Slide CIV 308 DinamikaStr PengRekGempa CIV 308 P11

a home base to excellence

Pertemuan

–

11

Earthquake Analysis of Linear MDoF System

Mata Kuliah : Dinamika Struktur & Pengantar Rekayasa Kegempaan

Kode : CIV - 308

a home base to excellence



TIU :

 Mahasiswa dapat menjelaskan fenomena-fenomena dinamik secara fisik.

 Mahasiswa dapat membuat model matematik dari masalah teknis yang ada

serta mencari solusinya



TIK :

 Mahasiswa dapat menghitung respon struktur MDoF akibat beban

a home base to excellence

 Sub Pokok Bahasan :

 Persamaan Gerak Sistem MDoF Akibat Beban Gempa Bumi

 Analisis Riwayat Waktu

a home base to excellence



Equation of Motion

 With

 Introducing the modal analysis equation ,

 and pre-multiply with [f]T

 

u 

 

f

 

q

 

m

 

u







 

c

 

u





 

k

 

u





 

m

  

1

u





_g

t



     

      

1 1 1 1

1

a home base to excellence

    

f T m f

 

q 

    

f T c f

 

q 

    

f T k f

 

q  

   

f T m

  

1 u_g t

M_n C_n K_n L_n

M_n = Generalized Mass C_n = Generalized Damping K_n = Generalized Stiffness

L_n = Earthquake Excitation Factor

mass modal

effective

Factor ion

Participat Modal

2

  



n n

n n

M L

M L

a home base to excellence

 Dividing Eq.(1) by M_n, gives :

 Let

 Eq. (2) becomes :

 The q_n(t) is readily available once Eq.(4) has been solved for D_n(t), utilizing numerical time stepping methods for SDF

systems.

 

t

u

q

q

q





_n



2



_n



_n



_n





_n2 _n







_n





_g

 

t

D

 

t

q

_n





_{n n}

(2)

 

t

u

D

D

D





_n



2



_n



_n



_n





_n2 _n









_g

(3)

a home base to excellence

Response History Analysis

Response Spectrum Analysis

 

         

u

_n

t



f

_n

q

_n

t





_n

f

_n

D

_n

t

n jn n

jn

D

u





f

n jn j n

jn

m

A

f





f

 

 

f_n t





_n

 

m

   

f

_n A_n t

(5)

(6)

(7)

a home base to excellence



BS Response from each mode can be

combine using either SRSS

a home base to excellence

Example 1

 Determine maximum Base Shear

due to El Centro Acc.

 Use Respon Spectrum Method

 Use SRSS Method to combine BS

a home base to excellence

Tugas 8

 Determine maximum Base Shear

due to El Centro Acc.

 Use Respon Spectrum Method

 Use SRSS Method to combine BS