LONGITUDINAL ANALYSIS & DESIGN OF BOX GIRDER

Basic Design Data

Overall Span (C/C spacing of exp. joint) = 48.750 m

Effective Span (C/C spacing of Bearing) = 47.750 m
Distance between C/L of Brg. and C/L of Exp. Joint = 0.500 m
Girder end to bearing centre line = 0.240 m
Expansion gap = 0.040 m
Width of deck = 9.750 m
Depth of Box Girder = 2.500 m
Grade of Concrete of Girder = 40 Mpa
Age of concrete for at transfer 14 days
Maturity of concrete for at transfer 87 %
Strength concrete at the time of transfer 34.8 Mpa
Age of girder at the time of casting of SIDL 56 days
Maturity of girder at the time of casting of SIDL 100 %
Extra time dependent loss to be considered 20.0 %
Wearing coat thickness = 0.065 m

565263434.xlsx/Input Page- Date:12/17/2021

 CALCULATION OF SECTION PROPERTIES OF SINGLE CELL BOX GIRDER
DW

HW2 HW1 CH1 Td 1 2

HH1 5
HH2 6 3
Tw 4
C2 C1 11 7
HW3 K2
HH3 10
Angle q

K1 Ts 8 9

IW SW

NOTE : 1. ALL DIMENSIONS ARE TO BE GIVEN IN METERS

2. CELLS SHADED ARE NOT BE GIVEN ANY INPUT

D away from
SECTION Support L/8 L/4 3L/8 L/2
support

Web Inclination, q (deg) 17.6501 17.6501 17.6501 17.6501 17.6501 17.6501

Total Depth D 2.500 2.200 1.900 1.600 1.300 1.000

DW 9.750 9.750 9.750 9.750 9.750 9.750
Top Flange
Td 0.225 0.225 0.225 0.225 0.225 0.225
C1 1.500 1.500 1.500 1.500 1.500 1.500
C2 0.000 0.000 0.000 0.000 0.000 0.000
cantilever Ttip 0.200 0.200 0.200 0.200 0.200 0.200
Tf 0.300 0.300 0.300 0.300 0.300 0.300
IW 0.700 0.700 0.700 0.700 0.700 0.700
Web D1 2.200 2.200 2.200 2.200 2.200 2.200
Tw 0.600 0.579 0.480 0.310 0.310 0.310
SW 6.750 6.750 6.750 6.750 6.750 6.750
Ts 0.550 0.260 0.260 0.260 0.260 0.260
soffit Slab D2 0.000 -0.300 -0.600 -0.900 -1.200 -1.500
K1 0.0000 -0.0955 -0.1909 -0.2864 -0.3818 -0.4773
K2 0.1750 0.0827 0.0827 0.0827 0.0827 0.0827
HW1 0.409 0.485 0.582 0.750 0.750 0.750
t. hnch1 HH1 0.083 0.097 0.116 0.150 0.150 0.150
CH1 1.850 1.850 1.850 1.850 1.850 1.850
HW2 0.000 0.000 0.000 0.000 0.000 0.000
t. hnch2
HH2 0.000 0.000 0.000 0.000 0.000 0.000
HW3 0.000 0.000 0.088 0.300 0.300 0.300
bot. hnch
HH3 0.000 0.000 0.044 0.150 0.150 0.150

Area 1.5188 1.5188 1.5188 1.5188 1.5188 1.5188

Yt 0.1125 0.1125 0.1125 0.1125 0.1125 0.1125
A.Yt 0.1709 0.1709 0.1709 0.1709 0.1709 0.1709
1 A.Yt2 0.0192 0.0192 0.0192 0.0192 0.0192 0.0192

