## 2 Establishment of the Analysis Model
### Application of Moving Loads  
The parameters of the load were consistent with Lanzhou BRT operating vehicles, which are shown in Table 5. Because the wheelbase was relatively long and the load of the rear axle was obviously greater than that of the front axle, only the load of the rear axle was taken for modeling analysis. To reduce computational efforts, the two-wheel load of the rear axle was simplified into a single-wheel rectangle based on Equations (3)-(6); the length/width ratio of the rectangle was 0.8712/0.6 [46]. As a result, the simplified load, as shown in Figure 2, acted on an area 0.32 m long and 0.22 m wide, and the specific ground pressure was 0.733 MPa. Measurements were obtained at four points: point A, at the center of one of the loading regions; point B, at the inner edge of one of the loading regions; point C, at the middle of the loading regions; and point D, at the middle of points B and C. The horizontal force coefficient was 0.5. User subroutines DLOAD and UTRACLOAD [47] were programmed in Fortran 77 to simulate the movement of vertical and horizontal loads.  
\[\frac{p_{i}}{p}=\left(\frac{P_{i}}{P}\right)^{\frac{1}{3}} \tag{3}\]  
\[A=\frac{P_{i}}{p_{i}}=L_{\mathrm{a}}L_{\mathrm{b}} \tag{4}\]  
\[L_{\mathrm{a}} =0.8712L \tag{5}\]  
\[L_{\mathrm{b}} =0.6L \tag{6}\]  
where \(P\) denotes the standard design axle load of 100 kN; \(p\) denotes the standard design specific ground pressure of 0.70 MPa; \(A\) denotes the area of the simplified single-wheel rectangle; \(P_{i}\) denotes the load distributed on the wheel (kN); \(p_{i}\) denotes the specific ground pressure (MPa); \(L_{\mathrm{a}}\) denotes the length of the simplified single-wheel rectangle; and \(L_{\mathrm{b}}\) denotes the width of the simplified single-wheel rectangle.  
Based on the measured data for Lanzhou BRT vehicle operation speeds, the initial speed of the moving load was set to 10 km/h, 20 km/h, 30 km/h or 40 km/h. In each initial speed case, a deceleration of \(-\)2 m/s\({}^{2}\) was adopted to simulate the entrance process of BRT braking, and the running time was 0.5 s. Because different initial braking speeds lead  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Total Daily**} & \multirow{2}{*}{**Duration of**} & \multirow{2}{*}{**Wind Speed (m/s)**} \\  & & & \\  & **Radiation (MJ/m\({}^{2}\))** & & \\ \hline Value & 20.75 & 10.70 & 1.50 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Meteorological parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Time of Day**} & \multirow{2}{*}{**Air**} & \multirow{2}{*}{**Time of Day**} & \multirow{2}{*}{**Air**} & \multirow{2}{*}{**Time of Day**} & \multirow{2}{*}{**Time of Day**} & \multirow{2}{*}{**Air**} \\  & & & & & & & \\ \hline
00:30 & 23.8 & 06:30 & 22.0 & 12:30 & 32.0 & 08:30 & 30.6 \\
01:00 & 23.2 & 07:00 & 22.6 & 13:00 & 32.7 & 19:00 & 30.0  
to different braking distances, to facilitate the comparison of stress results under various speed conditions, the braking distances of four levels were symmetrically distributed on the wheel path based on the middle section of the model, which was the fixed location for extracting mechanical response. The braking starting position and corresponding braking distances of the load are shown in Figure 3.