Shear Warping Behaviour of Elastic Beams With Annular Cross-Section

Abstract

The paper presents a mechanical model for predicting the elastic response of beams with annular cross-section under generic load conditions. The kinematical assumptions deal with a uniform in-plane infinitesimal rotation coupled with warping axial displacements. In addition to the body force field, generic external loads can be applied both at the ends of the beam and on its lateral surface as a function of all spatial variables. It is possible to account, as an examples, for different force fields on the inner and outer lateral boundary. Shear warping dependent deformations are simulated. The effect of thickness, usually neglected in classical thin-walled beam theory, is now considered, thus allowing the accurate study of beams with a moderately high thickness. A novel approach for deriving energy consistent shear correction factors is proposed. Although in its present form the proposed model is developed for the study of homogeneous elastic tubes (closed cross-section), it is easy to upgrade the underlying developments for the purpose of studying both the elastic response of radially inhomogeneous (functionally graded) beams as well as open cross-sections where torsional warping and shear warping effects exist in a coupled manner.