Post on 07-Apr-2018
8/6/2019 Modal Espectral
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CURSOIngeniera Sismo Resistente II
Anlisis Ssmico porSuperposicin Modal Espectral
Ing. Omart Tello Malpartida
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Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Introduccin
M
25
0
0
0
0
0
25
0
0
0
0
0
20
0
0
0
0
0
20
0
0
0
0
0
15
k1 50000 k2 40000 k3 40000 k4 30000 k5 20000
K
k1 k2
k20
0
0
k2
k2 k3k3
0
0
0
k3k3 k4
k4
0
0
0k4
k4 k5
k5
0
00
k5
k5
K
90000.00
40000.00
0.00
0.00
0.00
40000.00
80000.00
40000.00
0.00
0.00
0.00
40000.00
70000.00
30000.00
0.00
0.00
0.00
30000.00
50000.00
20000.00
0.00
0.00
0.00
20000.00
20000.00
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Calculo de Frecuencias Angulares yPeriodos de vibracin
K1 M1
K K1
3600.00
1600.00
0.00
0.00
0.00
1600.00
3200.00
2000.00
0.00
0.00
0.00
1600.00
3500.00
1500.00
0.00
0.00
0.00
1500.00
2500.00
1333.33
0.00
0.00
0.00
1000.00
1333.33
evp eigenvals K1( )
5to 1ro
4to 2do
evp
6016.82
4227.54
175.661093.43
2619.89
1ro Freq sort evp( ) Freq
175.66
1093.43
2619.894227.54
6016.82
3ro4to
2do5to
3ro
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
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Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Calculo de Frecuencias Angulares yPeriodos de vibracin
i 1 5
i Freq i Ti2
i
1 13.25 T1 0.47
2 33.07 T2 0.19
3 51.18 T3 0.12
4 65.02 T4 0.10
5 77.57 T5 0.08
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Calculo de modos de vibracin
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
v eigenvecs K1( )
5to 4to 1ro 2do 3ro
v
0.387
0.585
0.6420.298
0.085
0.613
0.240
0.4580.543
0.250
0.141
0.302
0.4300.550
0.634
0.328
0.514
0.3490.126
0.700
0.433
0.265
0.3370.551
0.571
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Normalizando los modos de vibracin
V1v 3
v1 3V1
1.000
2.140
3.045
3.896
4.487
V3v 5
v1 5V3
1.000
0.613
0.778
1.273
1.319
V4v 2
v1 2
V4
1.000
0.392
0.748
0.886
0.408
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
V2v 4
v1 4V2
1.000
1.567
1.063
0.384
2.134
V5v 1
v1 1
V5
1.000
1.511
1.659
0.770
0.219
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Matriz de modos de vibracinNormalizados
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
V1
1 1V
1 2 1V1 3 1V1 4 1V1 5 1
V2
1 1V
2 2 1V2 3 1V2 4 1V2 5 1
V3
1 1V
3 2 1V3 3 1V3 4 1V3 5 1
V4
1 1V
4 2 1V4 3 1V4 4 1V4 5 1
V5
1 1V
5 2 1V5 3 1V5 4 1V5 5 1
1.000
2.140
3.045
3.896
4.487
1.000
1.567
1.063
0.384
2.134
1.000
0.613
0.778
1.273
1.319
1.000
0.392
0.748
0.886
0.408
1.000
1.511
1.659
0.770
0.219
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Calculo de Me y Ke
MeT
M Me
930.53
0.00
0.00
0.00
0.00
0.00
180.20
0.00
0.00
0.00
0.00
0.00
105.02
0.00
0.00
0.00
0.00
0.00
58.23
0.00
0.00
0.00
0.00
0.00
149.69
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Ke T K Ke
163461.99
0.00
0.000.00
0.00
0.00
197033.12
0.000.00
0.00
0.00
0.00
275138.890.00
0.00
0.00
0.00
0.00246170.59
0.00
0.00
0.00
0.000.00
900633.61
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Calculo de Vector de masasparticipantes . .T L M I
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
I
1
1
1
1
1
LT
M IL
284.63
45.73
19.0811.83
8.31
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Calculo de Masas Efectivas
Le 1 1
L1 1( )
2
Me 1 1( )Le 1 1 87.06
Le 2 1
L 2 1( )2
Me 2 2( )Le 2 1 11.6
Le 3 1L 3 1( )
2
Me3 3( )
Le 3 1 3.47
Le 4 1
L4 1( )
2
Me4 4( )
Le 4 1 2.4
Le5 1
L5 1( )
2
Me5 5( )
Le5 1
0.46
2i
i
i
L Le
2
1
ni
i i
L
M Masa efectiva total
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Mtotal
1
5
i
Lei 1
Mtotal 105.00
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Factor deParticipacinModal (FPMi)
. .. .
