# Stresses in cylindrical cones

## Main Question or Discussion Point

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.

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You should use the Roark manual.

Here is a link to it.

http://www.roarksformulas.com/

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

Thanks
Matt

minger
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.

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.

minger
For a cone with half angle $$\alpha$$ 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:
$$\sigma_2 = \frac{qR}{t\cos\alpha}$$

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

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

What is E and ν? and am I correct to assume that this is a cricular, straight cone?

What is E and ν?
E is the modulus of elasticity
v is Poisson's ratio

As minger stated

For a cone with half angle $$\alpha$$ ...
For a straight cone, the half angle $$\alpha$$ is set to zero.

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

Thanks
Matt

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!