Analisis Sismico Modal Espectral

(1)

gravedad =

DIRECCION X - X

[K] =

0.000 0.000 -2548.752 0.000 0.000 0.000 -2548.752 5097.503 0.000 -2548.752 2548.752 -2548.752 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -2548.752 5097.503 0.000 -2548.752 0.000 0.000 0.000 0.000 2396.770 KN/cm 5059.393 -2662.622 0.000 -2548.752 5211.374 -2662.622 0.000 F1 5097.503 -2548.752 1471.180 KN 2153.086 KN 2153.086 KN 2153.086 KN 2144.627 KN 2203.073 KN 9.81 m/s^2 1.500 KN*s^2/cm 2.195 KN*s^2/cm 2.195 KN*s^2/cm 2.195 KN*s^2/cm 2.186 KN*s^2/cm 2.246 KN*s^2/cm

DETERMINACION DE LAS FORMAS MODALES

F6 F5 F4 F3 F2 2548.752 KN/cm 2548.752 KN/cm 2548.752 KN/cm 2548.752 KN/cm 2662.622 KN/cm

(2)

[m] =

|[K] - W²[m]| =

=

MODIFICAR VALORES

valores característicos

w1 =

w1² =

w2 =

w2² =

w3 =

w3² =

w4 =

w4² =

w5 =

w5² =

w6 =

w6² =

2757.443 rad/s

3800.831 rad/s

4445.984 rad/s

52.511 rad/s

61.651 rad/s

66.678 rad/s

73.888 rad/s

+ 2.6930E+20

8.596 rad/s

25.091 rad/s

39.951 rad/s

629.539 rad/s

1596.116 rad/s

7.7845E+01 * w^12 -1.0356E+06 * w^10 + 5.1465E+09 * w^8 -1.1730E+13 * w^6 + 1.2013E+16 * w^4 -4.4704E+18 * w^2 -2.186w² -2548.75 0.00 0.00 -2548.75 -2548.75 0.00 0.00 0.00 -2548.75 -2548.75 0.00 0.00 0.00 0.00 -2548.75 -2.195w² 5097.50 0 2548.75 -1.500w² 1.4997 5059.39 -2.246w² 0 0 0 0 2.1948 0 0.00 -2662.62 0.00 0.00 0.00 0.00 0 0 0 0 -2662.62 -2548.75 0.00 0.00 0.00 0.00 -2548.75 0.00 5097.50 -2.195w² 5097.50 -2.195w² 5211.37 0 0 0 2.1948 0 0 0 0 2.1948 0 0 0 0 0 2.1862 0 0 0 0

(3)

ɸ11 ɸ12 ɸ13 ɸ14 ɸ15 ɸ16 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 *ɸ11 + *ɸ12 + *ɸ13 + *ɸ14 + *ɸ15 + *ɸ16 = 0 asumiendo: ɸ11 = ɸ12 = ɸ13 = ɸ14 = ɸ15 = ɸ16 = 0 0.000 0.000 0.000 0.000 -2548.752 4935.335 3.744 3.581 3.190 2.597 1.838 1.000 ɸ 16.625 13.875 11.125 8.375 5.625 2.875 1.000 1.838 2.597 3.190 3.581 3.744 h 0.000 0.000 0.000 -2548.752 4935.335 4893.459 -2662.622 0.000 0.000 0.000 -2662.622 5049.843 -2548.752 0.000 0.000 0.000 0.000 -2548.752 4935.335 -2548.752 0.000 -2548.752 0.000 0.000 0.000 0.000 -2548.752 2437.944 0.000 -2548.752 4935.335 -2548.752 0.000 0.000 0.000 0.000 -2548.752 4935.335 -2548.752 0.000 = 0 0.000 0.000 0.000 -2548.752 4935.335 -2548.752 0.000 0.000 0.000 0.000 -2548.752 2437.944 0.000 -2662.622 5049.843 -2548.752 0.000 0.000 0.000

FORMAS MODALES

PARA: W1^2 =

73.888 rad/s

x = -2548.752 0.000 4893.459 -2662.622 0.000 0.000 0.000 0.000 0 2 4 6 8 10 12 14 16 18 0.0000 2.0000 4.0000

(4)

