Shear Stress Solutions for Curved Beams: A Structural Analysis Approach

Area of Science:

• Mechanical Engineering
• Structural Analysis
• Applied Mathematics

Background:

• Shear stress analysis in curved beams is crucial for structural integrity in civil and mechanical engineering.
• Existing methods for predicting shear stress in curved beams have limitations in accuracy and ease of use.

Purpose of the Study:

• To develop and validate novel analytical solutions for shear stress in isotropic curved beams with compact sections and variable thickness.
• To provide engineers with simpler, more accurate tools for predicting shear stress in common beam geometries.

Main Methods:

• Developed two new analytical solutions based on Cook's proposal and mechanics of materials.
• Validated solutions using computational finite element models (FEM) for rectangular, circular, elliptical, and triangular cross-sections.
• Compared results with existing equations and FEM predictions across various radius ratios (b/a).

Main Results:

• The proposed solutions accurately predict shear stress in curved beams for 1 < b/a ≤ 5.
• Maximum relative differences with FEM were 8% (1 < b/a ≤ 2) and 16% (2 < b/a ≤ 5).
• The neutral axis location predicted by the new solutions closely matches FEM results.

Conclusions:

• The new analytical solutions offer a significant improvement over existing methods for shear stress prediction in curved beams.
• These solutions are simpler and more practical for engineers, expanding the knowledge in elasticity theory.
• The approach is validated for various cross-sections and radius ratios, showing good agreement with FEM analysis.