# Influence Analysis of Traveling Wave Effect on Rail Interaction of Long-Span Suspension Bridge
## 5 Response of Beam-Rail System under Traveling Wave Effect  
### Track Seismic Response  
Figure 10 is the longitudinal force envelope diagram of the rail under the apparent wave velocity of 200 m/s\(-\)8000 m/s and consistent excitation (the apparent wave velocity is \(\infty\)). Table 4 gives the stresses of the rails at different positions. The junction points of the north subgrade approach bridge, the north main approach bridge junction, the south main approach bridge junction, and the south subgrade approach bridge junction are named as points A, B, C, and D, respectively. In the subsequent calculation and analysis, if there is no special instruction, they still use this naming method. It can be seen from the analysis that no matter whether the traveling wave effect is considered or not, the absolute maximum rail stress of the whole bridge appears at points A and D, this is because at points B and C, the longitudinal movement of the steel truss is not restricted, but the longitudinal movement of the rails in the side span of the main bridge is restricted by the boundary conditions of the approach bridge and the roadbed, resulting in a great accumulation of the seismic stress of the rails at points A and D and reaching the maximum value; the rails at points B and C, due to the existence of the rail expansion regulator, keep their stress at a small value all the time; due to the existence of the beam end expansion device and the fact that the main bridge is a semi-floating system, the longitudinal displacement of the main bridge is not restricted. Due to the existence of the beam end expansion device, and the main bridge for the semi-floating system, the main bridge in the longitudinal displacement is not limited, the rails on the main bridge can be moved together with the main beam, the beam-rail relative displacement is always kept small, so the stress on the rails of the main bridge are small. The absolute value of the rail stress at point A decreases with the increase in the apparent wave velocity, and the maximum value of the tensile stress and the minimum value of the compressive stress of the rail gradually approach 115.6 MPa and \(-\)127.9 MPa  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Apparent Wave Speed (m/s)**} & \multirow{2}{*}{**Stress of Rail at Point**} & \multirow{2}{*}{**Stress of Rail at Point**} & \multirow{2}{*}{**Stress of Rail at Point**} & \multirow{2}{*}{**Stress of Rail at Point**} & \multirow{2}{*}{**Stress of Rail at Point**} & \multirow{2}{*}{**Main Bridge Span**} \\  & & & & **B (MPa)** & & & **C (MPa)** & & **D (MPa)** & \\ \hline
200 & 206.5 & \(-197.1\) & 34.8 & \(-33.3\) & 37.5 & \(-46.3\) & 202.2 & \(-189.9\) & 50.6 & \(-49.6\) \\
500 & 163.7 & \(-150.1\) & 36.0 & \(-36.4\) & 39  
under consistent excitation. s is basically the same, and compared with the consistent excitation, the absolute value of the maximum tensile and compressive stress increases by about 78.6% and 54.1% when the apparent wave velocity is 200 m/s; the absolute maximum value of rail stress at point D decreases with the increase of apparent wave speed at low apparent wave speed, and oscillates around the value under consistent excitation at high apparent wave speed, and the absolute maximum value of tensile stress at apparent wave speed of 200 m/s increases about 57.8% and 64.6% respectively compared with consistent excitation; the absolute maximum value of rail stress at the middle of the main bridge span basically decreases with the increase of apparent wave speed, and the maximum and minimum value of tensile stress at apparent wave speed of 500 m/s changes to 51.8 MPa and \(-\)50.6 MPa respectively compared with consistent excitation. Compared with the consistent excitation, the maximum and minimum values of tensile and compressive stresses at the apparent wave speed of 500 m/s change to 51.8 MPa and \(-\)50.6 MPa respectively, which are much larger than the rail stresses under the consistent excitation.