# Influence of Lower Lateral Bracing on the Seismic Pounding Damage to Slab-On-Girder Steel Bridges
## 3 Numerical Results
### Response under Horizontal Bidirectional Seismic Actions  
Under horizontal two-way seismic actions, due to the rotation of the bridge deck, the steel beam does not bound uniformly with all the keys on the abutment and piers but concentrates on the keys at the corner points. In addition, due to the coupling of longitudinal and transverse seismic effects, the seismic response of the bridge is greater. In this paper, horizontal bidirectional seismic action is considered as simultaneously input accelerating time histories along the longitudinal (\(x\) direction) and transverse (\(y\) direction) directions to calculate the seismic response of the bridge. The seismic acceleration time history in the \(x\) direction is the NS component of the ELC, and the seismic acceleration time history in the \(y\) direction is the WE component of the ELC. The relative displacement of the steel beam at the bearing is shown in Figure 13. It can be seen that the relative displacement of the beam, represented by the results of Position 1 and Position 8, does not exceed the displacement limit of the bearing. So, the beam will not slip off the bearing under the action of earthquakes. The seismic rounding damage to steel beams can be further analyzed under this premise. Figure 14 shows the stress cloud of the bridge in the event of a lateral bounding, and it can be seen that the bounding damage of the steel beam is more serious under horizontal two-way seismic actions. The damaged areas of the steel beam without lower lateral bracing include webs, beam ends, supporting sififteners, and steel keys. The damage to the steel beam with lower lateral bracing includes only webs, supporting sifteners, and steel keys in direct contact with the steel keys. From the perspective of the damaged area, the lower lateral bracing effectively reduces the damaged area of the steel web. Figure 15 shows the stress distribution of the steel web along the beam height under its own weight at the time of the bounding and after the earthquake. It can be seen that the stress distribution of steel beams is significantly amplified due to seismic action. As shown in Figure 15b, from the results of the peak stress, the stress of the two steel beams at the steel key exceeded the elastic limit at the time of the bounding, but the stress of the steel beam with lower lateral bracing was always less than the stress of the steel beam without lower lateral bracing. The stress of the steel beam with lower lateral bracing at the steel key is 89% of that of the steel beam without lower lateral bracing, while the stress of the steel beam with lower lateral bracing in other parts is only 41% of that of the steel beam without lower lateral bracing on average. After the end of the seismic action, the distribution of residual stress showed a similar phenomenon. As shown in Figure 15c, the residual stress of the steel beam with lower lateral bracing at the steel key is 90% of that of the steel beam without lower lateral bracing, while the residual stress of the steel beam  
Figure 13: Relative displacement of the steel beam at the bearing. with lower lateral bracing in other parts is only 32% of the steel beam without lower lateral bracing on average. Although the lower lateral bracing only slightly reduces the stress at the key, it significantly reduces the stress on other parts of the steel beam. The vertical displacement and stress time history of the lower lateral bracing are further plotted in Figure 16. The reference point of vertical displacement is the midpoint of the lower lateral bracing, and the reference point of the stress is the connection point of the lower lateral bracing and the steel beam. It can be seen that when the bounding occurs, the stress peak occurs at the connection between the lower lateral bracing and the steel beam, and the lower lateral bracing has an upward vertical displacement.