## 3 Numerical Simulation of the Rail-Cum-Road Cable-Stayed Bridge  
The Huanggang Yangtze River bridge was used as the prototype bridge. This is a cable-stayed bridge with a steel truss girder and two pylons and has a semi-floating system. The main girder consists of double bridge decks, four-lane highways with a design speed of 100 km per hour for the upper layer, and two-track high-speed railways with a 200 km per hour design speed for the sublayer. The bridge's total length is 1218.5 m, and the main span is 567 m; the span configuration is shown in Figure 4. The main bridge is supported by two sliding bearings at each of the side piers, auxiliary piers, and pylons, with the upstream side bearing restraining the vertical displacement degrees of freedom, the downstream side \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Order**} & \multicolumn{2}{c}{**FEM Results (Hz)**} & \multicolumn{2}{c}{**Numerical Model Results (Hz)**} & \multicolumn{2}{c}{**Errors**} \\ \cline{2-7}  & **In-Plane** & **Out-Plane** & **In-Plane** & **Out-Plane** & **In-Plane** & **Out-Plane** \\ \hline
1 & 0.43098 & 0.41902 & 0.43081 & 0.41879 & 0.0\% & 0.1\% \\
2 & 0.83822 & 0.83831 & 0.83759 & 0.83759 & 0.1\% & 0.1\% \\
3 & 1.25859 & 1.25818 & 1.25683 & 1.25638 & 0.1\% & 0.1\% \\
4 & 1.67887 & 1.67892 & 1.67518 & 1.67518 & 0.2\% & 0.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the first four modal frequencies. Figure 3: FEM of the cable. bearing restraining the vertical and transverse displacement degrees of freedom, and four longitudinal viscous dampers installed at each pylon. A long-span rail-cum-road cable-stayed bridge is subjected to the combined action of wind, trains, vehicles, and environmental temperatures during its operation period [28], and the long-term mechanical properties of the steel truss girders, cables, and pylons are worthy of attention during the service period under these loads. To accurately simulate the dynamic and static mechanical behavior of the bridge, a fine finite element model was established based on the ANSYS software [29], as shown in Figure 5, in which the steel trusses, the longitudinal and transverse ribs of the orthotropic anisotropic deck, were simulated using BEAM188 elements, the deck slabs were simulated using SHELL181 elements, the cables were simulated using LINK180 elements, and the concrete pylons were simulated using SOLID65 elements. These elements are recommended by the users' guide documentation of ANSYS software to simulate slender to moderately stubby/thick beam structures, thin to moderately thick shell structures, sagging cables, and solids with or without reinforcing bars, respectively. There are 41,268 nodes and 125,508 elements, of which 25,994 are beam elements, 11,902 are shell elements, 152 are link elements, and 87,460 are solid elements. The size for beam and shell elements is within the range of 1.7 to 7.4 m, while for solid elements, they fall within the range of 1.2 to 4.2 m, as listed in Table 2, and the force and displacement convergence criteria are adopted and controlled by the default settings of the solver. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element Type** & **Amounts** & **Element Size (Meters)** \\ \hline BEAM188 & 25,994 & 1.7–7.4 \\ SHELL181 & 11,902 & 1.7–7.4 \\ LINK180 & 152 & / \\ SOLID65 & 87,460 & 1.2–4.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Element summaries. Figure 4: Front elevation of the bridge (units: meters). Figure 5: FEM of the bridge: (**a**) the whole bridge; (**b**) the steel truss beam; and (**c**) the pylon. The material of the steel truss girder was a high-strength structural steel with a yield strength of 390 Mpa. The connections among the deck slabs simulated by shell elements and the longitudinal and transverse ribs simulated by beam elements were processed by coupling their degrees of freedom.