565263434.xlsx/Prop Page- Date:12/17/2021

 1
Iself-xx 0.0064 0.0064 0.0064 0.0064 0.0064 0.0064
Iself+A.Y t
2
0.0256 0.0256 0.0256 0.0256 0.0256 0.0256
IY-Y 5.7665 5.7665 5.7665 5.7665 5.7665 5.7665
Area 0.6000 0.6000 0.6000 0.6000 0.6000 0.6000
Yt 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000
A.Yt 0.0600 0.0600 0.0600 0.0600 0.0600 0.0600
2 A.Yt2 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060
Iself 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020
Iself+A.Yt2 0.0080 0.0080 0.0080 0.0080 0.0080 0.0080
IY-Y 10.3219 10.3219 10.3219 10.3219 10.3219 10.3219
Area 0.1500 0.1500 0.1500 0.1500 0.1500 0.1500
Yt 0.2333 0.2333 0.2333 0.2333 0.2333 0.2333
A.Yt 0.0350 0.0350 0.0350 0.0350 0.0350 0.0350
3 A.Y t
2
0.0082 0.0082 0.0082 0.0082 0.0082 0.0082
Iself 0.0001 0.0001 0.00008 0.0001 0.0001 0.0001
Iself+A.Y t
2
0.0083 0.0083 0.0083 0.0083 0.0083 0.0083
IY-Y 2.2711 2.2711 2.2711 2.2711 2.2711 2.2711
Area 0.1259 0.1215 0.1007 0.0651 0.0651 0.0651
Yt 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
A.Yt 0.0315 0.0304 0.0252 0.0163 0.0163 0.0163
4 A.Yt2 0.0079 0.0076 0.0063 0.0041 0.0041 0.0041
Iself 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
Iself+A.Yt2 0.0080 0.0077 0.0064 0.0041 0.0041 0.0041
IY-Y 1.18344 1.14995 0.98477 0.67197 0.67197 0.67197
Area 0.033947 0.047045 0.067512 0.1125 0.1125 0.1125
Yt 0.2527 0.2573 0.2637 0.2750 0.2750 0.2750
A.Yt 0.0086 0.0121 0.0178 0.0309 0.0309 0.0309
5 A.Y t
2
0.00217 0.00312 0.00469 0.00851 0.00851 0.00851
Iself 0.000013 0.000025 0.000050 0.000141 0.000141 0.000141
Iself+A.Y t
2
0.00218 0.00314 0.00474 0.00865 0.00865 0.00865
IY-Y 0.1532709483 0.2228260942 0.3394140145 0.624796875 0.624796875 0.624796875
Area 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
Yt 0.30800 0.32200 0.34100 0.37500 0.37500 0.37500
A.Yt 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
6 A.Yt2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
Iself 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
Iself+A.Yt2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
IY-Y 0 0 0 0 0 0
Area 2.07781 1.99294 1.34995 0.67665 0.48146 0.28628
Yt 1.12500 1.12000 0.97000 0.82000 0.67000 0.52000
A.Yt 2.33754 2.23209 1.30945 0.55486 0.32258 0.14886
7 A.Y t
2
2.62973 2.49994 1.27017 0.45498 0.21613 0.07741
Iself 0.471403 0.446683 0.201997 0.060989 0.021971 0.004619
Iself+A.Y t
2
3.10113 2.94662 1.47216 0.51597 0.23810 0.08203
IY-Y 16.331703427 15.800978915 11.459738953 6.2876947412 4.6150622131 2.82930776
Area 3.71250 1.80464 1.85427 1.90391 1.95355 2.00318
Yt 2.22500 2.07000 1.77000 1.47000 1.17000 0.87000
A.Yt 8.26031 3.73560 3.28206 2.79875 2.28565 1.74277
8
565263434.xlsx/Prop Page- Date:12/17/2021
 8 A.Yt2 18.37920 7.73269 5.80925 4.11416 2.67421 1.51621
Iself 0.093586 0.010166 0.010446 0.010725 0.011005 0.011285
Iself+A.Yt2 18.47278 7.74285 5.81970 4.12488 2.68521 1.52749
IY-Y 14.095898438 7.2450463904 7.8594632978 8.5076708776 9.1905736603 9.9090761763
Area 0 0.0286363636 0.1145454545 0.2577272727 0.4581818182 0.7159090909
Yt 2.5 2.3 2.1 1.9 1.7 1.5
A.Yt 0.00000 0.06586 0.24055 0.48968 0.77891 1.07386
9 A.Yt2 0.00000 0.15149 0.50515 0.93040 1.32415 1.61080
Iself 0.000000 0.000143 0.002291 0.011598 0.036655 0.089489
Iself+A.Yt2 0.00000 0.15163 0.50744 0.94199 1.36080 1.70028
IY-Y 0 0.3323798765 1.3546425902 3.1052555339 5.6237297896 8.9506201282
Area 0.09625 0.02151 0.02151 0.02151 0.02151 0.02151
Yt 2.13333 2.02667 1.72667 1.42667 1.12667 0.82667
A.Yt 0.20533 0.04359 0.03714 0.03069 0.02423 0.01778
10 A.Y t
2
0.43804 0.08835 0.06413 0.04378 0.02730 0.01470
Iself 0.00162 0.00008 0.00008 0.00008 0.00008 0.00008
Iself+A.Y t
2
0.43966 0.08843 0.06421 0.04386 0.02738 0.01478
IY-Y 1.1347373698 0.2631980603 0.2777579373 0.2927097774 0.3080535807 0.3237893472
Area 0.00000 0.00000 0.00387 0.04500 0.04500 0.04500
Yt 1.95000 1.94000 1.62533 1.29000 0.99000 0.69000
A.Yt 0.00000 0.00000 0.00629 0.05805 0.04455 0.03105
11 A.Yt2 0.00000 0.00000 0.01023 0.07488 0.04410 0.02142
Iself 0.00000 0.00000 0.00000 0.00006 0.00006 0.00006
Iself+A.Yt2 0.00000 0.00000 0.01023 0.07494 0.04416 0.02148
IY-Y 0 0 0.0375868153 0.4958676382 0.5247889705 0.5545303441
AREA, A m2 8.315 6.285 5.7812 5.351 5.406 5.518
S A .Yt m3 11.109 6.385 5.1843 4.245 3.769 3.327
SIself+A.Y t
2
m4 22.066 10.982 7.9267 5.756 4.410 3.401
Yt m 1.336 1.016 0.897 0.793 0.697 0.603
Yb m 1.164 1.184 1.003 0.807 0.603 0.397
Ix-x m 4
7.224 4.495 3.278 2.389 1.783 1.394
IY-Y m 4
51.259 43.374 40.673 38.345 39.918 42.224
Zt m 3
5.407 4.424 3.655 3.011 2.557 2.312
Zb m3 6.206 3.796 3.267 2.961 2.957 3.512

