Buckling in telescoping hydraulic cylinders

[Boothby171]

I started to examine a multi-stage telescoping hydraulic cylinder for Euler buckling (it actually is rigidly mounted at its base stage, and has side loads as well, so there are interaction equations to be dealt with), when I realised something important.

My "d'oh" moment of the day.

The walls of the cylinder--all the cylinders that contain oil, actually--are NOT under axial compression loads. They are under outward hydraulic pressure from the oil. They see a hoop stress. Euler's buckling equation doesn't enter into it.

So, now how do I determine stability? The overlap at each stage has a moment associated with it, and since all components are springs (the world's a spring...), there is a lateral and torsional deflectiomns from each subsequent stage on the stage before it. At some point, the deflections and the lateral and COMPRESSIVE forces heterodyne, and the system destabilizes. How do I calculate that without going any further into a master's thesis?

And do I even start thinking about the fact that the hoop stresses from the outward pressure of the oil actually OFFSET the compressive wall stresses in the cylinders, thereby improving the system response!?!

Or have I gone and made a simple problem needlessly difficult?

Thanks in advance!

 

[BigInch]

Design for compression and tension separately. Use an allowable compressive stress with a calculation based on prevention of buckling, similar to what AISC does in their steel column load allowables (for an "O" section). Then add the secondary eccentric column load (and other lateral loads as applicable) to get the additive secondary stresses. Hoop stress would tend to reduce the compressive loads, but I would not consider that help, as a measure of extra safety, since buckling is usually initiated by some type of highly localized out of roundness compressive failure mechanism.

Lastly, design for tension allowables using hoop stress + residual tensile bending loads (if any) from the compressive case.

When in doubt, keep it conservative. IMO.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[Boothby171]

The telescoping cylinder itsself will never see tension. It's purely a compression column.

But as I picture it, the cylinder walls NEVER see any axial compression! (Except maybe the top-most stage) Even the bottom-most stage doesn't carry any axial load--it's all hoop stress from the opil pressure...all the way up! I'll see a slight modification from the weight of the oil, but it's driven by the pressure from supporting the next stage up...

Until I put the lateral loading into it. Then it bends like a cantilever (or a series of cantilevers with springs between them).

And I agree--I'll "keep" any benefit I might see to the compressive side from the tensile hoop stress as a measure of conservatism.

Thanks for the response.

--Boothby

"The biggest cause of trouble in the world today is that the stupid people are so sure about things and the intelligent folks are so full of doubts." - Bertrand Russell

 

[BigInch]

Yes it seems like it should be as you say. I had this mental picture of compressive loads and buckling columns, but it does appear that it could never buckle. Only the fluid sees compression. A capped telescoping cylinder system loaded with only internal pressure by a piston on the end must only see hoop stress. Axial tension is prohibited (the two cylinders would separate) and Compressive loads would only move one cylinder over the other until they hit a stop. When stopped, the columns could begin to take compression, or tension loads at maximum extension. Compressive loads on the fluid would be converted to tension in the cylinder walls, at least until any lateral loads are applied, adding compressive and tensile bending stress and ...lateral shear.... The resulting lateral shear stress may be relatively small, but don't ignore it, at least until you're sure its effects are negligable.

Add the hoop tension and the tensile bending stress together on the two planes of a small element and use Mohr's circle (or Von Misses, Tresca, etc.) to find the maximum shear tensile stress. Then apply the safety factor.
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BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com