## 3 Seismic Fragility Assessment Procedure  
### FEMA P695 Procedure  
A seismic fragility assessment for three analytical model was conducted using the procedure of FEMA P695, one of the methodologies for evaluating the seismic performance coefficients of structural systems that are not prescribed in the standard. The FEMA P695 procedure verifies if seismic-force-resisting systems have an acceptable probability of collapse and a collapse margin ratio (CMR) for the maximum considered earthquake based on the collapse fragility curve obtained by incremental dynamic analysis (IDA). The spectral shape of ground motion records is an important factor that influences the result of IDA and the corresponding collapse fragility. [PERSON] and [PERSON] found that the spectral shape for the MCE level ground motion of the western area of United States and the shape design spectrum shape of ASCE 7-05 are different significantly over a certain period of time [29; 30; 31]. In addition, the structural analysis for those spectra having such differences showed that there is a considerable difference in collapse prevention performance. [PERSON] and [PERSON] proposed a conditional spectrum to compensate for that kind of difference. The conditional spectrum has a spectral acceleration corresponding to a specific return period at a control frequency, and spectral accelerations at other periods are determined \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{\
\begin{tabular}{c} **Analytical** \\ **Model** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Component** \\ **Wall** \\ \end{tabular} } & \multicolumn{5}{c}{**DCR (Demand/Capacity)**} \\ \cline{3-8}  & & & **Rotation** & **Axial** & \multicolumn{2}{c}{**Shear**} \\ \cline{3-8}  & & **Ratio** & **Angle** & **Strain** & **Design to \(1.0V_{u}\)** & **Design to \(1.2V_{u}\)** & **Design to \(1.5V_{u}\)** \\ \hline \multirow{4}{*}{Model A} & R1 & & 0.19 & 0.53 & 0.40 & 0.48 & 0.60 \\  & R2 & & 0.40 & 0.77 & 0.72 & 0.86 & 0.99 \\  & T1 & 0.70 & 0.26 & 0.75 & 0.64 & 0.77 & 0.97 \\  & T2 & & 0.19 & 0.92 & 0.99 & 0.99 & 0.99 \\  & R3 & & 0.39 & 0.83 & 0.99 & 0.98 & 0.99 \\ \hline \multirow{4}{*}{Model B} & R1 & & 0.19 & 0.95 & 0.98 & 0.97 & 0.99 \\  & R2 & & 0.12 & 0.30 & 0.25 & 0.30 & 0.38 \\ \cline{1-1}  & T1 & 0.61 & 0.31 & 0.50 & 0.46 & 0.55 & 0.69 \\ \cline{1-1}  & T2 & & 0.30 & 0.75 & 0.81 & 0.97 & 0.98 \\ \cline{1-1}  & R3 & & 0.17 & 0.82 & 0.99 & 0.98 & 0.98 \\ \hline \multirow{4}{*}{Model C} & R1 & & 0.15 & 0.55 & 0.70 & 0.84 & 0.99 \\ \cline{1-1}  & R2 & & 0.30 & 0.87 & 0.99 & 0.96 & 0.98 \\ \cline{1-1}  & T1 & 0.48 & 0.15 & 0.26 & 0.06 & 0.08 & 0.10 \\ \cline{1-1}  & T2 & & 0.18 & 0.44 & 0.17 & 0.20 & 0.25 \\ \cline{1-1}  & R3 & & 0.17 & 0.51 & 0.28 & 0.34 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Design results for average response of seven ground motions. Figure 6: Example of design result for R3 in Model A.  
by a percentile conditional on the spectral acceleration at the control frequency. The conditional spectrum thus provides statistical information about the variability of the spectrum at periods other than the control frequency. In this study, ground motion suites for the IDA were selected and scaled using the conditional spectrum. In FEMA P695, when the spectral shape of the general structural design standard is used, the CMR is modified to the adjusted collapse margin ratio (ACMR) using a correction factor called the spectral shape factor (SSF) to take into account difference in the spectral shape mentioned above. However, the conditional spectrum was used directly as the target response spectrum for ground motion suites used in the performance evaluation in this study. Therefore, values of ACMR in this study are the same as those of CMR without modification. The FEMA P695 criteria for collapse prevention require that the CMR be above a specified allowable value and the collapse probability at the MCE level of spectral acceleration be less than 10%.