565263434.xlsx/Prop Page- Date:12/17/2021

DER

Ttip

Tf

D1 D

D2

565263434.xlsx/Prop Page- Date:12/17/2021

Summary of Bending Moments & Shear Forces at Various Sections

Selfweight of Box Girder:

2.25 10.19 11.935 C.L of Span

w2
w1 w3

0.5 23.875

w1 = 21.83 t/m
w2 = 15.78 t/m Five % extra taken for blister,
w3 = 14.49 t/m deviator & future prestressing
Support Reaction = 376.2 t

B.M & S.F

Daway from 1/8th span 1/4th span 3/8th span
Component Support Section
support section section section
Mid span

B.M (t.m) 278.0 1322.0 3521.0 6427.0 8161.0 8728.0

S.F (t) 644.1 644.1 618.0 487.2 300.1 108.5

Due to SIDL
C.L of Span

0.5 23.875

w = 3.60 t/m
Support Reaction = 87.8 t

Daway from 1/8th span 1/4th span 3/8th span

Component Support Section
support section section section
Mid span

Design B. Moment 20.2 121.1 323.0 588.9 747.1 799

Design S.F 58.8 58.8 56.2 43.7 26.6 9.0

Carriageway Live Load

Impact Factor = 1.084 Distorsion taken = 5%

Daway from 1/8th span 1/4th span 3/8th span

Component Support Section
support section section section
Mid span

Governing Live Load 37.4 36.2 93.6 166.3 203.5 212.7

Bending Moment Carriageway Live Load

(incl. impact) & 42.6 41.2 106.5 189.2 231.6 242.0
distortion

565263434.xlsx / bm-sf Page-

 Daway from 1/8th span 1/4th span 3/8th span
Component Support Section
support section section section
Mid span

Governing Live Load 29.8 17.3 16.0 12.7 9.1 6.5

Ecc of Live Load 1.780 1.780 1.780 1.780 1.780 1.780

Shear Force
Carriageway Live Load
33.9 19.6 18.1 14.5 10.3 7.3
(incl. impact) & distortion

Summary of Design Forces

A. Bending Moments at various sections (in T.m)

Daway from 1/8th span 1/4th span 3/8th span
Component Support Section
support section section section
Mid span

Self Wt. Of Box Girder 278.0 1322.0 3521.0 6427.0 8161.0 8728.0
Superimposed Dead Load 20.2 121.1 323.0 588.9 747.1 798.5
Carriageway Live Load 42.6 41.2 106.5 189.2 231.6 242.0
TOTAL DESIGN B.M (t.m) 341 1484 3950 7205 9140 9769

B. Summary of Shear Forces at various sections (in T)

Ultimate Load Factor :
DL = 1.25 Ecc of DeadLoad wrt c/l of box = 0m
SIDL = 2 Ecc of SIDL wrt c/l of box = 0m
LL = 2.5
Daway from 1/8th span 1/4th span 3/8th span
Component Support Section
support section section section
Mid span

Self Wt. Of Box Girder 644.1 644.1 618.0 487.2 300.1 108.5
Superimposed Dead Load 58.8 58.8 56.2 43.7 26.6 9.0
Carriageway Live Load 33.9 19.6 18.1 14.5 10.3 7.3
TOTAL ULT. DESIGN S.F (t) 1008 972 930 733 454 172
CORRESPONDING MULT. (t.m) 494 1998 5313 9685 12274 13112
CORRESPONDING TULT. (t.m) 151 87 81 64 46 33

565263434.xlsx / bm-sf Page-

Calculation of Prestressing Force & Its Effects at Various Sections

A. CONSTRUCTION PROGRAM & PRESTRESSING STAGES

ACTIVITY DAY AFTER CASTING fcj (MPa)
i) Completion of casting of Box Girder 0 day
ii) 1st Stage prestress 14 day 34.80
iii) Completion of wearing coat, crash barrier 56 day 40.00

B. TENDON PARTICULARS

1) Nominal Diameter D 15.2 mm

2) Nominal Area A 140 sq.mm
3) Nominal Mass Pu 1.1 Kg/m
4) Yield Strength Fy 1670 MPa
5) Tensile Strength Fu 1860 MPa
6) Minimum Breaking Load Pn 260.7 KN
7) Young's Modulus of Elasticity Eps 195 Gpa
8) Jacking Force at Transfer (% of Breaking Loa Pj 76.5 %
9) Slip at Jacking end s 6 mm
10) Coefficient of Friction m 0.17 per radian
11) Wobble Friction Coefficient k 0.002 per metre
12) Relaxation of prestressing steel at 70% uts Re1 35.0 Mpa
13) Relaxation of prestressing steel at 50% uts Re2 0 MPa
14) Age of concrete for 1st Stage prestressing td1 14 days
15) Dia of Prestressing Duct qd 110 mm
16) Concrete Grade Fcu 40 MPa
17) Modulus of Elasticity of Concrete (28 days) Ec 31622.8 Mpa

