# Influence of Lower Lateral Bracing on the Seismic Pounding Damage to Slab-On-Girder Steel Bridges
## 3 Numerical Results
### Response under Transverse Seismic Actions  
Under the effect of the transverse seismic actions, the steel keys on the steel beams' sides bound with the concrete keys on the abutments and piers. At the time of bounding, the huge impact force is transferred to the steel beams through the steel block and leads to its damage. The stress state of the steel beam at the time of bounding is shown in Figure 10. It can be seen that the steel beam without lower lateral bracing produces a larger high-stress zone at the time of bounding. Specifically, all the damages to the steel beams without lower lateral bracing are concentrated at the location of the keys on the side beams (at position A in Figure 10). The center beams bear almost no lateral force (at position B in Figure 10). In contrast, for the steel beam with lower lateral bracing, the damage at the key location on the side beam is mitigated because the lower lateral bracing partially transfers the bounding force from location A to location B on the center beam. The lateral bounding damage of the steel beam was significantly mitigated due to the sharing and transfer of the bounding force by the lower lateral bracing. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**NO.**} & \multicolumn{2}{c}{**Frequency/Hz**} & \multirow{2}{*}{**Error/\%**} & \multirow{2}{*}{**Mode Shape Description**} \\  & **Test** & **FEM** & & \\ \hline
1 & 2.91 & 2.80 & 3.81 & Vertical antisymmetric bending \\
2 & 3.66 & 3.46 & 2.51 & Vertical bending on side spans \\
3 & 4.76 & 4.64 & 5.43 & Vertical symmetrical bending \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of natural vibration characteristics. Figure 9: The first three-order vertical natural modes. (**a**) First-order mode shape; (**b**) second-order mode shape; (**c**) third-order mode shape. The transverse seismic bounding causes the steel beam to experience high stress and also leads to the residual deformation of the steel beam. As shown in Figure 11a, under the transverse bounding force, the steel beam will be deformed by rotations inward. Since the stress of the steel beam under bounding will exceed the elastic limit of the steel, the rotational deformation at the bottom of the beam is irreversible. After the end of the seismic action, the displacement angle between the top and bottom plates of the beam is shown in Figure 11b. It can be seen that due to the sharing of the bounding force by the lower lateral bracing and the enhancement of the transverse stiffness of the steel beam, the displacement angle of the bracing steel beam is significantly smaller than that of the non-bracing steel beam. In addition, at the pier and abutment positions, the lower lateral bracing can significantly reduce the displacement angle of the beam to 40% of the original one. The stress time history of the steel beam and the lower lateral bracing is shown in Figure 12a, and it can be seen that a bounding occurred at 12.3 s. The bounding caused stress peaks of 464 MPa, 437 MPa, and 242 MPa for the steel beam without lower lateral bracing, the steel beam with lower lateral bracing, and the lower lateral bracing, respectively. After the bounding, the residual stresses of the steel beam without lower lateral bracing, the steel beam with lower lateral bracing, and the lower lateral bracing were 371 MPa, 249 MPa, and 97 MPa, respectively. The residual stress of the steel beam with lower lateral bracing and the lower lateral bracing to the steel beam without lower lateral bracing accounted for 67% and 26%, respectively; that is, lower lateral bracing shared about 1/3 of the bounding impact. Moreover, the stress peak of the lower lateral bracing does not exceed the elastic limit of the steel when experiencing a bounding, and it always remains elastic under the  
Figure 10: Stress cloud diagram of steel beam (unit: MPa). (**a**) Pounding of steel beams without lower lateral bracing; (**b**) bounding of steel beams with lower lateral bracing. action of earthquakes.