A New Unified Strength of Materials Solution for Stresses in Curved Beams and Rings

Abstract

Presently existing strength of materials solutions for stresses in curved beams use an incorrect normal force equilibrium condition to define neutral axis location, and to reach a simplified solution, which neglects the curvature effect on stresses due to normal force. This article presents a new but a most general form of the strength of materials solution for determining tangential normal stresses in curved beams, including reductions to special cases. The neutral axis phenomenon is clarified and experimentally verified. Several numerical examples are included, some of which offer photoelastic experimental results, where results predicted by the exact elasticity solution, method of the article, Winkler’s theory, and the conventional simplified method are compared. The hook, diametrically loaded cut, and full ring applications are included. It is shown that simplified theory leads to very large errors. Results by the method offered are very reliable with small errors which are comparable with those of exact elasticity solutions. Stress and deflection analyses of curved beams with varying thicknesses of cross-sections by exact elasticity solutions are given in a separate article [6].