Civil Engineering Reference
In-Depth Information
Let the mass be 218.9 Mg on each floor, giving a total mass of 2,189 Mg for the entire frame.
This gives
2
3
218
:
90
0
.
.
4
5
.
.
0
218
:
9
M
dd
= 218
:
9×
I
=
Mg
ð7
:
182Þ
.
.
.
.
.
.
.
0
218
:
9
0
0
Using the resulting condensed
K
e
stiffness matrix and the diagonal
M
dd
mass matrix, the
10 periods of vibration are calculated and summarized in Figure 7.34. The damping is assumed
to be 3% in all ten modes.
Assume that all 140 plastic hinges exhibit elastic-plastic behavior with moment capacity of
the
i
th plastic hinge,
m
c
,
i
, calculated as
m
c
,
i
=
f
y
×
Z
i
i
=1,…, 140
ð7
:
183Þ
where
f
y
is the yield stress of steel and
Z
i
is the plastic section modulus of the
i
th plastic hinge.
This gives
Δθ
0
i
ðÞ=0
m
i
ðÞ=
m
c
,
i
m
i
ðÞ≤
m
c
,
i
if
m
i
ðÞ>
m
c
,
i
,
then
i
=1,…, 140
ð7
:
184Þ
60
40
x
10
(
t
)
x
7
(
t
)
50
30
40
20
30
10
20
10
0
0
-10
-10
-20
Geo nonlinear
Geo linear
Geo nonlinear
Geo linear
-20
-30
-30
-40
-40
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
7
30
x
4
(
t
)
x
1
(
t
)
6
25
5
20
4
15
3
10
2
5
1
0
0
-5
-1
Geo nonlinear
Geo linear
Geo nonlinear
Geo linear
-10
-2
-15
-3
-20
-4
0
5
10
15
20
0
5
10
15
20
Time (s)
Time (s)
Figure 7.35
Global displacement responses of the 10-story frame with geometric nonlinearity.
