Second-order plastic-zone analysis of steel frames. Part I: numerical formulation and examples of validation.

Abstract

This paper presents a second-order plastic-zone formulation for the non-linear analysis and design of plane steel frames with geometric imperfections and residual stress. The proposed numerical methodology has an inelastic formulation based on the plastic-zone method performed by the so-called “slice technique". This methodology also uses a beam-column finite element model based on the Bernoulli-Euler theory and described in the updated Lagrangian co-rotational system. The considered hypothesis and the adopted kinematic relation lead to an element stiffness matrix whose terms represent the constitutive law and second-order effects. An incremental-iterative Newton-Raphson strategy solves the global non-linear equation system and, at the internal force recovery level, in each iteration, an axial-force iterative process is proposed to obtain the axial-force balance at the element ends, more precisely determining the plasticity spread. Three benchmark structural problems are studied and the present work's findings validate the proposed numerical formulation and the axial-force iterative process. A companion paper discusses in depth the influence of geometrical imperfections and residual stress in steel frame design.