Flexure of a Beam of Curvilinear Polygonal Section

Abstract

Recently L. M. MILNE-THOMISON [l] has developed complex variable techniques to obtain the solution of flexure problem of beams of different cross-sections which can be mapped conformally onto the unit circle @(z) is the required complex flexure function which can be determined from the integral equation Y where [ is a point inside the unit circle y in the c-plane in the [-plane. Expression for the required single flexure function @(z) can be obtained by using CAUCHY'S theorem. The torsion function, the shearing stress and the centre of flexure can be determined of very easily. Solution of the flexure problem of beams the following cross-sections are obtained by L. M. MILNE-THOMSON: (a) Circle (b) Cardioid (c) One loop of BERNOULLIS Leminscate.