Analisis Sismico Por Superposicion Modal (1)

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ANALISIS SISMICO POR SUPERPOSICION MODAL DIRECCION X-X R igidez LateraldelEntrepiso M atriz de R igidez lateralde em trepiso D ireccion X-X (Ton/cm ) k1 = 4,761.20 9314.88 -4553.68 0.00 0.00 0.00 0.00 0.00 k2 = 4,553.68 -4553.68 9107.36 -4553.68 0.00 0.00 0.00 0.00 k3 = 4,553.68 0.00 -4553.68 9107.36 -4553.68 0.00 0.00 0.00 k4 = 4,553.68 K = 0.00 0.00 -4553.68 9107.36 -4553.68 0.00 0.00 k5 = 4,553.68 0.00 0.00 0.00 -4553.68 9107.36 -4553.68 0.00 k6 = 4,553.68 0.00 0.00 0.00 0.00 -4553.68 6857.09 -2303.41 k7 = 2,303.41 0.00 0.00 0.00 0.00 0.00 -2303.41 2303.41 M asa delEntrepiso M atriz de m asas delentrepiso (Ton-seg2/cm) m 1 = 1.15 1.15 0 0 0 0 0 0 m 2 = 1.13 0 1.13 0 0 0 0 0 m 3 = 1.13 0 0 1.13 0 0 0 0 m 4 = 1.13 M = 0 0 0 1.13 0 0 0 m 5 = 1.13 0 0 0 0 1.13 0 0 m 6 = 1.13 0 0 0 0 0 1.13 0 m 7 = 0.79 0 0 0 0 0 0 0.79 CALCULO DE FRECUENCIAS ANGULARES Y PERIODOS DE VIBRACION >>K1=M^-1*K 8099.9 -3959.7 0 0 0 0 0 -4029.8 8059.6 -4029.8 0 0 0 0 0 - 4029.8 8059.6 -4029.8 0 0 0 K1 = 0 0 - 4029.8 8059.6 -4029.8 0 0

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Transcript of Analisis Sismico Por Superposicion Modal (1)

Page 1: Analisis Sismico Por Superposicion Modal (1)

ANALISIS SISMICO POR SUPERPOSICION MODALDIRECCION X-X

Rigidez Lateral del Entrepiso Matriz de Rigidez lateral de emtrepiso Direccion X-X (Ton/cm)

k1 = 4,761.20 9314.88 -4553.68 0.00 0.00 0.00 0.00 0.00

k2 = 4,553.68 -4553.68 9107.36 -4553.68 0.00 0.00 0.00 0.00

k3 = 4,553.68 0.00 -4553.68 9107.36 -4553.68 0.00 0.00 0.00

k4 = 4,553.68 K = 0.00 0.00 -4553.68 9107.36 -4553.68 0.00 0.00

k5 = 4,553.68 0.00 0.00 0.00 -4553.68 9107.36 -4553.68 0.00

k6 = 4,553.68 0.00 0.00 0.00 0.00 -4553.68 6857.09 -2303.41

k7 = 2,303.41 0.00 0.00 0.00 0.00 0.00 -2303.41 2303.41

Masa del Entrepiso Matriz de masas del entrepiso (Ton-seg2/cm)

m1 = 1.15 1.15 0 0 0 0 0 0

m2 = 1.13 0 1.13 0 0 0 0 0

m3 = 1.13 0 0 1.13 0 0 0 0

m4 = 1.13 M = 0 0 0 1.13 0 0 0

m5 = 1.13 0 0 0 0 1.13 0 0

m6 = 1.13 0 0 0 0 0 1.13 0

m7 = 0.79 0 0 0 0 0 0 0.79

CALCULO DE FRECUENCIAS ANGULARES Y PERIODOS DE VIBRACION

>>K1=M^-1*K

8099.9 -3959.7 0 0 0 0 0 -4029.8 8059.6 -4029.8 0 0 0 0 0 -4029.8 8059.6 -4029.8 0 0 0

K1 = 0 0 -4029.8 8059.6 -4029.8 0 0 0 0 0 -4029.8 8059.6 -4029.8 0 0 0 0 0 -4029.8 6068.2 -2038.4 0 0 0 0 0 -2915.7 2915.7

