Parametric Solution of Stresses in Beams

Abstract

This paper describes the parametric analysis of the distribution of stresses in uniformly loaded beams, aimed at being of use to the designer. The range of parameters covers the field, from very tall beams (columns resting on two supports) to thin beams that can be analyzed using the common bending theory. The study includes the influence of the horizontal reaction which may be associated with the supports. Results of the analysis, obtained primarily by using photoelasticity, are given by curves corresponding to five ratios β between the width W of the beam and its height H. Interpolation for any other β should be easy. The unexpected appearance of a large tensile stress concentration at the bottom boundary off the axis of symmetry and off the neighborhood of the supports, for some ratios of span to height, should be emphasized, as it is the highest tensile stress in the structure.