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PHASE 1: BEAM STRESSES
CONSIDERING POST TENSIONED
STRANDS AND SELF-WEIGHT
(Net beam with transformed strands)
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MECHANICAL PROPERTIES:
- Gross beam
- Net Beam (without ducts)
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MIDDLE SPAN SECTION
N shape b h A yi A(yi) A(yi-ycg) I Icinch inch inch inch inch inch inch inch
1 20 8 160 50 8000 102141 8532 12 6 36 44 1584 13363 723 8 38 304 27 8208 1561 365814 18 9 81 11 891 15278 3655 26 8 208 4 832 89418 1109
789 19515 221760 38981 260741
ycg = 24.73 inch
N shape b h A yi A(yi) A(yi-ycg) I Icm m m m m m m m
1 0.508 0.203 0.1032 1.270 0.1311 0.0425 0.000362 0.305 0.152 0.0232 1.118 0.0260 0.0056 0.000033 0.203 0.965 0.1961 0.686 0.1345 0.0006 0.015234 0.457 0.229 0.0523 0.279 0.0146 0.0064 0.000155 0.660 0.203 0.1342 0.102 0.0136 0.0372 0.00046
0.5090 0.3198 0.0923 0.0162 0.1085
ycg = 0.628 m
ANCHORAGE SECTION
N shape b h A yi A(yi) A(yi-ycg) I Ic
inch inch inch inch inch inch inch inch
3 20 46 920 31 28520 24056 1622274 6 3 9 9 81 2566 55 26 8 208 4 832 99636 1109
1137 29433 126258 163341 289599
ycg = 25.89 inch
N shape b h A yi A(yi) A(yi-ycg) I Icm m m m m m m m
3 0.508 1.168 0.5935 0.787 0.4674 0.0100 0.067524 0.152 0.076 0.0058 0.229 0.0013 0.0011 0.000005 0 660 0 203 0 1342 0 102 0 0136 0 0415 0 00046
MECHANICAL PROPERTIES BEAM TYPE IV AASHTO (GROSS SECTION)
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x y DEEP x y DEEP
ANCHORAGE SECTION 0 mm 257.5 mm 400 mm ANCHORAGE SECTION 0 mm 607.5 mm -50 mm
MIDDLE OF THE SPAN 14500 mm 120 mm MIDDLE OF THE SPAN 14500 mm 390 mm
a = 6.54E-07 a = 1.03E-06
x y x y x y x y x y x y x y x y
0 257.5
1000 239.2 8000 147.6 15000 120.2 22000 156.8 750 585.6 8000 433.7 15000 390.3 22000 448.2
2000 222.2 9000 139.8 16000 121.5 23000 167.3 1750 558.2 9000 421.3 16000 392.3 23000 464.7
3000 206.5 10000 133.2 17000 124.1 24000 179.0 2750 532.8 10000 411.0 17000 396.5 24000 483.4
4000 192.1 11000 128.0 18000 128.0 25000 192.1 3750 509.6 11000 402.7 18000 402.7 25000 504.1
5000 179.0 12000 124.1 19000 133.2 26000 206.5 4750 488.3 12000 396.5 19000 411.0 26000 526.8
6000 167.3 13000 121.5 20000 139.8 27000 222.2 5750 469.2 13000 392.3 20000 421.3 27000 551.7
7000 156.8 14000 120.2 21000 147.6 28000 239.2 6750 452.1 14000 390.3 21000 433.7 28000 578.6
29000 257.5 29000 607.5
PARABOLA BOTTOM TENDON PARABOLA TOP TENDON
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duct 4.1 inch (ducts are 20 mm down than the center of gravity of the tendons )
x yd,bottom yd,top yb,g A duct y tendons Ayb,g Ab,g yb,n Ab,n
mm mm mm mm mm2 mm mm3 mm2 mm mm20 237.5 587.5 657.5 85.2 412.5 482320455 733547 657.6 733377
1000 219.2 558.6 657.5 85.2 388.9 482320455 733547 657.6 733377
2000 202.2 531.7 628.2 85.2 366.9 319793554 509031 628.3 508861
3000 186.5 506.8 628.2 85.2 346.7 319793554 509031 628.3 508861
4000 172.1 484.1 628.2 85.2 328.1 319793554 509031 628.3 508861
5000 159.0 463.4 628.2 85.2 311.2 319793554 509031 628.3 508861
6000 147.3 444.7 628.2 85.2 296.0 319793554 509031 628.4 508861
7000 136.8 428.2 628.2 85.2 282.5 319793554 509031 628.4 508861
8000 127.6 413.7 628.2 85.2 270.7 319793554 509031 628.4 5088619000 119.8 401.3 628.2 85.2 260.5 319793554 509031 628.4 508861
10000 113.2 391.0 628.2 85.2 252.1 319793554 509031 628.4 508861
11000 108.0 382.7 628.2 85.2 245.3 319793554 509031 628.4 508861
12000 104.1 376.5 628.2 85.2 240.3 319793554 509031 628.4 508861
13000 101.5 372.3 628.2 85.2 236.9 319793554 509031 628.4 508861
14000 100.2 370.3 628.2 85.2 235.2 319793554 509031 628.4 508861
15000 100.2 370.3 628.2 85.2 235.2 319793554 509031 628.4 508861
16000 101.5 372.3 628.2 85.2 236.9 319793554 509031 628.4 508861
17000 104.1 376.5 628.2 85.2 240.3 319793554 509031 628.4 508861
18000 108.0 382.7 628.2 85.2 245.3 319793554 509031 628.4 50886119000 113.2 391.0 628.2 85.2 252.1 319793554 509031 628.4 508861
20000 119.8 401.3 628.2 85.2 260.5 319793554 509031 628.4 508861
21000 127.6 413.7 628.2 85.2 270.7 319793554 509031 628.4 508861
22000 136.8 428.2 628.2 85.2 282.5 319793554 509031 628.4 508861
23000 147.3 444.7 628.2 85.2 296.0 319793554 509031 628.4 508861
24000 159.0 463.4 628.2 85.2 311.2 319793554 509031 628.3 508861
25000 172.1 484.1 628.2 85.2 328.1 319793554 509031 628.3 508861
26000 186.5 506.8 628.2 85.2 346.7 319793554 509031 628.3 508861
27000 202.2 531.7 628.2 85.2 366.9 319793554 509031 628.3 50886128000 219.2 558.6 657.5 85.2 388.9 482320455 733547 657.6 733377
29000 237.5 587.5 657.5 85.2 412.5 482320455 733547 657.6 733377
MECHANICAL PROPIERTIES NET BEAM TYPE IV AASHTO (ducts are not groutted)
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duct 4.1 inch Aduct = 85.2 mm beam depth 1.3716 m
x yd,bottom yd,top yb,g Ib,g yb,n I ducts Ib,n Wn,sup Wn,inf
mm mm mm mm m mm m m m m
0 237.5 587.5 657.5 0.1205 657.6 0.001556 0.1190 0.1666 0.1809
1000 219.2 558.6 657.5 0.1205 657.6 0.001731 0.1188 0.1664 0.1807
2000 202.2 531.7 628.2 0.1085 628.3 0.001637 0.1069 0.1438 0.1701
3000 186.5 506.8 628.2 0.1085 628.3 0.001799 0.1067 0.1436 0.1699
4000 172.1 484.1 628.2 0.1085 628.3 0.001961 0.1066 0.1434 0.1696
5000 159.0 463.4 628.2 0.1085 628.3 0.002118 0.1064 0.1432 0.1693
6000 147.3 444.7 628.2 0.1085 628.4 0.002269 0.1063 0.1430 0.1691
7000 136.8 428.2 628.2 0.1085 628.4 0.002410 0.1061 0.1428 0.1689
8000 127.6 413.7 628.2 0.1085 628.4 0.002538 0.1060 0.1426 0.16879000 119.8 401.3 628.2 0.1085 628.4 0.002652 0.1059 0.1425 0.1685
10000 113.2 391.0 628.2 0.1085 628.4 0.002750 0.1058 0.1423 0.1683
11000 108.0 382.7 628.2 0.1085 628.4 0.002830 0.1057 0.1422 0.1682
12000 104.1 376.5 628.2 0.1085 628.4 0.002892 0.1056 0.1421 0.1681
13000 101.5 372.3 628.2 0.1085 628.4 0.002933 0.1056 0.1421 0.1680
14000 100.2 370.3 628.2 0.1085 628.4 0.002954 0.1056 0.1420 0.1680
15000 100.2 370.3 628.2 0.1085 628.4 0.002954 0.1056 0.1420 0.1680
16000 101.5 372.3 628.2 0.1085 628.4 0.002933 0.1056 0.1421 0.1680
17000 104.1 376.5 628.2 0.1085 628.4 0.002892 0.1056 0.1421 0.1681
18000 108.0 382.7 628.2 0.1085 628.4 0.002830 0.1057 0.1422 0.1682
19000 113.2 391.0 628.2 0.1085 628.4 0.002750 0.1058 0.1423 0.1683
20000 119.8 401.3 628.2 0.1085 628.4 0.002652 0.1059 0.1425 0.1685
21000 127.6 413.7 628.2 0.1085 628.4 0.002538 0.1060 0.1426 0.1687
22000 136.8 428.2 628.2 0.1085 628.4 0.002410 0.1061 0.1428 0.1689
23000 147.3 444.7 628.2 0.1085 628.4 0.002269 0.1063 0.1430 0.1691
24000 159.0 463.4 628.2 0.1085 628.3 0.002118 0.1064 0.1432 0.1693
25000 172.1 484.1 628.2 0.1085 628.3 0.001961 0.1066 0.1434 0.1696
26000 186.5 506.8 628.2 0.1085 628.3 0.001799 0.1067 0.1436 0.1699
27000 202.2 531.7 628.2 0.1085 628.3 0.001637 0.1069 0.1438 0.170128000 219.2 558.6 657.5 0.1205 657.6 0.001731 0.1188 0.1664 0.1807
29000 237.5 587.5 657.5 0.1205 657.6 0.001556 0.1190 0.1666 0.1809
MECHANICAL PROPIERTIES NET BEAM TYPE IV AASHTO (ducts are not groutted)
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FLEXURAL STRESSES AT BEAM EDGE
FIBERS
- Bottom Tendon Posttensioning stresses
- Elastic Shortness
- Top Tendon Posttensioning stresses
- Self-Weight stresses
T t l t t T f
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EXTENSION CALCULATION BOTTOM TENDON AT TRANSFER
Strands/ tendon 14
Tensile strength 1860 Mpa ASTM 416 M weight 1.102 kg/m LOW RELAXATION
Stressing % 75% fpu 5.9.3-1 AASHTO LRFD Area 140 mm2 ASTM416 M
Stressing force 1395 MpaForce 2734.20 kN
E 197000 1 Mpa 5.4.4.2 AASHTO LRFD 2007
L 29000 mm
0.20 TABLE 5.9.5.2.2b-1 AASHTO LRFD 2007
K 0.00066 per m TABLE 5.9.5.2.2b-1 AASHTO LRFD 2007
A strand 140 mm ASTM 416 M
x y dx dy True L dy / dx x e-(+kx)
P P avg Px Py
mm mm mm mm mm rad kN kN mm kN kN
0 257.5 0.019 0.000856 2734.20 2734.20 0.001000 239.2 250 -4.46 250.04 0.018 0.000327 0.00023 0.9998 2731.68 2732.00 1.769 2731.68 0.89
2000 222.2 250 -4.13 250.03 0.016 0.000327 0.00023 0.9998 2729.16 2729.48 1.767 2729.16 0.89
3000 206.5 250 -3.80 250.03 0.015 0.000327 0.00023 0.9998 2726.65 2726.96 1.766 2726.65 0.89
4000 192.1 250 -3.47 250.02 0.014 0.000327 0.00023 0.9998 2724.14 2724.45 1.764 2724.14 0.89
5000 179.0 250 -3.15 250.02 0.012 0.000327 0.00023 0.9998 2721.63 2721.94 1.763 2721.63 0.89
6000 167.3 250 -2.82 250.02 0.011 0.000327 0.00023 0.9998 2719.12 2719.44 1.761 2719.12 0.89
7000 156.8 250 -2.49 250.01 0.010 0.000327 0.00023 0.9998 2716.62 2716.93 1.759 2716.62 0.89
8000 147.6 250 -2.17 250.01 0.009 0.000327 0.00023 0.9998 2714.11 2714.43 1.758 2714.11 0.89
9000 139.8 250 -1.84 250.01 0.007 0.000327 0.00023 0.9998 2711.61 2711.93 1.756 2711.61 0.89
10000 133.2 250 -1.51 250.00 0.006 0.000327 0.00023 0.9998 2709.12 2709.43 1.754 2709.12 0.89
11000 128.0 250 -1.19 250.00 0.005 0.000327 0.00023 0.9998 2706.62 2706.93 1.753 2706.62 0.89
12000 124.1 250 -0.86 250.00 0.003 0.000327 0.00023 0.9998 2704.13 2704.44 1.751 2704.13 0.88
13000 121.5 250 -0.53 250.00 0.002 0.000327 0.00023 0.9998 2701.64 2701.95 1.749 2701.64 0.88
14000 120.2 250 -0.20 250.00 0.001 0.000327 0.00023 0.9998 2699.15 2699.46 1.748 2699.15 0.88
15000 120.2 250 0.12 250.00 0.001 0.000327 0.00023 0.9998 2696.66 2696.97 1.746 2696.66 0.88
16000 121.5 250 0.45 250.00 0.002 0.000327 0.00023 0.9998 2694.18 2694.49 1.745 2694.18 0.88
