hormigón armado

UNIVERSIDAD CATLICA BOLIVIANA "SAN PABLO"

CLCULO DE LA SOLICITACIONES DE UNA VIGA DE HORMIGN ARMADO POR EL MTODO DE ALBERT CAQUOT

ING. MIGUEL MUOZ BLACK Univ. Ibarra Tapia Ximena Fernanda

JUEGO DE CARGA 1

q 70 kN EI constanteg 50 kNq+g 120 kN

120 12050

5 6 7Luces de caquot

54.8

7

Wi Wd Mb625 -230.4 246.453782

Wi Wd Mc230.4 -1715 465.499501

CALCULO DE REACCIONES

TRAMO MOMENTO w MOMENTO e CARGA LONGITUD

A-B 0 246.453782 120 5 250.709244B-C 246.453782 465.499501 50 6 113.49238C-D 465.499501 0 120 7 486.499929

L1L2L3

VERTICAL IZQUIERDA




TRAMO X D REACCION V(X)

A-B

0 0 120 250.709244 250.7092440.5 0.5 120 250.709244 190.7092441 1 120 250.709244 130.709244

1.5 1.5 120 250.709244 70.70924372 2 120 250.709244 10.7092437

2.5 2.5 120 250.709244 -49.29075633 3 120 250.709244 -109.290756

3.5 3.5 120 250.709244 -169.2907564 4 120 250.709244 -229.290756

4.5 4.5 120 250.709244 -289.2907565 5 120 250.709244 -349.290756

B-C

0 5 50 113.49238 113.492380.5 5.5 50 113.49238 88.492381 6 50 113.49238 63.49238

1.5 6.5 50 113.49238 38.492382 7 50 113.49238 13.49238

2.5 7.5 50 113.49238 -11.507623 8 50 113.49238 -36.50762

3.5 8.5 50 113.49238 -61.507624 9 50 113.49238 -86.50762

4.5 9.5 50 113.49238 -111.507625 10 50 113.49238 -136.50762

5.5 10.5 50 113.49238 -161.507626 11 50 113.49238 -186.50762

C-D

0 11 120 486.499929 486.4999290.5 11.5 120 486.499929 426.4999291 12 120 486.499929 366.499929

1.5 12.5 120 486.499929 306.4999292 13 120 486.499929 246.499929

2.5 13.5 120 486.499929 186.4999293 14 120 486.499929 126.499929

3.5 14.5 120 486.499929 66.49992884 15 120 486.499929 6.49992879

4.5 15.5 120 486.499929 -53.50007125 16 120 486.499929 -113.500071

5.5 16.5 120 486.499929 -173.5000716 17 120 486.499929 -233.500071

6.5 17.5 120 486.499929 -293.5000717 18 120 486.499929 -353.500071

XGRAFICO




349.290756186.50762

353.500071

VERTICAL" DERECHA




M(X)

0110.354622190.709244241.063866261.418487251.773109212.127731142.48235342.8369748-86.8084034-246.453782-246.453782-195.957592-157.961402-132.465212-119.469022-118.972832-130.976642-155.480452-192.484262-241.988071-303.991881-378.495691-465.499501-465.499501-237.249537-38.9995727129.250392267.500356375.75032

454.000285502.250249520.500214508.750178467.000142395.250107293.500071161.750036

0




JUEGO DE CARGA 2


50 50120


54.8

7

Wi Wd Mb260.416667 -552.96 234.346218

Wi Wd Mc552.96 -714.583333 303.300499



A-B 0 234.346218 50 5 78.1307563 171.869244B-C 234.346218 303.300499 120 6 348.50762 371.49238C-D 303.300499 0 50 7 218.328643 131.671357

L1L2L3

VERTICAL IZQUIERDA

VERTICAL" DERECHA




TRAMO X D REACCION V(X) M(X)

A-B

0 0 50 78.1307563 78.1307563 00.5 0.5 50 78.1307563 53.1307563 32.81537821 1 50 78.1307563 28.1307563 53.1307563

1.5 1.5 50 78.1307563 3.1307563 60.94613452 2 50 78.1307563 -21.8692437 56.2615126

2.5 2.5 50 78.1307563 -46.8692437 39.07689083 3 50 78.1307563 -71.8692437 9.39226891

3.5 3.5 50 78.1307563 -96.8692437 -32.79235294 4 50 78.1307563 -121.869244 -87.4769748

4.5 4.5 50 78.1307563 -146.869244 -154.6615975 5 50 78.1307563 -171.869244 -234.346218

B-C

0 5 120 348.50762 348.50762 -234.3462180.5 5.5 120 348.50762 288.50762 -75.09240851 6 120 348.50762 228.50762 54.1614015

