Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

[+] Author and Article Information
C. Bagci

Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38505

J. Mech. Des 115(3), 346-358 (Sep 01, 1993) (13 pages) doi:10.1115/1.2919198 History: Received July 01, 1991; Online June 02, 2008


Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Copyright © 1993 by The American Society of Mechanical Engineers
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