# 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
### Structural Safety Review Methods for Corbel Beams  
Because of the cantilever structure of the corbel, its spatial stress state differs greatly from that of the corbel beam, and the joint bearing structure formed by the corbel beam and the gate pier has a load-bearing capacity that is much larger than that of the cantilever structure. Thus, it is necessary to improve the code for review of the corbel in _the Code for Design of Hydraulic Concrete Structures_ (SL191-2008) to enable its use in the safety assessment of the corbel beam.  
To use the radial gate corbel beam of the gate pier local tension area crack control test as an example, its crack control should meet the requirements of Formula (4).  
When the gate pier is thrust by one side of the radial gate support:  
\[F_{k}\leq\frac{0.55f_{ik}bB}{\frac{0}{B}+0.20} \tag{4}\]  
where \(F_{k}\)--calculated by the standard value of the load on the gate pier side of the radial gate support thrust value (N); \(b\)--radial gate support width (mm); B--thickness of the gate pier (mm); \(e_{0}\)--distance between thrust force of radial gate support and the center line of gate pier thickness (N); \(f_{tk}\)-- standard value of concrete axial tensile strength (N/mm\({}^{2}\)).  
According to the specification, this review formula is derived from the model test. Under the thrust exerted on one side of the gate pier near the radial gate support, cracks appear perpendicular to the thrust direction at the junction of the support and the gate pier, and develop along the thickness direction of the gate pier. The corbel crack resistance  
Figure 7: Schematic diagram of the force on the corbel beam of the outlet entrance.  
is related to the concrete tensile strength, the relative position of the support in the gate pier, the effective distribution width of the support, the thickness of the gate pier, and the stress state under different thrusts. Therefore, based on the safety review specification of the corbel, this paper proposes two kinds of safety assessment methods for corbel beams applicable to different types of reservoirs and conducts the comparative analysis.  
Safety assessment by theoretical mechanics method  
The corbel crack resistance is related to the concrete tensile strength, the effective distribution width of the support, and other factors, but according to the principle of safety assessment, we can presume that the bending moment at the junction of the corbel beam and gate pier has the greatest influence on the crack control in the local tensile area of the gate pier. Therefore, we calculate the equivalent coefficient \(a\) according to the ratio of the bending moment at the fixed end of the corbel beam gate pier and the bending moment of the corbel in this section, and then include it in Formula (4) for calculation [28; 29; 30]. This method is simple and suitable for the safety assessment of the corbel beam of the curved gate of small projects with simple force conditions.  
Structural safety assessment of corbel beams by finite element simulation based on real state  
Method (2) is based on the safety inspection and test data for finite element simulation, analyzing the stress distribution state of the corbel beam structure under the real state, finding out the dangerous area of its stress concentration, and assessing the working state of the corbel beam structure in combination with the field inspection. Then, the shear force of the corbel beam structure subjected to the center point of the radial gate support thrust at the cross-section is calculated and brought into equation (4) for calculation [31; 32; 33]. Finally, considering the field test data, simulation results analysis, and review calculation results, an accurate safety assessment of the corbel beam structure is made. This method is applicable to the safety review of the corbel beam of medium and large-scale reservoir radial gates with complex force conditions.