# Experimental Study on Dynamic Effects of a Long-span Railway Continuous Beam Bridge
## 7 Analysis of Dynamic Effects of Train-Bridge System  
The variation law of bridge vertical vibration with train speeds and the resonance speed of the train-bridge system can be obtained by vibration analysis of the bridge under moving load. The calculated speed range is 5-150 km/h for the freight train and 10-200 km/h for the passenger train. Figure 17 shows the IMs calculated from deflections (without considering the track irregularity) with one freight train (or passenger train) traveling on the bridge. There are several peaks in the IM curves, and the peaks of the side span and central span appear at different positions, which shows that the resonance may occur at multiple speeds when the train is traveling on the bridge and the resonance of each span of the continuous beam bridge occur at different loading condition. Figure 16: Comparison of numerical and measured deflection histories at the mid-span of the central span with one freight train passing through the bridge at 80 km/h. The impact factor curves of the two side spans are consistent, while the impact factor curves of the side span and the central span are different. This phenomenon shows that the long-span continuous bridge cannot maintain the continuity of its deformation, especially under instantaneous impact load. Each span of the continuous bridge acts as a simply supported beam. The subtle difference between the IMs of two side spans indicates that the impact effects of the train entering the bridge from different directions on the bridge are different. Moreover, the maximum IMs of the side span are slightly higher than those of the central span. Thus, for three-span continuous bridge, the impact effects of moving trains on the central span are less than the impact effects of moving trains on the side spans. Furthermore, the IMs of the bridge under the moving passenger train is larger than those under the moving freight train. The reason is that, although the total weight of the freight train is less than that of the passenger train, the axle load of the freight train is greater than that of the passenger train. Meanwhile, the freight train has a shorter axle spacing, so that the maximum weight of the passenger train loaded on the bridge is less than the maximum weight of the freight train loaded on the bridge. Therefore, the freight train causes greater load effects and the passenger train causes greater impact effects, which is consistent with the experimental results. Another interesting finding is that although the IM does not increase obviously with the increase of the train speed, the peak values of the IM at high speeds are significantly greater than those at low speeds. Figure 17 shows a weak correlation between the IM and the train speed. But, there exists a linear increasing trend from the overall development trend of the IM with the increase of train speed [17; 28]. When a freight train crosses the bridge at a speed of 145 km/h, the bridge has a maximum IM of 0.05. When a passenger train crosses the bridge at a speed of 185 km/h, the bridge has a maximum IM of 0.12. The maximum value appear in the mid-span of the right span. Figure 18 shows the IMs calculated from deflections with considering the track irregularity. It can be seen that the track irregularity has significant influence on the calculated value of the IMs by comparing Figures 16 and 18. The calculated values of the IMs with consideration of the track irregularity are larger than that without consideration of the track irregularity, especially when the train is running at high speeds. Moreover, after considering the track irregularity, the location of the peak of the IM curve has changed, which indicates that the track irregularity will influence the occurrence of train-bridge resonance. As [PERSON] and [PERSON] [3] reported, the resonance of the vehicle-bridge system is determined by the vehicle speed, the road roughness, and the bridge frequency. Therefore, multiple factors should be taken into account when analyzing the impact effect of moving trains on the bridge.