# Study on Seismic Isolation of Long Span Double Deck Steel Truss Continuous Grider Bridge
## 3 Seismic Response of Structures
### Isolation Structure  
The whole bridge is isolated, that is, 0#-3# piers are all equipped with FPBs. Parameters R and \(\upmu\) of the FPBs are optimized, respectively.  
The design of radius R of the FPB needs to be calculated according to the natural vibration period of the non-seismic isolation structure. Generally, the isolation period is more than two times that of the natural vibration period to determine the radius. Based on the nonlinear time history analysis of the isolation structure, the moment at the bottom of the pier and the relative displacement between piers and beams were obtained under an earthquake action in the longitudinal bridge direction (see Figure 10).  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Key Section**} & \multicolumn{2}{c}{**Bending Moment of Longitudinal Bridge Direction**} & \multicolumn{2}{c}{**Bending Moment of Transverse Bridge Direction**} \\  & \multicolumn{2}{c}{**(kN\(\cdot\)m)**} & \multicolumn{2}{c}{**(kN\(\cdot\)m)**} \\ \cline{2-7}  & **Force** & **Resistance** & **U** & **Force** & **Resistance** & **U** \\ \hline
0\# pier bottom & \(4.86\times 10^{5}\) & \(4.37\times 10^{5}\) & 0.90 & \(6.02\times 10^{5}\) & \(1.92\times 10^{6}\) & 3.19 \\
1\# pier bottom & \(1.35\times 10^{6}\) & \(8.37\times 10^{5}\) & 0.62 & \(1.16\times 10^{6}\) & \(2.85\times 10^{6}\) & 2.46 \\
2\# pier bottom & \(2.16\times 10^{5}\) & \(8.36\times 10^{5}\) & 3.87 & \(1.25\times 10^{6}\) & \(2.85\times 10^{6}\) & 2.28 \\
3\# pier bottom & \(5.33\times 10^{5}\) & \(4.46\times 10^{5}\) & 0.84 & \(6.68\times 10^{5}\) & \(1.92\times 10^{6}\) & 2.87 \\ \hline \hline \end{tabular} Note: u = resistance/force, representing the ability to resist earthquake.  
\end{table}
Table 2: Calculation of seismic capacity of pier.  
Figure 10: Seismic response of the longitudinal bridge direction (radius of curvature, R). (**a**) Bending moment at the bottom of pier (**b**) Relative displacement between piers and beams.  
Under the action of an E2 earthquake, the bending moment at the bottom of the 1# pier and 2# pier decreases with an increase in R, but it does not change much for the 0# pier and 3# pier. When R = 3 m, the bending moment at the bottom of the 1# pier reaches 6.32E + 5 KN-m, so it is necessary to increase the radius to reduce the bending moment at the bottom of pier; the relative displacement between the pairs and beams increases with the increase in R, but the seismic response is relatively similar.  
This section studies the isolation effect of the friction coefficient of FPB on the structure. When the R remains unchanged, friction coefficient \(\mu\) is taken as 0.01-0.05, to calculate the stiffness of FPB, respectively; results are shown in Figure 11.  
When the friction coefficient changes from 0.01 to 0.05, the relative displacement between pairs and beams decreases significantly, and the bending moment at the bottom of pier increases gradually. Although the enlargement of the friction coefficient increases the energy dissipation capacity of the bearing and can effectively \"grasp\" the main beam, the excessive friction force cannot effectively block the transmission of the inertial force between the pier and beam. At that time, the seismic energy is transferred from the main beam to the pier column, resulting in the pier suffering too much internal force, which cannot give full play to the energy dissipation function of the isolation bearing.  
Based on research on the variation of the parameters above, R can be taken as 7.0-10.0 m, and \(\mu\) as 0.02-0.03, which can effectively utilize the isolation performance of FPB. In the study of combined seismic dissipation and isolation (CSDI), the parameters within this range are used to analyze the FPB. The whole bridge isolation scheme can effectively reduce the seismic response. Due to the characteristics of FPB, there will be some residual deformation, which will cause additional stress of the bearing.