An Elastic Wedge Under Moment Loading: The Carothers Paradox Revisited

Abstract In this paper, a semi-infinite wedge of arbitrary angle under moment loading is studied. The moment may be located at any position within the wedge. First, to treat this issue in a general sense, the fundamental solution for a pointwise moment is derived by virtue of an assembly of deliberately distributed four concentrated forces. Then, using conformal mapping technique, the analytical solution for the semi-infinite wedge interacting with the pointwise moment is derived. Based on this solution, the wedge subjected to any moment loading is formulated. As an application, the Carothers problem, namely, the wedge vertex subjected a concentrated moment is analyzed. To resolve the so-called the Carothers paradox, a modified and practical model is proposed. The solutions developed in this study provide a basic block to study the problems of a wedge under complex moment loading conditions. Our results show that the stress distribution behavior distanced from the wedge vertex is categorically determined by its open angle.