Assessing seismic risks for new and existing buildings using performance-based earthquake engineering (PBEE) methodology - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 320

analytical capability to accurately model the nonlinear dynamic response
of the structure. Figures 12.10 and 12.11 show the maximum inter-story drift
ratio and fl oor acceleration in the H1 direction obtained from the time
history analyses, respectively. The dash line represents the maximum
response obtained from each earthquake and the solid line represents the
mean of the maximum responses.

12.3.4 Results of the performance assessment

Using the procedure presented in Section 12.3.3, the performance of the
prototype model under different levels of earthquake shaking intensities
was analyzed. Figure 12.12 shows the repair cost distributions for Designs
A, B, and C at all fi ve hazard levels considered. As expected, as the shaking
intensity increases, the repair cost increases. The result shows Design C has
the lowest total repair cost as compared to Designs A and B for all hazard
levels considered. Designs A and B have comparable distributions of the
repair cost for all hazard levels. The probable maximum loss (PML) could
be defi ned as the 90% non-exceedance cost for the DBE shaking intensity.
By this defi nition, the PML are 19.9, 20.7, and 16.9 million USD for the
Designs A, B, and C, respectively.
The distribution of the repair cost at each hazard level (Fig. 12.12) can
be multiplied by the slope of the hazard curve, and integrated through all
hazard levels to obtain the annualized loss curve (Fig. 12.13). Additionally,
the mean annualized loss (MAL) can be calculated by integrating the area
under the loss curve (Der Kiureghian 2005). As shown in Fig. 12.13, the
annual rate of exceeding any fi xed repair costs increases from Design C to
A to B. Additionally, the MAL is $326,000, $336,000, and $282,000 for
Designs A, B, and C, respectively. This information can be used to evaluate
whether Design A, B, or C is a better long-term investment option. For
comparison purpose, the initial construction cost obtained from the TBI
research (Moehle et al. 2011) for the three designs are shown in Table 12.5.
The results shows Design C might cause 2 million more in the initial con-
struction cost; however, on average Design C will have $44,000 to $54,000
less in earthquake related cost per year compared with designs A and B,

Table 12.5 Initial structural and content costs in millions of $US

Design A Design B Design C

Structural cost* 126 126 128

Structural cost* + content* 140 140 143

* The values presented are above the grade construction only.
Source: Moehle et al . (2011).