Pipeline Strain

[alchemon]

Hello all,

I have done stress calculations for multiple years and have a good understanding of hoop vs longitudinal stresses for buried pipelines. Recently I have gotten involved with pipeline strain but I am struggling to understand two key things:

First, several codes talk about a 0.5% or 2% strain threshold. However what does 2% strain mean? If according to Hooke's law, strain = stress/Young's modulus, does 2% strain mean then that the stress state is limited to 0.02*Young's Modulus. For steel at 30,000,000 psi, this results in stress at about 600,000 psi (so that stress/Young's Modulus= 30,000,000 psi).

Second, is it appropriate to consider the strain in a combined sense? For example, the Von Mises criteria allows for combining inter planar stresses. Is it the combined interplanar stress which is then compared to the 2% threshold stated above?

I am thinking that the procedure is to calculate up all the individual stresses, sum then per Von Mises criteria, and provided that this doesn't exceed 2% of Young's Modulus, it is acceptable (assuming that 2% is used).

Sorry, just struggling to find any real world examples of strain calculations with the threshold whereas multiple for stress seem to exist.

 

[1503-44]

[Δ]L = P*L/A/E

P load 60,000 lbs
L Length 100 in
A Area 1 in2
E Young's Modulus 30E6 psi
S[sub]Y[/sub] Yield Strength = 60,000 psi

Stress [σ] = P/A = 60,000lbs /1in2 = 60,000 psi
Elongation [Δ]L = P*L /A /E = 60,000lbs * 100in /1in2 /30E6psi = 0.2 in
Strain [ε] = [Δ]L/L = 0.2in /100in = 0.002

Nominal yield strain ε[sub]Y[/sub] of the pipe material under uniaxial conditions
ε[sub]Y[/sub] = σ[sub]Y[/sub] /E
ε[sub]Y[/sub] = 60,000psi /30,000,000psi = 0.002

For example, a 3% strain limit (0.03) gives a value of strain, more than 10 times higher than the nominal yield strain ε[sub]Y[/sub] of 0.002

For a 40ft long pipe, a 3% tensile strain implies elongation of
40ft * 12in/ft * 0.03 = 14.4 in!
Remembering that ε[sub]Y[/sub] = 0.002 where [Δ]L is only = 0.96in

How you combine stresses or strains should be in accordance with your pipe design code.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[goutam_freelance]

The 0.2% strain criterion is used for determining yielding under uniaxial stress in ductile metals. Yielding refers to the condition when a significant plastic deformation occurs.

The von Mises failure criterion refers to failure under multiaxial stress conditions when the distortion strain energy under failure condition becomes equivalent to uniaxial or any other stress state under failure conditions.

If we take uniaxial stress, the limit is yield stress (0.2% strain criterion). So the equivalent to uniaxial failure is when the von Mises stress becomes equal to uniaxial yield stress.

So the 0.2% strain criterion is used only for determining failure in uniaxial stress conditions as we perform a tensile stress in a machine.

The von Mises criterion is a distortion energy-based criterion and to my knowledge, similar criterion using strain conditions does not exist.

Regarding "this doesn't exceed 2% of Young's Modulus,", this is not accurate, refer stress-strain curve below:

The curve at 0.2% strain point may not be in the linear part of the curve. So the 0.2% of Young's modulus concept may not be accurate.

NOTE: The 2% criterion as mentioned by me earlier was a mistake(influenced by an earlier post)

 

[LittleInch]

Can you be a bit more precise as to where you find these in an example code, e.g. B31.4.

The only 0.5% I know is the definition essentially of SMYS, where the stress/strain line slope reaches half the elastic slope (hence the 0.5) is the determination of SMYS. I can't recall seeing anywhere else a 0.5% strain number, but feel free to advise where it crops up.

The 2% permanent strain is the limit applied to acceptable permanent strain in a pipeline, primarily due to cold bending, but can also be applied to extreme events where the stress has exceeded the SYMS.

Cold bending of pipes has occurred since pipes were first made, but the question then arises of how much permanent strain is allowable. The custom and practice which passes the test of time then gets written into design codes and the 2% limt is a max value which has sufficient long use to show that it is acceptable.

When you look at the minimum cold bending radius in something like B 31.4, you find that the max axial strain on the extrados of the bend is close to 2%.

also as per your OP, think about the numbers. If a 2% stain results in 600,000 psi, but your SMYS is only 60,000 then you won't get there. You will be yielding.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[goutam_freelance]

Actually, it is a 0.2% strain criterion as per different codes. I have corrected my post.

