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.
For steel framed structures with small geometric nonlinearity, the conventional first-order plastic hinge method (FPHM) estimates rapidly the failure mode and ultimate strength of frames according to the proportionality property. However, it ignores the combined action of multiple internal forces on the development of plastic hinge, leading to mistakes in estimating the failure mode and ultimate strength of frames. Though the second-order plastic hinge method (SPHM) and the refined plastic hinge method (RPHM) overcome this problem, they lose the FPHM’s proportionality property and the high efficiency of computation as well. In this paper, the generalized plastic hinge method (GPHM) featuring proportionality property is proposed for steel framed structures to overcome the drawbacks of the conventional FPHM, the SPHM and the RPHM. Firstly, a linearly elastic analysis is performed on the steel framed structure between the formation of any two plastic hinges; then the strength reduction factor is developed by means of the generalized yield criterion (GYC) for modification of the sectional strength of frame component under multiple internal forces during loading process. Secondly, the element bearing ratio (EBR) is defined on the basis of the homogeneous generalized yield function and is in proportion to the loading, so that the position of generalized plastic hinge and the corresponding load increment are determined for each loading step according to this proportional property. Furthermore, the balance vector is developed by means of the GYC and the slope-deflection relation to modify the result of the calculated load increment. Finally, several examples are presented to validate the much higher computational efficiency and accuracy of the proposed method by comparing it with the plastic zone analysis (PZA), the SPHM and the conventional FPHM.
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