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>>evp=eig(K1) 1.5252 1.2870 0.9576

evp = 10^4 * 0.6231 0.3629 0.0192 0.1571

>>Freq=sort(evp) 0.0192 0.1571 0.3629

Freq = 10^4 * 0.6231 0.9576 1.2870 1.5252

>> Wi=sqrt(Freq) 13.8586 39.6392 60.2422

Wi = 78.9397 97.8562 113.4481 123.4991

>>Ti=2*pi()./Wi 0.4534 0.1585 0.1043

Ti = 0.0796 0.0642 0.0554 0.0509

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CALCULO DE LOS MODOS DE VIBRACION NORMALIZADOS

1.000 1.000 1.000 1.000

1.997 1.649 1.129 0.472

2.899 1.655 0.241 -0.786

v1= 3.663 v2= 1.016 v3= -0.864 v4= -0.829

4.252 -0.019 -1.191 0.410

4.639 -1.047 -0.446 1.015

4.966 -2.271 1.821 -0.891

1.000 1.000 1.000

-0.373 -1.205 -1.806

-0.860 0.438 2.224

v5= 0.696 v6= 0.682 v7= -2.163

0.598 -1.252 1.636

-0.921 0.813 -0.758

0.404 -0.236 0.179

MATRIZ DE MODOS DE VIBRACION NORMALIZADOS

1.000 1.000 1.000 1.000 1.000 1.000 1.000

1.997 1.649 1.129 0.472 -0.373 -1.205 -1.806

2.899 1.655 0.241 -0.786 -0.860 0.438 2.224

ø = 3.663 1.016 -0.864 -0.829 0.696 0.682 -2.163

4.252 -0.019 -1.191 0.410 0.598 -1.252 1.636

4.639 -1.047 -0.446 1.015 -0.921 0.813 -0.758

4.966 -2.271 1.821 -0.891 0.404 -0.236 0.179

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CALCULO DE Me y Ke

>> Me=øT*M*ø

94.5452 0.0089 -0.0055 0.0040 0.0022 0.0089 -0.0036 0.0089 13.7977 -0.0013 -0.0033 -0.0023 -0.0048 0.0012 -0.0055 -0.0013 7.9468 0.0024 0.0010 0.0019 0.0011

Me= 0.0040 -0.0033 0.0024 4.8577 -0.0008 -0.0021 0.0002 0.0022 -0.0023 0.0010 -0.0008 4.1819 0.0012 0.0003 0.0089 -0.0048 0.0019 -0.0021 0.0012 6.0953 -0.0013 -0.0036 0.0012 0.0011 0.0002 0.0003 -0.0013 19.4106

>>Ke= øT *K* ø

0.1816 -0.0000 -0.0000 0.0000 -0.0000 0.0001 -0.0001 -0.0000 0.2168 -0.0000 -0.0001 -0.0000 -0.0001 0.0000 -0.0000 -0.0000 0.2884 0.0001 0.0001 0.0000 0.0001

Ke = 10^5* 0.0000 -0.0001 0.0001 0.3027 -0.0001 -0.0001 0.0001 -0.0000 -0.0000 0.0001 -0.0001 0.4005 0.0001 0.0001 0.0001 -0.0001 0.0000 -0.0001 0.0001 0.7845 -0.0002 -0.0001 0.0000 0.0001 0.0001 0.0001 -0.0002 2.9605

CALCULO DEL VECTOR DE MASAS PARTICIPANTES Li= øT *M* I

>> Li=fi'*M*I

24.7916 3.0329 1.3106

Li = 0.7648 0.4974 0.3714 0.3117

1 1 1

I = 1 1 1 1

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CALCULO DE MASAS EFECTIVAS ¿i=Li2

Mei

>> LL=[Li Li Li Li Li Li Li]

24.7916 24.7916 24.7916 24.7916 24.7916 24.7916 24.7916 3.0329 3.0329 3.0329 3.0329 3.0329 3.0329 3.0329 1.3106 1.3106 1.3106 1.3106 1.3106 1.3106 1.3106

LL = 0.7648 0.7648 0.7648 0.7648 0.7648 0.7648 0.7648 0.4974 0.4974 0.4974 0.4974 0.4974 0.4974 0.4974 0.3714 0.3714 0.3714 0.3714 0.3714 0.3714 0.3714 0.3117 0.3117 0.3117 0.3117 0.3117 0.3117 0.3117

>> Li2=¿LL.^2

614.6254 614.6254 614.6254 614.6254 614.6254 614.6254 614.6254 9.1987 9.1987 9.1987 9.1987 9.1987 9.1987 9.1987 1.7176 1.7176 1.7176 1.7176 1.7176 1.7176 1.7176