Engineers, think what we have done to the environment !

https://www.linkedin.com/in/goutam-das-59743b30/

 

[LittleInch]

Ah, that makes a difference.

I think lookin actually at API 5L, that this is simply one way of determining the Yield strength of a material. ASME B 31.4 and PD 8010 for instance just point you to the material specification for the definition of SMYS which is normally API 5L

So in API 5L
Whilst table 6 uses Rt0.5, meaning the stress at which the material has "0.5% total extension", there is also an alternative Rp0.2 where this uses a different definition (*"0.2% non proportional extension"). This seems to apply to steel grades above L625 or X90 ( see table 7) otherwise the Rt0,5 applies.

Again whilst this essentially means that if your pipeline was actually made from material which had an actual yield strength equal to its specified one, then it could permanently strain by up to 0.5% and still be considered satisfactory, even though it has actually then work hardened a little bit.

In reality most pipelines never come close to seeing SMYS and the actually measured point of yield of the pipe is higher than the minimum.

The only ones I know of are some Gas pipeline codes which deliberately in hydrotest exceed the SMYS by 5 or 10% or until the slope of the pressure / volume graph for the test pressure goes to half slope. I personally don't like that, but the idea is that is "blunts" any cracks in the pipe and also work hardens it a little bit.





Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[alchemon]

Hello all,

First, someone asked as to where I found the 2% strain reference:

ASME B31.8, 833.5, allows for specifically design exceeding yield, and (b) of this same section does specifically mention a strain limit of 2% if you design for exceeding yield (various criteria must be met).

Second, I see the flaw in my original thought logic, which is primarily that Hooke's law applies only to the linear portion of the stress-strain curve (usually assumed to around 0.2% strain). After which, the stress-strain relationship is non-linear and therefore Hooke's law cannot be applied. In order to determine strain exceeding 0.2% a different methodology (aka not Hooke's law) would need to be used.

One final question:

For hoop strain, is the characteristic length, L = pipe inner diameter whereas ∆L is the change in inner diameter. Also, for axial/longitudinal strain, is the characteristic length L the physical pipe length and ∆L the change in pipe length?

 

[LittleInch]

Hoop stress it should be the inner circumference. which is of course proportional to D. axial you are correct, for an unrestrained (not buried) pipe.

Determining strain in the plastic region is basically having a limit of the yield stress plus maybe 10%, but as your strain continues, the area decreases and hence the force required remains steady or starts to fall until it breaks.

and basically yes, some codes allow for certain strain based design criteria to be limited to max 2%. Not commonly used onshore at least. I have seen it used for some high temperature lines at bends, but rarely.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[alchemon]

LittleInch, what would be the characteristic length for axial strain for a buried/restrained line? Overall length cannot move much in that case.

 

[LittleInch]

There isn't one.

That's why programs like Ceasar exist as its only the last bit from the virtual anchor which actually move and even then not in a linear fashion.

Same thing happens at bends.

But fully restrained means exactly that. The stress increases as the pipeline is subject to axial loads but whether this is "real" stress or not is a different subject.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[1503-44]

Buried restrained does not move.
Unrestrained considers full movement.
Buried partially restrained can move between both the above.
Problem is that is often difficult to be absolutely sure a pipeline is fully restrained anywhere for a number of reasons. Even if you do a full Caesar analysis, are you certain of how much restraint the soil can provide at all points along the pipeline?

Movement can occurs at points where the pipeline enters or exits soil, such at pipeline ends, or at risers entering compressor/pump stations, at pig launchers, above ground block valves, where pipelines are enclosed in vaults, etc., where "virtual anchors" are formed. Basically anywhere that restraining soil adhesion and shear are not yet summing up to equalize the force necessary to provide full restraint, which can cause small movements of the pipeline. Also possibly occurring where point loads are applied to the pipeline from time to time, such as when a block valve is closed, leaving a high pressure imbalance (P x A) from one side of the valve to the other, or at soil transitions where one soil may be weak in relation to another, where the pipeline enters a casing, or anywhere soil restraint force vectors are misaligned, as at both vertical or horizontal bends. An expanding or contracting pipeline, due to thermal or pressure loads, may want to grow towards the trench wall at horizontal bends, or rise out of the trench at overheads. As it is often impractical to check every point on a long pipeline for movements, or difficult to depend on sufficient soil strength needed to fully restrain a pipeline being present everywhere, IMO pipelines should be designed for both unrestrained and restrained stresses at every point, unless the engineer can know for certain that only one condition is possible, such as at a full anchor, or the pipeline is above ground.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[alchemon]

Yes, good points made - fully restrained is an idealized condition where as we all know, the soil does not fully restrain (for underground).