Civil Engineering Reference
In-Depth Information
5.5.3 Force Analogy Method for Dynamical CBFs under
Earthquake Loads
Example 5.6 Seismic dynamical analysis for a one-bay one-story CBF
Consider the same illustration presented in Section 5.5.1, but the only difference is that the
SDOF CBF is subjected to ground acceleration
x
g
ðÞ, as shown in Figure 5.23 and the governing
equation of motion:
Mx
ðÞ+
C
_
x
ðÞ+
F
ðÞ= −
Mx
g
ðÞ
ð5
:
84Þ
where
_
x
ðÞand
x
ðÞrepresent the velocity and acceleration of the system, respectively,
m
is the
system mass, and
c
is the viscous damping coefficient. Let's discuss how to solve the response
of the system under the ground motion using the FAM.
Solution
By performing static condensation using Eqs. (5.57), (5.58) and (5.59), there are
3
2
2
2
24
EI
/
L
+
EA
cos
β
/
l
6
EI
/
L
6
EI
/
L
c
c b b
c
c
c
c
KK
KK
dd
dr
2
2
=
6/
EI L
4/ 4/
EI L
+
EI
L
2/
EI
L
cc
cc bb
bb
rd
rr
2
2
6/
EI L
2/
EI
L
4/ 4/
EI L
+
EI L
cc
bb
cc bb
ð5
:
85Þ
2
2
2
2
2
6/ 6/ 6/ 6/ 0 0 s
EI L
EI L
EI L
EI L
EA
β
/
l
cc cc cc cc
b b
K
K
′
d
2
2
2
2
=
2/ 4/ 0 0 4/ 2/
EI L
EI L
EI L
EI
L
0
cc cc
bb bb
′
r
2
2
2
2
0 0 2/ 4/ 2/ 4/
EI L
EI L
EI L
EI L
0
cc cc bb bb
ð5
:
86Þ
x
3
#5
E, I
b
, L
b
3
#6
x
2
x
1
#2
#4
2
1
E, I
c
, L
c
E, I
c
, L
c
#7
E, A, l
b
β
PHL
#1
#3
x
g
Figure 5.23
One-bay one-story model under earthquakes.