17000 124.1 250 0.78 250.00 0.003 0.000327 0.00023 0.9998 2691.70 2692.01 1.743 2691.70 0.88
18000 128.0 250 1.10 250.00 0.005 0.000327 0.00023 0.9998 2689.22 2689.53 1.741 2689.22 0.88
19000 133.2 250 1.43 250.00 0.006 0.000327 0.00023 0.9998 2686.74 2687.05 1.740 2686.74 0.88
20000 139.8 250 1.76 250.01 0.007 0.000327 0.00023 0.9998 2684.26 2684.57 1.738 2684.26 0.88
(+Kx)
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x y dx dy True L dy / dx x e-(+kx)
P P avg Px Py
mm mm mm mm mm rad kN kN mm kN kN(+Kx)
21000 147.6 250 2.08 250.01 0.009 0.000327 0.00023 0.9998 2681.79 2682.10 1.737 2681.79 0.88
22000 156.8 250 2.41 250.01 0.010 0.000327 0.00023 0.9998 2679.32 2679.63 1.735 2679.32 0.88
23000 167.3 250 2.74 250.02 0.011 0.000327 0.00023 0.9998 2676.85 2677.16 1.733 2676.85 0.88
24000 179.0 250 3.07 250.02 0.012 0.000327 0.00023 0.9998 2674.39 2674.69 1.732 2674.39 0.87
25000 192.1 250 3.39 250.02 0.014 0.000327 0.00023 0.9998 2671.92 2672.23 1.730 2671.92 0.87
26000 206.5 250 3.72 250.03 0.015 0.000327 0.00023 0.9998 2669.46 2669.77 1.729 2669.46 0.87
27000 222.2 250 4.05 250.03 0.016 0.000327 0.00023 0.9998 2667.00 2667.31 1.727 2667.00 0.87
28000 239.2 250 4.37 250.04 0.018 0.000327 0.00023 0.9998 2664.54 2664.85 1.726 2664.54 0.87
29000 257.5 250 4.70 250.04 0.019 0.000327 0.00023 0.9998 2662.09 2662.40 1.724 2662.09 0.87
29001.74 202.647
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0 1 00 0 2 00 0 3 00 0 4 00 0 5 00 0 6 00 0 7 00 0 8 00 0 9 00 0 1 0 00 0 1 1 00 0 1 2 00 0 1 3 00 0 1 4 00 0 1 5 00 0 1 6 00 0 1 7 00 0 1 8 00 0 1 9 00 0 2 0 00 0 2 1 00 0 2 2 00 0 2 3 00 0 2 4 00 0 2 5 00 0 2 6 00 0 2 7 00 0 2 8 00 0 2 9 00 0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.86 0.83 0.80 0.77 0.74 0.71 0.68 0.65 0.62 0.59 0.55 0.52 0.49 0.46 0.43 0.40 0.37 0.34 0.31 0.28 0.25 0.22 0.18 0.15 0.12 0.09 0.06 0.03 0.00
0.00 0.83 1.66 1.60 1.54 1.48 1.42 1.35 1.29 1.23 1.17 1.11 1.05 0.98 0.92 0.86 0.80 0.74 0.68 0.62 0.55 0.49 0.43 0.37 0.31 0.25 0.18 0.12 0.06 0.00
0.00 0.80 1.60 2.40 2.31 2.21 2.12 2.03 1.94 1.84 1.75 1.66 1.57 1.48 1.38 1.29 1.20 1.11 1.01 0.92 0.83 0.74 0.65 0.55 0.46 0.37 0.28 0.18 0.09 0.00
0.00 0.77 1.54 2.30 3.07 2.95 2.83 2.70 2.58 2.46 2.33 2.21 2.09 1.97 1.84 1.72 1.60 1.47 1.35 1.23 1.11 0.98 0.86 0.74 0.61 0.49 0.37 0.25 0.12 0.00
0.00 0.74 1.47 2.21 2.95 3.68 3.53 3.38 3.22 3.07 2.92 2.76 2.61 2.46 2.30 2.15 1.99 1.84 1.69 1.53 1.38 1.23 1.07 0.92 0.77 0.61 0.46 0.31 0.15 0.00
0.00 0.71 1.41 2.12 2.82 3.53 4.23 4.05 3.86 3.68 3.50 3.31 3.13 2.94 2.76 2.58 2.39 2.21 2.02 1.84 1.66 1.47 1.29 1.10 0.92 0.74 0.55 0.37 0.18 0.00
0.00 0.67 1.35 2.02 2.70 3.37 4.04 4.72 4.50 4.29 4.07 3.86 3.65 3.43 3.22 3.00 2.79 2.57 2.36 2.14 1.93 1.72 1.50 1.29 1.07 0.86 0.64 0.43 0.21 0.00
0.00 0.64 1.29 1.93 2.57 3.21 3.86 4.50 5.14 4.90 4.65 4.41 4.16 3.92 3.67 3.43 3.18 2.94 2.69 2.45 2.20 1.96 1.71 1.47 1.22 0.98 0.73 0.49 0.24 0.00
0.00 0.61 1.22 1.83 2.45 3.06 3.67 4.28 4.89 5.50 5.23 4.95 4.68 4.40 4.13 3.85 3.58 3.30 3.03 2.75 2.48 2.20 1.93 1.65 1.38 1.10 0.83 0.55 0.28 0.00
0.00 0.58 1.16 1.74 2.32 2.90 3.48 4.06 4.64 5.22 5.80 5.50 5.19 4.89 4.58 4.28 3.97 3.67 3.36 3.06 2.75 2.44 2.14 1.83 1.53 1.22 0.92 0.61 0.31 0.00
0.00 0.55 1.10 1.65 2.20 2.75 3.30 3.85 4.40 4.94 5.49 6.04 5.71 5.37 5.04 4.70 4.36 4.03 3.69 3.36 3.02 2.69 2.35 2.01 1.68 1.34 1.01 0.67 0.34 0.00
0.00 0.52 1.04 1.56 2.07 2.59 3.11 3.63 4.15 4.67 5.18 5.70 6.22 5.85 5.49 5.12 4.76 4.39 4.03 3.66 3.29 2.93 2.56 2.20 1.83 1.46 1.10 0.73 0.37 0.00
0.00 0.49 0.97 1.46 1.95 2.44 2.92 3.41 3.90 4.39 4.87 5.36 5.85 6.34 5.94 5.54 5.15 4.75 4.36 3.96 3.56 3.17 2.77 2.38 1.98 1.58 1.19 0.79 0.40 0.00
0.00 0.46 0.91 1.37 1.83 2.28 2.74 3.20 3.65 4.11 4.57 5.02 5.48 5.94 6.39 5.97 5.54 5.11 4.69 4.26 3.84 3.41 2.98 2.56 2.13 1.70 1.28 0.85 0.43 0.00
0.00 0.43 0.85 1.28 1.70 2.13 2.55 2.98 3.41 3.83 4.26 4.68 5.11 5.53 5.96 6.39 5.93 5.47 5.02 4.56 4.11 3.65 3.19 2.74 2.28 1.82 1.37 0.91 0.46 0.00
0.00 0.39 0.79 1.18 1.58 1.97 2.37 2.76 3.16 3.55 3.95 4.34 4.74 5.13 5.53 5.92 6.32 5.83 5.35 4.86 4.38 3.89 3.40 2.92 2.43 1.94 1.46 0.97 0.49 0.00
0.00 0.36 0.73 1.09 1.46 1.82 2.19 2.55 2.91 3.28 3.64 4.01 4.37 4.74 5.10 5.46 5.83 6.19 5.68 5.16 4.64 4.13 3.61 3.10 2.58 2.06 1.55 1.03 0.52 0.00
0.00 0.33 0.67 1.00 1.33 1.67 2.00 2.34 2.67 3.00 3.34 3.67 4.00 4.34 4.67 5.00 5.34 5.67 6.00 5.46 4.91 4.37 3.82 3.28 2.73 2.18 1.64 1.09 0.55 0.00
0.00 0.30 0.61 0.91 1.21 1.51 1.82 2.12 2.42 2.73 3.03 3.33 3.64 3.94 4.24 4.54 4.85 5.15 5.45 5.76 5.18 4.61 4.03 3.45 2.88 2.30 1.73 1.15 0.58 0.00
0.00 0.27 0.54 0.82 1.09 1.36 1.63 1.91 2.18 2.45 2.72 3.00 3.27 3.54 3.81 4.09 4.36 4.63 4.90 5.18 5.45 4.84 4.24 3.63 3.03 2.42 1.82 1.21 0.61 0.00
0.00 0.24 0.48 0.73 0.97 1.21 1.45 1.69 1.94 2.18 2.42 2.66 2.90 3.15 3.39 3.63 3.87 4.11 4.35 4.60 4.84 5.08 4.45 3.81 3.18 2.54 1.91 1.27 0.64 0.00
0.00 0.21 0.42 0.63 0.85 1.06 1.27 1.48 1.69 1.90 2.12 2.33 2.54 2.75 2.96 3.17 3.38 3.60 3.81 4.02 4.23 4.44 4.65 3.99 3.32 2.66 1.99 1.33 0.66 0.00
0.00 0.18 0.36 0.54 0.72 0.91 1.09 1.27 1.45 1.63 1.81 1.99 2.17 2.35 2.54 2.72 2.90 3.08 3.26 3.44 3.62 3.80 3.98 4.17 3.47 2.78 2.08 1.39 0.69 0.00
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.06 1.21 1.36 1.51 1.66 1.81 1.96 2.11 2.26 2.41 2.56 2.71 2.87 3.02 3.17 3.32 3.47 3.62 2.90 2.17 1.45 0.72 0.00
0.00 0.12 0.24 0.36 0.48 0.60 0.72 0.84 0.96 1.08 1.21 1.33 1.45 1.57 1.69 1.81 1.93 2.05 2.17 2.29 2.41 2.53 2.65 2.77 2.89 3.01 2.26 1.51 0.75 0.00
0.00 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 0.99 1.08 1.17 1.26 1.35 1.44 1.54 1.63 1.72 1.81 1.90 1.99 2.08 2.17 2.26 2.35 1.57 0.78 0.00
0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.78 0.84 0.90 0.96 1.02 1.08 1.14 1.20 1.26 1.32 1.38 1.44 1.50 1.56 1.62 0.81 0.00
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.60 0.63 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0 50 96 138 177 212 244 272 297 318 336 350 360 367 371 371 367 360 349 335 317 296 271 243 211 176 137 95 49 0
BENDING MOMENT CAUSED BY THE VERTICAL FORCES INDUCED BY POST TENSIONING STRESS AT BOTTOM TENDON (TRANSFER)
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11/92
x Yp,inf yb,n M Px Ab,n Ib,n ev Wsup Winf sup (M) inf (M) sup (P) inf (P) M'=Pev sup (M') inf (M') sup inf
mm mm mm kNm kN m m m m m KN/m KN/m KN/m KN/m kNm KN/m KN/m KN/m KN/m
0 257.5 657.6 0 -2734 0.733 0.1190 0.400 0.167 0.181 0 0 -3728 -3728 -1094 6564 -6045 2836 -9773
1000 239.2 657.6 -50 -2732 0.733 0.1188 0.418 0.166 0.181 298 -275 -3725 -3725 -1143 6868 -6326 3442 - 10325
2000 222.2 628.3 -96 -2729 0.509 0.1069 0.406 0.144 0.170 665 -562 -5363 -5363 -1108 7707 -6515 3009 - 12441
3000 206.5 628.3 -138 -2727 0.509 0.1067 0.422 0.144 0.170 962 -813 -5358 -5358 -1150 8010 -6771 3614 -12943
4000 192.1 628.3 -177 -2724 0.509 0.1066 0 .436 0.143 0.170 1235 -1044 -5353 -5353 -1188 8288 -7007 4170 -13404
5000 179.0 628.3 -212 -2722 0.509 0.1064 0 .449 0.143 0.169 1483 -1254 -5348 -5348 -1223 8542 -7221 4676 -13824
6000 167.3 628.4 -244 -2719 0.509 0.1063 0 .461 0.143 0.169 1708 -1444 -5344 -5344 -1254 8770 -7414 5134 -14201
7000 156.8 628.4 -272 -2717 0.509 0.1061 0 .472 0.143 0.169 1908 -1613 -5339 -5339 -1281 8972 -7585 5542 -14537
8000 147.6 628.4 -297 -2714 0.509 0.1060 0 .481 0.143 0.169 2083 -1761 -5334 -5334 -1305 9149 -7735 5899 -14830
9000 139.8 628.4 -318 -2712 0.509 0.1059 0 .489 0.142 0.168 2234 -1888 -5329 -5329 -1325 9300 -7863 6205 -15080
10000 133.2 628.4 -336 -2709 0.509 0.1058 0 .495 0.142 0.168 2359 -1994 -5324 -5324 -1341 9425 -7968 6460 -15286
11000 128.0 628.4 -350 -2707 0.509 0.1057 0 .500 0.142 0.168 2460 -2079 -5319 -5319 -1354 9523 -8051 6663 -15449
12000 124.1 628.4 -360 -2704 0.509 0.1056 0 .504 0.142 0.168 2535 -2143 -5314 -5314 -1364 9594 -8111 6815 -15569
13000 121.5 628.4 -367 -2702 0.509 0.1056 0 .507 0.142 0.168 2585 -2185 -5309 -5309 -1369 9639 -8149 6914 -15644
14000 120.2 628.4 -371 -2699 0.509 0.1056 0 .508 0.142 0.168 2609 -2206 -5304 -5304 -1372 9657 -8164 6962 -15675
15000 120.2 628.4 -371 -2697 0.509 0.1056 0 .508 0.142 0.168 2608 -2205 -5299 -5299 -1370 9648 -8157 6957 -15662
16000 121.5 628.4 -367 -2694 0.509 0.1056 0 .507 0.142 0.168 2582 -2183 -5295 -5295 -1366 9612 -8127 6900 -15604
17000 124.1 628.4 -360 -2692 0.509 0.1056 0 .504 0.142 0.168 2531 -2140 -5290 -5290 -1357 9550 -8074 6791 -15504
18000 128.0 628.4 -349 -2689 0.509 0.1057 0 .500 0.142 0.168 2454 -2075 -5285 -5285 -1346 9462 -7999 6631 -15359
19000 133.2 628.4 -335 -2687 0.509 0.1058 0 .495 0.142 0.168 2353 -1989 -5280 -5280 -1330 9347 -7902 6420 -15171
20000 139.8 628.4 -317 -2684 0.509 0.1059 0 .489 0.142 0.168 2226 -1882 -5275 -5275 -1311 9206 -7783 6157 -1494021000 147.6 628.4 -296 -2682 0.509 0.1060 0 .481 0.143 0.169 2075 -1754 -5270 -5270 -1289 9040 -7643 5845 -14667
22000 156.8 628.4 -271 -2679 0.509 0.1061 0 .472 0.143 0.169 1899 -1605 -5265 -5265 -1263 8849 -7481 5483 -14352
23000 167.3 628.4 -243 -2677 0.509 0.1063 0 .461 0.143 0.169 1699 -1436 -5260 -5260 -1234 8633 -7299 5072 -13995
24000 179.0 628.3 -211 -2674 0.509 0.1064 0 .449 0.143 0.169 1475 -1247 -5256 -5256 -1202 8393 -7096 4612 -13598
25000 192.1 628.3 -176 -2672 0.509 0.1066 0 .436 0.143 0.170 1227 -1037 -5251 -5251 -1166 8129 -6872 4105 -13160
