Investigation of stress distribution of changes of section of members under two dimensional bending and direct stress

The application of the complex variable to the theory of elasticity by Huschelishvili and C.A.M. Gray, in cases V7here the shape being investigated can be transformed to the imit circle, leads to an infinite set of simultaneous equations in an infinite number of unknovjns say). Results are normally only possible by successive approximation and then only if the equations are in a suitable form. This thesis attempts to find solutions for various such sets, and particularly for the change of section shape. In most cases, x^ does not approach 0 as n approaches infinity and so consideration of only a finite number of terms would not be expected to produce good results. Hovjever, by choosing suitable initial values for the x^^ and inserting these in the equations^ the infinite series so formed can often be determined analytically, and made to agree very closely with the right hand sides. In this way, solutions were found for various sets of equations. The stresses in a long cantilever viith concentrated end loads viere completely determined. In the case of the change section, the m.ost difficult part, that of calculation of the sum of the principal stresses, has been done, although not with satisfactory accuracy as for the cantilever.