Muros de Corte

altura edificio 31.5 h1 4.5N° pisos 10 h2 3

H nivel s(ton) s(KN) 1.6*s (KN)31.5 10 99.33 993.3 1589.2828.5 9 89.87 898.7 1437.9225.5 8 80.41 804.1 1286.5622.5 7 70.95 709.5 1135.219.5 6 61.49 614.9 983.8416.5 5 52.03 520.3 832.4813.5 4 42.57 425.7 681.1210.5 3 33.11 331.1 529.767.5 2 23.65 236.5 378.44.5 1 14.19 141.9 227.04

EJE X Dimension x Dimension ymuro de 0.6 12viga 0.25 0.4columna 0.4 0.4

Iv= 0.0013333333Ic= 0.0021333333Im= 86.4

RIGIDEZ RELATIVAlongitud 5 6Kv=Iv/L 0.0002666667 0.0002222222longitud 4.5 3Kc=Ic/L 0.0004740741 0.0007111111

5785.7142857

nivel Iv Ic Im Total suma KV suma Kc suma KC/Kv1 0.0013333333 0.0021333333 172.8 0.0030222222 0.006637037 2.19607843137

2-10 0.0013333333 0.0021333333 172.8 0.0030222222 0.009955556 3.29411764706

Cálculo de rigideces por las ecuaciones de Wilbur:

Piso 1

0.4553571429

piso 2-10

0.3035714286

47765.19028

65163.66084

66579.083

66579.083

· Primer piso:

· Segundo piso:

· Tercer a noveno piso

· Decimo piso

-Aplicación del método:

NIVEL Fi (KN) Vi (KN) δi(m) Ki (KN/m)(m)

10 1589.28 1589.28 0.030282 66579.083 0.825 0.02498259 1437.92 3027.2 0.026288 66579.083 0.725 0.01905878 1286.56 4313.76 0.022320 66579.083 0.625 0.01395037 1135.2 5448.96 0.018423 66579.083 0.613 0.01129336 983.84 6432.8 0.014658 66579.083 0.42 0.00615635 832.48 7265.28 0.011103 66579.083 0.32 0.00355304 681.12 7946.4 0.007852 66579.083 0.24 0.00188463 529.76 8476.16 0.005010 66579.083 0.16 0.00080162 378.4 8854.56 0.002691 65163.661 0.08 0.00021531 227.04 9081.6 0.001018 47765.190 0.03 0.0000305

CICLO 1

NIVEL(m) (KN) (KN) (KN) (m)

10 0.0059237875 394.40034018 1194.87966 1194.8797 0.0229099 0.0051084334 340.11481075 2687.085189 1492.2055 0.0252868 0.0026569658 176.89834303 4136.861657 1449.7765 0.0214987 0.0051370501 342.02008654 5106.939913 970.0783 0.0177706 0.0026032132 173.31954993 6259.48045 1152.5405 0.0141605 0.0016684687 111.08511469 7154.194885 894.7144 0.0107434 0.0010829613 72.102569124 7874.297431 720.1025 0.0076103 0.0005863227 39.036825818 8437.123174 562.8257 0.0048632 0.0001847493 12.038941689 8842.521058 405.3979 0.0026161 0.0000305385 1.4586772633 9080.141323 237.6203 0.000991

Aplicando el criterio de convergencia

NIVEL

10 1.29510175 -0.0020731 0.023381797

9 1.05259362 0.0062268 0.024974373

8 1.05898319 0.0075473 0.021077229

7 1.05786685 0.0064762 0.017415243

6 1.08086848 0.0080036 0.013561083

5 1.10127986 0.0071904 0.010082134

· Valores iniciales:

4 1.12866710 0.0057253 0.006957217

3 1.18371210 0.0040612 0.004232503

2 1.34975358 0.0024005 0.00199377

1 1.88904170 0.0009603 0.000538871

CICLO 2


10 -0.001592576 -106.032257 1695.312257 1695.3123 0.0293499 0.0038971443 259.46829004 2767.73171 1072.4195 0.0254838 0.0036619865 243.81170359 4069.948296 1302.2166 0.0216457 0.00385416 256.60643723 5192.353563 1122.4053 0.0178746 0.0034789484 231.62519368 6201.174806 1008.8212 0.0142305 0.0031249169 208.05410253 7057.225897 856.0511 0.0107874 0.002724714 181.40895578 7764.991044 707.7651 0.0076353 0.0022387338 149.05284444 8327.107156 562.1161 0.0048762 0.0014548985 94.80651267 8759.753487 432.6463 0.0026221 0.0005388711 25.739281142 9055.860719 296.1072 0.000993


