Stresses near a plate vertex due to a shear force on one of the edges

P.C.J. Hoogenboom
Delft University of Technology, Faculty of Civil Engineering and Geosciences, Delft, the Netherlands

A closed form solution is presented for the stresses near a rectangular vertex of linear elastic plate loaded by an evenly distributed shear force on one of the edges. The force method and the Airy stress function have been applied in the derivations. Remarkable is that the stress in the vertex depends on the direction in which the vertex is approached. The consequences for structural analysis are discussed.

Key words: Elasticity theory, Airy stress function, biharmonic equation, singular point, plain stress, plain strain, polar coordinates