Assignment 6

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  • A 0.025

    B 120

    C 10

    Ep 2.00E+05

    eu 0.047000001

    fpu 1860

    Bottom cover 60 mm

    Pi 450 KN

    Ap 600 mm2

    fp 750 MPa

    p 0.00375 750

    at bottom fiber

    Fc 8.5 MPa

    F'c 40 Mpa

    c 0.000225177

    'c 0.002 8.50002

    at location of PS wire

    Fc 7.3 MPa

    F'c 40 Mpa

    c 0.000191687

    'c 0.002 7.300024

    compressive strain

    c 0.000225177

    = 0.67316547

    = 0.160975195

    c= 403.4205085 mm

    C= 524590.0016 N

    -5.58169E-07

  • f'c 40 MPa

    'c 0.002

    depth of section 600 mm

    location of PS wires 540 mm

    B 300 mm

    p 0.00375

    A 0.025

    B 120

    C 10

    Ep 2.00E+05 MPa

    eu 0.047

    fpu 1860 MPa

    Ap 600 mm2

    t strain ratio = = b c cp 'p F'p

    -0.00023 403.4205

    0.00019 0.095 0.672117 0.136869 8.54E-05 413.9335 5.79E-05 0.003808 761.5686

    0.00025 0.125 0.673913 0.177755 0.000209 326.6664 0.000163 0.003913 782.6382

    0.0005 0.25 0.681818 0.336111 0.000996 200.527 0.000846 0.004597 919.082

    0.00075 0.375 0.690476 0.475216 0.001966 165.6959 0.001694 0.005444 1087.38

    0.001 0.5 0.7 0.595238 0.002975 150.9485 0.002577 0.006328 1257.905

    0.0015 0.75 0.722222 0.778846 0.005071 136.9571 0.004414 0.008164 1540.767

    0.002 1 0.75 0.888889 0.007635 124.5514 0.006671 0.010421 1660.685

    0.0025 1.25 0.785714 0.92803 0.010462 115.7187 0.009166 0.012916 1687.565

    0.003 1.5 0.833333 0.9 0.012884 113.3193 0.011296 0.015046 1699.789

    0.0035 1.75 0.9 0.810185 0.014443 117.0382 0.012649 0.016399 1706.807

    0

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    -0.000005 0 0.000005 0.00001 0.000015 0.00002

    Mo

    men

    t

    Curvature rad/mm

    M vs

  • `

    M KN-m

    P'p KN C equilibrium Ap only

    -5.58E-07 0

    456941.2 456941.2 6.17E-08 4.59E-07 183.185

    469582.9 469582.9 -1.29E-06 7.653E-07 201.8867

    551449.2 551449.2 -2.772E-06 2.493E-06 260.0847

    652427.8 652427.8 -1.888E-06 4.526E-06 314.9892

    754742.7 754742.7 -8.871E-08 6.625E-06 367.6865

    924460.3 924460.3 -6.403E-09 1.095E-05 453.4878

    996411.1 996411.1 -1.681E-05 1.606E-05 491.5229

    1012539 1012539 6.9116E-07 2.16E-05 500.7401

    1019874 1019874 4.6741E-07 2.647E-05 502.577

    1024084 1024084 4.163E-07 2.99E-05 499.0698

    0.00002 0.000025 0.00003 0.000035

    Curvature rad/mm

  • f'c 40 MPa

    'c 0.002

    depth of section 600 mm

    location of PS wires 540 mm

    B 300 mm

    p 0.00375

    A 0.025

    B 120

    C 10

    Ep 2.00E+05 MPa

    eu 0.047

    fpu 1860 MPa

    Ap 600 mm2

    top strain ratio = = bottom c cp strain in PS due to t

    'p (net strain in

    PS)

    -0.00023 403.4205

    0.00019 0.095 0.672117 0.136869 8.41E-05 415.8636 5.67E-05 0.00380684

    0.00025 0.125 0.673913 0.177755 0.000204 330.6548 0.000158 0.003908405

    0.0005 0.25 0.681818 0.336111 0.000932 209.4929 0.000789 0.004538951

    0.00075 0.375 0.690476 0.475216 0.001796 176.7542 0.001541 0.005291441

    0.001 0.5 0.7 0.595238 0.002675 163.2695 0.002307 0.00605754

    0.0015 0.75 0.722222 0.778846 0.004608 147.3577 0.003997 0.007746951

    0.002 1 0.75 0.888889 0.006846 135.6526 0.005962 0.009711638

    0.0025 1.25 0.785714 0.92803 0.009345 126.6325 0.008161 0.011910896

    0.003 1.5 0.833333 0.9 0.011518 123.9812 0.010066 0.01381662

    0.0035 1.75 0.9 0.810185 0.012909 127.9756 0.011268 0.015018562

    0

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    -0.000005 0 0.000005 0.00001 0.000015

