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

40

60

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

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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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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

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6

respuestaU(t)en

(cm)

tiempo(t)

Respuesta a cargas sismicas por laintegral de Duhamel