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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Width, D
Height of notch, h
Radius in notch, r
Notch sensitivity, q

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Kt	Kf
♦  Stress-concentration factor due to tension
♦  Stress-concentration factor due to in-plane bending
♦  Stress-concentration factor due to out-of-plane bending

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, where norminal stress is computed via basic stress analysis formulas using the net cross-section. The reduced stress concentration factor K_f is derived from K_t via the the notch sensivity factor.

The equation for K_t is a set of semi-analytic equations of the form:
  K_t = C₁ + C₂[2h/D] + C₃[2h/D]² + C₄[2h/D]³
The C's are sets of equations of the form:
   C_i = a₁ + a₂√[h/r] + a₃[h/r],
with the applicable set determined by the value of h/r and the type of loading.
Also,
  K_f = 1 + q(K_t - 1)

where
     K_t = theoretical stress concentration factor
     K_f = reduced stress concentration factor
     D = width of member
     h = height of each notch
     r = radius of the arc in the notch
     q = notch sentivity
     a's = constant coefficients tabulated in first reference below.

All length values are given here in the same units.

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.