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Formula for the tensile stress on a spinning ring

  1. Feb 27, 2008 #1
    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. jcsd
  3. Feb 27, 2008 #2
    Go to the library and look in Roark's Formulas for Stress and Strain.
     
  4. Feb 27, 2008 #3

    FredGarvin

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    For a ring:

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

    [tex]\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)[/tex]

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

    The maximum value of [tex]\sigma_r[/tex] happens at [tex]r=\sqrt{ab}[/tex]
     
  5. Feb 27, 2008 #4
    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.
     
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