C. FORCES AFTER FRICTION SLIP (For Friction & Slip calculation refer next few sheets)

Support Daway from 1/8th span 1/4th span 3/8th span

Section Section support section section section
Mid span

Distance from Left support 0.00 2.50 5.97 5.97 5.97 5.97
COMPONENT UNIT
Cable No. 7 Cable No. 6 Cable No. 5 Cable No. 4 Cable No. 3 Cable No. 2 Cable No. 1

No. of Ecc. From

2 m 1.672 1.505 1.274 0.876 0.478 0.130
Cables sofit

Px (per Cable) t 326.5 335.8 343.1 347.4 350.7 333.6

No. of Ecc. From

1.052 m 0.000 0.000 0.000 0.000 0.167 0.130
Cables sofit

Px (per Cable) t 303.4 304.1 318.6 338.6 339.5 339.5

No. of Ecc. From

2 m 0.522 0.312 0.130 0.130 0.130 0.130
Cables sofit

Px (per Cable) t 317.0 325.0 336.5 343.1 342.0 340.9

No. of Ecc. From

1.052 m 0.248 0.130 0.130 0.130 0.130 0.130
Cables sofit

Px (per Cable) t 0.0 0.0 0.0 307.3 338.6 339.5

No. of Ecc. From

2 m 0.522 0.312 0.130 0.130 0.130 0.130
Cables sofit

Px (per Cable) t 328.7 330.6 338.4 341.4 339.7 335.6

No. of Ecc. From

2 m 0.248 0.130 0.130 0.130 0.130 0.130
Cables sofit

Px (per Cable) t 317.0 325.0 336.5 343.1 342.0 340.9

No. of Ecc. From

1.052 m 0.248 0.130 0.130 0.130 0.130 0.130
Cables sofit

Px (per Cable) t 338.2 345.3 347.0 350.0 353.0 356.0

TOTAL NO. OF CABLE 10.1 10.1 10.1 11.2 11.2 11.2
TOTAL Px (STAGE-1) t 3253 3316 3409 3798 3834 3791
Cg from Bottom m 0.638 0.474 0.356 0.251 0.196 0.130
Ecc. From cg m 0.526 0.710 0.647 0.555 0.407 0.267

565263434.xlsx/Prestress Page- Date-12/17/2021

TOTAL PRIMARY BM t.m 1710 2353 2205 2109 1560 1012

565263434.xlsx/Prestress Page- Date-12/17/2021

CALCULATION OF LOAD DUE TO TEMPERATURE GRADIENT

Total Height of the girder h = 2.5 m

C.G. of Girder from bottom Y = 1.525 m
M.O.I. of the Section I = 4.6758 m4
Area of the Section A = 4.9663 m2
Modulus of Elasticity of Concrete Ec = 3.16E+07 KN/m2
Coefficient of thermal expansion of concrete a = 1.17E-05 o
C

Section Modulus at the top ZT = 4.7957 m3

Section Modulus at the bototm of top slab ZBS = 6.2344 m3
Section Modulus at the bottom ZB = 3.0661 m3

T1 = 17.8 o
C h1 = 0.15 m
T2 = 4.0 o
C h2 = 0.25 m
T3 = 2.1 o
C h3 = 0.15 m

1.0 COMPUTATION OF STRESSES DUE TO RISE IN TEMPERATURE

17.8 9.750 m
0.15 Stress 1.000 m
1 6581.0 0.225
2 4.0 0.25 1478.9 0.000 0.175

2.275 0.651
1.95
Y
0
3 0.15 776.4 0.26
2.1 4.5

Section of Girder at Span

1.1 STRESSES AT SPAN SECTION

Stresses

Stress due to Stress due to

y Assuming End
Height Stress b Force e Moment release of release of Final Stress
Segment from top Restrained
Axial Force Moment

m KN/m2 m KN m m KNm KN/m2 KN/m2 KN/m2 KN/m2

1 0.150 6581.0 9.750 5893.80 0.059 0.916 5397.69 6581.02 -1442.85 -1209.37 3928.8
2 0.075 1478.9 9.750 919.22 0.185 0.790 725.91 1478.88 -1442.85 -930.28 -894.3
3 0.175 1035.2 1.000 90.58 0.283 0.692 62.65 1035.22 -1442.85
4 0.150 776.4 4.500 262.04 2.450 -1.475 -386.51 776.41 -1442.85 1891.57 1225.1
7165.64 5799.75

