An analytical formulation to extract the capacity curve of steel structures

Abstract

Among the methods for evaluating the nonlinear performance of structures, pushover analysis is an appropriate alternative instead of direct time history analysis. To accurately extract the capacity curve of a structure, according to the loading regulations/protocols such as FEMA-356 and ATC-40, lateral loads are incrementally applied to the structure in experimental tests until the structural failure occurs. Because of the cost and time-consuming nature of experimental tests, proposing mathematical/analytical methods could be the appropriate tools to predict the capacity curves of a system. The present study proposes a new method to find the capacity curves of cantilever steel beams based on mathematical formulations, structural analysis, and material properties. The reason to select a simple beam in this study is to shed more light on the unknown aspects of the system’s behavior. Therefore, in this research, the effect of axial load is ignored to clarify the nonlinear behavior of complicated systems such as frames. The strains, stresses, and other responses corresponding to large geometric deformations have been extracted in two cases with and without strain hardening by considering changes in the behavior of materials. The proposed method has been verified using the finite-element method with Abaqus software. The results indicate that the proposed method has acceptable accuracy and could be applied in the pushover analysis of steel structures.