Using a performance-based earthquake engineering (PBEE) approach to estimate structural performance targets for bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 535

among the candidate IMs. According to Luco and Cornell (2007), the
desired properties of an IM include effi ciency, suffi ciency, scaling robustness ,
and feasibility . An effi cient IM is defi ned as one that results in a relatively
small variability in the structural response given the level of IM; therefore,
the variance of the PSDM is the quantitative measure of the effi ciency. An
IM is defi ned as effi cient if the variance of the PSDM is small and using an
effi cient IM will reduce the number of nonlinear dynamic analyses. A suf-
fi cient IM is defi ned as one that brings negligible conditional dependency
to the structural response from the previous chain of Equation 20.1. In
other words, if an IM is suffi cient, the EDP will be independent of the
earthquake parameters (earthquake magnitude, distance, etc.). Suffi ciency
of an IM is desirable, because it reduces the complexity in the PSDA cal-
culation as well as the record selection procedure (Luco and Cornell, 2007).
If an insuffi cient IM is used and the selected records do not represent the
hazard at the site, the performance-based seismic evaluation will be biased
(Tothong and Cornell, 2006).
Scaling robustness is used to defi ne the possibility of introducing bias to
the structural demand by scaling the time histories used in nonlinear
dynamic analyses. If an IM is robust, no statistically strong relationship
exists between the structural response and the scale factors used for the
scaling of records. Finally, feasibility of the ground motion measure should
be considered for selecting an appropriate IM. Since the annual rate of
exceeding the IM is determined by PSHA, the IM should be computable
in terms of scenario earthquake parameters. Hazard maps and hazard
curves are available or easily computable for some IMs, but other IMs
require more effort, or even structure-specifi c information for their deter-
mination. An IM with higher effi ciency may be less desirable on the basis
of feasibility (Giovenale et al. , 2004). Peak ground acceleration (PGA) and
spectral acceleration ( S a ( T 1 )) at the fundamental period ( T 1 ) of the struc-
ture are the most commonly adopted IMs in the structural engineering
applications (Shome and Cornell, 1999; Nielson and DesRoches, 2007;
Padgett et al. , 2008).
Following the selection of ground motions and IMs, sample models of the
particular class of structures are generated by varying key design parame-
ters (e.g. model dimensions, damping ratio, material strengths, etc.) within
the allowable range of code requirements. The selected and scaled time
histories are employed in nonlinear dynamic analyses of these sample
models and important response parameters are monitored throughout the
analysis. Typically, peak values of responses are recorded and plotted versus
the peak value of the IM for that ground motion for each analysis (Mackie
and Stojadinovic, 2003). The EDPs are selected among the peak values of
monitored structural response parameters; however the results of previous
analysis or experiments on that class of structures may be used as a basis