# The Bearing Performance and Sectional Design Method of Yielding U-Shaped Steel Support
## 4 Analysis of the Influence Mechanism on the Bearing Performance of Yielding U-Shaped Steel Support
### Analysis of the Influence Mechanism on Bearing Performance
#### 4.2.1 Influence Analysis of Load Forms  
1. Analysis of Support Deformation under Different Stress Modes  
In the schemes of different stress modes, the typical deformation patterns of the support are shown in Figure 13.  
It can be known through an analysis of the support deformation diagrams that:  
In the A54-H\({}_{1}\) scheme, the maximum deformation of the support appears in the middle of the straight leg. The straight leg bends inward and there is a tendency for the top position to bulge upward. In the A54-H\({}_{4}\) scheme, under the action of strong side pressure, the support inclines towards the side with weak side pressure, showing a \"parallelogram\" deformation pattern. In the A54-H\({}_{2}\), A54-H\({}_{3}\) and A54-H\({}_{5}\) schemes, the deformation patterns of the support are basically the same. The maximum deformation of the support appears in the middle of the top of the support frame. The top of the support frame bends downward, showing an \"M\"-shaped failure pattern, and the deformation of the straight leg is not obvious. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Section Area** & **Theoretical** & **Moment of Inertia (cm\({}^{\ddagger}\))** & **Radius of Inertia (cm)** & **Cross-Section** & **Static Moment** & **Modulus (cm\({}^{\ddagger}\))** & **(cm)** \\ \hline S & M & Ix & ly & ix & iy & Wx & Wx & Sc \\ \hline
37 & 29 & 612 & 771 & 4.07 & 4.57 & 106 & 102 & 212.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: U29 steel cross-sectional parameter table. Figure 13: Deformation of steel support under different load forms (mm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Density (kg/m)** & **Elastic Modulus** & **Poisson’s Ratio** & **Yield Strength (MPa)** & **Tensile Strength** \\ \hline
20 MnVK (Baowu Steel Group (Shanghai, China)) & 7850 & 210 & 0.3 & 390 & 570 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material parameters of the numerical model. The main reasons for this are as follows: When the horizontal load acting on the support is greater than the vertical load, the support as a whole is subjected to the bending moments in the horizontal inward and vertical downward directions. When the inward bending moment at the straight leg is greater than the downward bending moment at the top, the support first generates deformation at the straight leg. Conversely, when the downward bending moment is greater than the inward bending moment at the straight leg, the top first generates deformation. When the support is subjected to asymmetric horizontal loads, since the support is fixed at the bottom, the straight leg on the side with greater pressure starts to move towards the opposite side from the top position and finally shows a \"parallelogram\" failure pattern. Analysis of the Internal Forces of Support under Different Stress Modes  
In the schemes of different stress modes, the typical internal force distributions of the support are shown in Figure 14.  
It can be known through the analysis of the internal force diagrams of the support that:  
In the A54-H\({}_{1}\) scheme, the maximum axial force is 156 kN and the maximum bending moment is 59.8 kN\(\cdot\)m; these are located at the top and the bottom foot, respectively. In the A54-H\({}_{2}\) scheme, the maximum axial force is 135.7 kN and the maximum bending moment is 52.8 kN\(\cdot\)m; these are located at the straight leg and the support shoulder, respectively. In the A54-H\({}_{3}\) scheme, the maximum axial force is 63.3 kN, and the maximum bending moment is 50.2 kN\(\cdot\)m; these are located at the straight leg and the support shoulder, respectively. In the A54-H\({}_{5}\) scheme, the maximum axial force is 128.7 kN, and the maximum bending moment is 49.6 kN\(\cdot\)m; these are located at the straight leg and the support shoulder, respectively.