Main Beam Prestress

Multibuild Consultants, Vapi

document.xls Loadings - Page 1/35

6.0 ) Loadings

Various loads considered in design are discussed in cl, 2.0.

The forces thus obtained from ETABS is summarized in cl. 6.5, 6.6 & 6.7


Story Beam Load Loc P V2 V3 T M21ST SLAB B89 EQX 0.375 0 -0.22 0 -0.354 01ST SLAB B89 EQX 1.405 0 -0.22 0 -0.354 01ST SLAB B89 EQX 2.434 0 -0.22 0 -0.354 01ST SLAB B89 EQX 3.464 0 -0.22 0 -0.354 01ST SLAB B89 EQX 4.493 0 -0.22 0 -0.354 01ST SLAB B89 EQX 5.523 0 -0.22 0 -0.354 01ST SLAB B89 EQX 6.553 0 -0.22 0 -0.354 01ST SLAB B89 EQX 7.582 0 -0.22 0 -0.354 01ST SLAB B89 EQX 8.612 0 -0.22 0 -0.354 01ST SLAB B89 EQX 9.641 0 -0.22 0 -0.354 01ST SLAB B89 EQX 10.671 0 -0.22 0 -0.354 01ST SLAB B89 EQX 11.7 0 -0.22 0 -0.354 01ST SLAB B89 EQX 12.73 0 -0.22 0 -0.354 01ST SLAB B89 EQY 0.375 0 -34.5 0 0.18 01ST SLAB B89 EQY 1.405 0 -34.5 0 0.18 01ST SLAB B89 EQY 2.434 0 -34.5 0 0.18 01ST SLAB B89 EQY 3.464 0 -34.5 0 0.18 01ST SLAB B89 EQY 4.493 0 -34.5 0 0.18 01ST SLAB B89 EQY 5.523 0 -34.5 0 0.18 01ST SLAB B89 EQY 6.553 0 -34.5 0 0.18 01ST SLAB B89 EQY 7.582 0 -34.5 0 0.18 01ST SLAB B89 EQY 8.612 0 -34.5 0 0.18 01ST SLAB B89 EQY 9.641 0 -34.5 0 0.18 01ST SLAB B89 EQY 10.671 0 -34.5 0 0.18 01ST SLAB B89 EQY 11.7 0 -34.5 0 0.18 01ST SLAB B89 EQY 12.73 0 -34.5 0 0.18 0


M3-1.296-1.075-0.853-0.632

-0.41-0.1890.0320.2540.4750.6970.918

1.141.361

-225.375-189.857

-154.34-118.823

-83.305-47.788

-12.2723.24758.76594.282

129.799165.317200.834


document.xls Force-Summary - Page 4/35

6.5) Bending moment (kN-m) summary for B…. ( Refer Appendix - B)

SECTION 1 2 3 4 5 6 7 8 9 10 11 12 13

Distance 0 1.03 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

Self wt. of Beam Mo -235 -80 46 143 209 246 254 232 180 99 -12 -153 -323

SIDL M1 -60 -23 7 30 46 54 56 51 38 19 -8 -42 -83

Live Load M2 -166 -44 55 131 182 210 215 196 153 87 -3 -116 -253

Earthquake EQ-Y V4 -225 -190 -154 -119 -83 -48 -12 23 59 94 130 165 201

Total BM(D+S+L) M11 -461 -102 55 176 259 305 316 290 226 127 -10 -184 -394

Total BM(D+S+0.5L+E) M12 -603 -134 107 292 418 488 503 461 360 205 -9 -279 -605

Note : Distance is from face of column ( Ref. Fig 1)

6.6) Shear force ( kN) summary for B…. ( Refer Appendix - B)

SECTION 1 2 3 4 5 6 7 8 9 10 11 12 13

Distance 0.0 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

Self wt. of Beam V1 165 137 108 79 50 22 7 36 65 93 122 151 180

SIDL V2 39 33 26 19 12 5 2 9 16 22 29 36 43

Live Load V3 130 107 85 62 39 16 7 30 53 76 99 122 145

Earthquake EQ-Y V4 35 35 35 35 35 35 35 35 35 35 35 35 35

Total SF(D+S+L) V11 334 277 219 160 101 43 16 75 134 191 250 309 368

Total SF(D+S+0.5L+E) V12 304 259 212 164 117 70 48 95 143 188 236 283 331

6.7 ) Torsion ( kN-m) summary for B….

SECTION 1 2 3 4 5 6 7 8 9 10 11 12 13

Distance 0.0 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

Self wt. of Beam T1 0 0 0 0 0 0 0 0 0 0 0 0 0

SIDL T2 0 0 0 0 0 0 0 0 0 0 0 0 0

Live Load T3 0 0 0 0 0 0 0 0 0 0 0 0 0


document.xls CS-prop - Page 5/35

7.0) Summary of Sectional properties : (Ref. fig 2)

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

Dist. Of point of anchorage (m)

WIDTH "B" ( m) 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45

Depth 'D' (m) 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60

0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270

0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300

0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300

0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027

0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027

Area 'A' (m2)

CG from top Yt (m)

CG from bottom Yb (m)

INA (m4 )

Zt (m3)

Zb (m3)


document.xls stresses - Page 6/35

8.0 ) Summary of Stresses due to bending moments : (Ref. cl 6.5 & 7.0)

SECT. 1 2 3 4 5 6 7 8 9 10 11 12 13

C/s Propr 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027

0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027

Mo ft -8.704 -2.963 1.704 5.296 7.741 9.111 9.407 8.593 6.667 3.667 -0.444 -5.667 -11.963

fb 8.704 2.963 -1.704 -5.296 -7.741 -9.111 -9.407 -8.593 -6.667 -3.667 0.444 5.667 11.963

M1 ft -2.222 -0.852 0.259 1.111 1.704 2.000 2.074 1.889 1.407 0.704 -0.296 -1.556 -3.074

fb 2.222 0.852 -0.259 -1.111 -1.704 -2.000 -2.074 -1.889 -1.407 -0.704 0.296 1.556 3.074

M2 ft -6.148 -1.630 2.037 4.852 6.741 7.778 7.963 7.259 5.667 3.222 -0.111 -4.296 -9.370

fb 6.148 1.630 -2.037 -4.852 -6.741 -7.778 -7.963 -7.259 -5.667 -3.222 0.111 4.296 9.370

Zt

Zb


document.xls cable det. - Page 7/35

9.0) Details of cable :

ii) Nos. of strand in cable no. 1, 2 = 2 x 4 = 8 Nos.

i) Nos. of strand in cable no. 3, 4 = 1 x 4 = 4 Nos.

iii) Nos. of strand in cable no. 5 & 6 = 0 x 0 = 0 Nos.

