180 0.000
(rad)
0.0000
0.2590
0.2590
0.2590
0.2590
(rad) (t)
0.000 245.72 0.00
0.284 231.80 5.67 1193.810
0.284 230.15 6.34 825.739
0.284 228.18 7.14 982.670
0.284 226.24 7.93 974.053
(tm)
Total Area of Px diag
(tm)
Average Cable Force after Friction Loss, P % Average Friction Loss Cable Extension
(t)
Estimation of Slip Losses in
(mm)
3976.272 129.520 47.29% 115
Cable3
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing X (m) Anchorage Force at Null Point (t) 227.05 Nodal Force above Null Point (t) 84.037tm Area of Force Diag above Null Point (tm) Force after Slip Loss ) P (t) % Loss due to Slip Horizontal Force after Slip Loss PH (t) Vertical Force after Slip Loss PV (t)
15.350 m from Anchorage 227.05 t (After Friction Loss by Linear Interpolation) 103.9tm 19.894
= = 0.000
5.000
8.575
12.863
17.150
18.67
4.75 58.536 222 4.10 222.31 0.00
3.10 14.018 224 2.69 223.96 0.00
227.054741 1.13 9.060 226 0.99 225.92 0.00
0.00 2.422 226 0.00 226.24 0.00
208 15.19 206.96 24.33
29
Cable3
Drawing Data Type = 18K 13 Jacking Force = 246 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 337 t 2 Mod. of Elasticity Es = 1.95E+07 t/m Y1(mm) p (mm) = 400 1000 Y2(mm) q(mm) = 282 1382 Y3(mm) r (mm) = 120 1382 Y4(mm) s (mm) = 120 23172 Y5(mm) t (mm) = 282 1382 Y6(mm) u (mm) = 400 1382 a (mm) v (mm) = 1000 1000 b(mm) Z1 (mm) = 2764 0 c(mm) Z2 (mm) = 23172 0 d(mm) Z3 (mm) = 2764 -90 e(mm) Z4 (mm) = 1000 -180
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Elongation = 115 Exit Angle = 6.704 Length = 30742mm Wobble coeff. k = 0.002 Area of Cable = 1776.6 UTS of One Strand = 18.737 t Z5 (mm) -180 Z6 (mm) -90 Z7 (mm) 0 Z8 (mm) 0 rL(m) 24.003 Trans RL1 (m) Trans RL2 (m)
mm Degree per m mm^2
-10.8818 10.9
Cable3 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 400 341 282 244 163 124 120 120 120 120 120 120 120 120 120 120 120 120
(rad) -180 0 0 -6 -86 -172 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180 -180
Elevation Radius (m) inc. straight inc. straight inc. straight 24.003 24.003 24.003 straight straight straight straight straight straight straight straight straight straight straight straight
30
Cable4 Projected Length Cable Type Type of Duct Coeff. of Friction, µ a (mm) b(mm) d(mm) c(mm) e(mm) Y1(mm) Y6(mm) Y3(mm) Y4(mm) Y2(mm) Y5(mm) o θL( ) o θR( ) aL(per m) aR(per m)
= = = =
30700 17K HDPE 0.170
Profile in Elevation 1000 13000 13000 2700 1000 1450 1450 500 500 1323 1323 7.219 -7.219 4.8718E-03 -4.8718E-03
mm 13
Wobble coeff. k Mod. of Elasticity Es Ratio of Jacking force to UTS Slip at Live Anchorage s
(dy/dx)L 0.127 (d2y/dx2)L 0.010 rL (m) 105.111 (dy/dx)R -0.127 (d2y/dx2)R -0.010 Rr (m) -105.111 0.126 θL( rad) -0.126 θR( rad) Length 30700 a1 (mm) 1008 b1(mm) 13035 c1(mm) 2700 d1(mm) 13035 e1(mm) 1008 Le(mm) 30785
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm) Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm)
1000 1382 1382 23172 1382 1382 1000 0 0 0 0 0 0 0 0
q(m) apL1 cp1 q1(m) (dz/dx) L1 (d2z/d2x) L1 RpL1 (m) r(m) apL2 cp2 r1(m) (dz/dx) L2 (d2z/d2x) L2 RpL2 (m) t(m)
Cable Profile Results in Elevation From Live End Xe1(m) Xe2(m) Xe3(m) Xe4(m) Xe5(m) Xe6(m) Y1(m) Y2(m)
0.000 1.000 14.000 16.700 29.700 30.700 1.450 1.323
0.500 0.500 1.323 1.450 0.005 -0.005 0.126 -0.126
30785mm
Estimation of Friction Losses in Cable Type Type of Duct Coeff. of Friction Wobble coeff. Mod. of Elasticity Ratio of Jacking force to UTS Slip at Live Anchorage
µ k Es s
0.0020 per m 1.950E+07 t/m^2 0.729 6 mm
Profile in Plan apR1 1.38 cp2 0.000 t1(m) 19099240.0 (dz/dx) R1 1.382 (d2z/d2x) R1 0.000 0.000 RpR1 (m) -1.91E+07 u(m) 1.38 apR2 0.000 cp2 19099240.0 u1(m) 1.382 (dz/dx) R2 0.0000 (d2z/d2x) R2 RpR2 (m) 0.000 1.9E+07 1.4
0.000 19099240.0 1.382 0.000 0.000 1.9E+07 1.4E+00 0.000 19099240.0 1.382 0.000 0.000 -1.9E+07
p1(mm) q1(mm) r1(mm) s1(mm) t1(mm) u1(mm) v1(mm) LP(mm)
1000 1382 1382 23172 1382 1382 1000 30700
Cable Profile Results in Plan
Y3(m) Y4(m) Y5(m) Y6(m) aL(per m) aR(per m) θL( rad) θR( rad)
Length of Cable4
= = = =
= = = = = = =
From Live End Xp1(m) Xp2(m) Xp3(m) Xp4(m) Xp5(m) Xp6(m) Xp7(m) Xp8(m)
0.000 1.000 2.382 3.764 26.936 28.318 29.700 30.700
zp1(m) zp2(m) zp3(m) zp4(m) zp5(m) zp6(m) zp7(m) zp8(m)
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
apL1 apL2 apR1 apR2 θp1 θp2 θp3 θp4
0.000 0.000 0.000 0.000 0.0000 0.0000 0.0000 0.0000
(between Anchorages)
Cable4 17K HDPE 0.170 0.002 1.95E+07 0.729 6.000
13
per m 2 t/m
Area of one Strand UTS of one Strand Area of Cable UTS of Cable Length of Cable Jacking force
A= Pu = L= Po =
= = = = = =
98.7 mm^2 18.737 t 1677.9 mm^2 319 t 30.700m 232 t
mm
31
At any distance "x", from Live Anchorage, PRESTRESS Force after Friction loss = Distance from Stressing Anchorage Elevation Angle Cumulative Change in Elevation Angle Ordinate from Soffit
Px = P0e
-(µθ µθ+kx) µθ
X
(m)
0.000
5.000
8.575
12.863
17.150
α
(rad)
0.1260
0.0875
0.0528
0.0111
-0.0044
Σ∆α
(rad)
0.0000
0.0385
0.0732
0.1149
0.1304 501
Y
(rad)
1450
895
643
506
Ordinate from C/L
Z
(rad)
0
0
0
0
0
Plan Angle Cumulative Change in Plan TotalAngle Change in
φ
(rad)
0.000
0.000
0.000
0.000
0.000
∆Σφ
(rad)
0.0000
0.0000
0.0000
0.0000
0.0000
Angle Force after Friction Loss
θ= Px
(rad) (t)
0.000 232.07
0.039 228.26
0.073 225.30
0.115 221.80
0.130 219.33
0.00
1.64
2.92
4.43
5.49
1150.833
810.750
958.595
945.566
% Loss due to Friction Area of Px diag
(tm)
Total Area of Px diag Average Cable Force after Friction Loss, P
(tm)
3865.743
(t)
125.920
(mm)
45.74% 118
% Average Friction Loss Cable Extension
Cable4
Estimation of Slip Losses in
Assuming slip travels up to Force at Null point s.Es.A/2 Distance from Stressing Anchorage Force at Null Point (t)
X
(m) 219.73
Nodal Force above Null Point (t) Area of Force Diag above Null Point (tm) Force after Slip Loss ) P % Loss due to Slip Horizontal Force after Slip Loss PH Vertical Force after Slip Loss PV
Cable4 Drawing Data Type = 17K Jacking Force = 232 t Duct = HDPE Coeff. of Friction, µ = 0.170 UTS of Cable = 319 t Mod. of Elasticity Es = 1.95E+07 Y1(mm) Y2(mm) Y3(mm) Y4(mm) Y5(mm) Y6(mm) a (mm) b(mm) c(mm) d(mm) e(mm)
= = = = = = = = = = =
16.448 m from Anchorage 219.73 t (After Friction Loss by Linear Interpolation) 98.2tm 0.000
= =
98.157tm (t) (t) (t)
13
t/m
2
0.000
5.000
8.575
12.863
17.150
-
-
-
219.734878
-
12.34
8.53
5.57
2.07
0.00
207 10.63 205.75 26.06
52.159 211 7.47 210.40 18.45
25.198 214 4.94 213.87 11.30
16.371 218 1.86 217.66 2.41
4.429 219 0.00 219.33 -0.96
Elongation = Exit Angle = Length = Wobble coeff. k = Area of Cable = UTS of One Strand = 1450 1323 500 500 1323 1450 1000 13000 2700 13000 1000
p (mm) q(mm) r (mm) s (mm) t (mm) u (mm) v (mm) Z1 (mm) Z2 (mm) Z3 (mm) Z4 (mm)
118 7.219 30785mm 0.002 1677.9 18.737 t
1000 1382 1382 23172 1382 1382 1000 0.0001 0.0001 0.00005 0
mm Degree per m mm^2
Z5 (mm) Z6 (mm) Z7 (mm) Z8 (mm) rL(m)
0 0.00005 0.0001 0.0001 105.111
Trans RL1 (m) -19099240.0 Trans RL2 (m) 19099240.0
32
Ordinates for Distance from Stressing Anchorage x (m) 0.000 0.500 1.000 1.350 2.350 3.350 4.350 5.350 6.350 7.350 8.350 9.350 10.350 11.350 12.350 13.350 14.350 15.350
Cable4 Distance from Mid Span x (m) 15.350 14.850 14.350 14.000 13.000 12.000 11.000 10.000 9.000 8.000 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0.000
Cable Ordinate Y Z from Soffit from C/L of girder of Girder (rad) 1450 1387 1323 1280 1161 1053 954 865 785 715 656 605 565 534 513 502 500 500
(rad) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Elevation Radius (m) inclined straight inclined straight inclined straight 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 105.111 straight straight
33
Summary of Total Prestress Force at Various Sections Distance from Stressing X (m) Anchorage Horizontal Forces after Slip Loss PH (t) Cable No 1 1Nos Cable No 2 1Nos Cable No 3 1Nos Cable No 4 1Nos Sum PH Vertical Ordinates Y (m) Cable No 1 Cable No 2 Cable No 3 Cable No 4 Ph.Y (tm) Cable No 1 Cable No 2 Cable No 3 Cable No 4 Sum PH.Y Y of CG of Cables (m) Vertical Component of Prestress PV Cable No 1 Cable No 2 Cable No 3 Cable No 4 Prestress Force Cable No 1 Cable No 2 Cable No 3 Cable No 4 Area of Cables As Cable No 1 Cable No 2 Cable No 3 Cable No 4 Ultimate Force Pu Cable No 1 Cable No 2 Cable No 3 Cable No 4 Sum Total Total Total Ordinate of CG of Cables
P
(t) 1Nos 1Nos 1Nos 1Nos Sum PV (t) 1Nos 1Nos 1Nos 1Nos Sum P 2 (mm ) 1Nos 1Nos 1Nos 1Nos Sum As (t) 1Nos 1Nos 1Nos 1Nos 4
P (t) PH (t) PV (t) Pu (t) Y (m) P/Pu
0.000
5.000
8.575
12.863
17.150
205.50 215.00 206.96 205.75 833.21
210.25 222.94 222.31 210.40 865.89
213.79 228.25 223.96 213.87 879.86
217.64 230.25 225.92 217.66 891.47
219.18 230.57 226.24 219.33 895.31
1.100 0.750 0.400 1.450
0.527 0.211 0.120 0.895
0.268 0.120 0.120 0.643
0.126 0.120 0.120 0.506
0.121 0.120 0.120 0.501
226 161 83 298 768 0.922
111 47 27 188 373 0.430
57 27 27 138 249 0.283
28 28 27 110 192 0.216
27 28 27 110 191 0.214
26.85 30.05 24.33 26.06 107.29
19.02 13.41 0.00 18.45 50.87
11.66 0.00 0.00 11.30 22.96
2.49 0.00 0.00 2.41 4.90
-0.99 0.00 0.00 -0.96 -1.95
207 217 208 207 840.12
211 224 222 211 868
214 228 224 214 880
218 230 226 218 891
219 231 226 219 895
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
1678 1777 1777 1678 6909
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
318.529 337.266 337.266 318.529 1312
840.12 833.21 107.29 1311.59 0.922 0.64
868.18 865.89 50.87 1311.59 0.430 0.66
880.48 879.86 22.96 1311.59 0.283 0.67
891.50 891.47 4.90 1311.59 0.216 0.68
895.32 895.31 -1.95 1311.59 0.214 0.68
34
6. PRESTRESS SUMMARY STAGE - 1 SECTION Support 5.00 L 8.58 L 12.86 L 17.150 L
X (m) 1.050 5.000 9.625 13.913 18.200
F (t) 840.1 868.2 880.5 891.5 895.3
CGfrom bot. (m) 0.922 0.430 0.283 0.216 0.214
Fh (t) 833.2 865.9 879.9 891.5 895.3
Fv (t) 107.3 50.9 23.0 4.9 -2.0
35
STRESS CHECK WITH 20% LOSS Item
1
2
3
4
5
Support
End Varying
L/4
3L/8
L/2
m
1.050
5.000
8.575
13.913
18.200
m2 m m m4 m3 m4
1.619 2.400 1.241 0.820 0.707 0.661
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
0.974 2.400 1.221 0.635 0.538 0.520
Area of Composite section Depth of Composite section CG from bottom Inertia of Composite section Zt Zb
m2 m m m4 m3 m4
2.201 2.600 1.574 1.501 1.462 0.954
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
1.556 2.600 1.699 1.233 1.369 0.726
Dead Load Moments 1st Stage
t-m
-55.11
152.05
259.22
344.56
385.16
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.4
640.1 -662.5
715.5 -740.5
Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
Stress at CG of Cable GR1
t/m2
83.4
-292.3
-498.3
-662.4
-740.5
Segment Length Average Stress for Each Segment
m t/m2
3.950 -104.4
3.575 -395.3
5.338 -580.4
4.288 -701.4
0.000 0.0
Average Stress at CG of Cables
t/m2
-462.4
Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
Stress at CG of Cable
t/m2
21.4
-189.2
-382.7
-545.2
-610.9
Segment Length Average Stress for Each Segment
m t/m2
3.950 -83.9
3.575 -286.0
5.338 -464.0
4.288 -578.1
0.000 0.0
Average Stress at CG of Cables
t/m2
-367.9
3.74 865.9 0.430 0.790 -0.441 2.546
3.74 879.9 0.283 0.937 -0.715 2.829
3.74 891.5 0.216 1.005 -0.839 2.959
3.74 895.3 0.214 1.007 -0.844 2.963
Chainage of Section from left support
Unit
Section Property (Beam Only) Area of beam Depth of beam CG from bottom Inertia of beam Zt Zb Section Property (Composite)
