Chapter 7 - Steady-State Limit Analysis of Framed Structures Using Incremental Perturbation Method

Abstract

The purpose of this chapter is to present a new method for finding the steady-state limit (SSL) of arbitrary shaped frames subjected to dead loads and subsequent cyclic loads. In the chapter, geometrical and material nonlinearities are taken into account using the Total Lagrangian formulation and a bi-linear kinematic hardening rule. Incremental perturbation method is employed to solve the combined and highly non-linear equations. It describes the governing equations and outlines the fundamental concepts of the SSL theory. When elastoplastic beam-columns are subjected to a completely reversed cyclic bending with stepwisely increasing amplitude under a compressive axial force, its hysteretic behavior is arranged into three classes. The first one is the convergent behavior to a symmetric steady state, in which a pair of the deflected configurations at load reversals is symmetric with respect to the initial member axis; the second one is the convergent behavior to an asymmetric steady state, where the deflected shapes involve a certain anti-symmetric mode and the third one is the divergent behavior, where deformation grows proportionally or exponentially with respect to the number of the cycles. The concepts called the symmetry limit (SL) and the steady-state limit (SSL) were introduced as the critical steady states that bound these three classes of behavior. The symmetry limit is the critical steady state at which transition from the symmetric steady state to the asymmetric steady state occurs. The SSL is the critical steady state beyond which the beam-columns will no longer exhibit any convergent behavior.