# STRESS CONCENTRATION FACTORS AT U-SHAPED CIRCUMFERENTIAL GROOVE OF A SHAFT

Theoretical stress concentration factors (K_{t}) of
U-shaped circumferential groove can be calculated by this calculator for tension, bending and torsion loads. In addition to stress concentration factor calculation, the calculator can be used to find maximum stress values at the groove of the shaft 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.

The formulas and parameters used in the calculator are given in " List of Equations " section of this page.

###### Note 1: Maximum stress is occurred at point A.

###### Note 2: * Geometry rises σ_{nom} by a factor of K_{t }. (K_{t } = σ_{nom}/σ_{max})

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Note 3: ** Geometry rises τ_{nom} by a factor of K_{t }. (K_{t } = τ_{nom}/τ_{max})

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Note 4: ^{o} σ_{nom} = 4P/(πd^{2}) (Nominal tension stress occurred due to tension load)

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Note 5: ^{+} σ_{nom} = 32M/(πd^{3}) (Nominal tension stress occurred due to bending)

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Note 6: ^{x }τ_{nom} = 16T/(πd^{3}) (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.

K_{t}: Theoretical stress
concentration factor in elastic range = (σ_{max}/σ_{nom})

##### List of Equations:

##### Reference: