STRESS-CONCENTRATION FACTORS: RADIAL HOLE IN HOLLOW OR SOLID CIRCULAR SHAFT

INPUT   DATA ♥ EXAMPLE Of Input/Output

Title  

Outer Diameter, D   m  

    

Inner Diameter, d   m  
Radius of hole, r   m  
Notch sensitivity, q    
Applied Force, P   N  
Applied Moment, M   N.m  
Applied Torsion, T   N.m  

     Reset

OUTPUT   VARIABLES   &   GRAPHS

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

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 Kt 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 Kf is derived from Kt via the the notch sensivity factor.

Consider a circular shaft with a radial hole drilled completely through it. The shaft may be hollow (d > 0) or solid (d = 0). The shaft is subjected to one form of loading: axial tension, bending, or torsion. In the bending case, the hole is assumed farthest from the bending axis. The applicable equations are:

For axial tension: σnom = 4P/π(D2 - d2)
For bending: σnom = 32MD/π(D4 - d4)
For torsion: σnom = 16TD/π(D4 - d4)

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

Also,
  Kf = 1 + q(Kt - 1) and
σmax=Kfσnom

where
     Kt = theoretical stress concentration factor
     Kf = reduced stress concentration factor
     σnom = nominal stress based on basic stress-analysis equation
     σmax = max stress arising from stress concentration
     D = outside diameter
     d = inside diameter
     r = radius of radial hole
     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