Total no. of strands = 12 Nos.

Ultimate stress of each strand (From Fressynet Prestressing Manual) = 1860

Area of each strand (Nominal dia of strand is 15.3 mm ) = 140

(From Fressynet Prestressing Manual)

Total area of prestressing steel = 12 x 140 = 1680

Ultimate strength of each strand = 1860 x 140 = 260400 N

= 260.4 kN

Ultimate strength of cables

Total strength of cable no. 3, 4 = 4 x 260.4 = 1042 kN

Total strength of cable no. 1, 2 = 8 x 260.4 = 2083 kN

Total strength of cable no. 5, 6 0 x 260.4 = 0 kN

Factored strength of cables

Factored strength of cable no. 3, 4 = 1042 x 0.8 = 833 kN

Factored strength of cable no. 1, 2 = 2083 x 0.8 = 1667 kN

N/mm2

mm2

mm2


document.xls cable det. - Page 8/35

Factored strength of cable no. 5 & 6 = 0 x 0.8 = 0 kN


document.xls cab. profile & forces - Page 9/35

10.0) Cable profile ( Ref EPMC-DTD-AZN-STR-DWD-53264 ) ###

0.129492

Sr. Cable No. Y1 X1 Angle at start Inclined Straight Total

No. Tan(theta) In Degrees Length Length Length

1 1 2 1, 2 525 - 125 = 400 6178 0.1288 7.38 12382 0 12382

2 3 4 3, 4 525 - 125 = 400 6178 0.1295 7.38 12382 0 12382

3 5 6 5, 6 310 - 225 = 85 6178 0.0138 0.79 12357 0 12357 ###

###

10.1 ) Cable ordinates and c.g. from bottom about various section in (mm) :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X x 0 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

1 , 2 y 525 403 303 225 169 136 125 136 169 225 303 403 525

3 , 4 y 525 403 303 225 169 136 125 136 169 225 303 403 525

Combined CG

1 , 2 , 3 & 4 525 403 303 225 169 136 125 136 169 225 303 403 525

5, 6 y 310 284 263 246 234 227 225 227 234 246 263 284 310

Combined

c.g. of all 525 403 303 225 169 136 125 136 169 225 303 403 525

cables

1 to 6

Nos. of strand in cable no. 1, 2 = 8

Nos. of strand in cable no. 3, 4 = 4

Nos. of strand in cable no. 5 & 6 = 0

Total no. of cable = 12



10.2 ) Horizontal angle in radians at various section :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

cab. No.

1, 2 0.1288 0.1075 0.0861 0.0647 0.0432 0.0216 0.0000 0.0216 0.0431 0.0646 0.0861 0.1075 0.1288

cab. No.

3, 4 0.1288 0.1075 0.0861 0.0647 0.0432 0.0216 0.0000 0.0216 0.0431 0.0646 0.0861 0.1075 0.1288

cab. No.

5, 6 0.0275 0.0229 0.0183 0.0138 0.0092 0.0046 0.0000 0.0046 0.0092 0.0138 0.0183 0.0229 0.0275

10.3 ) Horizontal angle at various section (in Degree ) :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0 1.03 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

cab. No.

1, 2 7.38 6.16 4.93 3.70 2.47 1.24 0.00 1.24 2.47 3.70 4.93 6.16 7.38

cab. No.

3, 4 7.38 6.16 4.93 3.70 2.47 1.24 0.00 1.24 2.47 3.70 4.93 6.16 7.38

cab. No.

5, 6 1.58 1.31 1.05 0.79 0.53 0.26 0.00 0.26 0.53 0.79 1.05 1.31 1.58

10.4 ) Forces after losses due to slip in each cable (KN) : ( Ref. cl 11.0 & 11.1 )

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.00 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

cab. No.

1, 2 697 704 711 718 732 739 746 753 760 762 757 750 743

cab. No.

3, 4 658 665 671 677 702 699 697 704 710 717 724 717 711

cab. No.



5, 6 #DIV/0! #DIV/0! #DIV/0! #DIV/0! ### ### #DIV/0! #DIV/0! #DIV/0! 0 0 0 0

10.5 ) Total Forces after losses due to slip (KN) :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.00 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

cab. No.

1, 2 2 Nos. 1395 1408 1422 1435 1463 1477 1491 1506 1520 1525 1515 1501 1486

cab. No.

3, 4 1 Nos. 658 665 671 677 702 699 697 704 710 717 724 717 711

cab. No.

5, 6 0 Nos. 0 0 0 0 0 0 0 0 0 0 0 0 0

Total 2053 2073 2093 2113 2165 2176 2188 2209 2230 2242 2239 2218 2197

Avg. force in cable = 2169 KN Avg. stress in cable 1, 2 ,3 & 4 1291 = 0.694 UTS

Avg. stress in cable 5 & 6 #DIV/0! = #DIV/0! UTS

Force per strand = 2169 = 181 KN

12

Avg. Stress in cable = 181 x 1000 = 1291 = 0.694 UTS

140

10.6 ) Horizontal component of force at various section (in KN ) :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.00 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

cab. No.

1, 2 1383 1400 1416 1432 1462 1477 1491 1505 1519 1522 1509 1492 1474

cab. No.

3, 4 653 661 668 676 701 699 697 704 710 716 722 713 705

cab. No.

1, 2 , 3 & 4 2036 2061 2085 2108 2163 2176 2188 2209 2228 2237 2231 2205 2179

cab. No.

N/mm2

N/mm2

N/mm2



5, 6 0 0 0 0 0 0 0 0 0 0 0 0 0

Total 2036 2061 2085 2108 2163 2176 2188 2209 2228 2237 2231 2205 2179

10.7 ) Vertical component of force at various section (in KN ) :

section 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.00 1.03 2.06 3.09 4.12 5.15 6.18 7.21 8.24 9.27 10.30 11.33 12.36

cab. No.