Li2=¿ 0.5849 0.5849 0.5849 0.5849 0.5849 0.5849 0.5849

0.2474 0.2474 0.2474 0.2474 0.2474 0.2474 0.2474 0.1380 0.1380 0.1380 0.1380 0.1380 0.1380 0.1380 0.0972 0.0972 0.0972 0.0972 0.0972 0.0972 0.0972

>> Led=Li2/Me

6.4840 44.6359 77.2700 126.5773 146.9690 100.8593 31.6615 0.0970 0.6680 1.1564 1.8944 2.1996 1.5095 0.4739 0.0181 0.1247 0.2159 0.3537 0.4107 0.2819 0.0885

Led = 0.0062 0.0425 0.0735 0.1205 0.1399 0.0960 0.0301 0.0026 0.0180 0.0311 0.0509 0.0592 0.0406 0.0127 0.0015 0.0100 0.0173 0.0284 0.0330 0.0226 0.0071 0.0010 0.0071 0.0122 0.0200 0.0232 0.0159 0.0050

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>> Lei=diag(Led)

6.4840 0.6680 0.2159

Lei = 0.1205 0.0592 0.0226 0.0050

Masa total efectiva: MasaTotal=∑i

7 ¿iM i

>> Mtotal =sum(Lei)Mtotal = 7.59

FACTOR DE PARTICIPACION MODAL FPM i=øT . M . IøT∗Mø

=LiMei

>> FPM=LL/Me

0.2615 1.8004 3.1168 5.1056 5.9282 4.0683 1.2771 0.0320 0.2203 0.3813 0.6246 0.7252 0.4977 0.1562 0.0138 0.0952 0.1648 0.2699 0.3134 0.2151 0.0675

FPMi = 0.0081 0.0555 0.0961 0.1575 0.1829 0.1255 0.0394 0.0052 0.0361 0.0625 0.1024 0.1189 0.0816 0.0256 0.0039 0.0270 0.0467 0.0765 0.0888 0.0610 0.0191 0.0033 0.0226 0.0392 0.0642 0.0745 0.0511 0.0161

>> i = diag(FPM)

0.2615 0.2203 0.1648

i = 0.1575 0.1189 0.0610 0.0161

Sumatoria de participación de modos: ∑i

7

i=1

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>> sum(i) ans = 1 (Ok)

FACTOR DE PARTICIPACION DE MASAS Pi=

[ Li2Mi]

Mtotal

x100

>> Pi=Lei/sum(Lei)*100

85.5951 8.8186 2.8505

Pi = 1.5900 0.7808 0.2989 0.0661

Sumatoria de participación efectiva de masas: ∑i

7

Pi=100

>> sum(Pi)

ans = 100.00 (Ok)

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CALCULO DE DESPLAZAMIENTOS MAXIMOS

Sd=Sv❑= Sv❑2

1er Modo

>> 1=fi(:,1)

1.0000 1.9970 2.8990

1 = 3.6630 4.2520 4.6390 4.9660

i(1,1) = 13.8586Ti(1,1) = 0.4534i (1,1) = 0.2615

Del espectro Sa1=224.00

>> Sd1=Sa1/i(1,1)^2

Sd1 = 1.1663

>>Umax1=1*Sd1*i (1,1)

0.3050 0.6092 0.8843

Umax1 = 1.1173 1.2970 1.4150 1.5148

2do Modo

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>> 2=fi(:,2)

1.0000 1.6490 1.6550

2 = 1.0160 -0.0190 -1.0470 -2.2710

i(2,1) = 39.6392Ti(2,1) = 0.1585i (2,1) = 0.2213 Del espectro Sa2=224.00

>> Sd2 = Sa2/i(2,1)^2

Sd2 = 0.1426

>>Umax2=2*Sd1*i (2,1)

0.0314 0.0518 0.0520

Umax2 = 0.0319 -0.0006 -0.0329 -0.0713

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3er Modo>> 3=fi(:,3)

1.0000 1.1290 0.2410

3 = -0.8640 -1.1910 -0.4460 1.8210

i(3,1) = 60.2422Ti(3,1) = 0.1043i (3,1) = 0.1648

Del espectro Sa3=224.00

>> Sd3 = Sa3/i(3,1)^2

Sd3 = 0.0617

>>Umax3=3*Sd3*i (3,1)

0.0102 0.0115 0.0025

Umax3 = -0.0088 -0.0121 -0.0045 0.0185

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4to Modo>> 4=fi(:,4)

