Toward a consistent beam theory

Abstract

It is well known that the Euler-Bernoulli theory of the bending of beams makes use of a contradicting assumption of zero shear strains and nonzero shear stresses. Sometimes, this type oJ assumption is also carried over to more refined shear deformation theories. This paper outlines a theory thai avoids this assumption. With the aid of the specific example of a tip loaded cantilever beam, it is shown that the present theory gives Euler Bernoulli solutions in that part of the beam where shear deformation is unimportant and a shear deformation type of solution in the pari of the beam where shear deformation is important, with transition stress patterns between the two. Numerical studies, with a shear modulus representative of sandwich beams, bring out the usefulness of the present theory for the analysis of such soft-cored beams.