# Investigating the Reliability of Nonlinear Static Procedures
## 4 Masonry Building Prototype: Modeling and Preliminary Nonlinear Analyses
### Description and Modeling
The structural configurations A and C are conceived to verify the sensitivity of the results when varying different global mechanisms activated in the structure (whether the prevailing shear failure mode in piers--expected to occur in case C--or the flexural failure mode in piers and spandrels--expected to occur in case A). Configuration B is instead conceived as a typical example of the epistemic uncertainty that analysts might encounter when investigating real URM buildings and associated with the quality of the interlocking between vertical walls (as further discussed in [81]). As already introduced in Section 3, 125 models are generated through a Monte Carlo process, so as to obtain a fragility curve that only includes the dispersion related to the uncertainties in the mechanical properties of the masonry. More specifically, uncertain parameters of the following wall typologies present in the structure (Figure 6c clarifies where the three masonry typologies are located) are considered:  
* Unconsolidated cut stone masonry, which characterizes the majority of the wall panels;
* Consolidated (through injections) cut stone masonry, which involves some internal side panels oriented perpendicularly to the main facade;
* Full brick masonry with lime mortar, which some internal pillars and an internal wall are composed of. The mechanical parameter values of these masonry types are generated stochastically, having assumed a range of variation consistent with the reference values proposed in Table C8.5.I of the Circular of NTC 2028 [82], and summarized in Table 4.  
Figure 7: Constitutive laws assumed according to NTC2018 [8] and Updating EC8-3 rel.2019 [56] for (**a**) pier and (**b**) spandrel elements. For the purposes of Monte Carlo sampling for the generation of the mechanical parameters, it is decided to adopt criteria similar to those already established within the RINTC 2018 project [83], the use of which has been consolidated in other applications [52]. Indeed, the actual sampling interval adopted for Monte Carlo sampling (Table 5) is obtained by taking as a reference interval the one in Table 4[82], further amplified by accounting for possible masonry characteristics (e.g., good mortar quality or good interlocking between transversal walls) compatible with the examined masonry types. The stochastic parameters for the wall panels in the models are determined using the median value and the dispersion within each parameter interval, as illustrated in Table 6.  
In particular, the following parameters are considered to be uncertain: the elastic Young's modulus E; the elastic shear modulus G; the compressive masonry strength \(f_{m}\); the masonry shear strength \(\tau_{0}\); the specific weight \(\rho\); the drift thresholds associated with a relevant strength decay in the constitutive law assumed for piers (namely, the shear drift \(\theta_{T}\) and the flexural drift \(\theta_{PF}\)). As commonly recommended in the Standards in the absence of more detailed information [49], the masonry's cracked stiffness is considered to be half of its elastic stiffness. Thus, every generated model is analyzed, carrying out NLSA in the X and Y directions, positive and negative verses, with \"uniform\" and \"modal\" load patterns considered, for a total of 1000 NLSAs performed. However, because the Standards require one to consider only the worst verification outcomes among those obtained from the above cases (positive or negative vers, uniform or modal LP), the uniform one, being the most punitive distribution, is considered for the discussion of the results presented in the subsequent sections. Figure 8 reports the results of NSPs in terms of fragility curves, where it is possible to notice how that derived from the uniform load pattern is always the one associated with the lowest value of the median IM.