Pipeline Stress Analysis 6

[ONENGINEER]

I am a soil engineer but recently involved in stress calculations for gas pipelines. Could someone introduces to me a classical method of calculation? Going through some calculations by others has not been conclusive to me. In particular:

What factor of sefaty is used in oil&gas projects to calculate maximum allowable stress. Of course as in other disciplines, there may not be a unique f.o.s but still looking for a so-called industry standard.

Is the code b31.8 the only code used in o&g design work? If not what is/are the others?

I have read in another Eng-Tip posting that "max bending stress= maximum allowable stress-0.3*hoop stress-thermal stresses" What about the longtudinal stresses, which would also exist if hoop stress existed. Where does the coefficient 0.3 come from. What is the range of this coefficient used by varios designers in the US practice? I guess shear and tortional stresses could also come to this equation but if so what numerical coefficient shoiuld be associated with them.

I know the above questions are primitive ones for the knowledgeable experts on this site but the responses would be a starting point for me.

 

[danschwind]

B31.8 is surely not the only one, but start by going through it and all your questions will be answered. Then, you can go after the other codes from other places in the world (ISO, etc).

Daniel
Rio de Janeiro - Brazil

 

[LittleInch]

Max allowable for combined stress or Von Mises is usually 0.9 x SMYS, but can vary. different parameter can be listed for the individual stresses so hoop is not often > 0.72, Axial can be 0.8 or 0.9 , but read the code.

B 31.8 is a common code, but then you can get ISO 13623, EN codes and individual country codes, BS PD 8010, IGEM TD/1, AS 2885 etc

It's not easy to say, but my guess is the 0.3 is Poisson ratio for steel so in certain cases it can reduce stress axially and in others increases it. Depends if your pipe is trying to expand or contract, whether it is fully restrained, is it also being elastically bent. Most pipelines tend to heat up in operation compared to their as laid condition, but not all.

Torsion everyone normally ignores as its too small and you can't calculate it anyway and shear you avoid like the plague.

This is why people employ design and stress engineers to give them the answers using inputs from valued colleagues like soils engineers for pipe soil friction, upheaval buckling etc.


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

 

[ONENGINEER]

Thank you for the prompt answers. I can now go through B31.8 with more confidence.

LittleInch, for the allowable I have seen 0.5 x SMYS in other calculations. This is where it was confusing for me. Although the FOS is eventually a designer's choice but still(?)

I saw another designer notes as "max bending stress= maximum allowable stress - axial stress" in which the hoop stress was not counted (?).

Just familirizing myself with the concepts, when going through pipeline stress analysis reports for HDD projects under construction.

 

[StressGuy]

Oneengineer,

I'd recommend picking up a copy of this book:

https://www.asme.org/publications-s...pipe-stress-engineering/print-on-demand-books

For someone starting out, it's about a good a reference as you'll find for learning about pipe stress engineering/analysis if you don't have access to an experienced mentor.

This is another very good one, specific to ASME B31.3, which is the primary code for oil/gas/process unit design:

https://www.amazon.com/Process-Pipi...p-0791883795/dp/0791883795/ref=dp_ob_title_bk

B31.8 is limited to pipelines.

Edward L. Klein
Pipe Stress Engineer
Houston, Texas

"All the world is a Spring"

All opinions expressed here are my own and not my company's.

 

[1503-44]

A mash up of some of my previous posts.
----

You need to get your hands on B31.8.  Due to its many class factors, its a lot different than B31.1, 3 and even the liquid pipeline code B31.4

If you are a U.S DOT regulated pipeline, you will also need to follow this one to the letter as well,
CFR Title 49, Part 192 gas pipelines or
194 liquids for liquid pipelines

==============
Pipeline design code might be one of several.  ANSI B31.8 / CFR Title 49 Part 192 in the USA, but could be different elsewhere.  There you will find the minimum loading conditions, Area Classification Factors and pre-approved pipe material yield stresses, and the limiting stresses.  With Area Class Factors, internal pressure, pipe diameter, wall thickness and yield stress you will be able to determine an initial allowed design pressure for various wall thicknesses using the Barlow based formula (PD/2tDF <= yield stress), or given the pipeline design pressure, you will be able to determine the minimum wall thickness required for installing the pipe through each different class factor area you have along the pipeline.

The first step is to use the Barlow formula to determine the minimum wall thicknesses you will need for each class factor through which your pipeline will be installed.  That wall thickness will technically only be sufficient for hoop stress, as Barlow's formula does not address combined stresses.  There is a higher allowable for combined stresses, so you can have additional axial and bending stresses, analyze those in combination with hoop stress and find the combined stress to check against the higher combined allowable stress.  So total stress is not just limited to checking hoop stress against the Barlow allowable.  If you find areas where total stesses cannot be limited to the combined stress allowable using your initial wall thickness determinations, including hoop stress, you may have to increase the wall thickness for those specific areas.

