## 2 Finite Element Numerical Simulation
### Analysis of Calculation Results
#### 2.3.2 Transverse Axial Bias Loads  
The object of this paper is that the steel spherical hinge drag moment is greater than the unbalance moment of the swiveling body, which means that the swiveling body maintains the equilibrium state through the steel spherical hinge drag moment and the swiveling body's own unbalance moment [28]; the swiveling body structure does not rotate. When the steel spherical hinge friction moment is greater than the unbalance moment of the swiveling body, the maximum allowable eccentricity of the swiveling body structure can be obtained from Equation (1) [29]. The maximum allowable eccentricity of the T-shaped rigid bridge is calculated to be 0.2574 m. Therefore, the effect of eccentricity values of 0 mm, 10 mm, 50 mm, 100 mm, 150 mm, 200 mm, 250 mm, 257.4 mm, and 350 mm on the steel spherical hinge and upper turntable has been investigated, respectively. In this paper, in order to change the eccentricity value, the overall eccentricity of the concrete structure above the steel spherical hinge is changed, and the model is analyzed numerically. \[\mathrm{e_{max}}=\frac{\mathrm{M_{z}}}{\mathrm{G}}=\frac{0.99\mathrm{\mu} \mathrm{GR}}{\mathrm{G}}=0.99\mathrm{\mu}\mathrm{R}. \tag{1}\]  
In the formula, the variables are as follows:  
Mz--Friction moment of the steel spherical hinge, N\(\cdot\)m;  
G--Self-weight of bridges, kN;  
R--Radius of steel spherical hinge, m;  
\(\mathrm{\mu}\)--Coefficient of static friction of steel spherical hinge. Let me explain in detail the two technical words above. Eccentricity limit: During the construction of a transverse bridge, the steel spherical hinge will have a certain amount of eccentricity with its concrete superstructure, which is unavoidable and can be caused by the design of the drawings as well as by the construction process. The maximum permissible eccentricity during the construction of the bridge is the eccentricity limit. Bias loads: As a result of the eccentricity condition of the transverse bridge, the superstructure will generate a certain amount of bias load on the steel spherical hinge, the degree of which is related to the size of the eccentricity and the level of applied load. Depending on the location of the eccentricity, the bias loads can be classified as transverse axial bias loads, longitudinal axial bias loads, and longitudinal and transverse axial bias loads. The effect of different transverse axial bias loads on the upper turntable and steel spherical hinge stresses was obtained by Ansys finite element analysis, and the results are shown in Figure 13a. From the figure, it can be seen that the stress on the steel spherical hinge structure and the upper turntable increases with the increase in the eccentricity distance; the stress on the upper turntable is obviously smaller than that on the steel spherical hinge structure. Eccentricity of 257.4 mm at the local enlargement shown in Figure 13b; from the figure, it can be seen that when the limit eccentricity is 257.4 mm, the  
Figure 12: Summary diagrams: (**a**) summary diagram of stresses; (**b**) summary diagram of deformations. upper turntable normal compressive stress has been close to the allowable stress value of C50 concrete compressive strength of 37.5 MPa, which is in the limit of the working condition. At this time, the equivalent stress on the upper turntable has reached 39.103 MPa, exceeding the allowable stress value. When the eccentricity is 210 mm, the equivalent stress on the upper turntable is at the limit working condition. When the eccentricity distance is 350 mm, the stress suffered by the steel spherical hinge structure is still far less than its yield strength, so the size of the eccentricity distance of the bridge structure is mainly limited by the upper turntable. The ultimate transverse axial bias loads of this bridge are 210 mm, and the eccentricity distance is too large, which leads to the collapse of the upper turntable and the structural overturning of the bridge.