26000 206.5 628.3 -137 -2669 0.509 0.1067 0 .422 0.144 0.170 955 -807 -5246 -5246 -1126 7842 -6629 3551 -12683
27000 222.2 628.3 -95 -2667 0.509 0.1069 0.406 0.144 0.170 660 -558 -5241 -5241 -1083 7532 -6367 2951 - 12166
28000 239.2 657.6 -49 -2665 0.733 0.1188 0.418 0.166 0.181 296 -272 -3633 -3633 -1115 6700 -6170 3362 - 10076
29000 257.5 657.6 0 -2662 0.733 0.1190 0.400 0.167 0.181 0 0 -3630 -3630 -1065 6391 -5886 2761 -9516
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF THE POST TENSION AT BOTTOM TENDON (TRANSFER)
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BOTTOM TENDONx sup inf y cp P
mm KN/m KN/m mm KN/m2 KN
0 2836 -9773 607.5 -6701 -80
1000 3442 -10325 578.6 -7422 -89
2000 3009 -12441 551.7 -8647 -104
3000 3614 -12943 526.8 -9360 -112
4000 4170 -13404 504.1 -10010 -120
5000 4676 -13824 483.4 -10600 -127
6000 5134 -14201 464.7 -11129 -133
7000 5542 -14537 448.2 -11598 -139
8000 5899 -14830 433.7 -12006 -144
9000 6205 -15080 421.3 -12354 -148
10000 6460 -15286 411.0 -12642 -151
11000 6663 -15449 402.7 -12870 -154
12000 6815 -15569 396.5 -13038 -15613000 6914 -15644 392.3 -13147 -157
14000 6962 -15675 390.3 -13196 -158
15000 6957 -15662 390.3 -13185 -158
16000 6900 -15604 392.3 -13115 -157
17000 6791 -15504 396.5 -12985 -155
18000 6631 -15359 402.7 -12797 -153
19000 6420 -15171 411.0 -12549 -15020000 6157 -14940 421.3 -12243 -147
21000 5845 -14667 433.7 -11878 -142
22000 5483 -14352 448.2 -11454 -137
TOP TENDON
ELASTIC SHORTNESS AT TOP TENDON BECAUSE OF POST TENSIONING OF BOTTOM TENDON
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x y dx dy True L dy / dx x e-(+kx)
P P - P P avg Px Py
mm mm mm mm mm rad kN KN kN mm kN kN(+Kx)
21000 433.7 250 3.30 250.02 -0.013 0.000517 0.00027 0.9997 2673.23 2531.03 2530.81 1.639 2531.03 1.31
22000 448.2 250 3.81 250.03 -0.016 0.000517 0.00027 0.9997 2670.36 2533.23 2532.92 1.640 2533.23 1.3123000 464.7 250 4.33 250.04 -0.018 0.000517 0.00027 0.9997 2667.50 2536.14 2535.74 1.642 2536.13 1.31
24000 483.4 250 4.85 250.05 -0.020 0.000517 0.00027 0.9997 2664.63 2539.74 2539.26 1.644 2539.74 1.31
25000 504.1 250 5.37 250.06 -0.022 0.000517 0.00027 0.9997 2661.78 2544.05 2543.48 1.647 2544.05 1.32
26000 526.8 250 5.88 250.07 -0.024 0.000517 0.00027 0.9997 2658.92 2549.06 2548.40 1.650 2549.06 1.32
27000 551.7 250 6.40 250.08 -0.026 0.000517 0.00027 0.9997 2656.06 2554.78 2554.03 1.654 2554.78 1.32
28000 578.6 250 6.92 250.10 -0.028 0.000517 0.00027 0.9997 2653.21 2566.49 2565.81 1.662 2566.49 1.33
29000 607.5 250 7.44 250.11 -0.030 0.000517 0.00027 0.9997 2650.37 2572.26 2571.51 1.666 2572.26 1.33
29004.35 192.425
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7/23/2019 20150608 Beam
15/92
0 1 00 0 2 00 0 3 00 0 4 00 0 5 00 0 6 00 0 7 00 0 8 00 0 9 00 0 1 0 00 0 1 1 00 0 1 2 00 0 1 3 00 0 1 4 00 0 1 5 00 0 1 6 00 0 1 7 00 0 1 8 00 0 1 9 00 0 2 0 00 0 2 1 00 0 2 2 00 0 2 3 00 0 2 4 00 0 2 5 00 0 2 6 00 0 2 7 00 0 2 8 00 0 2 9 00 0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 1.32 1.27 1.23 1.18 1.13 1.08 1.04 0.99 0.94 0.90 0.85 0.80 0.75 0.71 0.66 0.61 0.57 0.52 0.47 0.42 0.38 0.33 0.28 0.24 0.19 0.14 0.09 0.05 0.00
0.00 1.26 2.53 2.43 2.34 2.25 2.15 2.06 1.97 1.87 1.78 1.69 1.59 1.50 1.40 1.31 1.22 1.12 1.03 0.94 0.84 0.75 0.66 0.56 0.47 0.37 0.28 0.19 0.09 0.00
0.00 1.21 2.42 3.64 3.50 3.36 3.22 3.08 2.94 2.80 2.66 2.52 2.38 2.24 2.10 1.96 1.82 1.68 1.54 1.40 1.26 1.12 0.98 0.84 0.70 0.56 0.42 0.28 0.14 0.00
0.00 1.16 2.32 3.48 4.64 4.46 4.27 4.09 3.90 3.71 3.53 3.34 3.16 2.97 2.79 2.60 2.41 2.23 2.04 1.86 1.67 1.49 1.30 1.11 0.93 0.74 0.56 0.37 0.19 0.00
0.00 1.11 2.22 3.33 4.44 5.55 5.32 5.09 4.86 4.62 4.39 4.16 3.93 3.70 3.47 3.24 3.01 2.77 2.54 2.31 2.08 1.85 1.62 1.39 1.16 0.92 0.69 0.46 0.23 0.00
0.00 1.06 2.12 3.18 4.24 5.30 6.36 6.08 5.81 5.53 5.25 4.98 4.70 4.42 4.15 3.87 3.59 3.32 3.04 2.76 2.49 2.21 1.94 1.66 1.38 1.11 0.83 0.55 0.28 0.00
0.00 1.01 2.02 3.03 4.04 5.05 6.06 7.07 6.75 6.43 6.11 5.79 5.47 5.14 4.82 4.50 4.18 3.86 3.54 3.22 2.89 2.57 2.25 1.93 1.61 1.29 0.96 0.64 0.32 0.00
0.00 0.96 1.92 2.88 3.85 4.81 5.77 6.73 7.69 7.33 6.96 6.59 6.23 5.86 5.49 5.13 4.76 4.40 4.03 3.66 3.30 2.93 2.56 2.20 1.83 1.47 1.10 0.73 0.37 0.00
0.00 0.91 1.83 2.74 3.65 4.57 5.48 6.39 7.31 8.22 7.81 7.40 6.99 6.58 6.16 5.75 5.34 4.93 4.52 4.11 3.70 3.29 2.88 2.47 2.05 1.64 1.23 0.82 0.41 0.00
0.00 0.87 1.73 2.60 3.46 4.33 5.19 6.06 6.92 7.79 8.65 8.20 7.74 7.29 6.83 6.38 5.92 5.47 5.01 4.56 4.10 3.64 3.19 2.73 2.28 1.82 1.37 0.91 0.46 0.00
0.00 0.82 1.64 2.45 3.27 4.09 4.91 5.73 6.54 7.36 8.18 9.00 8.50 8.00 7.50 7.00 6.50 6.00 5.50 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00
0.00 0.77 1.54 2.31 3.08 3.86 4.63 5.40 6.17 6.94 7.71 8.48 9.25 8.71 8.17 7.62 7.08 6.53 5.99 5.44 4.90 4.35 3.81 3.27 2.72 2.18 1.63 1.09 0.54 0.00
0.00 0.72 1.45 2.17 2.90 3.62 4.35 5.07 5.80 6.52 7.25 7.97 8.70 9.42 8.83 8.24 7.65 7.06 6.48 5.89 5.30 4.71 4.12 3.53 2.94 2.35 1.77 1.18 0.59 0.00
0.00 0.68 1.36 2.04 2.71 3.39 4.07 4.75 5.43 6.11 6.78 7.46 8.14 8.82 9.50 8.86 8.23 7.60 6.96 6.33 5.70 5.07 4.43 3.80 3.17 2.53 1.90 1.27 0.63 0.00
0.00 0.63 1.26 1.90 2.53 3.16 3.79 4.43 5.06 5.69 6.32 6.96 7.59 8.22 8.85 9.49 8.81 8.13 7.45 6.78 6.10 5.42 4.74 4.07 3.39 2.71 2.03 1.36 0.68 0.00
0.00 0.59 1.17 1.76 2.35 2.93 3.52 4.11 4.69 5.28 5.87 6.45 7.04 7.63 8.22 8.80 9.39 8.67 7.94 7.22 6.50 5.78 5.06 4.33 3.61 2.89 2.17 1.44 0.72 0.00
0.00 0.54 1.08 1.62 2.17 2.71 3.25 3.79 4.33 4.87 5.41 5.96 6.50 7.04 7.58 8.12 8.66 9.20 8.44 7.67 6.90 6.14 5.37 4.60 3.83 3.07 2.30 1.53 0.77 0.00
0.00 0.50 0.99 1.49 1.98 2.48 2.98 3.47 3.97 4.47 4.96 5.46 5.95 6.45 6.95 7.44 7.94 8.43 8.93 8.12 7.31 6.50 5.68 4.87 4.06 3.25 2.44 1.62 0.81 0.00
0.00 0.45 0.90 1.35 1.80 2.26 2.71 3.16 3.61 4.06 4.51 4.96 5.41 5.86 6.31 6.77 7.22 7.67 8.12 8.57 7.71 6.86 6.00 5.14 4.29 3.43 2.57 1.71 0.86 0.00
0.00 0.41 0.81 1.22 1.62 2.03 2.44 2.84 3.25 3.65 4.06 4.47 4.87 5.28 5.69 6.09 6.50 6.90 7.31 7.72 8.12 7.22 6.32 5.41 4.51 3.61 2.71 1.80 0.90 0.00
0.00 0.36 0.72 1.08 1.44 1.81 2.17 2.53 2.89 3.25 3.61 3.97 4.33 4.70 5.06 5.42 5.78 6.14 6.50 6.86 7.22 7.58 6.64 5.69 4.74 3.79 2.84 1.90 0.95 0.00
0.00 0.32 0.63 0.95 1.27 1.58 1.90 2.21 2.53 2.85 3.16 3.48 3.80 4.11 4.43 4.74 5.06 5.38 5.69 6.01 6.33 6.64 6.96 5.96 4.97 3.98 2.98 1.99 0.99 0.00
0.00 0.27 0.54 0.81 1.09 1.36 1.63 1.90 2.17 2.44 2.71 2.99 3.26 3.53 3.80 4.07 4.34 4.61 4.89 5.16 5.43 5.70 5.97 6.24 5.20 4.16 3.12 2.08 1.04 0.00
0.00 0.23 0.45 0.68 0.91 1.13 1.36 1.59 1.81 2.04 2.27 2.49 2.72 2.94 3.17 3.40 3.62 3.85 4.08 4.30 4.53 4.76 4.98 5.21 5.44 4.35 3.26 2.17 1.09 0.00
0.00 0.18 0.36 0.54 0.73 0.91 1.09 1.27 1.45 1.63 1.82 2.00 2.18 2.36 2.54 2.72 2.90 3.09 3.27 3.45 3.63 3.81 3.99 4.17 4.36 4.54 3.40 2.27 1.13 0.00
0.00 0.14 0.27 0.41 0.55 0.68 0.82 0.95 1.09 1.23 1.36 1.50 1.64 1.77 1.91 2.05 2.18 2.32 2.46 2.59 2.73 2.86 3.00 3.14 3.27 3.41 3.55 2.36 1.18 0.00
0.00 0.09 0.18 0.27 0.36 0.46 0.55 0.64 0.73 0.82 0.91 1.00 1.09 1.18 1.28 1.37 1.46 1.55 1.64 1.73 1.82 1.91 2.01 2.10 2.19 2.28 2.37 2.46 1.23 0.00
0.00 0.05 0.09 0.14 0.18 0.23 0.27 0.32 0.37 0.41 0.46 0.50 0.55 0.60 0.64 0.69 0.73 0.78 0.82 0.87 0.92 0.96 1.01 1.05 1.10 1.14 1.19 1.24 1.28 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0 75 144 207 265 318 365 407 444 476 502 523 538 548 553 553 548 537 521 500 474 442 405 363 316 263 205 142 74 0
BENDING MOMENT CAUSED BY THE VERTICAL FORCES INDUCED BY POST TENSIONING STRESS AT TOP TENDON (TRANSFER)
-
7/23/2019 20150608 Beam
16/92
x Yp,inf yb,n M Px Ab,n Ib,n ev Wsup Winf sup (M) inf (M) sup (P) inf (P) M'=Pev sup (M') inf (M') sup inf
mm mm mm kNm kN m m m m m KN/m KN/m KN/m KN/m kNm KN/m KN/m KN/m KN/m
0 607.5 657.6 0 -2654 0.733 0.1190 0.050 0.167 0.181 0 0 -3619 -3619 -133 797 -734 -2822 -43531000 578.6 657.6 -75 -2642 0.733 0.1188 0.079 0.166 0.181 448 -412 -3603 -3603 -209 1255 -1156 -1900 -5171
2000 551.7 628.3 -144 -2625 0.509 0 .1069 0.077 0.144 0.170 998 -844 -5158 -5158 -201 1399 -1183 -2761 -7185
3000 526.8 628.3 -207 -2613 0.509 0.1067 0.102 0.144 0.170 1442 -1219 -5136 -5136 -265 1847 -1562 -1846 -7916
4000 504.1 628.3 -265 -2603 0.509 0.1066 0.124 0.143 0.170 1850 -1564 -5115 -5115 -323 2256 -1907 -1009 -8585
5000 483.4 628.3 -318 -2593 0.509 0.1064 0.145 0.143 0.169 2221 -1878 -5095 -5095 -376 2625 -2219 -249 -9192
6000 464.7 628.4 -365 -2583 0.509 0.1063 0.164 0.143 0.169 2556 -2161 -5077 -5077 -423 2956 -2499 435 -9737
7000 448.2 628.4 -407 -2575 0.509 0.1061 0.180 0.143 0.169 2854 -2413 -5060 -5060 -464 3249 -2747 1043 -10219
8000 433.7 628.4 -444 -2567 0.509 0.1060 0.195 0.143 0.169 3115 -2633 -5045 -5045 -500 3504 -2962 1574 -10640
9000 421.3 628.4 -476 -2560 0.509 0.1059 0.207 0.142 0.168 3338 -2822 -5031 -5031 -530 3721 -3146 2029 -10999
10000 411.0 628.4 -502 -2554 0.509 0.1058 0.217 0.142 0.168 3525 -2980 -5018 -5018 -555 3901 -3298 2408 -1129711000 402.7 628.4 -523 -2548 0.509 0.1057 0.226 0.142 0.168 3674 -3106 -5007 -5007 -575 4044 -3419 2711 -11532
12000 396.5 628.4 -538 -2543 0.509 0.1056 0.232 0.142 0.168 3786 -3201 -4998 -4998 -590 4149 -3508 2937 -11706
13000 392.3 628.4 -548 -2539 0.509 0.1056 0.236 0.142 0.168 3860 -3263 -4989 -4989 -599 4218 -3566 3088 -11819