1, 2 179 151 122 93 63 32 0 32 66 98 130 161 191

cab. No.

3, 4 85 71 58 44 30 15 0 15 31 46 62 77 91

cab. No.

1, 2 , 3 & 4 264 222 180 136 93 47 0 48 96 145 193 238 282

cab. No.

5, 6 0 0 0 0 0 0 0 0 0 0 0 0 0

Total 264 222 180 136 93 47 0 48 96 145 193 238 282


document.xls slip loss-1 - Page 13/35

For cable 1 & 2

Cable 1 4 T13 k= 0.003 0.30

Area= 560 mm2 Es= 195000 MPa

P ult 1042 kN

P jacking 0.800 833 kN

Point 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

Y 0.525 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

0.000 1.030 1.029 1.030 1.029 1.030 1.030 1.029 1.030 1.029 1.030 1.029 1.030

0.000 0.122 0.100 0.078 0.056 0.033 0.011 0.011 0.033 0.056 0.078 0.100 0.122

parabola parabola parabola parabola parabola parabola parabola parabola parabola parabola parabola parabola parabola

q 0.1288 0.1288 0.1075 0.0861 0.0647 0.0432 0.0216 0.0000 0.0216 0.0431 0.0646 0.0861 0.1075 0.1288

0.0000 0.0213 0.0427 0.0641 0.0856 0.1072 0.1288 0.1503 0.1719 0.1934 0.2149 0.2362 0.2575

l 0.000 1.037 1.034 1.033 1.030 1.031 1.030 1.029 1.031 1.030 1.033 1.034 1.037 12.389

Total length 'L' 0.000 1.037 2.071 3.104 4.135 5.165 6.195 7.224 8.255 9.285 10.318 11.352 12.389

0.0000 0.0095 0.0190 0.0285 0.0381 0.0477 0.0572 0.0668 0.0763 0.0859 0.0954 0.1049 0.1144

Friction coefficcient 1.000 1.0000 0.9905 0.9812 0.9719 0.9626 0.9535 0.9444 0.9354 0.9265 0.9177 0.9090 0.9004 0.8919

Prestressing Force 833 833 825 818 810 802 795 787 779 772 765 757 750 743

Effect of Slip 6.0 mm

Fix pt dtst from A = 9.60 m

Point 1 2 3 4 5 6 7 8 9 10 Fixed Pt 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 9.600 10.296 11.325 12.355

Before slip 833 0.000 833 1.030 825 1.029 818 1.030 810 1.029 802 1.030 795 1.030 787 1.029 779 1.030 772 1.029 765 0.334 762 1.030 757 1.029 750 1.030 743

After slip 697 697 704 711 718 725 732 739 746 753 760 762 757 750 743

Average loss of force 136 129 114 99 85 70 56 41 27 12 2 0 0 0

loss of elongation 6.0 mm

Elongation at jacking 0.00 7.88 7.78 7.70 7.61 7.53 7.46 7.38 7.32 7.25 7.20 7.14 7.09 89 mm

136

11.0 ) 'Calculation of Friction Losses and Slip

m=

DX

DY

Change in angle 'Dq

mq+kl



For cable 3 & 4

4 T13 k= 0.003 0.300

Area= 560 mm2 Es= 195000 MPa

P ult 1042 kN


Point 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

Y 0.525 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

0.000 1.030 1.029 1.030 1.029 1.030 1.030 1.029 1.030 1.029 1.030 1.029 1.030

0.000 0.122 0.100 0.078 0.056 0.033 0.011 0.011 0.033 0.056 0.078 0.100 0.122


q 0.1288 0.1288 0.1075 0.0861 0.0647 0.0432 0.0216 0.0000 0.0216 0.0431 0.0646 0.0861 0.1075 0.1288

0.00 0.02 0.04 0.06 0.17 0.15 0.13 0.15 0.17 0.19 0.21 0.24 0.26

l 0.000 1.037 1.034 1.033 1.030 1.031 1.030 1.029 1.031 1.030 1.033 1.034 1.037 12.389

Total length 'L' 0.000 1.037 2.071 3.104 4.135 5.165 6.195 7.224 8.255 9.285 10.318 11.352 12.389

0.0000 0.0095 0.0190 0.0285 0.0640 0.0606 0.0572 0.0668 0.0763 0.0859 0.0954 0.1049 0.1144





Point 1 2 3 4 5 6 7 8 9 10 Fixed Pt 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.310 10.296 11.325 12.355

Before slip 797 0.000 797 1.030 789 1.029 782 1.030 774 1.029 747 1.030 750 1.030 753 1.029 745 1.030 738 1.029 731 1.044 724 1.030 724 1.029 717 1.030 711

After slip 658 658 665 671 677 702 699 697 704 710 717 724 724 717 711

Average loss of force 139 132 118 104 71 48 53 49 35 21 7 0 0 0

loss of elongation 6.0 mm


elongation


m=

DX

DY

Change in angle 'Dq

mq+kl



For cable 5 & 6

Cable 1 0 T13 k= 0.003 0.30

Area= 0 mm2 Es= 195000 MPa

P ult 0 kN


Point 1 2 3 4 5 6 7 8 9 10 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

Y 0.310 0.310 0.284 0.263 0.246 0.234 0.227 0.225 0.227 0.234 0.246 0.263 0.284 0.310

0.000 1.030 1.029 1.030 1.029 1.030 1.030 1.029 1.030 1.029 1.030 1.029 1.030

0.000 0.026 0.021 0.017 0.012 0.007 0.002 0.002 0.007 0.012 0.017 0.021 0.026


q 0.0275 0.0275 0.0229 0.0183 0.0138 0.0092 0.0046 0.0000 0.0046 0.0092 0.0138 0.0183 0.0229 0.0275

0.0000 0.0046 0.0092 0.0138 0.0367 0.0321 0.0275 0.0321 0.0367 0.0413 0.0458 0.0504 0.0550

l 0.000 1.030 1.029 1.030 1.029 1.030 1.030 1.029 1.030 1.029 1.030 1.029 1.030 12.357

Total length 'L' 0.000 1.030 2.060 3.090 4.119 5.149 6.179 7.208 8.238 9.267 10.297 11.326 12.357

0.0000 0.0045 0.0089 0.0134 0.0234 0.0251 0.0268 0.0313 0.0357 0.0402 0.0446 0.0491 0.0536





Point 1 2 3 4 5 6 7 8 9 10 Fixed Pt 11 12 13

X 0.000 0.000 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.310 10.296 11.325 12.355

Before slip 0 0.000 0 1.030 0 1.029 0 1.030 0 1.029 0 1.030 0 1.030 0 1.029 0 1.030 0 1.029 0 1.044 0 1.030 0 1.029 0 1.030 0

After slip #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0 0 0 0

Average loss of force #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0 0 0

loss of elongation #DIV/0! mm


elongation


m=

DX

DY

Change in angle 'Dq

mq+kl



9478.83

7 9.47883

138.245



9693.24

7 9.69324

135.187



#DIV/0!

