Post on 14-Apr-2018
7/27/2019 Duhamel grafica para la simulacion de una onda sismica
1/4
Evaluacion de la Integral de Duhamel para cargas sismicas (Acelerograma)
Amortigua-
miento b0.1 Periodo(T) 0.40
Umax 0.514172
frecuencia
cir.s/a(w)
15.71frecuencia
cir.c/a(wD)15.629
t
Carga
sismica(Ug)
tiempo de la
carga(t)
exp(bwt) Integral (1) Integral (2) Integral (3) Integral (4) A B U(t) cm.
0 0 1.000000 0.006366 -0.063343 0.000807 0.003972 0 0 0
6.54 0.01 1.015832 0.016404 -0.062555 0.000812 0.004022 0.002 0.000 0.000
13.08 0.02 1.031915 0.026352 -0.060177 0.000849 0.004171 0.008 0.002 0.001
19.62 0.03 1.048252 0.035958 -0.056218 0.000949 0.004411 0.018 0.006 0.003
26.16 0.04 1.064848 0.044971 -0.050726 0.001143 0.004726 0.032 0.014 0.007
32.7 0.05 1.081706 0.053147 -0.043790 0.001456 0.005093 0.047 0.027 0.013
39.24 0.06 1.098832 0.060255 -0.035537 0.001911 0.005483 0.063 0.046 0.022
45.78 0.07 1.116229 0.066082 -0.026132 0.002523 0.005860 0.079 0.072 0.033
52.32 0.08 1.133901 0.070442 -0.015774 0.003301 0.006186 0.093 0.104 0.049
58.86 0.09 1.151853 0.073179 -0.004690 0.004243 0.006417 0.102 0.144 0.067
65.4 0.1 1.170089 0.074173 0.006865 0.005341 0.006510 0.106 0.190 0.090
71.94 0.11 1.188614 0.073344 0.018617 0.006575 0.006422 0.103 0.241 0.115
78.48 0.12 1.207432 0.070653 0.030279 0.007916 0.006111 0.089 0.297 0.145
85.02 0.13 1.226548 0.066109 0.041555 0.009325 0.005541 0.066 0.356 0.177
91.56 0.14 1.245966 0.059766 0.052151 0.010755 0.004683 0.030 0.416 0.213
98.1 0.15 1.265693 0.051726 0.061782 0.012150 0.003516 -0.019 0.475 0.251
91.56 0.16 1.285731 0.042136 0.070174 0.013450 0.002028 -0.077 0.526 0.292
85.02 0.17 1.306087 0.031185 0.077078 0.014588 0.000221 -0.139 0.565 0.333
78.48 0.18 1.326765 0.019105 0.082275 0.015496 -0.001894 -0.202 0.592 0.373
71.94 0.19 1.347770 0.006161 0.085580 0.016106 -0.004289 -0.264 0.608 0.411
65.4 0.2 1.369108 -0.007349 0.086850 0.016352 -0.006924 -0.324 0.614 0.444
58.86 0.21 1.390783 -0.021107 0.085987 0.016173 -0.009745 - 0.378 0.610 0.473
52.32 0.22 1.412802 -0.034777 0.082946 0.015517 -0.012684 - 0.427 0.599 0.494
45.78 0.23 1.435170 -0.048012 0.077734 0.014343 -0.015661 - 0.469 0.583 0.508
39.24 0.24 1.457891 -0.060469 0.070410 0.012620 -0.018588 - 0.503 0.563 0.514
32.7 0.25 1.480973 -0.071811 0.061092 0.010335 -0.021365 -0.529 0.542 0.511
26.16 0.26 1.504419 -0.081719 0.049948 0.007492 -0.023890 - 0.547 0.521 0.499
19.62 0.27 1.528237 -0.089899 0.037198 0.004112 -0.026057 - 0.559 0.502 0.478
13.08 0.28 1.552432 -0.096091 0.023112 0.000238 -0.027758 - 0.566 0.488 0.448
6.54 0.29 1.577010 -0.100077 0.007998 -0.004071 -0.028892 - 0.569 0.478 0.409
0 0.3 1.601978 -0.101686 -0.007799 -0.008731 -0.029365 -0.569 0.475 0.362
0 0.31 1.627340 -0.100804 -0.023905 -0.013643 -0.029093 -0.296 0.362 0.307
