# Stress Concentration Factor – Why a Specific Range?

I was trying to find the stress concentration factor for a specific situation and I found two different resources for it.

Ref: Shigley's mechanical engineering design

Ref: Roark's Formulas for Stress and Strain

However, I found both resources were only applicable for d/w <0.3

Why is it data can only be found in this specific range? The example I have has a value of 0.5 and is therefore outside the range so I am unsure how to proceed and what the implications are of it being outside the stress concentration factor range.

Any help is greatly appreciated, thanks

## 1 Answer

From what I see, in this picture from the Shigley book, if I really had to, I would extrapolate to 0.5 (or more precisely interpolate between the limit cases). The limit cases for very thick plate (d/h=0) and very thin plate ($$d/h\approx \infty$$) have values for d/w close to 0.7. (I would hazard a guess that these solutions are based on analytical assumptions for plane stress and plane strain)

So, I would extrapolate the graph and treat the data with caution. If its a critical part I would increase it by a factor of safety, or try some numerical method.

As to why that happens, my guess is that basically, when the hole becomes too wide, then its not anymore easy to estimate the stresses experimentally or analytically. Too many factors would start to creep in. That would increase the variance of the results to the point that the stress concentration factors might not be relevant.

• d/w=0.3 means that there is roughly d of extra material on both sides of the hole. Many sources and design rules state the hole should be at minimum the diameter of hole to twice that from the edge. After that it probably should be analyzed and tested separately like you surmise. Nov 27 '20 at 20:32