Second-order plastic-hinge analysis of planar steel frames using corotational beam-column element

•The 7th-order polynomial function is assumed as deflection solution of beam-column.•The element stiffness matrix formulation is developed in the corotational context.•Additional axial strain caused by the element bending is integrated in formulation.•Refined plastic-hinge is applied to simulate the lumped inelastic behavior.•The developed program is a reliable tool for nonlinear analysis of steel frames.

A new beam-column element for nonlinear analysis of planar steel frames under static loads is presented in this paper. The second-order effect between axial force and bending moment and the additional axial strain due to the element bending are incorporated in the stiffness matrix formulation by using the approximate seventh-order polynomial function for the deflection solution of the governing differential equations of a beam-column under end axial forces and bending moments in a corotational context. The refined plastic-hinge method is used to model the material nonlinearity to avoid the further division of the beam-columns in modeling the structure. A Matlab computer program is developed based on the combined arc-length and minimum residual displacement methods and its results are proved to be reliable by modeling one or two proposed elements per member in some numerical examples.