Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Abstract

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.