    Mo

    men

    t

    Curvature rad/mm

    M vs

  • `

    M KN-m

    F'p P'p KN s (in steel

    Fs (stress

    in steel) Ps KN C equilibrium Ap , Ast

    -5.582E-07 0

    761.3386 456.8032 5.67E-05 11.34311 2.268621 459.0718 2.7068E-05 4.569E-07 183.7414

    781.6418 468.9851 0.000158 31.65615 6.33123 475.3163 1.0677E-05 7.561E-07 203.7128

    907.5871 544.5523 0.000789 157.7654 31.55307 576.1053 -3.157E-06 2.387E-06 269.9526

    1057.195 634.3172 0.001541 308.2634 61.65268 695.9699 -1.186E-05 4.243E-06 333.354

    1206.75 724.0499 0.002307 461.4831 92.29662 816.3474 -0.0008092 6.125E-06 394.1778

    1491.108 894.6648 0.003997 500 100 994.6648 -1.018E-06 1.018E-05 484.1904

    1642.035 985.2207 0.005962 500 100 1085.221 4.5772E-06 1.474E-05 530.8143

    1680.057 1008.034 0.008161 500 100 1108.034 -7.524E-06 1.974E-05 543.2155

    1693.052 1015.831 0.010066 500 100 1115.831 -9.859E-07 2.42E-05 544.9062

    1699.644 1019.786 0.011268 500 100 1119.787 -0.0003 2.735E-05 540.1973

    0.000015 0.00002 0.000025 0.00003

    Curvature rad/mm

    M vs

  • f'c 40 MPa

    'c 0.002

    depth of section 600 mm

    location of PS wires 540 mm

    B 300 mm

    p 0.00375

    A 0.025

    B 120

    C 10

    Ep 2.00E+05 MPa

    eu 0.047

    fpu 1860 MPa

    Ap 600 mm2

    t strain ratio = = b c cp 'p F'p

    -0.00023 403.4205

    0.00019 0.095 0.672117 0.136869 8.91E-05 408.4236 6.12E-05 0.003811 762.2371

    0.00025 0.125 0.673913 0.177755 0.000216 321.5561 0.00017 0.00392 783.9511

    0.0005 0.25 0.681818 0.336111 0.001026 196.6335 0.000873 0.004623 924.3989

    0.00075 0.375 0.690476 0.475216 0.002021 162.3865 0.001744 0.005494 1097.186

    0.001 0.5 0.7 0.595238 0.003058 147.8645 0.002652 0.006402 1271.818

    0.0015 0.75 0.722222 0.778846 0.005243 133.4619 0.004569 0.008319 1556.49

    0.002 1 0.75 0.888889 0.008001 119.9915 0.007001 0.010751 1666.549

    0.0025 1.25 0.785714 0.92803 0.011049 110.7103 0.009694 0.013444 1690.866

    0.003 1.5 0.833333 0.9 0.013717 107.6766 0.012045 0.015795 1703.705

    0.0035 1.75 0.9 0.810185 0.015572 110.1108 0.013665 0.017415 1711.971

    0

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    600

    -0.000005 0 0.000005 0.00001 0.000015 0.00002

    Mo

    men

    t

    Curvature rad/mm

    M vs

  • M KN-m

    P'p KN sc Fsc Psc KN C equilibrium Ap , Asc

    -5.582E-07 0

    457.3423 0.000162 32.4175599 6.483511987 450.8588 -6.83498E-06 4.652E-07 184.6935

    470.3706 0.000203 40.6703685 8.134073703 462.2369 -0.000348427 7.775E-07 203.4286

    554.6393 0.000347 69.4863763 13.89727526 540.7421 -2.65392E-05 2.543E-06 262.4232

    658.3119 0.000473 94.5766618 18.91533237 639.3967 -0.000179123 4.619E-06 318.5077

    763.0906 0.000594 118.844593 23.76891862 739.3223 -0.000621368 6.763E-06 372.3811

    933.8939 0.000826 165.130059 33.02601185 900.8679 -1.5777E-06 1.124E-05 458.9042

    999.9293 0.001 199.985853 39.9971706 959.9321 -4.16041E-06 1.667E-05 494.3681

