# Stresses in cylindrical cones

1. Jan 15, 2010

### tuoni

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. Jan 15, 2010

### CFDFEAGURU

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

3. Jan 15, 2010

### 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.

4. Jan 15, 2010

### tuoni

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.

5. Jan 15, 2010

### 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

6. Jan 17, 2010

### tuoni

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

7. Jan 17, 2010

### CFDFEAGURU

E is the modulus of elasticity
v is Poisson's ratio

As minger stated

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

8. Jan 17, 2010

### tuoni

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!

9. Jan 17, 2010