Shear Stresses in Beams with Discontinuity in Depth

The shear stresses arising in the region around a change in depth of a beam are studied. The discontinuities considered include changes with and without fillets. It is well known that such discontinuities produce high local shear stresses and various forms of analyses have been applied to this problem. However, despite the many analyses, it is difficult for a designer to obtain a quantitative estimate of the magnitude of shear stress in a particular situation without resorting to analysis. To overcome this difficulty the finite element method has been used to generate parametric solutions, presented in the form of graphs, which allow an estimate to be made of the maximum shear stress occuring over a range of geometry at the discontinuity. The accuracy of the finite element solutions has been gaged against photoelastic analyses of model beams.