    1014.52 0.001145 229.022531 45.80450612 968.7152 -1.51268E-06 2.258E-05 502.9597

    1022.223 0.001328 265.665602 53.13312048 969.0896 -1.01279E-06 2.786E-05 505.3338

    1027.183 0.001593 318.565989 63.71319787 963.4694 -8.47983E-07 3.179E-05 503.116

    0.00002 0.000025 0.00003 0.000035

    Curvature rad/mm

  • f'c 40 MPa

    'c 0.002

    depth of section 600 mm

    location of PS wires 540 mm

    B 300 mm

    p 0.00375

    A 0.025

    B 120

    C 10

    Ep 2.00E+05 MPa

    eu 0.047

    fpu 1860 MPa

    Ap 600 mm2

    t strain ratio = = b c cp 'p F'p

    -0.00023 403.4205

    0.00019 0.095 0.672117 0.136869 8.77E-05 410.4562 6E-05 0.00381 761.9884

    0.00025 0.125 0.673913 0.177755 0.000211 325.6746 0.000165 0.003915 782.8898

    0.0005 0.25 0.681818 0.336111 0.000958 205.7156 0.000812 0.004563 912.3082

    0.00075 0.375 0.690476 0.475216 0.001844 173.5006 0.001584 0.005334 1065.688

    0.001 0.5 0.7 0.595238 0.002745 160.2154 0.00237 0.006121 1218.798

    0.0015 0.75 0.722222 0.778846 0.004761 143.7442 0.004135 0.007885 1508.714

    0.002 1 0.75 0.888889 0.007167 130.8992 0.006251 0.010001 1650.873

    0.0025 1.25 0.785714 0.92803 0.009883 121.1312 0.008645 0.012395 1683.941

    0.003 1.5 0.833333 0.9 0.012293 117.7036 0.010763 0.014514 1696.936

    0.0035 1.75 0.9 0.810185 0.013957 120.2935 0.012212 0.015962 1704.564

    0

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    -0.000005 0 0.000005 0.00001 0.000015 0.00002 0.000025

    Mo

    men

    t

    Curvature rad/mm

    M vs

  • P'p KN s Fs Ps KN sc Fsc Psc KN C equilibrium

    457.193 6E-05 11.99315 2.398631 0.000162 32.44521 6.489041 453.1026 4.27968E-05

    469.7339 0.000165 32.90483 6.580967 0.000204 40.78835 8.15767 468.1573 -8.58576E-05

    547.3849 0.000812 162.4983 32.49967 0.000354 70.83352 14.1667 565.7179 -2.81215E-06

    639.4127 0.001584 316.8571 63.37142 0.000491 98.12699 19.6254 683.1587 -4.45979E-06

    731.2788 0.00237 474.0925 94.81849 0.000626 125.1008 25.02017 801.0771 2.93249E-05

    905.2286 0.004135 500 100 0.000874 174.7775 34.9555 970.2731 -7.38904E-07

    990.5236 0.006251 500 100 0.001083 216.6528 43.33055 1047.193 -0.000288996

    1010.365 0.008645 500 100 0.001262 252.3346 50.46691 1059.898 -5.32054E-06

    1018.162 0.010763 500 100 0.001471 294.1469 58.82939 1059.332 -6.43451E-07

    1022.739 0.012212 500 100 0.001754 350.8539 70.17078 1052.568 -0.00026618

    0.000025 0.00003 0.000035

    Curvature rad/mm

  • M KN-m

    Ap , Asc , Ast

    -5.58E-07 0

    4.629E-07 185.2904

    7.676E-07 205.3459

    2.431E-06 272.6137

    4.323E-06 337.4054

    6.242E-06 399.6706

    1.044E-05 490.3615

    1.528E-05 534.8792

    2.064E-05 546.1312

    2.549E-05 548.3245

    2.91E-05 545.091

  • PRESTRESSED CONCRETE STRUCTURES

    ASSIGNMENT 6

    P Sameer Kumar Sarma

    Ce13p1007

    The given cross section is analysed for different cases of Asc, Ast by assuming initial top strain.

    For this particular top strain the depth of neutral axis is found by tra