A Timoshenko beam theory with pressure corrections for layered orthotropic beams

A Timoshenko beam theory for layered orthotropic beams is presented. The theory consists of a novel combination of three key components: average displacement and rotation variables that provide the kinematic description of the beam, stress and strain moments used to represent the average stress and strain state in the beam, and the use of exact axially-invariant plane stress solutions to calibrate the relationships between all these quantities. These axially-invariant solutions, which we call the fundamental states, are also used to determine a shear strain correction factor as well as corrections to account for effects produced by externally-applied loads. The shear strain correction factor and the external load corrections are computed for a beam composed of isotropic layers. The proposed theory yields Cowper’s shear correction for a single isotropic layer, while for multiple layers new expressions for the shear correction factor are obtained. A body-force correction is shown to account for the difference between Cowper’s shear correction and the factor originally proposed by Timoshenko. Numerical comparisons between the theory and finite-elements results show good agreement.