Hoop Stress for Short, thick walled section 1

[aggiegrads]

I am trying to find and equation or algorithm for calculating hoop stress for a short section of thick walled cylinder.

The standard formulas for calculating stresses assume a relatively long cylinder, which is not the case in my application. The r/t ratio is about 2.7 and the l/r ratio is around 0.5. I have found a source for thin walled tubes, but not thick-walled tubes.

Thanks,

Steven

 

[desertfox]

Hi aggiegrads

You might try looking in the book "formula's for stress and strain by Roark and Young.

The formula I quote here is for internal pressure only with
the longitudinal stress balanced or at zero.

max hoop stress (thk cyl)=p*((a^2+b^2)/(a^2-b^2))


where p = internal pressure

a = outer radius of cylinder

b = inner radius of cylinder

max hoop stress occurs at inner radius b


hope this helps

regards desertfox

 

[aggiegrads]

Desertfox,

Thanks for your reply, but that is the point of my post. That formula (I have Roark's sitting in front of me) is for relatively long, uniform sections of tube. As I said in my first post, I have a very short section. The wall thickness is almost as long as the length. I have literature that is applicable to short sections for thin-walled tube, but none for thick walled.

The formula you gave me is the one I am currently using.

 

[prex]

The stresses in a cylinder, whatever its length, is exactly what is represented in those formulae, with or without longitudinal stress, depending on how the end effect is applied or suppressed.
You are perhaps speaking of border effects, such as those that may be due to the connection to a flat end: these exist in all cylinders, except that in short cylinders they might be present throughout its entire length, whereas in long cylinders they die out rapidly. However these are, even in short cylinders, the so called local effects, that give rise to secondary stresses, and are therefore treated separately from the circumferential stress.
Can you better explain what formula you are referring to for thin short cylinders?

prex

http://www.xcalcs.com

Online tools for structural design

 

[aggiegrads]

The source I have for thin-walled tubes is an article from Machine Design magazine called "Stress and Deflection in Short Tubes." The author presents an algorithm for finding a correction factor for the existing thin-wall equations:

S = P * r / t
and
d = s * r / E

The article does not say that the equations do not apply to thick wall tubes, but it does not say that they do, either.

Thanks.

Steven Soto
National Oilwell

 

[prex]

Again, I can't see any reason for correcting stresses and deflection in short tubes, unless one wants to include the effect of the end cap (and the result would depend on the type of cap, flat or domed).
I suppose that the article should explain what effect it is addressing.
What can assure you of is that a short or long cylinder, where end effects are suppressed (this can be obtained with two end caps bolted together and with an Oring on cylinder ends), will show the same stresses and deformation when subject to pressure only.

prex

http://www.xcalcs.com

Online tools for structural design