ɸ21 ɸ22 ɸ23 ɸ24 ɸ25 ɸ26 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 *ɸ21 + *ɸ22 + *ɸ23 + *ɸ24 + *ɸ25 + *ɸ26 = 0 asumiendo: ɸ21 = ɸ22 = ɸ23 = ɸ24 = ɸ25 = ɸ26 = 11.125 0.111 8.375 1.016 5.625 1.369 2.875 1.000 0.000 0.000 0.000 0.000 0.000 0.000 -2548.752 1604.648 1.000 1.369 1.016 0.111 -0.853 -1.355 h ɸ 16.625 -1.355 13.875 -0.853 0.000 -2548.752 3715.799 -2548.752 0.000 0.000 0.000 0.000 -2548.752 3715.799 -2548.752 0.000 0.000 0.000 0.000 -2548.752 3715.799 -2548.752 0.000 0.000 0.000 0.000 -2548.752 1604.648 3645.609 -2662.622 0.000 0.000 0.000 0.000 -2662.622 3835.098 -2548.752 0.000 0.000 0.000 = x 0.000 -2548.752 3715.799 -2548.752 0.000 0.000 = 0 0.000 0.000 -2548.752 3715.799 -2548.752 0.000 0.000 0.000 0.000 -2548.752 3715.799 -2548.752 3645.609 -2662.622 0.000 0.000 0.000 0.000 -2662.622 3835.098 -2548.752 0.000 0.000 0.000 0 2 4 6 8 10 12 14 16 18 -2.0000 0.0000 2.0000

(5)

ɸ31 ɸ32 ɸ33 ɸ34 ɸ35 ɸ36 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 *ɸ31 + *ɸ32 + *ɸ33 + *ɸ34 + *ɸ35 + *ɸ36 = 0 asumiendo: ɸ31 = ɸ32 = ɸ33 = ɸ34 = ɸ35 = ɸ36 = 1.012 h ɸ 16.625 1.012 13.875 0.062 11.125 -0.973 8.375 -0.670 5.625 0.554 2.875 1.000 0.000 0.000 0.000 0.000 0.000 -2548.752 1594.368 -2548.752 0.000 0.000 0.000 0.000 -2548.752 155.098 1.000 0.554 -0.670 -0.973 0.062 0.000 -2662.622 1722.002 -2548.752 0.000 0.000 0.000 0.000 -2548.752 1594.368 -2548.752 0.000 0.000 0.000 0.000 -2548.752 1594.368 -2548.752 0.000 0.000 0.000 0.000 -2548.752 1594.368 -2548.752 0.000 0.000 0.000 0.000 -2548.752 155.098 1474.926 -2662.622 0.000 0.000 0.000 0.000 -2662.622 1722.002 -2548.752 0.000 0.000 0.000 = x 0.000 -2548.752 1594.368 -2548.752 0.000 0.000 = 0 0.000 0.000 -2548.752 1594.368 -2548.752 0.000

FORMAS MODALES

PARA: W3^2 = 1596.116 rad/s

1474.926 -2662.622 0.000 0.000 0.000 0 2 4 6 8 10 12 14 16 18 -2.0000 0.0000 2.0000

(6)

ɸ41 ɸ42 ɸ43 ɸ44 ɸ45 ɸ46 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 *ɸ41 + *ɸ42 + *ɸ43 + *ɸ44 + *ɸ45 + *ɸ46 = 0 asumiendo: ɸ41 = ɸ42 = ɸ43 = ɸ44 = ɸ45 = ɸ46 = 2.875 1.000 0.000 0.000 1.000 -0.426 -0.908 0.766 0.622 -0.998 h ɸ 16.625 -0.998 13.875 0.622 11.125 0.766 8.375 -0.908 5.625 -0.426 0.000 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -1586.513 -1133.115 -2662.622 0.000 0.000 0.000 0.000 -2662.622 -816.848 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 = 0 0.000 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -1586.513 -1133.115 -2662.622 0.000 0.000 0.000 0.000 -2662.622 -816.848 -2548.752 0.000 0.000 0.000 = x 0.000 -2548.752 -954.496 -2548.752 0.000 0.000 0 2 4 6 8 10 12 14 16 18 -2.0000 0.0000 2.0000

(7)

ɸ51 ɸ52 ɸ53 ɸ54 ɸ55 ɸ56 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 *ɸ51 + *ɸ52 + *ɸ53 + *ɸ54 + *ɸ55 + *ɸ56 = 0 asumiendo: ɸ51 = ɸ52 = ɸ53 = ɸ54 = ɸ55 = ɸ56 = 11.125 0.615 8.375 0.542 5.625 -1.306 2.875 1.000 0.000 0.000 0.000 0.000 0.000 0.000 -2548.752 -3151.253 1.000 -1.306 0.542 0.615 -1.326 1.072 h ɸ 16.625 1.072 13.875 -1.326 0.000 -2548.752 -3244.510 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -3244.510 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -3244.510 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -3151.253 -3476.295 -2662.622 0.000 0.000 0.000 0.000 -2662.622 -3097.864 -2548.752 0.000 0.000 0.000 = x 0.000 -2548.752 -3244.510 -2548.752 0.000 0.000 = 0 0.000 0.000 -2548.752 -3244.510 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -3244.510 -2548.752

FORMAS MODALES

PARA: W5^2 = 3800.831 rad/s

-3476.295 -2662.622 0.000 0.000 0.000 0.000 -2662.622 -3097.864 -2548.752 0.000 0.000 0.000 0 2 4 6 8 10 12 14 16 18 -2.0000 0.0000 2.0000

(8)

ɸ61 ɸ62 ɸ63 ɸ64 ɸ65 ɸ66 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 *ɸ61 + *ɸ62 + *ɸ63 + *ɸ64 + *ɸ65 + *ɸ66 = 0 asumiendo: ɸ61 = ɸ62 = ɸ63 = ɸ64 = ɸ65 = ɸ66 = -1.137 h ɸ 16.625 -1.137 13.875 1.837 11.125 -2.223 8.375 2.227 5.625 -1.850 2.875 1.000 0.000 0.000 0.000 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -4118.772 1.000 -1.850 2.227 -2.223 1.837 0.000 -2662.622 -4508.274 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000 0.000 0.000 0.000 -2548.752 -4118.772 -4925.142 -2662.622 0.000 0.000 0.000 0.000 -2662.622 -4508.274 -2548.752 0.000 0.000 0.000 = x 0.000 -2548.752 -4660.484 -2548.752 0.000 0.000 = 0 0.000 0.000 -2548.752 -4660.484 -2548.752 0.000 -4925.142 -2662.622 0.000 0.000 0.000 0 2 4 6 8 10 12 14 16 18 -5.0000 0.0000 5.0000

(9)

NORMALIZACION DE LOS MODOS

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + = 9.79407 2.246* 1.000² 2.186* 1.369² 2.195* 1.016² 2.195* 0.111² 2.195* -0.853² 1.500* -1.355² = 3.60371

DETERMINACION DE LOS FACTORES DE PARTICIPACION MODAL

2.246* 1.000² 2.186* 1.838² 2.195* 2.597² 2.195* 3.190² 2.195* 3.581² 1.500* 3.744² 0.615² 2.195* 0.062² 1.500* 1.012² = 2.74335 2.246* 1.000² 2.186* -0.426² 2.195* -0.908² 2.195* 0.766² 2.195* 0.622² 1.500* -0.998² = 2.84291 2.246* 1.000² 2.186* 0.554² 2.195* -0.670² 2.195* -0.973² 2.195* 0.102 0.188 0.265 0.326 0.366 0.382 -1.326² 1.500* 1.072² = 3.60952 2.246* 1.000² 2.186* -1.850² 2.195* 2.227² 2.195* -2.223² 2.195* 1.837² 1.500* -1.137² = 6.38754 2.246* 1.000² 2.186* -1.306² 2.195* 0.542² 2.195* 0.219 -0.351 0.277 -0.362 0.150 0.170 -0.367 0.297 0.277 0.380 0.282 0.031 -0.237 -0.376 0.365 0.202 -0.244 -0.355 0.022 0.369 0.157 -0.290 0.349 -0.348 0.288 -0.178 0.352 -0.150 -0.319 0.269

ɸ𝑖

𝑛

₌

ɸ

𝑚𝑖 ∗ ɸ𝑖

2 𝑚𝑖 ∗ ɸ12₌ 𝑚𝑖 ∗ ɸ22₌ 𝑚𝑖 ∗ ɸ32₌ 𝑚𝑖 ∗ ɸ42₌ 𝑚𝑖 ∗ ɸ52₌ 𝑚𝑖 ∗ ɸ62₌

ɸ1

𝑛

₌

_ɸ2

𝑛

₌

_ɸ3

𝑛

₌

_ɸ4

𝑛

₌

_ɸ5

𝑛

₌

_ɸ6

𝑛

₌

(10)

FPM1 = + + + + + FPM2 = + + + + + FPM3 = + + + + + FPM4 = + + + + + FPM5 = + + + + + FPM6 = + + + + + 0.277 2.186* 0.380 2.195* 0.282 2.195* 0.031 2.195* 2.246* 0.102 2.186* 0.188 2.195* 0.265 2.195* 0.326 2.195* 0.366 1.500* 0.382 = 3.3120 0.297 = 0.1747 2.246* 0.352 2.186* -0.150 2.195* -0.319 2.195* 0.269 2.195* -0.237 1.500* -0.376 = 1.0565 2.246* 0.365 2.186* 0.202 2.195* -0.244 2.195* -0.355 2.195* 0.022 1.500* 0.369 = 0.5474 2.246* -0.178 = 0.0844

DETERMINACION DE LA ACELERACION ESPECTRAL

COEF.

SISMICO VALOR ESPECIFICACION

2.246* 0.157 2.186* -0.290 2.195* 0.349 2.195* -0.348 2.195*

0.219 1.500* -0.351 = 0.3057 2.246* 0.277 2.186* -0.362 2.195* 0.150 2.195* 0.170 2.195* -0.367 1.500*

R 7 CONCRETO ARMADO: DUAL Tp 0.4 SUELO MUY RIGIDO

Z 0.4 ZONA 3

U 1 EDIFICACION COMUN S2 1 SUELO MUY RIGIDO

0.288 1.500* 2.500 Sai 76.690 cm/s² 140.143 cm/s² 140.143 cm/s² 140.143 cm/s² 140.143 cm/s² 140.143 cm/s² 8.596 rad/s 25.091 rad/s 39.951 rad/s 52.511 rad/s 61.651 rad/s 66.678 rad/s w T 0.73096 0.25042 0.15727 0.11965 0.10192 0.09423 C 1.368 2.500 2.500 2.500 2.500

𝐹𝑃𝑀

𝑖

= 𝑚𝑖 ∗ ɸ𝑖

𝑆𝑎𝑖 =

𝑍𝑈𝑆𝐶

𝑅

∗ 𝑔

𝑇 =

2𝜋

𝑤

𝐶 ≤ 2.5 ∗

𝑇𝑝

𝑇

(11)

F1

_*

0.1021 0.1876 0.2651 0.3257 0.3656 0.3822

*

DETERMINACION DE LA FUERZA SISMICA

2.2457 2.1862 2.1948 2.1948 2.1948 1.4997

3.312 *

=

76.690 cm/s²

=

58.240 KN 104.195 KN 147.796 KN 181.581 KN 203.813 KN 145.593 KN 2.1948 -0.2368 -76.936 KN 1.4997 -0.3761 -83.500 KN 2.2457 0.3645 62.795 KN 2.2457 0.2775 92.266 KN 2.1862 0.3799 122.978 KN

F2

=

1.056 *

2.1948_2.1948

_*

0.2818_0.0309

*

140.143 cm/s²

=

91.573 KN_{10.040 KN} 2.1948 0.0224 3.778 KN 1.4997 0.3688 42.430 KN 2.2457 0.3518 33.848 KN 2.1862 0.2019 33.862 KN

F3

=

0.547 *

2.1948_2.1948

_*

-0.2444_-0.3548

*

140.143 cm/s²

=

-41.144 KN_{-59.733 KN} 2.1948 0.2186 20.560 KN 1.4997 -0.3512 -22.569 KN 2.1862 -0.1497 -14.022 KN

F4

=

0.306 *

2.1948_2.1948

_*

-0.3195_0.2693

*

140.143 cm/s²

=

-30.046 KN_{25.330 KN}

𝐹𝑖 = 𝐹𝑃𝑀𝑖 ∗ 𝑚𝑖 ∗ ɸ𝑖

𝑛

_{∗ 𝑆𝑎𝑖}

(12)

2.1948 -0.3672 -19.732 KN 1.4997 0.2970 10.904 KN 2.2457 0.1566 4.160 KN 2.1862 -0.3617 -19.358 KN

F5

=

0.175 *

2.1948_2.1948

_*

0.1502_0.1705

*

140.143 cm/s²

=

8.071 KN_{9.160 KN} 2.1948 0.2876 7.470 KN 1.4997 -0.1779 -3.158 KN

DETERMINACION DE LA FUERZA DE DISEÑO APLICANDO EL CRITERIO DE SUPERPOSICION

MODAL

1 2.1862 -0.2896 -7.491 KN

F6

=

0.084 *

2.1948_2.1948

_*

_-0.34800.3487

*

140.143 cm/s²

=

_{-9.037 KN}9.055 KN -83.500 KN -76.936 KN 10.040 KN 91.573 KN 122.978 KN 92.266 KN 62.795 KN 33.862 KN -41.144 KN -59.733 KN 3.778 KN 42.430 KN F2 F3 2 3 4 5 6 58.240 KN 104.195 KN 147.796 KN 181.581 KN 203.813 KN 145.593 KN NIVEL F1 67.011 KN 71.635 KN 58.787 KN 82.128 KN 66.431 KN F6 -22.569 KN 20.560 KN 25.330 KN -30.046 KN -14.022 KN 33.848 KN 15.231 KN -19.358 KN 8.071 KN 9.160 KN -19.732 KN 10.904 KN F4 F5 Fd 15.232 Tn 19.568 Tn 21.185 Tn 20.787 Tn 25.181 Tn 20.147 Tn 131.214 KN 164.899 KN 145.136 KN 136.186 KN 124.947 KN 98.485 KN 149.421 KN 191.958 KN 207.821 KN 203.923 KN 247.027 KN 197.645 KN Fd -3.158 KN 7.470 KN -9.037 KN 9.055 KN -7.491 KN 4.160 KN 50.936 KN

𝐹𝑑 = 0.25 ∗ |𝐹𝑖| + 0.75 𝐹𝑖

2 0.25



F_i

0.75 

F

_i2

(13)

DETERMINACION DEL CORTANTE

12.5159 0.1021 324.581 KN 3.6945 0.3656 343.076 KN 1.4997 0.3822 145.593 KN 12.5159 0.2775 514.218 KN 10.2702 0.1876 489.491 KN

Q1

=

3.312 *

8.0840

_*

0.2651

*

76.690 cm/s²

=

544.374 KN 5.8892 0.3257 487.234 KN 12.5159 0.3645 349.970 KN 10.2702 0.2019 159.077 KN 3.6945 -0.2368 -129.505 KN 1.4997 -0.3761 -83.500 KN 10.2702 0.3799 577.727 KN

Q2

=

1.056 *

8.0840_5.8892

_*

0.2818_0.0309

*

140.143 cm/s²

=

337.289 KN_{26.940 KN} -151.546 KN 5.8892 -0.3548 -160.281 KN 3.6945 0.0224 6.360 KN 1.4997 0.3688 42.430 KN

Q3

=

0.547 *

8.0840

_*

-0.2444

*

140.143 cm/s²

=

12.5159 0.3518 188.641 KN 10.2702 -0.1497 -65.874 KN

Q4

=

0.306 *

8.0840_5.8892

_*

-0.3195_0.2693

*

140.143 cm/s²

=

-110.668 KN_{67.967 KN} 3.6945 0.2186 34.609 KN 1.4997 -0.3512 -22.569 KN

𝑄𝑖 = 𝐹𝑃𝑀𝑖 ∗ ∅𝑖

𝑛

_{∗ 𝑚𝑖 ∗ 𝑆𝑎𝑖}

(14)

12.5159 0.2770 84.885 KN 10.2702 -0.3617 -90.940 KN 8.0840 0.1502 29.727 KN

Q5

=

0.175 *

1.4997 0.2970 10.904 KN 12.5159 0.1566 23.186 KN 10.2702 -0.2896 -35.193 KN 5.8892 0.1705 24.580 KN 3.6945 -0.3672 -33.214 KN

*

140.143 cm/s²

=

33.354 KN 5.8892 -0.3480 -24.250 KN 3.6945 0.2876 12.574 KN 1.4997 -0.1779 -3.158 KN

Q6

=

0.084 *

8.0840

_*

0.3487

*

140.143 cm/s²

=

Q Q 1 324.581 KN 514.218 KN 349.970 KN 188.641 KN 84.885 KN 23.186 KN 283.878 KN 548.875 KN 832.753 KN 84.888 Tn

DETERMINACION DEL CORTANTE APLICANDO EL CRITERIO DE SUPERPOSICION MODAL

NIVEL Q1 Q2 Q3 Q4 Q5 Q6 -160.281 KN 67.967 KN 24.580 KN -24.250 KN 157.743 KN 389.441 KN 901.786 KN 91.925 Tn 3 544.374 KN 337.289 KN -151.546 KN -110.668 KN 29.727 KN 33.354 KN 263.853 KN 501.613 KN 765.466 KN 78.029 Tn 2 489.491 KN 577.727 KN 159.077 KN -65.874 KN -90.940 KN -35.193 KN 314.806 KN 586.979 KN 197.645 KN 20.147 Tn 6 145.593 KN -83.500 KN 42.430 KN -22.569 KN 10.904 KN -3.158 KN 66.431 KN 131.214 KN 547.183 KN 55.778 Tn 5 343.076 KN -129.505 KN 6.360 KN 34.609 KN -33.214 KN 12.574 KN 138.244 KN 277.573 KN 415.818 KN 42.387 Tn 4 487.234 KN 26.940 KN