Stress due to Dead Load Top Bottom Stress after Eloss
Stress at 21 st day before 1st stage of stressing
Detail of 1st StagePrestressing after 21 days No. of Cables of 19 T 13 Prestressing Force (P2) CG of Cables from Bottom Eccentricity of Cables Prestressing Factor (Top) Prestressing Factor (Bottom)
t m m
3.74 833.2 0.922 0.318 0.167 1.100
36
Elastic Shortening Loss (ELOSS) Eloss of GR2 Cables P2-Eloss
t t
23.2 810.0
23.2 842.6
23.2 856.6
23.2 868.2
23.2 872.1
t/m2 t/m2
135.5 890.7
-371.6 2145.6
-612.1 2423.6
-728.9 2568.7
-735.8 2584.0
Stress due to P2-Eloss(2) Top Bottom
Stress after Stressing Cables Top Bottom
t/m t/m2
2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
Stress at CG of Cable
t/m2
621.9
1504.9
1682.7
1726.8
1677.6
Segment Length Average Stress for Each Segment
m t/m2
3.950 1063.4
3.575 1593.8
5.338 1704.8
4.288 1702.2
0.000 0.0
Increase in Avg. Stress at CG of Cable
t/m2
1533.3
t t
23.2 810.0
23.2 842.6
23.2 856.6
23.2 868.2
23.2 872.1
t/m2 t/m2
135.5 890.7
-371.6 2145.6
-612.1 2423.6
-728.9 2568.7
-735.8 2584.0
Top Bottom
t/m2 t/m2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
Stress at CG of Cable
t/m
2
621.9
1504.9
1682.7
1726.8
1677.6
Segment Length Average Stress for Each Segment
m t/m2
3.950 1063.4
3.575 1593.8
5.338 1704.8
4.288 1702.2
0.000 0.0
Increase in Avg. Stress at CG of Cable
t/m2
1533.3
Elastic Shortening Loss (ELOSS) Eloss of GR2 Cables P2-Eloss Stress due to P2-Eloss(2) Top Bottom
Stress after Stressing Cables
Check for Eloss for cable
t
23.7
Shuttering Load Moments
t-m
0.00
36.63
55.15
68.93
73.53
t/m2 t/m2
0.0 0.0
68.0 -70.4
102.4 -106.0
128.1 -132.5
136.6 -141.4
0.5*$C$144*(ecable/econc21)*(nocable2-1)/2*acable*ifeloss
0.5
Stress due to Shuttering (for deck slab casting) Top Bottom
37
Losses From 21st day to 28th day Creep loss of Cable Shrinkage loss of Cable =(shr21-shr28)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
Total Loss (C+S+R)
t t
11.0 0.6
11.0 0.6
11.0 0.6
11.0 0.6
11.0 0.6
t
11.1 0.618
13.4
14.4
15.3
15.5
t
22.7
25.0
26.0
26.8
27.1
t/m2 t/m2
-3.8 -24.9
11.0 -63.6
18.5 -73.4
22.5 -79.2
22.8 -80.2
2
53.7 949.2
-10.1 1719.3
-9.5 1745.8
61.8 1694.5
139.1 1622.0
Stress due to (C+S+R) Top Bottom Stress at 28 th day before casting of deck slab Top Bottom
t/m 2 t/m
Stress at CG of Cable
t/m
2
605.09
1409.15
1538.69
1547.64
1489.99
Segment Length Average Stress for Each Segment
m 2 t/m
3.950 1007.1
3.575 1473.9
5.338 1543.2
4.288 1518.8
0.000 0.0
Average Stress at CG of Cable
t/m2
1399.2
Check for Creep loss of Cable
t
11.4
t-m
0.00
120.56
182.85
231.25
250.99
t/m2 t/m2
0.0 0.0
224.0 -231.8
339.7 -351.5
429.6 -444.6
466.3 -482.5
Dead Load Moments due to Deck Slab
0.4 (creep21-creep28)*ifcreep*nocable2*acable*C190*ecable/1000
Stress due to Deck load moments Top Bottom
Stress after casting of deck slab Top Bottom
t/m2 t/m2
53.7 949.2
213.8 1487.5
330.1 1394.3
491.4 1249.9
605.4 1139.4
t/m2 t/m2 t/m2
0.0 0.0 0.0
-26.8 -20.8 50.5
-40.3 -31.3 76.0
-50.4 -39.2 95.0
-53.7 -41.8 101.3
-5.1 -4.0 9.7
-6.5 -5.1 12.3
-7.1 -5.5 13.3
Stress due to release of Shuttering Load Top of Deck Top of Girder Bottom of Girder
Stress release due to hardening of solid slab i.e density reduces from 2.6 to 2.5 t/m3 Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 2 t/m
0.0 0.0 0.0
-3.4 -2.6 6.4
38
Stress after release of Shuttering Load & hardening of deck slab t/m2 t/m2 t/m2
0.0 53.7 949.2
-30.1 190.4 1544.3
-45.4 294.8 1479.9
-56.8 447.2 1357.2
-60.8 558.1 1254.0
Creep loss of Cable Shrinkage loss of Cable =(shr28-shr56)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
t t
8.2 3.0
8.2 3.0
8.2 3.0
8.2 3.0
8.2 3.0
t
6.0 0.33
7.3
7.8
8.2
8.4
Total Loss (C+S+R)
t
17.2
18.5
19.0
19.4
19.6
0.009 1.137
-0.284 2.391
-0.392 2.594
-0.441 2.687
-0.442 2.690
t/m2 t/m2 t/m2
-0.2 -1.6 -19.6
5.2 1.4 -44.1
7.4 3.1 -49.3
8.6 3.9 -52.2
8.7 3.9 -52.7
Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
Stress at CG of Cable
t/m2
592.41
1265.60
1297.03
1228.13
1144.47
Segment Length Average Stress for Each Segment
m t/m2
3.950 929.0
3.575 1281.3
5.338 1262.6
4.288 1186.3
0.000 0.0
Top of Deck Top of Girder Bottom of Girder Losses from 28 to 56 day
Prestressing Factor (after Composite action) Cable Top Bottom
Stress due to (C+S+R) Top of Deck Top of Girder Bottom of Girder Stress at 56th day before laying SIDL
Average Stress at CG of Cable
t/m2
1170.6
Check for Creep loss of Cable
t
8.4
0.1
Stress after Shift of bearings Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
t-m
34.00
89.00
164.80
205.30
219.00
t/m2 t/m2 t/m2
23.3 18.7 -35.7
65.0 50.6 -122.6
120.4 93.6 -227.1
150.0 116.7 -282.9
160.0 124.4 -301.8
SIDL applied at 56th day Moments due to SIDL Stress due to SIDL Top of Deck Top of Girder Bottom of Girder
39
t/m2
-13.02
-88.99
-186.10
-243.96
-260.69
Creep loss of Cable Shrinkage loss of Cable =(shr56-shr_infinity)*nocable2*acable*ecable*ifshr Relaxation loss of Cable Relaxation Factor
t t
18.9 28.2
18.9 28.2
18.9 28.2
18.9 28.2
18.9 28.2
t
36.9 2.048
44.6 47.8 =2+1-0.334-0.62
50.6
51.5
Total Loss (C+S+R)
t
84.0
91.7
94.9
97.7
98.6
t/m2 t/m2 t/m2
-0.7 -8.0 -95.5
26.0 7.2 -219.2
37.2 15.4 -246.3
43.1 19.6 -262.4
43.6 19.9 -265.2
Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
22.4 62.8 798.4
66.2 249.6 1158.4
119.6 406.9 957.3
144.7 587.3 759.6
151.5 706.3 634.4
Stress at CG of Cable
t/m2
500.21
962.53
858.45
704.30
591.44
Segment Length Average Stress for Each Segment
m t/m2
3.950 731.4
3.575 910.5
5.338 781.4
4.288 647.9
0.000 0.0
Average Stress at CG of Cable
t/m2
763.4
Stress at CG of Cable Losses from 56th day to Infinity
Stress due to (C+S+R) Top of Deck Top of Girder Bottom of Girder Stress during Service at Infinity
Check for Creep loss of Cable
t
21.2
2.4
Moment due to Live Load
t-m
6.4
169.6
306.3
376.3
400.7
Stress Due to Live Load Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
4.4 3.5 -6.7
123.9 96.4 -233.7
223.7 174.1 -422.1
274.9 213.8 -518.6
292.7 227.7 -552.1
t/m2 t/m2 t/m2
26.7 66.3 791.7
190.0 345.9 924.7
343.3 581.0 535.2
419.6 801.1 241.0
444.1 934.0 82.3
t m t/m2 t/m2 t/m2
83.95 0.93 -52.91 80.95 -43.41
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
83.95 0.80 -41.16 92.16 -38.67
302.1 673.1 496.5
378.4 893.3 202.4
403.0 1026.2 43.6
Stress at Service with Live Load Top of Deck Top of Girder Bottom of Girder Stress due to Differential Shrinkage & Creep Force Eccentricity Top of Deck Slab Top of Girder Bottom
Stress after Differential Shrinkage & Creep (at service condition with Live Load) Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-26.2 147.3 748.3
148.8 438.1 886.1
40
SUMMARY OF SHORT-TERM LOSSES 1st Stage Prestressing Loss due to Friction & Slip Loss due to Elastic shortening % Loss due to Friction & Slip Total Loss
t t t
159.0 23.2 15.9 182.2
130.9 23.2 13.1 154.2
118.6 23.2 11.9 141.9
107.6 23.2 10.8 130.9
103.8 23.2 10.4 127.0
SUMMARY OF LONG-TERM LOSSES 1st Stage Prestressing Loss due to Creep Loss due to Shrinkage Loss due to Relaxation of Steel Total Loss (C+S+R) % Loss in terms of applied Force (After Friction & Slip)
t t t t
38.1 31.7 54.0 123.8 14.7
38.1 31.7 65.3 135.1 15.6
38.1 31.7 70.1 139.9 15.9
38.1 31.7 74.1 143.9 16.1
38.1 31.7 75.4 145.2 16.2
Total (C+S+R)
t
123.8
135.1
139.9
143.9
145.2
14.7
15.6
15.9
16.1
16.2
% Loss in terms of applied Force (After Friction & Slip) SUMMARY OF LONG-TERM+SHORT TERM LOSSES Total Loss in 1st Stage % Loss in terms of Jacking Force
t
306.1 30.6
289.3 29.0
281.8 28.2
274.7 27.5
272.2 27.2
Total Loss % Loss in terms of Jacking Force
t
306.1 30.6
289.2 29.0
281.8 28.2
274.7 27.5
272.2 27.2
41
STRESS SUMMARY Item Section
Unit m
1
2
3
4
5
Support
End Varying
L/4
3L/8
L/2
1.050
5.000
9.625
13.913
18.200
Permissible stress t/m2
Stress at 21 st day before 1nd stage of stressing Top Bottom
t/m2 t/m2
-77.9 83.4
282.5 -292.3
481.5 -498.3
640.1 -662.4
715.5 -740.5
> <
-229.4 2293.6
OK OK
t/m2 t/m2
57.5 974.1
-89.2 1853.3
-130.5 1925.3
-88.8 1906.3
-20.3 1843.5
> <
-229.4 2293.6
OK OK
Stress after Stressing GR1 Cables Top Bottom
Stress at 28 th day before casting of deck slab Top Bottom
t/m2 t/m2
53.7 949.2
-10.1 1719.3
-9.5 1745.8
61.8 1694.5
139.1 1622.0
> <
-229.4 2293.6
OK OK
t/m2 t/m2
53.7 949.2
213.8 1487.5
330.1 1394.3
491.4 1249.9
605.4 1139.4
> <
-229.4 2293.6
OK OK
t/m2 t/m2 t/m2
-0.2 52.1 929.6
-24.9 191.8 1500.2
-38.0 297.9 1430.7
-48.3 451.0 1304.9
-52.1 562.0 1201.4
> > <
-305.4 -229.4 2293.6
OK OK OK
t/m2 t/m2 t/m2
22.4 62.8 798.4
66.2 249.6 1158.4
119.6 406.9 957.3
144.7 587.3 759.6
151.5 706.3 634.4
> > <
-305.4 0 1529.1
OK OK OK
t/m2 t/m2 t/m2
26.7 66.3 791.7
190.0 345.9 924.7
343.3 581.0 535.2
419.6 801.1 241.0
444.1 934.0 82.3
> > <
-305.4 0 1529.1
OK OK OK
403.0 1026.2 43.6
> > <
-305.4 0 1529.1
OK OK OK
Stress after casting of deck slab Top Bottom
Stress at 56th day before laying SIDL Top of Deck Top of Girder Bottom of Girder Stress during Service at Infinity Top of Deck Top of Girder Bottom of Girder Stress at Service with Live Load Top of Deck Top of Girder Bottom of Girder
Stress after Differential Shrinkage & Creep (at service condition with Live Load) Top of Deck Top of Girder Bottom of Girder
t/m2 t/m2 t/m2
-26.2 147.3 748.3
148.8 438.1 886.1
302.1 673.1 496.5
378.4 893.3 202.4
42
Shrinkage Model Shrinkage Model
(Microstrain)
Total shrinkage strain
(Refer Cl: 6.4.2.6 of IRC; 112-2011)
εcs
=
+
εcd
=
Drying Shrinkage Strain
εca
=
Autogenious Shrinkage strain
εcd
Basic Drying Shrinkage Strain
εca
(Refer Annexure A2.6 of IRC; 112-2011)
fcmo
=
is the mean compressive strength (Mpa)
fcm
=
12.5 Mpa
=
is the co-efficient which depends on the type of cement
=
4 for Normal cement
=
is the co-efficient which depends on the type of cement
=
0.12 for Normal cement
αds1 αds2
RH
=
is the ambient relative humidity (Percent)
RH0
=
100 percent
=
0.88627
Residual Shrinkage Strain
( upto 7 days)
0.000206
0.000203
0.000203
0.000203
0.000203
Residual Shrinkage Strain
( upto 14 days)
0.000198
0.000195
0.000195
0.000195
0.000195
Residual Shrinkage Strain
( upto 21 days)
0.000193
0.000190
0.000190
0.000190
0.000190
Residual Shrinkage Strain
( upto 28 days)
0.000190
0.000187
0.000187
0.000187
0.000187
Residual Shrinkage Strain
( upto 42 days)
0.000182
0.000176
0.000176
0.000176
0.000176
Residual Shrinkage Strain
( upto 56 days)
0.000178
0.000173
0.000173
0.000173
0.000173
Differential Shrinkage Strain
( upto 7 days)
0.000030
0.000033
0.000033
0.000033
0.000033
Differential Shrinkage Strain
( upto 14 days)
0.000038
0.000041
0.000041
0.000041
0.000041
Differential Shrinkage Strain
( upto 21 days)
0.000043
0.000046
0.000046
0.000046
0.000046
Differential Shrinkage Strain
( upto 28 days)
0.000046
0.000049
0.000049
0.000049
0.000049
Differential Shrinkage Strain
( upto 42 days)
0.000055
0.000060
0.000060
0.000060
0.000060
Differential Shrinkage Strain
( upto 56 days)
0.000058
0.000063
0.000063
0.000063
0.000063
Differential Shrinkage Strain
( upto Infinity days)
0.000236
0.000238
0.000238
0.000238
0.000238
43
Ac
Concrete cross sectional area Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At 7 days
Age of concrete in days at the time considered t End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
0.0
0.0
0.0
0.0
0.0
7.0
7.0
7.0
7.0
7.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.41089
0.41089
