r - The Hong Kong Polytechnic University

Displacement (cm)
70
60
50
40
30
μ=4.5
PGA=0.75g
T=2.75s
H=12.96m
T=4.29s
H=20.22m
20
Capacity displacement
10
Demand displacement
0
0 1 2 3 4 5 6 7 8
Period (seconds)
Displacement (cm)
70 μ=5
60
PGA=0.75g
50
40
30
20
10
T=3.85s
H=17.22m
T=3.32s
H=14.85m
Capacity displacement
Demand displacement
0
0 1 2 3 4 5 6 7 8
Period (seconds)
Figure 8 Results of DBELA using secant stiffness method under different ductility levels
As we have already discussed, different equivalent linearization procedures can be used to generate the capacity
and demand displacement curves during the post-yield limit states. For the first, a group of DBELA procedures
using secant stiffness methodology suggested by H. Crowley and R. Pinho are carried out and the loss
assessment results with the ductility factors increasing from 3.5 to 5.0 are plotted in Figure 8.
Another DBELA procedures using equivalent stiffness linearization method are conducted with the ductility
factors varies from 2.5 to 4.0. A Stiffness Degrading Model (STDG) is chosen to represent the RC frame, and
the coefficients for equivalent linear parameters used in Equation (12)-(13) are listed in Table 2. The post-yield
stiffness ratio α is obtained from a pushover analysis in this paper, then a linear interpolation is carried out to get
the coefficients’ value. Finally, the results of DBELA which use this equivalent linearization method are plotted
in Figure 9.
Table 2 Coefficients for equivalent linear parameters for STDG, Equation (12)-(13).
α stands for post-yield stiffness ratio
α A B C D E F G H
0% 0.1916 -0.0429 0.0652 -0.0179 0.0796 0.1820 0.1000 0.0129
5% 0.1886 -0.0447 0.0654 -0.0180 0.1233 0.1502 0.1004 0.0132
10% 0.1871 -0.0470 0.0682 -0.0193 0.1577 0.1257 0.0881 0.0164
20% 0.1520 -0.0363 0.0646 -0.0180 0.1538 0.0924 0.1088 0.0075
Displacement (cm)
70
μ=2.5
PGA=0.75g
60
50
40
30
T=5.99s
H=46.77m
20
Capacity displacement
10
Demand displacement
T=0.46s
H=3.59m
0
0 1 2 3 4 5 6 7 8
Period (seconds)
Displacement (cm)
70
60
50
40
30
20
10
μ=3.0
PGA=0.75g
T=1.36s
H=9.65m
T=4.86s
H=34.46m
Capacity displacement
Demand displacement
0
0 1 2 3 4 5 6
Period (second)
-307-