0 0.32 1.653104 -0.097372 -0.039926 -0.018690 -0.028010 -0.296 0.362 0.246
0 0.33 1.679276 -0.091395 -0.055461 -0.023738 -0.026065 -0.296 0.362 0.180
0 0.34 1.705862 -0.082941 -0.070103 -0.028643 -0.023231 -0.296 0.362 0.113
0 0.35 1.732870 -0.072142 -0.083460 -0.033249 -0.019504 -0.296 0.362 0.045
0 0.36 1.760304 -0.059194 -0.095155 -0.037400 -0.014906 -0.296 0.362 -0.022
0 0.37 1.788173 -0.044352 -0.104843 -0.040934 -0.009487 -0.296 0.362 -0.087
0 0.38 1.816484 -0.027927 -0.112218 -0.043697 -0.003326 -0.296 0.362 -0.147
0 0.39 1.845242 -0.010280 -0.117021 -0.045544 0.003469 -0.296 0.362 -0.202
0 0.4 1.874456 0.008188 -0.119050 -0.046344 0.010764 -0.296 0.362 -0.251
0 0.41 1.904132 0.027041 -0.118166 -0.045983 0.018400 -0.296 0.362 -0.292
0 0.42 1.934279 0.045819 -0.114298 -0.044375 0.026192 -0.296 0.362 -0.324
0 0.43 1.964902 0.064050 -0.107448 -0.041461 0.033940 -0.296 0.362 -0.348
0 0.44 1.996010 0.081261 -0.097691 -0.037215 0.041425 -0.296 0.362 -0.362
0 0.45 2.027611 0.096988 -0.085179 -0.031645 0.048423 -0.296 0.362 -0.367
0 0.46 2.059712 0.110791 -0.070137 -0.024799 0.054701 -0.296 0.362 -0.364
0
20
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80
100
0 0.1 0.2 0.3
acel.en(cm/seg2)
carga sismica
7/27/2019 Duhamel grafica para la simulacion de una onda sismica
2/4
0 0.47 2.092322 0.122264 -0.052860 -0.016763 0.060034 -0.296 0.362 -0.351
0 0.48 2.125447 0.131044 -0.033710 -0.007666 0.064202 -0.296 0.362 -0.330
0 0.49 2.159097 0.136826 -0.013106 0.002329 0.067004 -0.296 0.362 -0.302
0 0.5 2.193280 0.139371 0.008484 0.013016 0.068261 -0.296 0.362 -0.268
0 0.51 2.228004 0.138510 0.030551 0.024160 0.067823 -0.296 0.362 -0.228
0 0.52 2.263278 0.134157 0.052557 0.035493 0.065578 -0.296 0.362 -0.184
0 0.53 2.299110 0.126310 0.073952 0.046725 0.061456 -0.296 0.362 -0.136
0 0.54 2.335509 0.115052 0.094179 0.057545 0.055430 -0.296 0.362 -0.087
0 0.55 2.372485 0.100557 0.112696 0.067635 0.047528 -0.296 0.362 -0.0380 0.56 2.410046 0.083084 0.128985 0.076673 0.037828 -0.296 0.362 0.011
0 0.57 2.448202 0.062976 0.142568 0.084345 0.026465 -0.296 0.362 0.059
0 0.58 2.486962 0.040650 0.153017 0.090351 0.013626 -0.296 0.362 0.103
0 0.59 2.526335 0.016595 0.159973 0.094417 -0.000448 -0.296 0.362 0.144
-0.5
-0.4-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.40.5
0.6
0 0.2 0.4 0.6
respuestaU(t)en
(cm)
tiempo(t)
Respuesta a cargas sismicas por laintegral de Duhamel
7/27/2019 Duhamel grafica para la simulacion de una onda sismica
3/4
Evaluacion de la Integral de Duhamel para cargas sismicas (Acelerograma)
Amortigua-
miento b0.1 Periodo(T) 0.60
Umax 14.722
frecuencia
cir.s/a(w)10.47 frecuenciacir.c/a(wD) 10.419 t
Carga
sismica(Ug)
tiempo de la
carga(t)
exp(bwt) Integral (1) Integral (2) Integral (3) Integral (4) A B U(t) cm.