0.41089
0.41089
0.41089
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000027
0.000027
0.000027
0.000027
0.000027
Total shrinkage strain ε cd = ε ca+ ε cd
0.000030
0.000033
0.000033
0.000033
0.000033
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
7.0
7.0
7.0
7.0
7.0
14.0
14.0
14.0
14.0
14.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.52684
0.52684
0.52684
0.52684
0.52684
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000034
0.000034
0.000034
0.000034
0.000034
Total shrinkage strain ε cd = ε ca+ ε cd
0.000038
0.000041
0.000041
0.000041
0.000041
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
Concrete cross sectional area
from table 6.7of IRC:112-2011
Ac
kh
Age of concrete in days at the time considered t At 14 days
1.56
Autogenous shrinkage strain ε ca
Perimeter of that part of the cross-section which is exposed to drying u Notional size (mm) of the cros-section h 0 = 2A c /u
End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)] Autogenous shrinkage strain ε ca
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011 At 21 days
2.20
kh
0.70
0.70
0.70
0.70
0.70
Age of concrete in days at the time considered t
14.0
14.0
14.0
14.0
14.0
(t s )
21.0
21.0
21.0
21.0
21.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.60009
0.60009
0.60009
0.60009
0.60009
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000039
0.000039
0.000039
0.000039
0.000039
Total shrinkage strain ε cd = ε ca+ ε cd
0.000043
0.000046
0.000046
0.000046
0.000046
End of curing in days Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
44
Ac
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
Age of concrete in days at the time considered t
21.0
21.0
21.0
21.0
21.0
(t s )
28.0
28.0
28.0
28.0
28.0
0.021
0.038
0.038
0.038
0.038
3.734E-06
6.66E-06
6.66E-06
6.66E-06
6.66E-06
0.65295
0.65295
0.65295
0.65295
0.65295
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000042
0.000042
0.000042
0.000042
0.000042
Total shrinkage strain ε cd = ε ca+ ε cd
0.000046
0.000049
0.000049
0.000049
0.000049
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
28.0
28.0
28.0
28.0
28.0
42.0
42.0
42.0
42.0
42.0
0.042
0.073
0.073
0.073
0.073
7.312E-06
1.28E-05
1.28E-05
1.28E-05
1.28E-05
0.72642
0.72642
0.72642
0.72642
0.72642
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000047
0.000047
0.000047
0.000047
0.000047
Total shrinkage strain ε cd = ε ca+ ε cd
0.000055
0.000060
0.000060
0.000060
0.000060
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
Notional size (mm) of the cros-section h 0 = 2A c /u
400.9
269.5
269.5
269.5
269.5
from table 6.7of IRC:112-2011
0.70
0.70
0.70
0.70
0.70
42.0
42.0
42.0
42.0
42.0
56.0
56.0
56.0
56.0
56.0
0.042
0.073
0.073
0.073
0.073
7.312E-06
1.28E-05
1.28E-05
1.28E-05
1.28E-05
0.77612
0.77612
0.77612
0.77612
0.77612
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000050
0.000050
0.000050
0.000050
0.000050
Total shrinkage strain ε cd = ε ca+ ε cd
0.000058
0.000063
0.000063
0.000063
0.000063
Concrete cross sectional area Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u
At 28 days
from table 6.7of IRC:112-2011
End of curing in days
kh
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At 42days
Age of concrete in days at the time considered t End of curing in days
(t s )
β ds (t,ts) = (t-
Co-efficient for drying shrinkage strain t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd
β as(t,ts)
Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)] Autogenous shrinkage strain ε ca
Concrete cross sectional area
Ac
Perimeter of that part of the cross-section u to drying
which is exposed
kh
At 56 days
Age of concrete in days at the time considered t End of curing in days
(t s )
Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
45
Ac
2.20
1.56
1.56
1.56
1.56
10.98
11.55
11.55
11.55
11.55
400.9
269.5
269.5
269.5
269.5
0.70
0.70
0.70
0.70
0.70
56.0
56.0
56.0
56.0
56.0
14056.0
14056.0
14056.0
14056.0
14056.0
0.978
0.988
0.988
0.988
0.988
0.0001711
0.000173
0.000173
0.000173
0.000173
1.00000
1.00000
1.00000
1.00000
1.00000
Autogenous shrinkage strain ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Autogenous shrinkage strain ε ca = β as(t,ts) + ε ca
0.000065
0.000065
0.000065
0.000065
0.000065
Total shrinkage strain ε cd = ε ca+ ε cd
0.000236
0.000238
0.000238
0.000238
0.000238
Concrete cross sectional area
Perimeter of that part of the cross-section which is exposed to drying u Notional size (mm) of the cros-section h 0 = 2A c /u from table 6.7of IRC:112-2011
kh
At Infinity
Age of concrete in days at the time considered t End of curing in days
(t s )
Co-efficient for drying shrinkage strain
β ds (t,ts) = (t-
t s ) / [(t-t s )+0.04*sqrt(h 0 3 )] Drying Shrinkage strain ε cd = β ds (t,ts) .Kh. ε cd Co-efficient for autogenous shrinkage strain =1-exp[-0.2*sqrt(t)]
β as(t,ts)
46
Creep Strain Creep strain of concrete where φ σc Ec
= = = =
φ x σc/Ec creep coefficient (calculated as per IRC-112) constant Compressive stress applied to the concrete at time t Modulus of Elasticity of concrete
Compressive stress at CG of the tendons at transfer stage Compressive stress at CG of the tendons after application of SIDL Comp stress at CG of the tendons after application of LL (losses upto infinity) Modulus of Elasticity of Concrete
= = = =
7.073 5.888 3.846 34000
N/mm2 N/mm2 N/mm2 N/mm2
Calculation of Creep Coefficient The development of creep with time may be taken as β (t,to) x φ (inf,to) φ (t,to) = where β (t,to) ((t - to)/(β H+(t-to)))^0.3 = t is the age of the concrete in days at the time considered to is the age of the concrete in days at time of loading=21 days (t - to) is the actual duration of loading in days βH is a coefficient depending on the relative humidity ( RH in percent) and the notional member size (ho in mm). βH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 <= 1500 for fcm <=45 βH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 α<= 1500α for fcm >=45 fcm = 55 α = SQRT(45/fcm) =0.904534034 Grade of concrete β H f (inf,to) b (t,to)
=
f (t,to)
=
Creep Creep Creep Creep
Strain Strain Strain Strain
for
at at at at
21 28 56 infinity
21 28 56 90 28 56 90
days days days days days days days
= = = = = = = = = = = =
1.500 0.0000 0.2386 0.3589 0.3796 0.3579 0.5384 0.5695 0.000000 0.000050 0.000093 0.000170
47
Check For Ultimate Moment b
ηfcd
εcu3 εcsu1 x
Fc
λx
h d2 d1
As2 As1
Fs2
εs2 εs1
Section Schematic
Strain
Stress-Strain Relationship of concrete at ULS:
Fs1 Stress
Considering Rectangular stress block
εc3
0.0018
0.0018
Compression strain at peak stress for rectangular Stress distribution
εcu3
0.0035
0.0035
Ultimate compression strsin for rectangular stress distribution
η
1.00
1.00
Co-efficient to convert to rectangular stress block
λ
0.80
0.80
Co-efficient to convert to rectangular stress block
0.67
0.67
Co-efficient to convert the strength in the test to strength in structural member
1.00
1.00
αc
fcd
Co-efficient to convert to rectangular stress block 2
20.1
20.1
N/mm
Co-efficient to convert to rectangular stress block
25.125
25.125
N/mm2
Co-efficient to convert to rectangular stress block
48
Section under considaration
Sec 1-1
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
1. Ultimate Applied Moment, Mu (KNm)
-343
9072
15728
19791
21387
2. Overall Depth, D (m)
2.600
2.600
2.600
2.600
2.600
3. Cg of Cable from sofit, Yord (m)
0.922
0.430
0.283
0.216
0.214
71
71
71
71
71
9.9E-05
9.9E-05
9.9E-05
9.9E-05
9.9E-05
6. Area of Section (m )
2.20
1.56
1.56
1.56
1.56
7. Effective depth , d
1.678
2.170
2.317
2.384
2.386
8.Effective flange width , Bf (m)
3.00
3.00
3.00
3.00
3.00
9.Effective Flange thickness, t (m)
0.200
0.200
0.200
0.200
0.200
10.Width of web, b (m)
0.650
0.300
0.300
0.300
0.300
11.Ultimate force per Cable (KN)
183.9
183.9
183.9
183.9
183.9
12.Ultimate tensile strength of steel , fpu (Mpa)
1863.7
1863.7
1863.7
1863.7
1863.7
13.Prestressing Force after all Loss (Kn)
6930.56
7098.63
7173.54
7243.80
7268.74
175.26
175.26
175.26
175.26
175.26
16.Total Compression, C (KN)
11357
11357
11357
11357
11357
17. Initial Prestress, fpe (Mpa)
989
1013
1024
1034
1037
18. Initial strain in tendon
0.0051
0.0052
0.0052
0.0053
0.0053
19. Strain due to bending in tendon
0.030
0.040
0.043
0.044
0.044
20. Total strain in tendon
0.0351
0.0450
0.0480
0.0494
0.0495
21. fpu/1.15 (MPa)
1620.6
1620.6
1620.6
1620.6
1620.6
22.Corresponding Strain
0.013
0.013
0.013
0.013
0.013
23. 0.9*fpu/1.15 (MPa)
1458.5
1458.5
1458.5
1458.5
1458.5
24.Corresponding Strain
0.007
0.007
0.007
0.007
0.007
Ultimate Design Flexural Moment MEd
4. No of Cable Strands 2
5. Area of each Strand (m ) 2
14.Ultimate Flexural Capacity 15. Assume neutral axis from compression flange, X (mm)
1620.6
1620.6
1620.6
1620.6
1620.6
2
26. Area of Steel , As (m )
0.007
0.007
0.007
0.007
0.007
27. Total Tension, T (KN)
11357
11357
11357
11357
11357
28. T-C
0
0
0
0
0
29. CG of Compression Zone from compressive flange (mm)
88
88
88
88
88
30. Z (mm)
1590
2082.0
2229.2
2296.5
2298.8
31. Flexural Capacity, Mu =T*Z (KNm)
18059
23645
25317
26080
26107
OK
OK
OK
OK
OK
25. Fb (Mpa)
Status
49
Check for Ultimate Shear Shear Corresponding to Maximum Moment Grade of Concrete
45
Mpa
Grade of Steel
500
Mpa
fcd
45.00
Mpa
fyk
435
Mpa
fywd
348
Mpa
Section COMPONENT
Sec 1-1
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
UNIT
Ultimate Shear Capacity of Section uncracked in Flexure (Cl. 10.3.2 of IRC 112-2011) Ult. Applied Shear Force, Vult
KN
2046.9
1567.0
1290.8
653.5
319.8
Overall Width, bw
m
0.650
0.300
0.300
0.300
0.300
Overall Depth, h
m
2.600
2.600
2.600
2.600
2.600
0.513
0.513
0.513
0.513
0.513
19503
9001
9001
9001
9001
OK
OK
OK
OK
OK
v =0.6[1-(fck/310)] Max Shear Check VEd <=0.5bw d ν fcd
KN
Area of Section
m2
2.201
1.556
1.556
1.556
1.556
Horizontal Component of prestress after all losses
KN
6930.6
7098.6
7173.5
7243.8
7268.7
Cg of cable from sofit, Yord
m
0.922
0.430
0.283
0.216
0.214
Comp. Stress due to prestress, σcp
Mpa
3.148
4.563
4.611
4.656
4.672
Effect of Vertical Prestress, Vpr
KN
-1072.9
-508.7
-229.6
-49.0
19.5
Second Moment of Area, I
m4
1.501
1.233
1.233
1.233
1.233
First Moment of Area b/w Centroidal and Extreme Comression fibre about centroidal axis, S
m
3
1.462
1.369
1.369
1.369
1.369
Vrdc = SQRT((fctd)^2+fctd.σcp).I.bw/s
KN
31051
12762
12768
12774
12776
50
51
Provision of Shear Reinforcement (Cl. 10.3.3.2 of IRC 112-2011) Ultimate Applied Shear, VEd
kN
2047
1567
1291
653
320
Design Shear Capacity, Vc
kN
1011
786
834
858
861
Vertical component of Prestress
kN
-1073
-509
-230
-49
20
Net VEd
kN
3120
2076
1520
702
300
No
No
No
Yes
Yes
Shear R/f Required
Shear R/f Required
Shear R/f Required
Minimum R/f
Minimum R/f
3119.8
2075.8
1520.4
0.0
0.0
αcw
1.070
1.101
1.102
1.103
1.104
ν1
0.60
0.60
0.60
0.60
0.60
Is VEd less than Vc ? Reqirement of shear reinforcement VEd
KN
Shear Reinforcement :-
2
i) Aswmax / S = 0.5*bw*αcw*ν1*fcd/(fywd)
mm /m
27.0
12.8
12.8
12.8
12.9
ii) 0.072 x (SQRT(fck))/fyk
mm2/m
25.3
15.1
16.1
16.6
16.6
Governing Shear reinforcement
mm /m
2
27.0
15.1
16.1
16.6
16.6
Shear RF Due to ultimate loads, Asv/Sv = VEd/(z*fywd)
mm /m
2
5346
2751
1887
0
0
Design Shear Reinforcement/web
mm /m
2
2673
1375
943
8
8
Spacing
125
125
150
200
200
Bar Dia
16
12
12
12
12
1608
905
754
565
565
OK
OK
OK
OK
OK
Reinforcement provided
52
