## 5 Damping System
### Influence of Damper Types on Seismic Responses  
The influence of the damper type on the seismic response of a super-long-span suspension bridge with a lattice composite tower was analyzed. The damper types were a viscous damper (VD), a buckling-restrained brace (BRB) and a friction damper combined with a shear-link beam (FD-SLB). The parameters of the dampers were as follows. The viscous damper had a damping coefficient of 1000 kN(m/s)\({}^{-0.5}\) and a velocity index of 0.5. The buckling-restrained brace had a yield force of 1500 kN and a bi-linear constitutive relationship, in which the second stiffness coefficients were 0.02, 0.06 and 0.10, respectively. The friction damper had sliding forces of 1000 kN and 1500 kN, respectively, and the shear-link beam had a shear stiffness of \(5\times 10^{4}\) kN/m.  
As shown in Figure 14, 72 dampers were installed among the sub-towers along the transverse and longitudinal directions.  
Seismic responses from different types of dampers exposed to far-fault and near-fault earthquakes were calculated and compared. The displacement and the acceleration responses along the height of the tower are shown in Figure 15. It is noted that the tower response of the suspension bridge under the near-fault ground motion was larger than that of the far-fault ground motion, and the results agree well with the earthquake-induced response tendency of long-span bridges in the literature [27; 28].  
The results demonstrated that the friction damper combined with the shear-link beam (FD-SLB) performed better than the other two types of dampers (VD and BRB) at reducing seismic responses. When using El Centro earthquake excitation data, the control effects of all types of dampers on the displacement of the tower were similar because the displacement responses of the tower were small and the tower was mostly in an elastic state. When using Chi-Chi earthquake excitation data, the displacement responses of the tower markedly increased compared with those exposed to El Centro earthquake data, which agreed with the results in reference [28]. The displacement of the dampers significantly increased; thus, the energy dissipation ratio of the damping system also improved. This indicated that FD-SLB could significantly decrease the seismic response of super-long-span suspension bridges, especially those exposed to near-fault ground motions, as it satisfied the energy dissipation requirements more effectively.  
Figure 14: Damper distribution in the sub-towers.  
To verify the accuracy of the above analyses, scaled shaking-table tests of the lattice composite tower with viscous dampers were performed. Four dampers were installed in a bottom-middle distribution, as shown in Figure 16. The design parameters and test scheme were the same as those listed in Section 4.2. The velocity power index and the viscous coefficient of the viscous damper were 0.9 and 58 N s/mm, respectively. The mechanical properties of the viscous dampers can be found in reference [15].  
Figure 15: Displacement along the height of the tower with different types of dampers: (**a**) El Centro, PGA = 400 gal; (**b**) Chi-Chi, PGA = 400 gal; (**c**) El Centro, PGA = 800 gal; (**d**) Chi-Chi, PGA = 800 gal.  
The displacement history along the height of the lattice composite tower used in the test is provided in Figure 17. These results were compared with the displacement responses of the original main tower. The displacement damping rate at 2/3 the height of the tower was 60.8% in the test and 54.5% in the FEA results. The displacement control effect at the tower top was 52.1% in the test and 48.3% in the FEA results. The test results demonstrated the accuracy of the finite element model and analysis method. It was noted that the bottom-middle damper arrangement scheme could significantly decrease the seismic response of the super-long-span suspension bridge.