## 2 Finite Element Numerical Simulation
### Analysis of Calculation Results  
#### 2.3.1 Different Rotation Angles  
Bridges were modeled when the rotation angles were \(0^{\circ}\), \(8^{\circ}\), \(18^{\circ}\), \(28^{\circ}\), \(38^{\circ}\), \(48^{\circ}\), \(58^{\circ}\), \(68^{\circ}\), \(78^{\circ}\), and \(88^{\circ}\), respectively, and Ansys analysis is performed on different models so as to simulate the state of the whole bridge when the T-shaped rigid bridge is leveled to a particular angle. The simulation results for which the translational angle is \(0^{\circ}\) (unturned) and \(88^{\circ}\) (turned) are shown below. Note: In this paper, the equivalent stress clouds are in MPa, and the total deformation clouds are in mm. The equivalent stress clouds of the upper turntable for unturned and completed turns are shown in Figure 6. From the figure, it can be seen that the maximum stress point is located in the upper turntable and the upper steel spherical hinge contact and is biased to the right width of the transverse bridge, the value of 33.806 MPa, which is smaller than the allowable stress value of 37.5 MPa for the compressive strength of C50 concrete. The overall stress change in the upper turntable is shown as follows: the stress in the contact area between the upper turntable and the outer edge of the upper steel spherical hinge is the largest and gradually shrinks to the edge and center of the upper turntable. The total deformation clouds of the upper turntable for unturned and completed turns are shown in Figure 7. From the figure, it can be seen that the upper steel spherical hinge and the upper turntable contact with the smallest deformation, and this is the center of the gradual increase to the edge; the largest deformation end is located in the edge of the turntable by the cross-bridge to the right, the value of 3.5761 mm. The overall deformation of the upper turntable showed that the deformation at the contact of the upper turntable with the upper steel spherical hinge was the smallest, and the deformation gradually increased outward along the transverse bridge direction. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Materials** & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Young’s** \\ **Modulus/MPa** \\ \end{tabular} &
\begin{tabular}{c} **Friction** \\ **Coefficient** \\ \end{tabular} \\ \hline Upper steel & & Q235 & 0.3 & \(2.10\times 10^{5}\) & 0.06 \\ spherical hinge & Q235 & 0.3 & \(2.10\times 10^{5}\) & 0.06 \\ Supporting legs & Q355B & 0.3 & \(2.06\times 10^{5}\) & 0.06 \\ Pier & C40 & 0.2 & \(3.25\times 10^{4}\) & - \\ Upper turntable & C50 & 0.2 & \(3.45\times 10^{4}\) & - \\ Lower turntable & C50 & 0.2 & \(3.45\times 10^{4}\) & - \\ Roof cap & C50 & 0.2 & \(3.45\times 10^{4}\) & - \\ Bridge & C55 & 0.2 & \(3.55\times 10^{4}\) & - \\ Lower cap & C55 & 0.2 & \(3.55\times 10^{4}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters for finite element modeling. Figure 5: Grid independence verification: **(a)** steel spherical hinge; **(b)** concrete bridge. The equivalent stress clouds of the upper steel spherical hinge for unturned and completed turns are shown in Figure 8. From the figure, it can be seen that most of the stress values of the upper steel spherical hinged surface are in the interval of 1\(\sim\)25 MPa, and the stress concentration exists only at the edge. The maximum equivalent stress of the upper steel spherical hinge is 95.546 MPa, which is smaller than the yield strength of Q235 steel, satisfying the material requirements, and the maximum stress is located at the contact between the spherical surface of the upper steel spherical hinge and the outer ring bar of the lower steel spherical hinge. The overall stress change in the upper steel spherical hinge shows that the maximum stress is at the edge of the upper steel spherical hinge circumference and gradually shrinks to the center.