1.0000 0.4720 -0.7860

4 = -0.8290 0.4100 1.0150 -0.8910

i(4,1) = 78.9397Ti(4,1) = 0.0796i (4,1) = 0.1575

Del espectro Sa4=224.00

>> Sd4 = Sa4/i(4,1)^2

Sd4 = 0.0359

>>Umax4=4*Sd4*i (4,1)

0.0057 0.0027 -0.0044

Umax4 = -0.0047 0.0023 0.0057 -0.0050

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5to Modo>> 5=fi(:,5)

1.0000 -0.3730 -0.8600

5 = 0.6960 0.5980 -0.9210 0.4040

i(5,1) = 97.8562Ti(5,1) = 0.0642i (5,1) = 0.1189

Del espectro Sa5=224.00

>> Sd5 = Sa5/i(5,1)^2

Sd5 = 0.0234 >>Umax5=5*Sd5*i (5,1)

0.0028 -0.0010 -0.0024

Umax5 = 0.0019 0.0017 -0.0026 0.0011

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6to Modo>> 6=fi(:,6)

1.0000 -1.2050 0.4380

6 = 0.6820 -1.2520 0.8130 -0.2360

i(6,1) = 113.4481Ti(6,1) = 0.0554i (6,1) = 0.0610

Del espectro Sa6=224.00

>> Sd6 = Sa6/i(6,1)^2

Sd6 = 0.0174 >>Umax6=6*Sd6*i (6,1)

0.0011 -0.0013 0.0005

Umax6 = 0.0007 -0.0013 0.0009 -0.0003

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7mo Modo>> 7=fi(:,7)

1.0000 -1.8060 2.2240

7 = -2.1630 1.6360 -0.7580 0.1790

i(7,1) = 123.4991Ti(7,1) = 0.0509i (7,1) = 0.0161

Del espectro Sa7=224.0

>> Sd7 = Sa7/i(7,1)^2

Sd7 = 0.0147

>>Umax7=7*Sd7*i (7,1)

0.2358 -0.4259 0.5245

Umax7 = 10^-3* -0.5101 0.3858 -0.1788 0.0422

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COMBINACION POR SUPERPOSICION MODAL

U1 Sumatoria de Valores Absolutos (ABS)>>U1=[abs(Umax1)+abs(Umax2)+abs(Umax3)+abs(Umax4)+abs(Umax5)+abs(Umax6)+ abs(Umax7)]

0.3563 0.6778 0.9465

U1 = 1.1659 1.3154 1.4618 1.6111

U2 raíz cuadrada de la suma de los cuadrados (RCSC)>> U2=[sqrt(Umax1.^2+Umax2.^2+Umax3.^2+Umax4.^2+Umax5.^2+Umax6.^2+Umax7.^2)]

0.3069 0.6115 0.8858

U2 = 1.1178 1.2971 1.4155 1.5166

NORMA NTE-030: 025ABS+0.75SRSS>> Umax=[0.25*U1+0.75*U2]

0.3192 0.6281 0.9010

Umax= 1.1299 1.3016 1.4270 1.5402

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i

DISTORSION DE ENTREPISO

>> Δi=Umax/100

0.0032 0.0063 0.0090

Δi= 0.0113

0.0130 0.0143 0.0154

0.0011 0.0013 0.0017

i= 0.0023

0.0027 0.0031 0.0032

Cumplen todas las distorsiones (i )son menores a 0.07 (Pórtico de concreto)

Page 17: Analisis Sismico Por Superposicion Modal (1)

V1=1

520

V2=1

406

V3=1

243

V4=1

042

V5=7

82

V6=5

71

V7=2

61

CALCULO DE CORTANTE DE ENTREPISO

>> k1=476120; k2=455368; k3=455368; k4=455368; k5=455368; k6=455368; k7=230341;

>> V1=k1*Deltas(1,1)V1 = 1520.00

>> V2=k2*(Deltas(2,1)-Deltas(1,1))V2 = 1406.21

>> V3=k3*(Deltas(3,1)-Deltas(2,1))V3 = 1242.96

>> V4=k4*(Deltas(4,1)-Deltas(3,1))V4 = 1042.06

>> V5=k5*(Deltas(5,1)-Deltas(4,1))V5 = 782.31

>> V6=k6*(Deltas(6,1)-Deltas(5,1))V6 = 571.00

>> V7=k7*(Deltas(7,1)-Deltas(6,1))V7 = 260.69

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FUERZAS SISMICAS DEL ANALISIS DINAMICO X-X

>> F1=V1-V2F1 = 113.78

>>F2=V2-V3F2 = 163.26

>> F3=V3-V4F3 = 200.90

>> F4=V4-V5F4 = 259.75

>> F5=V5-V6F5 = 211.31

>> F6=V6-V7F6 = 310.31

>> F7=V7F7 = 260.69

>> F1+F2+F3+F4+F5+F6+F7

∑i

7

Fi=1520

Page 19: Analisis Sismico Por Superposicion Modal (1)

