I am analysing the piping at a receipt station for a 42" X70 gas pipeline. Pressure elongation is significant and therefore i have included bourdon effects in the analysis. When this is activated Caesar applies the strain to all load cases with pressure. Therefore i am having an issue with failure at some tee intersections in the sustained case (W+P1) due to the elongation of the pipeline. By my understaing, this elongation is a self limiting load and therefore it seems overly conservative to require the stresses resulting from this to meet the sustained allowable.

To treat this as a self limiting load in Caesar, the only option i can see is to determine the temperature rise that is equivalent to the pressure elongation and apply this temperature to the model so that it is treated as an expansion stress.

Am I correct in believing the stress due to pressure elongation does not need to be applied to the sustained case and if so, can anyone provide some advise on how they have delt with this situation?

Pressure loads are usually not considered to be self-limiting, with good reason. Thought problem - if a pipe is adversely affected by pressure, what mechanism is going to provide the self-relief? I bet you can't answer that.

Pressure elongation is normally not considered in the B31 Code family, so I doubt that you will find any guidance in any of them. Pressure elongation for large bore pipelines is a real effect, but since the B31 Codes do not consider it, I don't believe it is implemented in CAESAR II. You may want to consider doing the calculations by hand.

I am not sure why the Bourdon effect has anything to do with pressure elongation of the pipe. It has to do with the tendency of elbows to straighten under internal pressure (and to curl further under external pressure, a less-common issue). See B31.3 Appendix C Note 7. This note applies only to elbows and miter bends, not to tees.

The only relief you are going to find for your pressure elongation is from axial line stops, and lateral restraints on perpendicular legs. For a line this large, these loads are going to be astronomical. You may want to consider putting pressure-balanced expansion joints in your system to absorb the movement instead. This may well be a less expensive way to control the position of your branch outlets than what you are doing.

Its a good question and I wish it was addressed more explicitly by US and Australian codes. My thoughts are as follows-

-Pressure elongation of the pipeline can be treated as a secondary effect much like the thermal expansion of a vessel, with a caveat as follows. Run the model first with the so-called Bourdon effect switched on and get the displacement at the branch, but disconnect the branch to ensure you get the maximum possible displacement.
-Switch off bourdon and either impose the above displacement in the operating case or use an equivalent temperature. To avoid confusion over temperature an equivalent expansion value could be entered rather than a temperature. The equivalent expansion coefficient could be estimated using LC Peng's 1978 paper which is required reading on this topic. In that paper it is recommended to convert pressure to equivalent expansion in long pipelines. Obviously check your output to ensure that the displacement at the branch is as expected.
-You may find of course that your expansion stress fails now.

Heres a thought experiment - a mainline isolation valve is placed just before the branch. Pressure is held in the pipeline and released in the station. Does the branch know whether the displacement imposed is due to thermal or pressure effects? Does the displacement increase if the branch yields ? Marginally perhaps but the maximum effect of this can be taken into account by releasing the branch when calculating the displacement.

Thankyou for your response CraigB. I agree bourdon effect has to do with the tendency of elbows to straighten however this is the term Caesar uses for both rotational and translational pressure elongation effects so therefore i have used it here.

As i see it, the pressure will cause the pipe to elongate a certain amount according to the pressure applied and generate displacements in the piping. Once this displacement reaches its set amount then it will stop whether or not the pipe has yielded and therefore the stresses due to the elongation are self limiting. Of course you would still need to also consider the other effects of pressure that are not self limiting seperately.

The tee that is causing problems is at the pig launcher just afer the pipeline comes above ground. The only practicle place for an anchor is below ground and as you point out the loads for a pipe this size are astronmical (over 600tonne). Even with this anchor modelled and allowing for some movement of the anchor, the displacements at the tee in question are sufficient to cause overstress in the sustained case when the pressure elongation effect is modelled in caesar. I have calculated pressure elongation to be equivalent to approx 32degC temperature rise. It seems over conservative to require the displacement stresses due to pressure elongation be incorporated into the sustained stress requirements.

Hi All
For me, Pressure is a primary force so we should not consider it's effect as secondary.
Thermal effect diminish with time due to yielding or creep, Pressure effect keep on continuing even if some yield or creep appear.

If branch is failing when pressure elongation included we need to add more flexibility, May be just adding one more elbow in each(affected by adding Burdon effect) branch will solve the problem or adding some support nearer may help since it is a sustain failure.

