Unified Formulations of the Shear Coefficients in Timoshenko Beam Theory

Two elastostatic approaches are presented in order provide a simple, but technically effective, assessment of shear coefficients in Timoshenko beam theory. First the elasticity solution of Saint-Venant's flexure problem is used to set forth a unified formulation of Cowper's formula for shear coefficients. Afterward a novel elasticity-based displacement field for a Timoshenko beam is introduced and an energy-consistent variational scheme is developed using the Reissner principle. The new variational framework is then applied to elliptical, circular, and rectangular cross sections. Validation of the results is given by numerical comparison with the other shear deformation factors over an extended range of Poisson's and aspect ratios. Unlike previous treatments, the proposed shear coefficients for shallow cross sections do not result in numerical instability. (C) 2017 American Society of Civil Engineers.