FUERZAS SISMICAS DEL ANALISIS DINAMICO X-X(METODO ALTERNO)

>> Fd=K*Umax/100

113.78 163.26 200.90

Fd = 259.75 211.31 310.31 260.69

>> sum(Fd) ans = 1520.00

∑i

7

Fdi=1520

Page 20: Analisis Sismico Por Superposicion Modal (1)

ANALISIS SISMICO POR SUPERPOSICION MODALDIRECCION Y-Y

Rigidez Lateral del Entrepiso Matriz de Rigidez lateral de emtrepiso Direccion Y-Y (Ton/cm)

k1 = 4,094.45 8063.32 -3968.87 0.00 0.00 0.00 0.00 0.00

k2 = 3,968.87 -3968.87 7937.74 -3968.87 0.00 0.00 0.00 0.00

k3 = 3,968.87 0.00 -3968.87 7937.74 -3968.87 0.00 0.00 0.00

k4 = 3,968.87 K = 0.00 0.00 -3968.87 7937.74 -3968.87 0.00 0.00

k5 = 3,968.87 0.00 0.00 0.00 -3968.87 7937.74 -3968.87 0.00

k6 = 3,968.87 0.00 0.00 0.00 0.00 -3968.87 5961.43 -1992.56

k7 = 1,992.56 0.00 0.00 0.00 0.00 0.00 -1992.56 1992.56

Masa del Entrepiso Matriz de masas del entrepiso (Ton-seg2/cm)

m1 = 1.15 1.15 0 0 0 0 0 0

m2 = 1.13 0 1.13 0 0 0 0 0

m3 = 1.13 0 0 1.13 0 0 0 0

m4 = 1.13 M = 0 0 0 1.13 0 0 0

m5 = 1.13 0 0 0 0 1.13 0 0

m6 = 1.13 0 0 0 0 0 1.13 0

m7 = 0.79 0 0 0 0 0 0 0.79

CALCULO DE FRECUENCIAS ANGULARES Y PERIODOS DE VIBRACION

>>K1=M^-1*K

7011.6 -3451.2 0 0 0 0 0 -3512.3 7024.5 -3512.3 0 0 0 0 0 -3512.3 7024.5 -3512.3 0 0 0

K1 = 0 0 -3512.3 7024.5 -3512.3 0 0 0 0 0 -3512.3 7024.5 - 3512.3 0 0 0 0 0 -3512.3 5275.6 -1763.3 0 0 0 0 0 -3512.3 2522.2

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>>evp=eig(K1) 1.3290 1.1206 0.8327

evp = 10^4 * 0.5409 0.3146 0.0167 0.1364

>>Freq=sort(evp)

0.0167 0.1364 0.3146

Freq = 10^4 * 0.5409 0.8327 1.1206 1.3290

>> Wi=sqrt(Freq)

12.9146 36.9296 56.0920

Wi = 73.5428 91.2500 105.8576 115.2813

>>Ti=2*pi()./Wi 0.4865 0.1701 0.1120

Ti = 0.0854 0.0689 0.0594 0.0545

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CALCULO DE LOS MODOS DE VIBRACION NORMALIZADOS

1.000 1.000 1.000 1.000

1.983 1.636 1.120 0.464

2.872 1.637 0.237 -0.786

v1= 3.625 v2= 1.002 v3= -0.858 v4= -0.826

4.205 -0.022 -1.185 0.406

4.585 -1.038 -0.450 1.013

4.908 -2.258 1.817 -0.886

1.000 1.000 1.000

-0.381 -1.215 -1.819

-0.859 0.447 2.245

v5= 0.700 v6= 0.683 v7= -2.186

0.599 -1.260 1.654

-0.922 0.817 -0.765

0.402 -0.238 0.182

MATRIZ DE MODOS DE VIBRACION NORMALIZADOS

1.000 1.000 1.000 1.000 1.000 1.000 1.000

1.983 1.636 1.120 0.464 -0.381 -1.215 -1.819

2.872 1.637 0.237 -0.786 -0.859 0.447 2.245

ø = 3.625 1.002 -0.858 -0.826 0.700 0.683 -2.186

4.205 -0.022 -1.185 0.406 0.599 -1.260 1.654

4.585 -1.038 -0.450 1.013 -0.922 0.817 -0.765

4.908 -2.258 1.817 -0.886 0.402 -0.238 0.182

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CALCULO DE Me y Ke

>> Me=øT*M*ø

92.5288 -0.0044 -0.0028 -0.0024 0.0039 -0.0011 0.0068 -0.0044 13.5830 0.0035 0.0008 -0.0013 0.0016 -0.0035 -0.0028 0.0035 7.8866 -0.0030 0.0029 -0.0001 0.0040

