## 4 Prediction on Ultimate Bearing Capacity
### Bearing Capacity of Flexural-Torsional Buckling Mode
For reinforced steel angle, the influence of the reinforced plate on the moment of inertia of the steel angle section in the strong axis direction is very small, so the critical load \(P_{y}\) for bending instability of the reinforced steel angle is approximately equal to that of the unreinforced steel angle. Therefore, the main consideration is the contribution of the reinforced plate to the torsional instability load \(P_{\omega}\). As shown in Equation (23), considering the effect of reinforced plates on the torsional inertia moment of the reinforced steel angle section, the cross-sectional twisting inertia moment (\(I_{t}\)) of the built-up steel angle can be determined by \(I_{t}=I_{ta}+I_{tb}\), where \(I_{t}\) is the inertia moment of steel angle, and \(I_{tb}\) is the inertia moment of reinforcement plate. Although the above analysis is based on elastic bending and torsional instability, it reveals the mechanical mechanism of strengthening plates in improving the bending and torsional bearing capacity of reinforced steel angle; that is, by increasing the torsional moment of inertia of the reinforced section to enhance the torsional stiffness of the member, thereby improving the ultimate bending and torsional buckling bearing capacity of the member. Based on this idea, it is possible to use the torsional moment of inertia \(I_{t}\) of the reinforced steel angle to calculate the flexural and torsional bearing capacity on the basis of the existing standard calculation methods for flexural and torsional instability. Other calculation parameters, such as the radius of gyration and cross-sectional area, are still the same as those of the unreinforced steel angle. Using this method in conjunction with the specifications to calculate the ultimate bearing capacity of reinforced steel angle under bending and torsion buckling and comparing it with the test values measured on specimens with bending and torsion instability, the results are shown in Tables 5 and 6. From Table 5, it can be found that the calculation results of design code GB 50017 are far lower than the ultimate bearing capacity of the reinforced angle steel measured in the experiment. During the loading process of the LR1-1-1 specimen, due to significant deformation, the end plate and reinforcement plate contacted each other, causing the reinforcement plate to directly bear vertical loads, which was not in line with the actual situation, resulting in an excessively measured ultimate bearing capacity. Except for LR1-1, the method in GB 50017 predicts that the bearing capacity of other specimens is about 35% lower, and the calculation formula is too conservative. The results of the American standard calculation in Table 6 are in good agreement with the experimental values, indicating the correctness of the theory of plate reinforcement under bending and torsion instability. Except for LR1-1-1, the predicted bearing capacity of all other specimens is slightly lower than the experimental value, with a maximum error of 6.67%. While leaving a certain safety margin, the bearing capacity of the reinforced angle steel is fully utilized.