Civil Engineering Reference
In-Depth Information
assessment of the structures using IDA can result in very conservative and
biased predictions.
Epsilon,
, which is computed by subtracting the mean predicted
μ
ln
S
a
(M,R,T) from the record's ln
S
a
(
T
), and dividing by the logarithmic
standard deviation (as estimated by the ground motion prediction equa-
tion). is a proxy of spectral shape (Baker and Cornell, 2006a). As the epsilon
value increases, the spectral shapes tend to be more peaked. Specifi cally,
ε
ε
at a given period
T
is given by Eq. [21.2]:
()
−
(
)
ln
ST
μ
MR,T
,
()
=
a
ln
S
ε
T
[21.2]
a
()
σ
T
ln
S
a
ln
S
a
(M,
¯
,T) and
where
ln
S
a
(
T
) are the predicted mean and standard devia-
tion, respectively, of ln
S
a
at a given period
T
and ln
S
a
(
T
) is the natural loga-
rithm of the spectral acceleration of interest. The two parameters are
obtained from ground motion prediction equations (GMPE). Rare strong
ground motions have peaked spectral shapes that can be represented by
positive epsilon values at the fundamental period,
μ
σ
(
T
1
). This peaked spec-
tral shape is very different from a typical shape of uniform hazard spectra
and accounting for this has been shown to increase the computed collapse
capacity signifi cantly. The values of spectral acceleration at the longer
periods are important, because the effective period of the structure increases
as the structure undergoes inelastic deformation. This is even more impor-
tant for modern structures that have high ductility capacities and are
designed for high inelastic demands. Similarly, the values of spectral accel-
eration at shorter periods can be important especially for structures with
signifi cant contributions of higher modes in the seismic response.
ε
21.5.2 Record selection strategies
Record selection for inelastic time history analysis is a critical issue and
many different methods have been developed and used for this purpose.
This subject is even more important for the case of IDA and collapse capac-
ity evaluation of structures (e.g., Tehrani
et al.
, 2012).
A realistic record selection strategy should take into account important
characteristics of the ground motion records which infl uence the structural
response. Such important aspects of records mainly include
M
,
R
,
, and site
conditions. Owing to the limited number of available natural records, select-
ing ground motions with similar
M
,
R
and
ε
values to match target values
obtained through seismic deaggregation is not straightforward. Usually
one or two of these parameters are chosen as key parameters for record
selection. Accordingly, different record selection methodologies may be
utilized.
ε
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