Abstract
This paper describes a numerical method for solving directly the problem of the torsion of a bar of constant cross section having one or more internal longitudinal holes. The method involves the use of finite differences and can be used with either the iteration procedure due to Liebmann (1), or the relaxation procedure attributed to Southwell (2). The method avoids the necessity of combining a number of separate solutions since it establishes the necessary conditions around the hole by a special condition which amounts in general to treating the entire hole as a single point in a network, and determining the elevation of this point (i.e., the elevation of the stress function for torsion at the boundary of the hole) by a relation similar in form to that used for regular points of the network. The calculations by this method appear to converge at least as rapidly as for a section without a hole.
