# Braking Performance and Response Analysis of Trains on Bridges Under Seismic Excitation
## 4 Conclusions  
This study evaluated the emergency braking performance of a subway train on a ten-span simply supported girder bridge under seismic excitation by means of a fully coupled multi-body/finite element model. The main findings are:  
Under the design-basis earthquake (PGA \(\approx\) 0.10 g), the train's derailment coefficient and lateral car body acceleration increase by 37% and 45%, respectively, while the bridge's lateral and vertical accelerations increase by 62% and 30%, confirming that seismic action markedly amplifies both vehicle and structural response. Introducing a constant emergency brake deceleration of 1.2 m/s\({}^{2}\) during the earthquake lowers the peak derailment coefficient from 0.46 to 0.37 (\(-\)19%) and the peak lateral bridge acceleration from 1.8 m/s\({}^{2}\) to 1.4 m/s\({}^{2}\) (\(-\)22%). Vertical bridge response is only mildly affected (\(-\)4%). Therefore, timely braking not only protects passenger safety by reducing derailment risk but also mitigates seismic demand on the bridge structure. Future work will extend the model to higher-PGA ground motions and to different bridge types (continuous and cable-stayed) in order to develop generalized braking response envelopes for urban rail seismic design. Conceptualization, H.M. and P.X. ; methodology, H.M.; software, H.M. and X.X. ; validation, Y.L. and X.X. ; formal analysis, H.M.; investigation, P.X. ; resources, Y.L. ; data curation, X.X. ; writing--original draft preparation, Y.L. ; writing--review and editing, Y.L. and X.X. ; visual \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Operating Condition** & \begin{tabular}{c} **Peak Lateral** \\ **Bridge Acc.** \\ **(m/s\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Reduction** \\ **vs. +EQ,** \\ **-BK** \\ \end{tabular} & \begin{tabular}{c} **Peak Vertical** \\ **Bridge Acc.** \\ **(m/s\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Reduction** \\ **vs. +EQ,** \\ **-BK** \\ \end{tabular} & \
\begin{tabular}{c} **Peak** \\ **Deralment** \\ **Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **Reduction** \\ **vs. +EQ,** \\ **-BK** \\ \end{tabular} \\ \hline \(-\)EQ, \(-\)BK & & & & & & \\ (no earthquake, constant speed) & & & & & & \\ \(-\)EQ, \(+\)BK (no earthquake, braking) & & & & & & \\ \(+\)EQ, \(-\)BK (earthquake, constant speed) & & & & & & \\ \(+\)EQ, \(+\)BK & & & & & & \\ (earthquake, braking) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
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