# V-SHAPED CIRCUMFERENTIAL GROOVE

V-shaped circumferential groove on a shaft. Stress concentration factors (Kt) calculator for torsion loads.

 INPUT PARAMETERS Parameter Value Diameter of larger shaft section [D] mm cm m inch ft Diameter of smaller shaft section [d] Radius [r] Angle [θ] deg Torque [T] N*m lbf*in lbf*ft

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - TORSION Parameter Value Stress concentration factorn [Kt] * --- --- Nominal shear stress at shaft [τnom ] x --- MPa psi ksi Maximum shear stress due to torsion (at Point-A) [τmax ] ---

Note 1: Maximum stress is occured at point A.

Note 2: * Geometry rises τnom by a factor of Kt. (Kt = τnommax)

Note 3: x τnom= 16T/(πd3) (Nominal shear stress occurred due to torsion)

Note 4: V-shaped stress concentration factor is dependent on U-shaped stress concentration factor. Input parameters shall satisfy both cases.

### Definitions:

Stress Concentration Factor: Dimensional changes and discontinuities of a member in a loaded structure causes variations of stress and high stresses concentrate near these dimensional changes. This situation of high stresses near dimensional changes and discontinuities of a member (holes, sharp corners, cracks etc.) is called stress concentration. The ratio of peak stress near stress riser to average stress over the member is called stress concentration factor.

Kt: Theoretical stress concentration factor in elastic range = (σmaxnom)

### Formulas:

 Torsion 0°≤ θ ≤90°, Kt is independent of r/d  90°≤ θ ≤ 125°, Kt is applicable only if r/d ≤ 0.01. $${ C }_{ 1 }=0.2026\sqrt { \theta } -0.06620\theta +0.00281\theta \sqrt { \theta }$$ $${ C }_{ 2 }=-0.2226\sqrt { \theta } +0.07814\theta -0.002477\theta \sqrt { \theta }$$ $${ C }_{ 3 }=1+0.0298\sqrt { \theta } -0.01485\theta -0.000151\theta \sqrt { \theta }$$ Ktu=Stress concentration factor for U-shaped groove (θ=0) $${ C }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\sqrt { { K }_{ tu } } +{ C }_{ 3 }{ K }_{ tu }$$ τnom=16T/πd3 τmax=τA=Ktτnom