XVII.—An Analytical Theory of the Equilibrium of an Isotropic Elastic Rod of Circular Section

Abstract

The main purpose of the following investigation is to improve the existing Approximate Theory of Beams by bringing it into closer relationship than has hitherto been done with exact solutions of the fundamental differential equations of equilibrium. In its aim, method, and results the paper closely resembles one already published in these Transactions on the corresponding Theory for Plates (vol. xli., 1904). It is less comprehensive than the latter paper, as it deals only with a beam of circular section; but the analysis is of such a nature that the chief results can be extended almost immediately to a beam of any form of section, on the assumption merely of certain Existence Theorems.