API 5L is the pipe production specification typically used for a range of strength in pipeline steels, so you will find the yield stress for all grades of material in API 5L, which will also be listed under the same material designation in ANSI B31.8, but in B31.8, you will find the class factors which must be applied to calculate your hoop stress allowable.  

Axial stress is due to an axial load applied to the pipe and is equal to S = p/A. p is load and A is the cross-sectional area of the pipe wall. It will be either tension, or compression, corresponding to the direction of the applied load.

Stress in the Axial Direction can also be caused by internal pressure and is nominally equal to the circumferencial stress, S = P*D/2/t, * Poisson_Ratio. P = pressure, D = diameter, t = wall thickness. Poisson_Ratio for steel pipe is usually taken as 0.3
If the pipe is unrestrained, the pipe will shorten without generating stress. If the pipe is held rigidly fixed at both ends, S will result as an axial tension stress.

If the pipe has closed ends, another axial stress can be generated from internal pressure, as the pressure will act on each closed end surface to generate an end force F = pi*D^2/4 * P
If the pipe is not axially restrained, the pipe will elongate with the resulting axial stresss = F/A in tension. If the pipe is held rigidly fixed at both ends by an anchor, or is well embedded in soil, the anchor or soil will take that load and an opposite compressive axial stress, F/A, will be introduced into the pipe.

If there are changes in temperature, thermal axial stress can be generated. If the temperature is increased, a compressive axial stress can be introduced into the pipe, or if temperature is decreased, a tension stress can be introduced. Thermal stresses are only generated if the pipe is held fixed at both ends, otherwise the pipe will expand or contract, respectively, without generating any additional stress.

Bending can introduce another axial stress Sb = M * c/I , tension on one side and compression on the other. M is bending moment, c is the pipe radius, I is the moment of intertia.

Total Axial stresses is the algebraic summation of all of the above.
==================

B31 uses Tresca's max shear stress.

https://www.eng-tips.com/viewthread.cfm?qid=40138

Comparison of Tresca and von Mises

https://www.failurecriteria.com/misescriteriontr.h...

See John Breen's response

http://forums.coade.com/ubbthreads/ubbthreads.php?...

Combining Stress including hoop stresses is mentioned in all these codes
B31.4 Paragraph 402.7 & A402.3.5
B31.8 Paragraph 833.4
B31.1 Vii-5.0
B31.3 Paragraph 302.3.6 - SL due to sustained loads, such as pressure ..

The pressure component of axial stress in all pipe, is

1.) In Restrained segments is related to hoop stress by Poisson's ratio ν,
axial stress due to pressure = P * D /2 /wt * ν

2.) In Unrestrained segments, the longitudinal pressure stress component
axial stress due to pressure = P x Ainternal/ Awall

≈============
PD/4t is not half the hoop stress, it is the AXIAL tension stress created by pressure acting on a pipe with capped ends, or a closed valve. Pressure * Pipe's x-sectional Inside Area / x-sectional Area of the Pipe wall. If you approximate that axial stress, it is equal to 1/2 the hoop stress, or D/4t, where D is the average wall thickness = OD- t.

≈==========
Take a closer look at primary stresses,

Bourdon pressure "expansion" results in contraction in the axial direction, which, if restrained, produces axial tension.  As longitudinal stress is the result of Poisson's ratio x hoop stress, its much less than the hoop stress.  Plotting these principal stresses on Mohr's diagram results in hoop stress (tension) far to the left and axial stress (also tension) between hoop stress and 0.  The result is a lesser maximum shear stress than when Bourdon axial stress is not considered at all.  Burdon "None" therefore results in a conservative design for a straight pipe, and going by what's been said above, for a curved pipe too.  I would guess, probably from being the result of secondary effects.


Poisson's ratio is 0.3, so contraction is 30% of hoop stress.  End Cap Effect is 50% of hoop stress in tension - 30% of hoop stress, leaves 20% of hoop stress net axial expansion.  Since axial stress is tension and hoop stress is tension, Mohr's maximum shear stress is reduced.

============
Total effective stress limit is 0.9 SMYS for either gas or liquid pipelines.
The area class design factors apply to Barlow calculation and to "total longitudinal stress", each of which do not address "total effective stress" as does API RP 1102. The area class design factors 0.4, 0.5, 0.6, 0.72, 0.8, for gas pipelines and 0.72 for oil pipelines do not apply to total effective stress based on the Von Mises formula. B31.4 and B31.8 do not use Von Mises formula. They are a Tresca stress calculations, so the failure criteria is different when using the Von Mises total effective stress formula in API RP 1102, hence that is = 0.9 SMYS.


Thermal stresses are left for later. Let us know when you get there.


A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[GD2]

ONENGINEER,
Basic allowable stress for pipe wall thickness calculation is different than allowable stresses for stress analysis. For stress analysis, Pipelines will be usually evaluated for restrained and un-restrained conditions. Stress equations to use will be given in the code, in this case B31.8.