0 0 1.000000 0.009549 -0.095014 0.001815 0.008937 0 0 0
6.54 0.01 1.010527 0.019584 -0.094490 0.001818 0.008987 0.358 0.640 -0.593
13.08 0.02 1.021165 0.029613 -0.092909 0.001843 0.009137 0.717 1.281 -1.082
19.62 0.03 1.031915 0.039528 -0.090265 0.001910 0.009385 1.075 1.921 -1.451
26.16 0.04 1.042778 0.049214 -0.086566 0.002040 0.009724 1.434 2.562 -1.690
32.7 0.05 1.053755 0.058561 -0.081831 0.002254 0.010144 1.792 3.202 -1.789
39.24 0.06 1.064848 0.067457 -0.076089 0.002571 0.010633 2.151 3.842 -1.744
45.78 0.07 1.076057 0.075794 -0.069383 0.003007 0.011174 2.509 4.483 -1.552
52.32 0.08 1.087385 0.083469 -0.061767 0.003579 0.011749 2.868 5.123 -1.215
58.86 0.09 1.098832 0.090382 -0.053306 0.004299 0.012336 3.226 5.764 -0.736
65.4 0.1 1.110399 0.096441 -0.044076 0.005177 0.012911 3.585 6.404 -0.122
71.94 0.11 1.122089 0.101560 -0.034162 0.006218 0.013448 3.943 7.045 0.616
78.48 0.12 1.133901 0.105663 -0.023661 0.007426 0.013919 4.302 7.685 1.466
85.02 0.13 1.145837 0.108683 -0.012675 0.008800 0.014295 4.660 8.325 2.413
91.56 0.14 1.157900 0.110563 -0.001316 0.010333 0.014548 5.019 8.966 3.441
98.1 0.15 1.170089 0.111260 0.010298 0.012018 0.014648 5.377 9.606 4.531
91.56 0.16 1.182406 0.110739 0.022043 0.013838 0.014566 4.972 10.310 5.024
85.02 0.17 1.194853 0.108981 0.033793 0.015777 0.014275 4.567 11.015 5.582
78.48 0.18 1.207432 0.105979 0.045418 0.017811 0.013749 4.162 11.719 6.200
71.94 0.19 1.220142 0.101741 0.056786 0.019914 0.012964 3.756 12.423 6.873
65.4 0.2 1.232987 0.096286 0.067765 0.022054 0.011899 3.351 13.127 7.594
58.86 0.21 1.245966 0.089649 0.078227 0.024199 0.010538 2.946 13.832 8.353
52.32 0.22 1.259083 0.081880 0.088044 0.026309 0.008866 2.540 14.536 9.140
45.78 0.23 1.272337 0.073040 0.097094 0.028344 0.006876 2.135 15.240 9.942
39.24 0.24 1.285731 0.063204 0.105261 0.030263 0.004564 1.730 15.944 10.744
32.7 0.25 1.299266 0.052460 0.112435 0.032019 0.001931 1.324 16.648 11.533
26.16 0.26 1.312943 0.040907 0.118516 0.033569 -0.001015 0.919 17.353 12.293
19.62 0.27 1.326765 0.028658 0.123413 0.034866 -0.004262 0.514 18.057 13.008
13.08 0.28 1.340731 0.015831 0.127048 0.035864 -0.007790 0.109 18.761 13.661
6.54 0.29 1.354845 0.002558 0.129353 0.036520 -0.011573 -0.297 19.465 14.238
0 0.3 1.369108 -0.011024 0.130275 0.036791 -0.015580 -0.702 20.170 14.722
0 0.31 1.383520 -0.024772 0.129773 0.036637 -0.019773 0.205 14.722 14.511
0 0.32 1.398085 -0.038536 0.127825 0.036022 -0.024109 0.205 14.722 14.147
