# SHOULDER FILLET IN A STEPPED CIRCULAR SHAFT

Shoulder fillet in a stepped circular shaft. Stress concentration factors (Kt) for tension, bending and 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] 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 [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 [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 [τmax ] ---

Note 1: * Geometry rises σnom by a factor of Kt . (Kt = σmaxnom)

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

Note 3: o σnom = 4P/(πd2) (Nominal tension stress occurred due to tension load)

Note 4: + σnom = 32M/(πd3) (Nominal tension stress occurred due to bending)

Note 5: x τnom = 16T/(πd3) (Nominal shear stress occurred 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)

### Formulas:

 Tension $$0.1\le h/r\le 2.0$$ $$2.0\le h/r\le 20.0$$ $${ C }_{ 1 }=0.926+1.157\sqrt { h/r } -0.099h/r$$ $${ C }_{ 1 }=1.200+0.860\sqrt { h/r } -0.022h/r$$ $${ C }_{ 2 }=0.012-3.036\sqrt { h/r } +0.961h/r$$ $${ C }_{ 2 }=-1.805-0.346\sqrt { h/r } -0.038h/r$$ $${ C }_{ 3 }=-0.302+3.977\sqrt { h/r } -1.744h/r$$ $${ C }_{ 3 }=2.198-0.486\sqrt { h/r } +0.165h/r$$ $${ C }_{ 4 }=0.365-2.098\sqrt { h/r } +0.878h/r$$ $${ C }_{ 4 }=-0.593-0.028\sqrt { h/r } -0.106h/r$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$ $${ \sigma }_{ nom }={ 4P }/{ \pi { d }^{ 2 } }$$ $${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$ Bending $$0.1\le h/r\le 2.0$$ $$2.0\le h/r\le 20.0$$ $${ C }_{ 1 }=0.947+1.206\sqrt { h/r } -0.131h/r$$ $${ C }_{ 1 }=1.232+0.832\sqrt { h/r } -0.008h/r$$ $${ C }_{ 2 }=0.022-3.405\sqrt { h/r } +0.915h/r$$ $${ C }_{ 2 }=-3.813+0.968\sqrt { h/r } -0.260h/r$$ $${ C }_{ 3 }=0.869+1.777\sqrt { h/r } -0.555h/r$$ $${ C }_{ 3 }=7.423-4.868\sqrt { h/r } +0.869h/r$$ $${ C }_{ 4 }=-0.810+0.422\sqrt { h/r } -0.260h/r$$ $${ C }_{ 4 }=-3.839+3.070\sqrt { h/r } -0.600h/r$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$ $${ \sigma }_{ nom }={ 32M }/{ \pi { d }^{ 3 } }$$ $${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$ Torsion $$0.25\le h/r\le 4.0$$ $${ C }_{ 1 }=0.905+0.783\sqrt { h/r } -0.075h/r$$ $${ C }_{ 2 }=-0.437-1.969\sqrt { h/r } +0.553h/r$$ $${ C }_{ 3 }=1.557+1.073\sqrt { h/r } -0.578h/r$$ $${ C }_{ 4 }=-1.061+0.171\sqrt { h/r } +0.086h/r$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$ $${ \tau }_{ nom }={ 16T }/{ \pi { d }^{ 3 } }$$ $${ \tau }_{ max }={ K }_{ t }{ \tau }_{ nom }$$