Shaft diameter for a grooved shaft in bending (given Kt)

Sizes the diameters of a grooved/shouldered shaft in bending from the applied bending moment, yield strength, target endurance ratio and a prescribed geometric stress concentration factor Kt.

✓ validated against legacyoriginal: /calculators/c3_2.htm

Shaft diameter for a grooved shaft in bending (given Kt) — original diagram from /calculators/c3_2.htm

Bending moment in grooved section, MNmYield strength, Rₚ₀.₂MPaRatio endurance strength σₑ/Rₚ₀.₂Shaft diameter ratio, d/DStress concentration factor, Kₜ

Shaft diameter, d20.8 mm

Shaft diameter, D26.1 mm

No dedicated diagram exists in the legacy archive for c3_2.htm — reuses the grooved-shaft photo from stress-conc-grooved-shaft-tension (e1_3a.htm), since this calculator sizes the same grooved-shaft geometry, just solving for diameter given Kt rather than for Kt given diameter.

Method & references

Shaft diameters sized from a prescribed geometric stress concentration factor Kt (e.g. read from a Kt chart) so bending stress at the groove stays under σₑ = sf·Rₚ₀.₂.

Mechanical properties of metals reference table

The computation is a literal port of the original client-side JavaScript from /calculators/c3_2.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Shaft diameter for a grooved shaft in bending (given Kt) — Engineering ABC