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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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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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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)

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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

.