# Formula for the tensile stress on a spinning ring

1. Feb 27, 2008

### boab

I'm having a problem finding and equation that will give me the tensile stress acting on a spinning ring, like the rim of a flywheel, that is trying to "pull itself apart". The ring has no spokes or disc, but is just a ring spinning on its axis. I need to know how fast the ring can spin before it separates from the tensile stress acting on the material it is made of.
I seem to have stepped in over my head.

2. Feb 27, 2008

### TVP45

Go to the library and look in Roark's Formulas for Stress and Strain.

3. Feb 27, 2008

### FredGarvin

For a ring:

$$\sigma_r = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2-\frac{a^2b^2}{r^2}-r^2\right)$$

$$\sigma_{\theta} = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2+\frac{a^2b^2}{r^2}-\frac{1+3\nu}{3+\nu}r^2\right)$$

where:
$$a$$ = outer radius
$$b$$ = inner radius
$$\rho$$ = mass density
$$\nu$$ = Poisson's ratio
$$\omega$$ = angular velocity

The maximum value of $$\sigma_r$$ happens at $$r=\sqrt{ab}$$

4. Feb 27, 2008

### boab

Well I thank you very much for the quick reply, and the effort! You have saved the day, and advanced the project.
Cliff

I used to be Cliff, now its "boab: as something got lost in my previous registration.