Slide TSP302 DinamikaStr PengRekGempa TSP 302 P4

(1)

a home base to excellence

Pertemuan - 4

Single Degree of Freedom System

Arbitrary Force

Mata Kuliah : Dinamika Struktur & Pengantar Rekayasa Kegempaan Kode : TSP – 302

(2)

 TIU :

 Mahasiswa dapat menjelaskan tentang teori dinamika struktur.

 Mahasiswa dapat membuat model matematik dari masalah teknis yang ada serta mencari solusinya.

 TIK :

(3)

 Sub Pokok Bahasan :

(4)

Duhamel’s Integral – Undamped System

 An impulsive loading is a load which is applied during a short

duration of time.

 The corresponding impulse of this type of load is defined as

the product of the force and the time of its duration.

F(

t

)

∙

d

t

t + dt F(t)

t

Using Duhamel’s Integral, the

displacement response at time t due to continuous F(t) is :

  _     

t

n n

d t

sin F

m t

u

0

1

t t 

t

(5)

SDoF System Without Damping

        _

SDoF System With Damping

(6)

 Response to Step Force With Finite Rise Time

(7)

 Response to Rectangular Pulse Force

(8)

Response to Rectangular Pulse Force

 _{The maximum deformation is :}

 With deformation response factor :

 The maximum value of the equivalent static force is :

(9)

Exercise

 A one-story, idealized as a 3,6 m high frame

with two columns hinged at the base and a rigid beam, has a natural period of 0,5 sec. Each column is a wide-flange steel section W8x18. Its properties for bending about its major axis are I_x = 2,570 cm4_{, S = I}

x/c = 249

cm3_{; E = 200 GPa. Neglecting damping,}

(10)

Response to Half Cycle Sine Pulse Force

(11)

 For t_d/T_n = ½

 

   _  _

n n

n o

st T

t cos T

t T

t sin u

t

u 2 2 2 2

1

For t < t_d

For t > t_d

 

   _  ₂_

1 2

2

n o

st T

t cos

u t

(12)

Response to Symmetrical Triangular Pulse Force

p(t)

u(t)

m

k

p(t)

p_o

t