Effects of axial-shear-flexure interaction in static and dynamic responses of steel beams

This paper proposes analytical model for axial-shear-flexure interaction, with inelastic shear stress and strain distributions, for 2D beam elements with AISC flanged and hollow box cross-sections. The shear stress and shear strain distributions within the beam section, for an applied shear force, are developed considering both elastic and inelastic ranges. Standard shear stress distribution is adopted for the elastic range. The distribution of the plastic component of the shear stress is assumed to have a quadratic variation. The shear stress and strain distributions are verified adequately with the finite element software ABAQUS/CAE with 3D brick elements. Further, incremental axial load (P), bending moment (M), and shear force (V) are applied to the section, along the various direction vectors in the PVM space, up until the section attained a certain level of plasticization according to the von-Mises material model, to generate the (P, V, M) points. Using these (P, V, M) data points, a quadratic PVM surface equation is proposed by combining an elliptical and a planar surface with a smoothening function. The PVM interaction is then integrated with an existing force based beam formulation with full geometric nonlinearity. Force-displacement responses obtained with the PVM interaction for 2D beams agreed well with the ABAQUS models simulated with 3D inelastic brick elements. Static responses with P-M interaction predicted higher yield force and lower displacement demand, for lower span to depth ratios and heavier flanged sections. Dynamic responses with the PVM interaction predicted higher displacement demand than that with the P-M interaction.