Displacement of a Ring Subject to Uniform Radial Loads

Abstract

Thick rings are extensively used in various machine elements and structures. These rings are ordinarily acted upon by irregular loadings on their boundaries. However, there are cases where the rings are subject to uniformly distributed radial loads. Examples are the cases of a ring fitted on a rotationally symmetric wheel by heating or a ring rotating with a constant angular speed, etc. The solution for stresses and displacements in a ring subject to a uniformly distributed radial load is also important for the fact that it serves as the first component in the Fourier series for the solution of the general case of inplane loading of a ring. In this investigation the displacements of rings with various cross sections under the actions of uniform radial loads are obtained. Two different methods of theory of elasticity are employed to find the solutions for rings with solid circular and tapered cross sections. An approximate third solution is also derived for the case of a ring with a symmetrical cross section having no re-entrant corners. Numerical results for the displacements of various rings indicate that the latter solution accurately matches the former elasticity solutions, and the classical solution for rectangular cross-section rings, in a wide range.