## 2 Dynamic Response of a Multi-Story STMF with SMAs
### An Alternative Design Approach
\begin{tabular}{c} Linear \\ response \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ \hline \end{tabular}  \\
1 & 0.03 & 1.1\% & 0.05 & 1.8\% & \begin{tabular}{c} Linear \\ response \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ Negligible \\ \hline \end{tabular}  \\
1 & 0.03 & 1.1\% & 0.05 & 1.8\% &
\begin{tabular}{c} Linear \\ response \\ NegligFor the Northridge earthquake, for case DC1, SMAs respond in the limits of superelasticity (Table 13) as well. Compared to SMA displacements dimensioned according to \(V_{ne}\), a decrease of 62% is observed at the 8 th floor's maximum strain and a tremendous decrease in strain at the 9 th floor. The maximum inter-story drift diagram (Figure 8b) shows uniform drifts for case DC1, which are smaller at upper floors compared to those of the conventional structure and the structure with SMAs according to \(V_{ne}\) drifts. Case DC2 gives larger SMA strains than case DC1 but is still within the limits of superelasticity. However, the drift diagram shows an uneven distribution with drifts on the 9 th floor approaching the 2% target drift limit, indicating that plastic hinges may have been formed at members outside the special segment. Case DC3 leads to a very stiff special segment; plastic hinges may form again at the members that are supposed to remain elastic, and SMAs on every floor exhibit negligible strains. For the Kocaeli earthquake, SMA strains for the case DC1 (Table 14) are larger at lower floors and negligible at the 8 th and 9 th floors due to the increased strength provided in the special segments. Case DC2 leads to a more flexible structure, with SMA strains exceeding the limit of superelasticity. The above remarks are also depicted in the maximum inter-story \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)** & & & **(m)** & \\ \hline
9 & Linear & \multirow{2}{*}{Negligible} & \multirow{2}{*}{0.1} & \multirow{2}{*}{3.7\%} & Linear & \multirow{2}{*}{Negligible} \\  & response & & & & & & \\
8 & 0.025 & & 0.9\% & 0.08 & 3.0\% & & \\
7 & 0.025 & & 0.9\% & 0.08 & 3.0\% & & \\
6 & Linear & \multirow{2}{*}{Negligible} & \multirow{2}{*}{0.075} & \multirow{2}{*}{2.8\%} & Linear & \multirow{2}{*}{Negligible} \\  & response & & & & & & \\
5 & 0.05 & & 0.05 & 0.05 & 2.0\% & & \\
4 & 0.045 & & 0.065 & & 2.4\% & & \\
3 & 0.04 & & 0.07 & & 2.6\% & & \\
2 & Linear & \multirow{2}{*}{Negligible} & \multirow{2}{*}{0.06} & \multirow{2}{*}{2.2\%} & Linear & \multirow{2}{*}{Negligible} \\  & response & & & & & & \\
1 & 0.04 & & 0.055 & & 2.0\% & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Maximum SMA displacements for NE for the configurations investigated. Figure 8: Comparison of maximum inter-story drifts for **(a)** LPE; **(b)** NE. drifts diagram (Figure 9a), as inter-story drifts for the DC1 case at the upper floors are not only smaller than the corresponding ones of the conventional structure but also lower than the 2% target drift limit. For the Imperial Valley earthquake, SMA strains for the case DC1 (Table 15) are close to each other except for the bottom and the 9 th floors. By comparing to the corresponding values of the distribution of SMAs according to \(V_{ne}\), it can be perceived that placing smaller diameters (0.056 m) at lower floors than the one derived from \(V_{ne}\) dimensioning provokes larger strains to SMAs.