Shear stress solutions for curved beams: a structural analysis approach
Loading...
Date
2024-12-06
Authors
Palencia Díaz, Argemiro
Velilla Díaz, Wilmer
Contreras, Victor
Guillén-Rujano, Renny
Hernández-Pérez, Adrián
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.
Description
Keywords
Citation
Guillén-Rujano, R., Contreras, V., Palencia-Díaz, A., Velilla-Díaz, W., & Hernández-Pérez, A. (2024). Shear Stress Solutions for Curved Beams: A Structural Analysis Approach. Materials, 17(23), 5982. https://doi.org/10.3390/ma17235982