Analytical study of Bernoulli and Timoshenko beam theories for varied boundary conditions

Abstract

In this paper is analyzed the difference that occurs in the displacements using the Bernoulli and Timoshenko beam theories by varying the relationship between span and height of the cross section and changing the boundary conditions of the structural element. The analyzes were restricted to rectangular cross section beams. It was demonstrated that the effect of the shear coefficient (Timoshenko’s theory), in comparison with Bernoulli’s theory, amplifies the displacements obtained in the structure due to the reduction of the span/height relationship and the increase of the degree of internal static indeterminacy, reaching in some cases a difference of more than double. Limit ratios of span size and cross section height were proposed as a function of the boundary condition for the consideration of the shear coefficient.