## 2 Calculation Theory and Model
### Calculation Parameters
#### 2.2.2 Load Parameters  
The parameters and load values are obtained from the actual situation and code [27]. The highest and lowest rail temperatures are 59.1 \({}^{\circ}\)C and \(-\)17.7 \({}^{\circ}\)C, respectively. The design stress-free rail temperature is considered to be 20 \(\pm\) 5 \({}^{\circ}\)C. When calculating the expansion force of the rail, 15 \({}^{\circ}\)C is taken for the concrete beam and 25 \({}^{\circ}\)C for the steel truss beam. The dynamic bending stress caused by the train at the rail head (bottom) is 144.39 MPa \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Beam** & & \\ \hline Items & Units & Steel truss beam & Concrete beam \\ Modulus of elasticity & N/m\({}^{2}\) & 2.1 \(\times\) 10\({}^{11}\) & 3.6 \(\times\) 10\({}^{10}\) \\ Poisson ratio & — & 0.3 & 0.2 \\ Coefficient of thermal expansion & /\({}^{\circ}\)C & 1.2 \(\times\) 10\({}^{-5}\) & 1.0 \(\times\) 10\({}^{-5}\) \\ Density & kg/m\({}^{3}\) & 7875 & 2625 \\ \hline \multicolumn{4}{c}{Main tower} \\ Items & Units & Parameter & \\ Modulus of elasticity & N/m\({}^{2}\) & 3.6 \(\times\) 10\({}^{10}\) & \\ Poisson ratio & — & 0.2 & \\ Coefficient of thermal expansion & /\({}^{\circ}\)C & 1.0 \(\times\) 10\({}^{-5}\) & \\ Density & kg/m\({}^{3}\) & 2625 & \\ \hline \multicolumn{4}{c}{Main cable and susender} \\ Items & Units & Main cable & Suspender \\ Cross sectional area & m\({}^{2}\) & 1.32 \(\times\) 10\({}^{-2}\) & 1.062 \\ Modulus of elasticity & N/m\({}^{2}\) & 1.98 \(\times\) 10\({}^{11}\) & 1.98 \(\times\) 10\({}^{11}\) \\ Coefficient of thermal expansion & /\({}^{\circ}\)C & 1.2 \(\times\) 10\({}^{-5}\) & 1.2 \(\times\) 10\({}^{-5}\) \\ Poisson ratio & — & 0.3 & 0.3 \\ \hline \multicolumn{4}{c}{Side span beam} \\ Items & Units & 32 m & 57 m \\ Cross sectional area & m\({}^{2}\) & 8.64 & 11.89 \\ Vertical inertia moment & m\({}^{4}\) & 18.55 & 46.62 \\ Distance from neutral axis to upper flange & m & 1.00 & 1.84 \\ Distance from neutral axis to lower flange & m & 2.05 & 3.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters. Figure 5: Bridge span layout. (N1–4, 1, 2, 3, 5, 6, 7, S1–4 refer to the number of piers). (128.04 MPa). The adhesion coefficient between wheel and rail is 0.164. As the braking force is transferred along the vehicle segment by segment during braking, there is a certain time difference between each train segment. In this paper, the braking load length is 400 m. ZK standard live load and I lane load are adopted Figure 6). These two load diagrams are respectively common load diagrams of high-speed railway and expressway in China. The location of the concentrated load can be specified arbitrarily. El-Centro seismic wave is selected in this calculation because of its large peak value and wide frequency band, and it is suitable for a foundation consisting of sand and stone. The seismic fortification intensity is 7 degrees and the peak acceleration is 0.15 g. The time-history curve of seismic acceleration with baseline correction is shown in Figure 7. The modified time-history curve does not drift from baseline, and the acceleration power spectral density curve and the power spectral density curve are close to the original one. It is assumed that the direction of seismic propagation is the same as the bridge trend. The vehicle model is considered as a multi-degree freedom system composed of the car body, bogies, wheelsets, and spring-damping suspension device. The car body, bogies,  
Figure 6: Load diagram: (**a**) ZK live load; (**b**) I lane load. Figure 7: Seismic time-history curve: (**a**) Time-acceleration; (**b**) Time-displacement; (**c**) Frequency-power spectral density. and wheelsets are all simulated as rigid bodies. The car body and bogie have 5 degrees of freedom, including bouncing, swaying, nodding, yawing and rolling, while the wheelest has 4 degrees of freedom, including bouncing, swaying, yawing and rolling. The axle load of the vehicle is 17 t, and relevant vehicle mechanical parameters are referred to [30]. The speed of the vehicle is 250 km/h.