r - The Hong Kong Polytechnic University

Displacement (cm)
70
60
50
40
30
20
10
μ=3.5
PGA=0.75g
T=2.87s
H=19.07m
T=4.08s
H=27.11m
Capacity displacement
Demand displacement
Displacement (cm)
70
60
50
40
30
20
10
μ=4
PGA=0.75g
Capacity displacement
Demand displacement
0
0 1 2 3 4 5 6
Period (seconds)
0
0 1 2 3 4 5 6
Period (seconds)
Figure 9 Results of DBELA using equivalent stiffness method (STDG)
However, we should notice that the equivalent viscous damping ratio used in the secant stiffness procedure is
deduced from a TF hysteretic model, but the latter procedure adopts a bilinear STDG model. That’s because
solving the equivalent linear parameters is quite a complex and time-consuming procedure, even when a new
statistical approach utilizing the technique of particle swarm optimization (PSO) is developed to determine the
parameters of equivalent linearization method, very limited hysteretic models are available. Since the TT, STDG
and PB hysteretic model have their area of complete cycle of stabilized force-displacement responses not differ
much with each other. Actually they give much close outcomes which again prove that DBELA is not so
sensitive to hysteretic models mentioned herein.
Then the two kinds of loss assessment results using the secant and equivalent stiffness linearization method are
compared together, and obliviously they give much different results and a simple comparison showed in Table 3.
The results then will be checked by a group of inelastic dynamic time-history analysis the same as in the yield
limit state.
Table 3 Comparison of the DBELA results between using the secant and equivalent stiffness methodology
Number of floors 4 5 6 7 8 9
Total height 12m 15m 18m 21m 24m 27m
Result of DBELA Secant stiffness 4~4.5 >5 4.5~5 4~4.5 3.5~4 3.5~4
( μ ) Equivalent stiffness 3~3.5 3~3.5 3~3.5 3.5~4 3.5~4 3~3.5
Ductility factor μ
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Average ducitility factor
4-storey RC frame
PGA=0.75g
0.0
0 2 4 6 8 10 12 14 16 18 20
Serial number of artificially waves
Ductility factor μ
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Average ductility factor
5-storey RC frame
PGA=0.75g
0.0
0 2 4 6 8 10 12 14 16 18 20
Serial number of artificially waves
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