14000 390.3 628.4 -553 -2535 0.509 0.1056 0.238 0.142 0.168 3896 -3294 -4983 -4983 -604 4250 -3593 3164 -11870
15000 390.3 628.4 -553 -2533 0.509 0.1056 0.238 0.142 0.168 3895 -3293 -4977 -4977 -603 4245 -3589 3163 -11859
16000 392.3 628.4 -548 -2531 0.509 0.1056 0.236 0.142 0.168 3856 -3260 -4973 -4973 -597 4204 -3555 3087 -11787
17000 396.5 628.4 -537 -2529 0.509 0.1056 0.232 0.142 0.168 3779 -3195 -4970 -4970 -587 4127 -3489 2935 -11654
18000 402.7 628.4 -521 -2529 0.509 0.1057 0.226 0.142 0.168 3665 -3098 -4969 -4969 -571 4013 -3393 2709 -11460
19000 411.0 628.4 -500 -2529 0.509 0.1058 0.217 0.142 0.168 3514 -2970 -4969 -4969 -550 3863 -3266 2407 -11206
20000 421.3 628.4 -474 -2530 0.509 0.1059 0.207 0.142 0.168 3325 -2811 -4971 -4971 -524 3677 -3109 2031 -10891
21000 433.7 628.4 -442 -2531 0.509 0.1060 0.195 0.143 0.169 3100 -2621 -4974 -4974 -493 3455 -2921 1581 -10515
22000 448.2 628.4 -405 -2533 0.509 0.1061 0.180 0.143 0.169 2838 -2399 -4978 -4978 -456 3196 -2702 1056 -10080
23000 464.7 628.4 -363 -2536 0.509 0.1063 0.164 0.143 0.169 2540 -2147 -4984 -4984 -415 2902 -2454 458 -9585
24000 483.4 628.3 -316 -2540 0.509 0.1064 0.145 0.143 0.169 2206 -1865 -4991 -4991 -368 2572 -2174 -213 -9030
25000 504.1 628.3 -263 -2544 0.509 0.1066 0.124 0.143 0.170 1836 -1552 -5000 -5000 -316 2205 -1864 -959 -8416
26000 526.8 628.3 -205 -2549 0.509 0.1067 0.102 0.144 0.170 1430 -1209 -5009 -5009 -259 1802 -1523 -1777 -7742
27000 551.7 628.3 -142 -2555 0.509 0 .1069 0.077 0.144 0.170 989 -836 -5021 -5021 -196 1362 -1151 -2670 -7008
28000 578.6 657.6 -74 -2566 0.733 0.1188 0.079 0.166 0.181 443 -408 -3500 -3500 -203 1219 -1123 -1837 -5031
29000 607.5 657.6 0 -2572 0.733 0.1190 0.050 0.167 0.181 0 0 -3507 -3507 -129 773 -712 -2735 -4219
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF THE POST TENSION AT TOP TENDON (TRANSFER)
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x M Wsup Winf sup inf
mm kNm m m KN/m KN/m
0 0 0.167 0.181 0 01000 180 0.166 0.181 -1082 997
2000 343 0.144 0.170 -2385 2016
3000 493 0.144 0.170 -3431 2900
4000 630 0.143 0.170 -4393 3714
5000 755 0.143 0.169 -5271 4456
6000 867 0.143 0.169 -6064 5126
7000 967 0.143 0.169 -6771 5724
8000 1054 0.143 0.169 -7391 62499000 1129 0.142 0.168 -7925 6700
10000 1191 0.142 0.168 -8370 7077
11000 1241 0.142 0.168 -8727 7379
12000 1279 0.142 0.168 -8996 7606
13000 1304 0.142 0.168 -9175 7757
14000 1316 0.142 0.168 -9265 7833
14250 1317 0.142 0.168 -9273 7840
14500 1318 0.142 0.168 -9276 784214750 1317 0.142 0.168 -9273 7840
15000 1316 0.142 0.168 -9265 7833
16000 1304 0.142 0.168 -9175 7757
17000 1279 0.142 0.168 -8996 7606
18000 1241 0.142 0.168 -8727 7379
19000 1191 0.142 0.168 -8370 7077
20000 1129 0.142 0.168 -7925 6700
21000 1054 0.143 0.169 -7391 624922000 967 0.143 0.169 -6771 5724
23000 867 0.143 0.169 -6064 5126
24000 755 0.143 0.169 -5271 4456
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF ITS SELF WEIGHT
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x sup inf sup inf sup inf sup inf
mm KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m20 2836 -9773 -2822 -4353 0 0 14 -14126
1000 3442 -10325 -1900 -5171 -1082 997 459 -14500
2000 3009 -12441 -2761 -7185 -2385 2016 -2136 -17610
3000 3614 -12943 -1846 -7916 -3431 2900 -1663 -17959
4000 4170 -13404 -1009 -8585 -4393 3714 -1232 -18276
5000 4676 -13824 -249 -9192 -5271 4456 -843 -18560
6000 5134 -14201 435 -9737 -6064 5126 -495 -18812
7000 5542 -14537 1043 -10219 -6771 5724 -187 -190328000 5899 -14830 1574 -10640 -7391 6249 81 -19221
9000 6205 -15080 2029 -10999 -7925 6700 309 -19379
10000 6460 -15286 2408 -11297 -8370 7077 497 -19507
11000 6663 -15449 2711 -11532 -8727 7379 646 -19603
12000 6815 -15569 2937 -11706 -8996 7606 757 -19669
13000 6914 -15644 3088 -11819 -9175 7757 828 -19705
14000 6962 -15675 3164 -11870 -9265 7833 861 -19712
15000 6957 -15662 3163 -11859 -9265 7833 855 -19688
16000 6900 -15604 3087 -11787 -9175 7757 812 -19635
17000 6791 -15504 2935 -11654 -8996 7606 731 -19552
18000 6631 -15359 2709 -11460 -8727 7379 612 -19441
19000 6420 -15171 2407 -11206 -8370 7077 456 -19300
20000 6157 -14940 2031 -10891 -7925 6700 264 -19131
21000 5845 -14667 1581 -10515 -7391 6249 34 -18934
22000 5483 -14352 1056 -10080 -6771 5724 -231 -18708
23000 5072 -13995 458 -9585 -6064 5126 -534 -18454
24000 4612 -13598 -213 -9030 -5271 4456 -872 -18172
25000 4105 -13160 -959 -8416 -4393 3714 -1246 -17862
26000 3551 -12683 -1777 -7742 -3431 2900 -1657 -17524
TENDONS +SWBOTTOM TENDON TOP TENDON SELF WEIGHT
SUM OF TENSIONS: POST TENSION + SELF WEIGHT AT TRANSFER
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PHASE 2: BEAM STRESSES
CONSIDERING POST TENSIONED
STRANDS, SELF-WEIGHT AND DECK
WEIGHT
(Gross beam transformed )
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MECHANICAL PROPERTIES:
- Gross transformed beam
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x Apt1 yp1 Apt1yp1 Apt2 yp2 Apt2yp2 yp Aptyp
mm m2 mm m m2 mm m m m0 0.0079 257.518 2.0245 0.0079 607.518 4.7759 0.433 0.0068
1000 0.0079 239.204 1.8805 0.0079 578.550 4.5482 0.409 0.0064
2000 0.0079 222.198 1.7468 0.0079 551.651 4.3368 0.387 0.0061
3000 0.0079 206.501 1.6234 0.0079 526.822 4.1416 0.367 0.0058
4000 0.0079 192.111 1.5103 0.0079 504.061 3.9626 0.348 0.0055
5000 0.0079 179.030 1.4074 0.0079 483.370 3.8000 0.331 0.0052
6000 0.0079 167.257 1.3149 0.0079 464.748 3.6536 0.316 0.0050
7000 0.0079 156.791 1.2326 0.0079 448.195 3.5234 0.302 0.0048
8000 0.0079 147.634 1.1606 0.0079 433.711 3.4096 0.291 0.0046
9000 0.0079 139.786 1.0989 0.0079 421.296 3.3120 0.281 0.004410000 0.0079 133.245 1.0475 0.0079 410.950 3.2306 0.272 0.0043
11000 0.0079 128.012 1.0064 0.0079 402.673 3.1656 0.265 0.0042
12000 0.0079 124.088 0.9755 0.0079 396.466 3.1168 0.260 0.0041
13000 0.0079 121.472 0.9549 0.0079 392.328 3.0842 0.257 0.0040
14000 0.0079 120.164 0.9447 0.0079 390.259 3.0680 0.255 0.0040
15000 0.0079 120.164 0.9447 0.0079 390.259 3.0680 0.255 0.0040
16000 0.0079 121.472 0.9549 0.0079 392.328 3.0842 0.257 0.0040
17000 0.0079 124.088 0.9755 0.0079 396.466 3.1168 0.260 0.0041
18000 0.0079 128.012 1.0064 0.0079 402.673 3.1656 0.265 0.004219000 0.0079 133.245 1.0475 0.0079 410.950 3.2306 0.272 0.0043
20000 0.0079 139.786 1.0989 0.0079 421.296 3.3120 0.281 0.0044
21000 0.0079 147.634 1.1606 0.0079 433.711 3.4096 0.291 0.0046
22000 0.0079 156.791 1.2326 0.0079 448.195 3.5234 0.302 0.0048
23000 0.0079 167.257 1.3149 0.0079 464.748 3.6536 0.316 0.0050
24000 0.0079 179.030 1.4074 0.0079 483.370 3.8000 0.331 0.0052
25000 0.0079 192.111 1.5103 0.0079 504.061 3.9626 0.348 0.0055
26000 0.0079 206.501 1.6234 0.0079 526.822 4.1416 0.367 0.0058
27000 0.0079 222.198 1.7468 0.0079 551.651 4.3368 0.387 0.0061
28000 0.0079 239.204 1.8805 0.0079 578.550 4.5482 0.409 0.006429000 0.0079 257.518 2.0245 0.0079 607.518 4.7759 0.433 0.0068
CENTER OF GRAVITY OF TENDONS
BOTTOM TENDON TOP TENDON CENTER OF GRAVITY
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x Ab,g yb,g Ab,gyb,g Ib,g Ap Ab,g-p yp yg-p
mm m m m m m m m m
0 0.7335 0.658 0.4823 0.1205 0.0039 0.7296 0.433 0.659
1000 0.7335 0.658 0.4823 0.1205 0.0039 0.7296 0.409 0.6592000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.387 0.630
3000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.367 0.630
4000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.348 0.630
5000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.331 0.631
6000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.316 0.631
7000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.302 0.631
8000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.291 0.631
9000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.281 0.631
10000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.272 0.631
11000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.265 0.63112000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.260 0.631
13000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.257 0.631
14000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.255 0.631
15000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.255 0.631
16000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.257 0.631
17000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.260 0.631
18000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.265 0.631
19000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.272 0.631
20000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.281 0.63121000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.291 0.631
22000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.302 0.631
23000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.316 0.631
24000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.331 0.631
25000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.348 0.630
26000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.367 0.630
27000 0.5090 0.628 0.3198 0.1085 0.0039 0.5051 0.387 0.630
28000 0.7335 0.658 0.4823 0.1205 0.0039 0.7296 0.409 0.659
29000 0.7335 0.658 0.4823 0.1205 0.0039 0.7296 0.433 0.659
MECHANICAL PROPERTIES BEAM TYPE IV AASHTO (BEAM WITHOUT STRANDS AREA)
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x Ib,g yb,g Ap yp Ap(yp-ybg) Ib,g-p
mm m m m m m m0 0.1205 0.658 0.0039 0.433 0.0009 0.1197
