Civil Engineering Reference
In-Depth Information
2
4
3
5
0
:
984883
0
:
006568
0
:
009900 0
:
000038
0
:
006568
0
:
994998
0
:
000038 0
:
009958
F
d
=
ð3
:
152aÞ
−3
:
00868
1
:
30649
0
:
975012 0
:
009671
1
:
30649
−0
:
996660 0
:
009671 0
:
989906
2
4
3
5
2
4
3
5
−0
:
000099
−0
:
000100
−0
:
009847
−0
:
009996
0
:
030087
−0
:
013065
−0
:
013065
0
:
009967
ð3
:
152bÞ
H
d
=
,
G
d
=
2
:
95525
−1
:
28072
−1
:
28072
0
:
998293
Therefore, using on the matrices presented in Eq. (3.152), Eq. (3.137) becomes
<
=
<
=
x
1
x
2
x
1
x
2
x
1
x
2
x
1
x
2
x
0
1
x
0
2
=
F
d
+
H
d
a
k
+
G
d
ð3
:
153Þ
:
;
k
+1
:
;
k
k
Assume that the plastic hinges exhibit elastic-plastic behavior with moment capacities of
m
b
= 15.0 kN m for the two beams and
m
c
= 20.0 kN m for the four columns. This gives
Δθ
0
i
=0
m
i
=20
:
0
m
i
≤ 20
:
0
m
i
>20
:
0
,
if
then
i
=1,…, 8
ð3
:
154aÞ
Δθ
0
i
=0
m
i
=15
:
0
m
i
≤ 15
:
0
m
i
>15
:
0
,
if
then
i
=9,…, 12
ð3
:
154bÞ
and Eqs. (3.134b) and (3.134c) become
<
=
<
=
<
=
<
=
Δθ
0
1
Δθ
0
2
.
Δθ
0
12
θ
0
1
θ
0
2
.
θ
0
12
θ
0
1
θ
0
2
.
θ
0
12
m
1
m
2
.
m
12
k
−
K
00
x
0
1
x
0
2
x
1
x
2
=
K
0
T
+
K
00
=
K
−1
K
0
,
ð3
:
155Þ
:
;
k
+1
:
;
:
;
k
:
;
k
k
Consider now the two-story moment-resisting frame is subjected to the 1994 Northridge
earthquake ground motion as shown in Figure 3.3. The nonlinear dynamic responses are
calculated using Eqs. (3.153) and (3.155), and the displacement, velocity, acceleration, and
inelastic displacement responses are plotted in Figures 3.13 to 3.16, respectively.
15
30
x
1
(
t
)
x
2
(
t
)
10
20
5
10
0
0
-5
-10
-10
-20
-15
-30
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
Figure 3.13
Global displacement responses of the two-story moment-resisting frame.