T
ii i T
i
L M I FPM
M
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
1
L1 1( )
Me1 1( )
1 0.31
2
L2 1( )
Me2 2( )
2 0.25
3
L3 1( )
Me3 3( )
3 0.18
4
L4 1( )
Me 4 4( )
4 0.2
5
L5 1( )
Me5 5( )
5 0.06
Sumatoria de participacion de modos
1
5
i
i 1.00
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Factor deParticipacinde Masas
P1Le 1 1 100Mtotal P1 82.92
P2
Le 2 1 100Mtotal
P2 11.05
P3
Le 3 1 100Mtotal
P3 3.30
P4
Le 4 1 100Mtotal
P4 2.29
P5
Le 5 1 100Mtotal
P5 0.44
Sumatoria de participacion efectiva
Suma
1
5
i
Pi
Suma 100.00
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
2i
i
L
M Pi
Mtotal
> 90 %
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ANALISIS MODAL ESPECTRAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Espectro NTE-030
Z = 0.4 LimaU = 1.3 Centro Comerci g = 980S = 1.2 S2 Tp = 0.6R = 6.0 Muro estruct.
ZUS.g = 101.92
R
SaT C = 2.5( Tp/T) C ZUS.g. C
R0.1 15.00 2.50 254.80.2 7.50 2.50 254.80.3 5.00 2.50 254.80.4 3.75 2.50 254.80.5 3.00 2.50 254.80.6 2.50 2.50 254.80.7 2.14 2.14 218.40.8 1.88 1.88 191.10.9 1.67 1.67 169.91.0 1.50 1.50 152.91.1 1.36 1.36 139.01.2 1.25 1.25 127.4
1.3 1.15 1.15 117.61.4 1.07 1.07 109.21.5 1.00 1.00 101.91.6 0.94 0.94 95.61.7 0.88 0.88 89.91.8 0.83 0.83 84.91.9 0.79 0.79 80.52.0 0.75 0.75 76.42.1 0.71 0.71 72.82.2 0.68 0.68 69.5
2.3 0.65 0.65 66.52.4 0.63 0.63 63.72.5 0.60 0.60 61.22.6 0.58 0.58 58.82.7 0.56 0.56 56.62.8 0.54 0.54 54.62.9 0.52 0.52 52.73.0 0.50 0.50 51.0
0.08 18.75 2.5 254.80.10 15.00 2.5 254.8
0.12 12.50 2.5 254.80.19 7.89 2.5 254.80.47 3.19 2.5 254.8
SaT C = 2.5( Tp/T) C ZUS.g. C
R
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ANALISIS MODAL ESPECTRAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Espectro NTE-030
Z = 0.4 LimaU = 1.3 Centro Comerci g = 980
S = 1.2 S2 Tp = 0.6R = 6.0 Muro estruct.
ZUS.g = 101.92R
SaT C = 2.5( Tp/T) C ZUS.g. C
R0.1 15.00 2.50 254.80.2 7.50 2.50 254.80.3 5.00 2.50 254.80.4 3.75 2.50 254.80.5 3.00 2.50 254.80.6 2.50 2.50 254.80.7 2.14 2.14 218.40.8 1.88 1.88 191.10.9 1.67 1.67 169.91.0 1.50 1.50 152.91.1 1.36 1.36 139.0
1.2 1.25 1.25 127.41.3 1.15 1.15 117.61.4 1.07 1.07 109.21.5 1.00 1.00 101.91.6 0.94 0.94 95.61.7 0.88 0.88 89.91.8 0.83 0.83 84.91.9 0.79 0.79 80.52.0 0.75 0.75 76.4
0.08 18.75 2.5 254.80.10 15.00 2.5 254.80.12 12.50 2.5 254.80.19 7.89 2.5 254.80.47 3.19 2.5 254.8
SaT C = 2.5( Tp/T) C ZUS.g. C
R
Espectro NTE-030
0.0
50.0
100.0
150.0
200.0
250.0
300.0
T (seg)
S a
( m / s e g
2 )
Sa
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ANALISIS MODAL ESPECTRAL2
Sv SaSd
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Calculo de Desplazamientos Mx imos
1er Modo :1 13.25 T 1
0.47 1 0.31
Del espectro : Sa1 254.8 Sd1Sa1
1 2Sd1 1.45
11 1
1.00
2.14
3.05
3.904.49
Umax1 1 Sd1 1 Umax1
0.444
0.950
1.351
1.7281.991
2do Modo : 2 33.07 T 2 0.19 2 0.25
Del espectro : Sa2 254.8 Sd2Sa2
2 2
Sd2 0.23
22 2
1.00
1.57
1.06
0.38
2.13
Umax2 2 Sd2 2 Umax2
0.059
0.093
0.063
0.023
0.126