0 #DIV/0!

#DIV/0!


document.xls First I- stage - Page 19/35

12.0 ) Resultant stresses immediately after first stage prestress :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

Horizontal cable Ref.

Force (kN) Cl. 10.6 2036 2061 2085 2108 2163 2176 2188 2209 2228 2237 2231 2205 2179

Area of section Ref.

Cl. 7.0 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270

Cl. 7.0 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

c.g. of c/s from Bottom Ref.

Yb (mm) Cl. 7.0 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300

c.g. of cable from Ref.

Bottom (mm) Cl. 7.0 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

Eccentricity -0.225 -0.103 -0.003 0.075 0.131 0.164 0.175 0.164 0.131 0.075 -0.003 -0.103 -0.225

e = Yb - c.g.

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

P/A 7.5 7.6 7.7 7.8 8.0 8.1 8.1 8.2 8.3 8.3 8.3 8.2 8.1

-17.0 -7.8 -0.2 5.9 10.5 13.2 14.2 13.4 10.8 6.2 -0.2 -8.4 -18.1

-17.0 -7.8 -0.2 5.9 10.5 13.2 14.2 13.4 10.8 6.2 -0.2 -8.4 -18.1

24.5 15.5 7.9 2.0 -2.4 -5.1 -6.1 -5.2 -2.5 2.1 8.5 16.6 26.2

-9.4 -0.2 7.5 13.7 18.5 21.3 22.3 21.6 19.0 14.5 8.0 -0.2 -10.1

Stress at c.g. 20.3 10.3 7.7 9.3 12.6 15.3 16.4 15.5 12.9 9.8 8.3 11.0 21.7

Due to prestress

Stress due to M0

At top -8.7 -3.0 1.7 5.3 7.7 9.1 9.4 8.6 6.7 3.7 -0.4 -5.7 -12.0

At bottom 8.7 3.0 -1.7 -5.3 -7.7 -9.1 -9.4 -8.6 -6.7 -3.7 0.4 5.7 12.0

Resultant stress

At top 15.8 12.5 9.6 7.2 5.3 4.0 3.3 3.4 4.1 5.7 8.0 10.9 14.3

At bottom -0.7 2.8 5.8 8.4 10.7 12.2 12.9 13.0 12.4 10.8 8.5 5.5 1.9

Depth of Beam (m) 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600

Stress at

c.g. of cable 13.739 9.303 7.739 7.948 9.191 10.296 10.890 10.811 10.042 8.925 8.261 9.097 12.705

Avg. stress at c.g. of cable = 9.9

(mm2)

I (m4)

Zt (m3)

Zb (m3)

P e/ Zt

P e/ Zb

P/A - Pe/Zt

P/A + Pe/Zb

N/mm2


document.xls Mod-Losses-FIRST STAGE - Page 20/35

13.0 ) LOSSES IN FIRST STAGE PRESTRESS :

( As per IS : 1343-1980, Cl 18.5)

Average stress in cable at first stage cable due to first stage prestress = 1291 ( Ref. cl 10.5 )

Average stress in concrete at CG of first stage cable = 9.9 ( Ref. cl 12.0 )

13.1) Loss due to elastic shortening : (IS 1343:1980, Cl 18.5.2.4 b)

= 1 x modular ratio x avg. stress in concrete at c.g. of cable

2

Grade of concrete at the time of stressing = 35

Ec = 5000 x 35

= 29580

m = 195000 = 6.6

29580

Loss = 0.5 x 6.6 x 9.9 = 32.7 = 2.53 %

13.2) Due to creep of concrete : (IS 1343:1980, Cl 18.5.2.1)

Creep strain between 3 days = 0.00083 - 0.00044 = 0.00039

Age of loading @ 28 days Take creep coefficient = 1.6

Loss = 1.6 x 9.9 x 6.6 = 104.6 = 8.1 %

13.3) Due to shrinkage of concrete : (IS 1343:1980, Cl 18.5.2.2)

Shrinkage strain = 0.0002/Log(t +2) = 0.00021

Between 3 and 21 days

Loss = 0.00021 x 195000 = 40.9 = 3.2 %

13.4) Loss due to relaxation of H.T. steel at first stage loss : (IS 1343:1980, Cl 18.5.2.3)

@ 0.694 UTS = = 70.0 = 5.42 %

Total loss due to elastic shortening, creep , shrinkage & relaxation :

= 32.7 + 104.6 + 40.9 + 70.0 = 248 = 19.2 %

% instantaneous loss = 2.53 %

Balance loss = 19.2 - 2.53 = 16.7 %

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2


document.xls Mod-Losses-FIRST STAGE - Page 21/35

Initial Relaxation

stress Loass

0.5 fp 0

0.55 17.5

0.6 fp 35

0.68 61.95

0.7 fp 70

0.75 80

0.8 fp 90


document.xls perm-stress - Page 22/35

17.0) Permissible stresses

These permissible stresses at various stages are as per design basis report cl. 7.10.7.1

Using IS: 1343-1980, the allowable stresses in flexure can be summaraied as follows for Type-2 post-tensioned members

