# 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  
Different approaches are available in the literature to derive fragility curves from NLDAs, including Incremental Dynamic Analysis (IDA, [58; 59]), Multiple-Stripe Analysis (MSA, [60]), and the Cloud Method ([61; 62]). In this paper, the NLDAs are executed according to Cloud Analysis [62], which offers the advantage of a high level of computational efficiency. The first relevant issue when deriving fragility curves from NLDAs consists in the appropriate selection of recordings [6; 20; 21; 22] and the choice of optimal intensity measures for probabilistic seismic demand analyses [63; 64; 65; 66; 67]. Figure 3: Adopted framework for the derivation of fragility curves from NLSA and NLDA. Usually, accelerograms are selected from databases of ground motion recordings during past earthquakes by ensuring compatibility with the seismic hazard of the target site [6; 20; 21; 22; 68]. The sensitivity of the structural responses to the input motions makes the careful choice and scaling of actual ground motions a critical aspect in earthquake engineering [20; 22]; this is because increasing scale factors during the scaling process may result in the overestimation of the deformation demands [21]. In this paper, the accelerograms selected for the aims of the MARS (Seismic Risk Maps) project [69] are used [26]. This project was funded by the Italian Civil Protection Department (DPC) and then jointly developed with researchers from the University Laboratories Network for Earthquake Engineering (ReLUIS), with the aim of developing fragility curves through different approaches (including that based on NLDAs) to be used to address seismic risk analyses at a national scale. To this aim, within the MARS project, a set of 125 accelerograms is firstly selected using the Select&Match software package (release March 2022)) [26; 27]. More specifically, a set of 85 recorded (unscaled) and a set of 40 spectrally matched accelerograms compatible with the target spectrum of L'Aquila are extracted, for a total of 125 accelerograms. The target spectrum is specified as the uniform hazard spectrum at L'Aquila for return periods of 50, 100, 200, 475, 975, 2475, 5000, and 10,000 years, considering soil category A [26; 70; 71; 72]. The purpose of this choice is not to make a specific reference to the L'Aquila site but to scan the intensity levels of ground motion gradually increasing from very low to very high, in order to select a large set of input motions with intensity levels encompassing a sufficiently wide range, in order to be used in NLDAs to construct site-independent fragility curves, constrained both at very low and very high levels of seismic hazard. The 125 records are associated in pairs with the models generated for the examined case study, once applying the EW component to the X direction and the NS to the Y direction and once by reversing them, for a total of 250 NLDAs. Each pair is randomly associated with one of the 125 models generated by Monte Carlo sampling, as illustrated in Sections 3.2 and 4, to account for the uncertainty in the materials' properties. Performing a cloud analysis with unscaled natural accelerograms preserves all seismic event information, including \"record-to-record variability\". It has been proven that, when using unscaled accelerograms in conjunction with NLDAs, there exists a correlation between the chosen engineering demand parameter (EDP) and the intensity measure (IM) values of the applied seismic signals. The maximum displacement demand is chosen as the reference EDP representative of the structural response of the building, with the peak ground acceleration (PGA) being selected as the IM parameter. The choice of the PGA among other possible alternatives [52; 73] is justified by the fact that the examined case study is quite rigid [74].