## 3 Numerical Study
### Description of the Prototype Buildings  
Three RC-framed prototype structures were designed with three (N3), six (N6) and nine (N9) stories, having an open first story and upper stories infilled with masonry walls. The prototypes follow the construction practices of the Dominican Republic and were designed (without seismic provision) to sustain gravity loads only. Section dimensions and reinforcement were checked using American Concrete Institute ACT 318-99 [26]. N3 and No prototypes had four-by-three spans, whereas N9 had three-by-three spans, as seen in Figure 3. The flooring system entailed two-way slabs 0.16 m thick, supported by beams in both directions. The masonry infill walls were 0.15 m thick. The material mechanical properties typically used in the Dominican Republic are summarised in Table 1, while Table 2 shows the members' dimensions linked to the notation in Figure 3. Table 2 also shows the inertial masses \(m_{i}\), corresponding to the self-weight and live loads, to be considered in the dynamic analysis. It is worth noting that the study focuses on the ground motions acting only in the \(X\) direction, so only the elements in this direction were defined herein. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Concrete**} & \multicolumn{3}{c}{**Steel**} & \multicolumn{3}{c}{**Masonry**} \\ \hline \(\sigma_{c}\) (MPa) & \(E_{c}\) (GPa) & \(\sigma_{y}\) (MPa) & \(E_{s}\) (GPa) & \(\sigma_{m}\) (MPa) & \(E_{m}\) (GPa) & 20.6 & 21.5 & 274 & 206 & 2.3 & 2.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the materials. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Story/Floor:**} & \multicolumn{2}{c}{**1**} & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Prototype & Frame & \(m_{i}\) (kNs\({}^{2}\)/cm) & 4.771 & 4.707 & 2.877 & - & - & - & - & - & - & - \\ \hline \multirow{8}{*}{N3} & \multirow{3}{*}{Exteriors:} & Beams & \(30\times 60\) & \(30\times 60\) & \(25\times 50\) & & & & & & & \\ \cline{3-10}  & & & C1 & \(30\times 30\) & \(30\times 30\) & \(25\times 25\) & & & & & & \\ \cline{3-10}  & & & C2 & \(30\times 30\) & \(30\times 30\) & \(25\times 25\) & & & & & & & \\ \cline{3-10}  & & & Beams & \(30\times 60\) & \(30\times 60\) & \(25\times 50\) & & & & & & & \\ \cline{3-10}  & & & C3 & \(30\times 30\) & \(30\times 30\) & \(25\times 25\) & & & & & & & \\ \cline{3-10}  & & & C4 & \(35\times 35\) & \(30\times 30\) & \(25\times 25\) & & & & & & & \\ \hline \multirow{8}{*}{N6} & \multirow{3}{*}{Exteriors:} & \multirow{3}{*}{Exteriors:} & \multirow{3}{*}{Columns} & \(m_{i}\) (kNs\({}^{2}\)/cm) & 4.862 & 4.775 & 4.749 & 4.739 & 4.718 & 2.881 & - & - & - \\ \cline{3-10}  & & & Beams & \(30\times 60\) & \(30\times 60\) & \(30\times 60\) & \(30\times 60\) & \(30\times 60\) & \(25\times 50\) & & & \\ \cline{3-10}  & & & C1 & \(30\  
These prototype structures were seismically upgraded with hysteretic dampers in the first story, as shown in Figure 3. The lateral strength \({}_{s}Q_{y1}\) and stiffness \({}_{s}k_{1}\) provided by the dampers in the first story, and the corresponding inter-story drifts at yielding \({}_{s}\delta_{y1}\), are given in Table 3.