I doubt how much pressure balance bellow as suggested by CraigB will help in terms of stress & cost.

Regards

Habib

Thankyou MPB, you have given me some good ideas to consider. Using an equivalent expansion value seems like a good option so as not to cause any confusion over temperatures. I will give this a try and see how the results turn out.

From Pipe Stress Engineering by Peng and Peng.

"Pressure elongation is often mistreated as a sustained load because of its association with pressure, which is a sustained load. Just like thermal expansion, pressure elongation generates a displacement that is a self limiting load. Its effect on the piping system is determined by the potential axial displacement of each leg of the piping. Once the disaplcement reaches the potential elongation amount, it stops regardless of whether or not the yielding occurs in the piping. This pressure elongation is generally included in the flexibility analysis the same was as thermal expansion is. In general, pressure elongation is added to thermal expansion to become the total displacement load in the analysis.

Excellent book BTW, worth every cent.

Hi Dude

Thanks for your information.
I need to relook the issue.

Regards

Habib

The proper answer lies in meaning of the word self limiting and the nature of secondary stress. With secondary stress, not only the word self limiting comes but also "absence of gross plastic deformation" and "redistribution" of load comes.

In case of primary stress ( load driven) the displacement can be uncontrolled depending on the magnitude of loading.However in case of displacement control, the displacement is actually "controlled" and hence cannot be infinite.In the example of pressure elongation, if the pressure magtitude is high, the pipe can undergo bursting failure.This would happen if an uncontrolled magnitude of pressure is applied.However if the pipe has not undergone bursting, the pressure is obviously not of "that magnitude to create an uncontrolled displacement". The displacement that this pressure imposes on the system is again a "controlled" one.This is the basic difference in pressure applied as a load and the pressure induced displacement imposed on a system.

This however does not indicate why it should be self limiting and what exactly is self limiting and how the other terms in the definition of secondary stress come.

The pressure elongation will obviously not produce gross plastic deformation , as it that has to happen the "uncontrolled" pressure would have done it.

The load deformation relation is P=KD where symbols have usual meaning.

For non linearity , K is a function of D. Non linearity can be in three different forms material ( plasticity),geometric ( load and stress can change depening on the geometric deformation) and contact ( a very simple example, a guide with gap)all may act together or individually.

If load imposed is constant, it will not reduce on its own i.e. a 500N applied will not on its own become 450N.

However if displacement is the input and since in non iinearity K is a function of D ( and sometimes P also is a function of D) and as K drops, say due to plasticity or other two forms of non linearity ( a classic example of geometric non linearity is a volter's pole which resists load with membrane or bending action depending on whether the pole is straight or bent), the developed load drops.

In the above discussion, we have already seen that the pressure elongation will not cause uncontrolled deformation unless the pressure itself is very high which will result in a bursting type failure. Now, when the elongation happens and it is restrained ( if there is no restraint, there is no stress generated), stresses will be generated.How and why will they be self limiting?

The answer lies in the mathematical expression above that if D is applied, P generated can reduce if K reduces due to all/any form of non linearity.

Hence it has the characterestic of self limiting.

The self limiting parameter also has the term "redistrubution" associated with it as due to change in K there is redistribution of load in a system with stiffer parts taking higher loads.

Hence the pressure induced elongation is a secondary stress.

The concept of self limiting was wonderfully explained to me by Mr. Thomas J Vaan Laan.I was fortunate enough to learn this thing from him.

Regards

Anindya, that is an excellent explanation. Thankyou for taking the time to share that with me.

Since the pressure elongation is a secondary stress, it seems it would be useful if in Caesar, it was possible to select which load cases the bourdon effect was applied to. Therefore you could still run the sustained stress (W+P) withouth bourdon effects but include the bourdon in the operating and expansion case. Maybe something for Coade to consider?

I have done some futher modelling of this system using both the bourdon effect in Caesar and camparing it against using an equivalent temperature. With some modifications to the piping I am able to get the stresses in the system to pass with bourdon effect activated. In this case sustained stress was the concern as the pressure elongation is included in the sustained stress.

If i now take the same model and use an equivalent temperature and with no bourdon activated I now get a failure in the expansion case.

So I have modelled it in 2 ways and one passes and the other doesnt but which one is correct? It seems clear from the explanations others have given here that it should be treated as an expansion stress. Given this, modelling the system using the bourdon effects option in Caesar and treating the elongation as a sustained stress was not conservative as I first thought.

Adam, I have come up against the same issues when modelling pipeline scraper stations with Bourdon turned on.

