## 5 Case Study
### Comparison of Results  
In the case of single-floor houses constructed with reinforced masonry, the damage assessment is closely related to the maximum ground acceleration (PGA). On the other hand, for two-floor and three-tofive-floor houses, the damage assessment is directly related to spectral acceleration, specifically SA (T = 0.3 s) and SA (T = 0.6 s), respectively. This allows us to more accurately assess the vulnerability of different types of houses to seismic events. Furthermore, to compare our results with other studies, we calculated vulnerability functions using the previously mentioned procedures for two spectral acceleration values: SA (T = 0.3 s) and SA (T = 0.6 s). Figure 14 presents vulnerability functions specifically designed for reinforced masonry structures, developed by severalauthors. Among these, [PERSON] et al. created functions for European houses, classifying them into three ductility levels: low (DUL), moderate (DUM), and high (DUH) [54]. Likewise, [PERSON] contributed functions with global applicability, suitable for various seismic threats, following the HAZUS methodology [37]. The functions presented in this article, like those of [PERSON] et al., are divided into three categories corresponding to low (L), moderate (M), and high (H) seismic levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Housing**} & \multirow{2}{*}{**Expected Value**} & \multicolumn{3}{c}{**Loss Rate for Code Seismic Design Level (\%)**} \\ \cline{3-5}  & & **Low** & **Moderate** & **High** \\ \hline RM2/L (1–3 floors) & 0.5 g of PGA & 30 & 7 & 1.8 \\ RM2/M (4–7 floors) & 0.5 g of SA (T = 0.5 s) & 44 & 5 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Loss rate for low- and medium-height housing structures at different levels of seismic design. Figure 13: Vulnerability functions for medium-height masonry structures (RM2/M) with spectral accelerations of SA (0.5 s). (**a**) Low seismic design code level, (**b**) moderate seismic design code level, and (**c**) high seismic design code level. Table 9 presents a summary reflecting the probabilities of loss rates in different types of houses, including one-floor, two-floor, and three-tofive-floor reinforced masonry houses. These probabilities werecalculated considering a spectral acceleration of 0.5 g and compared with historical accelerations recorded in the study area, which can vary in the range of 0.20 to 0.50 g [29]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \
\begin{tabular}{c} **Numero de Pisos** \\ **Number of Floors** \\ \end{tabular} &
\begin{tabular}{c} **Expected** \\ **Value** \\ **IM** \\ \end{tabular} & **Masonry House** & **Loss Rate (\%)** \\ \hline \hline \multirow{8}{*}{1 floor} & \multirow{8}{*}{0.5 g of PGA} & RM2/L/L & 30 \\  & & RM2/L/M & 7 \\  & & RM2/L/H & 1.8 \\ \cline{2-3}  & & RM2L/L ([PERSON] et al.) [37] & 19.7 \\  & & RM2L/M ([PERSON] et al.) [37] & 17.4 \\ \cline{2-3}  & & RM2L/H ([PERSON] et al.) [37] & 14.4 \\ \cline{2-3}  & & MR/LWAL + DUL ([PERSON] et al.) [54] & 9.7 \\  & & MR/LWAL + DUM ([PERSON] et al.) [54] & 4.7 \\  & & MR/LWAL + DUH ([PERSON] et al.) [54] & 1.8 \\ \hline \multirow{8}{*}{2 floors} & \multirow{8}{*}{0.5 g of SA} & RM2/L/L & 30 \\  & & RM2/L/M & 3.4 \\ \cline{1-1} \cline{2-3}  & (T = 0.30 s) & RM2/L/H & 0.3 \\ \cline{1-1} \cline{2-3}  & & MR/LWAL + DUL ([PERSON] et al.) [54] & 5.3 \\ \cline{1-1} \cline{2-3}  & & MR/LWAL + DUM ([PERSON] et al.) [54] & 3.5 \\ \cline{1-1} \cline{2-3}  & & MR/LWAL + DUH ([PERSON] et al.) [54] & 1.5 \\ \hline \multirow{8}{*}{3–5 floors} & \multirow{8}{*}{0.5 g of SA} & RM2/M/L & 52 \\  & & RM2/M/M & 6 \\ \cline{1-1} \cline{2-3}  & & RM2/M/H & 1 \\ \cline{1-1} \cline{2-3}  & & RM2M/L ([PERSON] et al.) [37] & 20.1 \\ \cline{1-1} \cline{2-3}  & & RM2M/M ([PERSON] et al.) [37] & 16.4 \\ \cline{1-1} \cline{2-3}  & & RM2M/H ([PERSON] et al.) [37] & 11.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of results for1-, 2-, and 3–5-floor houses.