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ANALISIS MODAL ESPECTRAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Calculo de Desplazamientos Mx imos
3er Modo : 3 51.18 T 3 0.12 3 0.18
Del espectro : Sa3 254.8 Sd3Sa3
3 2
Sd3 0.10
33 3
1.00
0.61
0.78
1.27
1.32
Umax3 3 Sd3 3 Umax3
0.018
0.011
0.014
0.023
0.023
4to Modo :4 65.02 T 4
0.10 4 0.20
Del espectro : Sa4 254.8 Sd4Sa4
4 2
Sd4 0.06
44 4
1.00
0.39
0.75
0.89
0.41
Umax4 4 Sd4 4 Umax4
0.012
0.005
0.009
0.011
0.005
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ANALISIS MODAL ESPECTRAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Calculo de Desplazamientos Mx imos
5to Modo : 5 77.57 T 5 0.08 5 0.06
Del espectro : Sa5 254.8 Sd5Sa5
5 2Sd5 0.04
55 5
1.00
1.51
1.66
0.77
0.22
Umax5 5 Sd5 5 Umax5
0.002
0.004
0.004
0.002
0.001
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COMBINACION PORSUPERPOSICION MODAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
U1 = Sumatoria de Valores Absolutos (ABS)
U1
Umax11 1
Umax21 1
Umax31 1
Umax41 1
Umax51 1
Umax12 1
Umax22 1
Umax32 1
Umax42 1
Umax52 1
Umax13 1
Umax23 1
Umax33 1
Umax43 1
Umax53 1
Umax14 1
Umax24 1
Umax34 1
Umax44 1
Umax54 1
Umax15 1
Umax25 1
Umax35 1
Umax45 1
Umax55 1
U1
0.54
1.06
1.44
1.79
2.15
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COMBINACION PORSUPERPOSICION MODAL
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
U2= Raiz Cuadrada de la Suma de los Cuadrados ( RCSC)
U2
Umax11 1
2Umax2
1 1 2
Umax31 1
2Umax4
1 1 2
Umax51 1
2
Umax12 1
2Umax2
2 1 2
Umax32 1
2Umax4
3 1 2
Umax54 1
2
Umax13 1 2 Umax2 3 1 2 Umax3 3 1 2 Umax4 3 1 2 Umax5 3 1 2
Umax14 1
2Umax2
4 1 2
Umax34 1
2Umax4
4 1 2
Umax54 1
2
Umax15 1
2Umax2
5 1 2
Umax35 1
2Umax4
5 1 2
Umax55 1
2
U2
0.45
0.95
1.35
1.73
1.99
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COMBINACION PORSUPERPOSICION MODAL
Norma NTE-030: 0.25ABS+0.75SRSS
Umax
0.25 U1 1 1 0.75 U2 1 1
0.25 U1 2 1 0.75 U2 2 1
0.25 U1 3 1 0.75 U2 3 1
0.25 U1 4 1 0.75 U2 4 1
0.25 U1 5 1 0.75 U2 5 1
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
Umax
0.47
0.98
1.37
1.74
2.03
1
Umax 1 1
100 1 0.0047
2
Umax2 1
100 2 0.0098
3
Umax 3 1
100 3 0.0137
4
Umax4 1
100 4 0.0174
5
Umax5 1
100 5 0.0203
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Distorsin de Entrepiso
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
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Calculo de Cortantes de Entrepiso
V1 k1 1
V2 k2 2 1 V
3k3 3 2
V4 k4 4 3 V5 k5 5 4
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
V1
234.93
V2
204.45
V
3
157.52
V4
110.52
V5
57.88
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Fuerzas Ssmicas del Anlisis Dinmico
F 1 V 1 V 2
F 2 V 2 V 3
F3
V3
V4
F4
V4
V5
F5
V5
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
V1
5
iFi
F1
30.48
F2
46.93
F3
47.00
F4
52.64
F5
57.88
V 234.93
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Fuerzas Ssmicas del Anlisis Dinmico(Mtodo Alternativo)
Ing. Sismo Resistente II Ing. Omart Tello Malpartida
V1
5
iFi V 234.93
Fd KUmax
100 Fd
30.48
46.93
47.00
52.64
57.88
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Preguntas .?