I agree it should treated as secondary stress and would also like to see Coade allow some control over which load cases pressure elongation is added to (perhaps a tick box on each line in the load case editor).

Richard, can we get this added in the next version of Caesar?

Probably not in 5.30, we've already started on that one. I'll put it on the development list though.

A cautionary note I would add for this type of calculation-
If you have a long pipeline but you're only modelling up to the 'virtual anchor' in the buried pipeline, be sure that your model does not underestimate the expansion at the free end(or if there is an anchor block, underestimate the anchor load).
This applies particularly if using the old buried pipe modeller method (pre version 5.20, but still available in 5.20.) The reason being that the axial soil stiffness generated by the modeller defaults to a very low figure. The 'virtual anchor' length as listed in the output from the modeller is calculated assuming infinite stiffness. The virtual anchor will not in fact build up and the full expansion will not arise unless you model significantly more straight length, I would say at least 3 times the calculated virtual anchor length.
You can check on this by looking through your displacement report and checking for near-zero displacement occurring over several nodes. Also check the axial load in the pipeline at that location and compare to the theoretical fully restrained load. Alternatively, just model up to the virtual anchor and place a physical anchor there after the buried modeller has done its work - this should overpredict the expansion.

For those who have not yet purchased the new Peng book, his argument here was first published in an ASME paper. That paper is available on the web at Pressure Elongation.
There's a picture in that document (and not in the book) that settles what I believe to be misunderstanding here. I am referring to the phrase "pressure elongation generates a displacement that is a self-limiting load". He is NOT saying that pressure is self-limiting. He is saying that it generates a DISPLACEMENT that is self-limiting. The illustration shows a small diameter branch coming off a long, large diameter run. The long run exends along its axis due to the force of pressure. This pressure-based deflection of the header is the self-limiting load on the branch piping. The branch must have sufficient flexibility to safely accept this pressure displacement.
Pressure is NOT self-limiting. If it was, expansion joints would not need tie rods.
I might suggest the following approach to address this load in a CAESAR II analysis. Again this is a LONG run with branch piping and we're concerned about branch stress.
1) turn on Bourdon (translation only) to see where the header moves due to pressure alone
2) enter this deflection as a length of header pipe in the proper side of and close to the branch and call it a CUT LONG
3) with Bourdon turned off, sustained stress will come from W+P
4) expansion stress range will come from (T+W+P+CS)-(W+P)
Of course there can be several other ways of doing it. (I didn't run this so let me know if it works.)

I think the whole issue here (and the fact that I didn't see when I made my first post) is that there is no rational piping geometry where pressure can cause gross axial displacement without first producing a hoop stress failure.

So it seems that axial pressure stress can be considered to be self-limiting. And your methodology would be correct.

It looks like you are going to have to do a lot of hand calculations in order to perform this analysis effectively. If I was forced to choose between the CAESAR II "Bourdon case" and an analysis where the axial elongation was modeled as a synthetic temperature increment, I am not sure which way I would go.

Dear Members,

12” Sch 40 Carbon steel pipe,
Design Pressure – 47.5 barg
Design Temp – 84 deg C

Approximate length 3000 meter

Please clarify the following query,

Is the pressure stiffening effect and Bourdon effect shall be considered simultaneously?

In case of ASME B31.4, the pressure stiffening effect is applicable, and can I also activate the bourdon effect at the same time.

As the bourdon and pressure stiffening effects are related to the displacement due to pressure.

Please clarify...

The pressure stiffening effect (on bends) is not the same as the Bourdon pressure effect. There are a number of good earlier posts in this forum on Bourdon, which explain how it is calculated. The pressure stiffening effect is shown in the SIF table.

There seems like there may still be some confusion on axial pressure stress and axial elongation due to pressure.

Sresses directly caused by the internal pressure are primary and not self-limiting, these are the hoop stress and axial pressure stress. If either of these cause yielding, failure is imminent. Of course, a pipe would always fail due to hoop stress before axial pressure stress.

The axial elongation due to pressure is a displacement that is constant for a given pressure, in the same way that axial elongation due to temperature is a displacement that is constant for a given temperature change. The stresses that these displacements may cause, such as bending stresses around elbows and tees, are self-limiting, as the displacement will not increase if yielding occurs.

The pressure elongation effect is usually over-shadowed by temperature elongation effects, but one place it can be significant is large diameter, high pressure, low temperature pipelines in stiff layouts.