1.5 6.5 120 348.50762 168.50762 153.4152122 7 120 348.50762 108.50762 222.669022

2.5 7.5 120 348.50762 48.50762 261.9228323 8 120 348.50762 -11.49238 271.176642

3.5 8.5 120 348.50762 -71.49238 250.4304524 9 120 348.50762 -131.49238 199.684262

4.5 9.5 120 348.50762 -191.49238 118.9380715 10 120 348.50762 -251.49238 8.1918815

5.5 10.5 120 348.50762 -311.49238 -132.5543096 11 120 348.50762 -371.49238 -303.300499

C-D

0 11 50 218.328643 218.328643 -303.3004990.5 11.5 50 218.328643 193.328643 -200.3861771 12 50 218.328643 168.328643 -109.971856

1.5 12.5 50 218.328643 143.328643 -32.05753452 13 50 218.328643 118.328643 33.3567868

2.5 13.5 50 218.328643 93.3286426 86.27110813 14 50 218.328643 68.3286426 126.685429

3.5 14.5 50 218.328643 43.3286426 154.5997514 15 50 218.328643 18.3286426 170.014072

4.5 15.5 50 218.328643 -6.67135736 172.9283935 16 50 218.328643 -31.6713574 163.342715

5.5 16.5 50 218.328643 -56.6713574 141.2570366 17 50 218.328643 -81.6713574 106.671357

6.5 17.5 50 218.328643 -106.671357 59.58567877 18 50 218.328643 -131.671357 0

XGRAFICO




JUEGO DE CARGA 3


120 50120


54.8

7

Wi Wd Mb625 -552.96 339.388235

Wi Wd Mc552.96 -714.583333 303.300499



A-B 0 339.388235 120 5 232.122353B-C 339.388235 303.300499 120 6 366.014623C-D 303.300499 0 50 7 218.328643

L1L2L3

VERTICAL IZQUIERDA





A-B

0 0 120 232.122353 232.1223530.5 0.5 120 232.122353 172.1223531 1 120 232.122353 112.122353

1.5 1.5 120 232.122353 52.12235292 2 120 232.122353 -7.87764706

2.5 2.5 120 232.122353 -67.87764713 3 120 232.122353 -127.877647

3.5 3.5 120 232.122353 -187.8776474 4 120 232.122353 -247.877647

4.5 4.5 120 232.122353 -307.8776475 5 120 232.122353 -367.877647

B-C

0 5 120 366.014623 366.0146230.5 5.5 120 366.014623 306.0146231 6 120 366.014623 246.014623

1.5 6.5 120 366.014623 186.0146232 7 120 366.014623 126.014623

2.5 7.5 120 366.014623 66.01462283 8 120 366.014623 6.0146228

3.5 8.5 120 366.014623 -53.98537724 9 120 366.014623 -113.985377

4.5 9.5 120 366.014623 -173.9853775 10 120 366.014623 -233.985377

5.5 10.5 120 366.014623 -293.9853776 11 120 366.014623 -353.985377

C-D

0 11 50 218.328643 218.3286430.5 11.5 50 218.328643 193.3286431 12 50 218.328643 168.328643

1.5 12.5 50 218.328643 143.3286432 13 50 218.328643 118.328643

2.5 13.5 50 218.328643 93.32864263 14 50 218.328643 68.3286426

3.5 14.5 50 218.328643 43.32864264 15 50 218.328643 18.3286426

4.5 15.5 50 218.328643 -6.671357365 16 50 218.328643 -31.6713574

5.5 16.5 50 218.328643 -56.67135746 17 50 218.328643 -81.6713574

6.5 17.5 50 218.328643 -106.6713577 18 50 218.328643 -131.671357

XGRAFICO




367.877647353.985377131.671357

VERTICAL" DERECHA




M(X)

0101.061176172.122353213.183529224.244706205.305882156.36705977.4282353-31.5105882-170.449412-339.388235-339.388235-171.380924-33.373612574.6336989152.64101

200.648322218.655633206.662944164.67025692.6775673-9.3151213-141.30781

-303.300499-303.300499-200.386177-109.971856-32.057534533.356786886.2711081126.685429154.599751170.014072172.928393163.342715141.257036106.67135759.5856787

0




JUEGO DE CARGA 4


50 120120


54.8

7

Wi Wd Mb260.416667 -552.96 234.346218

Wi Wd Mc552.96 -1715 542.682353



A-B 0 234.346218 50 5 78.1307563B-C 234.346218 542.682353 120 6 308.610644C-D 542.682353 0 120 7 497.52605

L1L2L3

VERTICAL IZQUIERDA





A-B

0 0 50 78.1307563 78.13075630.5 0.5 50 78.1307563 53.13075631 1 50 78.1307563 28.1307563

