Modal Espectral

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


3/25

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



4/25


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


5/25

Calculo de modos de vibracin


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


6/25

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


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


7/25

Matriz de modos de vibracinNormalizados


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


8/25

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


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


9/25

Calculo de Vector de masasparticipantes . .T L M I


I

1

1

1

1

1

LT

M IL

284.63

45.73

19.0811.83

8.31


10/25

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


Mtotal

1

5

i

Lei 1

Mtotal 105.00


11/25

Factor deParticipacinModal (FPMi)

. .. .

T

ii i T

i

L M I FPM

M


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


12/25

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


2i

i

L

M Pi

Mtotal

> 90 %


13/25

ANALISIS MODAL ESPECTRAL


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


R


14/25



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


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


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


15/25

ANALISIS MODAL ESPECTRAL2

Sv SaSd


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


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


16/25




3er Modo : 3 51.18 T 3 0.12 3 0.18


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


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


17/25




5to Modo : 5 77.57 T 5 0.08 5 0.06


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


18/25

COMBINACION PORSUPERPOSICION MODAL


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


19/25



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


20/25


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


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


21/25

Distorsin de Entrepiso



22/25

Calculo de Cortantes de Entrepiso

V1 k1 1

V2 k2 2 1 V

3k3 3 2

V4 k4 4 3 V5 k5 5 4


V1

234.93

V2

204.45

V

3

157.52

V4

110.52

V5

57.88


23/25

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


V1

5

iFi

F1

30.48

F2

46.93

F3

47.00

F4

52.64

F5

57.88

V 234.93


24/25

Fuerzas Ssmicas del Anlisis Dinmico(Mtodo Alternativo)


V1

5

iFi V 234.93

Fd KUmax

100 Fd

30.48

46.93

47.00

52.64

57.88


25/25

Preguntas .?

Documents

Modal Espectral