Refined Bending Theory for Beams of Circular Cross Section

The secondary influences, besides the transverse shear deformation and the rotatory inertia, that affect the bending behavior of beams are identified. Incorporating these influences, a shear-deformation theory is developed for beams of solid circular cross section. Because an a-priori knowledge of the stresses is necessary to account for the secondary influences, a procedure is developed to obtain a statically equivalent three-dimensional stress field. Using this procedure, an engineering stress field is developed, and is compared with an exact solution for the beams of circular cross section. The stress field is later used to develop the shear-deformation theory that accounts for all the bending-related secondary influences. The theory is evaluated considering the propagation of traveling flexural waves.