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population count and shaking estimate form the key input for damage and
loss analyses for both the semi-empirical and analytical models. The popula-
tion exposure, inventory and vulnerability data are used to estimate total
casualties and thus account for spatially varying shaking intensity and expo-
sure at different grid cells as discussed in Jaiswal and Wald (2010).
31.4.3 Analytical model
In the analytical approach, the same building inventory and occupancy-
related databases derived for the semi-empirical approach are used;
however, the structural collapse rates are determined from the Hazus the
capacity-spectrum methodology which estimates the response of a structure
from spectrum demand and spectral-capacity curves (NIBS-FEMA, 2009).
In principle, the demand spectrum represents the site-adjusted input ground
motion, typically accounting for nonlinear structural behavior and hyster-
etic energy dissipation, whereas the spectral capacity of a structure is
expressed in terms of an idealized curvilinear graph defi ned by its yield and
ultimate control points. The capacity-spectrum method provides an esti-
mate of median response of an idealized nonlinear single degree of freedom
(SDOF) oscillator where the spectral-capacity and demand curves intersect.
This point is referred to as the performance point. The spectral displace-
ment
S
d
associated with the performance point forms an input to fragility
functions that give the probability of different damage states.
The damage and casualties associated with slight, moderate, and exten-
sive damage states are ignored for PAGER purposes since they form a very
small fraction of total fatalities. Porter (2009) simplifi es the iterative process
for PAGER and directly tabulates the mean-collapse fragilities and indoor
fatality rates as a function of 5% damped spectral accelerations at either
0.3 s or 1.0 s periods. The fatality rates given structural collapse are the same
as in the semi-empirical approach. The mean-collapse fragilities are derived
primarily for Hazus model building types (MBTs) using the Hazus capacity
and fragility parameters. For non-US building types, the basic MBTs were
mapped to PAGER-STR types (see Jaiswal and Wald, 2008, for details)
using a preliminary mapping scheme. In general, the structural capacities
are quite different between the basic MBTs and corresponding PAGER-
STR as discussed in D'Ayala
et al.
(2010).
In order to understand and evaluate the differences between structural
capacity and fragility parameters and to propose procedures for estimating
collapse vulnerability of non-US building types, a parallel effort is under-
way under the auspices of the WHE (World Housing Encyclopedia)-
PAGER Project. Preliminary analyses suggest that there could be signifi cant
differences in estimated structural capacities of reinforced concrete types
depending upon the modelling assumption or methodology adopted for
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