## 6 Conclusions  
In this study, five different methodologies for developing fragility curves are evaluated to assess the seismic performance of real RC structures subjected to structural bounding. For this purpose, the discrete probability data points deduced based on the empirical  
Figure 14: Influence of the PSDM assumptions on the fragility assessment of the eight-story RC frame in terms of \(\mu_{\varphi,\text{max}}\) (C20) as a function of the PGA. Examined assumptions: Case 1—lognormality, Case 2—lognormality and power law model, Case 3—PSDM’s assumptions. Fragility curves (**a**) without the bounding effect, (**b**) \(\text{d}_{\text{g}}=0.0\) cm, (**c**) \(\text{d}_{\text{g}}=4.5\) cm, and (**d**) \(\text{d}_{\text{g}}=9.0\) cm. Figure 13: Influence of the PSDM assumptions on the fragility assessment of the eight-story RC frame in terms of \(\text{TDR}_{\text{max}}\) (\(\%\text{H}_{\text{tot}}\)) as a function of the PGA. Examined assumptions: Case 1—lognormality, Case 2—lognormality and power law model, Case 3—PSDM’s assumptions. Fragility curves (**a**) without the bounding effect, (**b**) \(\text{d}_{\text{g}}=0.0\) cm, (**c**) \(\text{d}_{\text{g}}=4.5\) cm, and (**d**) \(\text{d}_{\text{g}}=9.0\) cm. CDF method are utilized to validate the fragility curves developed through MLE, MM, IM percentiles, and PSDM procedures. Displacement-based and curvature-based fragility curves are developed. The use of probabilistic seismic demand models on the fragility assessment of the bounding risk is further estimated. Linear and bilinear PSDMs are developed, while the validity of the assumptions commonly used to produce a PSDM is examined. Finally, the influence of the PSDMs' assumptions on the derivation of the fragilities for the structural bounding effect is identified. The examined structural bounding cases are between an eight-story RC frame and a three-story rigid structure that have equal story heights (floor-to-floor interaction). The main outcomes of this study are as follows:  
* The MLE, MM, and IM percentiles procedures are developing fragilities that are in a good agreement with the probability data points of the empirical CDF method. * The IM percentiles method gives more conservative results in terms of \(\mathrm{TDR}_{\mathrm{max}}\,|\,\mathrm{PGA}\), in comparison to the other methodologies of this study. Nevertheless, in the case of \(\mu_{\varphi,\mathrm{max}}\,|\,\mathrm{PGA}\), the fragility curve is moved towards greater values of PGA when \(\mathrm{d}_{\mathrm{g}}=0.0\) cm. This result indicates that the IM-percentiles-based local fragility curve cannot accurate capture the increased inelastic demands of the column due to the bounding effect, when \(\mathrm{d}_{\mathrm{g}}=0.0\) cm. * The displacement-based fragilities that are developing from the PSDMs are shifted to greater values of PGA in comparison to the deduced fragilities based on the MLE, MM, and IM percentiles procedures. * The curvature-based fragilities that are developing from the PSDMs are shifted to lower values of PGA in comparison to the deduced fragilities based on the MLE, MM, and IM percentiles procedures. * Similar results regarding the fragility assessment of the RC structure between the examined methodologies are deduced when the performance level controls the seismic behavior of the eight-story RC frame structure at low levels of IM. * The observed shift on the fragility curves is owed to the different values of medians \(\mu\) that methodologies estimate. * The lognormality assumption that is evaluated for each level of PGA showing that it is not always satisfied especially in the case of maximum curvature ductility. * The homoscedasticity assumption of developing the PSDM of \(\mathrm{IDR}_{\mathrm{max}}\) and \(\mathrm{TDR}_{\mathrm{max}}\) is not satisfied within the overall range of PGA. * The use of a linear PSDM fails to properly describe the local inelastic demands of the structural RC member.