## 5 Seismic Performance Analysis
### Seismic Responses under the SLEs  
For the prototype bridge, according to the bending moment-curvature analysis results, the yield curvatures of the main pier in longitudinal and transverse directions are 0.00056 and 0.00039, respectively. Under SLEs, the maximum curvature in the longitudinal direction equaling 0.00024 is observed at the top of the tall piers. The maximum curvature in the transverse direction of the bridge is 0.00002. Both of the curvature values are less than the yield curvatures. Therefore, the RC tall-pier bridge remains elastic when subject to SLEs.  
For the new composite tall piers, under the SLEs, the maximum curvature at the top and bottom of the tall piers are 0.00082 and 0.00018, respectively. Both values are less than the yield curvature of 0.00240. Meanwhile, the maximum stress of the steel beams is 75 MPa, which is less than the yield stress of 345 MPa. Besides, the maximum stress of EDMSPs equals 81 MPa and is less than its yield stress. Therefore, the new composite tall-pier bridge is in the elastic state. Table 5 shows the average values of maximum displacements under different seismic actions. The results indicate that the lateral displacements of the new composite tall-pier bridge are close to the prototype bridge under the SLEs. Both the seismic responses of two bridges meet the requirements of damage limitation state when subject to the SLEs. Figure 7 compares the maximum displacement responses of the bridge under the SLEs. Although the maximum displacements of new composite tall-pier bridge are larger than the prototype one under some ground motions considering SLEs, the seismic performances of two bridges are similar. Both the prototype and the new bridges remain elastic without damage.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **Event** & **Station** & \(\mathbf{d}\) (**km)** & **PGA** & **PGV/PGA** & **Site** \\  & & & & **(s)** & **(s)** & **Type** \\ \hline Eq1 & Chi Chi Taiwan & TCU65 & 0.6 & 0.431 & 1.43 & C \\ Eq2 & Imperial Valley 06 & El Centro Array \#6 & 1.4 & 0.438 & 0.90 & D \\ Eq3 & Imperial Valley 06 & El Centro Array \#7 & 0.6 & 0.337 & 1.41 & C \\ Eq4 & Loma Prieta & Saratoga-Aloha Ave & 8.5 & 0.512 & 0.80 & C \\ Eq5 & Irpinia Italy 01 & Sturno & 10.8 & 0.371 & 1.74 & A \\ Eq6 & Chi Chi Taiwan & TCU102 & 1.5 & 0.297 & 3.79 & B \\ Eq7 & Duzce Turkey & Duzce & 6.6 & 0.296 & 1.34 & C \\ \hline \hline \end{tabular}
\end{table}
Table 4: Near-fault velocity pulsed ground motion records.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Average Displacement (cm)**} \\ \cline{3-5}
**Position** & **Direction** & \begin{tabular}{c} **Prototype** \\ **Pier(\(\delta_{\text{P}}\))** \\ \end{tabular} & \
\begin{tabular}{c} **New** \\ **Pier(\(\delta_{\text{N}}\))** \\ \end{tabular} &
\begin{tabular}{c} \(\frac{\delta_{\text{P}}\cdot\delta_{\text{N}}}{\delta_{\text{N}}}\) \\ \end{tabular} \\ \hline Top of piers & Longitudinal & 7.49 & 7.39 & 1.1\% \\ Top of piers & Transverse & 5.46 & 5.12 & 6.7\% \\ Relative displacement between superstructure and piers & 3.73 & 3.49 & 6.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of average displacements under the SLEs.