Slide TSP302 DinamikaStr PengRekGempa TSP 302 P11

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Mata Kuliah
Kode
SKS

: Dinamika Struktur & Pengantar Rekayasa Kegempaan
: TSP – 302
: 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 :
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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 qn  nug t 

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

qn 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 :

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(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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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 :

1.
Equations for the floor
displacement and the story
shears for the shear frame in
figure subjected to ground
motion üg(t)
2.
Plot the time history of the
floor displacement if the shear
frame subjected to El Centro
1940 N-S Ground Motion

4,5 m

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