1000 0.1205 0.658 0.0039 0.409 0.0010 0.1196
2000 0.1085 0.628 0.0039 0.387 0.0009 0.1076
3000 0.1085 0.628 0.0039 0.367 0.0010 0.1075
4000 0.1085 0.628 0.0039 0.348 0.0011 0.1074
5000 0.1085 0.628 0.0039 0.331 0.0012 0.1074
6000 0.1085 0.628 0.0039 0.316 0.0012 0.1073
7000 0.1085 0.628 0.0039 0.302 0.0013 0.1072
8000 0.1085 0.628 0.0039 0.291 0.0013 0.10729000 0.1085 0.628 0.0039 0.281 0.0014 0.1072
10000 0.1085 0.628 0.0039 0.272 0.0014 0.1071
11000 0.1085 0.628 0.0039 0.265 0.0014 0.1071
12000 0.1085 0.628 0.0039 0.260 0.0014 0.1071
13000 0.1085 0.628 0.0039 0.257 0.0015 0.1071
14000 0.1085 0.628 0.0039 0.255 0.0015 0.1071
15000 0.1085 0.628 0.0039 0.255 0.0015 0.1071
16000 0.1085 0.628 0.0039 0.257 0.0015 0.1071
17000 0.1085 0.628 0.0039 0.260 0.0014 0.1071
18000 0.1085 0.628 0.0039 0.265 0.0014 0.107119000 0.1085 0.628 0.0039 0.272 0.0014 0.1071
20000 0.1085 0.628 0.0039 0.281 0.0014 0.1072
21000 0.1085 0.628 0.0039 0.291 0.0013 0.1072
22000 0.1085 0.628 0.0039 0.302 0.0013 0.1072
23000 0.1085 0.628 0.0039 0.316 0.0012 0.1073
24000 0.1085 0.628 0.0039 0.331 0.0012 0.1074
25000 0.1085 0.628 0.0039 0.348 0.0011 0.1074
26000 0.1085 0.628 0.0039 0.367 0.0010 0.1075
27000 0.1085 0.628 0.0039 0.387 0.0009 0.1076
28000 0.1205 0.658 0.0039 0.409 0.0010 0.1196
29000 0.1205 0.658 0.0039 0.433 0.0009 0.1197
MOMENT OF INERTIA OF GROSS BEAM WITHOUT STRANDS AREA
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Ep = 197000 Mpa 0.0157 m
Ec = 36057 Mpa
n = Ep/Ec = 5.000
x Ab,g-p yg-p Ab,g-pyg-p yp Aptyp yt Ab,g-p(yg-p-yt) Apt(yp-yt)
mm m m m m m m m m
0 0.7296 0.659 0.4806 0.4325 0.0068 0.664 2.40E-05 2.11E-04
1000 0.7296 0.659 0.4807 0.4089 0.006 0.664 2.00E-05 2.56E-04
2000 0.5051 0.630 0.3183 0.3869 0.006 0.637 2.54E-05 2.46E-04
3000 0.5051 0.630 0.3184 0.3667 0.006 0.637 2.11E-05 2.87E-04
4000 0.5051 0.630 0.3184 0.3481 0.005 0.636 1.75E-05 3.27E-04
5000 0.5051 0.631 0.3185 0.3312 0.005 0.636 1.45E-05 3.65E-04
6000 0.5051 0.631 0.3186 0.3160 0.005 0.636 1.21E-05 4.01E-047000 0.5051 0.631 0.3186 0.3025 0.005 0.635 1.01E-05 4.35E-04
8000 0.5051 0.631 0.3187 0.2907 0.005 0.635 8.52E-06 4.66E-04
9000 0.5051 0.631 0.3187 0.2805 0.004 0.635 7.27E-06 4.93E-04
10000 0.5051 0.631 0.3187 0.2721 0.004 0.635 6.30E-06 5.16E-04
11000 0.5051 0.631 0.3188 0.2653 0.004 0.634 5.58E-06 5.35E-04
12000 0.5051 0.631 0.3188 0.2603 0.004 0.634 5.06E-06 5.50E-04
13000 0.5051 0.631 0.3188 0.2569 0.004 0.634 4.73E-06 5.60E-04
14000 0.5051 0.631 0.3188 0.2552 0.004 0.634 4.57E-06 5.64E-04
15000 0.5051 0.631 0.3188 0.2552 0.004 0.634 4.57E-06 5.64E-0416000 0.5051 0.631 0.3188 0.2569 0.004 0.634 4.73E-06 5.60E-04
17000 0.5051 0.631 0.3188 0.2603 0.004 0.634 5.06E-06 5.50E-04
18000 0.5051 0.631 0.3188 0.2653 0.004 0.634 5.58E-06 5.35E-04
19000 0.5051 0.631 0.3187 0.2721 0.004 0.635 6.30E-06 5.16E-04
20000 0.5051 0.631 0.3187 0.2805 0.004 0.635 7.27E-06 4.93E-04
21000 0.5051 0.631 0.3187 0.2907 0.005 0.635 8.52E-06 4.66E-04
22000 0.5051 0.631 0.3186 0.3025 0.005 0.635 1.01E-05 4.35E-04
23000 0.5051 0.631 0.3186 0.3160 0.005 0.636 1.21E-05 4.01E-04
24000 0.5051 0.631 0.3185 0.3312 0.005 0.636 1.45E-05 3.65E-04
25000 0.5051 0.630 0.3184 0.3481 0.005 0.636 1.75E-05 3.27E-0426000 0.5051 0.630 0.3184 0.3667 0.006 0.637 2.11E-05 2.87E-04
27000 0.5051 0.630 0.3183 0.3869 0.006 0.637 2.54E-05 2.46E-04
28000 0.7296 0.659 0.4807 0.4089 0.006 0.664 2.00E-05 2.56E-04
GIRDER BEAM STRANDS
PROPERTIES OF TRANSFORMED GROSS BEAM
Apt = Ap(n-1) =
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x Ab,g-p + Apt Ib,g-p It yt,inf yt,sup Wt,sup Wt,inf
mm m m m m m m m m
0 0.7453 2.36E-04 0.1197 0.1199 0.664 0.707 0.1695 0.1804
1000 0.7453 2.76E-04 0.1196 0.1198 0.664 0.708 0.1694 0.1805
2000 0.5208 2.72E-04 0.1076 0.1079 0.637 0.734 0.1469 0.1693
3000 0.5208 3.08E-04 0.1075 0.1078 0.637 0.735 0.1467 0.1693
4000 0.5208 3.44E-04 0.1074 0.1078 0.636 0.735 0.1466 0.1694
5000 0.5208 3.79E-04 0.1074 0.1077 0.636 0.736 0.1464 0.1694
6000 0.5208 4.13E-04 0.1073 0.1077 0.636 0.736 0.1463 0.1695
7000 0.5208 4.45E-04 0.1072 0.1077 0.635 0.736 0.1463 0.1695
8000 0.5208 4.74E-04 0.1072 0.1077 0.635 0.737 0.1462 0.1696
9000 0.5208 5.00E-04 0.1072 0.1077 0.635 0.737 0.1461 0.1696
10000 0.5208 5.23E-04 0.1071 0.1077 0.635 0.737 0.1461 0.1697
11000 0.5208 5.41E-04 0.1071 0.1076 0.634 0.737 0.1460 0.169712000 0.5208 5.55E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
13000 0.5208 5.64E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
14000 0.5208 5.69E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
15000 0.5208 5.69E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
16000 0.5208 5.64E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
17000 0.5208 5.55E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
18000 0.5208 5.41E-04 0.1071 0.1076 0.634 0.737 0.1460 0.1697
19000 0.5208 5.23E-04 0.1071 0.1077 0.635 0.737 0.1461 0.1697
20000 0.5208 5.00E-04 0.1072 0.1077 0.635 0.737 0.1461 0.1696
21000 0.5208 4.74E-04 0.1072 0.1077 0.635 0.737 0.1462 0.1696
22000 0.5208 4.45E-04 0.1072 0.1077 0.635 0.736 0.1463 0.1695
23000 0.5208 4.13E-04 0.1073 0.1077 0.636 0.736 0.1463 0.1695
24000 0.5208 3.79E-04 0.1074 0.1077 0.636 0.736 0.1464 0.1694
25000 0.5208 3.44E-04 0.1074 0.1078 0.636 0.735 0.1466 0.1694
26000 0.5208 3.08E-04 0.1075 0.1078 0.637 0.735 0.1467 0.1693
27000 0.5208 2.72E-04 0.1076 0.1079 0.637 0.734 0.1469 0.1693
28000 0.7453 2.76E-04 0.1196 0.1198 0.664 0.708 0.1694 0.1805
29000 0.7453 2.36E-04 0.1197 0.1199 0.664 0.707 0.1695 0.1804
PROPERTIES OF TRANSFORMED GROSS BEAM
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FLEXURAL STRESSES AT BEAM EDGEFIBERS
- Bottom Tendon Posttensioning stresses
- Top Tendon Posttensioning stresses
- Self-Weight stresses
- Deck Weight stresses
T t l t t D k P
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x Yp,inf yt M Px Ab,g-p + Apt It ev Wsup Winf sup (M) inf (M) sup (P) inf (P) M'=Pev sup (M') inf (M') sup inf
mm mm m kNm kN m m m m m KN/m KN/m KN/m KN/m kNm KN/m KN/m KN/m KN/m
0 258 664 0 -2734 0.7453 0.1199 0.407 0.1695 0.1804 0 0 -3668 -3668 -1113 6563 -6167 2894 -98351000 239 664 -50 -2732 0.7453 0.1198 0.425 0.1694 0 .1805 293 -275 -3665 -3665 -1161 6852 -6432 3480 -10372
2000 222 637 -96 -2729 0.5208 0.1079 0.415 0.1469 0 .1693 651 -565 -5240 -5240 -1133 7712 -6692 3124 -12497
3000 207 637 -138 -2727 0.5208 0.1078 0.430 0.1467 0 .1693 942 -816 -5235 -5235 -1173 7996 -6929 3703 -12980
4000 192 636 -177 -2724 0.5208 0.1078 0.444 0 .1466 0.1694 1208 -1045 -5230 -5230 -1210 8256 -7144 4233 -13420
5000 1 79 636 -212 -2722 0.5208 0.1077 0.457 0 .1464 0.1694 1450 -1254 -5226 -5226 -1243 8491 -7339 4715 -13818
6000 1 67 636 -244 -2719 0.5208 0.1077 0.468 0 .1463 0.1695 1668 -1441 -5221 -5221 -1273 8701 -7513 5149 -14175
7000 157 635 -272 -2717 0.5208 0.1077 0.478 0 .1463 0.1695 1862 -1607 -5216 -5216 -1300 8887 -7667 5534 -14490
8000 148 635 -297 -2714 0.5208 0.1077 0.487 0 .1462 0.1696 2032 -1752 -5211 -5211 -1323 9049 -7800 5870 -14763
9000 140 635 -318 -2712 0.5208 0.1077 0.495 0 .1461 0.1696 2178 -1876 -5206 -5206 -1342 9186 -7913 6157 -14995
10000 133 635 -336 -2709 0.5208 0.1077 0.501 0 .1461 0.1697 2299 -1979 -5202 -5202 -1358 9298 -8005 6396 -1518611000 128 634 -350 -2707 0.5208 0.1076 0.506 0 .1460 0.1697 2396 -2061 -5197 -5197 -1371 9387 -8077 6585 -15336
12000 124 634 -360 -2704 0.5208 0.1076 0.510 0 .1460 0.1697 2468 -2123 -5192 -5192 -1380 9450 -8129 6726 -15444
13000 121 634 -367 -2702 0.5208 0.1076 0.513 0 .1460 0.1697 2516 -2164 -5187 -5187 -1385 9490 -8162 6819 -15513
14000 120 634 -371 -2699 0.5208 0.1076 0.514 0 .1460 0.1697 2539 -2184 -5182 -5182 -1387 9505 -8174 6862 -15540
15000 1 20 634 -371 -2697 0.5208 0.1076 0.514 0 .1460 0.1697 2539 -2183 -5178 -5178 -1386 9497 -8166 6858 -15527
16000 1 21 634 -367 -2694 0.5208 0.1076 0.513 0 .1460 0.1697 2514 -2162 -5173 -5173 -1381 9464 -8139 6804 -15474
17000 124 634 -360 -2692 0.5208 0.1076 0.510 0 .1460 0.1697 2464 -2120 -5168 -5168 -1373 9407 -8092 6703 -15380
18000 128 634 -349 -2689 0.5208 0.1076 0.506 0 .1460 0.1697 2390 -2057 -5163 -5163 -1362 9326 -8025 6553 -15246
19000 133 635 -335 -2687 0.5208 0.1077 0.501 0 .1461 0.1697 2292 -1974 -5159 -5159 -1347 9222 -7939 6355 -15071
20000 140 635 -317 -2684 0.5208 0.1077 0.495 0 .1461 0.1696 2170 -1870 -5154 -5154 -1329 9093 -7833 6110 -14856
21000 148 635 -296 -2682 0.5208 0.1077 0.487 0 .1462 0.1696 2024 -1745 -5149 -5149 -1307 8941 -7707 5816 -14601
22000 157 635 -271 -2679 0.5208 0.1077 0.478 0 .1463 0.1695 1854 -1599 -5144 -5144 -1282 8765 -7562 5475 -14305
23000 167 636 -243 -2677 0.5208 0.1077 0.468 0 .1463 0.1695 1660 -1433 -5140 -5140 -1254 8566 -7397 5086 -13969
24000 1 79 636 -211 -2674 0.5208 0.1077 0.457 0 .1464 0.1694 1442 -1246 -5135 -5135 -1222 8343 -7212 4650 -13593
25000 1 92 636 -176 -2672 0.5208 0.1078 0.444 0 .1466 0.1694 1200 -1039 -5130 -5130 -1187 8098 -7007 4167 -13176
26000 207 637 -137 -2669 0.5208 0.1078 0.430 0.1467 0 .1693 935 -810 -5125 -5125 -1148 7829 -6783 3638 -12719
27000 222 637 -95 -2667 0.5208 0.1079 0.415 0.1469 0 .1693 646 -561 -5121 -5121 -1107 7537 -6539 3062 -12221
28000 239 664 -49 -2665 0.7453 0.1198 0.425 0.1694 0 .1805 291 -273 -3575 -3575 -1132 6684 -6274 3399 -10121