1.5 1.5 50 78.1307563 3.13075632 2 50 78.1307563 -21.8692437

2.5 2.5 50 78.1307563 -46.86924373 3 50 78.1307563 -71.8692437

3.5 3.5 50 78.1307563 -96.86924374 4 50 78.1307563 -121.869244

4.5 4.5 50 78.1307563 -146.8692445 5 50 78.1307563 -171.869244

B-C

0 5 120 308.610644 308.6106440.5 5.5 120 308.610644 248.6106441 6 120 308.610644 188.610644

1.5 6.5 120 308.610644 128.6106442 7 120 308.610644 68.6106443

2.5 7.5 120 308.610644 8.610644263 8 120 308.610644 -51.3893557

3.5 8.5 120 308.610644 -111.3893564 9 120 308.610644 -171.389356

4.5 9.5 120 308.610644 -231.3893565 10 120 308.610644 -291.389356

5.5 10.5 120 308.610644 -351.3893566 11 120 308.610644 -411.389356

C-D

0 11 120 497.52605 497.526050.5 11.5 120 497.52605 437.526051 12 120 497.52605 377.52605

1.5 12.5 120 497.52605 317.526052 13 120 497.52605 257.52605

2.5 13.5 120 497.52605 197.526053 14 120 497.52605 137.52605

3.5 14.5 120 497.52605 77.52605044 15 120 497.52605 17.5260504

4.5 15.5 120 497.52605 -42.47394965 16 120 497.52605 -102.47395

5.5 16.5 120 497.52605 -162.473956 17 120 497.52605 -222.47395

6.5 17.5 120 497.52605 -282.473957 18 120 497.52605 -342.47395

XGRAFICO




171.869244411.389356

342.47395

VERTICAL" DERECHA




M(X)

032.815378253.130756360.946134556.261512639.07689089.39226891-32.7923529-87.4769748-154.661597-234.346218-234.346218-95.040896414.264425893.5697479142.87507

162.180392151.485714110.79103640.0963585-60.5983193-191.292997-351.987675-542.682353-542.682353-308.919328-105.15630368.6067227212.369748326.132773409.895798463.658824487.421849481.184874444.947899378.710924282.47395

156.2369750




JUEGO DE CARGA 5


50 5050


54.8

7

Wi Wd Mb260.416667 -230.4 141.411765

Wi Wd Mc230.4 -714.583333 226.117647



A-B 0 141.411765 50 5 96.7176471B-C 141.411765 226.117647 50 6 135.882353C-D 226.117647 0 50 7 207.302521

L1L2L3

VERTICAL IZQUIERDA





A-B

0 0 50 96.7176471 96.71764710.5 0.5 50 96.7176471 71.71764711 1 50 96.7176471 46.7176471

1.5 1.5 50 96.7176471 21.71764712 2 50 96.7176471 -3.28235294

2.5 2.5 50 96.7176471 -28.28235293 3 50 96.7176471 -53.2823529

3.5 3.5 50 96.7176471 -78.28235294 4 50 96.7176471 -103.282353

4.5 4.5 50 96.7176471 -128.2823535 5 50 96.7176471 -153.282353

B-C

0 5 50 135.882353 135.8823530.5 5.5 50 135.882353 110.8823531 6 50 135.882353 85.8823529

1.5 6.5 50 135.882353 60.88235292 7 50 135.882353 35.8823529

2.5 7.5 50 135.882353 10.88235293 8 50 135.882353 -14.1176471

3.5 8.5 50 135.882353 -39.11764714 9 50 135.882353 -64.1176471

4.5 9.5 50 135.882353 -89.11764715 10 50 135.882353 -114.117647

5.5 10.5 50 135.882353 -139.1176476 11 50 135.882353 -164.117647

C-D

0 11 50 207.302521 207.3025210.5 11.5 50 207.302521 182.3025211 12 50 207.302521 157.302521

1.5 12.5 50 207.302521 132.3025212 13 50 207.302521 107.302521

2.5 13.5 50 207.302521 82.3025213 14 50 207.302521 57.302521

3.5 14.5 50 207.302521 32.3025214 15 50 207.302521 7.30252101

4.5 15.5 50 207.302521 -17.6974795 16 50 207.302521 -42.697479

5.5 16.5 50 207.302521 -67.6974796 17 50 207.302521 -92.697479

6.5 17.5 50 207.302521 -117.6974797 18 50 207.302521 -142.697479

XGRAFICO




153.282353164.117647142.697479

VERTICAL" DERECHA




M(X)

