Analisis de porticos
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analisis de un portico
Transcript of Analisis de porticos
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PROBLEMA: En la estructura cargada como se muestra por el mtodo de distribuciones con
desplazamientos horizontales determinar:
a) Los momentos en los extremos de las barras.
b) Las reacciones en los apoyos.
c) Los diagramas N, V y M.
d) Las deflexiones en el centro de las vigas.
SOLUCIN:
a) Calculo de Momentos
1. Prtico sin desplazamiento
1.4 1.4 1.4 1.42.82.8
3.78
3.15
4.08 T/m
3.4 T 3.4 T
5.1 T5.1 T 4.08 T4.08 T
5.1 T/m
3.4 T/m
14 T
21 T
4.08 T/m
3.4 T 3.4 T
5.1 T5.1 T 4.08 T4.08 T
5.1 T/m
3.4 T/m
14 T
21 T
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1.1. Momentos de Empotramiento:
12 = 12.455 . 21 = +12.455 . 34 = 18.683 . 43 = +18.683 . 45 = 14.946 . 54 = +14.946 .
1.2. Factores de Distribucin:
Nudo1:
12 = 742.746 12 = 0.776 13 = 214.286 13 = 0.224 = 957.032
Nudo2:
21 = 742.746 21 = 0.776 24 = 214.286 34 = 0.224 = 2494.048
Nudo3:
31 = 214.286 31 = 0.086 34 = 2041.667 34 = 0.819 36 = 238.095 36 = 0.095 = 2494.048
Nudo4:
42 = 214.286 42 = 0.045 43 = 2041.667 43 = 0.426 47 = 1102.293 47 = 0.230 45 = 1430.339 45 = 0.299 = 4783.585
Nudo5:
54 = 1430.339 54 = 0.908 58 = 145.185 58 = 0.092 = 957.032
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1.3. Proceso Iterativo
1 3 2 4
0.224 0.776 0.776 0.224
-12.455 12.455
0.803
2.610 9.042 4.521
-6.587
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13.173 -3.803
-0.031 -0.062
1.482 5.136 2.568
-0.972 -1.944 -0.561
-0.036 0.009
0.226 0.782 0.391
-0.155 -0.310 -0.090
-0.009 0.009
0.037 0.127 0.064
-0.028 -0.057 -0.016
-0.002 0.003
0.007 0.023 0.012
-0.006 -0.011 -0.003
0.000 0.001
0.001 0.005 0.002
-0.001 -0.002 -0.001
0.000 0.000
0.000 0.001 0.000
0.000 0.000 0.000
0.000
5.089 -5.089 4.514 -4.514
3 1 4 5 5 2
0.086 0.095 0.819 0.426 0.230 0.046 0.299 0.908 0.092
-18.683 18.683 -14.946 14.946
1.607 1.775 15.301 7.651 -1.901 -6.785 -13.571 -1.375
1.305 -0.575 -1.151 -0.621 -0.124 -0.808 -0.404
-0.063 -0.069 -0.598 -0.299 -0.281 0.183 0.367 0.037
0.741 0.084 0.169 0.091 0.018 0.118 0.059
-0.071 -0.078 -0.676 -0.338 -0.045 -0.027 -0.054 -0.005
0.113 0.087 0.175 0.094 0.019 0.123 0.061
-0.017 -0.019 -0.164 -0.082 -0.008 -0.028 -0.056 -0.006
0.018 0.025 0.050 0.027 0.005 0.035 0.018
-0.004 -0.004 -0.036 -0.018 -0.002 -0.008 -0.016 -0.002
0.003 0.006 0.012 0.006 0.001 0.008 0.004
-0.001 -0.001 -0.008 -0.004 0.000 -0.002 -0.004 0.000
0.001 0.001 0.003 0.001 0.000 0.002 0.001
0.000 0.000 -0.002 -0.001 0.000 0.000 -0.001 0.000
0.000 0.000 0.001 0.000 0.000 0.000 0.000
3.633 1.603 -5.235 24.850 -0.401 -2.317 -22.134 1.351 -1.351
0.801 -0.200 0.000
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1.4. Cortante en las Columnas
14 T
2.769 T 2.169 T
5.089 2.769 T 4.514 2.169 T
3.633 2.769 T 2.317 2.169 T
2.769 T 2.169 T
21 T
0.636 T 0.159 T 0.357 T
1.603 0.636 T 0.401 0.159 T 1.351 0.357 T
0.801 0.636 T 0.200 0.159 T 0.357 T
0.636 T 0.159 T 0.357 T
0.801 0.200
V12 = 14 + 2.769 - 2.169 = 14.600 T
21 - 2.769 + 2.169
0.636 - 0.159 - 0.357=V345 = 20.520 T
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2 prtico con desplazamiento en el nivel 3-4-5