2.0 COMPUTATION OF STRESSES DUE TO FALL IN TEMPERATURE

10.6 Stress h = 2.500 m

1 0.25 -3919.0
2 0.7 0.2 -258.8 h1 = 0.250 m T1 = 10.6 o
C
h2 = 0.200 m T2 = 0.7 o
C
h3 = 0.200 m T3 = 0.8 o
C
h4 = 0.250 m T4 = 6.6 o
C
1.6

3 0.8 0.2 -295.8

4 0.250 -2440.2
6.6

565263434.xlsx/Temp Page- Date:12/17/2021

2.1 STRESSES AT SPAN SECTION
Stresses

Stress due to Stress due to

y Assuming End
Height Stress b Force e Moment release of release of Final Stress
Segment from top Restrained
Axial Force Moment

m KN/m2 m KN m m KNm KN/m2 KN/m2 KN/m2 KN/m2

1 0.225 -3919.0 9.750 -4984.05 0.085 0.890 -4434.24 -3919.03 1324.65 465.22 -2129.2
2 0.025 -624.8 1.000 -11.05 0.236 0.739 -8.17 -624.83 1324.65 357.86 1057.7
3 0.150 -258.8 1.000 -24.26 0.310 0.665 -16.13 -258.80 1324.65
4 0.050 -64.7 0.651 -1.05 0.417 0.558 -0.59 -64.70 1324.65
5 0.200 -295.8 0.651 -19.24 2.183 -1.208 23.25 -295.78 1324.65
4 0.250 -2440.2 4.500 -1538.96 2.408 -1.433 2204.80 -2440.15 1324.65 727.66 -387.8
-6578.61 -2231.07

565263434.xlsx/Temp Page- Date:12/17/2021

Check for Longitudinal Flexural Stresses

Concrete Grade 40 MPa

Allowable stresses in concrete :

Temporary compressive stress after 14 days 17.40 MPa
Temporary tensile stress after 14 days 1.74 MPa
Temporary compressive stress after 28 days 20.00 MPa
Temporary tensile stress after 28 days 2.00 MPa
Service Stage compressive stress 13.46 MPa
Modulus of rupture 2.95 MPa
Factor for extra time dependent loss considered : 1.2 (Should be 1.0 as well as 1.2)

Support 1/8th span 1/4th span 3/8th span

S. No. SECTION Unit Mid span
Section section section section

Length of Segment m 5.969 5.969 5.969 5.969

1 Section Properties, Box Girder
2 Area, A m2 8.3152 5.7812 5.3511 5.4060 5.5182
3 c.g from soffit, Yb m 1.1640 1.0032 0.8067 0.6028 0.3970
4 M.O.I m4 7.2238 3.2776 2.3886 1.7826 1.3943
5 Zt m3 5.4071 3.6549 3.0110 2.5569 2.3124
6 Zb m 3
6.2061 3.2670 2.9610 2.9572 3.5121
7
8 B.M due to self wt tm 278.0 3521.0 6427.0 8161.0 8728.0
9 top stress due to DL t/m2 51.4 963.4 2134.5 3191.8 3774.4
10 bottom stress due to DL t/m2 -44.8 -1077.7 -2170.5 -2759.7 -2485.1
11 Stage 1 Prestressing at 14 days after casting
12 Stage 1 P. Force after friction & slip t 3253.4 3409.2 3797.8 3833.6 3791.0
13 Eccentricty of cables from bottom m 0.6384 0.3564 0.2515 0.1959 0.1300
14 top stress due to P t/m2 75 -14 9 99 249
15 bottom stressdue to P t/m2 667 1265 1422 1237 975
16 Total Stress after prestress
17 top stress t/m2 126 950 2144 3291 4024
18 bottom stress t/m2 622 187 -749 -1523 -1510
19 Immediate Losses in Cables
20 Stress at C.G of Cables t/m2 495.5 295.7 -457.7 -1145.9 -1222.2
21 Av. Stress at c.g of Tendon t/m2 -417.8
22 Elastic Shortening Loss (Total in t) t -38.23
23 Force in Prestressing Cables after ES t 3291.6 3447.5 3836.0 3871.8 3829.2
24 Avg force per cable 325.8 341.2 379.7 347.1 343.2
25 % of UTF 0.66 0.69 0.77 0.70 0.69
26 Av. Force in Cables after Elastic Short. Loss t 3678.9
27 % of Av. Force in Cables wrt UTF 0.708
28 Relaxation Loss (Total in t) t 323.77
29 % of Relxation Loss in 4 hours % 7.51
Stress due to Losses in Prestress on account of E.
30 Shortening & Immediate Relaxation "P"
31 top stress t/m2 0.32 -0.06 0.03 0.36 0.92
32 bottom stress t/m2 2.85 5.17 5.21 4.49 3.58
33 Stress at C.G of Cables due to loss t/m2 2.2 4.4 4.7 4.2 3.4
34 Av. Stress at c.g of Tendon due to loss t/m2 4.0
35 Stress at Transfer after Prestress
36 top stress t/m2 127 950 2144 3291 4025
37 bottom stress t/m2 625 192 -743 -1519 -1506
38 OK OK NOT OK NOT OK NOT OK
39 Av. Stress at c.g of Tendon after Immediate Loss t/m2 -413.8
40 Losses in Stage 1 Cables,14-56 days
41 % of Relxation Loss in 14-56 days % 28.60
42 Residual Shrinkage Strain at 14 days 0.00025