Concrete strength Ref. clause Tension value Compression value

At transfer

fci Cl. 19.3.3 & Fig 8A -3 Mpa 0.455 * fci

In Service

fcu Cl. 22.7.1(b) & Fig 7 -3 Mpa 0.380 * fci

Permissible stress at first stage prestress If concrete grade is 35 Mpa

Permissible stress in service If concrete grade is 45 Mpa

Concrete strength Ref. clause Tension value Compression value

At transfer

fci Cl. 19.3.3 & Fig 8A -3 Mpa 15.9 Mpa

In Service

fcu Cl. 22.7.1(b) & Fig 7 -3 Mpa 17.1 Mpa

Multibuild Consultants, Vapi Delhi Metro Rail CorporationJaipur Metro : Stage-1 ( JP/EW/C2)

document.xls Recap - Total 04/18/2023 22:18:22

16.0) Resultant stresses at all stages :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

First stage prestressing

top 24.5 15.5 7.9 2.0 -2.4 -5.1 -6.1 -5.2 -2.5 2.1 8.5 16.6 26.2

bot. -9.4 -0.2 7.5 13.7 18.5 21.3 22.3 21.6 19.0 14.5 8.0 -0.2 -10.1

Mo top -8.7 -3.0 1.7 5.3 7.7 9.1 9.4 8.6 6.7 3.7 -0.4 -5.7 -12.0

bot. 8.7 3.0 -1.7 -5.3 -7.7 -9.1 -9.4 -8.6 -6.7 -3.7 0.4 5.7 12.0

Resultant stress top 15.8 12.5 9.6 7.2 5.3 4.0 3.3 3.4 4.1 5.7 8.0 10.9 14.3

bot. -0.7 2.8 5.8 8.4 10.7 12.2 12.88 13.0 12.4 10.8 8.5 5.5 1.9

top 0.62 0.39 0.20 0.05 -0.06 -0.13 -0.15 -0.13 -0.06 0.05 0.21 0.42 0.66

2.53 bot. -0.24 -0.01 0.19 0.35 0.47 0.54 0.56 0.55 0.48 0.37 0.20 -0.01 -0.26

M1 top -2.22 -0.85 0.26 1.11 1.70 2.00 2.07 1.89 1.41 0.70 -0.30 -1.56 -3.07

bot. 2.22 0.85 -0.26 -1.11 -1.70 -2.00 -2.07 -1.89 -1.41 -0.70 0.30 1.56 3.07


bot. 1.3 3.6 5.7 7.6 9.5 10.7 11.4 11.7 11.4 10.5 9.0 7.0 4.7

M2 top -6.15 -1.63 2.04 4.85 6.74 7.78 7.96 7.26 5.67 3.22 -0.11 -4.30 -9.37

bot. 6.15 1.63 -2.04 -4.85 -6.74 -7.78 -7.96 -7.26 -5.67 -3.22 0.11 4.30 9.37


bot. 7.4 5.2 3.7 2.8 2.7 2.9 3.4 4.4 5.8 7.3 9.1 11.3 14.1

top 4.1 2.6 1.3 0.3 -0.4 -0.9 -1.0 -0.9 -0.4 0.3 1.4 2.8 4.4

16.7 bot. -1.6 0.0 1.3 2.3 3.1 3.5 3.7 3.6 3.2 2.4 1.3 0.0 -1.7

Resultant stress top 4.0 7.8 10.8 12.9 14.1 14.5 14.2 13.3 11.6 9.4 6.4 2.7 -1.9

bot. 9.0 5.3 2.4 0.5 -0.3 -0.6 -0.3 0.8 2.6 4.9 7.8 11.3 15.8

Min stress 1.3 3.6 2.4 0.5 -0.3 -0.6 -0.3 0.8 2.6 4.9 6.4 2.7 -1.9

Max stress 14.2 12.1 12.1 13.3 14.1 14.5 14.2 13.3 11.6 10.5 9.1 11.3 15.8

Maximum allowable tensile stress in serivce condition is -3.0 < -1.9 SAFE

Maximum allowable compressive stress in serivce condition is 17.1 > 15.8 SAFE

Maximum allowable tensile stress at transfer -3.0 < -0.7 SAFE

Maximum allowable compressive stress transfer 15.9 > 15.8 SAFE

P/A - Pe/Zt gir

P/A + Pe/Zb

% Instantaneos loss due to first stage prestressing

% balance loss due to first stage prestressing


document.xls ULS Shear - Page 24/35

19.0 ) ULS shear force summary at various sections : ( Ref. Cl. 6.6, 10.6, 10.7 & cl. 15 )

i ) Shear in normal condition :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

ULS factor

V11 (kN) 1.5 334 277 219 160 101 43 16 75 134 191 250 309 368

V11 ULS shear (kN) 501 416 329 240 152 65 24 113 201 287 375 464 552

1645 1665 1684 1703 1747 1758 1768 1784 1800 1807 1802 1781 1760

213 180 145 110 75 38 0 38 78 117 156 192 228

ii ) Shear in Earthquake condition :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

ULS factor

V12 (kN) 1.5 304 259 212 164 117 70 48 95 143 188 236 283 331

V12 ULS shear (kN) 456 388 317 246 175 105 71 143 214 282 353 425 496

1645 1665 1684 1703 1747 1758 1768 1784 1800 1807 1802 1781 1760

213 180 145 110 75 38 0 38 78 117 156 192 228

Horizontal component of prestress force (kN) after all losses

Vertical component prestress force (kN) after all losses

Horizontal component of prestress force (kN) after all losses

Vertical component prestress force (kN) after all losses


document.xls Shear Chk - Page 25/35

19.1) DESIGN OF SHEAR FORCE AS OBTAINED FROM CL. 19.0 ( i) The shear reinf. Is designed as per IS 1343: Cl 22.4.1

Grade of concrete = 45 No. of duct = 2 Clear cover = 40 mm

Fy = 415 Mpa Avg. duct Dia. = 70 mm

Section uncracked in flexure :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

b = Thickness of web after deducting dia. Of duct (in mm) 357 357 357 357 357 357 357 357 357 357 357 357 357

(assuming ducts are grouted)

d = over alldepth of girder (mm) 600 600 600 600 600 600 600 600 600 600 600 600 600

ft = Max. principle tensile stress 0.24 x fck 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

fcp = compressive stress at c.g. of section 13.74 9.30 7.74 7.95 9.19 10.30 10.89 10.81 10.04 8.93 8.26 9.10 12.70

due to prestress ( Ref cl. 16 )

Vco = Ult. shear resistance of a uncracked section in flexure (kn) 646 547 508 514 545 571 584 583 565 538 522 542 624

