# Investigating the Reliability of Nonlinear Static Procedures
## 5 Results
Figure 13: Configuration of Visso B’s fragility curves: in the first row is the X-analysis, and in the second row is the Y-analysis; the method of bilinearization of the capacity curve is fixed (in order of row according to Updating EC8-3 rel.2019 [56], NTC18 [8], [PERSON] et al., 2019 [32]) and we include all the possible methods to calculate the displacement capacity (N2 [PERSON] [33], N2 [PERSON] [57], N2 [PERSON] [32], CSM [34]). Figure 14 provides a more comprehensive overview of the results achieved using the N2 method according to the application criteria recommended in the Updating ECS-3 rel.2019 document, with the three examined case studies. Again, it is evident that, in all cases, the results are not conservative. The only method that successfully approximates the real capacity of the analyzed structures is the CSM approach based on the use of overdamped spectra. In fact, the fragility curves obtained with the CSM are always slightly to the right of the curves obtained from the NLDAs; this is a desirable outcome, since nonlinear static analyses are expected to be less accurate than dynamic ones, so obtaining more conservative static fragility curves is reasonable and in line with the use of a more simplified approach. In the case of the CSM method, no differences are obtained using k = 0.66 or k = 1; this is because, in these cases, the \(\eta\) coefficient in Equation (8) is saturated and set equal to the lower limit (\(\eta\) = 0.55). Moreover, by comparing the results reported in the three lines of Figures 11-13 (i.e., varying the approach adopted for the equivalent bilinearization), it is possible to observe that the CSM method is almost insensitive to the chosen criterion, while the other NSPs exhibit some variations. The reason is that the N2-based methods use the \(T^{*}\) value to enter into the spectrum, while the CSM uses the secant period at NC \(T_{u}\), which is closer to the physics of the phenomenon (with \(T^{*}\) being more representative of the pseudo-elastic response) and affects only the evaluation of the equivalent damping associated with the ultimate displacement capacity. Figure 15 compares the \(T_{u}\) and T* values for all the examined cases. It is worth noting that, in all cases, \(T_{u}\) is significantly higher than T* and also greater than \(T_{c}\). Finally, Figure 16 illustrates the ductility associated with the ultimate displacement capacity at NC. The difference in the ductility in the positive and negative directions is due to the change in the structural response in terms of damage, as already discussed in Section 4. The results reported in Figure 16 are also useful to understand when the limitations recommended by the Standard to q* in the N2-based approaches become relevant. Figure 14: Fragility curves: (**a**) represents the X-analysis, (**b**) represents the Y-analysis; the figures represent the three examined case studies, i.e., C, A, and B structural configurations of the Visso School building, with the continuous lines derived from NDP and the indented lines derived from NSP. Figure 15: \(T^{*}\) and \(T_{u}\) values: in the first column is the X-analysis and in the second column is the Y-analysis; the figures represent, in the order of the rows, the three examined case studies, i.e., C, A, and B structural configurations of the Visso School building, with the first 125 values of T corresponding to the positive direction and the last 125 values corresponding to the negative direction.