On Flexure of Shear Deformable Isotropic Rectangular Propped Cantilever Beams

This paper presents a comparison study on the flexure of shear deformable isotropic rectangular propped cantilever beams by utilizing newly developed variationally consistent two-variable-refined beam theory, variationally inconsistent single-variable refined beam theory, and variationally inconsistent Levinson beam theory. The beam is assumed to be under the action of uniformly distributed transverse load. It should be noted that governing differential equations of two-variable-refined beam theory are derived by utilizing Hamilton’s principle. Whereas, beam gross equilibrium equations are utilized in the case of single-variable-refined beam theory as well as Levinson beam theory to derive their respective governing differential equations. All three beam theories take into account a parabolic variation of the beam transverse shear strain and hence the beam transverse shear stress through the beam thickness. These theories satisfy transverse shear stress-free beam surface conditions. Hence, these theories do not require a shear correction factor. Effects of the beam thickness-to-length ratio on the location of maximum beam transverse displacement and values of maximum non-dimensional beam transverse displacement, non-dimensional beam axial stress, and non-dimensional beam transverse shear stress are presented. Profiles of the non-dimensional beam transverse displacement, non-dimensional beam axial stress, and non-dimensional beam transverse shear stress for various values of the beam thickness-to-length ratio are also presented.