=

Section cracked in flexure :

fpt = compressive stress due to prestress ( Ref cl. 16 ) 11.1 7.5 6.3 6.4 7.4 8.3 8.8 8.7 8.1 7.2 6.7 7.3 10.3

0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

= (m) 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300

cg cable from bottom (m) 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

dt = 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552

db = Distance from extreme compression fibre to the tendons 0.07 0.20 0.30 0.38 0.43 0.46 0.48 0.46 0.43 0.38 0.30 0.20 0.08

at the section under consideration ( d - cg cable )

Mt = 307 229 202 206 227 247 257 256 242 223 211 226 289

Mu in (kn-m) ( Ref. Cl. 20) 692 153 83 264 389 458 474 435 339 191 15 276 590

Vu in (kn) ( Ref. Cl. 19.0 ) 501 416 329 240 152 65 24 113 201 287 375 464 552

Vcr = + Mtx Vu / Mu 229 640 830 220 127 76 55 107 182 367 5466 397 -

Min. Vcr = 144 144 144 144 144 144 144 144 144 144 144 144 144

Section is Cracked Uncracked Uncracked Cracked Cracked Cracked Cracked Cracked Cracked Uncracked Uncracked Cracked Cracked

Vertical cable force component after losse in (kn) ( Ref. Cl. 19.0 ) 213 180 145 110 75 38 0 38 78 117 156 192 228

Vc = minimum (Vco or Vcr ) 229 547 508 220 127 76 55 107 182 367 522 397 624

0 90 73 0 0 0 0 0 0 58 78 0 0

Vc/2 114 274 254 110 63 38 28 54 91 184 261 199 312

Remark : if Vu > Vc shear reinf.(SR) Required SR req. SR not req. SR not req. SR req. SR req. SR not req. SR not req. SR req. SR req. SR not req. SR not req. SR req. SR not req.

Required Shear reinforcement (SR)

Asv = Vu + 0.4 b. dt - Vc 2.4 -0.1 -0.3 1.1 1.1 0.9 0.8 1.0 1.1 0.3 -0.1 1.3 0.6

Sv 0.87 x fy x dt

Min. shear reinforcement required

Asv = 0.4 x b 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Sv 0.87 x fy

Provide shear reinforcement Leg 4 4 4 4 4 4 4 4 4 4 4 4 4

tor 10 10 10 10 10 10 10 10 10 10 10 10 10

@ c/c 100 100 100 100 150 150 150 150 150 100 100 100 100

shear reinforcement provided in 3.1 3.1 3.1 3.1 2.1 2.1 2.1 2.1 2.1 3.1 3.1 3.1 3.1

N/mm2

0.67 x b x dx ft2 + 0.8 x fcp x ft )

INA in m4

Yb

( 0.37x fck + 0.8x fpt) x I/Yb

0.037 x b x db x fck

0.1 x b x d x fck

mm2 / mm

mm2 / mm

mm2 / mm


document.xls Shear Chk - Page 26/35

Remark safe safe safe safe safe safe safe safe safe safe safe safe safe


document.xls Shear Chk EQ - Page 27/35

19.1) DESIGN OF SHEAR FORCE AS OBTAINED FROM CL. 19.0 ( i) The shear reinf. Is designed as per IS 1343: Cl 22.4.1

Grade of concrete = 45 No. of duct = 2 Clear cover = 40 mm

Fy = 415 Mpa Avg. duct Dia. = 70 mm

Section uncracked in flexure :

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

b = Thickness of web after deducting dia. Of duct (in mm) 357 357 357 357 357 357 357 357 357 357 357 357 357

(assuming ducts are grouted)

d = over alldepth of girder (mm) 600 600 600 600 600 600 600 600 600 600 600 600 600

ft = Max. principle tensile stress 0.24 x fck 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

fcp = compressive stress at c.g. of section 13.74 9.30 7.74 7.95 9.19 10.30 10.89 10.81 10.04 8.93 8.26 9.10 12.70

due to prestress ( Ref cl. 16 )

Vco = Ult. shear resistance of a uncracked section in flexure (kn) 646 547 508 514 545 571 584 583 565 538 522 542 624

=

Section cracked in flexure :

fpt = compressive stress due to prestress ( Ref cl. 16 ) 11.1 7.5 6.3 6.4 7.4 8.3 8.8 8.7 8.1 7.2 6.7 7.3 10.3

0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

= (m) 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300

cg cable from bottom (m) 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

dt = 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552

db = Distance from extreme compression fibre to the tendons 0.07 0.20 0.30 0.38 0.43 0.46 0.48 0.46 0.43 0.38 0.30 0.20 0.08

at the section under consideration ( d - cg cable )

Mt = 307 229 202 206 227 247 257 256 242 223 211 226 289

Mu in (kn-m) ( Ref. Cl. 20) 724 161 128 351 502 586 604 553 432 246 10 334 726

Vu in (kn) ( Ref. Cl. 19.0 ) 456 388 317 246 175 105 71 143 214 282 353 425 496

Vcr = + Mtx Vu / Mu 200 569 528 178 117 85 72 107 158 289 7167 304 -

Min. Vcr = 144 144 144 144 144 144 144 144 144 144 144 144 144

Section is Cracked Uncracked Uncracked Cracked Cracked Cracked Cracked Cracked Cracked Cracked Uncracked Cracked Cracked

Vertical cable force component after losse in (kn) ( Ref. Cl. 19.0 ) 213 180 145 110 75 38 0 38 78 117 156 192 228

Vc = minimum (Vco or Vcr ) 200 547 508 178 117 85 72 107 158 289 522 304 624

0 90 73 0 0 0 0 0 0 0 78 0 0

Vc/2 100 274 254 89 59 43 36 53 79 144 261 152 312

Remark : if Vu > Vc shear reinf.(SR) Required SR req. SR not req. SR not req. SR req. SR req. SR req. SR not req. SR req. SR req. SR not req. SR not req. SR req. SR not req.

