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Dumb question of the week.
4

Dumb question of the week.

Dumb question of the week.

(OP)
You have a cylinder subject to an internal pressure, with open ends, how do you calculate the axial strain?
I have the lame equations for radial and tangential, and I'm having a spot of weds afternoon brain fade as to how to calculate the axial..

RE: Dumb question of the week.

If it's a cylinder with open ends, how have you got any pressure?

Axial force, hence strain is either a result of temperature expansion between fixed points or end cap force, regardless of if there is an actual end cap...

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: Dumb question of the week.

(OP)
I knew the first question would be this....
You could have a cylinder with an expanding piston in either end?

RE: Dumb question of the week.

(OP)
Which is what we have got here at my work.

So I can calc the radial and tangenital stress/strain but I don't know how to calc the axial.

RE: Dumb question of the week.

What you're describing sounds like a compressor cylinder on a recip, except on a compressor cylinder the ends are far from open. Any chance of a picture?

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

RE: Dumb question of the week.

(OP)
I can't as its protected IP. I'll do a rough sketch of the concept hold on.

RE: Dumb question of the week.

(OP)
yep, thats what happens in real life, and the cylinder contracts. I want to be able to estimate the contraction.
I'm waiting for permission to post a sketch.

RE: Dumb question of the week.

Ok, now you've explained it a bit better, your ends aren't actually open, but what I think you have is a cylinder with some moving or even perhaps stationary ends / pistons which are not attached to the shell of the cylinder??

Therefore I can't see how it will have any significant axial force. You will get hoop stress and perhaps some bending stress.

What are the rough proportions of the length between your piston type ends and the diameter of your cylinder?

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: Dumb question of the week.

Does Roark's Chapter 12 provide a similar situation for you?

RE: Dumb question of the week.

(OP)
little inch, our observations are:
1) the cylinder bulges
2)the ends contract towards the middle
3) we have measured axial strain with strain guages

I can also replicate the deformation and strains using fea. An axisymmetric model of a cylinder with a pressure applied to a portion of the id, with z dirn (axial) fixed, we get very similar results to our physical tests and the product is in the field.

What I want to be able to do is to estimate axial strains by hand calc/spreadsheet. Lames eqn's predict the radial and tangenital stresses/strains perfectly in line with our FE and testing.
I think that I already have the answer but I am not 100% confident of my thinking/logic with the hand calcs wanted someone with more expertise to verify/point me in the right direction. Or was thinking that there may will be a readily available solution that I was unaware of.

monkeydog, will look at Roark's now cheers.

RE: Dumb question of the week.

(OP)

Quote (littleinch)

Therefore I can't see how it will have any significant axial force. You will get hoop stress and perhaps some bending stress.

If there is hoop and bending, there must be some axial?
Well there is defo axial strain as we measure it at various places and the ends contracting towards the middle visibly kind of proves it..

RE: Dumb question of the week.

In a totally “unrestrained” and frictionless system (i.e. with no end thrust applied to the cylinder as by welded caps etc,, nor for that matter even any friction due to end seals or stuffing boxes etc., and that’s not entirely possible!) I believe the shortening of an unrestrained or essentially “floating” cylinder is basically a primarily “Poisson” effect (in strength of materials parlance).
I believe you will find the practical shortening is quite slight in the case of materials with very high long-term moduli and quite low long-term Poisson’s ratio e.g. like steel and ductile iron, and perhaps quite startling for materials with very low long-term moduli and quite high long-term Poisson’s ratio like thermoplastics/hdpe pipe etc. Perhaps you could try out the quite simple formula:

∆L = µPL/(tE)

Against the results of your apparently more fancy analysis methods, and let us know what you find out. [As to “bulge”, I guess the cylinder probably would not expand outward quite as much, nor shorten quite as much, beyond the axial location of any end seals.]

RE: Dumb question of the week.

(OP)
rconner thanks, we believe it is a poisson effect also, and have been working on using the standard isotropic stress strain relationship, but there are issues (mostly with my understanding I think.)
Indeed bulging occurs between the location of the seals.
The assumptions are broadly similar to those we use in the FE, and the FE accurately describes the physical tests.

Forgive my ignorance but can you define the terms used?

∆L = change in length
L = Length?
µ = poissons ratio?
P = pressure?
t= thickness?
E = modulus?

RE: Dumb question of the week.

(OP)
PS another way of considering this is to think of a cylinder with another concentric cylinder inside- but with an interference fit, so that the inner cylinder exerts a pressure on the outer cylinder. Thus the outer cylinder expands radially, through poisson effect, it should contract axially.

RE: Dumb question of the week.

From Roark for a thick cylinder with zero longitudinal pressure (it is an exact solution):
ΔL=-PνL2b2/E/(a2-b2)
P=internal pressure,ν=Poisson's ratio,a=outer radius,b=inner radius
For a thin cylinder this reduces to -PνLb2/(tERm)≅-PνLRm/(tE) (rconner's formula above was incorrect).
However you state that you see a bulging? So this is a plastic tube, not a metallic one. Anyway, irrespective of the material, your situation is not the ideal one as per Roark's solution: at the gaskets the radial displacement is totally or partially restrained, and there is no pressure in the portion of cylinder beyond the gaskets. So you have also bending that, depending on the actual length to diameter ratio of the cylinder, might also contribute to the axial shortening (esp.for a material with low modulus and relatively high strain).

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Dumb question of the week.

(OP)
prex, been hunting through roark's and did not find that, what page/chapter?. Many thanks anyway.

Yes, sorry the situation is more complex than I describe, hence the FE, but the simplified/idealized calc is exactly what I am looking for.

RE: Dumb question of the week.

[my apologies, prex, I actually had the right formula for approximation but in my too quick ham-fingered typing left out "R" in the numerator = thanks]

RE: Dumb question of the week.

(OP)
got it. p683 of the 7th ed. Table 13.5

Gents thank you. I really appreciate it.

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