Civil Engineering Reference
In-Depth Information
Example 5.4 Nonlinear static analysis for a one-bay one-story CBF
A one-bay one-story CBF as shown in Figure 5.18 is selected to illustrate the application of the
FAM in CBF models. The columns in the frame are square steel tubes with dimensions of
250 × 250 × 6 mm and length of L
c
= 3.0 m, and the beams in the frame are square steel tubes
with dimensions of 200 × 150 × 4 mm and length of L
b
= 3.9 m. The brace is selected to the
same brace used in Example 5.1. The brace is made of square tube sections with dimensions
100 × 100 × 5 mm. The material properties for both braces and columns are
E
= 2.1 GPa and
σ
y
= 275 MPa. The CBF is subjected to a horizontal displacement of −3 mm on the roof, now solve
how much of load should be applied on the CBF.
Solution
First, stiffness matrices in the FAM are
2
4
3
5
x
1
62967286 8140000 8140000
8140000 19779000 1749500
8140000
K
=
x
2
x
3
N
=
m
ð5
:
61Þ
1749500 19779000
8140000
8140000
8140000
8140000
0
0
52114286
←
←
←
x
x
x
1
K
′ =
8140000 16280000
0
0
3498872 1749500
0
2
0
0
8140000 16280000 1749500 3498872
0
3
ð5
:
62Þ
16280000 8140000
0
0
0
0
0
←
←
←
←
←
←
←
δ″
θ
1
θ
2
θ
3
θ″
θ″
8140000 16280000
0
0
0
0
0
0
0
16280000 8140000
0
0
0
0
0
8140000 16280000
0
0
0
K
″ =
4
5
θ
6
0
0
0
0
3498872 1749500
0
0
0
0
0
1749500 498872
0
0
0
0
0
0
0
814285714
ð5
:
63Þ
100
x
3
5
#5
#6
L
b
x
2
x
1
3
100
#2
#4
5
1
2
6
L
c
L
c
#7
250
l
b
β
PHL #1
#3
Figure 5.18
one-bay one-story CBF model.
