I have a piece of steel, cylindrical (hollow), 200mm outside diameter with 160mm inside diameter (20mm wall thickness), and I need to screw a bolt through the outside of the cylinder towards the center.
I chose a 6mm thick bolt, which requires a 12mm washer (outside diameter).
This means I need to use a flat sander (or similar, maybe a dremmel) to shave off some of the outside of the cylinder, to make a flat plane for the washer to sit on, aiming for 12mm wide.
This will reduce the wall thickness slightly, and I need to calculate how much the wall thickness will shrink by, in order to make sure the bolt isn't slightly too long for the part I'm connecting it to on the inside of the cylinder.
(I might try sanding the bolt down by this amount, or find another mechanical solution - I haven't decided yet.)
I started drawing out a rough diagram to help me visualize and see if any of my past algebra/trig knowledge would help (I'm usually pretty good with basic trig), but since there's also a circle involved I got lost pretty quick.
Is calculus needed to approximate the change in wall thickness?
How should I go about finding this value?
If I understand correctly, the problem is straightforward:
You want to compute $d$ (or $r-d$, which amounts to the same thing).
Since $d^2+ ({w \over 2})^2 = r^2$ and so $d = \sqrt{r^2 - ({w \over 2})^2}$.
In this example, $w = 12$mm, $r = 100$mm and so $ d \approx 99.82$m, so the difference seems negligible. (To be expected since $\sqrt{1-x^2} \approx 1-{x^2 \over 2}$.)