# Influence Analysis of Traveling Wave Effect on Rail Interaction of Long-Span Suspension Bridge
## 5 Response of Beam-Rail System under Traveling Wave Effect
### Earthquake Response of Bridges
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Apparent Wave Speed (m/s)**} & \multicolumn{2}{c}{**Longitudinal Displacement of the Approach Bridge at Point A (mm)**} & \multicolumn{2}{c}{**Longitudinal Displacement of Main Bridge at Point B (mm)**} & \multicolumn{2}{c}{**Longitudinal Displacement of Main Bridge at Point D (mm)**} \\ \cline{2-7}  & **MAX** & **MIN** & **MAX** & **MIN** & **MAX** & **MIN** & **MAX** & **MIN** \\ \hline
200 & \(109\) & \(-100\) & \(366\) & \(-463\) & \(564\) & \(-418\) & \(92\) & \(-105\) \\
500 & \(74\) & \(-61\) & \(168\) & \(-223\) & \(269\) & \(-234\) & \(44\) & \(-60\) \\
1000 & \(56\) & \(-51\) & \(146\) & \(-171\) & \(122\) & \(-104\) & \(33\) & \(-49\) \\
2000 & \(46\) & \(-45\) & \(106\) & \(-127\) & \(60\) & \(-38\) & \(32\) & \(-43\) \\
4000 & \(42\) & \(-43\) & \(67\) & \(-93\) & \(48\) & \(-61\) & \(32\) & \(-54\) \\
8000 & \(38\) & \(-43\) & \(72\) & \(-86\) & \(73\) & \(-63\) & \(33\) & \(-43\) \\ \(\infty\) & \(36\) & \(-43\) & \(71\) & \(-81\) & \(85\) & \(-69\) & \(35\) & \(-43\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Longitudinal displacement of beam end at different apparent wave velocities. Figure 20 shows the displacement time-history curves of the main bridge end under the apparent wave velocity of 200 m/s, 8000 m/s and consistent excitation. The analysis shows that the displacement time history of the north and south main bridge ends is very close under the large apparent wave velocity and consistent excitation; that is, the displacement of the main bridge ends on the north and south sides approximately keeps  
Figure 19: Longitudinal displacement of beam end at different apparent wave velocities. changing synchronously, but the displacement value is different due to the longitudinal deformation of the main girder itself, but the limited deformation of the main girder of the approach bridge will not affect the approach bridge due to the existence of the telescopic device at the beam end. Therefore, in Table 6, the maximum and minimum displacements of the main bridge end on different sides of the same excitation are somewhat different, while the maximum and minimum displacements of the approach bridge end on different sides of the approach bridge are almost the same, which conforms to the force characteristics of the suspension bridge; at low apparent wave velocities, the displacements of the north and south main bridge ends no longer keep changing synchronously and are much larger than the displacements of the main bridge ends under consistent excitation. Table 8 shows the time for each point to reach the maximum positive longitudinal displacement under different apparent wave velocities and consistent excitation. It can be seen that at low apparent wave velocities, the timing of reaching the maximum positive longitudinal displacement at the north and south main approach bridge ends is different. The big moment is gradually approaching, which once again verified the conclusions obtained from the previous analysis. Additionally, comparing Table 6, it can be seen that the time when point A reaches the maximum positive longitudinal displacement is basically the same as the time when the rail stress at point A reaches the maximum tensile stress, and the time when point D reaches the maximum positive longitudinal displacement is basically the same as the time when the rail stress at point D reaches the minimum compressive stress.