Finite element model for advanced analysis of plane steel frames with hinged end conditions including von Mises criterion

Abstract

Traditionally, the design of steel structures is carried out in two steps: first, the structural analysis is performed, and then the cross-sections and structural members are checked individually. In contrast, in the advanced analysis, the effects related to global (P-Δ) and local (P-δ) instabilities and to the degradation of material stiffness are incorporated; therefore, there is no need to verify the resistance capacity of the structural members separately, which allows a better use of the load capacity of the structural system. Generally, research developed in this area of study is based on the classical Euler-Bernoulli theory; however, in the case of short elements, an analysis that includes the shear effects and the interaction between normal and shear stresses on cross-section yielding becomes necessary. Thus, this work aims to study the behavior of plane steel frames considering the influence of shear deformations by using advanced analysis. A geometrically exact formulation for analysis of rigid-hinged and hinged-rigid elements is presented. The proposed numerical methodology is implemented in finite element software and takes into account Timoshenko’s kinematic hypothesis, the distributed plasticity approach, residual stresses, and second-order effects. To assess the plastification state of the structural elements, the von Mises yield criterion is applied. From numerical examples available in the literature, the efficiency of the software in predicting the nonlinear behavior of steel frames is assessed. It is concluded that for short beams, the adoption of the von Mises criterion during the analysis leads to lower load capacities, compared to the results obtained considering only the normal stresses in the evaluation of the plastification state of the cross-sections.