565263434.xlsx / Flexure PAGE : Date :

 Support 1/8th span 1/4th span 3/8th span
S. No. SECTION Unit Mid span
Section section section section

43 Residual Shrinkage Strain at 56 days 0.00019

565263434.xlsx / Flexure PAGE : Date :

 Support 1/8th span 1/4th span 3/8th span
S. No. SECTION Unit Mid span
Section section section section

44 Shrinkage Loss (14-56 days) t 34.72

45 Creep Strain at 14 day / 10 Mpa 0.00046
46 Creep Strain at 56 day / 10 Mpa 0.00040
47 Losses due to Creep (14-56 days) t -14.61
Total Loss (Shrinkage+Creep+Relaxation), 14-56
t 112.70
48 days
top stress : losses due to creep + shrinkage +
t/m2 -2.60 0.45 -0.28 -2.91 -7.41
49 Relaxation
bottom stress : losses due to creep + shrinkage +
t/m2 -23.10 -41.81 -42.19 -36.36 -28.99
50 Relaxation
51 Stress at C.G of Cables due to loss t/m2 -17.9 -35.8 -38.0 -33.7 -27.9
52 Av. Stress at c.g of Tendon due to loss t/m2 -32.6
53 Total Losses in Prestress at 56 days t 98.8
54 Total Stress before SIDL at 56 days
55 top stress t/m2 124 950 2144 3288 4017
56 bottom stress t/m2 602 150 -786 -1555 -1535
57 OK OK NOT OK NOT OK NOT OK
58
59 SIDL Bending Moment tm 20.2 323.0 588.9 747.1 798.5
60 top stress due to SIDL t/m2 3.7 88.4 195.6 292.2 345.3
61 bottom stress due to SIDL t/m2 -3.3 -98.9 -198.9 -252.6 -227.4
62 Total Stress after SIDL
63 top stress t/m2 128 1039 2339 3580 4362
64 bottom stress t/m2 599 51 -985 -1808 -1763
65 OK OK NOT OK NOT OK NOT OK
66 Stress at C.G of cables after SIDL t/m2 478.3 192.2 -650.2 -1385.4 -1444.2
67 Av. Stress at c.g of cables t/m2 -581.6
68 Losses in prestress,56days to infinity
69 % Residual Relaxation Loss 63.90
70 Relaxation Loss ,56days to infinity t 206.88
71 Residual Shrinkage Strain at 56 days 0.00015
72 Shrinkage Loss,56days to infinity t 86.80
73 Creep Strain at 56 day / 10 Mpa 0.00040
74 Creep Loss,56days to infinity t -134.62
Stress due to Losses in Prestress on account of
75 CR+SH+RL
76 top stress t/m2 -3.7 0.6 -0.4 -4.1 -10.5
77 bottom stress t/m2 -32.6 -59.0 -59.5 -51.3 -40.9
78
79 Total Stress after SIDL & all Losses
80 top stress t/m2 124.2 1039.2 2338.9 3576.3 4352.0
81 bottom stress t/m2 565.9 -7.6 -1044.1 -1858.9 -1803.6
82 OK NOT OK NOT OK NOT OK NOT OK
83
84 LL Bending Moment tm 42.6 106.5 189.2 231.6 242.0
85 top stress due to LL t/m2 7.9 29.1 62.8 90.6 104.7
86 bottom stress due to LL t/m2 -6.9 -32.6 -63.9 -78.3 -68.9
87
88 STRESS DUE TO TEMP RISE
89 top stress due to temp-rise t/m2 392.9 392.9 392.9 392.9 392.9
90 bottom stress due to temp-rise t/m2 122.5 122.5 122.5 122.5 122.5
91
92 STRESS DUE TO TEMP FALL
93 top stress due to temp-fall t/m2 -212.9 -212.9 -212.9 -212.9 -212.9
94 bottom stress due to temp-fall t/m2 -38.8 -38.8 -38.8 -38.8 -38.8

565263434.xlsx / Flexure PAGE : Date :

 Support 1/8th span 1/4th span 3/8th span
S. No. SECTION Unit Mid span
Section section section section

95
96 Service stage checks without extra time dependent loss without temperature
97 top stress t/m2 132 1068 2402 3667 4457
98 bottom stress t/m2 559 -40 -1108 -1937 -1873
99 OK NOT OK NOT OK NOT OK NOT OK
100
101 Service stage checks without extra time dependent loss with temperature rise& 50% Liveload
102 top stress t/m2 521 1447 2763 4014 4797
103 bottom stress t/m2 685 99 -954 -1776 -1716
104 OK OK NOT OK NOT OK NOT OK
105
106 Service stage checks without extra time dependent loss with temperature fall & 50% Liveload
107 top stress t/m2 -85 841 2157 3409 4191
108 bottom stress t/m2 524 -63 -1115 -1937 -1877
109 OK OK NOT OK NOT OK NOT OK

