# STRESS CONCENTRATION FACTORS FOR LARGE CIRCUMFERENTIAL GROOVE IN CIRCULAR SHAFT

Theoretical stress concentration factors (Kt) of large circumferential groove in circular shaft can be calculated by this calculator for tension, bending and torsion loads. Maximum stress values at the groove of the shaft can also be calculated if loading parameters are known. See footnotes of the "Results" table for the necessary equations for the stress calculations.

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.

### Large Circumferential Groove in Circular Shaft:

 INPUT PARAMETERS Parameter Value Diameter of larger shaft section [D] mm cm m inch ft Diameter of smaller shaft section [d] Radius [r] Tension force [P] N kN lbf Bending moment [M] N*m lbf*in lbf*ft Torque [T]

Note:Use dot "." as decimal separator.

 RESULTS LOADING TYPE - TENSION Parameter Value Stress concentration factor[Kt] * --- --- Nominal tension stress at shaft [σnom ] o --- MPa psi ksi Maximum tension stress due to tension load (at Point-A) [σmax ] --- LOADING TYPE - BENDING Parameter Value Stress concentration factor [Kt] * --- --- Nominal tension stress at shaft [σnom ] + --- MPa psi ksi Maximum tension stress due to bending (at Point-A) [σmax ] --- LOADING TYPE - TORSION Parameter Value Stress concentration factor [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 σnom by a factor of Kt.  ( Kt = σmaxnom)

Note 3: ** Geometry rises τnom by a factor of Kt.  ( Kt = τmaxnom)

Note 4: o σnom= 4P/(πd2) (Nominal tension stress occurred due to tension load)

Note 5: + σnom = 32M/(πd3) (Nominal tension stress occured due to bending)

Note 6: x τnom = 16T/(πd3) (Nominal shear stress occureed due to  torsion)

### 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:

 Tension $$0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0$$ , $$1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10$$ $${ C }_{ 1 }=-81.39+153.10(D/d)-70.49{ (D/d) }^{ 2 }$$ $${ C }_{ 2 }=119.64-221.81(D/d)+101.93{ (D/d) }^{ 2 }$$ $${ C }_{ 3 }=-57.88+107.33(D/d)-49.34{ (D/d) }^{ 2 }$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$ $${ \sigma }_{ nom }=4P/\pi { d }^{ 2 }$$ $${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$ Bending $$0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0$$ , $$1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10$$ $${ C }_{ 1 }=-39.58+73.22(D/d)-32.46{ (D/d) }^{ 2 }$$ $${ C }_{ 2 }=-9.477+29.41(D/d)-20.13{ (D/d) }^{ 2 }$$ $${ C }_{ 3 }=82.46-166.96(D/d)+84.58{ (D/d) }^{ 2 }$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$ $${ \sigma }_{ nom }=32M/\pi { d }^{ 3 }$$ $${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$ Torsion $$0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0$$ , $$1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10$$ $${ C }_{ 1 }=-35.16+67.57(D/d)-31.28{ (D/d) }^{ 2 }$$ $${ C }_{ 2 }=79.13-148.37(D/d)+69.09{ (D/d) }^{ 2 }$$ $${ C }_{ 3 }=-50.34+94.67(D/d)-44.26{ (D/d) }^{ 2 }$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$ $${ \tau }_{ nom }=16T/\pi { d }^{ 3 }$$ $${ \tau }_{ max }=\tau _{ A }={ K }_{ t }{ \tau }_{ nom }$$