29000 258 664 0 -2662 0.7453 0.1199 0.407 0.1695 0.1804 0 0 -3572 -3572 -1083 6390 -6004 2818 -9576
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF THE POST TENSION AT BOTTOM TENDON(At time of deck pouring)
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x y yt M Px Ab,g-p + Apt It ev Wsup Winf sup (M) inf (M) sup (P) inf (P) M' sup (M') inf (M') sup inf
mm mm m kNm kN m m m m3 m3 KN/m2 KN/m2 KN/m2 KN/m2 kNm KN/m2 KN/m2 KN/m2 KN/m2
0 608 664 0 -2653 0.7453 0.1199 0.057 0.1695 0.1804 0 0 -3560 -3560 -151 891 -837 -2669 -43971000 579 664 -75 -2642 0.7453 0 .1198 0.086 0.1694 0.1805 440 -413 -3545 -3545 -226 1334 -1252 -1770 -5210
2000 552 637 -144 -2624 0.5208 0.1079 0.086 0.1469 0.1693 977 -848 -5038 -5038 -224 1529 -1326 -2532 -7212
3000 527 637 -207 -2613 0.5208 0.1078 0.110 0.1467 0.1693 1412 -1223 -5016 -5016 -287 1957 -1696 -1647 -7936
4000 504 636 -265 -2602 0.5208 0 .1078 0.132 0.1466 0.1694 1810 -1566 -4996 -4996 -344 2348 -2032 -839 -8594
5000 483 636 -318 -2593 0.5208 0 .1077 0.153 0.1464 0.1694 2172 -1877 -4978 -4978 -395 2700 -2334 -106 -9189
6000 465 636 -365 -2584 0.5208 0 .1077 0.171 0.1463 0.1695 2497 -2156 -4961 -4961 -441 3016 -2604 552 -9721
7000 448 635 -408 -2575 0.5208 0.1077 0.187 0.1463 0.1695 2787 -2404 -4945 -4945 -482 3294 -2841 1136 -10190
8000 434 635 -444 -2568 0.5208 0.1077 0.201 0.1462 0.1696 3039 -2620 -4930 -4930 -517 3535 -3048 1645 -10598
9000 421 635 -476 -2561 0.5208 0.1077 0.213 0.1461 0.1696 3256 -2805 -4917 -4917 -547 3741 -3223 2080 -10944
10000 411 635 -502 -2555 0.5208 0.1077 0.224 0.1461 0.1697 3436 -2958 -4905 -4905 -571 3911 -3367 2442 -11230
11000 403 634 -523 -2549 0.5208 0.1076 0.232 0.1460 0.1697 3580 -3080 -4895 -4895 -591 4045 -3481 2731 -11456
12000 396 634 -538 -2544 0.5208 0.1076 0.238 0.1460 0.1697 3687 -3172 -4885 -4885 -605 4145 -3566 2947 -11623
13000 392 634 -549 -2540 0.5208 0.1076 0.242 0.1460 0.1697 3758 -3232 -4878 -4878 -614 4209 -3620 3090 -11730
14000 390 634 -554 -2537 0.5208 0.1076 0.244 0.1460 0.1697 3793 -3262 -4871 -4871 -619 4239 -3646 3162 -11778
15000 390 634 -553 -2534 0.5208 0.1076 0.244 0.1460 0.1697 3792 -3261 -4866 -4866 -618 4235 -3642 3161 -11768
16000 392 634 -548 -2532 0.5208 0.1076 0.242 0.1460 0.1697 3754 -3229 -4862 -4862 -612 4196 -3608 3088 -11699
17000 396 634 -537 -2531 0.5208 0.1076 0.238 0.1460 0.1697 3680 -3166 -4859 -4859 -602 4122 -3546 2944 -11571
18000 403 634 -521 -2530 0.5208 0.1076 0.232 0.1460 0.1697 3571 -3073 -4857 -4857 -586 4015 -3455 2728 -11385
19000 411 635 -500 -2530 0.5208 0.1077 0.224 0.1461 0.1697 3425 -2948 -4857 -4857 -566 3873 -3334 2440 -11140
20000 421 635 -474 -2530 0.5208 0.1077 0.213 0.1461 0.1696 3243 -2793 -4858 -4858 -540 3697 -3184 2081 -10836
21000 434 635 -442 -2532 0.5208 0.1077 0.201 0.1462 0.1696 3025 -2608 -4861 -4861 -510 3486 -3005 1650 -1047322000 448 635 -405 -2534 0.5208 0.1077 0.187 0.1463 0.1695 2771 -2391 -4865 -4865 -474 3240 -2796 1147 -10051
23000 465 636 -363 -2536 0.5208 0 .1077 0.171 0.1463 0.1695 2482 -2143 -4870 -4870 -433 2960 -2556 573 -9569
24000 483 636 -316 -2540 0.5208 0.1077 0.153 0.1464 0.1694 2157 -1864 -4876 -4876 -387 2645 -2287 -74 -9027
25000 504 636 -263 -2544 0.5208 0.1078 0.132 0.1466 0.1694 1796 -1554 -4884 -4884 -336 2295 -1986 -793 -8424
26000 527 637 -205 -2548 0.5208 0.1078 0.110 0.1467 0.1693 1400 -1213 -4893 -4893 -280 1909 -1654 -1584 -7760
27000 552 637 -142 -2554 0.5208 0.1079 0.086 0.1469 0.1693 969 -840 -4903 -4903 -218 1488 -1291 -2447 -7035
28000 579 664 -74 -2566 0.7453 0 .1198 0.086 0.1694 0.1805 436 -409 -3443 -3443 -219 1296 -1216 -1711 -5068
29000 608 664 0 -2572 0.7453 0.1199 0.057 0.1695 0.1804 0 0 -3450 -3450 -146 864 -812 -2586 -4262
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF THE POST TENSION AT TOP TENDON (At time of deck pouring)
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x yt,inf M It Wt,sup Wt,inf sup inf
mm m kNm m m m KN/m KN/m
0 0.664 0 0.1204 0.1695 0.1804 0 01000 0.664 180 0.1205 0.1694 0.1805 -1063 998
2000 0.637 343 0.1085 0.1469 0.1693 -2335 2026
3000 0.637 493 0.1085 0.1467 0.1693 -3358 2910
4000 0.636 630 0.1086 0.1466 0.1694 -4297 3719
5000 0.636 755 0.1087 0.1464 0.1694 -5153 4454
6000 0.636 867 0.1088 0.1463 0.1695 -5924 5115
7000 0.635 967 0.1089 0.1463 0.1695 -6610 5702
8000 0.635 1054 0.1089 0.1462 0.1696 -7211 6216
9000 0.635 1129 0.1090 0.1461 0.1696 -7726 6656
10000 0.635 1191 0.1091 0.1461 0.1697 -8156 7022
11000 0.634 1241 0.1091 0.1460 0.1697 -8500 7315
12000 0.634 1279 0.1091 0.1460 0.1697 -8759 7534
13000 0.634 1304 0.1092 0.1460 0.1697 -8931 7681
14000 0.634 1316 0.1092 0.1460 0.1697 -9017 7754
14250 0.634 1317 0.1092 0.1459 0.1697 -9025 7761
14500 0.634 1318 0.1092 0.1459 0.1697 -9028 7763
14750 0.634 1317 0.1092 0.1459 0.1697 -9025 7761
15000 0.634 1316 0.1092 0.1460 0.1697 -9017 7754
16000 0.634 1304 0.1092 0.1460 0.1697 -8931 7681
17000 0.634 1279 0.1091 0.1460 0.1697 -8759 7534
18000 0.634 1241 0.1091 0.1460 0.1697 -8500 7315
19000 0.635 1191 0.1091 0.1461 0.1697 -8156 7022
20000 0.635 1129 0.1090 0.1461 0.1696 -7726 6656
21000 0.635 1054 0.1089 0.1462 0.1696 -7211 6216
22000 0.635 967 0.1089 0.1463 0.1695 -6610 5702
23000 0.636 867 0.1088 0.1463 0.1695 -5924 5115
24000 0.636 755 0.1087 0.1464 0.1694 -5153 4454
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF ITS SELF WEIGHT (DECK POURING)
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x sup inf sup inf sup inf sup inf
mm KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2
0 2894 -9835 -2669 -4397 0 0 226 -14233
1000 3480 -10372 -1770 -5210 -1063 998 647 -14584
2000 3124 -12497 -2532 -7212 -2335 2026 -1743 -17683
3000 3703 -12980 -1647 -7936 -3358 2910 -1303 -18006
4000 4233 -13420 -839 -8594 -4297 3719 -903 -18296
5000 4715 -13818 -106 -9189 -5153 4454 -543 -18554
6000 5149 -14175 552 -9721 -5924 5115 -222 -18781
7000 5534 -14490 1136 -10190 -6610 5702 59 -18977
8000 5870 -14763 1645 -10598 -7211 6216 304 -19145
9000 6157 -14995 2080 -10944 -7726 6656 511 -19284
10000 6396 -15186 2442 -11230 -8156 7022 681 -19394
11000 6585 -15336 2731 -11456 -8500 7315 815 -19477
12000 6726 -15444 2947 -11623 -8759 7534 914 -19533
13000 6819 -15513 3090 -11730 -8931 7681 978 -19562
14000 6862 -15540 3162 -11778 -9017 7754 1007 -19565
15000 6858 -15527 3161 -11768 -9017 7754 1002 -19541
16000 6804 -15474 3088 -11699 -8931 7681 962 -19492
17000 6703 -15380 2944 -11571 -8759 7534 888 -19417
18000 6553 -15246 2728 -11385 -8500 7315 781 -19316
19000 6355 -15071 2440 -11140 -8156 7022 639 -19189
20000 6110 -14856 2081 -10836 -7726 6656 464 -19037
21000 5816 -14601 1650 -10473 -7211 6216 255 -18859
22000 5475 -14305 1147 -10051 -6610 5702 12 -18654
23000 5086 -13969 573 -9569 -5924 5115 -265 -18423
24000 4650 -13593 -74 -9027 -5153 4454 -577 -18166
25000 4167 -13176 -793 -8424 -4297 3719 -923 -17882
26000 3638 -12719 -1584 -7760 -3358 2910 -1304 -17570
TENDONS +SWBOTTOM TENDON TOP TENDON SELF WEIGHT
SUM OF TENSIONS: POST TENSION + SELF WEIGHT WITH DECK POURED
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x M Wt,sup Wt,inf sup inf
mm kNm m m KN/m2 KN/m2
0 0 0.170 0.180 0 01000 193 0.169 0.180 -1140 1070
2000 372 0.147 0.169 -2535 2200
3000 538 0.147 0.169 -3666 3177
4000 690 0.147 0.169 -4704 4071
5000 827 0.146 0.169 -5650 4884
6000 952 0.146 0.169 -6502 5615
7000 1062 0.146 0.170 -7261 6264
8000 1158 0.146 0.170 -7925 68319000 1241 0.146 0.170 -8495 7317
10000 1310 0.146 0.170 -8970 7722
11000 1365 0.146 0.170 -9350 8046
12000 1407 0.146 0.170 -9636 8289
13000 1434 0.146 0.170 -9826 8451
14000 1448 0.146 0.170 -9921 8532
15000 1448 0.146 0.170 -9921 8532
16000 1434 0.146 0.170 -9826 8451
17000 1407 0.146 0.170 -9636 8289
18000 1365 0.146 0.170 -9350 8046
19000 1310 0.146 0.170 -8970 7722
20000 1241 0.146 0.170 -8495 7317
21000 1158 0.146 0.170 -7925 6831
22000 1062 0.146 0.170 -7261 6264
23000 952 0.146 0.169 -6502 5615
24000 827 0.146 0.169 -5650 4884
25000 690 0.147 0.169 -4704 4071
26000 538 0.147 0.169 -3666 3177
27000 372 0.147 0.169 -2535 2200
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF DECK WEIGHT
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x sup inf sup inf sup inf
mm KN/m2 KN/m2 KN/m2 KN/m2 KN/m2 KN/m2
0 226 -14233 0 0 226 -14233
1000 647 -14584 -1140 1070 -493 -13514
2000 -1743 -17683 -2535 2200 -4279 -15483
3000 -1303 -18006 -3666 3177 -4969 -14829
4000 -903 -18296 -4704 4071 -5607 -14224
5000 -543 -18554 -5650 4884 -6193 -13670
6000 -222 -18781 -6502 5615 -6725 -13166
7000 59 -18977 -7261 6264 -7201 -12714
8000 304 -19145 -7925 6831 -7621 -12314
9000 511 -19284 -8495 7317 -7984 -11966
10000 681 -19394 -8970 7722 -8289 -11672
11000 815 -19477 -9350 8046 -8535 -11431
12000 914 -19533 -9636 8289 -8721 -11244
13000 978 -19562 -9826 8451 -8848 -11111
14000 1007 -19565 -9921 8532 -8914 -11033
15000 1002 -19541 -9921 8532 -8920 -11010
16000 962 -19492 -9826 8451 -8864 -11041
17000 888 -19417 -9636 8289 -8747 -11128
18000 781 -19316 -9350 8046 -8570 -11270
19000 639 -19189 -8970 7722 -8331 -11467
20000 464 -19037 -8495 7317 -8031 -11719
21000 255 -18859 -7925 6831 -7670 -12027
22000 12 -18654 -7261 6264 -7249 -12391
23000 -265 -18423 -6502 5615 -6767 -12809
24000 -577 -18166 -5650 4884 -6227 -13282
