STRESS-CONCENTRATION FACTORS: CIRCULAR HOLE IN A RECTANGULAR MEMBER

INPUT   DATA ♥ EXAMPLE Of Input/Output

Title  

Width, D   m  

    

Center of circle, c   m  
Radius of circle, r   m  
Thickness, t   m  
Notch sensitivity, q    
Applied Force, P   N  
Applied Moment, M   N.m  

     Reset

OUTPUT   VARIABLES   &   GRAPHS

STRESS CONCENTRATION   Kt  Kf  σnom(106N)  σmax(106N) 
 ♦ Due to Tension  
 ♦  Due to in-plane Bending  
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. The applicable equations for a rectangular member with an on- or off-center hole are:

    

The equation for Kt is a set of semi-analytic equations of the form:
  Kt = C1 + C2[2c/D] + C3[2c/D]2 + C4[2c/D]3
 The C's are sets of equations of the form:
   Ci = a1 + a2[r/c] + a3[r/c]2,
 with the applicable set determined by the value of r/c 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 = norminal stress based on basic stress-analysis equation
     σmax = max stress arising from stress concentration
     D = width of member
     c = distance to center of circle
     r = radius of the circular hole
     q = notch sentivity
     a's = constant coefficients tabulated in first reference below.

Tips

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

BIBLIOGRAPHY