Civil Engineering Reference
In-Depth Information
Example 4.7 Nonlinear Static Analysis of the One-Story One-Bay RC Frame
Consider a one-story one-bay RC frame with flexural members as shown in Figure 4.11. The
columns of the RC frame are constructed with the SDOF flexural member shown in
Example 4.3, and the sectional parameters are illustrated in Figure 4.9(b). Therefore, the beha-
viors of hinges #1, #2, #3, #4, #7, and #8 can be obtained from Tables 4.1 and 4.2. With the
same materials and strengths of the concrete and reinforcement, the beam with the sectional
parameters are shown in Figure 4.11, and the parameters of the bending primary curve of
the beam are listed in Table 4.3. Let the length of the beam
L
b
=
L
c
= 3 m. Assume that only
a lateral force
F
1
= 150 kN is applied at the horizontal degree of freedom
x
1
, and external
moments
F
2
=
F
3
=0.
First, the global stiffness matrices
K
,
K
0
, and
K
00
should be assembled according to the pro-
cedure presented in Example 4.6 and are written as follows:
2
4
3
5
x
1
127812
−95859
−95859
kN
=
m
ð4
:
74Þ
K
=
−95859 238544
21333
x
2
x
3
ð
Þ
−95859
21333 238544
2
4
3
5
−
95859
−
95859
−
95859
−
95859
0
0
63906
63906
x
1
x
2
K
0
=
91705
195872
0
0
42667 21333
−95859
0
ð
kN
=
rad
Þ
0
0
91705
195872 21333 42667
0
−
95859
x
3
ð4
:
75Þ
200
8D16
x
2
x
3
#5
D8@200
#6
L
b
F
1
3
x
1
#2
#4
L
c
L
c
#7
#8
1
2
#1
#3
Figure 4.11
The one-story one-bay RC frame.
Table 4.3
The parameters of the bending primary curve.
m
cr
(kN-m)
θ
cr
(rad)
m
y
(kN-m)
θ
y
(rad)
θ
u
(rad)
θ
f
(rad)
21
0.000166
100
0.00129
0.00335
0.011
