Plastic hinge development of frame members using a nonlinear hardening rule

A nonlinear hardening rule that defines a yield surface translation for homogeneous frame member materials is proposed. The rule is defined as a nonlinear constitutive relationship that examines material behavior through a postelastic perspective. The gradual development of the postelastic states of a beam along its length and through its section thickness is analyzed. The model uses a hardening index parameter to guide the nonlinear stress-strain relationship, and a smooth function to model the web-flange intersection of frame members. As such, nonlinear curvature distributions with continuous derivatives are determined along the length of the member, which enables lateral displacements to be accurately predicted. Plastic hinge lengths and finite-element displacements are subsequently determined, and a nonlinear stiffness is derived. The model is formulated on a constitutive level and applies a smoothed-over cross section to derive a single internal moment expression for any postelastic state. Results are verified through experimental published literature.