Check for Ultimate Shear 2 Maximum Shear & Corresponding Moment Grade of Concrete
45
Mpa
Grade of Steel
500
Mpa
fcd
45.00
Mpa
fyk
435
Mpa
fywd
348
Mpa
Section
Sec 1-1
COMPONENT
Sec 2-2
Sec 3 - 3
Sec 4 - 4
Sec 5 - 5
UNIT
Ultimate Shear Capacity of Section uncracked in Flexure (Cl. 10.3.2 of IRC 112-2011) Ult. Applied Shear Force, Vult
KN
2112.0
1659.3
1237.1
774.9
367.5
Overall Width, bw
m
0.650
0.300
0.300
0.300
0.300
Overall Depth, h
m
2.600
2.600
2.600
2.600
2.600
0.513
0.513
0.513
0.513
0.513
19503
9001
9001
9001
9001
OK
OK
OK
OK
OK
2.201
1.556
1.556
1.556
1.556
v =0.6[1-(fck/310)] Max Shear Check VEd <=0.5bw d ν fcd
KN
2
Area of Section
m
Horizontal Component of prestress after all losses
KN
6930.6
7098.6
7173.5
7243.8
7268.7
Cg of cable from sofit, Yord
m
0.922
0.430
0.283
0.216
0.214
Mpa
3.148
4.563
4.611
4.656
4.672
KN
Comp. Stress due to prestress, σcp Effect of Vertical Prestress, Vpr
-1072.9
-508.7
-229.6
-49.0
19.5
1.501
1.233
1.233
1.233
1.233
Second Moment of Area, I
m
4
First Moment of Area b/w Centroidal and Extreme Comression fibre about centroidal axis, S
m
3
1.462
1.369
1.369
1.369
1.369
KN
31051
12762
12768
12774
12776
^2
Vrdc = SQRT((fctd) +fctd.σcp).I.bw/s
53
Provision of Shear Reinforcement (Cl. 10.3.3.2 of IRC 112-2011) Ultimate Applied Shear, VEd
kN
2112
1659
1237
775
367
Design Shear Capacity, Vc
kN
1011
786
834
858
861
Vertical component of Prestress
kN
-1073
-509
-230
-49
20
Net VEd
kN
3185
2168
1467
824
348
No
No
No
Yes
Yes
Shear R/f Required
Shear R/f Required
Shear R/f Required
Minimum R/f
Minimum R/f
3184.9
2168.1
1466.7
0.0
0.0
αcw
1.070
1.101
1.102
1.103
1.104
ν1
0.60
0.60
0.60
0.60
0.60
2
27.0
12.8
12.8
12.8
12.9
2
25.3
15.1
16.1
16.6
16.6
2
27.0
15.1
16.1
16.6
16.6
2
5458
2873
1820
0
0
2
2729
1436
910
8
8
Spacing
125
125
125
200
200
Bar Dia
16
12
10
10
10
1608
905
628
393
393
OK
OK
OK
OK
OK
Is VEd less than Vc ? Reqirement of shear reinforcement VEd
KN
Shear Reinforcement :-
i) Aswmax / S = 0.5*bw*αcw*ν1*fcd/(fywd)
mm /m
ii) 0.072 x (SQRT(fck))/fyk
mm /m
Governing Shear reinforcement
mm /m
Shear RF Due to ultimate loads, Asv/Sv = VEd/(z*fywd)
mm /m
Design Shear Reinforcement/web
mm /m
Reinforcement provided
54
10. TEMPERATURE As per sec. Fig.10 of IRC : 6 - 2010, for the combination of loads with diffferential temperature gradient effects, maximum 50% live load shall be considered . Effect of Temperature Rise F
=
EC α ∆t A
= = = =
EC α ∆t Α 2
3.35E+06 t/m 0 1.20E-05 / C Temperature differential X - sectional Area Where temp. differential is ∆t
TEMPERATURE GRADIENT ( FOR CONCRETE SUPERSTRUCTURE ) ( Refer IRC : 6 - 2010 ; clause 218.3 )
AT MID-SPAN POSITIVE TEMP. DIFFERENCES
17.8 8.60
1 150
1.61
2
4.0
250
3
0
150 0
4 2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
4
2.910 0.200 0.582 0.100 0.058 0.006 8.600 5.006 0.501
1.000 0.199 0.199 0.299 0.060 0.018 1.61 0.320 0.096
0.300 1.805 0.542 1.301 0.705 0.917 0.000 0.000 0.000
0.650 0.396 0.258 2.402 0.618 1.486 0.000 0.000 0.000
TOTAL
1.580 1.441 2.426 5.326 0.596
55
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
12.922 0.859 3.833 2.076
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000824
=
0.0000460
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 17.800 2.1E-04 -440.1
0.200 9.2E-06 3.200 3.8E-05 116.7
0.399 1.8E-05 0.000 0.0E+00 214.8
2.204 1.0E-04 0.000 0.0E+00 -63.5
2.600 1.2E-04 2.100 2.5E-05 -209.2
m m 0 c t/m2
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
151.5 706.3 634.4
+ + +
146.3 113.8 -276.1
-440.1
+ + +
-440.1 116.7 -209.2
= = =
297.8
-142.3 936.9 149.2
t/m2 t/m2 t/m2
-142.3 0.026 Point of zero stress
116.7
214.8
820.2
+
936.9
=
-63.5
-209.2
358.4
Consider 1 mt strip Area of steel required
=
1/2 x
= Provide
10
φ
@
149.2
250
0.7 mm/m
0.026 2.4 2 cm /m =
x
142.279 1.15
3.1
cm /m
x
2
OK
56
AT SUPPORT POSITIVE TEMP. DIFFERENCES
17.8 8.60
1 150
1.22
2
4.0
250
3
0
150
2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
2.910 0.200 0.582 0.100 0.058 0.0058 8.60 5.006 0.501
1.000 0.247 0.247 0.324 0.080 0.0259 1.22 0.302 0.098
0.650 2.153 1.399 1.524 2.132 3.2483 0.00 0.000 0.000
TOTAL
2.229 2.270 3.280 5.308 0.598
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
17.411 1.358 7.310 5.154
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000893
=
0.0000597
Calculation of Eigen Stress
Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 17.800 2.1E-04 -416.8
0.200 1.2E-05 3.200 3.8E-05 130.9
0.447 2.7E-05 0.000 0.0E+00 210.2
2.600 m 1.6E-04 m 2.100 0c 2.5E-05 2 -305.0 t/m
57
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
22.4 62.8 798.4
+ + +
2.2 1.8 -3.4
-416.8
+ + +
-416.8 130.9 -305.0
24.6
= = =
-392.2 195.4 490.0
t/m2 t/m2 t/m2
-392.2 Point of zero stress 64.6
0.133 195.4
130.9 210.2
+
=
-305.0
795.1
Consider 1 mt strip Area of steel required
=
1/2 x
= Provide
16 φ
@
490.0
150
0.133 x 392.201 2.4 x 1.15 2 9.5 cm /m 2 mm/m = 13.4 cm /m OK
58
TEMPERATURE As per sec. Fig.10 of IRC : 6 - 2010, for the combination of loads with diffferential temperature gradient effects, maximum 50% live load shall be considered . Effect of Temperature Fall F
=
EC α ∆t A
= = = =
EC α ∆t Α 2
3.35E+06 t/m 0 1.20E-05 / C Temperature differential X - sectional Area Where temp. differential is ∆t
TEMPERATURE GRADIENT ( FOR CONCRETE SUPERSTRUCTURE ) ( Refer IRC : 6 - 2000 ; clause 218.3 )
AT MID-SPAN REVERSE TEMP. DIFFERENCES
10.6 6.64
1 250 0.7
2
0.53
3
0
200
h
200 0.8 250
1.07
4 2.1
Temperature Fall case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
1
2
3
4
2.910 0.200 0.582 0.100 0.058 0.0058 6.64 3.865 0.387
1.000 0.199 0.199 0.299 0.060 0.0178 0.53 0.105 0.031
0.300 1.805 0.542 1.301 0.705 0.9170 0.00 0.000 0.000
0.650 0.396 0.258 2.402 0.618 1.4856 1.07 0.276 0.662
TOTAL
1.580 1.441 2.426 4.245 1.080
59
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T)
P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
10.300 1.556 3.833 2.076
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
=
0.0000597
=
0.0000301
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 10.600 1.3E-04 -226.3
0.200 6.0E-06 2.680 3.2E-05 72.2
0.399 1.2E-05 0.179 2.2E-06 152.8
2.204 6.6E-05 0.215 2.6E-06 -31.1
m m 0 c
2.600 7.8E-05 2.100 2.5E-05 -147.0
t/m2
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top of Deck = Top of Girder = Bottom =
151.5 706.3 634.4
+ + +
146.3 113.8 -276.1
-226.3
+ + +
-226.3 72.2 -147.0
= = =
297.8
71.5 892.4 211.4
t/m2 t/m2 t/m2
71.5 0.000 Point of zero stress
72.2
152.8
820.2
892.4
+
=
-31.1 -147.0 358.4
Consider 1 mt strip Area of steel required
Provide
10
φ
@
211.4
=
1/2 x
=
0.0 mm/m
250
0.000 2.4 2 cm /m =
x x 3.1
71.503 1.15 2
cm /m
OK
60
AT SUPPORT
REVERSE TEMP. DIFFERENCES
10.6 6.64
1 250
0.44
2
0.7
200
3
0
200 0.8 250 2.1
Temperature Rise case
Element No. Width Height Area Y A*Y A*Y^2 T A*T A*T*Y
TOTAL
1
2
3
2.910 0.200 0.582 0.100 0.058 0.0058 6.64 3.865 0.387
1.000 0.247 0.247 0.324 0.080 0.0259 0.44 0.109 0.035
0.650 2.153 1.399 1.524 2.132 3.2483 0.00 0.000 0.000
2.229 2.270 3.280 3.974 0.422
As per Dr. V. K . Raina's book ''Concrete Bridge Practice Analysis ,Design and Economics'' Chapter 30.
εo Sum(A) - θ X Sum(A*T) = α * Sum( A*T) εo Sum(A*Y) - θ X Sum(A*Y^2) = α * Sum( A*Y*T) P1 P2 P3 P4
= Sum(A*T) * Sum(A*Y^2) = Sum(A*Y*T) * Sum(A*Y) = Sum(A) * Sum(A*Y^2) = (Sum(A*Y))^2
= = = =
Extreme Fibre Strain (εo) = α * (P1 - P2) / (P3 -P4) θ
(εo*Sum (A) - α * Sum (A*T)) / Sum(A*Y)
13.036 0.958 7.310 5.154
12.078 2.156
=
0.0000672
=
0.0000450
Calculation of Eigen Stress Y Yxθ T αxT Fej =Ec x (εo -Yθ-α x T)
0.000 0.0E+00 10.600 1.3E-04 -275.7
0.200 9.0E-06 2.680 3.2E-05 12.8
0.447 2.0E-05 0.000 0.0E+00 83.4
2.600 m 1.2E-04 m 2.100 0c 2.5E-05 2 -326.0 t/m
61
Check for Stresses For checking of stresses with thermal effects only 50% Live load will be considered And Permissible stresses increased by 15% Clause : 3.2.1 of IRC :SP 33C Clause: 202.3 of IRC:6-1966 Top Deck = Top Girder = Bottom =
22.4 62.8 798.4
+ + +
-275.7
2.2 1.8 -3.4
+ + +
-275.7 12.8 -326.0
24.6
= = =
83.4
64.6
=
-326.0
795.1
=
16
φ
@
469.1
1/2 x
= Provide
0.153 77.4
+
Consider 1 mt strip Area of steel required
t/m2 t/m2 t/m2
-251.2 Point of zero stress
12.8
-251.2 77.4 469.1
150
7.0 mm/m
0.153 2.4 2 cm /m =
x x 13.4
251.2 1.15 2
cm /m
OK
62
11. END CROSS GIRDER B.0 Design of End Cross Girder at Temporary Lifting Condition / Jack up condition The end cross girder is designed as a continuous deep beam for bearing replacement condition, continuous over knife supports at the jack locations. The CL of jacks are taken to be 1061 mm from the CL of main girder. The reaction of main girder due to (DL+SIDL) are applied as load at the girder location as shown below.
-120.00 Mton
-110.00 Mton
-105.00 Mton
1.06m
2.12m
127.32 MTon-m
0 MTon-m
-120.00 Mton
127.32 MTon-m 20.83 MTon-m
14.41 MTon-m
-38.08 MTon-m
15.00 MTon-m
21.45 MTon-m
0 MTon-m
-40.13 MTon-m
63
BASIC DESIGN DATA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Distance between C/C Exp. Joint Effective span Overhang of girder off the bearing Overhang of slab off the bearing Expansion Joint Deck Width Angle of skew Clear carriage way Width of outer railing Width of Footpath Width of Crash Barrier Spacing of main girder c/c Spacing of cross girder c/c Thk of deck slab Thk of deck slab at overhang Length of cantilever Cantilever slab thk at fixed end Cantilever slab thk at free end Thk of wearing coat No of main girder Width of footh path Width of raillings Top Flange width of girder No of Intermediate cross girder Grade of concrete Grade of reinforcement Shape Factor λ strength Factor η
Leff
Ang Bcw
Wkerb Spmg Spcg Df Lcan Dcan1 Dcan2 Wc Nomg
bf Nocg Cgrade Sgrade
26.52 23.32 1.050 1.600 40.0 12.0 45.00 11.50 0.30 0.00 0.50 3.00 11.66 0.20 0.40 1.50 0.21 0.21 0.075 4 0.00 0.00 1.000 1.00 M35 Fe 500
m m m m mm m deg. m m m m m m m m m m m Nos
m Mpa Mpa
λ
0.80
IRC-112-Anexure A2- A2.9(2)
η
1.00
IRC-112-Anexure A2- A2.9(2)
28
Partial factor of safety (Basic and seismic)
ɣc
1.50
IRC-112-Cl 6.4.2.8
29
Partial factor of safety Accidental Coefficient to consider the influence of the strength
ɣc
1.20
IRC-112-Cl 6.4.2.8
α
0.67
fcd
40.00
Mpa
fcd
15.63 40.0 2.40 2.60 2.200 1.00 0.30 0.50 35 500 1.15 1 32000
Mpa mm t/m3 t/m3 t/m^3 t/m t/m t/m2 Mpa Mpa
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Design value of concrete comp strength for Basic and seismic Design value of concrete comp strength for Accidental Clear cover Unit weight of dry concrete Unit weight of wet concrete Unit Weight of wearing course Weight of Crash Barrier Weight of Railing Intensity of Load for shuttering Stress in concrete (compression) Stress in steel (tension) Partial factor of safety for basic and seismic
Partial factor of safety for Accidental
cov wcon wwc wrail
fck fyk γs γs
Ecm Es Modular ratio
200000.00
m
IRC-112 Fig 6.3 (Note) IRC-112 Fig 6.3 (Note) Mpa Mpa
6.250
64
Live Load calculations as per Effective Width Method The live load intensity on deck slab is calculated based on effective width method as given in Annexure-B.3 of IRC-112. The dispersion along span of deck slab is ignored, this is a safer side assumption as concentrated load produce worst effect than udl. C/C Spacing of Girder
=
3.000
m
Total Width of Deck
=
12.00
m
Cantilever length
=
1.500
m
Number of support
=
4.000
m
b/lo
=
3.887
α (Constant)
=
2.600
(Cont.)
