Shear Stress Solutions for Curved Beams: A Structural Analysis Approach

The shear stress on isotropic curved beams with compact sections and variable thickness is investigated. Two new solutions, based on Cook's proposal and the mechanics of materials approach, were developed and validated using computational finite element models (FEM) for four typical cross-sections (rectangular, circular, elliptical, and triangular) used in civil and mechanical structures, constituting a novel approach to predicting shear stresses in curved beams. They predict better results than other reported equations, are simpler and easier for engineers to use quickly, and join the group of equations found using the theory of elasticity, thereby expanding the field of knowledge. The results reveal that both equations are suitable to predict the shear stress on a curved beam with outer/inner radii ratios in the interval 1<b/a ≤ 5 aspect ratios. There is a maximum relative difference between the present solutions and finite element models of 8% within 1<b/a ≤ 2, and a maximum of 16% in 2<b/a ≤ 5. Additionally, the neutral axis of the curved beam can be located with the proposed solution and its position matches with that predicted by FEM. The displacement at the top face of the end of the curved beam induces a difference in the shear stress results of 8.0%, 7.0%, 6.5%, and 2.9%, for the circular, rectangular, elliptical, and triangular cross-sections, respectively, when a 3D FEM solution is considered. For small b/a ratios (near 1), the present solutions can be reduced to Collignon's formula.