# Research on the Safety Assessment of Corbel Beams of Reservoir Radial Gates Based on Real States
## 3 Finite Element Simulation and Safety Review of the Corbel Beam of the Radial Gate
### Computational Model  
Based on the two safety review methods proposed in the previous section, this paper utilizes three models for calculation and analysis. Model 1 and model 2 are the theoretical mechanical models of the corbel and corbel beam, and model 3 is the finite element simulation model of the joint force structure of the corbel beam and the gate pier under the real state. Theoretical mechanical model of the corbel. The corbel beam is considered as a protrusion from the fixed end of the side pier for calculation purposes, with a disconnect at the middle. The length of the bull leg is 1.5 m.  
According to Table 1, the horizontal hydrostatic pressure Px = 1783.6 kN, vertical hydrostatic pressure Py = 946.9 kN, and the self-weight of the corbel beam is 44.1 kN. In the theoretical mechanical model, its force is simplified to a thrust of 1998.62 kN at an angle of 26.82\({}^{\circ}\) in the horizontal direction, i.e., the unilateral support strand strut F = 999.31 kN, and the eccentricity is taken as the distance from the middle point of the supporting strut to the middle point of the gate pier b = 950 mm. The force sketch is shown in Figure 8.  
The formula for calculating the bending moment is shown in Equation (5). \[M=Fl \tag{5}\]  
where:  
\(F\)--The thrust force acting on the corbel, F = 999.31 kN;  
\(l\)--The distance between the force point and the edge, \(l\) = 950 mm. 2 Theoretical mechanical model of corbel beam. The length of the corbel beam is taken as the distance between the midpoint of the gate pier on both sides, L = 3000 mm, and the force is the same as the theoretical mechanical model of the corbel, i.e., it is subjected to two support winch thrusts at 950 mm from the midpoint of the gate pier on both sides, F = 999.31 kN. The mechanics model is shown in Figure 9.  
The formula for calculating the fixed end bending moment is shown in Equation (6):  
\[M=Fl(1-a) \tag{6}\]  
where:  
\(F\)--The thrust force acting on the corbel beam, F = 999.31 kN. \(l\)--The distance between the force point and the midpoint of the gate pier on both sides, \(l\) = 950 mm. \(a\)--\(a=l/L\), \(L\) is the distance between the midpoint of the gate pier on both sides, \(L\) = 3000 mm. 3 Finite element simulation of the joint force structure of the corbel beam and gate pier in the real state. The thickness of the gate pier in this model is 1 m, and the three dimensions of the corbel beam are 0.8 \(\times\) 1.2 \(\times\) 2 m. Considering that the corbel beam and the gate pier constitute a common force structure in the actual project, the gate pier in the 4 \(\times\) 6 m area near the corbel beam is modeled using finite element simulation, and the stress transmitted  
Figure 8: Schematic diagram of the force on the corbel model. Figure 9: Schematic diagram of the force on the corbel beam model. from the support strut is regarded as a thrust force of 2019.37 kN at an angle of 30.42\({}^{\circ}\) to the horizontal direction, which is uniformly distributed in two 60 \(\times\) 60 mm areas on the corbel beam. Furthermore, the corbel beam is connected to the edge of the gate pier by means of a fixed end. The mechanical parameters of the concrete are taken from the results of the core drilling test, assuming it is an isotropic material, and the density is taken as 2300 kg/m\({}^{3}\), the static modulus of elasticity is taken as 47.1 GPa, Poisson's ratio is taken as 0.18, the compressive strength is taken as 31.2 MPa, and the temperature is 22 \({}^{\circ}\)C. The finite element meshes are mainly regular hexahedrons.