RC Fiber-Based Beam-Column Element with Flexure-Shear-Torsion Interaction

Abstract

A new beam-column fiber element suitable for the analysis of RC members subjected to multi-axial loading conditions is presented. The element kinematics is based on the Timoshenko beam assumption combined with the Saint-Venant theory of torsion. Out-of-plane displacements perpendicular to the cross-section arising from torsional warping are considered. These are obtained at each individual section fiber as a product of the warping parameter and the warping function, the latter being defined at the start of the analysis from elastic material properties. Given the axial and shear strains acting on each section fiber, the corresponding stress state is determined from a three-dimensional, fixed-crack constitutive model for cracked concrete and uniaxial stress-strain relationships for steel, which is assumed to be smeared within the concrete matrix. Beam equilibrium assumptions of zero axial stress in the transverse directions and zero shear stress in the longitudinal one are imposed at each fiber in order to constrain the 3D constitutive model from six to three stress components. The procedure was implemented into a force-based beam-column finite element, i.e. with exact interpolation of section forces and an additional iteration loop at the section level, and verified against experimental case studies on RC members subjected to bending, shear and torsion.