An Extension of the Sand-Heap Analogy in Plastic Torsion Applicable to Cross Sections Having One or More Holes

In this paper, the author cites the basic theory of the sand-heap method of plasticity as developed by A. Nádai, which involves determination of the twisting moment in plastic torsion by means of the formula $M=2kmV$⁠. The author explains the principles upon which the analogy is modified to apply in the case of cross sections having one or more holes, such as a twisted shaft. The technique developed to meet such cases is described in detail and a mathematical analysis is given which results in a twisting-moment formula for a cross section with holes, equivalent in accuracy to that of the original equation for the simple case of a twisted bar.