Thickness of wearing coat
=
75.00
mm
Thickness of deck slab
=
200.00
mm
1Lane Class - A
TRANSVERSE ANALYSIS 1 FOR LIVE LOAD
Load on Wheel-1
=
57
kN
Load on Wheel-2
=
57
kN
Contact width across span
=
250
mm
Contact width along span
=
500
mm
Distance between two vehicle c/c of wheels (Traffic Direction)
=
1.200
m
Distance between two Wheels C/C (Transverse direction)
=
1.800
m
Minimum edge distance upto c/l of wheel
=
0.400
m
b1
=
0.400
m
initial position of first wheel
=
0.900
m
Final position of first wheel
=
9.300
m
Number of load generation
=
58
Transverse increament of Wheels
=
0.1448
Impact factor
=
1.5
Nos m
65
Wheel-1 Load Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Dist. of Position Nearest (X) Support 0.9 1.0448 1.1897 1.3345 1.4793 1.6241 1.769 1.9138 2.0586 2.2034 2.3483 2.4931 2.6379 2.7828 2.9276 3.0724 3.2172 3.3621 3.5069 3.6517 3.7966 3.9414 4.0862 4.231 4.3759 4.5207 4.6655 4.8103 4.9552 5.1 5.2448 5.3897 5.5345 5.6793 5.8241 5.969 6.1138 6.2586 6.4034 6.5483 6.6931 6.8379 6.9828 7.1276 7.2724 7.4172 7.5621 7.7069 7.8517 7.9966 8.1414 8.2862 8.431 8.5759 8.7207 8.8655 9.0103 9.1552 9.3
0.60 0.46 0.31 0.17 0.02 0.12 0.27 0.41 0.56 0.70 0.85 0.99 1.14 1.28 1.43 1.43 1.28 1.14 0.99 0.85 0.70 0.56 0.41 0.27 0.12 0.02 0.17 0.31 0.46 0.60 0.74 0.89 1.03 1.18 1.32 1.47 1.39 1.24 1.10 0.95 0.81 0.66 0.52 0.37 0.23 0.08 0.06 0.21 0.35 0.50 0.64 0.79 0.93 1.08 1.22 1.37 1.49 1.34 1.20
Wheel-2
beff
beff (mod)
P with Impact (kN)
1.12 0.95 0.77 0.60 0.42 0.71 1.04 1.33 1.58 1.80 1.98 2.13 2.24 2.31 2.35 2.35 2.31 2.24 2.13 1.98 1.80 1.58 1.33 1.04 0.71 0.45 0.81 1.12 1.40 1.65 1.86 2.03 2.16 2.26 2.32 2.35 2.34 2.29 2.21 2.09 1.93 1.74 1.51 1.25 0.95 0.61 0.56 0.90 1.21 1.48 1.71 1.91 2.07 2.19 2.28 2.33 2.35 2.33 2.27
1.12 0.95 0.77 0.60 0.42 0.71 1.04 1.26 1.39 1.50 1.59 1.66 1.72 1.75 1.77 1.77 1.75 1.72 1.66 1.59 1.50 1.39 1.26 1.04 0.71 0.45 0.81 1.12 1.30 1.42 1.53 1.61 1.68 1.73 1.76 1.77 1.77 1.75 1.70 1.64 1.57 1.47 1.36 1.22 0.95 0.61 0.56 0.90 1.20 1.34 1.46 1.55 1.63 1.70 1.74 1.77 1.77 1.76 1.74
76.34 90.36 110.69 142.83 201.26 120.52 82.48 67.66 61.47 57.00 53.74 51.39 49.76 48.73 48.23 48.23 48.73 49.76 51.39 53.74 57.00 61.47 67.66 82.48 120.52 188.57 106.00 76.11 65.67 60.04 55.96 52.99 50.86 49.41 48.54 48.18 48.32 48.97 50.16 51.98 54.57 58.13 63.03 69.85 90.30 140.34 153.21 94.91 71.03 63.87 58.74 55.01 52.30 50.38 49.10 48.38 48.17 48.45 49.25
Dist. of Position Nearest (X) Support 2.70 2.84 2.99 3.13 3.28 3.42 3.57 3.71 3.86 4.00 4.15 4.29 4.44 4.58 4.73 4.87 5.02 5.16 5.31 5.45 5.60 5.74 5.89 6.03 6.18 6.32 6.47 6.61 6.76 6.90 7.04 7.19 7.33 7.48 7.62 7.77 7.91 8.06 8.20 8.35 8.49 8.64 8.78 8.93 9.07 9.22 9.36 9.51 9.65 9.80 9.94 10.09 10.23 10.38 10.52 10.67 10.81 10.96 11.10
1.20 1.34 1.49 1.37 1.22 1.08 0.93 0.79 0.64 0.50 0.35 0.21 0.06 0.08 0.23 0.37 0.52 0.66 0.81 0.95 1.10 1.24 1.39 1.47 1.32 1.18 1.03 0.89 0.74 0.60 0.46 0.31 0.17 0.02 0.12 0.27 0.41 0.56 0.70 0.85 0.99 1.14 1.28 1.43 1.43 1.28 1.14 0.99 0.85 0.70 0.56 0.41 0.27 0.12 0.02 0.17 0.31 0.46 0.60
beff
beff (mod)
P with Impact (kN)
2.27 2.33 2.35 2.33 2.28 2.19 2.07 1.91 1.71 1.48 1.21 0.90 0.56 0.61 0.95 1.25 1.51 1.74 1.93 2.09 2.21 2.29 2.34 2.35 2.32 2.26 2.16 2.03 1.86 1.65 1.40 1.12 0.81 0.45 0.71 1.04 1.33 1.58 1.80 1.98 2.13 2.24 2.31 2.35 2.35 2.31 2.24 2.13 1.98 1.80 1.58 1.33 1.04 0.71 0.42 0.60 0.77 0.95 1.12
1.74 1.76 1.77 1.77 1.74 1.70 1.63 1.55 1.46 1.34 1.20 0.90 0.56 0.61 0.95 1.22 1.36 1.47 1.57 1.64 1.70 1.75 1.77 1.77 1.76 1.73 1.68 1.61 1.53 1.42 1.30 1.12 0.81 0.45 0.71 1.04 1.26 1.39 1.50 1.59 1.66 1.72 1.75 1.77 1.77 1.75 1.72 1.66 1.59 1.50 1.39 1.26 1.04 0.71 0.42 0.60 0.77 0.95 1.12
49.3 48.5 48.2 48.4 49.1 50.4 52.3 55.0 58.7 63.9 71.0 94.9 153.2 140.3 90.3 69.9 63.0 58.1 54.6 52.0 50.2 49.0 48.3 48.2 48.5 49.4 50.9 53.0 56.0 60.0 65.7 76.1 106.0 188.6 120.5 82.5 67.7 61.5 57.0 53.7 51.4 49.8 48.7 48.2 48.2 48.7 49.8 51.4 53.7 57.0 61.5 67.7 82.5 120.5 201.3 142.8 110.7 90.4 76.3
66
2Lane Class - A
TRANSVERSE ANALYSIS 2 FOR LIVE LOAD
Load on Wheel-1
=
57.000
kN
Load on Wheel-2
=
57.000
kN
Load on Wheel-3
=
57.000
kN
Load on Wheel-4
=
57.000
kN
Distance Between Two vehicle C/C of wheel (Traffic direction)
=
1.700
m
Distance between two Wheels C/C (Transverse direction)
=
1.800
m
initial position of first wheel( Wheel 1)
=
0.900
m
Final position of first wheel( Wheel 1)
=
5.800
m
Number of load generation
=
40
Transverse increament of Wheels
=
0.1225
nos m
67
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 38 39 40 41
0.9 1.0225 1.145 1.2675 1.39 1.5125 1.635 1.7575 1.88 2.0025 2.125 2.2475 2.37 2.4925 2.615 2.7375 2.86 2.9825 3.105 3.2275 3.35 3.4725 3.595 3.7175 3.84 3.9625 4.085 4.4525 4.575 4.6975 4.82 4.9425 5.065 5.1875 5.31 5.4325 5.555 5.6775 5.8
Dist. of Nearest Support 0.60 0.48 0.36 0.23 0.11 0.01 0.14 0.26 0.38 0.50 0.63 0.75 0.87 0.99 1.12 1.24 1.36 1.48 1.40 1.27 1.15 1.03 0.90 0.78 0.66 0.54 0.41 0.05 0.07 0.20 0.32 0.44 0.56 0.69 0.81 0.93 1.06 1.18 1.30
Wheel-2
beff
beff (mod)
1.12 0.97 0.83 0.68 0.53 0.43 0.74 1.01 1.26 1.49 1.69 1.86 2.01 2.13 2.22 2.29 2.33 2.35 2.34 2.31 2.24 2.16 2.04 1.90 1.74 1.55 1.33 0.52 0.59 0.88 1.14 1.38 1.59 1.78 1.94 2.07 2.18 2.26 2.32
1.12 0.97 0.83 0.68 0.53 0.43 0.74 1.01 1.23 1.34 1.44 1.53 1.60 1.66 1.71 1.75 1.77 1.77 1.77 1.75 1.72 1.68 1.62 1.55 1.47 1.37 1.26 0.52 0.59 0.88 1.14 1.29 1.40 1.49 1.57 1.64 1.69 1.73 1.76
P with Dist. of Impact Position Nearest (kN) Support 76.34 2.700 1.20 87.87 2.823 1.32 103.51 2.945 1.45 125.92 3.068 1.43 160.71 3.190 1.31 197.75 3.313 1.19 116.29 3.435 1.07 84.48 3.558 0.94 69.43 3.680 0.82 63.62 3.803 0.70 59.24 3.925 0.57 55.90 4.048 0.45 53.34 4.170 0.33 51.40 4.293 0.21 49.98 4.415 0.08 48.99 4.538 0.04 48.40 4.660 0.16 48.17 4.783 0.28 48.30 4.905 0.41 48.79 5.028 0.53 49.65 5.150 0.65 50.95 5.273 0.77 52.73 5.395 0.90 55.09 5.518 1.02 58.19 5.640 1.14 62.25 5.763 1.26 67.60 5.885 1.39 163.94 6.253 1.25 144.88 6.375 1.13 97.19 6.498 1.00 74.79 6.620 0.88 66.26 6.743 0.76 61.24 6.865 0.64 57.42 6.988 0.51 54.50 7.110 0.39 52.28 7.233 0.27 50.62 7.355 0.15 49.42 7.478 0.02 48.64 7.600 0.10
Wheel-3
beff
beff (mod)
2.27 2.32 2.35 2.35 2.32 2.27 2.19 2.08 1.95 1.79 1.61 1.40 1.16 0.90 0.61 0.50 0.79 1.07 1.31 1.53 1.72 1.89 2.03 2.15 2.24 2.30 2.34 2.29 2.23 2.14 2.02 1.87 1.70 1.50 1.28 1.03 0.76 0.46 0.65
1.74 1.76 1.77 1.77 1.76 1.73 1.69 1.64 1.57 1.50 1.40 1.30 1.16 0.90 0.61 0.50 0.79 1.07 1.26 1.37 1.46 1.55 1.62 1.67 1.72 1.75 1.77 1.75 1.71 1.67 1.61 1.54 1.45 1.35 1.24 1.03 0.76 0.46 0.65
P with Dist. of Impact Position Nearest (kN) Support 49.25 4.400 0.10 48.54 4.523 0.02 48.20 4.645 0.15 48.22 4.768 0.27 48.60 4.890 0.39 49.35 5.013 0.51 50.50 5.135 0.64 52.12 5.258 0.76 54.30 5.380 0.88 57.16 5.503 1.00 60.89 5.625 1.13 65.79 5.748 1.25 73.48 5.870 1.37 94.77 5.993 1.49 139.08 6.115 1.39 172.28 6.238 1.26 107.71 6.360 1.14 80.26 6.483 1.02 68.10 6.605 0.89 62.63 6.728 0.77 58.48 6.850 0.65 55.32 6.973 0.53 52.90 7.095 0.40 51.07 7.218 0.28 49.74 7.340 0.16 48.84 7.463 0.04 48.33 7.585 0.09 48.93 7.953 0.45 49.88 8.075 0.57 51.27 8.198 0.70 53.16 8.320 0.82 55.66 8.443 0.94 58.93 8.565 1.07 63.22 8.688 1.19 68.89 8.810 1.31 82.73 8.933 1.43 112.68 9.055 1.45 186.66 9.177 1.32 131.27 9.300 1.20
Wheel-4
beff
beff (mod)
0.65 0.46 0.76 1.03 1.28 1.50 1.70 1.87 2.02 2.14 2.23 2.29 2.34 2.35 2.34 2.30 2.24 2.15 2.03 1.89 1.72 1.53 1.31 1.07 0.79 0.50 0.61 1.40 1.61 1.79 1.95 2.08 2.19 2.27 2.32 2.35 2.35 2.32 2.27
0.65 0.46 0.76 1.03 1.24 1.35 1.45 1.54 1.61 1.67 1.71 1.75 1.77 1.77 1.77 1.75 1.72 1.67 1.62 1.55 1.46 1.37 1.26 1.07 0.79 0.50 0.61 1.30 1.40 1.50 1.57 1.64 1.69 1.73 1.76 1.77 1.77 1.76 1.74
P with Dist. of Impact Position Nearest (kN) Support 131.27 6.200 1.30 186.66 6.323 1.18 112.68 6.445 1.06 82.73 6.568 0.93 68.89 6.690 0.81 63.22 6.813 0.69 58.93 6.935 0.57 55.66 7.058 0.44 53.16 7.180 0.32 51.27 7.303 0.20 49.88 7.425 0.07 48.93 7.548 0.05 48.37 7.670 0.17 48.17 7.793 0.29 48.33 7.915 0.42 48.84 8.038 0.54 49.74 8.160 0.66 51.07 8.283 0.78 52.90 8.405 0.91 55.32 8.528 1.03 58.48 8.650 1.15 62.63 8.773 1.27 68.10 8.895 1.40 80.26 9.018 1.48 107.71 9.140 1.36 172.28 9.263 1.24 139.08 9.385 1.12 65.79 9.753 0.75 60.89 9.875 0.63 57.16 9.998 0.50 54.30 10.120 0.38 52.12 10.243 0.26 50.50 10.365 0.14 49.35 10.488 0.01 48.60 10.610 0.11 48.22 10.733 0.23 48.20 10.855 0.35 48.54 10.978 0.48 49.25 11.100 0.60
beff
beff (mod)
2.32 2.26 2.18 2.07 1.94 1.78 1.59 1.38 1.14 0.88 0.59 0.52 0.82 1.09 1.33 1.55 1.74 1.90 2.04 2.16 2.24 2.31 2.34 2.35 2.33 2.29 2.22 1.86 1.69 1.49 1.26 1.01 0.74 0.43 0.53 0.68 0.83 0.97 1.12
1.76 1.73 1.69 1.64 1.57 1.49 1.40 1.29 1.14 0.88 0.59 0.52 0.82 1.09 1.26 1.37 1.47 1.55 1.62 1.68 1.72 1.75 1.77 1.77 1.77 1.75 1.71 1.53 1.44 1.34 1.23 1.01 0.74 0.43 0.53 0.68 0.83 0.97 1.12
P with Impact (kN) 48.64 49.42 50.62 52.28 54.50 57.42 61.24 66.26 74.79 97.19 144.88 163.94 104.66 78.70 67.60 62.25 58.19 55.09 52.73 50.95 49.65 48.79 48.30 48.17 48.40 48.99 49.98 55.90 59.24 63.62 69.43 84.48 116.29 197.75 160.71 125.92 103.51 87.87 76.34
68
1Lane 40T Boggie (L-Type)
TRANSVERSE ANALYSIS 3 FOR LIVE LOAD
Load on Wheel-1
=
100
kN kN
Max. load on a wheel
=
100
Max. tyre pressure
=
5.273
Contact width along span
=
810
Distance between two loads across span = Distances between C/C of wheel Across the traffic Impact factor
1.22 5.273
Load on Wheel-2
=
100
kg/cm2
Contact area
=
1896.5
cm2
mm
Contact width across span
=
234.1
mm
m
1.93
=
0.384
m
=
1.93
=
1.25
Initial position of first wheel
=
2.13
m
Final Position of first wheel
=
7.940
m
Transverse increament
=
0.1162
m
kN
m
69
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
