# 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
Generally speaking, the influence of traveling wave effect on orbit cannot be ignored. The absolute maximum value of rail stress appears at point A (near the source side). Especially for the rails on the main bridge, the impact of the traveling wave effect is more obvious, and it is obviously inappropriate to only consider the consistent excitation. Figures 11 and 12 show the time history of rail stress and the relative displacement of beam and rail, respectively, at point A under different apparent wave velocities. Table 5 gives the Pearson product moment correlation coefficients (PPMCC) for seven groups of rail stress time course curves and beam-rail relative displacement curves at different apparent wave speeds. Analysis shows that: the time course curves of rail stress and the time course curves of beam-rail relative displacement have high similarity, and the peaks and valleys correspond to each other, that is, rail additional force is essentially caused by the relative displacement of the beam-rail, in line with the mechanism of rail additional force generation. The time course curves of the rail stress and the relative displacement of the beam-rail at high apparent wave velocity are very similar to the curves under consistent excitation; the relative displacement of the beam-rail at the smaller apparent wave speed is much larger than the relative displacement of the beam-rail under consistent excitation, so the absolute maximum value of the tensile stress of the rail at the smaller apparent wave speed is much larger than the absolute maximum value of the tensile stress under consistent excitation. Figure 11: Time-history curve of rail stress at point A under different apparent wave velocities. Figures 13-17 show the stress-time-history curves of the rail at points A and D under different apparent wave velocities and consistent excitation. The analysis shows that when the apparent wave velocity is small, the stress-time-history of point D (measured far away from the seismic source) lags behind that of point A (near the source side); as the apparent wave velocity increases, this hysteresis phenomenon gradually disappears, and with the disappearance of this hysteresis phenomenon, the stresses at points A and D eventually change synchronously with opposite values; that is, when the rail at point A is pulled, the rail at point D is under compression, and as shown in Table 6, the maximum tensile stress time at point A is gradually approaching the maximum compressive stress time at point D, and the stress values are the same, which is consistent with the stress characteristics of suspension bridges under consistent excitation. Figure 16: The stress–time-history curve of the rail at point A and point D when the apparent wave velocity is 8000 m/s. Figure 14: The stress–time-history curve of the rail at point A and point D when the apparent wave velocity is 500 m/s. Figure 15: The stress–time-history curve of the rail at point A and point D when the apparent wave velocity is 4000 m/s. Figure 18 shows the comparison of the rail stress time course curve at point D with the original curve when the apparent wave speed is 200 m/s shifted forward by 9.42 s. It can be seen that the curve is almost identical and there is a hysteresis.