## 7 Objective 2: Story and Global Ductility, Dynamic Analysis  
### Story Ductility  
The \(\mu_{S}\) values for the \(NS\) direction of the 3-level building, calculated according to Equation (3), are shown in Figure 5a-c, for seismic intensities of 0.4 g, 0.8 g, and 1.2 g, respectively; while those of the 10-level building for the same direction are given in Figure 5d-f, for seismic intensities of 0.2 g, 0.6 g, and 0.8 g, respectively. These results resemble those of \(\mu_{L\phi}\) in the sense that they do not show any trend with the strong motions; the additional observation that can be made is that bending local ductility values are, in general, larger than those of story ductility. The fundamental statistics, for all the seismic intensities and structural directions under consideration, are presented in Tables 6 and 7, for the 3- and 10-level buildings, respectively. It can be observed that, as for the case of \(\mu_{L\phi}\), the mean values of \(\mu_{S}\) do not present any tendency with the story number for the case of the 3-level building; for the 10-level building, unlike the case of \(\mu_{L\phi}\) the values do not tend to decrease with high.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Story**} & \multicolumn{8}{c}{**NS Direction**} & \multicolumn{8}{c}{**EW Direction**} \\ \cline{2-13}  & \multicolumn{8}{c}{**S\_/g Values**} & \multicolumn{8}{c}{**S\_/g Values**} & \multicolumn{8}{c}{\(S_{a}\)/g Values**} \\ \cline{2-13}  & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** \\ \cline{2-13}  & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** \\ \hline
1 & 1.00 & 0.  
By comparing the results of Tables 6 and 7 with those of Tables 4 and 5, it is concluded that, as observed from individual plots, \(\mu_{S}\) is much smaller than \(\mu_{L\phi}\) of beams; the values for the maximum seismic intensity range from 3.84 to 4.28 and from 2.49 to 5.19 for the 3- and 10-level models, respectively. As for \(\mu_{L\phi}\) for beams, the mean values and the uncertainty in the estimation tend to increase with the seismic intensity, however the uncertainty in the estimation is larger for \(\mu_{S}\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Dynamic analysis**} \\ \cline{2-13}  & \multicolumn{10}{c}{**NS direction**} & \multicolumn{10}{c}{**EW direction**} \\ \cline{2-13} \multirow{2}{*}{**Story**} & \multicolumn{10}{c}{**S/g values**} & \multicolumn{10}{c}{**S/g values**} & \multicolumn{10}{c}{**S/g values**} & \multirow{2}{*}{**PUSH**} \\ \cline{2-13} \cline{2-13}  & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & \\ \cline{2-13}  & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** & **MV** & **CV** \\ \hline
1 & 1.61 & 0.24 & 1.99 & 0.34 & 2.81 & 0.40 & 3.44 & 0.51 & 3.95 & 0.55 & 1.48 & 0.20 & 1.90 & 0.31 & 2.80 & 0.37 & 2.89 & 0.34 & 4.28 & 0.69 & 8.63 \\ \hline
2 & 1.70 & 0.18 & 2.20 & 0.29 & 2.86 & 0.46 & 3.31 & 0.42 & 3.99 & 0.50 & 1.65 & 0.17 & 2.15 & 0.24 & 2.58 & 0.31 & 3.09 & 0.32 & 3.54 & 0.45 & 7.66 \\ \hline
3 & 1.53 & 0.16 & 1.93 & 0.20 & 2.69 & 0.27 & 2.99 & 0.23 & 3.90 & 0.33 & 1.52 & 0.24 & 2.10 & 0.24 & 2.72 & 0.29 & 3.19 & 0.37 & 3.84 & 0.42 & 6.87 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistics for \(\mu_{S}\), 3-level building.  
Figure 5: Story ductility (\(\mu_{S}\)) values; _NS_ direction; 3-level building: (**a**) \(S_{a}\) = 0.4 g, (**b**) \(S_{a}\) = 0.8 g, (**c**) \(S_{a}\) = 1.2 g: 10-level buildings: (**d**) \(S_{a}\) = 0.2 g, (**e**) \(S_{a}\) = 0.6 g, (**f**) \(S_{a}\) = 0.8 g.