Me= -0.0024 0.0008 -0.0030 4.8283 -0.0022 0.0022 -0.0016 0.0039 -0.0013 0.0029 -0.0022 4.1952 -0.0002 -0.0008 -0.0011 0.0016 -0.0001 0.0022 -0.0002 6.1641 -0.0012 0.0068 -0.0035 0.0040 -0.0016 -0.0008 -0.0012 19.7628

>>Ke= øT *K* ø

0.1543 0.0001 -0.0001 0.0000 0.0000 0.0000 -0.0001 0.0001 0.1852 0.0001 -0.0000 0.0000 0.0000 0.0001 -0.0001 0.0001 0.2481 -0.0001 0.0001 0.0000 0.0000

Ke = 10^5* 0.0000 -0.0000 -0.0001 0.2611 -0.0001 0.0002 -0.0000 0.0000 0.0000 0.0001 -0.0001 0.3493 -0.0000 -0.0002 0.0000 0.0000 0.0000 0.0002 -0.0000 0.6907 -0.0001 -0.0001 0.0001 0.0000 -0.0000 -0.0002 -0.0001 2.6264

CALCULO DEL VECTOR DE MASAS PARTICIPANTES Li= øT *M* I

>> Li=fi'*M*I

24.5424 2.9991 1.3018

Li = 0.7563 0.4924 0.3653 0.3096

1 1 1

I = 1 1 1 1

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CALCULO DE MASAS EFECTIVAS ¿i=Li2

Mei

>> LL=[Li Li Li Li Li Li Li]

24.5424 24.5424 24.5424 24.5424 24.5424 24.5424 24.5424 2.9991 2.9991 2.9991 2.9991 2.9991 2.9991 2.9991 1.3018 1.3018 1.3018 1.3018 1.3018 1.3018 1.3018

LL = 0.7563 0.7563 0.7563 0.7563 0.7563 0.7563 0.7563 0.4924 0.4924 0.4924 0.4924 0.4924 0.4924 0.4924 0.3653 0.3653 0.3653 0.3653 0.3653 0.3653 0.3653 0.3096 0.3096 0.3096 0.3096 0.3096 0.3096 0.3096

>> Li2=¿LL.^2

602.3304 602.3304 602.3304 602.3304 602.3304 602.3304 602.3304 8.9948 8.9948 8.9948 8.9948 8.9948 8.9948 8.9948 1.6946 1.6946 1.6946 1.6946 1.6946 1.6946 1.6946

Li2=¿ 0.5720 0.5720 0.5720 0.5720 0.5720 0.5720 0.5720

0.2424 0.2424 0.2424 0.2424 0.2424 0.2424 0.2424 0.1335 0.1335 0.1335 0.1335 0.1335 0.1335 0.1335 0.0958 0.0958 0.0958 0.0958 0.0958 0.0958 0.0958

>> Led=Li2/Me

6.5102 44.3293 76.3368 124.8221 143.6040 97.6731 30.4900 0.0972 0.6620 1.1400 1.8640 2.1445 1.4586 0.4553 0.0183 0.1247 0.2148 0.3512 0.4040 0.2748 0.0858

Led = 0.0062 0.0421 0.0725 0.1185 0.1364 0.0928 0.0290 0.0026 0.0178 0.0307 0.0502 0.0578 0.0393 0.0123 0.0014 0.0098 0.0169 0.0277 0.0318 0.0216 0.0068 0.0010 0.0071 0.0121 0.0199 0.0228 0.0155 0.0049

Page 25: Analisis Sismico Por Superposicion Modal (1)

>> Lei=diag(Led)

6.5102 0.6620 0.2148

Lei = 0.1185 0.0578 0.0216 0.0049

Masa total efectiva: MasaTotal=∑i

7 ¿iM i

>> Mtotal =sum(Lei)Mtotal = 7.59

FACTOR DE PARTICIPACION MODAL FPM i=øT . M . IøT∗Mø

=LiMei

>> FPM=LL/Me

0.2653 1.8062 3.1104 5.0860 5.8513 3.9798 1.2423 0.0324 0.2207 0.3801 0.6215 0.7150 0.4863 0.1518 0.0141 0.0958 0.1650 0.2698 0.3104 0.2111 0.0659

