Civil Engineering Reference
In-Depth Information
1
30
0.8
1994 Northridge earthquake
20
0.6
0.4
10
0.2
0
0
-0.2
-10
-0.4
-0.6
-20
-0.8
-1
-30
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
200
1
0.8
150
0.6
100
0.4
50
0.2
0
0
-0.2
-50
-0.4
-100
-0.6
-150
-0.8
-200
-1
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
Figure 3.3
Response of a SDOF system with period of 1.0 s due to 1994 Northridge earthquake.
,
H
d
=
0
:
999124 0
:
009976
−0
:
17504 0
:
994945
−0
:
000100
−0
:
009949
F
d
=
ð3
:
37Þ
The recursive equation as given in Eq. (3.21) becomes
=
x
k
x
k
+
a
k
x
k
+1
x
k
+1
0
:
999124 0
:
009976
−0
:
17504 0
:
994945
−0
:
000100
−0
:
009949
ð3
:
38Þ
and Eq. (3.32) gives the calculation of the absolute acceleration response.
By subjecting the SDOF system to the 1940 El-Centro earthquake record as shown in
Figure 3.4, with the initial displacement and velocity both set equal to zero (i.e.
x
0
=
x
0
= 0),
it follows that the displacement, velocity, and absolute acceleration response histories can
be evaluated and the results are presented in Figure 3.4.
3.2 Dynamic Analysis with Material Nonlinearity
3.2.1 Force Analogy Method
Changing the displacement, not the stiffness, to capture the yielding force is the basic concept
of the FAM and was presented in detail for static analysis in Chapter 2. The details of the
method are briefly summarized here with the representation of the equations in time domain
for dynamic analysis.
