# How Are Stresses Calculated in Non-Standard Shaped Pressure Vessels?

• tuoni
In summary: There is a used version of Roark's Formulas for Stress and Strain for less than \$60.00 (US Dollars) on Amazon.
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.

You should use the Roark manual.

Here is a link to it.

http://www.roarksformulas.com/

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

Thanks
Matt

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.

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!

## 1. What causes stresses in cylindrical cones?

The stresses in cylindrical cones are caused by external forces applied to the cone, as well as internal pressures or loads within the cone itself. These forces can cause the cone to deform and result in stresses.

## 2. How are stresses calculated in cylindrical cones?

The stresses in cylindrical cones can be calculated using the principles of solid mechanics, specifically by applying the theory of elasticity. This involves considering the material properties of the cone and the applied external and internal forces.

## 3. What are the different types of stresses in cylindrical cones?

There are three main types of stresses in cylindrical cones: axial stress, circumferential stress, and radial stress. Axial stress is along the length of the cone, circumferential stress is around the circumference of the cone, and radial stress is perpendicular to the surface of the cone.

## 4. How do stresses in cylindrical cones affect the structural integrity?

The stresses in cylindrical cones can affect the structural integrity by causing the cone to deform or fail under certain loading conditions. Excessive stresses can lead to buckling, cracking, or other forms of failure, which can compromise the stability and strength of the cone.

## 5. What are some common applications of cylindrical cones where stresses are a concern?

Cylindrical cones can be found in various engineering and industrial applications, such as in rocket nozzles, missile bodies, and pressure vessels. In these applications, the stresses in the cones need to be carefully considered to ensure the safe operation and longevity of the structures.

• Mechanical Engineering
Replies
3
Views
1K
• Mechanical Engineering
Replies
6
Views
2K
• General Engineering
Replies
5
Views
23K
• Engineering and Comp Sci Homework Help
Replies
8
Views
4K
• Engineering and Comp Sci Homework Help
Replies
4
Views
2K
• Mechanical Engineering
Replies
16
Views
975
• Mechanics
Replies
17
Views
9K
• General Engineering
Replies
1
Views
8K
• General Engineering
Replies
7
Views
6K
• Mechanics
Replies
3
Views
1K