# Investigating the Reliability of Nonlinear Static Procedures
## 4 Masonry Building Prototype: Modeling and Preliminary Nonlinear Analyses
### Description and Modeling
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{Masorny typology} & \(f_{m}\) & \(\tau_{0}\) & E & G & \(\rho\) \\  & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] & [kN/m\({}^{3}\)] \\ \cline{2-7}  & min & min & min & min & min & \\  & med & med & med & med & \\  & max & max & max & max & \\  & 2.6 & 0.0056 & 1500 & 500 & \\ Cut stone & 3.2 & 0.0398 & 1740 & 580 & 21 \\  & 3.8 & 0.0740 & 1980 & 660 & \\  & 2.6 & 0.05 & 1200 & 400 & \\ Full brick masonry with lime mortar & 3.45 & 0.09 & 1500 & 500 & 18 \\  & 4.3 & 0.13 & 1800 & 600 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Building’s masonry typologies and related values of mechanical parameters [49]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Mortar**} & \multicolumn{3}{c}{**Cross**} & \multicolumn{2}{c}{**Injections**} \\  & & \multicolumn{2}{c}{**Connection**} & & & & & \\ \hline Cut stone increase & \multicolumn{2}{c}{1.3} & \multicolumn{2}{c}{1.5} & \multicolumn{2}{c}{1.5} \\ Full brick increase & \multicolumn{2}{c}{1.47} & \multicolumn{2}{c}{1.3} & \multicolumn{2}{c}{-} \\ \hline  & \multicolumn{2}{c}{\(f_{m}\) [N/mm\({}^{2}\)]} & \multicolumn{2}{c}{\(\tau_{0}\) [N/mm\({}^{2}\)]} & \multicolumn{2}{c}{E [N/mm\({}^{2}\)]} \\ \cline{2-7}  & min & median & \multicolumn{2}{c}{\(\max\) incremented} & min & median & \multicolumn{2}{c}{incremented} & min & median & \multicolumn{2}{c}{max incremented} \\ \hline Cut stone & \multirow{2}{*}{2.6} & \multirow{2}{*}{4.09} & \multirow{2}{*}{6.42} & \multirow{2}{*}{0.056} & \multirow{2}{*}{0.084} & \multirow{2}{*}{0.125} & \multirow{2}{*}{1500} & \multirow{2}{*}{1965} & \multirow{2}{*}{2574} \\ unconsolidated & & & & & & & & \\ Cut stone & \multirow{2}{*}{3.9} & \multirow{2}{*}{7.51} & \multirow{2}{*}{14.45} & \multirow{2}{*}{0.084} & \multirow{2}{*}{0.154} & \multirow{2}{*}{0.281} & \multirow{2}{*}{2250} & \multirow{2}{*}{3610} & \multirow{2}{*}{5792} \\ consolidated & & & & & & & & \\ Full brick & 2.6 & 4.62 & 8.21 & 0.050 & 0.111 & 0.248 & 1200 & 1781 & 2644 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Sampling interval adopted for Monte Carlo sampling. Figure 8: Fragility curve: in the first column is the X-analysis, in the second column is the Y-analysis; the three rows represent, in order, the three configurations, Visso C, Visso A, Visso B, with their two typologies of LP. \begin{table}
\begin{tabular}{c c c c} \hline  & **Parameter** & **Median Value** & \(\beta\) \\ \hline  & \(E\) & 1965 & 0.27 \\  & \(f_{m}\) & 4.09 & 0.45 \\ Cut stone & \(\tau_{0}\) & 0.084 & 0.40 \\ unconsolidated & \(\theta_{Sibert}\) & 0.005 & 0.57 \\  & \(\theta_{PF}\) & 0.010 & 0.51 \\ \hline  & \(E\) & 3610 & 0.47 \\  & \(f_{m}\) & 7.51 & 0.65 \\ Cut stone & \(\tau_{0}\) & 0.154 & 0.60 \\ consolidated & \(\theta_{Sibert}\) & 0.007 & 0.57 \\  & \(\theta_{PF}\) & 0.012 & 0.51 \\ \hline  & \(E\) & 1781 & 0.40 \\  & \(f_{m}\) & 4.62 & 0.58 \\ Full brick & \(\tau_{0}\) & 0.111 & 0.80 \\  & \(\theta_{Sibert}\) & 0.005 & 0.40 \\ \(\theta_{PF}\) & 0.010 & 0.40 \\ \hline \end{tabular}
\end{table} 
Table 6: Values adopted for the Monte Carlo sampling generation.