## 2 Dynamic Response of a Multi-Story STMF with SMAs
### An Alternative Design Approach
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DC1**} & \multicolumn{2}{c}{**DC2**} & \multicolumn{2}{c}{**DC3**} \\ \hline \multirow{2}{*}{**Floor**} & **Displacement** & \multirow{2}{*}{**Strain**} & **Displacement** & \multirow{2}{*}{**Strain**} & **Displacement** & \multirow{2}{*}{**Strain**} \\  & **(m)** & & **(m)** & & & \\ \hline
9 & 0.015 & 0.55\% & 0.06 & 2.2\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
8 & 0.015 & 0.55\% & 0.08 & 3.0\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
7 & 0.016 & 0.59\% & 0.08 & 3.0\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
6 & 0.02 & 0.74\% & 0.046 & 1.70\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
5 & 0.017 & 0.63\% & 0.043 & 1.59\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
4 & 0.017 & 0.63\% & 0.04 & 1.4\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
3 & 0.016 & 0.59\% & 0.045 & 1.6\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
2 & 0.015 & 0.55\% & 0.05 & 1.8\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
1 & 0.015 & 0.55\% & 0.04 & 1.4\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Maximum SMA displacements for K2E for the configurations investigated. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DC1**} & \multicolumn{2}{c}{**DC2**} & \multicolumn{2}{c}{**DC3**} \\ \hline \multirow{2}{*}{**Floor**} & **Displacement** & \multirow{2}{*}{**Strain**} & **Displacement** & \multirow{2}{*}{**Strain**} & **Displacement** & \multirow{2}{*}{**Strain**} \\  & **(m)** & & **(m)** & & & \\ \hline
9 & 0.01 & 0.36\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
8 & 0.014 & 0.52\% & 0.02 & 0.74\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
7 & 0.016 & 0.59\% & 0.045 & 1.6\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
6 & 0.017 & 0.63\% & 0.05 & 1.8\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
5 & 0.018 & 0.66\% & 0.05 & 1.8\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
4 & 0.017 & 0.63\% & 0.06 & 2.2\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
3 & 0.015 & 0.55\% & 0.06 & 2.2\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
2 & 0.016 & 0.59\% & 0.05 & 1.8\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\
1 & 0.018 & 0.66\% & 0.04 & 1.4\% &
\begin{tabular}{c} Linear \\ response \\ \end{tabular} & Negligible \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Maximum SMA displacements for CE for the configurations investigated. As it can be deduced from the above, for case DC1 SMAs responded, in general, in the limits of superelasticity, exhibiting strains that decreased at upper floors and increased at lower floors compared to the corresponding ones of the structure with SMAs according to \(V_{ne}\). This is also depicted on the maximum inter-story drifts as case DC1 drifts are larger at lower floors and smaller at upper floors. In addition, maximum inter-story drift diagrams show uniform drift distribution below the 2% target drift limit except in the excitation of the structure with the Kocaeli and Landers earthquakes. For the DC2 case, SMAs respond generally in the limits of superelasticity except for the Kocaeli earthquake. However, larger inter-story drifts occur at upper floors, exceeding, for some earthquakes, the 2% target drift limit, and the drift distribution is uneven for all earthquake records examined. The last case studied, designated as DC3, creates a very stiff special segment.