NIVEL

10 1.03991402 0.0059667 0.02912

9 1.03222700 0.0005086 0.02547

8 1.03206222 0.0005674 0.02163

7 1.03151849 0.0004589 0.01786

6 1.03154686 0.0006689 0.01421

5 1.03135572 0.0007050 0.01077

4 1.03122389 0.0006779 0.00761

3 1.03168662 0.0006434 0.00486

2 1.03480587 0.0006279 0.00260

1 1.04672557 0.0004539 0.00097

CICLO 3


10 0.0036523923 243.17292861 1346.107071 1346.1071 0.029079 0.0038401158 255.67138537 2771.528615 1425.4215 0.025258 0.0037669361 250.79915313 4062.960847 1291.4322 0.021467 0.0036506026 243.05377241 5205.906228 1142.9454 0.017736 0.0034437968 229.2848331 6203.515167 997.6089 0.014125 0.0031510614 209.79477665 7055.485223 851.9701 0.01071

4 0.0027584349 183.65406433 7762.745936 707.2607 0.007583 0.0022556072 150.17625585 8325.983744 563.2378 0.004842 0.0016280732 106.09120959 8748.46879 422.4850 0.002611 0.000972509 46.452075711 9035.147924 286.6791 0.00099


NIVEL

10 1.04160704 -0.0000493 0.02907

9 1.04058931 -0.0002130 0.02526

8 1.03973567 -0.0001660 0.02147

7 1.03875975 -0.0001293 0.01774

6 1.03772031 -0.0000877 0.01412

5 1.03660456 -0.0000565 0.01071

4 1.03543478 -0.0000321 0.00758

3 1.03423643 -0.0000124 0.00484

2 1.03307925 0.0000045 0.00260

1 1.03215436 0.0000142 0.00099

CICLO 4


10 0.0038097191 253.64760439 1335.6324 1335.6324 0.029079 0.0037950701 252.67228512 2774.5277 1438.8953 0.025268 0.0037318283 248.46170342 4065.2983 1290.7706 0.021467 0.0036106318 240.3925521 5208.5674 1143.2692 0.017736 0.0034137757 227.28605683 6205.5139 996.9465 0.014125 0.0031275165 208.22717888 7057.0528 851.5389 0.010714 0.0027394404 182.38942659 7764.0106 706.9578 0.007583 0.0022392883 149.08975796 8327.0702 563.0597 0.004842 0.0016186904 105.47979505 8749.0802 422.0100 0.002611 0.0009862381 47.107852748 9034.4921 285.4119 0.00099

NIVEL Fi (KN) Mu (KN-m)

10 1335.632 09 1438.895 4006.8971878 1290.771 6475.028937

7 1143.269 16600.182516 996.946 29933.89145 851.539 68076.890314 706.958 90525.357093 563.060 114877.82542 422.010 140703.62571 285.412 167583.8812

base 0.000 195115.4756

NIVEL Vu (KN) Mu (KN-m)

10 667.8161978 09 1387.2638574 2003.4485938 2032.6491483 3237.5144687 2604.283724 8300.0912566 3102.7569716 14966.94575 3528.5264106 34038.445154 3882.0052867 45262.678543 4163.535121 57438.912722 4374.5401025 70351.812831 4517.2460736 83791.94061

base 0 97557.73779

Calculo de los esfuerzos normales en el muro

U=1.2*D+1.6*L (Norma ACI)

D= 4.6 KN/m^2L= 3 KN/m^2U= 10.32 KN/m^2A= 59.025 m^2

N10 609.14

N9 1866.28N8 3123.41N7 4380.55N6 5637.69N5 6894.83N4 8151.97N3 9409.10N2 10666.24N1 11923.38

Base 13504.52

NIVEL Vu (KN) Mu (KN-m) Nu(KN)10 667.8161978 0 609.149 1387.2638574 2003.4485934 1866.288 2032.6491483 3237.5144684 3123.417 2604.283724 8300.0912561 4380.556 3102.7569716 14966.945698 5637.695 3528.5264106 34038.445155 6894.834 3882.0052867 45262.678545 8151.973 4163.535121 57438.912719 9409.102 4374.5401025 70351.812834 10666.241 4517.2460736 83791.940613 11923.38

base 0 97557.737791 13504.52

t= 0.6 mLw= 12 mhw= 31.5 m

Comprobacion a la esbeltez:

2.625

Se diseña como muro esbelto

Verificacion de la necesidad de elementos de borde

276865 es mayor que 4200

Es necesario utilizar elementos de borde

Pre dimensionando el elemento de borde:

Donde

3.132381E-05

= 3.132381E-05 Entonces usar 0.007

C= 2.8571428571

Luego la longitud del elemento de borde deberá estar entre los siguientes valores:

