A Simultaneous Coupled Nonlinear Algorithm for the Analysis of Steel Frames with Flexible Joints considering Joint Unloading

Abstract

This paper presents a finite element plasticity-based computer algorithm to analyze steel frames with flexible joints under static proportional loading, unloading, and reverse loading. Each connection mechanism is modeled using a rotational spring element with two nodes of identical spatial coordinates and the same translational degrees of freedom and different rotational degrees of freedom for modeling the relative rotation of the beam and ends of the connection. Instead of using a classical coupled nonlinear algorithm for the connection element and member geometric stiffness, a unique solution method is introduced that simultaneously iterates to find the incremental connection element and member geometric stiffness of the structure through solving the nonlinear system equation. To model unloading and reverse loading at the joints between beams and columns, a three-parameter, kinematics hardening model for moment-rotation behavior is considered. For proof-of-concept, a one-story, one-bay frame with two connections is considered for parametric study. It is shown that different connection constitutive equation (moment-rotation characteristic) in a frame could cause moment reversal in some connection(s).