0 0.33 1.412802 -0.052165 0.124420 0.034914 -0.028538 0.205 14.722 13.636
0 0.34 1.427675 -0.065505 0.119565 0.033286 -0.033007 0.205 14.722 12.989
0 0.35 1.442704 -0.078402 0.113284 0.031118 -0.037456 0.205 14.722 12.214
0 0.36 1.457891 -0.090704 0.105615 0.028395 -0.041822 0.205 14.722 11.323
0 0.37 1.473239 -0.102262 0.096615 0.025109 -0.046040 0.205 14.722 10.328
0 0.38 1.488747 -0.112932 0.086355 0.021260 -0.050041 0.205 14.722 9.241
0 0.39 1.504419 -0.122578 0.074921 0.016857 -0.053754 0.205 14.722 8.077
0 0.4 1.520256 -0.131071 0.062416 0.011917 -0.057107 0.205 14.722 6.849
0 0.41 1.536260 -0.138293 0.048955 0.006464 -0.060031 0.205 14.722 5.572
0 0.42 1.552432 -0.144136 0.034668 0.000534 -0.062455 0.205 14.722 4.262
0 0.43 1.568775 -0.148507 0.019694 -0.005830 -0.064311 0.205 14.722 2.932
0 0.44 1.585289 -0.151326 0.004185 -0.012577 -0.065536 0.205 14.722 1.598
0 0.45 1.601978 -0.152530 -0.011698 -0.019645 -0.066070 0.205 14.722 0.274
0
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100
0 0.1 0.2 0.3
acel.en(cm/seg2)
carga sismica
7/27/2019 Duhamel grafica para la simulacion de una onda sismica
4/4
0 0.46 1.618842 -0.152070 -0.027789 -0.026966 -0.065860 0.205 14.722 -1.025
0 0.47 1.635883 -0.149917 -0.043912 -0.034463 -0.064857 0.205 14.722 -2.286
0 0.48 1.653104 -0.146058 -0.059890 -0.042053 -0.063023 0.205 14.722 -3.496
0 0.49 1.670506 -0.140501 -0.075543 -0.049644 -0.060326 0.205 14.722 -4.643
0 0.5 1.688092 -0.133270 -0.090691 -0.057142 -0.056746 0.205 14.722 -5.716
0 0.51 1.705862 -0.124411 -0.105155 -0.064446 -0.052270 0.205 14.722 -6.705
0 0.52 1.723820 -0.113987 -0.118762 -0.071452 -0.046901 0.205 14.722 -7.601
0 0.53 1.741967 -0.102080 -0.131341 -0.078056 -0.040648 0.205 14.722 -8.3950 0.54 1.760304 -0.088791 -0.142733 -0.084149 -0.033538 0.205 14.722 -9.083
0 0.55 1.778835 -0.074238 -0.152785 -0.089626 -0.025605 0.205 14.722 -9.657
0 0.56 1.797561 -0.058555 -0.161359 -0.094383 -0.016900 0.205 14.722 -10.115
0 0.57 1.816484 -0.041891 -0.168327 -0.098319 -0.007484 0.205 14.722 -10.454
0 0.58 1.835606 -0.024411 -0.173579 -0.101338 0.002567 0.205 14.722 -10.672
0 0.59 1.854929 -0.006291 -0.177021 -0.103350 0.013168 0.205 14.722 -10.770
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
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0 0.2 0.4 0.6
respuestaU(t)en
(cm)
tiempo(t)
Respuesta a cargas sismicas por laintegral de Duhamel