= 1.6571428571

= 1.4285714286

Determinando así las dimensiones de los elementos de borde:

t= 60 cmb= 170 cm

Aplicando el procedimiento de diseño se tiene:

d=0.8*Lw= 960 cm d=0.8*Lw=

0.9

= 0.196031334

= 0.004163398

= 239.8117345 cm^2 usar 50 25mmusar 76 20mm

EJE X Dimension x Dimension ymuro de 0.35 6.25viga 0.25 0.4columna 0.4 0.4

Iv= 0.0013333333Ic= 0.0021333333Im= 7.1207682292

RIGIDEZ RELATIVAlongitud 4.5 6Kv=Iv/L 0.0002962963 0.000222222222longitud 4.5 3Kc=Ic/L 0.0004740741 0.000711111111

476.8371582031

nivel Iv Ic Im Total suma KV suma Kc suma KC/Kv Km/Kc1 0.0013333333 0.002133333333 14.24153645833 0.0036296296 0.006637 1.82857143 476.837158

2-10 0.0013333333 0.002133333333 14.24153645833 0.0036296296 0.0099556 2.74285714 476.837158

Cálculo de rigideces por las ecuaciones de Wilbur:

Piso 1

0.546875

piso 2-10

0.3645833333

50994.96318345

74085.5280692

76385.073

76385.073

· Primer piso:

· Segundo piso:

· Tercer a noveno piso

· Decimo piso:

-Aplicación del método:

NIVEL Fi (KN) Vi (KN) δi(m) Ki (KN/m)(m)

10 1589.28 1589.28 0.3678502 76385.073 0.825 0.303476469 1437.92 3027.2 0.3193336 76385.073 0.725 0.231516858 1286.56 4313.76 0.2711389 76385.073 0.625 0.169461827 1135.2 5448.96 0.2237947 76385.073 0.613 0.137186156 983.84 6432.8 0.1780560 76385.073 0.42 0.07478355 832.48 7265.28 0.1348775 76385.073 0.32 0.043160794 681.12 7946.4 0.0953873 76385.073 0.24 0.022892963 529.76 8476.16 0.0608601 76385.073 0.16 0.009737622 378.4 8854.56 0.0326903 74085.528069 0.08 0.002615221 227.04 9081.6 0.0123657 50994.963183 0.03 0.00037097

CICLO 1


10 0.0719596005 5496.639307318 -3907.35930732 -3907.3593 0.1668169 0.0620550325 4740.07816415 -1712.87816415 2194.4811 0.1496438 0.0322756671 2465.379177201 1848.380822799 3561.2590 0.1318467 0.0624026559 4766.631396445 682.3286035546 -1166.0522 0.1131656 0.0316227055 2415.502651507 4017.297348493 3334.9687 0.0937855 0.0202678334 1548.159928059 5717.120071941 1699.8227 0.0739594 0.0131553438 1004.871887731 6941.528112269 1224.4080 0.0543463 0.0071223934 544.0445397541 7932.115460246 990.5873 0.0359392 0.0022442535 166.2667027052 8688.293297295 756.1778 0.0199531 0.0003709695 18.91757599468 9062.682424005 374.3891 0.007777


NIVEL

10 1.6624362 -0.1366600 0.2212718

9 1.7329504 -0.0818736 0.1842716

8 1.8219694 -0.0376153 0.1488164

7 1.8064217 -0.0240213 0.1238884

6 2.1268668 0.0190014 0.0837175

5 2.4114321 0.0307982 0.0559325

· Valores iniciales:

4 2.7927408 0.0314532 0.0341555

3 3.5592426 0.0262016 0.0170992

2 5.8704096 0.0173379 0.0055687

1 13.3681243 0.0074065 0.0009250

CICLO 2


10 0.0370002 2826.2609 -1236.9809 -1236.9809 0.22929 0.0354552 2708.2507 318.9493 1555.9302 0.20168 0.0249280 1904.1261 2409.6339 2090.6846 0.17377 0.0401709 3068.4585 2380.5015 -29.1324 0.14586 0.0277850 2122.3569 4310.4431 1929.9416 0.11815 0.0217771 1663.4428 5601.8372 1291.3941 0.09124 0.0170563 1302.8454 6643.5546 1041.7174 0.06583 0.0115305 880.7594 7595.4006 951.8460 0.04282 0.0046436 344.0269 8510.5331 915.1325 0.02341 0.0009250 47.1709 9034.4291 523.8960 0.0090