2.1. Momentos de empotramiento.
36 =30403
12= 90 000
47 =40503
12= 416 666.667
58 =40283
12= 73 173.333
36 = 63 = 3 779.29
47 = 74 = 17 496.7
58 = 85 = 3 072.7
1 2
3 4 5
= 6(
)( /L)
Si: = 10
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2.2. Proceso Iterativo
1 4 2 5
0.224 0.776 0.776 0.224
2.257
-0.506 -1.751 -0.876 402.424
-9.385 -155.801 -311.602 -89.947
37.002 128.184 64.092 11.811
-3.204 -29.450 -58.901 -17.002
7.315 25.340 12.670 2.025
-0.734 -5.702 -11.403 -3.292
1.441 4.994 2.497 0.526
-0.161 -1.173 -2.346 -0.677
0.299 1.035 0.517 0.124
-0.035 -0.249 -0.498 -0.144
0.064 0.220 0.110 0.028
-0.008 -0.053 -0.107 -0.031
0.014 0.047 0.024 0.006
-0.002 -0.012 -0.023 -0.007
0.003 0.010 0.005 0.001
-0.0004 -0.002 -0.005 -0.001
0.001 0.002 0.001 0.0003
-0.0001 -0.001 -0.001 -0.0003
0.0001 0.0005 0.0002 0.0001
34.361 -34.361 -0.0002 -0.0001
-305.845 305.845
2 1 4 1 5 3
0.086 0.095 0.819 0.426 0.230 0.046 0.299 0.908 0.092
-3779.289 -17496.711 -3072.702
3726.799 7453.599 4024.243 804.849 5231.516 2615.758 1536.351
4.514 4.987 42.989 21.495 -44.973 -490.051 -980.102 -99.305
-0.253 109.382 218.764 118.112 23.622 153.545 76.773
-9.385 -10.367 -89.377 -44.688 -8.501 -34.855 -69.710 -7.063
18.501 18.753 37.507 20.250 4.050 26.325 13.163
-3.204 -3.539 -30.511 -15.256 -1.646 -5.976 -11.952 -1.211
3.657 4.873 9.746 5.262 1.052 6.840 3.420
-0.734 -0.810 -6.986 -3.493 -0.339 -1.553 -3.105 -0.315
0.721 1.147 2.294 1.238 0.248 1.610 0.805
-0.161 -0.177 -1.530 -0.765 -0.072 -0.365 -0.731 -0.074
0.149 0.256 0.512 0.276 0.055 0.359 0.180
-0.035 -0.039 -0.332 -0.166 -0.015 -0.082 -0.163 -0.017
0.032 0.056 0.112 0.060 0.012 0.079 0.039
-0.008 -0.008 -0.072 -0.036 -0.003 -0.018 -0.036 -0.004
0.007 0.012 0.024 0.013 0.003 0.017 0.009
-0.002 -0.002 -0.016 -0.008 -0.001 -0.004 -0.008 -0.001
0.001 0.003 0.005 0.003 0.001 0.004 0.002
0.000 0.000 -0.003 -0.002 -0.0002 -0.001 -0.002 0.000
0.0003 0.001 0.001 0.001 0.0001 0.001 0.000
-0.0001 -0.0001 -0.001 7679.645 -13327.251 778.341 4887.393 0.000 0.000
13.802 -3789.246 3775.444 1644.341 -1644.341 -3779.289 -17496.711
-3784.268 -15411.981 3072.702
-7563.557 -32908.692 1 -3072.702
0
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2.3. Cortantes en las columnas:
15.290 T 344.186 T
34.361 15.290 T 305.845 344.186 T
13.802 15.290 T 778.341 361.395 T
15.290 T 344.186 T
3003.387 T 12231.731 T 435.011 T
3789.246 13327.251 1644.3413003.387 T 12231.731 T 435.010719
7563.557 3003.387 T 32908.692 12231.731 T 435.011 T
3003.387 T 12231.731 T 435.011 T
7563.557 32908.692
V12 = 15.290 + 344.186 = 359.476 T
15.290 + 344.186 - 435.011
3003.387 + 12231.731V345 = = 16029.605 T
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3. Prtico con desplazamiento e el nivel 1-2
3.1 Momentos de empotramiento
13 =30303
12= 67 500
24 =30303
12= 67 500
13 = 31 = 4 081.633
24 = 42 = 4 081.633
12
3 4 5
6 7 8
= 6(
)( /L)
Si: = 10
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3.2. Proceso Iterativo:
1 3 2 4
0.224 0.776 0.776 0.224
-4081.633 -4081.633 138.127 883.345 3060.161 1530.080 93.878
-13.921 953.578 1907.156 550.519
-210.483 -729.174 -364.587 -30.214
10.280 153.183 306.365 88.435
-36.616 -126.847 -63.423 -1.543
2.688 25.207 50.414 14.553
-6.248 -21.646 -10.823 -1.398
0.604 4.742 9.484 2.738
-1.197 -4.148 -2.074 -0.421
0.132 0.968 1.936 0.559
-0.246 -0.854 -0.427 -0.101
0.029 0.205 0.410 0.118
-0.052 -0.181 -0.091 -0.023
0.006 0.044 0.088 0.025
-0.011 -0.039 -0.019 -0.005
0.001 0.009 0.019 0.005
-0.002 -0.008 -0.004 -0.001
0.000 0.002 0.004 0.001
-0.001 -0.002 -0.001 0.000
0.000 0.000 0.001 0.000
0.000 0.000 0.000 0.000
-3315.199 3315.199 0.000 0.000
3364.507 -3364.507
2 1 4 1 5 5
0.086 0.095 0.819 0.426 0.230 0.046 0.299 0.908 0.092
-4081.633 -4081.633
869.388 1738.776 938.776 187.755 1220.408 610.204
276.253 305.163 2630.829 1315.414 275.260 -277.033 -554.065 -56.139
441.673 -279.806 -559.611 -302.137 -60.427 -392.779 -196.389
-13.921 -15.377 -132.569 -66.285 44.218 89.161 178.322 18.068
-105.242 -14.291 -28.582 -15.432 -3.086 -20.061 -10.031
10.280 11.356 97.897 48.949 7.276 4.554 9.108 0.923
-18.308 -12.946 -25.892 -13.979 -2.796 -18.173 -9.086
2.688 2.969 25.597 12.798 1.369 4.125 8.250 0.836
-3.124 -3.896 -7.793 -4.207 -0.841 -5.469 -2.735
0.604 0.667 5.750 2.875 0.279 1.242 2.483 0.252
-0.599 -0.936 -1.873 -1.011 -0.202 -1.314 -0.657
0.132 0.146 1.257 0.629 0.059 0.298 0.597 0.060
-0.123 -0.210 -0.420 -0.227 -0.045 -0.295 -0.147
0.029 0.032 0.273 0.136 0.013 0.067 0.134 0.014
-0.026 -0.046 -0.092 -0.050 -0.010 -0.065 -0.032
0.006 0.007 0.059 0.030 0.003 0.015 0.029 0.003
-0.006 -0.010 -0.020 -0.011 -0.002 -0.014 -0.007
0.001 0.001 0.013 0.006 0.001 0.003 0.006 0.001
-0.001 -0.002 -0.004 -0.002 0.000 -0.003 -0.002
0.000 0.000 0.003 0.001 0.000 0.001 0.001 0.000
0.000 0.000 -0.001 -0.001 0.000 -0.001 0.000
0.000 0.000 0.001 2429.042 601.719 -3632.812 604.667 0.000 0.000
-3491.316 304.964 3186.353 35.983 -35.983
152.4818742 300.859449 0
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3.3 Cortante en las columnas.
2160.799 T 2221.371 T
3315.199 2160.799 T 3364.507 2221.371 T
3491.316 2160.799 T 3632.812 2221.371 T
2160.799 T 2221.371 T
121.017 T 238.777 T 9.519 T
304.964 601.719 35.983
121.017 T 238.777 T 9.5192566
152.482 121.017 T 300.859 238.777 T 9.519 T
121.017 T 238.777 T 9.519 T
152.482
V12 = - 2160.799 - 2221.371 = -4382.170 T2160.799 + 2221.371 + 121.017
238.777 + 9.519TV345 = = 4732.445
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4. Calculo de las Constantes.
16.600 + 359.476 4382.170 = 0 = 0.00231993 20.520 16 029.605 4732.445 = 0 = 0.00231993
5. Calculo de los momentos Finales.
M12= -5.089 + -34.361(0.00231993) + 3315.199(0.00231993) = 6.507 T.m M13= 5.089 + 34.361(0.00231993) + -3315.199(0.00231993) = -6.507 T.m M21= 4.514 + -305.845(0.00231993) + 3364.507(0.00231993) = 15.654 T.m M24= -4.514 + 305.845(0.00231993) + -3364.507(0.00231993) = -15.654 T.m M31= 3.633 + 13.802(0.00231993) + -3491.316(0.00231993) = -8.631 T.m M34= -5.235 + 3775.444(0.00231993) + 3186.353(0.00231993) = 14.746 T.m M36= 1.603 + -3789.246(0.00231993) + 304.964(0.00231993) = -6.114 T.m M42= -2.317 + 778.341(0.00231993) + -3632.812(0.00231993) = -13.306 T.m M43= 24.85 + 7679.645(0.00231993) + 2429.042(0.00231993) = 51.221 T.m M45= -22.134 + 4887.393(0.00231993) + 604.667(0.00231993) = -8.666 T.m M47= -0.401 + -13327.251(0.00231993) + 601.719(0.00231993) = -29.2 T.m M54= 1.351 + 1644.341(0.00231993) + 35.989(0.00231993) = 5.293 T.m M58= -1.351 + -1644.341(0.00231993) + -35.989(0.00231993) = -5.293 T.m M63= 0.801 + -7563.557(0.00231993) + 152.482(0.00231993) = -16.209 T.m M74= -0.2 + -32908.692(0.00231993) + 300.859(0.00231993) = -75.486 T.m M85= = 0 T.m
14.600
20.520
359.476 4 382.17
16 029.605 4 732.445
C.C.D . del1 nivel
C.C.D . del2 nivel
14.600
20.520
359.476 4 382.17
16 029.605 4 732.445
C.C.D . del1 nivel
C.C.D . del2 nivel
= + 1 + 2
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b) Calculo de las Reacciones
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c) Diagramas N, V y M
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d) Calculo de las deflexiones en el Centro de las Vigas.
2. Calculo de las Deflexiones en el centro de las Vigas:
Viga 1-2:
