STRESS CONCENTRATION FACTORS FOR LARGE CIRCUMFERENTIAL GROOVE IN CIRCULAR SHAFT

Theoretical stress concentration factors (K_t) of large circumferential groove in circular shaft 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.

Calculator:

INPUT PARAMETERS
Parameter	Symbol	Value	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.

 

Please Wait... 

RESULTS
LOADING TYPE - TENSION
Parameter	Symbol	Value	Unit
Stress concentration factor *	Kt	---	---
Nominal tension stress at shaft o	σnom	---	MPa psi ksi
Maximum tension stress due to tension load (at Point-A)	σmax	---
LOADING TYPE - BENDING
Parameter	Symbol	Value	Unit
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	Symbol	Value	Unit
Stress concentration factor **	Kt	---	---
Nominal shear stress at shaft x	τnom	---	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 σ_nom by a factor of K_t.  ( K_t = σ_max/σ_nom)

Note 3: ** Geometry rises τ_nom by a factor of K_t.  ( K_t = τ_max/τ_nom)

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

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

Note 6: ^x τ_nom = 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.

K_t: Theoretical stress concentration factor in elastic range = (σ_max/σ_nom)

List of Equations:

Tension
Bending
Torsion

Reference: