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Analisis Sismico Modal Espectral
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Analisis Sismico Modal Espectral
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Author:
Juan Manuel Chero Damian
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INGENIERIA ANTISISMICA
UNPRG - ING CIVIL
DETERMINACION DE LAS FORMAS MODALES gravedad =
9.81 m/s^2
DIRECCION X - X 1471.180 KN
1.500 KN*s^2/cm
F6 2548.752 KN/cm 2153.086 KN
2.195 KN*s^2/cm
F5 2548.752 KN/cm 2153.086 KN
2.195 KN*s^2/cm
F4 2548.752 KN/cm 2153.086 KN
2.195 KN*s^2/cm
F3 2548.752 KN/cm 2144.627 KN
2.186 KN*s^2/cm
F2 2662.622 KN/cm 2203.073 KN
2.246 KN*s^2/cm
F1 2396.770 KN/cm
[K] =
5059.393
-2662.622
0.000
0.000
0.000
0.000
-2662.622
5211.374
-2548.752
0.000
0.000
0.000
0.000
-2548.752
5097.503
-2548.752
0.000
0.000
0.000
0.000
-2548.752
5097.503
-2548.752
0.000
0.000
0.000
0.000
-2548.752
5097.503
-2548.752
0.000
0.000
0.000
0.000
-2548.752
2548.752
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA
[m] =
2.2457 0 0 0 0 0
0 2.1862 0 0 0 0
0 0 2.1948 0 0 0
0 0 0 2.1948 0 0
0 0 0 0 2.1948 0
UNPRG - ING CIVIL
0 0 0 0 0 1.4997
|[K] - W²[m]| =
=
=
5059.39 -2.246w²
-2662.62
0.00
0.00
0.00
0.00
-2662.62
5211.37 -2.186w²
-2548.75
0.00
0.00
0.00
0.00
-2548.75
5097.50 -2.195w²
-2548.75
0.00
0.00
0.00
0.00
-2548.75
5097.50 -2.195w²
-2548.75
0.00
0.00
0.00
0.00
-2548.75
5097.50 -2.195w²
-2548.75
0.00
0.00
0.00
0
-2548.75
2548.75 -1.500w²
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 + 2.6930E+20
MODIFICAR VALORES valores característicos w1 w2 w3 w4 w5 w6
= = = = = =
8.596 rad/s 25.091 rad/s 39.951 rad/s 52.511 rad/s 61.651 rad/s 66.678 rad/s
w1² w2² w3² w4² w5² w6²
= = = = = =
Juan Manuel Chero Damian
73.888 rad/s 629.539 rad/s 1596.116 rad/s 2757.443 rad/s 3800.831 rad/s 4445.984 rad/s
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W1^2 =
ɸ11
4893.459
-2662.622
0.000
ɸ12 ɸ13
-2662.622
5049.843
0.000
-2548.752
0.000
ɸ15 ɸ16
x
ɸ14
UNPRG - ING CIVIL
73.888 rad/s 0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
4935.335
-2548.752
0.000
0.000
0.000
-2548.752
4935.335
-2548.752
0.000
0.000
0.000
0.000
-2548.752
4935.335
-2548.752
0.000
0.000
0.000
0.000
-2548.752
2437.944
=
0
4893.459
*ɸ11
+
-2662.622
*ɸ12
+
0.000
*ɸ13
+
0.000
*ɸ14
+
0.000
*ɸ15
+
0.000
*ɸ16
=
0
-2662.622
*ɸ11
+
5049.843
*ɸ12
+
-2548.752
*ɸ13
+
0.000
*ɸ14
+
0.000
*ɸ15
+
0.000
*ɸ16
=
0
0.000
*ɸ11
+
-2548.752
*ɸ12
+
4935.335
*ɸ13
+
-2548.752
*ɸ14
+
0.000
*ɸ15
+
0.000
*ɸ16
=
0
0.000
*ɸ11
+
0.000
*ɸ12
+
-2548.752
*ɸ13
+
4935.335
*ɸ14
+
-2548.752
*ɸ15
+
0.000
*ɸ16
=
0
0.000
*ɸ11
+
0.000
*ɸ12
+
0.000
*ɸ13
+
-2548.752
*ɸ14
+
4935.335
*ɸ15
+
-2548.752
*ɸ16
=
0
0.000
*ɸ11
+
0.000
*ɸ12
+
0.000
*ɸ13
+
0.000
*ɸ14
+
-2548.752
*ɸ15
+
2437.944
*ɸ16
=
0
asumiendo: ɸ11 = ɸ12 = ɸ13 = ɸ14 = ɸ15 = ɸ16 =
1.000
18
1.838 2.597
16
3.190 3.581 3.744
14 12
h 16.625 13.875 11.125 8.375 5.625 2.875 0
ɸ 3.744
10
3.581 3.190
8
2.597 1.838
6
1.000 0.000
4 2 0 0.0000 2.0000 4.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W2^2 =
ɸ21
3645.609
-2662.622
0.000
ɸ22 ɸ23
-2662.622
3835.098
0.000
-2548.752
0.000
ɸ25 ɸ26
ɸ24
x
UNPRG - ING CIVIL
629.539 rad/s 0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
3715.799
-2548.752
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
=
0
3645.609
*ɸ21
+
-2662.622
*ɸ22
+
0.000
*ɸ23
+
0.000
*ɸ24
+
0.000
*ɸ25
+
0.000
*ɸ26
=
0
-2662.622
*ɸ21
+
3835.098
*ɸ22
+
-2548.752
*ɸ23
+
0.000
*ɸ24
+
0.000
*ɸ25
+
0.000
*ɸ26
=
0
0.000
*ɸ21
+
-2548.752
*ɸ22
+
3715.799
*ɸ23
+
-2548.752
*ɸ24
+
0.000
*ɸ25
+
0.000
*ɸ26
=
0
0.000
*ɸ21
+
0.000
*ɸ22
+
-2548.752
*ɸ23
+
3715.799
*ɸ24
+
-2548.752
*ɸ25
+
0.000
*ɸ26
=
0
0.000
*ɸ21
+
0.000
*ɸ22
+
0.000
*ɸ23
+
-2548.752
*ɸ24
+
3715.799
*ɸ25
+
-2548.752
*ɸ26
=
0
0.000
*ɸ21
+
0.000
*ɸ22
+
0.000
*ɸ23
+
0.000
*ɸ24
+
-2548.752
*ɸ25
+
1604.648
*ɸ26
=
0
asumiendo: ɸ21 = ɸ22 = ɸ23 = ɸ24 = ɸ25 = ɸ26 =
1.000
18
1.369 1.016
16
0.111 -0.853 -1.355
14 12
h 16.625 13.875 11.125 8.375 5.625 2.875 0.000
ɸ -1.355
10
-0.853 0.111
8
1.016 1.369
6
1.000 0.000
4 2 0 -2.0000 0.0000 2.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W3^2 = 1596.116 rad/s
ɸ31
1474.926
-2662.622
0.000
ɸ32 ɸ33
-2662.622
1722.002
0.000
-2548.752
0.000
ɸ35 ɸ36
ɸ34
x
UNPRG - ING CIVIL
0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
1594.368
-2548.752
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
=
0
1474.926
*ɸ31
+
-2662.622
*ɸ32
+
0.000
*ɸ33
+
0.000
*ɸ34
+
0.000
*ɸ35
+
0.000
*ɸ36
=
0
-2662.622
*ɸ31
+
1722.002
*ɸ32
+
-2548.752
*ɸ33
+
0.000
*ɸ34
+
0.000
*ɸ35
+
0.000
*ɸ36
=
0
0.000
*ɸ31
+
-2548.752
*ɸ32
+
1594.368
*ɸ33
+
-2548.752
*ɸ34
+
0.000
*ɸ35
+
0.000
*ɸ36
=
0
0.000
*ɸ31
+
0.000
*ɸ32
+
-2548.752
*ɸ33
+
1594.368
*ɸ34
+
-2548.752
*ɸ35
+
0.000
*ɸ36
=
0
0.000
*ɸ31
+
0.000
*ɸ32
+
0.000
*ɸ33
+
-2548.752
*ɸ34
+
1594.368
*ɸ35
+
-2548.752
*ɸ36
=
0
0.000
*ɸ31
+
0.000
*ɸ32
+
0.000
*ɸ33
+
0.000
*ɸ34
+
-2548.752
*ɸ35
+
155.098
*ɸ36
=
0
asumiendo: ɸ31 = ɸ32 = ɸ33 = ɸ34 = ɸ35 = ɸ36 =
1.000
18
0.554 -0.670
16
-0.973 0.062 1.012
14 12
h 16.625 13.875 11.125 8.375 5.625 2.875 0.000
ɸ 1.012
10
0.062 -0.973
8
-0.670 0.554
6
1.000 0.000
4 2 0 -2.0000 0.0000 2.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W4^2 = 2757.443 rad/s
ɸ41
-1133.115
-2662.622
0.000
ɸ42 ɸ43
-2662.622
-816.848
0.000
-2548.752
0.000
ɸ45 ɸ46
ɸ44
x
UNPRG - ING CIVIL
0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
-954.496
-2548.752
0.000
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
=
0
-1133.115
*ɸ41
+
-2662.622
*ɸ42
+
0.000
*ɸ43
+
0.000
*ɸ44
+
0.000
*ɸ45
+
0.000
*ɸ46
=
0
-2662.622
*ɸ41
+
-816.848
*ɸ42
+
-2548.752
*ɸ43
+
0.000
*ɸ44
+
0.000
*ɸ45
+
0.000
*ɸ46
=
0
0.000
*ɸ41
+
-2548.752
*ɸ42
+
-954.496
*ɸ43
+
-2548.752
*ɸ44
+
0.000
*ɸ45
+
0.000
*ɸ46
=
0
0.000
*ɸ41
+
0.000
*ɸ42
+
-2548.752
*ɸ43
+
-954.496
*ɸ44
+
-2548.752
*ɸ45
+
0.000
*ɸ46
=
0
0.000
*ɸ41
+
0.000
*ɸ42
+
0.000
*ɸ43
+
-2548.752
*ɸ44
+
-954.496
*ɸ45
+
-2548.752
*ɸ46
=
0
0.000
*ɸ41
+
0.000
*ɸ42
+
0.000
*ɸ43
+
0.000
*ɸ44
+
-2548.752
*ɸ45
+
-1586.513
*ɸ46
=
0
asumiendo: ɸ41 = ɸ42 = ɸ43 = ɸ44 = ɸ45 = ɸ46 =
1.000
18
-0.426 -0.908
16
0.766 0.622
14
-0.998
12 h 16.625 13.875 11.125 8.375 5.625 2.875 0.000
ɸ -0.998
10
0.622 0.766
8
-0.908 -0.426
6
1.000 0.000
4 2 0 -2.0000 0.0000 2.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W5^2 = 3800.831 rad/s
ɸ51
-3476.295
-2662.622
0.000
ɸ52
-2662.622
-3097.864
ɸ53
0.000
-2548.752
0.000
ɸ55 ɸ56
ɸ54
x
UNPRG - ING CIVIL
0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
-3244.510
-2548.752
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
=
0
-3476.295
*ɸ51
+
-2662.622
*ɸ52
+
0.000
*ɸ53
+
0.000
*ɸ54
+
0.000
*ɸ55
+
0.000
*ɸ56
=
0
-2662.622
*ɸ51
+
-3097.864
*ɸ52
+
-2548.752
*ɸ53
+
0.000
*ɸ54
+
0.000
*ɸ55
+
0.000
*ɸ56
=
0
0.000
*ɸ51
+
-2548.752
*ɸ52
+
-3244.510
*ɸ53
+
-2548.752
*ɸ54
+
0.000
*ɸ55
+
0.000
*ɸ56
=
0
0.000
*ɸ51
+
0.000
*ɸ52
+
-2548.752
*ɸ53
+
-3244.510
*ɸ54
+
-2548.752
*ɸ55
+
0.000
*ɸ56
=
0
0.000
*ɸ51
+
0.000
*ɸ52
+
0.000
*ɸ53
+
-2548.752
*ɸ54
+
-3244.510
*ɸ55
+
-2548.752
*ɸ56
=
0
0.000
*ɸ51
+
0.000
*ɸ52
+
0.000
*ɸ53
+
0.000
*ɸ54
+
-2548.752
*ɸ55
+
-3151.253
*ɸ56
=
0
asumiendo: ɸ51 = ɸ52 = ɸ53 = ɸ54 = ɸ55 = ɸ56 =
1.000
18
-1.306 0.542 0.615 -1.326 1.072
16
14 12
h 16.625 13.875 11.125 8.375 5.625 2.875 0.000
ɸ 1.072
10
-1.326 0.615
8
0.542 -1.306 1.000 0.000
6 4 2 0 -2.0000 0.0000 2.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA FORMAS MODALES
=
PARA: W6^2 = 4445.984 rad/s
ɸ61
-4925.142
-2662.622
0.000
ɸ62
-2662.622
-4508.274
ɸ63
0.000
-2548.752
0.000
ɸ65 ɸ66
ɸ64
x
UNPRG - ING CIVIL
0.000
0.000
0.000
-2548.752
0.000
0.000
0.000
-4660.484
-2548.752
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
=
0
-4925.142
*ɸ61
+
-2662.622
*ɸ62
+
0.000
*ɸ63
+
0.000
*ɸ64
+
0.000
*ɸ65
+
0.000
*ɸ66
=
0
-2662.622
*ɸ61
+
-4508.274
*ɸ62
+
-2548.752
*ɸ63
+
0.000
*ɸ64
+
0.000
*ɸ65
+
0.000
*ɸ66
=
0
0.000
*ɸ61
+
-2548.752
*ɸ62
+
-4660.484
*ɸ63
+
-2548.752
*ɸ64
+
0.000
*ɸ65
+
0.000
*ɸ66
=
0
0.000
*ɸ61
+
0.000
*ɸ62
+
-2548.752
*ɸ63
+
-4660.484
*ɸ64
+
-2548.752
*ɸ65
+
0.000
*ɸ66
=
0
0.000
*ɸ61
+
0.000
*ɸ62
+
0.000
*ɸ63
+
-2548.752
*ɸ64
+
-4660.484
*ɸ65
+
-2548.752
*ɸ66
=
0
0.000
*ɸ61
+
0.000
*ɸ62
+
0.000
*ɸ63
+
0.000
*ɸ64
+
-2548.752
*ɸ65
+
-4118.772
*ɸ66
=
0
asumiendo: ɸ61 = ɸ62 = ɸ63 = ɸ64 = ɸ65 = ɸ66 =
1.000
18
-1.850 2.227
16
-2.223 1.837 -1.137
14 12
h 16.625 13.875 11.125 8.375 5.625 2.875 0.000
ɸ -1.137
10
1.837 -2.223
8
2.227 -1.850 1.000 0.000
6 4 2 0 -5.0000 0.0000 5.0000
Juan Manuel Chero Damian
INGENIERIA ANTISISMICA
UNPRG - ING CIVIL
DETERMINACION DE LOS FACTORES DE PARTICIPACION MODAL NORMALIZACION DE LOS MODOS
ɸ𝑖 𝑛 =
ɸ 𝑚𝑖 ∗ ɸ𝑖 2
𝑚𝑖 ∗ ɸ12 =
2.246*
1.000² +
2.186*
1.838² +
2.195*
2.597² +
2.195*
3.190² +
2.195*
3.581² +
1.500*
3.744²
𝑚𝑖 ∗ ɸ22 =
2.246*
1.000² +
2.186*
1.369² +
2.195*
1.016² +
2.195*
0.111² +
2.195*
-0.853² +
1.500*
-1.355²
𝑚𝑖 ∗ ɸ32 =
2.246*
1.000² +
2.186*
0.554² +
2.195*
-0.670² +
2.195*
-0.973² +
2.195*
0.062² +
1.500*
1.012²
𝑚𝑖 ∗ ɸ42 =
2.246*
1.000² +
2.186*
-0.426² +
2.195*
-0.908² +
2.195*
0.766² +
2.195*
0.622² +
1.500*
-0.998²
𝑚𝑖 ∗ ɸ52 =
2.246*
1.000² +
2.186*
-1.306² +
2.195*
0.542² +
2.195*
0.615² +
2.195*
-1.326² +
1.500*
1.072²
𝑚𝑖 ∗ ɸ62 =
2.246*
1.000² +
2.186*
-1.850² +
2.195*
2.227² +
2.195*
-2.223² +
2.195*
1.837² +
1.500*
-1.137²
ɸ3𝑛 =
0.365 0.202 -0.244 -0.355 0.022 0.369
ɸ1𝑛 =
0.102 0.188 0.265 0.326 0.366 0.382
ɸ2𝑛 =
0.277 0.380 0.282 0.031 -0.237 -0.376
ɸ4𝑛 =
0.352 -0.150 -0.319 0.269 0.219 -0.351
Juan Manuel Chero Damian
ɸ5𝑛 =
0.277 -0.362 0.150 0.170 -0.367 0.297
ɸ6𝑛 =
= 9.79407
= 3.60371
= 2.74335
= 2.84291
= 3.60952
= 6.38754 0.157 -0.290 0.349 -0.348 0.288 -0.178
INGENIERIA ANTISISMICA
UNPRG - ING CIVIL
FACTORES DE PARTICIPACION MODAL 𝐹𝑃𝑀𝑖 = FPM1 = FPM2 = FPM3 = FPM4 = FPM5 = FPM6 =
2.246* 2.246* 2.246* 2.246* 2.246* 2.246*
0.102 0.277 0.365 0.352 0.277 0.157
+ + + + + +
2.186* 2.186* 2.186* 2.186* 2.186* 2.186*
0.188 0.380 0.202 -0.150 -0.362 -0.290
+ + + + + +
𝑚𝑖 ∗ ɸ𝑖 𝑛
2.195* 2.195* 2.195* 2.195* 2.195* 2.195*
0.265 0.282 -0.244 -0.319 0.150 0.349
+ + + + + +
2.195* 2.195* 2.195* 2.195* 2.195* 2.195*
0.326 0.031 -0.355 0.269 0.170 -0.348
+ + + + + +
2.195* 2.195* 2.195* 2.195* 2.195* 2.195*
0.366 -0.237 0.022 0.219 -0.367 0.288
DETERMINACION DE LA ACELERACION ESPECTRAL
COEF. SISMICO Z U S2 Tp R
VALOR 0.4 1 1 0.4 7
w
T
8.596 rad/s
0.73096
25.091 rad/s
0.25042
39.951 rad/s
0.15727
52.511 rad/s
0.11965
61.651 rad/s
0.10192
66.678 rad/s
0.09423
ESPECIFICACION ZONA 3 EDIFICACION COMUN SUELO MUY RIGIDO SUELO MUY RIGIDO CONCRETO ARMADO: DUAL
C 1.368 2.500 2.500 2.500 2.500 2.500
𝑆𝑎𝑖 =
𝑇=
𝑍𝑈𝑆𝐶 ∗𝑔 𝑅
2𝜋 𝑤
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
Juan Manuel Chero Damian
𝐶 ≤ 2.5 ∗
𝑇𝑝 𝑇
+ + + + + +
1.500* 1.500* 1.500* 1.500* 1.500* 1.500*
0.382 -0.376 0.369 -0.351 0.297 -0.178
= = = = = =
3.3120 1.0565 0.5474 0.3057 0.1747 0.0844
INGENIERIA ANTISISMICA
DETERMINACION DE LA FUERZA SISMICA 𝐹𝑖 = 𝐹𝑃𝑀𝑖 ∗ 𝑚𝑖 ∗ ɸ𝑖 𝑛 ∗ 𝑆𝑎𝑖
F1
F2
F3
F4
=
=
=
=
3.312 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
1.056 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
0.547 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
0.306 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
*
*
*
*
0.1021 0.1876 0.2651 0.3257 0.3656 0.3822
0.2775 0.3799 0.2818 0.0309 -0.2368 -0.3761
0.3645 0.2019 -0.2444 -0.3548 0.0224 0.3688
0.3518 -0.1497 -0.3195 0.2693 0.2186 -0.3512
* 76.690 cm/s²
* 140.143 cm/s²
* 140.143 cm/s²
* 140.143 cm/s²
=
58.240 KN 104.195 KN 147.796 KN 181.581 KN 203.813 KN 145.593 KN
=
92.266 KN 122.978 KN 91.573 KN 10.040 KN -76.936 KN -83.500 KN
=
62.795 KN 33.862 KN -41.144 KN -59.733 KN 3.778 KN 42.430 KN
=
33.848 KN -14.022 KN -30.046 KN 25.330 KN 20.560 KN -22.569 KN
Juan Manuel Chero Damian
UNPRG - ING CIVIL
INGENIERIA ANTISISMICA
F5
=
F6
=
0.175 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
0.084 *
2.2457 2.1862 2.1948 2.1948 2.1948 1.4997
*
*
0.2770 -0.3617 0.1502 0.1705 -0.3672 0.2970
0.1566 -0.2896 0.3487 -0.3480 0.2876 -0.1779
* 140.143 cm/s²
* 140.143 cm/s²
=
15.231 KN -19.358 KN 8.071 KN 9.160 KN -19.732 KN 10.904 KN
=
4.160 KN -7.491 KN 9.055 KN -9.037 KN 7.470 KN -3.158 KN
UNPRG - ING CIVIL
DETERMINACION DE LA FUERZA DE DISEÑO APLICANDO EL CRITERIO DE SUPERPOSICION MODAL 𝐹𝑑 = 0.25 ∗
|𝐹𝑖| + 0.75
𝐹𝑖 2
NIVEL
F1
F2
F3
F4
F5
F6
1 2 3 4 5 6
58.240 KN 104.195 KN 147.796 KN 181.581 KN 203.813 KN 145.593 KN
92.266 KN 122.978 KN 91.573 KN 10.040 KN -76.936 KN -83.500 KN
62.795 KN 33.862 KN -41.144 KN -59.733 KN 3.778 KN 42.430 KN
33.848 KN -14.022 KN -30.046 KN 25.330 KN 20.560 KN -22.569 KN
15.231 KN -19.358 KN 8.071 KN 9.160 KN -19.732 KN 10.904 KN
4.160 KN -7.491 KN 9.055 KN -9.037 KN 7.470 KN -3.158 KN
Juan Manuel Chero Damian
0.25 Fi
50.936 KN 67.011 KN 71.635 KN 58.787 KN 82.128 KN 66.431 KN
0.75
F
i
98.485 KN 124.947 KN 136.186 KN 145.136 KN 164.899 KN 131.214 KN
2
Fd
Fd
149.421 KN 191.958 KN 207.821 KN 203.923 KN 247.027 KN 197.645 KN
15.232 Tn 19.568 Tn 21.185 Tn 20.787 Tn 25.181 Tn 20.147 Tn
INGENIERIA ANTISISMICA
DETERMINACION DEL CORTANTE 𝑄𝑖 = 𝐹𝑃𝑀𝑖 ∗ ∅𝑖 𝑛 ∗
Q1
Q2
Q3
Q4
=
=
=
=
3.312 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
1.056 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
0.547 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
0.306 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
*
*
*
*
0.1021 0.1876 0.2651 0.3257 0.3656 0.3822
0.2775 0.3799 0.2818 0.0309 -0.2368 -0.3761
0.3645 0.2019 -0.2444 -0.3548 0.0224 0.3688
0.3518 -0.1497 -0.3195 0.2693 0.2186 -0.3512
* 76.690 cm/s²
* 140.143 cm/s²
* 140.143 cm/s²
* 140.143 cm/s²
𝑚𝑖 ∗ 𝑆𝑎𝑖
=
324.581 KN 489.491 KN 544.374 KN 487.234 KN 343.076 KN 145.593 KN
=
514.218 KN 577.727 KN 337.289 KN 26.940 KN -129.505 KN -83.500 KN
=
349.970 KN 159.077 KN -151.546 KN -160.281 KN 6.360 KN 42.430 KN
=
188.641 KN -65.874 KN -110.668 KN 67.967 KN 34.609 KN -22.569 KN
Juan Manuel Chero Damian
UNPRG - ING CIVIL
INGENIERIA ANTISISMICA
Q5
=
Q6
=
0.175 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
0.084 *
12.5159 10.2702 8.0840 5.8892 3.6945 1.4997
*
*
0.2770 -0.3617 0.1502 0.1705 -0.3672 0.2970
0.1566 -0.2896 0.3487 -0.3480 0.2876 -0.1779
* 140.143 cm/s²
* 140.143 cm/s²
=
84.885 KN -90.940 KN 29.727 KN 24.580 KN -33.214 KN 10.904 KN
=
23.186 KN -35.193 KN 33.354 KN -24.250 KN 12.574 KN -3.158 KN
UNPRG - ING CIVIL
DETERMINACION DEL CORTANTE APLICANDO EL CRITERIO DE SUPERPOSICION MODAL Q= 0.25 ∗
𝑄𝑖 + 0.75
𝑄𝑖 2
NIVEL
Q1
Q2
Q3
Q4
Q5
Q6
1 2 3 4 5 6
324.581 KN 489.491 KN 544.374 KN 487.234 KN 343.076 KN 145.593 KN
514.218 KN 577.727 KN 337.289 KN 26.940 KN -129.505 KN -83.500 KN
349.970 KN 159.077 KN -151.546 KN -160.281 KN 6.360 KN 42.430 KN
188.641 KN -65.874 KN -110.668 KN 67.967 KN 34.609 KN -22.569 KN
84.885 KN -90.940 KN 29.727 KN 24.580 KN -33.214 KN 10.904 KN
23.186 KN -35.193 KN 33.354 KN -24.250 KN 12.574 KN -3.158 KN
Juan Manuel Chero Damian
0.25 Qi 283.878 KN 314.806 KN 263.853 KN 157.743 KN 138.244 KN 66.431 KN
0.75
Q
2 i
548.875 KN 586.979 KN 501.613 KN 389.441 KN 277.573 KN 131.214 KN
Q
Q
832.753 KN 901.786 KN 765.466 KN 547.183 KN 415.818 KN 197.645 KN
84.888 Tn 91.925 Tn 78.029 Tn 55.778 Tn 42.387 Tn 20.147 Tn
INGENIERIA ANTISISMICA
UNPRG - ING CIVIL
DETERMINACION DE LOS DESPLAZAMIENTOS 𝑄𝑖 =
X1
=
3.312 *
