Shear Deformable Generalized Beam Theory for the Analysis of Thin-Walled Composite Members

Abstract

This paper presents the incorporation of shear deformation effects into a generalized beam theory (GBT) formulation developed to analyze the first-order (linear) and buckling behavior of composite thin-walled members made of laminated plates displaying arbitrary orthotropy, often designated as anisotropic laminates. Unlike other existing beam theories, the proposed GBT formulation incorporates in a unified fashion (1) elastic coupling effects, (2) warping effects, (3) cross-section in-plane deformation, and (4) shear deformation. The main concepts and procedures involved in the currently available GBT are adapted and/or modified to account for the specific aspects associated with shear deformation. In particular, the GBT equilibrium equations and boundary conditions are derived, and their terms are physically interpreted. A lipped channel section is considered to illustrate the performance of a GBT cross-section analysis, namely, the operations required to determine the (additional) set of shear deformation modes. Finally, to clarify the concepts involved in the proposed GBT formulation and illustrate its application and capabilities, two numerical examples are presented and discussed in detail: the first concerns the first-order and buckling behaviors of a lipped channel column exhibiting nonaligned orthotropy; and the second assesses the influence of shear deformation on the buckling behavior of lipped channel columns with cross-ply orthotropy.