Second-Order Generalized Plastic Hinge Method for Ultimate Bearing Capacity Estimation of Unbraced Steel Frames

The traditional first-order plastic hinge method (FPHM) utilizes the proportionality property to rapidly estimate the external load increment between any two adjacent plastic hinges, with superior computational efficiency. However, the FPHM cannot consider the influence of second-order effects and residual stresses. Although the refined plastic hinge method (RPHM) overcomes these problems, it must solve the nonlinear structural stiffness equation, resulting in low computational efficiency. In this paper, the second-order generalized plastic hinge method (sGPHM) is proposed to evaluate the ultimate bearing capacity of unbraced steel frames on the basis of using the proportionality property to estimate the external load increment. First, the element bearing ratio (EBR) that considers second-order effects and residual stresses is defined. Since the EBR and the external load are proportional, the plastic yield degree of the cross-section can be easily obtained. Then, the displacement increment and the load increment between any two adjacent plastic hinges can be rapidly estimated through the proportionality property between the EBR and the external load. Accumulating all load increments can determine the ultimate bearing capacity of frames. Finally, several benchmark frameworks in the literature are compared and analyzed with different methods to verify the superior calculation accuracy and efficiency of the proposed sGPHM.