Required Shear reinforcement (SR)

Asv = Vu + 0.4 b. dt - Vc 2.3 -0.3 -0.3 1.3 1.3 1.1 1.0 1.2 1.3 1.0 -0.2 1.6 0.4

Sv 0.87 x fy x dt

Min. shear reinforcement required

Asv = 0.4 x b 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Sv 0.87 x fy

Provide shear reinforcement Leg 4 4 4 4 4 4 4 4 4 4 4 4 4

tor 10 10 10 10 10 10 10 10 10 10 10 10 10

@ c/c 100 100 100 100 150 150 150 150 150 100 100 100 100

shear reinforcement provided in 3.1 3.1 3.1 3.1 2.1 2.1 2.1 2.1 2.1 3.1 3.1 3.1 3.1

N/mm2

0.67 x b x dx ft2 + 0.8 x fcp x ft )

INA in m4

Yb

( 0.37x fck + 0.8x fpt) x I/Yb

0.037 x b x db x fck

0.1 x b x d x fck

mm2 / mm

mm2 / mm

mm2 / mm


document.xls Shear Chk EQ - Page 28/35



document.xls BM ULT - Page 29/35

20.0 ) ULS Bending moment summary at various sections : ( Ref. Cl. 6.5 )

ULS strength of section is checked in normal & eathquake condition

i) ULS BM in normal condition

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

Distance 0 1.030 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

M11 -461 -102 55 176 259 305 316 290 226 127 -10 -184 -394

Total ULS mom (kN-m) -692 -153 83 264 389 458 474 435 339 191 -15 -276 -590

ii) ULS BM in Earthquake condition

Section 1 2 3 4 5 6 7 8 9 10 11 12 13

Distance 0 1.03 2.059 3.089 4.118 5.148 6.178 7.207 8.237 9.266 10.296 11.325 12.355

M12 -603 -134 107 292 418 488 503 461 360 205 -9 -279 -605

Total ULS mom (kN-m) -724 -161 128 351 502 586 604 553 432 246 -10 -334 -726

ULS factor are as follows :

1.5 M11

1.20 M12

Note : As per IS/CBC, cl. 10.3.1, The effect of creep, shrinkage, temperature need not be considered at ultimate limit state.

However this has been considered when adding to the moment which is conservative.


document.xls bm-ult - Page 30/35

20.1) ULS Check for moment as obtained from cl. 20.0 (i) with out earthquake :

i) Ultimate capacity of section considering failure by yielding of H.T. steel :

Mult. =

ii) Ultimate capacity of section by considering failure by crushing of concrete :

Mult. =

Calculation of Ultimate Moment Capacity at Various Sections

Grade of concrete = 45

Depth of girder = D ( Ref. Cl. 7.0 )

Width of section = B ( Ref. Cl. 7.0 )

c.g. of tendons from top = ( Ref. Cl. 10.1 )

Fpb/(0.87fpu ) ( Ref IRS CBC / Tab 25 )

Fpu = Fp * As

As = ( 12 + 0 ) 140 = 1680 ( Ref. Cl. 9.0 )

Sect. 1 2 3 4 5 6 7 8 9 10 11 12 13

(kN-m) -692 -153 83 264 389 458 474 435 339 191 -15 -276 -590 ( Ref. cl. 20.0 )

D m 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600

B m 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450

m 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

m 0.53 0.40 0.30 0.38 0.43 0.46 0.48 0.46 0.43 0.38 0.30 0.40 0.52

Ac 0.12 0.09 0.07 0.08 0.09 0.10 0.10 0.10 0.09 0.08 0.07 0.09 0.12

cg1 0.13 0.10 0.07 0.09 0.11 0.11 0.12 0.11 0.11 0.09 0.07 0.10 0.13

(kN-m) 824 436 238 378 499 579 607 579 499 378 246 436 741

As 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680

fp 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860

(Ap fp) / (b d fck) 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257

0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900

Xu/d 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488 0.488

fpu 1456 1456 1456 1456 1456 1456 1456 1456 1456 1456 1456 1456 1456

Xu m 0.26 0.20 0.15 0.18 0.21 0.23 0.23 0.23 0.21 0.18 0.15 0.20 0.26

Ast 0 0 0 0 0 0 0 0 0 0 0 0 0

(kN-m) 1021 783 578 729 837 902 924 902 838 730 589 783 1021

824 436 238 378 499 579 607 579 499 378 246 436 741


Note : 1) If ( Mult req < min ( Mult steel , Mult conc) then the section is safe

fpu Ap ( db - 0.42 xu)

0.4 fck. Ac ( db - cg1)

N/mm2

c.g.st

mm2

Mult. Req.

c.g.st

db = D-cgst or cgst

Mult. conc.

(mm2)

(N/mm2)

fpu/(0.87fpu

(mm2)

Mult. steel

Mult. Available


document.xls bm-ult - Page 31/35

2) Non-tensioned reinforcement in box-girder is not considered for resisting ULS moment.


document.xls bm ult EQ - Page 32/35

20.2) ULS Check for moment as obtained from cl. 20.0 (ii) with earthquake :

i) Ultimate capacity of section considering failure by yielding of H.T. steel :

Mult. =

ii) Ultimate capacity of section by considering failure by crushing of concrete :

Mult. =

Calculation of Ultimate Moment Capacity at Various Sections

Grade of concrete = 45

Depth of girder = D ( Ref. Cl. 7.0 )

Equivalent width of section = b ( Ref. Cl. 7.0 )

c.g. of tendons from top = ( Ref. Cl. 10.1 )

Fpb/(0.87fpu ) ( Ref IRS CBC / Tab 25 )

Fpu = Fp * As

As = ( 12 + 0 ) 140 = 1680 ( Ref. Cl. 9.0 )

Sect. 1 2 3 4 5 6 7 8 9 10 11 12 13

(kN-m) -724 -161 128 351 502 586 604 553 432 246 -10 -334 -726 ( Ref. cl. 20.0 )