76.6898
*
73.8879
X2
=
1.056 *
140.1429
*
629.5392
X3
=
0.547 *
140.1429
*
1596.1164
X4
=
0.306 *
140.1429
2757.4430
*
0.1021 0.1876 0.2651 0.3257 0.3656 0.3822
0.2775 0.3799 0.2818 0.0309 -0.2368 -0.3761
0.3645 0.2019 -0.2444 -0.3548 0.0224 0.3688
0.3518 -0.1497 -0.3195 0.2693 0.2186 -0.3512
=
=
0.351 cm 0.645 cm 0.911 cm 1.120 cm 1.257 cm 1.314 cm
0.065 cm 0.089 cm 0.066 cm 0.007 cm -0.056 cm -0.088 cm
=
0.018 cm 0.010 cm -0.012 cm -0.017 cm 0.001 cm 0.018 cm
=
0.005 cm -0.002 cm -0.005 cm 0.004 cm 0.003 cm -0.005 cm
𝐹𝑃𝑀𝑖 ∗ ∅𝑖 𝑛 ∗ 𝑆𝑎𝑖 𝑤𝑖 2
X5
=
0.175 *
140.1429
*
3800.8307
X6
=
0.084 *
140.1429
4445.9838
Juan Manuel Chero Damian
*
0.2770 -0.3617 0.1502 0.1705 -0.3672 0.2970
0.1566 -0.2896 0.3487 -0.3480 0.2876 -0.1779
=
0.00178 cm -0.00233 cm 0.00097 cm 0.00110 cm -0.00237 cm 0.00191 cm
=
0.00042 cm -0.00077 cm 0.00093 cm -0.00093 cm 0.00077 cm -0.00047 cm
INGENIERIA ANTISISMICA
UNPRG - ING CIVIL
DETERMINACION DE LOS DESPLAZAMIENTOS APLICANDO EL CRITERIO DE SUPERPOSICION MODAL Q= 0.25 ∗
|𝑋𝑖| + 0.75
𝑋𝑖 2
NIVEL
Q1
Q2
Q3
Q4
Q5
Q6
0.25 X i
0.75
1 2 3 4 5 6
0.3510 cm 0.6450 cm 0.9114 cm 1.1197 cm 1.2568 cm 1.3139 cm
0.0653 cm 0.0894 cm 0.0663 cm 0.0073 cm -0.0557 cm -0.0884 cm
0.0175 cm 0.0097 cm -0.0117 cm -0.0171 cm 0.0011 cm 0.0177 cm
0.0055 cm -0.0023 cm -0.0050 cm 0.0042 cm 0.0034 cm -0.0055 cm
0.0018 cm -0.0023 cm 0.0010 cm 0.0011 cm -0.0024 cm 0.0019 cm
0.0004 cm -0.0008 cm 0.0009 cm -0.0009 cm 0.0008 cm -0.0005 cm
0.1060 cm 0.1850 cm 0.2461 cm 0.2833 cm 0.3298 cm 0.3526 cm
0.2681 cm 0.4885 cm 0.6854 cm 0.8399 cm 0.9435 cm 0.9878 cm
DETERMINACION DE LAS DISTORCIONES
NIVEL
0.75*R*X
Δr
H
DISTORSION
VERIFICACION
6 5 4 3 2 1
7.0367 cm 6.6847 cm 5.8968 cm 4.8905 cm 3.5355 cm 1.9639 cm
0.3520 cm 0.7879 cm 1.0063 cm 1.3550 cm 1.5715 cm 1.9639 cm
275.0 cm 275.0 cm 275.0 cm 275.0 cm 275.0 cm 287.5 cm
0.0013 0.0029 0.0037 0.0049 0.0057 0.0068
CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007 CUMPLE < 0.007
Juan Manuel Chero Damian
X
2 i
X
0.75*R*X
0.3741 cm 0.6734 cm 0.9315 cm 1.1232 cm 1.2733 cm 1.3403 cm
1.9639 cm 3.5355 cm 4.8905 cm 5.8968 cm 6.6847 cm 7.0367 cm
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