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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Width, D		m
Depth of notch, h		m
Radius of circle, r		m
Notch sensitivity, q
Applied Force, P		N
Applied Moment, M		N.m
Applied Torsion, T		N.m

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OUTPUT   VARIABLES   &   GRAPHS

STRESS CONCENTRATION	Kt	Kf	σnom(106N)	σmax(106N)
♦ Due to axial Tension
♦  Due to Bending
♦  Due to Torsion

Stress Concentration In The Elastic Range

Stress concentration refers to the high stress that occurs in a small localized area of a loaded structure, mainly due to rapid changes in geometry. Geometry changes (also referred to as form irregularity or stess raisers) include the presence of holes, notches, steps, keyways, etc. The theoretical stress concentration factor K_t in the elastic range is defined as the ratio of the maximum stress in the stress raiser to the norminal stress. The reduced stress concentration factor K_f is derived from K_t via the the notch sensivity factor. The applicable equations for a circular shaft with a U-notch are:

For axial tension: σ_nom = 4P/π(D-2h)²
For bending: σ_nom = 32M/π(D-2h)³
For torsion: σ_nom = 16T/π(D-2h)³

where
     K_t = theoretical stress concentration factor
     K_f = reduced stress concentration factor
     σ_nom = nominal stress based on basic stress-analysis equation
     σ_max = max stress arising from stress concentration
     D = width of member
     h = depth of notch
     r = radius of the circular base of notch
     q = notch sentivity
     a's = constant coefficients tabulated in first reference below.
     P = axial force
     M = bending moment
     T = torque

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002, Chapter 17.
• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 6.