## 3 Numerical Simulation of the Rail-Cum-Road Cable-Stayed Bridge
The initial strain method was adopted to add initial tension to the cables, and the degrees of freedom of the two end nodes of the cable simulated by the link element were coupled to its vicinal nodes of the solid elements and beam elements. The nonlinear geometrical effects were considered by turning on the large deflection effects during the analysis period. Four fluid viscous dampers were installed between the main girder and crossbeam of the pylons to decrease the longitudinal vibration of the girder caused by earthquakes, winds, vehicles, and trains. The fluid viscous damper is a kind of velocity-dependent damper, and the damping force is only related to the relative velocity between its two end nodes, so it did not provide additional stiffness to the whole structure. The damping force, velocity exponent, and damping coefficient of the damper adopted were 3000 kilomewtons, 0.25, and 3998 kilonewton seconds per meter, respectively. The COMBIN37 element in the ANSYS software can simulate the fluid viscous damper, a unidirectional element with nonlinear capacity, as shown in Figure 6. The element is defined by two pairs of nodes: active nodes I and J, which determine the element's position, and optional control nodes K and J, which are used to control the nonlinear behavior of the element. The two pairs of nodes can have inconsistent degrees of freedom. Each has only one degree of freedom: a translation in a nodal coordinate direction, rotation about a nodal coordinate axis, pressure, or temperature. To simulate the behavior of the fluid viscous damper, the key options of the COMBIN37 element should be set as follows:  
* The first key option, KEYOPT(1), should be set as 2 to allow the control parameter to be the relative velocity of the two control nodes, K and L;
* Both the fourth key option KEYOPT(4) and the fifth key option KEYOPT(5) should be set as 1 to allow the element to always be activated;
* The sixth key option, KEYOPT(6), should be set as 2 to correct the damping parameter. The rest of the key options are set as defaults, and the damping parameter of the element is corrected as Equation (22). \[D=C_{0}+C_{1}|P|^{C_{2}}+C_{3}|P|^{C_{4}} \tag{22}\]  
where \(C_{0}\) is the initial damping coefficient set by the second real constant, \(C_{1}\) to \(C_{4}\) are the ninth to twelfth real constants, and P is the control parameter set by the second key option. By setting the real constants \(C_{0}\), \(C_{3}\), and \(C_{4}\) as zero and letting the control nodes K and J be coincident with the active nodes I and J, the damping force of the element can be corrected to Equation (23). \[F=\left(C_{0}+C_{1}|P|^{C_{2}}+C_{3}|P|^{C_{4}}\right)\cdot|v|\cdot\text{sgn} (v)=C_{1}|v|^{1+C_{2}}\text{sgn}(v) \tag{23}\]  
where \(v\) is the relative velocity of the active nodes I and J, and sgn is the sign function. Figure 6: COMBIN37 geometry. Equation (23) is similar to the mechanics model of the standard velocity-dependent damper shown in Equation (24). \[F=C|v|^{n}\text{sgn}(v) \tag{24}\]  
where \(C\) is the damping coefficient and \(n\) is the velocity index. It can be seen from Equations (23) and (24) that the ninth real constant, \(C_{1}\), should be set as the damping coefficient, and the tenth real constant, \(C_{2}\), should be set as the velocity index minus one.