Q= 0.25 ∗ 𝑄𝑖 + 0.75 𝑄𝑖

2 0.25



Q_i 2 0.75



Qi

(15)

DETERMINACION DE LOS DESPLAZAMIENTOS

0.1021 0.351 cm 0.1876 0.645 cm -0.2368 -0.3761 0.3645 0.2775 0.3799

X2

=

1.056 *

_*

0.2818_0.0309 0.911 cm 0.3257 1.120 cm 0.3656 1.257 cm 0.3822 1.314 cm

X1

=

3.312 *

_*

0.2651

=

0.004 cm

2757.4430

0.003 cm -0.3512 -0.005 cm 0.3518 -0.1497 -0.3195

X4

=

0.306 *

0.0224 0.3688 0.2019

X3

=

0.547 *

_*

-0.2444_-0.3548 0.00191 cm 76.6898

73.8879

0.065 cm 0.089 cm 140.1429

=

0.066 cm_{0.007 cm}

629.5392

-0.056 cm -0.088 cm 0.018 cm 0.010 cm 140.1429

=

-0.012 cm_{-0.017 cm}

1596.1164

0.001 cm 0.018 cm 0.005 cm -0.002 cm 0.2693 0.2186 140.1429 0.1566 0.00042 cm -0.2896 -0.00077 cm

X6

=

0.084 *

140.1429

*

0.3487

=

0.00093 cm -0.3480 -0.00093 cm 0.2770 0.00178 cm -0.3617 -0.00233 cm

X5

=

0.175 *

140.1429

*

0.1502

=

0.00097 cm 0.1705 0.00110 cm

3800.8307

-0.3672 -0.00237 cm 0.2970

4445.9838

0.2876 0.00077 cm -0.1779 -0.00047 cm

*

=

-0.005 cm

𝑄𝑖 =

𝐹𝑃𝑀𝑖 ∗ ∅𝑖

𝑛

∗ 𝑆𝑎𝑖

𝑤𝑖

2

(16)

1 0.3510 cm 0.0653 cm 0.0175 cm 0.0055 cm 0.0018 cm 0.0004 cm 0.1060 cm 0.2681 cm 0.3741 cm 1.9639 cm

MODAL

NIVEL Q1 Q2 Q3 Q4 Q5 Q6 3 0.9114 cm 0.0663 cm -0.0117 cm -0.0050 cm 0.0010 cm 0.0009 cm 0.2461 cm 0.6854 cm 0.9315 cm 4.8905 cm 2 0.6450 cm 0.0894 cm 0.0097 cm -0.0023 cm -0.0023 cm -0.0008 cm 0.1850 cm 0.4885 cm 6 1.3139 cm -0.0884 cm 0.0177 cm -0.0055 cm 0.0019 cm -0.0005 cm 0.3526 cm 0.9878 cm 1.1232 cm 5.8968 cm 5 1.2568 cm -0.0557 cm 0.0011 cm 0.0034 cm -0.0024 cm 0.0008 cm 0.3298 cm 0.9435 cm 1.2733 cm 6.6847 cm 4 1.1197 cm 0.0073 cm -0.0171 cm 0.0042 cm 0.0011 cm -0.0009 cm 0.2833 cm 0.8399 cm 1.3403 cm 7.0367 cm 0.6734 cm 3.5355 cm X 0.75*R*X 1 1.9639 cm Δr 0.3520 cm 0.7879 cm 1.0063 cm 1.3550 cm 1.5715 cm 1.9639 cm

DETERMINACION DE LAS DISTORCIONES

NIVEL 0.75*R*X 6 7.0367 cm H 275.0 cm 5 6.6847 cm 4 5.8968 cm 3 4.8905 cm 2 3.5355 cm 275.0 cm 275.0 cm 275.0 cm 275.0 cm 287.5 cm DISTORSION 0.0013 0.0029 0.0037 0.0049 0.0057 0.0068

VERIFICACION

CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007

Q= 0.25 ∗ |𝑋𝑖| + 0.75 𝑋𝑖

2 0.25



X_i 2 0.75



Xi