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So we have this homework problem, it is a rectangular filleted bar and we have to find the minimum thickness. I go and calculated the ratios but here's the problem: (D/d) = 1.375. What may the problem be? Well for this intro to Civil Engr. Course we are taught to find the stress concentration factors using a graph. This graph only has the lines plotted for (D/d) = [ 1.1 1.2 1.3 1.5 ]. How do you guys deal with this when the (D/d) ratio is not listed on a table? Is there some formula to derive the function?

I am a Mechanical Engineering Major taking an intro Civil Engineering Course (Mechanics Materials) , so I have limited knowledge in Civil Engineering terms.

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    $\begingroup$ Can you interpolate between values? $\endgroup$ – Solar Mike Feb 7 '19 at 22:33
  • $\begingroup$ I don't think we are allowed. But besides interpolation is there any other method? $\endgroup$ – Prandals Feb 7 '19 at 22:35
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In a comment under your question, you've said you don't think interpolation is allowed. You're wrong.

Interpolating between such graphs is standard fare in engineering. You'll do it many, many times for multiple different types of graphs.

So in this case, get the stress concentration factor for $D/d = 1.3$ and for $D/d = 1.5$, and then just interpolate:

$$f_{1.375} = f_{1.3}+\dfrac{f_{1.5}-f_{1.3}}{1.5-1.3}(1.375-1.3)$$


The only other method would be to find out the underlying equations used to plot those charts and then just calculate the actual result yourself. Problem is, you were likely given those charts instead of the equations because the equations are ugly and complicated.

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