## 3 Case-Study School Building
### Variability in the Masonry Infill Mechanical Properties  
In the past, only the structural components were involved in the design process, and consequently, the potentially aggravating effect of masonry infills on the RC frames (e.g., premature shear failure of the columns due to the interaction with the surrounding frames) was neglected. In contrast, past earthquake evidence demonstrated the relevant influence of masonry infills on the global and local behavior of RC buildings. The characterization of the mechanical properties of masonry infills and the definition of a mechanical model that represents their real behavior under seismic loads is particularly elaborate, as it depends on numerous factors (e.g., manufacturing techniques, compressive strength of bricks and mortar, brick with vertical or horizontal holes). Such complexity is further increased when existing buildings are to be analyzed, for which there is no sufficient information regarding the mechanical properties of the infills or when the results of in-situ tests on masonry infills, if any, are not easily available.  
To account for these sources of uncertainty, the macro-level distinction of infill types proposed by [PERSON] et al. [20] was used herein based on the results of experimental studies [33; 34; 35]. Accordingly, five masonry infill typologies, from weak to strong, classified according to their shear capacity, were thus selected as representative of the masonry infills typically present in RC buildings in Italy and other Mediterranean countries [36]. The choice of using the shear capacity as a parameter to distinguish between different masonry infill typologies is supported by numerical research studies [37], which noted that for existing buildings without seismic detailing, the maximum shear capacity of infills significantly affects both the overall seismic response and could cause the premature shear failure of RC columns. Table 1 reports the main properties of the selected typologies. To define the most consistent numerical modeling approach for each masonry infill typology, as discussed in detail in [PERSON] et al. [18], the main parameters affecting the hysteretic behavior were identified. The most common formulations available in the literature were investigated (i.e., the strut width relationships, the formulations to account for the presence of openings, failure mechanism models, and the formulations to define the backbone curve).  
Figure 4: (**a**) Hazard Curve at the site of the school building; (**b**) target spectra for CS(AvgSa) [30; 31] at IM level 6 together with the 25 selected individual records.  
Parametric nonlinear static analyses were carried out by combining the main formulations generally adopted to account for the influence of the identified parameters, and the resulting capacity curves were compared with the force-displacement curve and maximum envelope obtained from the experimental test of each masonry infill typology. The model minimizing the prediction error was finally selected for each masonry infill type. Hence, instead of selecting a priori, one of the formulations available in the literature for the definition of the hysteretic behavior of infills, the model that minimized the experimental test results prediction error was identified for each masonry infill type [18]. While the resulting backbone curves are provided in Figure 5, further details on the macro-classification, the verification that the selected infills typologies cover the range of variation of the main mechanical properties highlighted in different research studies [36; 38; 39], as well as the numerical modeling validation with experimental test results, can be found in [PERSON] et al. [18]. Finally, according to the in situ inspection, the exterior masonry infill walls were identified as double-leaf hollow clay brick masonry, which, at least in terms of geometrical properties, can be compared with type-2 masonry infill [35] Table 1.