# Seismic Effectiveness of Multiple Seismic Measures on a Continuous Gider Bridge
## 5 Calculation Analysis and Discussion
### Energy Dissipation  
The expansion device, restrainer, and unseating prevention devices consume seismic energy during their deformation under the action of an earthquake. Figure 13 shows the cumulative dissipated energy of seismic measures in each case under the action of the large earthquake. Figure 13a shows the cumulative dissipated energy of the expansion device in each case. In Cases 1, 3, 4, and 6, the expansion device has cumulative dissipated energies of 69,565 kJ, 67,066 kJ, 197 kJ, and 230 kJ, respectively. This indicates that the restrainer can reduce the impact force at the expansion joint to a certain extent, and the unseating prevention devices can completely control the displacement of the expansion device within 16 cm without bounding. Thus, the dissipated energy is smaller and is almost provided by the rubber material in the expansion device. The energy jump which occurs in the energy dissipation time history is the dissipated energy increment caused by the bounding at the expansion joint. When the bounding no longer occurs, and the dissipated energy of the expansion device no longer accumulates, the total consumed energy reaches a plateau. Figure 13b shows the dissipated energy of the restrainer in each case. In Cases 3, 5, and 6, the restrainer deforms and dissipates energy progressively, with ultimate cumulative dissipated energies of 82,055 kJ, 39,564 kJ, and 39,180 kJ, respectively. This shows that the installed restrainer can better  
Figure 13: Cumulative energy dissipation of seismic measure: (**a**) energy dissipation of expansion devices, (**b**) energy dissipation of the restrainer, (**c**) energy dissipation of the unseating prevention device. restrain the displacement and dissipate energy under the action of an earthquake. The restrainer dissipates a smaller energy in Cases 5 and 6, in which the restrainer and unseating prevention devices work together than Case 3, in which unseating prevention devices are not used. Figure 13c shows the dissipated energy of the unseating prevention devices in each case. With reciprocating motion in an earthquake, the unseating prevention devices bear a large impact force several times while they considerably deform. In Cases 4, 5, and 6, the unseating prevention devices continuously deform and dissipate energy, with ultimate cumulative dissipated energies of 37,173 kJ, 26,828 kJ, and 25,460 kJ, respectively. The dissipated energy and the force on the unseating prevention devices are reduced to a certain extent in Case 5, in which the restrainer is used, and the expansion device is used in Case 6, meaning that multiple seismic measures share the seismic load and thereby reduce the seismic load on each device. In summary, the joint application of the expansion device, restrainer, and unseating prevention devices effectively controls the excessive displacement of the bridge structure under the action of the earthquakes. Meanwhile, they cooperate with one another to share the impact force caused by the earthquake load and make the forces on the structure and seismic measures more reasonable. The multiple seismic measures show a much better seismic effect than a single seismic measure. Therefore, Case 6 is the best in all cases. Table 4 shows the seismic response of the structure at all magnitudes of earthquakes and the ratios of the seismic response to the initial design value in Case 6. Regarding the analysis of the seismic response of the structure at all magnitudes of earthquakes and the ratio of seismic response in Case 6 to Case 1 in Table 4, it can be seen that the displacements of the bridge girder and bearing generally decrease after the seismic measures are taken in each case. The displacement of the girder in Case 6 can be reduced to at most 48% of that in Case 1. The maximum displacement of the girder is 13.75 cm, which is smaller than the allowable deformation--16 cm--of the expansion joint at the girder end. The displacement of the bearing can be reduced to at most 34% of that in Case 1.