## 2 Dynamic Response of a Multi-Story STMF with SMAs
### Dynamic Time History Analysis
However, the incorporation of SMAs according to Table 1 makes the inter-story drift distribution more uniform with larger values on the lower floors and smaller on the upper floors, compared to those of the conventional structure. For the Kocaeli (K1E), the Imperial Valley (IVE), and the Kobe (K2E) earthquakes, SMAs deform in the limits of superelasticity at all floors (Tables 6-8). The incorporation of half the calculated diameter of SMAs per diagonal leads to a more flexible structure with SMA displacements exceeding the 6% limit. The maximum inter-story drift diagram for the Kocaeli earthquake (Figure 5a) reveals that the structure with the conventional STMF presents a more even distribution with lower values compared to those of the other two configurations. All inter-story drift values are equal or greater to the target drift limit of 2%, indicating that the structures undergo damage, while for the Imperial Valley (Figure 5b) and the Kobe earthquakes (Figure 6a), a more uniform drift distribution of the structure with the SMAs according to \(V_{ne}\) compared to the conventional STMF is revealed, with drifts below the 2% drift limit; the incorporation of half the calculated diameter of SMAs causes drifts larger than the 2% limit at upper floors and damage is caused. For the Chichi earthquake (CE), SMAs respond to the limits of superelasticity at all floors (Table 9). The incorporation of half the calculated diameter of SMAs per diagonal still gives SMA responses in the limits of superelasticity, unlike the previously examined earthquakes. The maximum inter-story drift diagram (Figure 6b) shows more uniform drifts for the incorporation of SMAs according to \(V_{ne}\) compared to the ones of the conventional structural structure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Floor**} & **Displacement** & **Corresponding** & **Displacement** & **Corresponding** \\  & **(m)** & **Strain** & **(m)** & **Strain** \\ \hline
9 & 0.05 & 1.8\% & 0.17 & 6.3\% \\
8 & 0.03 & 1.1\% & 0.1 & 3.6\% \\
7 & Linear response & Negligible & 0.065 & 2.4\% \\
6 & Linear response & Negligible & 0.045 & 1.6\% \\
5 & Linear response & Negligible & 0.04 & 1.4\% \\
4 & Linear response & Negligible & 0.045 & 1.6\% \\
3 & 0.02 & 0.74\% & 0.04 & 1.4\% \\
2 & 0.02 & 0.74\% & 0.035 & 1.3\% \\
1 & 0.02 & 0.74\% & 0.03 & 1.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: **SMAs**  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Floor**} & **Displacement** & **Corresponding** & **Displacement** & **Corresponding** \\  & **(m)** & **Strain** & **(m)** & **Strain** \\ \hline
9 & 0.026 & 0.95\% & 0.20 & 7.4\% \\
8 & 0.03 & 1.1\% & 0.08 & 3.0\% \\
7 & 0.02 & 0  
For the Landers earthquake (LE), SMAs deform within the limits of superelasticity at all floors (Table 10). The maximum inter-story drift diagram (Figure 7) shows that inter-story drifts, unlike the previously examined earthquakes, are not uniformly distributed along the height of the structure neither for the conventional nor for the incorporation of SMAs according to \(V_{ne}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Table 1 SMAs**} & \multicolumn{2}{c}{**Half the Diameter of Table 1**} \\ \hline \multirow{2}{*}{**Floor**} & **Displacement** & **Corresponding** & **Displacement** & **Corresponding** \\  & **(m)** & **Strain** & **(m)** & **Strain** \\ \hline
9 & 0.03 & 1.1\% & 0.12 & 4.4\% \\
8 & 0.03 & 1.1\% & 0.09 & 3.3\% \\
7 & 0.03 & 1.1\% & 0.09 & 3.3\% \\
6 & 0.035 & 1.3\% & 0.08 & 3.0\% \\
5 & 0.035 & 1.3\% & 0.06 & 2.2\% \\
4 & 0.03 & 1.1\% & 0.042 & 1.55\% \\
3 & 0.03 & 1.1\% & 0.04 & 1.4\% \\
2 & Linear & Negligible & 0.03 & 1.1\% \\
1 & Linear & Negligible & 0.03 & 1.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Maximum SMA displacements for LE. Figure 6: Comparison of maximum inter-story drifts for the design cases dealt with (a) K2E; (b) CE.