## 4 Trends of Damage as a Function of Seismic Intensity
Additionally, in Figure 13 simple linear fits are shown to visualize possible trends. In general, Figure 13 shows that larger damage (rotation) is expected for larger horizontal Sa (Figure 13 left) and that, the same occurs, but with even higher damage when the horizontal and vertical components act simultaneously (Figure 13 right). In both cases the plastic rotation is 0.0109. Analogous results and trends are listed in Tables 7-9 and Figure 14. The same conclusions can be drawn, except that the dispersion of the damage around the trend line is higher for the 10-story building under the action of both components (Figure 14 right). Results for other beams are not shown for brevity, but they exhibit similar trends but with a value of plastic rotation equal to 0.0114. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Component** & \(AF\) & **Sa-NILT** & **Sa-CALE** & **Sa-JAMI** & **Sa-SCRU** & **Sa-LANE** & **Sa-HMTT** & **Sa-RABO** \\ \hline \(Sa\ H_{SRSS}\) & 1.066 & 0.342 & 0.270 & 0.128 & 0.134 & 0.177 & 0.114 & 0.078 \\ \(Sa\ V_{SRSS}\) & 1.477 & 0.130 & 0.171 & 0.101 & 0.138 & 0.105 & 0.068 & 0.097 \\ \(Sa_{H\&V}\) & & 0.292 & 0.271 & 0.1438 & 0.176 & 0.173 & 0.111 & 0.117 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Resultant accelerations of the horizontal plus vertical components (6-story building). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Period** & \multicolumn{6}{c}{**Pseudospectral Vertical Acceleration**} \\ \cline{2-9}
**(s)** & \({}^{2}\Gamma_{vj}\) & \multicolumn{6}{c}{**2 Sa-NILT**} & \({}^{2}\)**Sa-CALE** & \({}^{2}\)**Sa-JAMI** & \({}^{2}\)**Sa-SCRU** & \({}^{2}\)**Sa-LANE** & \({}^{2}\)**Sa-HMTT** & \({}^{2}\)**Sa-RABO** \\ \hline
0.173 & 0.524 & 0.374 & 0.502 & 0.240 & 0.431 & 0.325 & 0.223 & 0.318 \\
0.164 & 0.046 & 0.432 & 0.495 & 0.247 & 0.493 & 0.353 & 0.231 & 0.278 \\
0.060 & 0.106 & 1.025 & 1.266 & 1.150 & 0.697 & 0.615 & 0.128 & 0.185 \\ \(\Sigma\Gamma_{v}=0.677\) & & & & & & & & \\ \(Sa\ V_{SRSS}\) & & 0.130 & 0.171 & 0.101 & 0.138 & 0.105 & 0.068 & 0.097 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accelerations due to horizontal earthquake in the 6-story building. Before proceeding to the next section, it is emphasized that Equation (3) leads to the consistent (quantifiable) trend shown in Figure 13 because the modes with the highest modal participation (not necessarily the first three) are used and an extrapolation is carried out to consider the 100% mass participation. Other combinations of the response (different \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Periodo**} & \multirow{2}{*}{\(\boldsymbol{\Gamma}_{H}\)} & \multicolumn{8}{c}{**Pseudospectral Horizontal Acceleration**} \\ \cline{3-10}  & & **Sa-NILT** & **Sa-CALE** & **Sa-JAMI** & **Sa-SCRU** & **Sa-LANE** & **Sa-HMTT** & **Sa-RABO** \\ \hline
0.8412 & 0.738 & 0.379 & 0.229 & 0.195 & 0.294 & 0.224 & 0.126 & 0.070 \\
0.2383 & 0.157 & 1.383 & 0.733 & 0.245 & 0.457 & 0.521 & 0.301 & 0.320 \\
0.1216 & 0.039 & 2.048 & 1.187 & 0.671 & 0.597 & 0.557 & 0.275 & 0.322 \\ \multicolumn{10}{c}{\(\Sigma\Gamma_{h}\) = 0.934} \\ \multicolumn{10}{c}{\(Sa\ H_{SRSS}\)} & \multicolumn{1}{c}{0.210} & \multicolumn{1}{c}{0.121} & \multicolumn{1}{c}{0.087} & \multicolumn{1}{c}{0.132} & \multicolumn{1}{c}{0.107} & \multicolumn{1}{c}{0.060} & \multicolumn{1}{c}{0.042} \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accelerations due to horizontal earthquake in the 10-story building. Figure 14: Rotation as a function of Sa for the 10-story building; for beams studied in Figures 10 and 11. Left for the horizontal component, right for the horizontal plus vertical component.