# Investigating the Reliability of Nonlinear Static Procedures
## 4 Masonry Building Prototype: Modeling and Preliminary Nonlinear Analyses  
### Description and Modeling  
The case study is inspired by the Visso School [28; 77; 78], a URM building permanently monitored by the Seismic Observatory of Structures of the Department of Civil Protection (DPC) and now demolished (due to severe damage that occurred after the 2016/2017 Central Italy earthquake). The seismic response of this structure was investigated in detail in the previous research of some of the authors, and the numerical model used here was extensively validated in [28] by executing NLDAs designed to simulate the actual response of the school building hit by the Central Italy seismic sequence. The building is  
Figure 5: Comparison of the acceleration response spectra derived from actual signals (grey, in blue their average) and the conventional format of Standards (red, with \(S=1\), \(\eta=1\), \(F_{0}=2\)). characterized by two stories, irregular in plan and regular in elevation, with a prevailing masonry typology composed of cut stone, with the localized presence of pillars constructed from full brick units with lime mortar. It presents diaphragms that are stiff in their planes. The in-plane configuration is depicted in Figure 6c. TreMuri software rel.2022 [79] is used to implement the model and perform the numerical nonlinear analyses. This software works according to equivalent frame (EF) modeling. Thus, walls are discretized into a set of masonry panels, i.e., piers and spandrels, where the nonlinear response is concentrated. These panels are connected by rigid nodes. Notably, this modeling strategy focuses on the in-plane (IP) response of URM walls, assuming that out-of-plane mechanisms are prevented. The research herein discussed in fact focuses only on the global IP response, which the NSPs illustrated in Section 2 refer to. The nonlinear response of the piers is simulated by adopting the multilinear constitutive laws developed by [80], suitable also for describing the most recent Standard proposals and depicted in Figure 7. In this figure, two types of Code-based nonlinear constituents are illustrated: one consistent with the current Italian Structural Code [8], which is elasto-plastic for piers and considers a residual strength capacity for a spandrel after an initial strength decay, and one consistent with \"Updating ECS-3 rel.2019\" [56], which is multilinear for both piers and spandrels. In the case of spandrels, the residual strength capacity is due to the contribution associated with the architrave or another tension-resistant element that is coupled (e.g., an RC beam). Figure 6: A 3D view of the geometric model (**a**), equivalent frame model adopted (**b**), and 2D in-plane configuration with the identification of the present masonry typologies (full brick; cut stone—unconsolidated; cut stone—S-consolidated) (**c**). The arrows indicate the main orientation of diaphragms. Starting from the actual geometrical architecture of the Visso School and maintaining the masonry types and diaphragm types that characterize it, three different structural configurations are considered (types A, B, and C), aiming to investigate the sensitivity of the nonlinear response to various structural details (i.e., the presence or not of RC ring beams) as well as the wall-to-wall connection's efficiency. More specifically,  
* Case A assumes the absence of reinforced concrete beams coupled to the spandrels and good interlocking between the external and internal walls;
* Case B assumes the absence of reinforced concrete beams coupled to the spandrels and poor interlocking between the external and internal walls;
* Case C assumes that RC ring beams are coupled to the spandrels and there is good interlocking between the external and internal walls.