042.108823571.717647188.826470693.435294185.544117665.152941232.2617647-13.1294118-71.0205882-141.411765-141.411765-79.7205882-30.52941186.1617647130.352941242.044117641.235294127.92647062.11764706-36.1911765

-87-150.308824-226.117647-226.117647-128.716387-43.815126128.586134588.487395

135.888655170.789916193.191176203.092437200.493697185.394958157.796218117.69747965.0987395

0


CLCULO DE LA SOLICITACIONES DE UNA VIGA DE HORMIGN ARMADO POR EL MTODO DE READAPTACIN PLSTICA


READAPTACIN PLSTICA

5 6 7

q 70g 50

120 0.583k 1.175

HACEMOS PREVALECER LOS MOMENTOS DE LOS APOYOS

MoMin

k*MoMt Me MwTRAMO 1 375.000 295.313 440.625 305.625APOYO 1 187.500 270.000TRAMO 2 540.000 317.250 634.500 364.500APOYO 2 270.000 367.500TRAMO 3 735.000 578.813 863.625 728.625

HACEMOS PREVALECER LOS MOMENTOS DE LOS TRAMOS

Mo Mt k*MoTRAMO 1 375.000 295.313 440.625 295.313APOYO 1 290.625 634.500 634.500TRAMO 2 540.000 317.250 634.500 317.250APOYO 2 142.406 634.500 634.500TRAMO 3 735.000 578.813 863.625 578.813

VALORES DE DISEO

)/2(++Mt

)/(+2+Mt


CLCULO DE LA SOLICITACIONES DE UNA VIGA DE HORMIGN ARMADO POR EL MTODO DE READAPTACIN PLSTICA


HACEMOS PREVALECER LOS MOMENTOS DE LOS APOYOS

305.625270.000364.500367.500728.625

VALORES DE DISEO


CLCULO DE LA SOLICITACIONES DE UNA VIGA DE HORMIGN ARMADO POR EL MTODO TRES MOMENTOS


TRES MOMENTOS 1


120 120120

5 6 7



A-B 0 308.51 120 5 238.298B-C 308.51 573.81 120 6 315.783333C-D 573.81 0 120 7 501.972857

VERTICAL IZQUIERDA





A-B

0 0 120 238.298 238.2980.5 0.5 120 238.298 178.2981 1 120 238.298 118.298

1.5 1.5 120 238.298 58.2982 2 120 238.298 -1.702

2.5 2.5 120 238.298 -61.7023 3 120 238.298 -121.702

3.5 3.5 120 238.298 -181.7024 4 120 238.298 -241.702

4.5 4.5 120 238.298 -301.7025 5 120 238.298 -361.702

B-C

0 5 120 315.783333 315.7833330.5 5.5 120 315.783333 255.7833331 6 120 315.783333 195.783333

1.5 6.5 120 315.783333 135.7833332 7 120 315.783333 75.7833333

2.5 7.5 120 315.783333 15.78333333 8 120 315.783333 -44.2166667

3.5 8.5 120 315.783333 -104.2166674 9 120 315.783333 -164.216667

4.5 9.5 120 315.783333 -224.2166675 10 120 315.783333 -284.216667

5.5 10.5 120 315.783333 -344.2166676 11 120 315.783333 -404.216667

C-D

0 11 120 501.972857 501.9728570.5 11.5 120 501.972857 441.9728571 12 120 501.972857 381.972857

1.5 12.5 120 501.972857 321.9728572 13 120 501.972857 261.972857

2.5 13.5 120 501.972857 201.9728573 14 120 501.972857 141.972857

3.5 14.5 120 501.972857 81.97285714 15 120 501.972857 21.9728571

4.5 15.5 120 501.972857 -38.02714295 16 120 501.972857 -98.0271429

5.5 16.5 120 501.972857 -158.0271436 17 120 501.972857 -218.027143

6.5 17.5 120 501.972857 -278.0271437 18 120 501.972857 -338.027143

XGRAFICO




361.702404.216667338.027143

VERTICAL" DERECHA




M(X)

0104.149178.298222.447236.596220.745174.89499.043-6.808

-142.659-308.51-308.51

-165.618333-52.7266667

30.16583.0566667105.948333

98.8461.7316667-5.37666667

-102.485-229.593333-386.701667

-573.81-573.81

-337.823571-131.83714344.1492857190.135714306.122143392.108571

448.095474.081429470.067857436.054286372.040714278.027143154.013571

0

JUEGO DE CARGA1JUEGO DE CARGA2JUEGO DE CARGA3JUEGO DE CARGA4JUEGO DE CARGA5READAPTACION3MOMENTOS

hormigón armado

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