Concentration of torsional shear stresses in axisymmetric bars with deep periodic grooves

The torsional stresses in round bars with deep periodic grooves are calculated by means of the formal analogy between the elastic problem and an auxiliary thermal problem. The analogy allows demanding three-dimensional analyses to be replaced with light two-dimensional analyses, easily implemented on general-purpose finite element packages. Following Neuber’s equivalence concept, the stress concentration in each periodically grooved bar is independently calculated by referring to a single groove of like geometry but lesser depth. Neuber’s approach predicts very closely the reference numerical results if supplemented with a heuristic depth correction function formerly developed by the authors for shallow periodic notches under torsion.