NIVEL

10 1.62658410 0.0079330 0.22615

9 1.63916259 0.0172824 0.19482

8 1.65454994 0.0249148 0.16387

7 1.62949180 0.0219196 0.13734

6 1.71561420 0.0344290 0.10379

5 1.78047794 0.0352909 0.07575

4 1.86688028 0.0316232 0.05109

3 2.05671354 0.0256920 0.02959

2 2.66330409 0.0178593 0.01227

1 4.61152804 0.0080999 0.00268

CICLO 3


10 0.0313338 2393.4381 -804.1581 -804.1581 0.232679 0.0309404 2363.3814 663.8186 1467.9766 0.204118 0.0265345 2026.8426 2286.9174 1623.0988 0.175457 0.0335546 2563.0739 2885.8861 598.9687 0.146816 0.0280320 2141.2277 4291.5723 1405.6862 0.118575 0.0246590 1883.5806 5381.6994 1090.1271 0.09125

4 0.0215036 1642.5512 6303.8488 922.1494 0.065613 0.0173166 1322.7307 7153.4293 849.5805 0.042582 0.0095929 710.6929 8143.8671 990.4378 0.023281 0.0026815 136.7412 8944.8588 800.9917 0.00896


NIVEL

10 1.59772946 0.0065254 0.23023

9 1.59144541 0.0092960 0.20066

8 1.58391905 0.0115746 0.17118

7 1.56053667 0.0094703 0.14341

6 1.57318993 0.0147816 0.11318

5 1.57590106 0.0154974 0.08559

4 1.58282404 0.0145137 0.06026

3 1.61771036 0.0129905 0.03762

2 1.76680067 0.0110040 0.01850

1 2.26923042 0.0062808 0.00545

CICLO 4


10 0.0295767988 2259.225926359 -669.945926359 -669.9459 0.233969 0.029474022 2251.375306851 775.8246931486 1445.7706 0.205078 0.0277734967 2121.480560073 2192.279439927 1416.4547 0.176107 0.030227339 2308.917480323 3140.042519677 947.7631 0.114726 0.0275939398 2107.765096437 4325.034903563 1184.9924 0.118725 0.0253235142 1934.338467497 5330.941532503 1005.9066 0.091244 0.02264288 1729.578032536 6216.821967464 885.8804 0.065513 0.0191186039 1460.375949576 7015.784050424 798.9621 0.042452 0.0130532623 967.05782704 7887.50217296 871.7181 0.023181 0.0054492703 277.8853404324 8803.714659568 916.2125 0.00892


10 -669.946 09 1445.771 -2009.837779088 1416.455 6505.967787783

7 947.763 17217.326006816 1184.992 30068.935964545 1005.907 35777.259245214 885.880 53278.943786133 798.962 73258.230340972 871.718 95504.025616681 916.212 120474.1093194

base 0.000 148259.572028


10 -334.9729631794 09 722.8853097537 -1004.918889548 708.2273733893 3252.9838938917 473.881539875 8608.6630034046 592.4961919427 15034.467982275 502.95331447 17888.629622614 442.9402174808 26639.471893073 399.48104148 36629.115170482 435.8590612678 47752.012808341 458.1062433038 60237.05465968

base 0 74129.78601399

Calculo de los esfuerzos normales en el muro

U=1.2*D+1.6*L (Norma ACI)

D= 4.6 KN/m^2L= 3 KN/m^2U= 10.32 KN/m^2A= 27.5625 m^2

N10 284.45

N9 893.58N8 1502.72N7 2111.86N6 2721.00N5 3330.13N4 3939.27N3 4548.41N2 5157.55N1 5766.69

Base 6375.83

NIVEL Vu (KN) Mu (KN-m) Nu(KN)10 -334.9729632 0 284.459 722.88530975 -1004.918889538 893.588 708.22737339 3252.983893891 1502.727 473.88153987 8608.663003404 2111.866 592.49619194 15034.46798227 2721.005 502.95331447 17888.62962261 3330.134 442.94021748 26639.47189307 3939.273 399.48104148 36629.11517048 4548.412 435.85906127 47752.01280834 5157.551 458.1062433 60237.05465968 5766.69

base 0 74129.78601399 6375.83

t= 0.35 mLw= 6.25 mhw= 31.5 m

Comprobacion a la esbeltez:

5.04

Se diseña como muro esbelto

Verificacion de la necesidad de elementos de borde

146386 es mayor que 4200

Es necesario utilizar elementos de borde

Pre dimensionando el elemento de borde:

Donde

0.0002830464

= 0.0002830464 Entonces usar 0.007

C= 1.4880952381

Luego la longitud del elemento de borde deberá estar entre los siguientes valores:

= 0.8630952381

= 0.744047619

Determinando así las dimensiones de los elementos de borde:

t= 0.6 mb= 0.9 m

Aplicando el procedimiento de diseño se tiene:

d=0.8*Lw= 5 m

0.9

= 5491.095260296

= 0.013555890245

= 406.6767073579 cm^2 usar 50 25mmusar 76 20mm

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Muros de Corte