NOTE : TENSION IS ALLOWED IN TEMP. CASE IN DECK SLAB, (STRESS<MODULUS OF RUPTURE)

110 FOR WHICH UNTENSIONED STEEL IS PROVIDED
111
112 Extra Time Dependent Loss ( 20%)
113 Relaxation Loss t 64.8
114 Creep Loss t -29.8
115 Shrinkage Loss t 24.3
116
117 Stress due to extra Losses in Prestress
118 top stress t/m2 -1.37 0.24 -0.15 -1.53 -3.89
119 bottom stress t/m2 -12.88 -20.72 -21.98 -20.38 -17.57
120
121 Service stage checks with extra time dependent loss without temperature load
122 top stress t/m2 131 1069 2402 3665 4453
123 bottom stress t/m2 546 -61 -1130 -1958 -1890
124 OK NOT OK NOT OK NOT OK NOT OK
125 Service stage checks with extra time dependent loss with temperature rise and 50% Live load
126 top stress t/m2 520 1447 2763 4013 4793
127 bottom stress t/m2 672 78 -976 -1796 -1733
128 OK OK NOT OK NOT OK NOT OK
129 Service stage checks with extra time dependent loss with temperature fall and 50% Live load
130 top stress t/m2 -86 841 2157 3407 4188
131 bottom stress t/m2 511 -83 -1137 -1957 -1894
132 OK OK NOT OK NOT OK NOT OK
NOTE : TENSION IS ALLOWED IN TEMP. CASE IN DECK SLAB, (STRESS<MODULUS OF RUPTURE)
FOR WHICH UNTENSIONED STEEL IS PROVIDED

SUMMARY OF LOSSES
Elastic Shortening Loss -38.23
Relaxation Loss 323.77
Creep Loss -149.23
Shrinkage Loss 121.52
TOTAL LOSS 257.84
Initial Force after Friction & Slip loss 3640.70
% LOSS 7.1

565263434.xlsx / Flexure PAGE : Date :

Check for Ultimate Shear
Grade of Concrete 40 Mpa
Perm. direct shear stress ; t v 4.70 Mpa (As per relevant standard)
Perm. direct shear stress ; t tv 0.42 Mpa (As per relevant standard)
Perm. shear stress in combined shear & torsion; t tu 4.75 Mpa (As per relevant standard)

Section
"d" away from
L/8 L/4 3L/8 L/2
COMPONENT Support
UNIT
Ultimate Shear Capacity of Section uncracked in Flexure (As per relevant standard)
Overall Width, bo m 1.215 1.007 0.651 0.651 0.651
Overall Depth, d m 2.500 2.500 2.500 2.500 2.500
Area of Section m2 6.285 5.781 5.351 5.406 5.518
Dia of duct, f m 0.110 0.110 0.110 0.110 0.110
Effective Width, b = bo-2/3f m 1.142 0.934 0.577 0.577 0.577

Maximum Principal Tensile Stress, ft = 0.24(fck)0.5 Mpa 1.52 1.52 1.52 1.52 1.52

Horizontal Component of prestress after all

KN 3081.1 3167.8 3528.8 3562.1 3522.5
losses
Cg of cable from sofit, Yord m 0.474 0.356 0.251 0.196 0.130
Comp. Stress due to prestress, fcp Mpa 0.490 0.548 0.659 0.659 0.638
Effect of Vertical Prestress, Vpr KN 0.0 0.0 0.0 0.0 0.0
Shear Capacity, Vco = 0.67*b.d.(ft2+.8fcp*ft)0.5 KN 3256.7 2696.1 1703.8 1703.7 1696.8
Vc = Vco + Vpr KN 3256.7 2696.1 1703.8 1703.7 1696.8
Ultimate Shear Capacity of Section cracked in Flexure (As per relevant standard)
Effective Width, b (m) m 1.142 0.934 0.577 0.577 0.577
D1 = (D - Yord) m 2.026 2.144 2.249 2.304 2.370
D2 = 0.8*D m 2.000 2.000 2.000 2.000 2.000
Depth , db m 2.026 2.144 2.249 2.304 2.370
Stress due to prestress. fpt KN/m2 1066.3 1175.1 1321.1 1149.1 906.2
Distance of extreme fibre from centroid, yb m 1.184 1.003 0.807 0.603 0.397
Second Moment of Area, I m4 4.495 3.278 2.389 1.783 1.394

Cracking Moment, Mt = (0.37*(fck)0.5+0.8*fpt).I/y KNm 12121.5 10716.4 10058.6 9638.5 10764.6

Ult. Applied Shear Force, Vult KN 9719 9303 7326 4540 1721
B. Moment corresponding to Ult. Shear Force,
Mult Knm 19977 53134 96846 122744 131121

Shear Capacity, Vcr = 0.037*b*db*(fck)0.5+Mt/M*V KN 6438.2 2344.8 1064.6 667.8 461.4

