On boundary effects due to nonuniform shear and torsional warping for open section anisotropic beams

Abstract

This work focuses on modeling nonuniform shear and torsional warping due to boundary restraints for open section anisotropic beams. A generalized displacement-based formulation is adopted for the two-dimensional (2D) sectional analysis incorporating the effects of classical elastic couplings and nonclassical three-dimensional (3D) warping deformations. A 9×9 sectional stiffness matrix is formulated which includes shear warping stiffnesses and related couplings in addition to generalized Timoshenko model for transverse shear and Vlasov model for nonuniform torsion. The formulation is implemented into a generic finite element (FE) analysis called refined displacement based sectional analysis code (RDSAC). Numerical examples are presented to validate the current analysis and to demonstrate the influence of nonuniform warping on the static response of open section anisotropic beams. The influence of fiber orientation angles, slenderness ratios, and warping boundary conditions on section stiffnesses and one-dimensional (1D) beam response is substantiated. The predictions show good correlation with those from state-of-the-art approaches, 3D FE analysis, and existing experimental data. It is indicated that both nonuniform shear and torsion are significant for open section composite beams even with high slenderness ratios. The effects of elastic couplings on 3D warping (uniform) deformations and nonuniform warping are also identified.