2.13 2.2462 2.3624 2.4786 2.5948 2.711 2.8272 2.9434 3.0596 3.1758 3.292 3.4082 3.5244 3.6406 3.7568 3.873 3.9892 4.1054 4.2216 4.3378 4.454 4.5702 4.6864 4.8026 4.9188 5.035 5.1512 5.2674 5.3836 5.4998 5.616 5.7322 5.8484 5.9646 6.0808 6.197 6.3132 6.4294 6.5456 6.6618 6.778 6.8942 7.0104 7.1266 7.2428 7.359 7.4752 7.5914 7.7076 7.8238 7.94
Dist. of Nearest Support 0.63 0.75 0.86 0.98 1.09 1.21 1.33 1.44 1.44 1.32 1.21 1.09 0.98 0.86 0.74 0.63 0.51 0.39 0.28 0.16 0.05 0.07 0.19 0.30 0.42 0.54 0.65 0.77 0.88 1.00 1.12 1.23 1.35 1.46 1.42 1.30 1.19 1.07 0.95 0.84 0.72 0.61 0.49 0.37 0.26 0.14 0.02 0.09 0.21 0.32 0.44
Wheel-2
beff
beff (mod)
1.68 1.84 1.98 2.10 2.19 2.26 2.31 2.33 2.33 2.31 2.26 2.19 2.10 1.98 1.84 1.67 1.49 1.28 1.04 0.78 0.50 0.56 0.84 1.09 1.32 1.53 1.71 1.87 2.00 2.12 2.21 2.27 2.31 2.33 2.33 2.30 2.25 2.17 2.08 1.95 1.81 1.64 1.45 1.23 1.00 0.73 0.45 0.61 0.89 1.14 1.36
1.45 1.53 1.60 1.66 1.71 1.74 1.76 1.78 1.78 1.76 1.74 1.70 1.66 1.60 1.53 1.45 1.35 1.25 1.04 0.78 0.50 0.56 0.84 1.09 1.27 1.37 1.46 1.54 1.61 1.67 1.71 1.75 1.77 1.78 1.77 1.76 1.73 1.70 1.65 1.59 1.51 1.43 1.33 1.23 1.00 0.73 0.45 0.61 0.89 1.14 1.29
P with Dist. of Impact Position Nearest (kN) Support 86.26 4.06 0.44 81.65 4.1762 0.32 78.08 4.2924 0.21 75.33 4.4086 0.09 73.27 4.5248 0.02 71.80 4.641 0.14 70.86 4.7572 0.26 70.40 4.8734 0.37 70.40 4.9896 0.49 70.87 5.1058 0.61 71.83 5.222 0.72 73.32 5.3382 0.84 75.40 5.4544 0.95 78.16 5.5706 1.07 81.76 5.6868 1.19 86.40 5.803 1.30 92.38 5.9192 1.42 100.19 6.0354 1.46 120.10 6.1516 1.35 159.63 6.2678 1.23 249.06 6.384 1.12 222.27 6.5002 1.00 149.05 6.6164 0.88 114.52 6.7326 0.77 98.39 6.8488 0.65 91.01 6.965 0.53 85.33 7.0812 0.42 80.93 7.1974 0.30 77.52 7.3136 0.19 74.91 7.4298 0.07 72.96 7.546 0.05 71.59 7.6622 0.16 70.74 7.7784 0.28 70.36 7.8946 0.39 70.45 8.0108 0.51 71.01 8.127 0.63 72.06 8.2432 0.74 73.65 8.3594 0.86 75.85 8.4756 0.98 78.75 8.5918 1.09 82.52 8.708 1.21 87.38 8.8242 1.32 93.66 8.9404 1.44 101.87 9.0566 1.44 125.56 9.1728 1.33 170.42 9.289 1.21 278.97 9.4052 1.09 203.41 9.5214 0.98 141.00 9.6376 0.86 110.12 9.7538 0.75 96.89 9.87 0.63
beff
beff (mod)
1.36 1.14 0.89 0.61 0.45 0.73 1.00 1.23 1.45 1.64 1.81 1.95 2.08 2.17 2.25 2.30 2.33 2.33 2.31 2.27 2.21 2.12 2.00 1.87 1.71 1.53 1.32 1.09 0.84 0.56 0.50 0.78 1.04 1.28 1.49 1.67 1.84 1.98 2.10 2.19 2.26 2.31 2.33 2.33 2.31 2.26 2.19 2.10 1.98 1.84 1.68
1.29 1.14 0.89 0.61 0.45 0.73 1.00 1.23 1.33 1.43 1.51 1.59 1.65 1.70 1.73 1.76 1.77 1.78 1.77 1.75 1.71 1.67 1.61 1.54 1.46 1.37 1.27 1.09 0.84 0.56 0.50 0.78 1.04 1.25 1.35 1.45 1.53 1.60 1.66 1.70 1.74 1.76 1.78 1.78 1.76 1.74 1.71 1.66 1.60 1.53 1.45
P with Impact (kN) 96.89 110.12 141.00 203.41 278.97 170.42 125.56 101.87 93.66 87.38 82.52 78.75 75.85 73.65 72.06 71.01 70.45 70.36 70.74 71.59 72.96 74.91 77.52 80.93 85.33 91.01 98.39 114.52 149.05 222.27 249.06 159.63 120.10 100.19 92.38 86.40 81.76 78.16 75.40 73.32 71.83 70.87 70.40 70.40 70.86 71.80 73.27 75.33 78.08 81.65 86.26
70
1Lane 40T Boggie (M-Type)
TRANSVERSE ANALYSIS 4 FOR LIVE LOAD
Load on Wheel-1
=
50
kN
Load on Wheel-2
=
50
kN
Load on Wheel-3
=
50
kN
Load on Wheel-4
=
50
kN
kg/cm2
Contact area
=
948.2
cm2
mm
Contact width across span
=
263
mm
m
b1
=
0.413
Max. load on a wheel
=
50
Max. tyre pressure
=
5.273
kN
Contact width along span
=
360
Distance between two loads across span
=
0.79
Impact factor
=
1.25
Initial Position of first wheel
=
1.905
m
Final position of first wheel
=
7.715
m
No of Load generation
=
50
Transverse increament
=
0.1162
m
m
71
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Wheel-2
beff
beff (mod)
1.905 2.0212 2.1374 2.2536 2.3698 2.486 2.6022 2.7184 2.8346 2.9508 3.067 3.1832 3.2994 3.4156 3.5318 3.648 3.7642 3.8804 3.9966 4.1128 4.229 4.3452 4.4614 4.5776 4.6938 4.81 4.9262 5.0424 5.1586
Dist. of Nearest Support 0.41 0.52 0.64 0.75 0.87 0.99 1.10 1.22 1.33 1.45 1.43 1.32 1.20 1.08 0.97 0.85 0.74 0.62 0.50 0.39 0.27 0.15 0.04 0.08 0.19 0.31 0.43 0.54 0.66
1.32 1.53 1.72 1.88 2.02 2.13 2.23 2.29 2.34 2.36 2.36 2.33 2.29 2.21 2.12 2.00 1.86 1.69 1.50 1.29 1.05 0.80 0.51 0.61 0.88 1.14 1.36 1.57 1.75
1.06 1.16 1.25 1.34 1.40 1.46 1.51 1.54 1.56 1.58 1.57 1.56 1.54 1.50 1.45 1.39 1.32 1.24 1.15 1.04 0.92 0.79 0.51 0.61 0.84 0.96 1.08 1.18 1.27
30 31
5.2748 5.391
0.77 0.89
1.91 2.04
1.35 1.42
46.34 44.14
6.0698 6.186
32
5.5072
1.01
2.15
1.47
42.47
33
5.6234
1.12
2.24
1.52
41.25
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
5.7396 5.8558 5.972 6.0882 6.2044 6.3206 6.4368 6.553 6.6692 6.7854 6.9016 7.0178 7.134 7.2502 7.3664 7.4826 7.5988 7.715
1.24 1.36 1.47 1.41 1.30 1.18 1.06 0.95 0.83 0.71 0.60 0.48 0.37 0.25 0.13 0.02 0.10 0.22
2.30 2.35 2.36 2.36 2.33 2.27 2.20 2.10 1.98 1.83 1.66 1.47 1.25 1.01 0.75 0.46 0.66 0.93
1.55 1.57 1.58 1.57 1.56 1.53 1.49 1.44 1.38 1.31 1.22 1.13 1.02 0.90 0.75 0.46 0.66 0.86
40.39 39.87 39.65 39.72 40.10 40.79 41.83 43.28 45.20 47.73 51.04 55.42 61.31 69.49 83.86 136.35 94.44 72.58
P with Dist. of Impact Position Nearest (kN) Support 59.12 2.7 1.20 53.81 2.8162 1.32 49.83 2.9324 1.43 46.81 3.0486 1.45 44.50 3.1648 1.34 42.74 3.281 1.22 41.44 3.3972 1.10 40.52 3.5134 0.99 39.94 3.6296 0.87 39.67 3.7458 0.75 39.69 3.862 0.64 40.01 3.9782 0.52 40.64 4.0944 0.41 41.62 4.2106 0.29 42.98 4.3268 0.17 44.81 4.443 0.06 47.22 4.5592 0.06 50.37 4.6754 0.18 54.52 4.7916 0.29 60.09 4.9078 0.41 67.77 5.024 0.52 78.86 5.1402 0.64 121.96 5.2564 0.76 102.47 5.3726 0.87 74.64 5.4888 0.99 64.90 5.605 1.11 58.03 5.7212 1.22 53.00 5.8374 1.34 49.22 5.9536 1.45
Wheel-3 P with Dist. of Impact Position Nearest (kN) Support 40.65 3.49 1.01 40.01 3.6062 0.89 39.69 3.7224 0.78 39.67 3.8386 0.66 39.94 3.9548 0.55 40.52 4.071 0.43 41.44 4.1872 0.31 42.74 4.3034 0.20 44.49 4.4196 0.08 46.79 4.5358 0.04 49.81 4.652 0.15 53.78 4.7682 0.27 59.09 4.8844 0.38 66.37 5.0006 0.50 76.79 5.1168 0.62 111.85 5.233 0.73 110.76 5.3492 0.85 76.56 5.4654 0.97 66.21 5.5816 1.08 58.97 5.6978 1.20 53.70 5.814 1.31 49.75 5.9302 1.43 46.74 6.0464 1.45 44.45 6.1626 1.34 42.71 6.2788 1.22 41.42 6.395 1.11 40.51 6.5112 0.99 39.93 6.6274 0.87 39.66 6.7436 0.76
beff
beff (mod)
2.29 2.33 2.36 2.36 2.34 2.29 2.23 2.13 2.02 1.88 1.72 1.53 1.33 1.09 0.84 0.56 0.56 0.84 1.10 1.33 1.54 1.72 1.88 2.02 2.14 2.23 2.30 2.34 2.36
1.54 1.56 1.57 1.58 1.56 1.54 1.51 1.46 1.40 1.34 1.25 1.16 1.06 0.94 0.81 0.56 0.56 0.82 0.94 1.06 1.16 1.26 1.34 1.41 1.46 1.51 1.54 1.57 1.58
1.43 1.31
2.36 2.33
1.57 1.56
39.69 40.02
6.8598 6.976
6.3022
1.20
2.28
1.54
40.66
6.4184
1.08
2.21
1.50
41.64
6.5346 6.6508 6.767 6.8832 6.9994 7.1156 7.2318 7.348 7.4642 7.5804 7.6966 7.8128 7.929 8.0452 8.1614 8.2776 8.3938 8.51
0.97 0.85 0.73 0.62 0.50 0.38 0.27 0.15 0.04 0.08 0.20 0.31 0.43 0.55 0.66 0.78 0.89 1.01
2.12 2.00 1.85 1.69 1.50 1.28 1.05 0.79 0.51 0.62 0.89 1.14 1.37 1.57 1.75 1.91 2.04 2.16
1.45 1.39 1.32 1.24 1.14 1.04 0.92 0.79 0.51 0.62 0.84 0.97 1.08 1.18 1.27 1.35 1.42 1.47
43.02 44.86 47.28 50.46 54.64 60.25 67.99 79.26 123.67 101.32 74.36 64.70 57.89 52.89 49.14 46.28 44.09 42.44
Wheel-4 P with Dist. of Impact Position Nearest (kN) Support 42.44 4.285 0.22 44.09 4.4012 0.10 46.28 4.5174 0.02 49.14 4.6336 0.13 52.89 4.7498 0.25 57.89 4.866 0.37 64.70 4.9822 0.48 74.36 5.0984 0.60 101.32 5.2146 0.71 123.67 5.3308 0.83 79.26 5.447 0.95 67.99 5.5632 1.06 60.25 5.6794 1.18 54.64 5.7956 1.30 50.46 5.9118 1.41 47.28 6.028 1.47 44.86 6.1442 1.36 43.02 6.2604 1.24 41.64 6.3766 1.12 40.66 6.4928 1.01 40.02 6.609 0.89 39.69 6.7252 0.77 39.66 6.8414 0.66 39.93 6.9576 0.54 40.51 7.0738 0.43 41.42 7.19 0.31 42.71 7.3062 0.19 44.45 7.4224 0.08 46.74 7.5386 0.04
beff
beff (mod)
0.93 0.66 0.46 0.75 1.01 1.25 1.47 1.66 1.83 1.98 2.10 2.20 2.27 2.33 2.36 2.36 2.35 2.30 2.24 2.15 2.04 1.91 1.75 1.57 1.36 1.14 0.88 0.61 0.51
0.86 0.66 0.46 0.75 0.90 1.02 1.13 1.22 1.31 1.38 1.44 1.49 1.53 1.56 1.57 1.58 1.57 1.55 1.52 1.47 1.42 1.35 1.27 1.18 1.08 0.96 0.84 0.61 0.51
P with Impact (kN) 72.58 94.44 136.35 83.86 69.49 61.31 55.42 51.04 47.73 45.20 43.28 41.83 40.79 40.10 39.72 39.65 39.87 40.39 41.25 42.47 44.14 46.34 49.22 53.00 58.03 64.90 74.64 102.47 121.96
0.15 0.27
0.80 1.05
0.79 0.92
78.86 67.77
7.8872
0.39
1.29
1.04
60.09
8.0034
0.50
1.50
1.15
54.52
8.1196 8.2358 8.352 8.4682 8.5844 8.7006 8.8168 8.933 9.0492 9.1654 9.2816 9.3978 9.514 9.6302 9.7464 9.8626 9.9788 10.095
0.62 0.74 0.85 0.97 1.08 1.20 1.32 1.43 1.45 1.33 1.22 1.10 0.99 0.87 0.75 0.64 0.52 0.40
1.69 1.86 2.00 2.12 2.21 2.29 2.33 2.36 2.36 2.34 2.29 2.23 2.13 2.02 1.88 1.72 1.53 1.32
1.24 1.32 1.39 1.45 1.50 1.54 1.56 1.57 1.58 1.56 1.54 1.51 1.46 1.40 1.34 1.25 1.16 1.06
50.37 47.22 44.81 42.98 41.62 40.64 40.01 39.69 39.67 39.94 40.52 41.44 42.74 44.50 46.81 49.83 53.81 59.12
beff
beff (mod)
2.16 2.04 1.91 1.75 1.57 1.37 1.14 0.89 0.62 0.51 0.79 1.05 1.28 1.50 1.69 1.85 2.00 2.12 2.21 2.28 2.33 2.36 2.36 2.34 2.30 2.23 2.14 2.02 1.88
1.47 1.42 1.35 1.27 1.18 1.08 0.97 0.84 0.62 0.51 0.79 0.92 1.04 1.14 1.24 1.32 1.39 1.45 1.50 1.54 1.56 1.57 1.58 1.57 1.54 1.51 1.46 1.41 1.34
0.64 0.52
1.72 1.54
1.26 1.16
49.75 53.70
7.6548 7.771
7.0922
0.41
1.33
1.06
58.97
7.2084
0.29
1.10
0.94
66.21
7.3246 7.4408 7.557 7.6732 7.7894 7.9056 8.0218 8.138 8.2542 8.3704 8.4866 8.6028 8.719 8.8352 8.9514 9.0676 9.1838 9.3
0.18 0.06 0.06 0.17 0.29 0.41 0.52 0.64 0.75 0.87 0.99 1.10 1.22 1.34 1.45 1.43 1.32 1.20
0.84 0.56 0.56 0.84 1.09 1.33 1.53 1.72 1.88 2.02 2.13 2.23 2.29 2.34 2.36 2.36 2.33 2.29
0.82 0.56 0.56 0.81 0.94 1.06 1.16 1.25 1.34 1.40 1.46 1.51 1.54 1.56 1.58 1.57 1.56 1.54
76.56 110.76 111.85 76.79 66.37 59.09 53.78 49.81 46.79 44.49 42.74 41.44 40.52 39.94 39.67 39.69 40.01 40.65
72
1Lane 70R Track
TRANSVERSE ANALYSIS 5 FOR LIVE LOAD
Load on Wheel-1
=
350
kN
Load on Wheel-2
=
350
kN
Contact width along span
=