Design Shear Capacity, Vc KN 3256.7 2344.8 1064.6 667.8 461.4

Check for Limiting Shear for Outer Girder (As per relevant standard)
Ultimate Shear, Vu KN 9718.8 9302.5 7326.0 4539.8 1720.6
Vu -Vpr KN 9718.8 9302.5 7326.0 4539.8 1720.6
Depth , db m 2.026 2.144 2.249 2.304 2.370
t=Vu/(b.db)/1000 MPa 4.202 4.646 5.644 3.413 1.258
Status OK OK NOT OK OK OK
Provision of Shear Reinforcement (As per relevant standard)
Is V less than Vc/2 ? No No No No No
V-Vc (in KN) KN 6462.1 6957.8 6261.3 3872.1 1259.2
Minimum reift., Asv / Sv =
mm2/m 1346.3 1116.1 720.8 720.8 720.8
0.4*b/(.87*fyv)
Shear Reinft. Due to ultimate loads, Asv/Sv = (V-Vc)/
mm2/m 7457 8030 7226 4469 1453
(0.87*fyv*dt)
Design Shear Reinforcement mm2/m 7457.5 8029.6 7225.8 4468.5 1453.2

565263434.xlsx/Ultimate Page- Date:12/17/2021

REINFORCEMENT REQUIRED FOR TORSION
Ult. Applied Torsional Moment, Tult Knm 873.49 807.66 643.59 458.47 326.96
Area enclosed on C/L of Box, Ao m
2 10.70 10.70 10.70 10.70 10.70
Perimeter of Ao m 13.90 13.90 13.90 13.90 13.90
Deck Thickness m 0.225 0.225 0.225 0.225 0.225
Sofit thickness m 0.260 0.260 0.260 0.260 0.260
Total Shear Stress due to torsion : Web MPa 0.07 0.07 0.09 0.07 0.05
Total Shear Stress due to torsion : deck MPa 0.18 0.17 0.13 0.10 0.07
Total Shear Stress due to torsion: sofit MPa 0.16 0.15 0.12 0.08 0.06
Status OK OK OK OK OK
Asv/Sv for torsion/web mm2/m 0.0 0.0 0.0 0.0 0.0
Tot Asl for torsion
Asl for deck mm2/m 0.0 0.0 0.0 0.0 0.0
Asl for web mm2/m 0.0 0.0 0.0 0.0 0.0
Asl for sofit mm /m2
0.0 0.0 0.0 0.0 0.0
EFFECT OF COMBINED TORSION & SHEAR
Total Shear Stress : Web MPa 4.27 4.72 5.74 3.48 1.30
Status OK OK NOT OK OK OK
Total Asv/Sv/web due to torsion & shear mm2/m 3729 4014.8 3612.9 2234.3 726.6
Minimum Asv/Sv/web mm2/m 673 558 360 360 360
Asv/Sv/web required mm /m2
3729 4015 3613 2234 727

Check for Ultimate Moment of Midspan Section (Which is more critical)

I) Failure by Yield of Steel

Area of high tensile steel, As, (mm2) 29674.96
Distance of cg of tendons from compression fibre, db, (mm) 2370.0

Ultimate tensile strength of steel, fp, MPa 1860

Ultimate Moment capacity of steel, Msult, kNm = 0.9*db*As*fp 117731.8

II) Failure by Crushing of Concrete

Width of web, b, (mm) 651
Width of flange, Bf, (mm) 9750
Thickness of flange, t, (mm) 225
Ultimate Moment capacity of concrete, Mcult, (kNm) =
124328.6
0.176*b*db2*fck + 2/3*0.8*(Bf-b)*(db-t/2)*t*fck
III) Ultimate Moment Capacity of Section 117731.8
IV) Applied Ultimate Moment 131121
Status NOT OK

565263434.xlsx/Ultimate Page- Date:12/17/2021

Calculation of Transverse steel in Web -

SL.NO. Units ZONE I : Support to L/8 ZONE II : L/8 to L/4 ZONE III : L/4 to L/2
For Torsion & For TOTAL For Torsion & For TOTAL For Torsion & For TOTAL
Shear Flexure AST Shear Flexure AST Shear Flexure AST
I II (I+II) I II (I+II) I II (I+II)
Outer Face cm2/m 18.64 14.84 33.5 20.07 14.84 34.9 11.17 14.84 26.0
1
Inner Face cm2/m 18.64 12.57 31.2 20.07 12.57 32.6 11.17 12.57 23.7

Provided 25T @ 200 +20T @ 200c/c in both face of Zone I

Provided 20T @ 100c/c in both face of Zone II
Provided 16T @ 200c/c + 20T @ 200c/c in both face of Zone III

565263434.xlsx/Reinf Page- Date:12/17/2021

Shear Parameters of Concrete:

Grade of Concrete 30 35 40 45 50 55 60
Vu 4.1 4.4 4.7 5 5.3 5.5 5.8
Vtc 0.37 0.4 0.42 0.42 0.42 0.42 0.42
Vtu 4.1 4.45 4.75 5.03 5.3 5.56 5.81

Table -2 : Creep of Concrete