Warping Solution for Shear Lag in Thin-Walled Orthotropic Composite Beams

Abstract

A warping solution for prismatic thin-walled orthotropic composite beams is presented. For beam-wall macroelements, the macro approach solution is applied to obtain the displacements as a sum of polynomial plus Fourier functions. The kinematics of a beam-wall are obtained from a generalized plane stress solution. Constitutive equations that account for both slender and stiffened FRP sections are proposed. A fast converging continuous closed-form solution is obtained for the macroelement. The wall displacement field is evaluated in terms of nodal line parameters. Elastic coefficients that account for warping effects are introduced to provide a mechanics interpretation of the formulation. The macroelement assembling technique is illustrated by presenting an explicit warping solution for bending of box beams. The warping solution is correlated with existing analytical solutions. An expression for both the effective width and the effective longitudinal modulus variation in flanges of box beams is presented. A design equation consistent with current practice is proposed.