4570
mm
Contact width across span
=
840
mm
Distance between two loads across span
=
2.06
m
b1
=
0.99
Impact factor
=
1.25
Initial Position of first wheel
=
3.985
Final position of first wheel
=
7.82
No of Load generation
=
50
Transverse increament
=
0.0767
m
73
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
3.985 4.0617 4.1384 4.2151 4.2918 4.3685 4.4452 4.5219 4.5986 4.6753 4.752 4.8287 4.9054 4.9821 5.0588 5.1355 5.2122 5.2889 5.3656 5.4423 5.519 5.5957 5.6724 5.7491 5.8258 5.9025 5.9792 6.0559 6.1326 6.2093 6.286 6.3627 6.4394 6.5161 6.5928 6.6695 6.7462 6.8229 6.8996 6.9763 7.053 7.1297 7.2064 7.2831 7.3598 7.4365 7.5132 7.5899 7.6666 7.7433 7.82
Dist. of Nearest Support 0.52 0.44 0.36 0.28 0.21 0.13 0.05 0.02 0.10 0.18 0.25 0.33 0.41 0.48 0.56 0.64 0.71 0.79 0.87 0.94 1.02 1.10 1.17 1.25 1.33 1.40 1.48 1.44 1.37 1.29 1.21 1.14 1.06 0.98 0.91 0.83 0.75 0.68 0.60 0.52 0.45 0.37 0.29 0.22 0.14 0.06 0.01 0.09 0.17 0.243 0.32
Wheel-2
beff
beff (mod)
2.10 1.96 1.82 1.66 1.49 1.32 1.13 1.05 1.24 1.42 1.59 1.75 1.90 2.04 2.17 2.29 2.40 2.50 2.59 2.67 2.74 2.80 2.85 2.89 2.91 2.93 2.94 2.94 2.92 2.90 2.87 2.83 2.77 2.71 2.64 2.55 2.46 2.35 2.24 2.11 1.98 1.83 1.68 1.51 1.34 1.15 1.02 1.22 1.40 1.57 1.73
2.08 1.96 1.82 1.66 1.49 1.32 1.13 1.05 1.24 1.42 1.59 1.75 1.90 2.04 2.12 2.18 2.23 2.28 2.33 2.37 2.40 2.43 2.45 2.47 2.49 2.50 2.50 2.50 2.49 2.48 2.46 2.44 2.42 2.38 2.35 2.31 2.26 2.21 2.15 2.09 1.98 1.83 1.68 1.51 1.34 1.15 1.02 1.22 1.40 1.57 1.73
P with Dist. of Impact Position Nearest (kN) Support 210.38 6.045 1.46 222.86 6.1217 1.38 240.80 6.1984 1.30 263.49 6.2751 1.22 292.89 6.3518 1.15 332.22 6.4285 1.07 387.21 6.5052 0.99 418.05 6.5819 0.92 353.41 6.6586 0.84 308.28 6.7353 0.76 275.13 6.812 0.69 249.86 6.8887 0.61 230.07 6.9654 0.53 214.25 7.0421 0.46 206.75 7.1188 0.38 201.04 7.1955 0.30 196.10 7.2722 0.23 191.81 7.3489 0.15 188.12 7.4256 0.07 184.97 7.5023 0.00 182.31 7.579 0.08 180.10 7.6557 0.16 178.32 7.7324 0.23 176.93 7.8091 0.31 175.93 7.8858 0.39 175.29 7.9625 0.46 175.01 8.0392 0.54 175.09 8.1159 0.62 175.53 8.1926 0.69 176.34 8.2693 0.77 177.52 8.346 0.85 179.08 8.4227 0.92 181.06 8.4994 1.00 183.47 8.5761 1.08 186.35 8.6528 1.15 189.74 8.7295 1.23 193.69 8.8062 1.31 198.27 8.8829 1.38 203.55 8.9596 1.46 209.63 9.0363 1.46 221.07 9.113 1.39 238.56 9.1897 1.31 260.63 9.2664 1.23 289.13 9.3431 1.16 327.11 9.4198 1.08 379.90 9.4965 1.00 427.18 9.5732 0.93 359.57 9.6499 0.85 312.70 9.7266 0.77 278.44 9.8033 0.70 252.42 9.88 0.62
beff
beff (mod)
2.94 2.93 2.91 2.87 2.83 2.78 2.72 2.65 2.56 2.47 2.37 2.26 2.13 2.00 1.86 1.70 1.54 1.36 1.18 1.00 1.19 1.37 1.55 1.71 1.86 2.01 2.14 2.26 2.38 2.48 2.57 2.65 2.72 2.78 2.84 2.88 2.91 2.93 2.94 2.94 2.93 2.91 2.88 2.84 2.79 2.73 2.66 2.57 2.48 2.38 2.27
2.50 2.49 2.48 2.47 2.45 2.42 2.39 2.35 2.31 2.27 2.21 2.16 2.10 2.00 1.86 1.70 1.54 1.36 1.18 1.00 1.19 1.37 1.55 1.71 1.86 2.01 2.10 2.16 2.22 2.27 2.31 2.36 2.39 2.42 2.45 2.47 2.48 2.49 2.50 2.50 2.49 2.48 2.47 2.45 2.42 2.39 2.36 2.32 2.27 2.22 2.16
P with Impact (kN) 175.06 175.45 176.20 177.33 178.84 180.75 183.10 185.91 189.23 193.10 197.58 202.76 208.72 218.88 235.83 257.15 284.59 320.97 371.19 439.27 367.65 318.46 282.73 255.72 234.70 217.97 208.34 202.43 197.29 192.85 189.01 185.73 182.95 180.63 178.73 177.25 176.15 175.42 175.05 175.04 175.39 176.10 177.18 178.65 180.51 182.81 185.57 188.82 192.63 197.04 202.13
74
70Rw+1lca
TRANSVERSE ANALYSIS 6 FOR LIVE LOAD
70RW Load on Wheel-1
=
85
Max. tyre pressure
=
5.273
Contact width along span
=
810
Distance between two loads across span
=
1.93
Impact factor
=
1.25
kN
Load on Wheel-2
=
85
Contact area for 70RW
=
1612.0
cm2
mm
Contact width across span
=
199.0
mm
m
b1
=
0.349
m
kg/cm
2
kN
1Lane Class - A Load on Wheel-1
=
57
kN
Load on Wheel-2
=
57
kN
Contact width across span
=
250
mm
Contact width along span
=
500
mm
Distance between two loads across span
=
1.200
m
Minimum edge distance upto c/l of wheel
=
0.400
m
b1
=
0.400
m
Load on Wheel-3
=
57.000
kN
Load on Wheel-4
=
57
kN
Impact factor
=
1.5
initial position of first wheel(70Rw)
=
2.130
initial position of 2nd wheel(1LCA)
=
7.740
Final position of 2nd wheel of 1LCA
=
11.100
m
Total movement of train
=
3.360
m
Number of load generation
=
20
Transverse increament of Wheels
=
0.168
m
m
75
Wheel-1 Load Case
Position
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
2.13 2.298 2.466 2.634 2.802 2.97 3.138 3.306 3.474 3.642 3.81 3.978 4.146 4.314 4.482 4.65 4.818 4.986 5.154 5.322 5.49
Dist. of Nearest Support 0.63 0.80 0.97 1.13 1.30 1.47 1.36 1.19 1.03 0.86 0.69 0.52 0.35 0.19 0.02 0.15 0.32 0.49 0.65 0.82 0.99
beff 1.64 1.87 2.05 2.18 2.27 2.30 2.28 2.22 2.10 1.94 1.73 1.47 1.16 0.80 0.40 0.72 1.09 1.41 1.68 1.90 2.07
Wheel-2 P with beff Impact (mod) (kN) 1.64 64.67 1.87 56.76 1.99 53.37 2.06 51.67 2.10 50.66 2.11 50.26 2.11 50.45 2.07 51.23 2.02 52.67 1.94 54.88 1.73 61.40 1.47 72.28 1.16 91.53 0.80 132.38 0.40 268.63 0.72 147.67 1.09 97.64 1.41 75.47 1.68 63.29 1.90 55.90 2.00 53.08
Position 4.06 4.228 4.396 4.564 4.732 4.9 5.068 5.236 5.404 5.572 5.74 5.908 6.076 6.244 6.412 6.58 6.748 6.916 7.084 7.252 7.42
Dist. of Nearest Support 0.44 0.27 0.10 0.06 0.23 0.40 0.57 0.74 0.90 1.07 1.24 1.41 1.42 1.26 1.09 0.92 0.75 0.58 0.42 0.25 0.08
beff 1.33 0.99 0.61 0.51 0.91 1.25 1.55 1.79 1.99 2.14 2.24 2.29 2.29 2.25 2.15 2.01 1.81 1.57 1.28 0.94 0.55
Wheel-3 P with beff Impact (mod) (kN) 1.26 84.15 0.99 107.10 0.61 174.17 0.51 207.58 0.91 117.33 1.23 86.72 1.37 77.38 1.50 71.00 1.60 66.59 1.67 63.62 1.72 61.77 1.75 60.86 1.75 60.82 1.72 61.64 1.68 63.40 1.60 66.25 1.51 70.50 1.39 76.66 1.24 85.66 0.94 112.97 0.55 192.67
Position 6.12 6.288 6.456 6.624 6.792 6.96 7.128 7.296 7.464 7.632 7.8 7.968 8.136 8.304 8.472 8.64 8.808 8.976 9.144 9.312 9.48
Dist. of Nearest Support 1.38 1.21 1.04 0.88 0.71 0.54 0.37 0.20 0.04 0.13 0.30 0.47 0.64 0.80 0.97 1.14 1.31 1.48 1.36 1.19 1.02
beff 2.34 2.28 2.17 2.01 1.81 1.55 1.25 0.89 0.49 0.73 1.10 1.43 1.70 1.93 2.11 2.24 2.32 2.35 2.33 2.27 2.15
Wheel-4 P with beff Impact (mod) (kN) 1.77 48.34 1.74 49.16 1.68 50.75 1.61 53.23 1.50 56.88 1.38 62.15 1.22 69.87 0.89 95.60 0.49 173.61 0.73 117.43 1.10 77.59 1.31 65.09 1.45 58.90 1.57 54.63 1.65 51.69 1.72 49.74 1.76 48.61 1.77 48.18 1.77 48.41 1.73 49.34 1.68 51.04
Position 7.92 8.088 8.256 8.424 8.592 8.76 8.928 9.096 9.264 9.432 9.6 9.768 9.936 10.104 10.272 10.44 10.608 10.776 10.944 11.112 11.28
Dist. of Nearest Support 0.42 0.59 0.76 0.92 1.09 1.26 1.43 1.40 1.24 1.07 0.90 0.73 0.56 0.40 0.23 0.06 0.11 0.28 0.44 0.61 0.78
beff 1.34 1.63 1.87 2.06 2.21 2.30 2.35 2.34 2.29 2.19 2.04 1.84 1.59 1.29 0.95 0.55 0.53 0.73 0.93 1.13 1.34
P with beff Impact (mod) (kN) 1.27 67.35 1.41 60.44 1.54 55.70 1.63 52.41 1.70 50.21 1.75 48.86 1.77 48.23 1.77 48.28 1.74 49.00 1.69 50.47 1.62 52.81 1.52 56.27 1.40 61.27 1.25 68.57 0.95 90.21 0.55 154.64 0.53 161.44 0.73 116.93 0.93 91.66 1.13 75.37 1.27 67.43
76
DESIGN FORCES FOR DECK SLAB INTRODUCTION : The RCC deck slab is analysed as 2-Dimensional frame considering 1m width of slab. The slab is supported over longitudinal girders. The concentrated live load for 1m width of deck slab is calculated as per effective width method given in AnnexureB-3 of IRC-112. The analysis of deck slab is carried out for Transverse Live Load. Analysis Models
Analysis Model with Member Numbering
Analysis Model with Node Numbering
77
Node 7
Node 8
Node 9
N ode 10
N ode 11
N ode 12
N ode 13
N ode 14
N ode 15
N ode 16
Node 6
Node 5
Node 4
DL SIDL (Except surfacing) SIDL (Surfacing) FPLL 1CLA (Max. Hog) TRANSVERSE ANALYSIS 1 FOR LIVE LOAD 1CLA (Max. Sag) TRANSVERSE ANALYSIS 1 FOR LIVE LOAD 2CLA (Max. Hog) TRANSVERSE ANALYSIS 2 FOR LIVE LOAD 2CLA (Max. Sag) TRANSVERSE ANALYSIS 2 FOR LIVE LOAD 1L 40T-L (Max. Hog) TRANSVERSE ANALYSIS 3 FOR LIVE LOAD 1L 40T-L (Max. Sag) TRANSVERSE ANALYSIS 3 FOR LIVE LOAD 1L 40T-M (Max. Hog) TRANSVERSE ANALYSIS 4 FOR LIVE LOAD 1L 40T-M (Max. Sag) TRANSVERSE ANALYSIS 4 FOR LIVE LOAD 1L 70R TR (Max. Hog) TRANSVERSE ANALYSIS 5 FOR LIVE LOAD 1L 70R TR (Max. Sag) TRANSVERSE ANALYSIS 5 FOR LIVE LOAD 1L70RW+1LCA(Max Hog) TRANSVERSE ANALYSIS 6 FOR LIVE LOAD 1L70RW+1LCA(Max Sag) TRANSVERSE ANALYSIS 6 FOR LIVE LOAD LL (Max. Hog) LL (Max. Sag)
11.12 3.01 5.28 0.01 16.9 -16.9 16.9 -16.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21.8 -21.8
25.04 7.99 11.10 3.77 18.44 6.76 2.16 2.99 1.02 4.98 11.88 3.78 5.27 1.79 8.76 0.01 0.00 0.00 0.00 0.01 33.8 22.1 7.4 3.4 6.8 -33.8 -22.1 -7.4 -3.4 -6.8 33.8 22.7 7.3 2.9 6.6 -33.8 -22.7 -7.3 -2.9 -6.6 7.6 7.8 11.1 4.7 10.5 -7.6 -7.8 -11.1 -4.7 -10.5 0.0 5.2 9.5 4.6 6.6 0.0 -5.2 -9.5 -4.6 -6.6 0.0 10.7 14.5 6.0 15.1 0.0 -10.7 -14.5 -6.0 -15.1 0.0 5.6 7.6 3.5 7.3 0.0 -5.6 -7.6 -3.5 -7.3 21.8 16.0 9.8 3.1 6.4 -21.8 -16.0 -9.8 -3.1 -6.4 Combination for ULS as per IRC-6
1.87 0.50 0.89 0.00 4.5 -4.5 5.5 -5.5 5.7 -5.7 4.7 -4.7 6.7 -6.7 4.3 -4.3 4.4 -4.4
16.25 4.39 7.71 0.01 6.2 -6.2 5.9 -5.9 9.1 -9.1 8.9 -8.9 11.8 -11.8 6.9 -6.9 2.6 -2.6
3.20 0.86 1.52 0.00 4.1 -4.1 5.4 -5.4 5.7 -5.7 5.7 -5.7 7.4 -7.4 2.8 -2.8 2.4 -2.4
14.73 3.98 6.99 0.01 6.9 -6.9 6.6 -6.6 10.5 -10.5 7.8 -7.8 15.5 -15.5 6.6 -6.6 1.8 -1.8
2.35 0.63 1.11 0.00 3.2 -3.2 3.2 -3.2 4.4 -4.4 4.4 -4.4 5.3 -5.3 3.0 -3.0 1.3 -1.3
7.39 1.99 3.51 0.00 7.3 -7.3 7.3 -7.3 10.7 -10.7 10.6 -10.6 13.8 -13.8 5.2 -5.2 0.9 -0.9
16.83 4.54 7.99 0.00 17.4 -17.4 18.2 -18.2 7.8 -7.8 6.9 -6.9 9.8 -9.8 10.6 -10.6 0.5 -0.5
36.17 9.76 17.17 0.01 25.6 -25.6 25.6 -25.6 11.4 -11.4 0.0 0.0 0.0 0.0 17.3 -17.3 0.0 0.0
18.36 4.96 8.72 0.01 12.8 -12.8 12.8 -12.8 0.0 0.0 0.0 0.0 0.0 0.0 8.6 -8.6 0.0 0.0
1.35*(DL+SIDL)+1.75*SIDL 1.35*(DL+SIDL)+1.75*SIDL+1.5*FPLL 1.35*(DL+SIDL)+1.75*SIDL+1.5*LL1 1.35*(DL+SIDL)+1.75*SIDL+1.5*LL2 1.35*(DL+SIDL)+1.75*SIDL+1.5*(FPLL+LL1) 1.35*(DL+SIDL)+1.75*SIDL+1.5*(FPLL+LL2) DESIGN HOG. DESIGN SAG