D m 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600

m 3.320 3.320 3.320 3.320 3.320 3.320 3.320 2.600 2.600 2.600 3.320 3.320 3.320

m 0.525 0.403 0.303 0.225 0.169 0.136 0.125 0.136 0.169 0.225 0.303 0.403 0.525

m 0.53 0.40 0.30 0.38 0.43 0.46 0.48 0.46 0.43 0.38 0.30 0.40 0.52

Assuming Xu m 0.25 0.35 0.30 0.35 0.30 0.30 0.30 0.30 0.30 0.35 0.30 0.30 0.30

Ac 0.83 1.16 1.00 1.16 1.00 1.00 1.00 0.78 0.78 0.91 1.00 1.00 1.00

cg1 0.13 0.18 0.15 0.18 0.15 0.15 0.15 0.15 0.15 0.18 0.15 0.15 0.15

(kN-m) 5976 4287 2375 3765 4526 5065 5244 3966 3545 2949 2464 4076 6049

As 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680 1680

fp 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860 1860

Xu/d 0.476 0.869 1.009 0.933 0.697 0.647 0.632 0.647 0.697 0.933 0.991 0.745 0.572

1.00 1.00 1.00 1.00 1.00 1.00 0.89 1.00 1.00 1.00 1.00 1.00 1.00

Ast 0 0 0 0 0 0 0 0 0 0 0 0 0

(kN-m) 1087 619 400 544 763 853 786 853 763 544 415 687 1019

1087 619 400 544 763 853 786 853 763 544 415 687 1019


Note : 1) If ( Mult req < min ( Mult steel , Mult conc) then the section is safe

2) Non-tensioned reinforcement in box-girder is not considered for resisting ULS moment.

fpb Aps ( db - cg1)

0.4 fck. Ac ( db - cg1)

N/mm2

c.g.st

mm2

Mult. Req.

bavg

c.g.st

db = D-cgst or cgst

Mult. conc.

(mm2)

(N/mm2)

fpb/(0.87fpu

(mm2)

Mult. steel

Mult. Available


document.xls Torsion-6 - Page 33/35

21.0) Design for torsion :

V6 & T6

Girder is designed for torsion as per IRS-CBC / Cl. 15.5.4. Critical torsion at each section is considered as per cl. 6.7

Permissible torsional shear stress 4.75 Mpa as per tab 17 / IRS-CBC

Torsion reinf. = Ast/Sv = T / (1.6*x1*y1*0.878fy)

Longitudinal reinf = AsL / SL = Ast/Sv

Section 1 2 3 4 5 6 7 8 10 11 12 13

Torsion 'T' ( Ref. Cl. 6.7 ) kN-m #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

ULS Torsion Tu = 1.5T kN-m #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Depth 'D' = hmin (m) m 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

Eeffective depth m 0.505 0.505 0.505 0.505 0.505 0.505 0.505 0.505 0.505 0.505 0.505 0.505

Effective width ( two webs) m #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

hwo m #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Ao 5.864 5.864 5.864 5.864 5.864 5.864 5.864 5.864 5.864 5.864 5.864 5.864

Torsional shear stress ' vt ' Mpa #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Shear force ( Ref. Cl. 6.6 ) kN #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

ULS shear force ( Ref. Cl. 19.2 ) kN #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

shear stress ' v ' Mpa #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

v + vt Mpa #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Remark #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Asv/Sv = T/(2*Ao*0.87*fy) #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Torsion reinf. AsL/SL = Asv/Sv #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Provide torsion reinforcement tor 16 16 16 16 16 16 16 20 20 20 20 20

@ c/c 150 150 150 150 150 150 150 125 125 125 125 125

Torsion reinforcement provided 1.34 1.34 1.34 1.34 1.34 1.34 1.34 2.51 2.51 2.51 2.51 2.513

Remark #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

m2

mm2/mm

mm2/mm

mm2/mm


document.xls End block - Page 34/35

22.0 ) DESIGN OF END BLOCK

The End Block is designed as per IRC-18 / Cl 17

a) Cable 19 T15 :

Width of End Block = 600 mm

Width of loaded area = 275 mm

Force in tendon = = ### kN

= 137.5 = 0.458

300

= 0.17

Therefore, Bursting tensile force = Fbst = 0.17 x ###

= 643 kn

Area of steel required = 643 x ###0.87 x 500

= ###

Provide 4 Nos. Tor 16 mm dia. 2 Legged stirrups

Giving Ast = ### > ### Safe

Bursting tensile force in the End Block ( Fbst ) :

(2 Yo )

(2 Ypo )

Pk

Ypo

Yo

Fbst

Pk

mm2

mm2 mm2


document.xls Summary - Page 35/35

27.0) SUMMARY

1) 6 Nos. - 19 T15 cables are required

2) First stage prestressing is applied after spine girder concrete gains M35 strength .

Cable 1 , 2 , 3 & 4 is stressed in first stage.

3) First concourse & platform beams & slab are then cast. After platform beams & slabs are cast, second stage

prestress shall be applied.

Cable 5 & 6 will be stressed in seecond atage prestressing.

4) Under first stage prestress, tensil stress of 1.0 Mpa is present at section-12. As 1.0 < 3.0 Mpa , SAFE

( Ref. cl. 17.0 & 18.0 )

5) Immediately after second stage prestress, compressive stress is present at all section

( Ref. cl. 18.2 )

6) During service condition( including creep, shrinkage & secondary moments), tensile stress of -0.9MPa &

compressive stress of 6.2MPa is present at section 11. As 0.9 < 3.0 Mpa & 6.2< 17.1 , SAFE ( Ref. cl. 17.0 & 18.0 )

7) Spine girder is checked for ultimate moment resisting capacity in cl. 20.1

8) Spine girder is checked for ultimate shear in cl. 19.1

4L Y16 @ 125c/c shear rebar ( for both webs) Is required at section 7 & 8 upto face of column

4L Y16 @ 125c/c shear rebar ( for both webs) Is provided for remaining portion

8) Spine girder is checked for ultimate torsion in cl. 21.0, 21.1, 21.2

2 L - Y20 @ 125c/c stirrups are required in webs, top slab & bottom slab of spine girder at section 7, 8.

2 L - Y16 @ 125c/c stirrups are required in webs, top slab & bottom slab of spine girder at all other sections.

Y25 @ 150 c/c rebars in longitudinal direction is provided along each face of web.

9) At the junction of spine & transverse girder at column, 8nos. - Y32 Inverted U-bars are provided along with

stirrups 6L Y16 @ 150 c/c ( ref. cl. 24.0 )

At column & spine girder junction, 6L - Y16 @ 100 c/c links is provided ( ref. cl. 24.0 )

10) At column & spine girder junction, Y16 @ 100 c/c ties shall be as per column reinf. Drg.

Main Beam Prestress

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