SHEAR DEFORMABLE BEAM THEORY WITH WARPING INDEPENDENT OF SHEAR DEFORMATION

Abstract

Although the Timoshenko beam theory assumes that cross sections remain plane, the shear stress is not constant through the beam thickness. Therefore, the shear stiffness of beams has to be modified by a shear correction factor through taking into account warping of cross sections. In this beam theory, warping is assumed to be proportional to the shear force. Whereas the shear force can be discontinuous, warping must be continuous due to compatibility condition of deformation. Therefore, the warping can not be proportional to the shear deformation. This paper proposes a beam theory taking into account the warping independent of the beam shear deformation. The effect of independently considered warping is evaluated through a series of analyses of simple cantilever beams. As a result, we conclude that the present theory predicts the deformation more accurately compared with other beam theories and that the effect of constraint of the cross-sectional deformation reduces the shear deformation within the length equivalent to the height of the beam.