V-SHAPED CIRCUMFERENTIAL GROOVE

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

Stress concentration factor for V-shaped groove
INPUT PARAMETERS
Parameter Value
Diameter of larger shaft section [D]
Diameter of smaller shaft section [d]
Radius [r]
Angle [θ] deg
Torque [T]


Note: Use dot "." as decimal separator.


 RESULTS
LOADING TYPE - TORSION
Stress concentration factor for V-shaped groove under torsion
Parameter Value
Stress concentration factorn [Kt] * --- ---
Nominal shear stress at shaft [τnom ] x ---
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 = τnom/τmax)

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 = (σmax/σnom)

Formulas:

Stress concentration factor for V-shaped groove
Torsion
Stress concentration factor for V-shaped groove under 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

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