Civil Engineering Reference
In-Depth Information
Table 21.5
Mean annual rate of exceeding different damage states
Mean annual rate of
exceeding the damage
state
Probability of exceeding the
damage state in 50 years
Damage
state
Using Eq.
[21.9]
Using Eq.
[21.10]
Using Eq. [21.9]
and Eq. [21.11]
Using Eq. [21.10]
and Eq. [21.11]
Yielding
1.40E−03
1.42E−03
6.77%
6.84%
Serviceability
1.01E−03
1.01E−03
4.93%
4.93%
Bar-buckling
9.79E−05
9.28E−05
0.49%
0.46%
Collapse
6.84E−05
6.96E−05
0.34%
0.35%
(
)
=−
(
)
P
exceeding the damage state in
T
years
1
exp
−
λ
⋅
T
[21.11]
DS
The mean annual rate of exceedance, along with the total probability of
failure in 50 years, are presented for different damage states in Table 21.5
using the integration of the fragility and hazard curves (Eq. [21.8]) and also
using the simplifi ed equation (Eq. [21.10]). The predictions using the two
equations are very close and therefore Eq. [21.10] can be used with suffi -
cient accuracy to estimate the mean annual rate of failure.
21.8 Conclusions and future trends
The application of the IDA method for assessing the seismic performance
and risk of bridges was presented. The IDA method is analytically intensive,
requiring many nonlinear analyses and currently is not widely used in prac-
tice. However, it is possible to develop IDA algorithms that can signifi cantly
reduce the computation time enabling the derivation of the key information
required to assess the seismic performance and risk. With the availability
of powerful computers, it is possible to perform a large volume of analyses
in a short amount of time. This makes the applicability of IDA more promis-
ing. The application of the IDA method enables a more thorough and
systematic assessment of the seismic performance of structures, taking into
account different sources of variability and assessing the performance for
a wide range of possible ground motion records with different frequency
contents and for different levels of seismic intensity. This makes the results
from the IDA method an invaluable tool for seismic risk assessments. It is
possible to enhance the IDA method by improving the scaling procedures
(e.g., by means of incorporating natural or simulated records corresponding
to different hazard levels rather than scaling a fi xed record) and by incor-
porating the important aspects of spectral shape, higher mode effects and
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