Slide CIV 308 DinamikaStr PengRekGempa CIV 308 P11

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Mata Kuliah
Kode
SKS

: Dinamika Struktur & Pengantar Rekayasa Kegempaan
: CIV - 308
: 3 SKS

Earthquake Analysis of Linear MDoF System
Pertemuan – 11

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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
gempa bumi

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Sub Pokok Bahasan :
 Persamaan Gerak Sistem MDoF Akibat Beban Gempa Bumi
 Analisis Riwayat Waktu
 Analisis Spektrum Respon

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Equation of Motion

mu  c u  k u  m1u t 

With

1
1
1  1

1

Introducing the modal analysis equation ,

u  f q
 and pre-multiply with [f]T

g

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f  mf q  f  c f q  f  k f q  f  m1u t 
T

T

T

T

g

Mn
Mn
Cn

Kn
Ln

Cn

Kn

= Generalized Mass
= Generalized Damping
= Generalized Stiffness
= Earthquake Excitation Factor



Ln
 Modal Participation Factor
Mn

Ln
 effective modal mass

Mn
2

Ln

(1)

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qn  2 nn qn  n q n  n ug t 

Dividing Eq.(1) by Mn, gives :
2

q n t   n Dn t 

(3)

Dn  2 nn D n  n 2 Dn  ug t 

(4)

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Let

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Eq. (2) becomes :



(2)

The qn(t) is readily available once Eq.(4) has been solved for
Dn(t), utilizing numerical time stepping methods for SDF
systems.

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u t   f q t    f D t 

Response History Analysis

 f n t   n mfn An t 
n

n

n

n

n

n

(5)

(6)

Response Spectrum Analysis

u jn  nf jn Dn

f jn  n m jf jn An

(7)
(8)

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BS Response from each mode can be
combine using either SRSS

Vb  





n

1


2
Vbn



1/ 2

or CQC Method



N
Vb  
 i 1


 i ,n .Vb ,i .Vb ,n 

n 1
N

1/ 2

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W2 = 24.000 kgf
W10x21

W10x21

f   ff11

21

 2  38,28

3m

u1
W10x45

1  10,76


u2

W1 = 11.600 kgf

W10x45

Example 1
 Determine maximum Base Shear
due to El Centro Acc.
 Use Respon Spectrum Method
 Use SRSS Method to combine BS
from each mode

4,5 m

f12  0,6809  3,0385

1 
f22   1

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f11 f12 f13  0 ,5546  1,004 5,3431 
f   f21 f22 f23   0,8526  0,662  2,6574
f
 
1
1 
 31 f32 f33   1

W10x21

W10x21

W10x21

3  39,53

W2 = 24.000 kgf

u3
3m

3m

u2

W1 = 11.600 kgf

u1
W10x45

 2  26,65

W10x21

1  7,934

W3 = 20.000 kgf

W10x45

Tugas 8
 Determine maximum Base Shear
due to El Centro Acc.
 Use Respon Spectrum Method
 Use SRSS Method to combine BS
from each mode

4,5 m