FPMi = 0.0082 0.0557 0.0958 0.1567 0.1803 0.1226 0.0383 0.0053 0.0362 0.0624 0.1020 0.1174 0.0798 0.0249 0.0039 0.0269 0.0463 0.0757 0.0871 0.0592 0.0185 0.0033 0.0228 0.0392 0.0641 0.0738 0.0502 0.0157

>> i = diag(FPM)

0.2653 0.2207 0.1650

i = 0.1567 0.1174 0.0592 0.0157

Page 26: Analisis Sismico Por Superposicion Modal (1)

Sumatoria de participación de modos: ∑i

7

i=1

>> sum(i) ans = 1 (Ok)

FACTOR DE PARTICIPACION DE MASAS Pi=

[ Li2Mi]

Mtotal

x100

>> Pi=Lei/sum(Lei)*100

85.7760 8.7220 2.8296

Pi = 1.5617 0.7616 0.2852 0.0639

Sumatoria de participación efectiva de masas: ∑i

7

Pi=100

>> sum(Pi)

ans = 100.00 (Ok)

Page 27: Analisis Sismico Por Superposicion Modal (1)

CALCULO DE DESPLAZAMIENTOS MAXIMOS

Sd=Sv❑= Sv❑2

1er Modo

>> 1=fi(:,1)

1.0000 1.9830 2.8720

1 = 3.6250 4.2050 4.5850 4.9080

i(1,1) = 12.9146Ti(1,1) = 0.2653i (1,1) = 0.2615

Del espectro Sa1=224.00

>> Sd1=Sa1/i(1,1)^2

Sd1 = 1.3430

>>Umax1=1*Sd1*i (1,1)

0.3513 0.6965 1.0088

Umax1 = 1.2733 1.4770 1.6105 1.7240

Page 28: Analisis Sismico Por Superposicion Modal (1)

2do Modo>> 2=fi(:,2)

1.0000 1.6360 1.6370

2 = 1.0020 -0.0220 -1.0380 -2.2580

i(2,1) = 36.9296Ti(2,1) = 0.2207i (2,1) = 0.2203 Del espectro Sa2=224.00

>> Sd2 = Sa2/i(2,1)^2

Sd2 = 0.1642

>>Umax2=2*Sd1*i (2,1)

0.0362 0.0592 0.0592

Umax2 = 0.0362 -0.0008 -0.0376 -0.0817

Page 29: Analisis Sismico Por Superposicion Modal (1)

3er Modo>> 3=fi(:,3)

1.0000 1.1200 0.2370

3 = -0.8580 -1.1850 -0.4500 1.8170

i(3,1) = 56.0920Ti(3,1) = 0.1650i (3,1) = 0.1648

Del espectro Sa3=224.00

>> Sd3 = Sa3/i(3,1)^2

Sd3 = 0.0712

>>Umax3=3*Sd3*i (3,1)

0.0117 0.0131 0.0028

Umax3 = -0.0101 -0.0139 -0.0053 0.0213

Page 30: Analisis Sismico Por Superposicion Modal (1)

4to Modo>> 4=fi(:,4)

1.0000 0.4640 -0.7860

4 = 0.8260 0.4060 1.0130 -0.8860

i(4,1) = 73.5428Ti(4,1) = 0.1567i (4,1) = 0.1575

Del espectro Sa4=224.00

>> Sd4 = Sa4/i(4,1)^2

Sd4 = 0.0414

>>Umax4=4*Sd4*i (4,1)

0.0065 0.0030 -0.0051

Umax4 = -0.0054 0.0026 0.0066 -0.0058

Page 31: Analisis Sismico Por Superposicion Modal (1)

5to Modo>> 5=fi(:,5)

1.0000 -0.3810 -0.8590

5 = 0.7000 0.5990 -0.9220 0.4020

i(5,1) = 91.2500Ti(5,1) = 0.1174i (5,1) = 0.1189

Del espectro Sa5=224.00

>> Sd5 = Sa5/i(5,1)^2

Sd5 = 0.0269 >>Umax5=5*Sd5*i (5,1)

0.0032 -0.0012 -0.0027

Umax5 = 0.0022 0.0019 -0.0029 0.0013

Page 32: Analisis Sismico Por Superposicion Modal (1)

6to Modo>> 6=fi(:,6)

