# STRESS CONCENTRATION FACTORS FOR V-SHAPED CIRCUMFERENTIAL GROOVE

Theoretical stress concentration factors (Kt) of V-shaped circumferential groove can be calculated by this calculator for torsion loads.

There exist some validity conditions for the equations which are used in the calculations. If input parameters don't satisfy validity conditions of equations, a warning message is given by the calculator.

### V-shaped Circumferential Groove: 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)

### List of Equations: 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

### Reference:

• Pilkey, W. D..(2005). Formulas for Stress, Strain, and Structural Matrices Formulas for Stress, Strain, and Structural Matrices .2nd Edition John Wiley & Sons