25000 -923 -17882 -4704 4071 -5627 -1381026000 -1304 -17570 -3666 3177 -4970 -14393
27000 -1720 -17229 -2535 2200 -4255 -15030
28000 625 14191 1140 1070 515 13122
TOTALPOST + SELF WEIGHT DECK WEIGHT
SUM OF STRESSES: POST TENSION + SELF WEIGHT + DECK WEIGHT
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PHASE 3: COMPOSITE SECTION
STRESSES AT SERVICE LIMIT III
SW+ASPHALT+BARRIER+0.8(LL+MM)
(Composite Section transformed )
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MECHANICAL PROPERTIES:
- Composite transformed beam+deck
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Ec,beam ( 45 MPa) 36057 Mpa slab wide 2.25 m
Ec,slab ( 35 MPa) 31799 Mpa slab thickness 0.25 m
nc 0.882 beam depth 1.3716 m
GIRDER EDGE
SECTION A yi A(yi) A(yi-ycg) I Ic
MIDDLE m m m m m
GIRDER 0.5090 0.6282 0.3198 0.0935 0.1085
DECK 0.4961 1.4966 0.7424 0.0959 0.0026
1.0051 1.0622 0.1894 0.1111 0.3006
ycg = 1.0568 mSbc = 0.2844 m
SECTION A yi A(yi) A(yi-ycg) I Ic
ANCHORAGE m m m m m
GIRDER 0.7335 0.6575 0.4823 0.0841 0.1205
DECK 0.4961 1.4966 0.7424 0.1243 0.0026
1.2296 1.2248 0.2084 0.1231 0.3315
ycg = 0.9960 mSbc = 0.3328 m
SECTION A yi A(yi) A(yi-ycg) I Ic
TRANSITION m m m m m
GIRDER 0.6097 0.6433 0.3922 0.0893 0.1126
DECK 0.4961 1.4966 0.7424 0.1098 0.0026
1.1058 1.1346 0.1992 0.1152 0.3143
ycg = 1.0261 m
Sbc = 0.3063 m
COMPOSITE SECTION: BEAM + DECK
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x yt Abt It Atd Id yd ytc Abt+Atd
mm m m m m m m m m
0 0.664 0.7292 0.1199 0.4961 0.0026 1.497 1.001 1.22521000 0.664 0.7292 0.1198 0.4961 0.0026 1.497 1.001 1.2252
2000 0.637 0.5046 0.1079 0.4961 0.0026 1.497 1.063 1.0007
3000 0.637 0.5046 0.1078 0.4961 0.0026 1.497 1.063 1.0007
4000 0.636 0.5046 0.1078 0.4961 0.0026 1.497 1.063 1.0007
5000 0.636 0.5046 0.1077 0.4961 0.0026 1.497 1.063 1.0007
6000 0.636 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
7000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
8000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
9000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
10000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.000711000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
12000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
13000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
14000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
15000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
16000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
17000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
18000 0.634 0.5046 0.1076 0.4961 0.0026 1.497 1.062 1.0007
19000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
20000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
21000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
22000 0.635 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
23000 0.636 0.5046 0.1077 0.4961 0.0026 1.497 1.062 1.0007
24000 0.636 0.5046 0.1077 0.4961 0.0026 1.497 1.063 1.0007
25000 0.636 0.5046 0.1078 0.4961 0.0026 1.497 1.063 1.0007
26000 0.637 0.5046 0.1078 0.4961 0.0026 1.497 1.063 1.0007
27000 0.637 0.5046 0.1079 0.4961 0.0026 1.497 1.063 1.0007
28000 0.664 0.7292 0.1198 0.4961 0.0026 1.497 1.001 1.2252
29000 0.664 0.7292 0.1199 0.4961 0.0026 1.497 1.001 1.2252
TRANSFORMED COMPOSITE SECTION: BEAM + DECK
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x Atb(yt-ytc) Ad(yd-yct) Atd It+Id Itc ytc Wct,sup Wct,inf
mm m m m m m m m m
0 0.0828 0.1217 0.4961 0.1225 0.3269 1.001 0.5271 0.32641000 0.0828 0.1218 0.4961 0.1224 0.3270 1.001 0.5271 0.3267
2000 0.0916 0.0932 0.4961 0.1104 0.2952 1.063 0.5287 0.2776
3000 0.0917 0.0933 0.4961 0.1104 0.2954 1.063 0.5287 0.2779
4000 0.0918 0.0934 0.4961 0.1104 0.2955 1.063 0.5288 0.2780
5000 0.0919 0.0934 0.4961 0.1103 0.2956 1.063 0.5288 0.2782
6000 0.0919 0.0935 0.4961 0.1103 0.2958 1.062 0.5289 0.2784
7000 0.0920 0.0936 0.4961 0.1103 0.2959 1.062 0.5290 0.2785
8000 0.0921 0.0937 0.4961 0.1103 0.2960 1.062 0.5290 0.2787
9000 0.0921 0.0937 0.4961 0.1102 0.2961 1.062 0.5291 0.2788
10000 0.0922 0.0937 0.4961 0.1102 0.2961 1.062 0.5291 0.278911000 0.0922 0.0938 0.4961 0.1102 0.2962 1.062 0.5291 0.2790
12000 0.0922 0.0938 0.4961 0.1102 0.2962 1.062 0.5291 0.2790
13000 0.0922 0.0938 0.4961 0.1102 0.2963 1.062 0.5292 0.2791
14000 0.0922 0.0938 0.4961 0.1102 0.2963 1.062 0.5292 0.2791
15000 0.0922 0.0938 0.4961 0.1102 0.2963 1.062 0.5292 0.2791
16000 0.0922 0.0938 0.4961 0.1102 0.2963 1.062 0.5292 0.2791
17000 0.0922 0.0938 0.4961 0.1102 0.2962 1.062 0.5291 0.2790
18000 0.0922 0.0938 0.4961 0.1102 0.2962 1.062 0.5291 0.2790
19000 0.0922 0.0937 0.4961 0.1102 0.2961 1.062 0.5291 0.2789
20000 0.0921 0.0937 0.4961 0.1102 0.2961 1.062 0.5291 0.2788
21000 0.0921 0.0937 0.4961 0.1103 0.2960 1.062 0.5290 0.2787
22000 0.0920 0.0936 0.4961 0.1103 0.2959 1.062 0.5290 0.2785
23000 0.0919 0.0935 0.4961 0.1103 0.2958 1.062 0.5289 0.2784
24000 0.0919 0.0934 0.4961 0.1103 0.2956 1.063 0.5288 0.2782
25000 0.0918 0.0934 0.4961 0.1104 0.2955 1.063 0.5288 0.2780
26000 0.0917 0.0933 0.4961 0.1104 0.2954 1.063 0.5287 0.2779
27000 0.0916 0.0932 0.4961 0.1104 0.2952 1.063 0.5287 0.2776
28000 0.0828 0.1218 0.4961 0.1224 0.3270 1.001 0.5271 0.3267
29000 0.0828 0.1217 0.4961 0.1225 0.3269 1.001 0.5271 0.3264
TRANSFORMED COMPOSITE SECTION: BEAM + DECK
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FLEXURAL STRESSES AT EDGE FIBERS OF
COMPOSITE SECTION AND TOP OF
BEAM
- Asphalt stresses at composite section
- Barrier stresses at composite section
- Live Load Stresses at composite section- Total Stresses Service Limit State III at
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x M Wct,sup Wct,inf sup inf
mm kNm m m KN/m KN/m
0 0 0.527 0.326 0 0
1000 59 0.527 0.327 -113 182
2000 114 0.529 0.278 -216 412
3000 165 0.529 0.278 -312 595
4000 212 0.529 0.278 -401 762
5000 254 0.529 0.278 -481 914
6000 292 0.529 0.278 -553 1050
7000 326 0.529 0.279 -617 1171
8000 356 0.529 0.279 -673 1277
9000 381 0.529 0.279 -721 1368
10000 402 0.529 0.279 -761 1443
11000 419 0.529 0.279 -793 1503
12000 432 0.529 0.279 -817 1549
13000 441 0.529 0.279 -833 1579
14000 445 0.529 0.279 -841 1594
15000 445 0.529 0.279 -841 1594
16000 441 0.529 0.279 -833 1579
17000 432 0.529 0.279 -817 1549
18000 419 0.529 0.279 -793 1503
19000 402 0.529 0.279 -761 1443
20000 381 0.529 0.279 -721 1368
21000 356 0.529 0.279 -673 1277
22000 326 0.529 0.279 -617 1171
23000 292 0.529 0.278 -553 1050
24000 254 0.529 0.278 -481 914
25000 212 0.529 0.278 -401 762
26000 165 0.529 0.278 -312 595
27000 114 0.529 0.278 -216 412
STRESS AT TOP AND BOTTOM OF THE BEAM BECAUSE OF ASPHALT
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x M Wct,sup Wct,inf sup inf
mm kNm m m KN/m KN/m
0 0 0.527 0.326 0 0
1000 46 0.527 0.327 -86 139
2000 88 0.529 0.278 -166 316
3000 127 0.529 0.278 -240 456
4000 163 0.529 0.278 -307 585
5000 195 0.529 0.278 -369 701
6000 224 0.529 0.278 -424 806
7000 250 0.529 0.279 -473 899
8000 273 0.529 0.279 -516 980
9000 293 0.529 0.279 -553 1050
10000 309 0.529 0.279 -584 110711000 322 0.529 0.279 -608 1154
12000 332 0.529 0.279 -627 1189
13000 338 0.529 0.279 -639 1212
14000 341 0.529 0.279 -645 1223
15000 341 0.529 0.279 -645 1223
16000 338 0.529 0.279 -639 1212
17000 332 0.529 0.279 -627 1189
18000 322 0.529 0.279 -608 115419000 309 0.529 0.279 -584 1107
20000 293 0.529 0.279 -553 1050
21000 273 0.529 0.279 -516 980
22000 250 0.529 0.279 -473 899
23000 224 0.529 0.278 -424 806
24000 195 0.529 0.278 -369 701
25000 163 0.529 0.278 -307 585
26000 127 0.529 0.278 -240 45627000 88 0.529 0.278 -166 316
28000 46 0.527 0.327 -86 139
29000 0 0 527 0 326 0 0
STRESS AT TOP AND BOTTOM OF THE COMPOSITE SECTION BECAUSE OF BARRIER WEIGHT
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sup inf sup inf sup inf
KN/m KN/m KN/m KN/m KN/m KN/m
0 0 0 0 0 0
-113 182 -86 139 -199 321
-216 412 -166 316 -382 728
-312 595 -240 456 -552 1051
-401 762 -307 585 -708 1346
-481 914 -369 701 -849 1615
-553 1050 -424 806 -977 1856
-617 1171 -473 899 -1090 2070
-673 1277 -516 980 -1189 2257
-721 1368 -553 1050 -1274 2417
-761 1443 -584 1107 -1344 2551
-793 1503 -608 1154 -1401 2657
-817 1549 -627 1189 -1443 2737
-833 1579 -639 1212 -1472 2791
-841 1594 -645 1223 -1486 2817
-841 1594 -645 1223 -1486 2817
-833 1579 -639 1212 -1472 2791
-817 1549 -627 1189 -1443 2737
-793 1503 -608 1154 -1401 2657
-761 1443 -584 1107 -1344 2551
-721 1368 -553 1050 -1274 2417
-673 1277 -516 980 -1189 2257
-617 1171 -473 899 -1090 2070
-553 1050 -424 806 -977 1856
-481 914 -369 701 -849 1615
-401 762 -307 585 -708 1346
-312 595 -240 456 -552 1051
-216 412 -166 316 -382 728
TOTAL
SUM OF TENSIONS: ASPHALT WEIGHT + BARRIER WEIGHT
ASPHALT BARRIER
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November 1, 2020 1:57:35 pmPage 1
C:\Users\Toshiba PC\Desktop\GRADO\BRIDGE58.20IV.qcb
Washington State Department of TransportationBridge and Structures Office
QConBridge 1.3 Release Date: 05-10-2005
Live Load Envelopes (Per Lane)
Span Point Min Shear(N) Max Shear(N) Min Moment(N-m) Max Moment(N-m)
1 0 -56.773e+03 498.290e+03 0.000e+00 0.000e+00