1.0000 -1.2150 0.4470

6 = 0.6830 -1.2600 0.8170 -0.2380

i(6,1) = 105.8576Ti(6,1) = 0.0592i (6,1) = 0.0610

Del espectro Sa6=224.00

>> Sd6 = Sa6/i(6,1)^2

Sd6 = 0.0200 >>Umax6=6*Sd6*i (6,1)

0.0012 -0.0015 0.0005

Umax6 = 0.0008 -0.0015 0.0010 -0.0003

7mo Modo>> 7=fi(:,7)

Page 33: Analisis Sismico Por Superposicion Modal (1)

1.0000 -1.8190 2.2450

7 = -2.1860 1.6540 -0.7650 0.1820

i(7,1) = 115.2813Ti(7,1) = 0.0157i (7,1) = 0.0161

Del espectro Sa7=224.0

>> Sd7 = Sa7/i(7,1)^2

Sd7 = 0.0169

>>Umax7=7*Sd7*i (7,1)

0.2706 -0.4923 0.6076

Umax7 = 10^-3* -0.5916 0.4476 -0.2070 0.0493

Page 34: Analisis Sismico Por Superposicion Modal (1)

COMBINACION POR SUPERPOSICION MODAL

U1 Sumatoria de Valores Absolutos (ABS)>>U1=[abs(Umax1)+abs(Umax2)+abs(Umax3)+abs(Umax4)+abs(Umax5)+abs(Umax6)+abs(Umax7)]

0.4104 0.7751 1.0798

U1 = 1.3287 1.4983 1.6641 1.8344

U2 raíz cuadrada de la suma de los cuadrados (RCSC)>> U2=[sqrt(Umax1.^2+Umax2.^2+Umax3.^2+Umax4.^2+Umax5.^2+Umax6.^2+Umax7.^2)]

0.3534 0.6992 1.0106

U2 = 1.2739 1.4771 1.6110 1.7260

NORMA NTE-030: 025ABS+0.75SRSS>> Umax=[0.25*U1+0.75*U2]

0.3676 0.7182 1.0279

Umax= 1.2876 1.4824 1.6243 1.7531

Page 35: Analisis Sismico Por Superposicion Modal (1)

i

DISTORSION DE ENTREPISO

>> Δi=Umax/100

0.0037 0.0072 0.0103

Δi= 0.0129

0.0148 0.0162 0.0175

0.0013 0.0014 0.0019

i= 0.0026

0.0031 0.0035 0.0037

Cumplen todas las distorsiones (i )son menores a 0.07 (Pórtico de concreto)

Page 36: Analisis Sismico Por Superposicion Modal (1)

V2=1

391

V1=1

505

V5=7

73

V4=1

031

V3=1

229

V7=2

57

V6=5

63

CALCULO DE CORTANTE DE ENTREPISO

>> k1=409445; k2=396887; k3=396887; k4=396887; k5=396887; k6=396887; k7=199256;

>> V1=k1*Deltas(1,1)V1 = 1505.25

>> V2=k2*(Deltas(2,1)-Deltas(1,1))V2 = 1391.19

>> V3=k3*(Deltas(3,1)-Deltas(2,1))V3 = 1229.26

>> V4=k4*(Deltas(4,1)-Deltas(3,1))V4 = 1030.67

>> V5=k5*(Deltas(5,1)-Deltas(4,1))V5 = 773.23

>> V6=k6*(Deltas(6,1)-Deltas(5,1))V6 = 563.02

>> V7=k7*(Deltas(7,1)-Deltas(6,1))V7 = 256.78

Page 37: Analisis Sismico Por Superposicion Modal (1)

FUERZAS SISMICAS DEL ANALISIS DINAMICO Y-Y

>> F1=V1-V2F1 = 114.07

>>F2=V2-V3F2 = 161.93

>> F3=V3-V4F3 = 198.59

>> F4=V4-V5F4 = 257.44

>> F5=V5-V6F5 = 210.21

>> F6=V6-V7F6 = 306.24

>> F7=V7F7 = 256.78

>> F1+F2+F3+F4+F5+F6+F7

∑i

7

Fi=1505 .25

Page 38: Analisis Sismico Por Superposicion Modal (1)

FUERZAS SISMICAS DEL ANALISIS DINAMICO Y-Y(METODO ALTERNO)

>> Fd=K*Umax/100

114.07 161.93 198.59

Fd = 257.44 210.21 306.24 256.78

>> sum(Fd) ans = 1505.25

∑i

7

Fdi=1505 .25