## 4 Seismic Risk Assessment  
The case-study school building was analyzed considering two different structural configurations: (1) completely infilled, neglecting the presence of the openings in the masonry panels, and (2) partially infilled, considering a reduction coefficient that accounts for the presence of the openings in the masonry panels, as per [PERSON] et al. [39], whose proposed relationship provided the best numerical fitting, for the selected masonry infills, to  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Type 1 [36]** & **Type 2 [35]** & **Type 3 [35]** & **Type 4 [37]** & **Type 5 [38]** \\ \hline \(\mathrm{t_{w}}\) & 80 & 240 & 300 & 350 & 150 \\ \hline \(\mathrm{E_{wv}}\) & 1873 & 1873 & 3240 & 5299 & 6401 \\ \hline \(\mathrm{E_{wh}}\) & 991 & 991 & 1050 & 494 & 5038 \\ \hline \(\mathrm{G_{w}}\) & 1089 & 1873 & 1296 & 2120 & 2547 \\ \hline \(\mathrm{f_{wv}}\) & 2.02 & 1.5 & 3.51 & 4.64 & 8.66 \\ \hline \(\mathrm{f_{wlat}}\) & 1.18 & 1.11 & 1.5 & 1.08 & 4.18 \\ \hline \(\mathrm{f_{wu}}\) & 0.44 & 0.25 & 0.3 & 0.359 & 1.07 \\ \hline \(\mathrm{t_{w}}\): thickness [mm]; \(\mathrm{E_{wv}}\): elastic modulus vertical direction [MPa]; \(\mathrm{E_{wh}}\): elastic modulus horizontal direction [MPa]; \(\mathrm{G_{w}}\): shear modulus [MPa]; \(\mathrm{f_{wv}}\): vertical strength [MPa]; \(\mathrm{f_{wlat}}\): lateral strength [MPa]; \(\mathrm{f_{wu}}\): shear sliding strength [MPa]. & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of the selected masonry infill types.  
Figure 5: Backbone curves for (a) masonry infill types 1–2–3 and (b) masonry infill types 4–5.  
experimental test results [18]. The presence of the openings, which were defined according to the real dimensions of the school building, was hence considered by multiplying the strut area obtained for the infill without opening by the aforementioned stiffness and strength reduction coefficient.  
Considering the still common trend in engineering practice of considering masonry infills as non-structural components, i.e., without an explicit contribution to the structural behavior, the results of the bare frame structural configurations are also provided and compared with those of the infilled counterparts, highlighting the role and the effects of accounting for the infills in the numerical models.  
The dynamic properties of the selected case-study building are summarized in Table 2 through the first four vibration modes, which allow us to clarify the importance of modeling assumptions on the dynamic behavior of the structure. The first vibration mode, T\({}_{1}\), varies between 1.32 s for the bare frame and 0.264 s in the case of a completely infilled frame and infill type 5 (strong infill). For both infilled configurations (1 and 2), the fundamental period decreases when moving from infill type 1 to infill type 5, as expected, which is further proof that the adopted infill typology macro-classification is not only valid in terms of strength but also in terms of stiffness. Moreover, looking at the higher modes, going from T\({}_{1}\) to T\({}_{4}\), the period of vibration starts to be less affected by the material properties of the infills, although the differences are still noticeable.