A Mechanics-Based Finite Element for the Analysis of Shear-Critical Slender Reinforced Beams and Columns

Abstract

This paper presents the derivation and validation of a mechanics-based finite element for the analysis of shear-critical slender reinforced concrete beams and columns. The element can capture the load-deformation behavior associated with axial loads, bending moments, and shear in uncracked or cracked reinforced concrete using only a small number of degrees of freedom and easily measurable input parameters: the gross cross-section dimensions and steel and concrete material stress/strain curves. The element is specifically derived to represent the full reinforced concrete cross section (i.e., one element is required over the depth of a member) and consists of four nodes, with two translational degrees of freedom (DOFs) per node. This formulation facilitates modeling the interface regions between walls or joint regions, beams, or columns and lowers the numerical complexity and number of decisions that the user must make. The element shows improvements to results from design codes when validated against experimental results for 782 beams without shear reinforcement and 167 beams with shear reinforcement taken from the literature. By reducing the number of degrees of freedom, the element will allow relatively rapid two-dimensional (2D) nonlinear analyses of full reinforced concrete buildings.