28.3 28.3 60.9 -4.3 60.9 -4.3 60.9 -4.33
46.9 46.9 56.6 37.3 56.6 37.3 56.6 0.0
4.8 4.8 11.4 -1.9 11.4 -1.9 11.4 -1.9
41.3 41.4 45.2 37.5 45.2 37.5 45.2 0.0
8.1 8.1 11.7 4.6 11.7 4.6 11.7 0.0
37.5 37.5 40.2 34.8 40.2 34.8 40.2 0.0
6.0 6.0 8.0 4.0 8.0 4.0 8.0 0.0
18.8 18.8 20.1 17.5 20.1 17.5 20.1 0.0
42.8 42.8 43.5 42.2 43.5 42.2 43.5 0.0
92.1 92.1 92.1 92.0 92.1 92.1 92.1 0.0
46.7 46.7 46.7 46.7 46.7 46.7 46.7 0.0
1.0*(DL+SIDL)+1.0*SIDL 1.0*(DL+SIDL)+1.0*SIDL+1.0*FPLL 1.0*(DL+SIDL)+1.0*SIDL+1.0*LL1 1.0*(DL+SIDL)+1.0*SIDL+1.0*LL2 1.0*(DL+SIDL)+1.0*SIDL+1.0*(FPLL+LL1) 1.0*(DL+SIDL)+1.0*SIDL+1.0*(FPLL+LL2) DESIGN HOG. DESIGN SAG
19.40 19.41 41.15 -2.35 41.16 -2.35 41.16 -2.350
63.7 20.3 28.2 9.6 63.7 20.3 28.2 9.6 96.3 44.3 43.0 14.3 31.1 -3.7 13.5 4.9 96.4 44.3 43.0 14.3 31.1 -3.7 13.5 4.9 96.4 44.3 43.0 14.3 0.00 -3.7 0.0 0.0 Combination for SLS as per IRC-6 43.68 13.93 19.36 6.58 43.69 13.93 19.36 6.58 65.43 29.92 29.19 9.70 21.93 -2.07 9.53 3.45 65.44 29.92 29.19 9.71 21.94 -2.06 9.54 3.46 65.44 29.9 29.2 9.7 0.000 -2.07 0.00 0.00
32.17 32.18 38.60 25.74 38.61 25.74 38.6 0.00
3.26 3.26 7.69 -1.17 7.69 -1.17 7.7 -1.17
28.35 28.35 30.90 25.79 30.91 25.80 30.9 0.00
5.58 5.58 7.95 3.22 7.95 3.22 8.0 0.00
25.70 25.70 27.50 23.90 27.51 23.90 27.5 0.00
4.10 4.10 5.45 2.75 5.45 2.75 5.4 0.00
12.89 12.89 13.78 11.99 13.78 11.99 13.8 0.00
29.36 29.36 29.81 28.91 29.81 28.91 29.8 0.00
63.10 63.11 63.11 63.1 63.12 63.1 63.1 0.0
32.03 32.04 32.03 32.0 32.04 32.0 32.0 0.0
SECTION
Node 3
Node 2
Summarry of unfactored B.M (KN-m)
78
Design for ULS condition Design Design Design Design Design Design Design Design
Hogging Moment at Cantilever Face at node 2,16 (end of haunch) Hogging Moment at Outer Support Node 4, 14 Hogging Moment at Outer Support 6,12 Hogging Moment at intermediate support Node 8,10 Hogging Moment at Intermediate Span at mid node 9 Hogging Moment atouter span at mid node 5,13 Sagging Moment at End Span(at node 5,13) Sagging Moment at mid of mid span( at node 9)
= = = = = = =
60.9 44.3 14.3 11.7 45.2 43.0 0.0 0.0
= = = = = = = = = = = =
35.0 32.0 500 40.0 200 32 1.000 0.800 0.400 1.150 40.0 16.0
KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m
DESIGN OF DECK SLAB fck fav fyk fcd Es Ec.eff
IRC-112-6.4.2.8
η λ β γs Clear Cover Bar dia to be used
Cantilever Face
SECTION
Mpa Mpa Mpa Mpa Gpa Gpa IRC-112 -A2.9
IRC-112 -6.2.2 mm mm
Outer Span (Face Outer Span (e Mid spans (Face Mid-End Span of outer Girder) of inner girder) of girders)
Midspan-Int. Span
DESIGN HOG.
60.9
44.3
14.3
11.7
43.0
45.2
DESIGN SAG
-4.3
-3.7
0.0
-1.9
0.0
0.0
b
1000
1000
1000
1000
1000
1000
145
145
145
145
145
145
Kav = M/bd f av (for Top)
0.0906
0.0658
0.0212
0.0174
0.0639
0.0672
Kav = M/bd2f av (for Bottom)
0.0064
0.0055
0.0000
0.0028
0.0000
0.0000
x= ((1+sqrt(1-4βKav))/(2*β))∗d (mm)
13.646
9.814
3.106
2.538
9.515
10.016
x= ((1+sqrt(1-4bKav))/(2*b))*d (mm)
0.9345
0.7934
0.0000
0.4072
0.0000
0.0000
Z for Top (mm)
131.4
135.2
141.9
142.5
135.5
135.0
Z for bottom (mm)
144.1
144.2
145.0
144.6
145.0
145.0
As required for Top (mm2)
1066.9
753.7
231.6
188.8
729.8
770.0
69.0
58.6
0.0
30.0
0.0
0.0
As provided at Top (mm2)
1398.0
1398.0
1398.0
1398.0
1398.0
1398.0
As provided at Bottom (mm2)
1398.0
1398.0
1398.0
1398.0
1398.0
1398.0
As
OK
OK
OK
OK
OK
OK
Remarks for Bottom As
OK
OK
OK
OK
OK
OK
d 2
As required for Bottom (mm2)
Remarks for Top
79
Min Ast Required min of ((0.26*fctm/fyk bt*d),(0.0013*bt*d)) Ast Required at top 1066.92 mm^2 16
Provide Ast provided qat Top
1398.01
Ast required at bottom
188.5 16
Provide Ast provided at top
1398.01
dia @
200
2
mm /m
c/c +
188.5
mm^2
10
dia @
200
c/c at bottom.
10
dia @
200
c/c
ok
mm^2 dia @
200
2
mm /m
c/c + ok
N ode 4
N ode 5
N ode 6
N ode 8
N ode 9
N ode 10
N ode 12
N ode 13
N ode 14
N ode 16
N ode 2
Calculation of`Longitudinal Reinforcement: Design BM for Longitudinal Reinforcement BM ARE IN KNm
0.2*(DL + SIDL)
5.7
4.1
5.6
1.9
1.0
8.3
1.6
1.2
3.8
8.6
9.3
0.2*(LL+ FPLL (Max. Hog))
4.4
3.2
2.0
0.6
0.9
0.5
0.5
0.3
0.2
0.1
0.0
0.2*(LL+ FPLL (Max. Sag))
-4.4
-3.2
-2.0
-0.6
-0.9
-0.5
-0.5
-0.3
-0.2
-0.1
0.0
Design Hogging BM
10.0
7.3
7.6
2.5
1.8
8.8
2.1
1.5
3.9
8.7
9.3
Design Sagging BM
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Provided Depth (mm)
SECTION
210
210
210
210
210
210
210
210
210
210
210
2
Reqd Ast (cm /m) (Top)
1.4
1.0
1.1
0.4
0.3
1.2
0.3
0.2
0.5
1.2
1.3
Reqd Ast (cm2/m) (Bottom)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Required longitudinal top reinforcement at cantilever support = 10
Provide Ast provided =
200
dia @ 3.9
cm2/m
c/c at top for cantilever support
2
cm /m
>
1.4
cm2/m
OK
2
Required longitudinal bottom reinforcement =
0.0
cm /m
Provide
10
dia @
Ast provided =
1.394
3.9
200
c/c at bottom except cantilever
2
cm /m
>
0.0
cm2/m
OK
Design for SLS condition Design Design Design Design Design Design Design Design
Hogging Moment at Cantilever Face at node 2,16 Hogging Moment at Outer Support Node 4, 14 Hogging Moment at Outer Support 6,12 Hogging Moment at intermediate support Node 8,10 Hogging Moment at Intermediate Span at mid node 9 Hogging Moment atouter span at mid node 5,13 Sagging Moment at End Span node 5, 13 Sagging Moment at Intermediate Span node no9
= = = = = = =
41.2 29.9 9.7 8.0 30.9 29.2 0.0 0.0
KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m KNm/m
80
SECTION
Cantilever Face
Outer Span (Face Outer Span (e Mid spans (Face Mid-End Span of outer Girder) of inner girder) of girders)
Midspan-Int. Span
DESIGN HOG.
41.2
29.9
9.7
8.0
29.2
30.9
DESIGN SAG
-2.35
0.0
-2.1
-1.2
0.0
0.0
b
1000
1000
1000
1000
1000
1000
d
145
145
145
145
145
145
dc= (-As Es + sqrt((AsEs)^2+2bAsEsEc.effd))bEc.eff (mm) (Top)
42.35
42.35
42.35
42.35
42.35
42.35
dc= (-As Es + sqrt((AsEs)^2+2bAsEsEc.effd))bEc.eff (mm) (bottom)
33.20
33.20
33.20
33.20
33.20
33.20
18781818.9
18781818.9
18781818.9
18781818.9
18781818.9
18781818.9
σc (Top) (Mpa)
14.8
10.8
3.5
2.9
10.5
11.2
σs (Top) (Mpa)
224.9
163.5
53.0
43.4
159.5
168.9
Check concrete
OK
OK
OK
OK
OK
OK
Check Steel
Ok
Ok
Ok
Ok
Ok
Ok
19425126.5
19425126.5
19425126.5
19425126.5
19425126.5
19425126.5
σc (Bottom) (Mpa)
0.6427
0.0000
0.5648
0.3197
0.0000
0.0000
σs (Bottom) (Mpa)
13.525
0.000
11.884
6.728
0.000
0.000
Check concrete
OK
OK
OK
OK
OK
OK
Check Steel
Ok
Ok
Ok
Ok
Ok
Ok
I (Hog) cracked M.I
I (Sag)
81
Check for crack width for maximum moments at node no 3. =
0.059 Hence OK
0.425k 1k 2ϕ is applicable ρ ρ .eff where spacing of bonded reinforcement with in the tension zone <=5*(C+ ϕ /2)
=
244.7 mm
=
240 mm
Wk
=
S r,max ( ε sm - ε cm )
S r,max
=
Maximum crack spacing
3.4c +
ϕ
=
is the bar diameter.Where different diameters are used in section an equivalent diameter canbe used ϕ eq
=
16.0 mm
C
=
Clear cover to longitudinal reinforcement
=
40.0 mm
K1
=
is the co-efficient which takes account of the bond properties of the bonded reinforcement
=
0.8
K2
=
is a co-fficient which takes into account of the distribution of strain
=
0.5
( ε sm - ε cm )
=
σ sc - k 1 f ct.eff / ρ ρ. eff (1+α e ρ ρ .eff ) Es
=
0.00024
σ sc
=
is the stress in the tension reinforcement assuming a cracked section
=
αe
=
is the ratio Es/Ec
=
6.250
ρ ρ. eff
=
A s /A c.eff
=
0.0250
A c.eff
=
is the effective area of concrete in tension surrounding the reinforcement of depth h c.eff , where h c.eff is the lesser of following
=
55882.36 mm2
= = = =
1000 210 145 42
>=0.6 σ sc / Es
1 One third of the tension zone depth of the cracked section,(h-x)/3, with x negative when whole section is in tension
b h d x
159.54 Mpa
mm mm mm mm
2 half of section depth,h/2, or 3 2.5*(h-d)
As
=
Area of tension reinforcement
=
1398 mm2
f ct.eff
=
is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur f ct.eff = f ctm
=
3.000 Mpa
82
Design of Transverse Cantilever of Slab A) Loads & Moments at Crash Barrier Side: 0 450
0 200
200
0
Water pipe
1000 Load due to self-weight of slab Cg of self-weight of slab Load due to RCC Railing Cg of RCC railing from edge of cantilever Cg from cantilever face Load due to wearing coat Cg from cantilever face Load due to Crash barrier Cg of crash barrier from edge of cantilever Intensity of FPLL CG of FPLL Intensity of Water Pipe C.G of Pipe Moment due to rcc railing Moment due to wearing coat Moment due to crash barrier Moment due to FPLL Moment due to selfwt of slab Moment due to pipe Load due to Class A wheel Wheel Contact Width Wheel Contact Length Clear distance from kerb face Effective width, beff 1st Wheel a b1 beff Concentrated maximum wheel load Spacing between consecutive , nearest axle Net beff Hence Load acting on the 1m width slab LL with Impact IF= Moment at the cantilever face due to LL
= = = = = = = = = = = = = = = = = = = = = = =
1.5
= = = = = = = = =
0.500 0.500 0.000 775 0.775 0.110 0.275 1.000 0.775 0.000 0.275 0.000 0.600 0.000 0.030 0.775 0.000 0.250 0.000
t m t mm m t m t mm t/m m t/m t/m t-m t-m t-m t-m t-m t-m
500 mm 250 mm 150 mm 1.2 a + b1 0.15 0.38 1.00 5.70 1.20 1.00 5.70 8.55 1.28
m m m t m m t t tm
83
2nd Wheel(it will not lie on the cantilever part) a b1 beff Concentrated maximum wheel load Spacing between consecutive , nearest axle Net beff Hence Load acting on the 1m width slab LL with Impact IF= 1.5 Moment at the cantilever face due to LL
= = = = = = = = =
Total desigm moment as ULS = 1.35*(DL+SIDL1)+1.75*SIDL+1.5*LL Total design moment at cantilever face = 3.360438 Total desigm moment as SLS = 1*(DL+SIDL1)+1*SIDL+1*LL Total design moment at cantilever face = 3.62
Total Design Moment due to DL+SIDL+LL
=
0.15 0.38 1.00 5.70 1.20 1.00 5.70 8.55 1.28
m m m t m m t t tm
3.62
tm
tm tm
END OF DESIGN REPORT
84
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