r - The Hong Kong Polytechnic University

Ductility factor μ
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Averge ductility factor
6-storey RC frame
PGA=0.75g
0.0
0 2 4 6 8 10 12 14 16 18 20
Serial number of artifically number
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
7-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
7.0
6.5
6.0
5.5
5.0
8-storey RC frame
PGA=0.75g
Average ductility factor
4.5
4.0
3.5
3.0
2.5
2.0
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
0.0
Average ductility factor
9-storey RC frame
PGA=0.75g
0 2 4 6 8 10 12 14 16 18 20
Serial number of artificially waves
Figure 10 Ductility levels of RC frames during inelastic dynamic time-history analysis
In Figure 10 we could see that when the RC frames are getting taller, the results of time-history analysis are
getting more scattered. In the 4-storey RC frame case that most ductility factors μ fall into the region between
3.0 and 3.5 which is exactly the same with the results of DBELA using the equivalent stiffness method. In the
5-storey RC frame case about half of the μ fall in the 3.0~3.5 region level, the average ductility level is a little
lower than 3.0, which is, though, disagree with either of the method, however is much closer with the result of
equivalent stiffness adopted method. The average ductility factors in the 6-storey frame case is exactly the same
with the results obtained from the equivalent stiffness method and result of the 7-storey is much close to the
results of equivalent stiffness method which condition is the much same with in the 5-storey frame case. Both of
the two methods give the same loss assessment outcome (ductility factor from 3.5 to 4.0) to an 8-storey RC
frame, and the average ductility factor is, the same with the 5 and 7-storey situation, a little lower than the
DBELA’s result level. The analysis result of 9-storey frame shows that the equivalent stiffness adopted method
give a more reasonable loss assessment outcome.
From the figure and augments above, we could say that, during the post-yield limit states, DBELA using a
secant stiffness equivalent linearization method gives a rather conservative loss assessment. And an equivalent
stiffness method gives a more reasonable loss assessment outcome than that using the secant stiffness. Even
though in some cases, such as 5- and 7-storey RC frame, the loss assessment result using equivalent stiffness
method are kind of little conservative due to the random character of the seismic wave , the frames’ geometrical
and material properties. DBELA gives sound loss assessment result in the post-yield limit states when the
equivalent stiffness linearization is adopted.
CONCLUSION
DBELA is a simplified method to carry out the earthquake loss assessment in an urban scale. The results are
checked by a series of time-history analysis, and DBELA gives sound assessment results during the yield limit
state. Since a secant stiffness methodology is adopted in the equivalent linearization procedure, DBELA gives
conservative results in the post-yield limits states. However, an equivalent stiffness method is chosen to replace
the secant stiffness method. Corresponding inelastic dynamic time-history analyses are also carried out to judge
the accuracy of DBELA using the equivalent stiffness method. Though there is a little offset of the results in
some cases due to the random character of the seismic wave and the frames’ geometrical and material properties,
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