Length Limitation for Pressure Calc in Thin Shells 1

[Ray1959]

I use Lame' equations to calculate Int. Yield and Collapse,
on components which are round. The length of the sections are invariably relatively short (less than 2ft).
I am trying to qualify a statement in a calculation regarding length criteria in a thin walled shell. The formula is simply: Length = OD x 8. If this criteria is exceeded, then the calculation reverts to the API Burst formula: Bst = (2.Ys.t)/D
Where can I find clarification behind the use of '8'.
Put another way...how long can a thin walled shell (pipe)
become, before succumbing to instability opposed to material strength ?
Appreciate your help.
Ray

 

[SnTMan]

Ray1959, just in general, I don't believe cylinders exposed to internal pressure only are subject to these kinds of instabilities. Strength of materials (and ASME Sec VIII, Div 1) formulas for required thickness, allowable pressure etc are not functions of length, as can be seen by the fact that no length term appears. I am not familiar with the API standards.

External pressure and external loadings such as bending are different cases and length may become inportant.

Regards,

Mike

 

[ggrindle]

Calculations on minimum wall should be based upon the super-position of all stresses combined. i.e internal pressure stress plus external load (pipe supports, etc), plus stress intensifications factors plus any other stress.

Just looking at the internal pressure, however, there should be no length limitation. The question is: are the other stresses negligible in comparison or are they significant enough that you should count them? There is the answer to your question

 

[Ray1959]

SnTMan & ggrindle, thanks for your help, however try this...
My equipment is not a 'pipe' as such (not part of a processing plant with piping supports etc), it is a downhole tool (oil industry) which is round in section with changes in wall section along it's length, etc, not a plain od/id pipe.
I run calc's over certain sections to see if it will succumb to the downhole pressure environment, eg...
imagine an od = 4.000"; id = 3.500"; Mat'l Yield = 105ksi; this geometry is a constant wall over say 0.5ft length, with the lower end capped. The tool is essentially suspended vertically downhole (10kft) as part of a completion, then subjected to internal pressure.
Ignoring any Factor of Safety for the moment, I would use Lame' eqns, to realise an Internal Yield of 13,938 psi and a Collapse of 12,305 psi.
However, if this geometry were say, 20ft long (with no supports), I do not believe the geometry would withstand the same loads. I reckon it would fail at a lower pressure. Failure in this instance would be the geometry 'ballooning', maybe not a catastrophic rupture, but an Engineering design disaster all the same.
With all this in mind, I reckon (?) length must have be a factor sometime. Something 1/4" versus the same geometry at say 20, 30, 50ft, subjected to the same loading, surely can not have the same answer.
Appreciate your help again.

 

[SnTMan]

Ray1959, not having access to your API stuff, it is hard to further address your question. I assume by "Internal Yield" you mean pressure to cause applied stress(es) to equal material yield, and I can only interpret "Collapse" as external pressure related, however:

My handbooks have no reference to length in the Lame' equations. My understanding of these formulas is that they apply to pressure stresses only, and that they only apply in the absence of discontinuities in geometry such as end closures, changes in section, etc. For such a case length is of no importance.

For closures or changes in section, the geometry at that location is what is important and again, length of the section between discontinuities is not.

For thick cylinders it seems to me you would need to calculate the hoop, radial and longitudinal stresses accounting for ALL loadings, and apply an appropriate failure criterion against the tri-axial stress to get to an allowable pressure.

Sorry I can't offer anything further.

Mike

 

[panduru]

I have a feeling there's a strong point here in the post of Ray1959. Let me continue to read postings and also do a re-read before further comment. Very interesting issue at hand.

 

[JStephen]

I'm not sure where that length limitation would come from.

Normally, in the design of piping and tanks, a cylindrical shell is treated as a long cylinder, in which case the length won't enter into the design at all. However, if the ends of the cylinder are restrained against radial displacement and/or rotation, it will increase the strength of the cylinder. The criteria you mention may be telling you when to disregard end effects in the design of the cylinder.

Roark's Formulas for Stress and Strain includes equations for cylinders with different end conditions. You could evaluate the stresses using some of the expressions given and might be able to come up with that limit from there.

 

[panduru]

Thanks JStephen, for the helpful post.

 

[coolbreeze]

I think the issue at hand has more to do with the differences in cross section than anything else. Realize that there are corresponding longitudinal stresses that exist with differences in cross section. This is simply due to internal pressures acting on a piston area. Those stresses are typically taken by the thinest x-section in your tool and must be accounted for in addition to any axial loads from the work string.