# Investigating the Reliability of Nonlinear Static Procedures
## 3 Criteria Adopted to Assess the Reliability of the Examined Approaches
### Assessment of the Reference/Target Fragility Curve by Nonlinear Dynamic Analyses
To establish whether the EDP value leads to the attainment of the NC LS, consistent criteria and thresholds with the NLSAs are used, i.e., those already introduced in Table 1. Moreover, to avoid including, in the statistical processing, results associated with a damage level even higher than the near collapse, a condition representative of the collapse is also introduced (namely \(\frac{V_{b}}{V_{max}}=0.5\) for the check at a global scale and \(DLmin\ \geq\ DL5\) for the check at a macroelement scale). Finally, the results obtained by the Cloud Analysis are post-processed by assuming a lognormal distribution (as is typical in risk analyses [42]) in order to define the median value of IM associated with the attainment of NC and its dispersion. The latter includes the record-to-record variability (intrinsically described by the record selection) and that associated with the structural variability (as described by the Monte Carlo sampling). Directly comparing the response from a single record with the NSP-derived solution would not be meaningful. The procedures of calculating the displacement demand are based on regularly smoothed response spectra. The shape of the response spectrum adopted is checked against the median spectrum derived from the recordings adopted in the NLDAs. Figures 4 and 5 compare the acceleration response spectra associated with the actual records used in executing the NLDAs (in grey) and the conventional ones according to the Standards format (in red), i.e., the one used in the case of NSPs. H1 refers to the signals applied in the X-EW direction, while H2 refers to those in the Y-NS direction. It is worth specifying that only the records that lead the NLDAs to satisfy the achievement of the NC limit state are examined; the acceleration response spectra marked in blue in Figures 4 and 5 refer to the average of such a subset of recordings. Data are reported for the three configurations examined of the investigated case study. The spectra according to the Standards format are defined according to the common format, in which the region at constant acceleration is estimated as \(S\cdot F_{0}\cdot PGA\cdot\eta\), where \(S\) is the maximum response spectral acceleration (5% damping) corresponding to the constant acceleration range of the horizontal elastic response spectrum; \(F_{0}\) is the short period site amplification factor; and \(\eta\) is the damping correction factor for the elastic response spectrum. In particular, \(S\) and \(\eta\) are assumed to be equal to 1, while \(F_{0}\) is alternatively equal to 2.5 (Figure 4) and 2 (Figure 5). The decision to consider both these options is made to investigate the sensitivity of the results of fragility curves derived from NSPs to this factor and, in particular, to obtain a shape as close as possible to the seismic input adopted in NLDAs (i.e., with a shape able to reproduce, on average, that of the set of accelerograms leading to the attainment of the NC).