# Seismic Effectiveness of Multiple Seismic Measures on a Continuous Gider Bridge
## 5 Calculation Analysis and Discussion
### Bending Moment  
In an earthquake, the pier bears a large horizontal seismic force, leading to a large bending moment at the bottom of the pier. Once the bending moment exceeds the yield moment at the bottom of the pier, plastic failure of the pier will occur. Figure 10 shows the change of bending moment at the bottom of the pier after different combinations of seismic measures are used for the bridge structure under the action of earthquakes. The piers have the same height, so the bending moment at the bottom of each pier has a linear relationship with the pier top displacement; i.e., the bending moment at the bottom of each pier changes in the same manner as the pier top displacement. Under the action of the Northridge earthquake, the bending moment at the bottoms of the piers is the biggest in Case 1; in particular, that of #1 and #5 piers is 7564 kN-m, and that of #2, #3, and #4 piers is 32,594 kN-m. The bending moment at the bottom of #1 and #5 piers does not change under the action of a small earthquake. Under the action of moderate, large, and Northridge earthquakes, the bending moment at the bottom of #1 and #5 piers increases compared with Cases 1 and 2, while the bending moment at the bottom of #2, #3, and #4 piers decreases. However, in Case 4, the displacement of the bearing has reached its allowable shear deformation when the unseating prevention devices control the bearing. Thus, the girder bears a relatively large impact force, and the unseating prevention devices have a bigger restraining force on the substructure and superstructure than the restrainer. That is why the bending moment at the bottom of #1 and #5 piers is greater in Case 4 than other cases. In Figure 10a, Case 1 and Case 2 have small and basically identical bending moments under earthquakes of different magnitudes, indicating that the expansion device insignificantly influences the bending moments of #1 and #5 piers. Under earthquakes of different magnitudes, Case 3 has a  
Figure 10: Moment of the pier bottom in different cases under different earthquakes: (**a**) side piers and (**b**) middle piers. slight bigger bending moment than Cases 1 and 2, but a much smaller bending moment than Cases 5 and 6. Case 4 has almost the biggest bending moment at the bottom of #1 and #5 piers in all the cases. Under the action of moderate, large, and Northridge earthquakes, the bending moment at the bottom of #1 and #5 piers is 16,775 kN-m, 30,729 kN-m, and 38,966 kN-m, respectively, which increase to 4.35, 6.02 and 5.15 times the original design value (7564 kN-m). In Cases 4, 5, and 6, the piers have a bigger bending moment at their bottom than their yield bending moment (28,650 kN-m) under the action of large and Northridge earthquakes, since the unseating prevention devices transfer less seismic load to #1 and #5 piers. In Figure 10b, the #2, #3, and #4 piers have a bigger bending moment at their bottom in Case 1 than other cases; under the Northridge earthquake, the piers have a bending moment of 32,594 kN-m at their bottom, and this is bigger than the yield bending moment (28,650 kN-m). The bending moment at the bottom of #2, #3, and #4 piers decreases after seismic measures are taken. Under the action of moderate, large, and Northridge earthquakes, the #2, #3, and #4 piers have a bending moment at their bottom of 14,232 kN-m, 20,783 kN-m and 17,592 kN-m, respectively, which decreases to about 74%, 82%, and 54% of the initial design value (32,594 kN-m), all of which do not exceed their ultimate bending moment in Case 6. The above analysis shows that the seismic measures increase the connection between the substructure and superstructure of the bridge, and primarily affect #1 and #5 piers with seismic measures. Thus, #1 and #5 piers with sliding rubber bearings bear a bigger seismic load, and the entire bridge gradually has an identical bending moment at the bottom of the piers.