Axially loaded pipes with internal pressure

[KOKONIS36]

Does anyone know or has any references on how to derive the equation for an axially-loaded pipe with internal pressure. I think the critical buckling load comes
Pcr. =EI(pi)(pi)/(L)(L)
which is the same as an axially loaded pipe without internal pressure.
But how do you prove it?

 

[Ron]

If you had a perfectly closed system with a straight pipe, the internal pressure would reduce the axial stress; however, I doubt that exists. In a relatively open system where pressure can redistribute, the pressure does not serve to resist buckling, so no need to consider the effect, unless the pressure is sufficient to deform the pipe. E and I are not dependent on applied stress unless significant deformation occurs.

 

[ishvaaag]

Galambos has a number of items on this thing. Check the V edition that I have at p 567. There is an increase in buckling strength in the ELASTIC buckling stress realm.

As soon as the Hencky-VonMises stress intensity exits the limit of proportionality, no gain in buckling critical stress.

 

[Ron]

ishvaag....wouldn't that be true only if the pressure increased from a volume decrease?

 

[JoshPlumSE]

A few words of caution here. In the process / industrial engineering world, pipe stress analysis and design is very different from your typical AISC building type structures.

In that world, design takes into account things such as internal pressure, slug loads, thermal loads and expansion, corrosion and such in a much more detailed way than those of us who normally work with buidlings would do. If you're dealing with one of these situations, then you really need to get your information from an experienced pipe-stress engineer, not a structural guy who dabbles in that area from time to time.

Josh

 

[ishvaaag]

Ron, I was just quoting briefly the reference, I am of course no expert on this. Would love to know more on many of these things, I`ll try tomorrow to get insight in your question.

 

[racookpe1978]

Going to the far exotic calc's, our Atlas rocket boosters have to be pressurized internally because their thin membrane shells around the fuel and oxidizer tanks are too weak to withstand the bending forces as the missile is raised up from the truck to the launch position.....

But, unless you're so limited by weight and have so much money that you can throw it away into space in one-shot missiles, I'd recommend not trying to "take advantage" of the small reduction in total stress that internal stress "may" bring - IF the pipe were perfectly straight and the pipe were perfectly fabricated.

Besides, I doubt that you could purchase a "pipe" with exactly the wall thickness you calculated, and will have to go to the next larger (standard wall) pipe anyway.

 

[Ron]

racookepe1978...I agree..not worth the effort for pipe. Your system is closed, so it makes a difference. For a system that is not sufficiently closed, it makes little or no difference.

There is a "major theme park in Central Florida" that uses pressurized pipe columns for one of its rides (a completely enclosed coaster ride, simulating a ride down a mountain)...not for the stress reduction capability, but for the crack warning that loss of pressure would show.

 

[ishvaaag]

I think to remember I once donwloaded a 1947 paper by Von Karman at NACA addressing the buckling of thin shells and addressing also the case, but have not looked at yet. In any case it is by probing further that we learn, I always like that.

I also remember another curious application of pipe columns with pressure, in a skyscraper in Pittsburg (the three lobed in plan) that has round columns infilled with water as a measure against fires. I always thought that very intresting, like the case where a plastic bag tank can't be pierced by a burning cigarette out of the refrigeration brought by water.

 

[ishvaaag]

This is another text by NASA (not NACA) and later

http://trs.nis.nasa.gov/archive/00000006/01/sp8007.pdf

Ron, ... have not the time presently to delve in this thing now. I may look, eventually and comment. The Von Karman paper I don't find yet may be somewhere. Something of the kind of what above.

Both Galambos IV and V editions have ample sections on this and more accurate than anything I may provide, so let the interested study the texts. I myself woud have to if some critical work so asked for.

Best wishes.

 

[Lion06]

I'm wondering why internal pressure helps? My first inclination is to say that the internal pressure hurts the situation, maybe not from an elastic member buckling standpoint, but from an overall stress standpoint. Wouldn't the internal pressure - which is causing tensile hoop stresses in the pipe, cause longitudinal compressive stresses in the pipe because of poisson's ratio? Is that not true? Does the longitudinal tensile stress from the pressure on the ends of the pipe win?

 

[Ron]

SEIT...yes, in a closed system, pressure on the ends would win over the longitudinal effect of Poisson's ratio due to internal pressure. At best, the longitudinal component would be a fraction of the direct end pressure. The longitudinal compressive stresses would not have a chance to build as the pipe would be lengthening as the pressure increased, due to the end pressure...but alas, it probably is not a closed system and you're just pushing the pressure restraint point around depending on the configuration and closure conditions.