1 1 -56.786e+03 491.368e+03 -14.241e+03 123.555e+031 2 -56.823e+03 484.476e+03 -28.484e+03 244.218e+031 3 -56.886e+03 477.615e+03 -42.727e+03 361.995e+031 4 -56.974e+03 470.784e+03 -56.969e+03 476.888e+031 5 -57.087e+03 463.985e+03 -71.211e+03 588.904e+031 6 -57.225e+03 457.218e+03 -85.454e+03 698.047e+031 7 -57.230e+03 451.492e+03 -99.696e+03 804.323e+031 8 -57.577e+03 443.782e+03 -113.938e+03 907.740e+031 9 -57.791e+03 437.113e+03 -128.181e+03 1.008e+061 10 -58.029e+03 430.478e+03 -142.423e+03 1.106e+06
1 11 -58.293e+03 423.876e+03 -156.665e+03 1.200e+061 12 -58.581e+03 417.309e+03 -170.908e+03 1.292e+061 13 -58.895e+03 410.777e+03 -185.150e+03 1.382e+061 14 -58.918e+03 405.130e+03 -199.392e+03 1.468e+061 15 -59.597e+03 397.817e+03 -213.635e+03 1.552e+061 16 -62.902e+03 391.391e+03 -227.877e+03 1.632e+061 17 -66.440e+03 385.001e+03 -242.119e+03 1.711e+061 18 -69.998e+03 378.648e+03 -256.362e+03 1.786e+061 19 -73.576e+03 372.331e+03 -270.604e+03 1.858e+061 20 -77.175e+03 366.052e+03 -284.846e+03 1.928e+061 21 -80.793e+03 359.811e+03 -299.089e+03 1.995e+061 22 -84.430e+03 353.608e+03 -313.331e+03 2.059e+061 23 -88.087e+03 347.443e+03 -327.573e+03 2.121e+061 24 -91.763e+03 341.317e+03 -341.816e+03 2.180e+061 25 -95.457e+03 335.230e+03 -356.058e+03 2.236e+061 26 -99.169e+03 329.183e+03 -370.300e+03 2.289e+061 27 -102.898e+03 323.175e+03 -384.543e+03 2.340e+061 28 -102.996e+03 317.789e+03 -398.785e+03 2.388e+061 29 -111.523e+03 311.282e+03 -413.027e+03 2.434e+061 30 -116.317e+03 305.396e+03 -427.270e+03 2.477e+061 31 -121.126e+03 299.552e+03 -441.512e+03 2.517e+06
1 32 -125.952e+03 293.749e+03 -455.754e+03 2.555e+061 33 -130.793e+03 287.988e+03 -469.997e+03 2.590e+061 34 -135.648e+03 282.270e+03 -484.239e+03 2.622e+061 35 -140.878e+03 276.594e+03 -498.481e+03 2.657e+061 36 146 264 03 270 962 03 512 724 03 2 690 06
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November 1, 2020 1:57:35 pmPage 2
C:\Users\Toshiba PC\Desktop\GRADO\BRIDGE58.20IV.qcb
Washington State Department of TransportationBridge and Structures Office
QConBridge 1.3 Release Date: 05-10-2005
Live Load Envelopes (Per Lane)
Span Point Min Shear(N) Max Shear(N) Min Moment(N-m) Max Moment(N-m)
1 70 -333.999e+03 107.312e+03 -996.963e+03 2.508e+06
1 71 -339.545e+03 103.381e+03 -1.011e+06 2.468e+061 72 -345.085e+03 99.503e+03 -1.025e+06 2.426e+061 73 -350.620e+03 95.679e+03 -1.039e+06 2.382e+061 74 -356.148e+03 91.909e+03 -1.053e+06 2.336e+061 75 -361.668e+03 88.194e+03 -1.068e+06 2.288e+061 76 -367.182e+03 84.533e+03 -1.082e+06 2.238e+061 77 -372.687e+03 80.928e+03 -1.096e+06 2.186e+061 78 -378.183e+03 77.377e+03 -1.110e+06 2.133e+061 79 -383.670e+03 73.882e+03 -1.125e+06 2.078e+061 80 -389.147e+03 70.443e+03 -1.139e+06 2.021e+06
1 81 -394.614e+03 67.059e+03 -1.153e+06 1.962e+061 82 -400.069e+03 63.788e+03 -1.167e+06 1.902e+061 83 -405.512e+03 60.714e+03 -1.182e+06 1.840e+061 84 -410.944e+03 57.691e+03 -1.196e+06 1.776e+061 85 -416.362e+03 54.719e+03 -1.210e+06 1.712e+061 86 -421.766e+03 51.956e+03 -1.224e+06 1.647e+061 87 -427.157e+03 49.515e+03 -1.460e+06 1.579e+061 88 -432.533e+03 47.115e+03 -1.477e+06 1.510e+061 89 -437.893e+03 44.757e+03 -1.493e+06 1.439e+061 90 -443.237e+03 42.441e+03 -1.510e+06 1.367e+061 91 -448.565e+03 40.168e+03 -1.527e+06 1.293e+061 92 -453.876e+03 37.936e+03 -1.544e+06 1.218e+061 93 -459.168e+03 35.746e+03 -1.560e+06 1.141e+061 94 -464.442e+03 33.599e+03 -1.579e+06 1.065e+061 95 -469.698e+03 31.494e+03 -1.599e+06 989.428e+031 96 -474.933e+03 29.432e+03 -1.622e+06 914.446e+031 97 -480.148e+03 27.412e+03 -1.647e+06 840.213e+031 98 -485.342e+03 25.434e+03 -1.674e+06 766.706e+031 99 -490.514e+03 23.499e+03 -1.702e+06 694.191e+031 100 -495.664e+03 21.607e+03 -1.733e+06 638.314e+031 101 -500.792e+03 19.757e+03 -1.765e+06 586.395e+03
1 102 -505.895e+03 17.951e+03 -1.799e+06 535.471e+031 103 -510.975e+03 16.187e+03 -1.835e+06 485.519e+031 104 -516.029e+03 14.466e+03 -1.873e+06 436.518e+031 105 -521.059e+03 12.788e+03 -1.912e+06 388.447e+031 106 526 062 03 11 152 03 1 969 06 341 291 03
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November 1, 2020 1:57:35 pmPage 3
C:\Users\Toshiba PC\Desktop\GRADO\BRIDGE58.20IV.qcb
Washington State Department of TransportationBridge and Structures Office
QConBridge 1.3 Release Date: 05-10-2005
Live Load Envelopes (Per Lane)
Span Point Min Shear(N) Max Shear(N) Min Moment(N-m) Max Moment(N-m)
2 23 -35.746e+03 459.168e+03 -1.560e+06 1.141e+06
2 24 -37.936e+03 453.876e+03 -1.544e+06 1.218e+062 25 -40.168e+03 448.565e+03 -1.527e+06 1.293e+062 26 -42.441e+03 443.237e+03 -1.510e+06 1.367e+062 27 -44.757e+03 437.893e+03 -1.493e+06 1.439e+062 28 -44.785e+03 433.360e+03 -1.477e+06 1.510e+062 29 -49.515e+03 427.157e+03 -1.239e+06 1.579e+062 30 -51.956e+03 421.766e+03 -1.224e+06 1.647e+062 31 -54.719e+03 416.362e+03 -1.210e+06 1.712e+062 32 -57.691e+03 410.944e+03 -1.196e+06 1.776e+062 33 -60.714e+03 405.512e+03 -1.182e+06 1.840e+06
2 34 -63.788e+03 400.069e+03 -1.167e+06 1.902e+062 35 -67.059e+03 394.614e+03 -1.153e+06 1.962e+062 36 -70.443e+03 389.147e+03 -1.139e+06 2.021e+062 37 -73.882e+03 383.670e+03 -1.125e+06 2.078e+062 38 -77.377e+03 378.183e+03 -1.110e+06 2.133e+062 39 -80.928e+03 372.687e+03 -1.096e+06 2.186e+062 40 -84.533e+03 367.182e+03 -1.082e+06 2.238e+062 41 -88.194e+03 361.668e+03 -1.068e+06 2.288e+062 42 -91.909e+03 356.148e+03 -1.053e+06 2.336e+062 43 -95.679e+03 350.620e+03 -1.039e+06 2.382e+062 44 -99.503e+03 345.085e+03 -1.025e+06 2.426e+062 45 -103.381e+03 339.545e+03 -1.011e+06 2.468e+062 46 -107.312e+03 333.999e+03 -996.963e+03 2.508e+062 47 -111.297e+03 328.449e+03 -982.721e+03 2.546e+062 48 -115.335e+03 322.895e+03 -968.478e+03 2.582e+062 49 -119.426e+03 317.337e+03 -954.236e+03 2.616e+062 50 -123.570e+03 311.776e+03 -939.994e+03 2.648e+062 51 -127.766e+03 306.212e+03 -925.751e+03 2.678e+062 52 -132.014e+03 300.647e+03 -911.509e+03 2.705e+062 53 -136.314e+03 295.080e+03 -897.267e+03 2.731e+062 54 -140.666e+03 289.513e+03 -883.024e+03 2.754e+06
2 55 -145.069e+03 283.945e+03 -868.782e+03 2.775e+062 56 -145.238e+03 278.819e+03 -854.540e+03 2.794e+062 57 -154.028e+03 272.812e+03 -840.297e+03 2.810e+062 58 -158.583e+03 267.247e+03 -826.055e+03 2.825e+062 59 163 188 03 261 684 03 811 813 03 2 837 06
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November 1, 2020 1:57:35 pmPage 4
C:\Users\Toshiba PC\Desktop\GRADO\BRIDGE58.20IV.qcb
Washington State Department of TransportationBridge and Structures Office
QConBridge 1.3 Release Date: 05-10-2005
Live Load Envelopes (Per Lane)
Span Point Min Shear(N) Max Shear(N) Min Moment(N-m) Max Moment(N-m)
2 93 -347.443e+03 88.087e+03 -327.573e+03 2.121e+06
2 94 -353.608e+03 84.430e+03 -313.331e+03 2.059e+062 95 -359.811e+03 80.793e+03 -299.089e+03 1.995e+062 96 -366.052e+03 77.175e+03 -284.846e+03 1.928e+062 97 -372.331e+03 73.576e+03 -270.604e+03 1.858e+062 98 -378.648e+03 69.998e+03 -256.362e+03 1.786e+062 99 -385.001e+03 66.440e+03 -242.119e+03 1.711e+062 100 -391.391e+03 62.902e+03 -227.877e+03 1.632e+062 101 -397.817e+03 59.597e+03 -213.635e+03 1.552e+062 102 -404.279e+03 59.233e+03 -199.392e+03 1.468e+062 103 -410.777e+03 58.895e+03 -185.150e+03 1.382e+06
2 104 -417.309e+03 58.581e+03 -170.908e+03 1.292e+062 105 -423.876e+03 58.293e+03 -156.665e+03 1.200e+062 106 -430.478e+03 58.029e+03 -142.423e+03 1.106e+062 107 -431.417e+03 57.802e+03 -128.181e+03 1.008e+062 108 -443.782e+03 57.577e+03 -113.938e+03 907.740e+032 109 -450.484e+03 57.389e+03 -99.696e+03 804.323e+032 110 -457.218e+03 57.225e+03 -85.454e+03 698.047e+032 111 -463.985e+03 57.087e+03 -71.211e+03 588.904e+032 112 -465.041e+03 56.976e+03 -56.969e+03 476.888e+032 113 -477.615e+03 56.886e+03 -42.727e+03 361.995e+032 114 -484.476e+03 56.823e+03 -28.484e+03 244.218e+032 115 -491.368e+03 56.786e+03 -14.241e+03 123.555e+032 116 -498.290e+03 56.773e+03 0.000e+00 0.000e+00
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November 1, 2020 1:56:15 pm
Page 1 of 1
C:\Users\Toshiba PC\Desktop\GRADO\BRIDGE58.20IV.qcb
Washington State Department of Transportation
Bridge and Structures Office
QConBridge 1.3 Release Date: 05-10-2005
Moment DiagramHScal e: 0. 25 m/ mm - VScal e: 49. 988e+03 N- m/ mm
2.500e+06
2.250e+06
2.000e+06
1.750e+06
1.500e+06
1.250e+06
1.000e+06
750.000e+03
500.000e+03
250.000e+03
0.000e+00
-250.000e+03
-500.000e+03
-750.000e+03
-1.000e+06
-1.250e+06
-1.500e+06
-1.750e+06
-2.000e+06
-2.250e+06
-2.500e+06
Li ve Load Envel ope
1 21 2 3
Live Loads are per Lane
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INTERIOR BEAM AASHTO 4.6.2.2.2b-1
- ONE LANE LOADED
- TWO OR MORE DESIGNED LANES LOADED
Where:
Kg Longitudinal stiffness parameter
Ebeam ( 45 MPa) 36057 Mpa
Edeck ( 35 MPa) 31799 MPa
I (moment of inertia of beam) = 0.1085 m
0.5090 m
0.8684 m
A (area of the beam ) =
eg (d between cof gravities) =
FACTOR OF DISTRIBUTION OF LIVE LOAD
=0.06+
4300
.
+
.
.
= 0.075 +
2900
.
+
.
.
= ( + )
=
=
36057
31799= 1.134
= 1134 01085+05090 08684 = 0558
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- ONE LANE LOADED
- TWO OR MORE DESIGNED LANES LOADED
Therefore, use ginterior = 0.913 Lanes per girder
EXTERIOR BEAM AASHTO 4.6.2.2.2d-1
Where :
de is the distance from exterior web of exterior beam to interior edge of curb or traffic barrier in
mm, 700 mm:
FACTOR OF DISTRIBUTION OF LIVE LOAD
=0.06+2000
4300
.
+2000
29000
.
0.558
29000 250
.
= 0.825
= 0.075 +2000
2900
.
+2000
29000
.
0.558
29000 250
.