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Stresses in cylindrical cones

  1. Jan 15, 2010 #1
    Are there standard algorithms for calculating stresses (axial, radial) in pressure vessels? I have found pages detailing circular cylindrical, thin- and thick-walled pressure vessels. However, what about other shapes?

    Are there some equations I can use to integrate to find stresses for e.g. cylindrical cones, hemispheres, and other shapes? I.e. if I have a circular cone, and know the function for the curvature of the tapering side (straight, ellipse, tangent, power, parabola, etc.), I can find the stresses.
  2. jcsd
  3. Jan 15, 2010 #2
    You should use the Roark manual.

    Here is a link to it.


    Be cautious of thier online calculator and hand check it's results until you become comfortable with it.

  4. Jan 15, 2010 #3


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    If you don't have access and ask nicely, I'm sure someone can post the equation. Roark is a must-have for any engineer though. It also lists edge effects and stresses at the ends IIRC.
  5. Jan 15, 2010 #4
    Oh! I tried registering and looking at the online calculator, but I guess I wouldn't see much without having paid for something ^^; Software was indeed insanely expensive, considering I need it only for a few small things.

    I did find a book called "Formulas for stress, strain, and structural matrices - Second edition" by Walter D. Pilkey. However, the maths turned out to be a little too much for me.

    The stress for a shell of revolution was exactly what I needed, but I couldn't quite figure out it, and the equations quickly ended up pretty long and complex.
  6. Jan 15, 2010 #5


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    For a cone with half angle [tex]\alpha[/tex] under uniform pressure q, at a position y, with a radius R (function of half angle and y), with tangential edge support, the:

    Meridional Stress
    \sigma_1 = \frac{qR}{2t\cos\alpha}

    Circumferential (Hoop) Stress:
    \sigma_2 = \frac{qR}{t\cos\alpha}

    Change in Radius:
    \Delta R = \frac{qR^2}{Et\cos\alpha}\left(1-\frac{\nu}{2}\right)

    Change in axial position:
    \Delta y = \frac{qR^2}{4Et\sin\alpha}\left(1-2\nu -3\tan^2\alpha)

    p.s. and thickness t
  7. Jan 17, 2010 #6
    What is E and ν? and am I correct to assume that this is a cricular, straight cone?
  8. Jan 17, 2010 #7
    E is the modulus of elasticity
    v is Poisson's ratio

    As minger stated

    For a straight cone, the half angle [tex]\alpha[/tex] is set to zero.

    Can you obtain a copy of Roark's Formulas for Stress and Strain from a library?

  9. Jan 17, 2010 #8
    I will try to find a copy of Roark's Formulas for Stress and Strain, I'm probably going to need it for a few other things anyway.

    Thank you for the help!
  10. Jan 17, 2010 #9
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