## 4 Seismic Fragility Assessment
### Seismic Fragility Curves  
Figure 18 illustrates the maximum IDR obtained from nonlinear dynamic analyses of two analytical models subjected to a suite of selected ground motion records. For the model  
Figure 17: Selected ground motions: (**a**) acceleration response spectra; (**b**) distribution of Sa at the fundamental period of the selected structure.  
without shear springs, the first story exhibits the highest mean IDR of 0.332%, closely followed by the second story with the IDR of 0.331%. Median IDRs show a marginal increase for the second story (0.294%) compared to the first story (0.274%). In the model with shear springs, the second story demonstrates the highest mean IDR, reaching 0.554%, while the first story follows closely at 0.553%. Median IDRs also indicate the second story as the most critical, with a value of 0.534% compared to 0.508% for the first story. Notably, the inclusion of shear springs results in IDRs more than twice as large as those observed in the model without shear springs under identical seismic inputs. This highlights the substantial influence of shear spring implementation on the structural performance evaluation.  
This study conducted seismic fragility assessments using the spectral acceleration of selected ground motions as the intensity measure and IDR derived from nonlinear time history analysis as the engineering demand parameter. Seismic fragility curves were developed through linear regression analysis, utilizing a natural logarithmic scale for the engineering demand parameter and intensity measure. Figure 19 provides a visual representation of the seismic fragility curves, highlighting the differences between models with and without shear springs. Figure 19a depicts the probability of exceeding various damage levels for both models. Figure 19b specifically highlights the differences in these probabilities between the two models (shear spring model minus non-shear spring model). Figure 19b reveals that, across all damage states, the model without shear springs consistently exhibits lower probabilities of exceedance compared to the model with shear springs. The most significant difference in the probability of exceeding a given damage level is observed when shear failure is assumed to correspond to the collapse prevention limit state at the spectral acceleration of 1.30 g, resulting in a 58.24% variation. In the serviceability limit state, a 48.80% difference occurs at 0.44 g. For the damage control limit state, a 27.83% difference is observed at 1.06 g, while the collapse prevention limit state alone shows a 21.68% difference at 1.32 g. These results indicate that the limit state most affected by the presence or absence of shear spring is the collapse prevention state, with a significant impact. Additionally, the substantial differences observed not only in the collapse prevention limit state but also in the serviceability limit state demonstrate the considerable influence of shear springs on the overall structural stability. These findings indicate that performance evaluations relying only on fiber-section-based elements significantly overestimate the seismic performance of the structure.  
Figure 18: Maximum IDR for each story: (**a**) non-shear model; (**b**) shear model.