Stress Distribution in a Reentrant Corner

Abstract

Abstract This paper deals with the stress distribution under plain strain in a corner of any angular magnitude, i.e., a plane with an angular incision or notch. It begins with a brief statement of the method employed by Dr. Th. von Karman in his exact treatment of a beam in bending (Aachen Abhandlungen, Heft 7, 1927). A generalization of this method is outlined which is applicable to the corner for any force distribution over the straight boundaries, and the solution is found for a concentrated load at any point of the boundary. The stresses are determined and shown to be infinite at the vertex of the corner. The discussion points out the very interesting paradox that stresses may be finite for certain continuous loadings, but become infinite if a portion of the load is removed.