longitudinal stress in pipe under internal pressure 1

[sbnz]

Hi,

An elementary question for the experts.

For piping under internal pressure, the longitudinal stress in pipe elements is the sum of a) stresses due to bending and b)longitudinal (or meridional) stress due to pressure ( pD/4t)

Question is, for a section of piping within 2 expansion joints, is it correct to say that the b) above (i.e., meridional stress) does not exist? For, the pressure force at the pipe closure / end can not transmit through the exp joint?

thanks in advance,

 

[chicopee]

Meridional stress does exist for pipes under pressure and if you look at pipe ruptures due to excessive pressure and due to freezing liquids, they'll rupture longitudinally first, regardless of the end conditions of the pipes.

 

[sbnz]

Of course, the longitudinal (meridional) stress exists in pipe under internal pressure. It is to counteract the pressure thrust that acts at the ends (pipe closures) or direction changes (i.e., bends). In magnitude, it is 1/2 of hoop stress or (hoop= Pr/t, longitudinal = Pr/2t)

 

[desertfox]

Hi sbnz

I think that your assumption is a reasonable one for the situation describe in your post.

 

[LittleInch]

You've not mentioned the poisson effect which would apply if your pipe was restrained or would affect the actual expansion if unrestrained - no stress as the contraction has been allowed, but some portion would remain if your end caps are anchored but your expansion joints have some spring effect.

See

http://www.datagenetics.com/blog/december22013/index.html

which explains the axial stress better,

see also

http://www.eng-tips.com/viewthread.cfm?qid=238877

and

http://www.eng-tips.com/viewthread.cfm?qid=238877

I can see your point though - assuming your pipe is free to move within two end caps, is there a force?

The issue will be how much your pipe is truly free to move relative to the end caps without spring force or friction.


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[BigInch]

Your pipe between expansion joints is unrestrained. You have no longitudinal stress, as the tension stress due to Poisson's effect does not develop when a pipe is free to contract in the axial direction. The expansion bellows allows that freedom. The pipe simply contracts without developing axial tension stress.

End cap stress cannot be transmitted through expansion bellows, so axial stresses cannot be found within any straight piece of pipe adjacent to an expansion bellows. However end cap pressure force must somehow be resisted in that pipe, so somewhere between the expansion bellows and the end cap, the pipe must be restrained. If not restrained, your pipe will pull out and away from the expansion bellows. In the restrained portion of that pipe, axial stress will be the result of end cap pressure stress (tension), PD/4/t, + poisson effect stress, poisson's ratio * PD/2/t (also tension), plus any thermal stress, - a dT/E, positive temperature differential yielding a (here negative) compressive stress component.

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[sbnz]

Thanks BigInch - you have confirmed what I thought, but had slight doubt to seek for a 2nd opinion.

I am aware of the main and intermediate anchors across the exp joints and have taken care of the pressure thrusts accordingly. Was just unsure if the intermediate pipe still has any longitudinal pressure stress.

cheers

 

[LittleInch]

Whilst I bow to the greater in depth knowledge of this by BI, my only point is whether the pipe between the expansion joints is truly un restrained as this depends on what form your expansion joint takes. Many metallic corrugated types still require some level of force to expand or contract, just much less than trying to compress solid pipe.

My motto: Learn something new every day

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

 

[BigInch]

LI, true, I was speaking in the theoretical context. I agree that reality would dictate that some axial load could be transferred into an expansion bellows, due to friction, binding, clamp and seals, etc., but in relation to what a pipe can typically have in regard to axial force, relatively very small, probably small enough to neglect entirely without consequence. It's more likely that pressure tension loads are carried by tension rods across the expansion joint, holding the pipe ends on either side together and keeping them from pulling out of the joint.

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