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

Abstract

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

Stress concentrations in periodic notches: a critical investigation of Neuber's method

“…6. Also for the shear stress analysis of the axisymmetric bar, Castagnetti and Dragoni used a numerical method relying on a thermal analogy, [19] Fig. 6.…”

“…Compared to the previous case, the thermal load in the volume is zero and the heat flux through the thin plate is steady in the axial direction. The shear stresses at any point of the bar is obtained by multiplying the local radius by the thermal gradient in the corresponding point of the plate, according to the procedure described in detail in [19].…”

“…The sharp and shallow notch is now replaced by a U-shaped notch (root radius of the same order of magnitude of the depth) with finite depth (of the same order of magnitude of the solid bar). The results here presented come from the works by Dragoni and Castagnetti [15,19].…”

Torsional stress distributions in tubes with external and internal notches

“…The last term on the right-hand side has been introduced to account for the linear decrease of the nominal shear stress on the net section of the solid bar. Equation (11), which is valid in the highly stressed zones close to the notch tip, can also be extended to the entire net section. The correct expression is 21…”

“…[2][3][4][5][6][7][8][9] Worthy of mention are also some recent analyses carried out by Dragoni and Castagnetti 10,11 who determined the torsional stresses in round bars with periodic grooves by means of a thermal analogy and showed that Neuber's approach for periodic notches well agrees with the numerical results only when supplemented with a heuristic depth correction function proposed by the same authors.…”