Post-yield material nonlinearity: Optimal homogeneous shear-frame sections and hysteretic behavior

A nonlinear hardening rule that describes a general yield surface change for frame members is proposed. The rule is valid for homogeneous materials and is defined by a nonlinear constitutive model. The model is given as the stress–strain relationship through the section thickness. The post-yield behavior of shear frame members is assessed using a hardening index parameter, a plastic strain coefficient, and a smooth and optimal mathematical function to model the geometry of structural wide-flange and tube sections. This enables a continuous distribution of post-yield curvatures to exist along the member length and results in accurate finite-element member displacement predictions. Steady-state hysteresis responses are determined for frame sections using the model’s nonlinearly degrading stiffness. The hardening rule is used to model the detailed material behavior of shear frame members that are subjected to lateral loads. The results of the model are validated through experimental published literature.