On the flexure of uniform anisotropic beams of rectangular section

Abstract

The simplest theory of beam flexure—Euler-Bernoulli theory—ignores all effects of shear. This is unacceptable for anisotropic composites and, although the Timoshenko shear correction terms may be used, the accuracy of these cannot be guaranteed. At the other end of the scale, exact solutions are difficult to obtain and not easily calculable. This paper develops a relatively simple two-dimensional theoretical analysis for beams of rectangular section whose accuracy can be estimated and against which results using Euler-Bernoulli-Timoshenko theory can be tested. The major approximation used is the neglect of transverse direct stresses and strains; it is estimated that this is satisfactory for beams of realistic aspect ratios, even for quite severe anisotropy. The analysis sheds light on the boundary conditions which are applied at the ends of beam sections and leads to a worthwhile improvement in accuracy over standard theory.