Civil Engineering Reference
In-Depth Information
Non-approved
Approved
50
NEL
PML
40
30
20
10
0
0.5
0.75
1
1. 2 5
1. 5
1. 7 5
Q
u
/
Q
un
27.11
Relationship between loss ratio and
Q
u
/
Q
un
.
the load-carrying capacity
Q
u
over the required load-carrying demand
Q
un
was varied from 0.7 to 1.5, by altering the sectional amount of reinforcement
of beams and columns. (Note that the higher ratio of
Q
u
/
Q
un
can impart
better seismic performance to a structure.) The adopted seismic risk analy-
sis procedure is similar to the previous case study discussed in Section
27.3.3.
Probabilistic seismic risk analysis was conducted for fi ve seismic design
levels (i.e. different values of
Q
u
/
Q
un
). The calculated values of NEL
475
and
PML
475
are shown in terms of
Q
u
/
Q
un
in Fig. 27.11 (note: NEL
475
and PML
475
are expressed as a fraction of the replacement cost of the building). These
results indicate that even though the loss ratio increases with the increasing
ratio of
Q
u
/
Q
un
, it becomes constant as the ratio of
Q
u
/
Q
un
becomes to be
greater than 1.0, which implies that the marginal gain due to increased
section strength becomes less as the seismic design level increases. It is also
found that the values of PML
475
are more sensitive to
Q
u
/
Q
un
in comparison
with those of NEL
475
, indicating that very low seismic design levels may
induce a disproportionate increase of the seismic loss level for rare situa-
tions. Such a tendency should be taken into account when decision making
regarding the selection of a suitable seismic design level is conducted.
27.4 Conclusions and future trends
The features in this chapter and future trends are summarized as follows:
•
Analytical formulations for the expected seismic risk, the seismic event
risk curve, the seismic risk curve, and risk indices such as NEL
and
PML,
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