GDD
Canada

 

[ONENGINEER]

GD2, Can I assume the restrained and un-restrained conditions would be accounted for in the longitudinal stress calculations, or do you believe these conditions would also affect the hoop stresses? I am going through 1503-44 comments to develop a design methodology for myself and can use your feedback to double check my understanding. Thanks.

 

[GD2]

ONENGINEER,
Follow para 832 and 833 of Code B31,8 for pipes stress/flexibility analysis for both restrained and un-restrained cases.

GDD
Canada

 

[1503-44]

Pipelines are buried and for the most part, so generally are fully restrained by soil, however certain pipe segments are subject to movement, so pipeline pipe is checked for both conditions.

Pressure creates hoop stress and hoop stress is normally the greatest principle stress, so it is always checked separately. Pressure causes longitudinal stress, by virtue of the Poisson effect, when the pipeline is restrained in the axial direction. Pipelines are fully restrained over most of their entire length, so longitudinal stress, the other principal stress, is also checked separately. If the pipeline is not restrained in the longitudinal direction, the pipe will move, expanding or contracting in the longitudinal direction until the longitudinal stress becomes zero. If there is only some movement allowed, say from weaker soil in that area, complete stress-free movement will not be achieved, which results in a non-zero longitudinal stress. It is sometimes not apparent where that will happen, a typical pipeline will go for many miles through many kinds of soil and many important parameters that affect the stress-strain relationship will remain unknown, thus a pipeline's longitudinal stress is checked for both restrained and unrestrained conditions.

Loads other than pressure can cause stresses in either or both directions, hoop or longitudinal, and those must be resolved into hoop and longitudinal stress components, then algebracially added into the hoop or longitudinal stresses and checked against the code allowable stresses. Lateral loads, such as wind or soil moving downhill against a pipeline will cause bending of the pipe and introduce bending moments. Bending moments are resolved into longitudinal stress by M c/I and shear VQ/I/t and added to the pipe's longitudinal and hoop stresses, for which the resulting total stress is checked against the corresponding stress limits of each provision of the design code.


Pressure stress is considered to cause longitudinal stress where the pipeline is longitudinally restrained, but longitudinal stresses and other loads usually are usually not considered to cause a corresponding change in hoop stress, since nothing much can restrain pipe from movement in the radial direction. Hoop stresses caused by non-pressure loads are secondary stresses and typically ignored, but we need to keep them in mind and limit them as necessary whenever they are significant, such as where longitudinal stresses effect hoop stress to the point where local buckling of the wall might occur. Hoop expansion of the pipe's circumference, even by a relatively large amount, has little implication to the expansion of the radius, which is where most restraint in that direction would be provided, except for some kind of collar restraint that acted to directly prohibit circumferential expansion. Soil alone would not have much effect by itself. In those special cases we may need to impose additional stress (or strain) limits in addition to what the design code requires. As hoop stress and longitudinal stress are each totaled and checked and limited separately, there is usually no need to combine them and check the combined stress against any other "combined stress" allowable. Certain conditions may warrant incorporating additional limitations in addition to those prescribed directly by code, such as when checking highway crossings using API 1102, where there is a specific combined stress calculation limited to 0.9 x SMYS. Always be aware that codes address the most common situations and cannot forsee all conditions that might have more severe requirements, thus code never prohibit the engineer from checking stresses in any manner s/he wishes, providing that as a minimum all code provisions are meet. So as long as the Tresca provisions are satisfied, one can use Von Mises as an additional criteria as the engineer sees fit.

Other than that, where longitudinal stresses become unmanageable for whatever reason, the best approach is to first increase flexibility to allow movement and a corresponding reduction in stress. Fixing a pipe to be more rigid, by adding guides and anchors, only increases stress. Guides and anchors should only be added when there is a necessity to control or limit movement, as such additions always come with increases in pipe stress and reaction forces..

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[ONENGINEER]

1503-44, Many thanks for your time. I summarized my understanding from your valuable comments in the attached excel file with partial examples. There are many details to add but I wonder if the table meets the basic requirements.

 

[1503-44]

"Actual hoop stress =4400" does not look right.

Hoop stress
P D / 2 / t =
2200 * 20 / 2 / 0.44 = 50000 psi

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[danschwind]

Two awesome posts by 1503-44. Can't get much better than that

Daniel
Rio de Janeiro - Brazil

 

[1503-44]

Thank you.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[1503-44]

A clarification if I may.

The following, from above, applies to longitudinal pressure stress and also to thermal contraction with colder temperatures.
"Poisson's ratio is 0.3, so contraction is 30% of hoop stress. End Cap Effect is 50% of hoop stress in tension - 30% of hoop stress, leaves 20% of hoop stress net axial expansion. Since axial stress is tension and hoop stress is tension, Mohr's maximum shear stress is reduced."

Thermal expansion due to higher temperatures imparts a compressive axial stress, so the max shear stress as found per Mohr's circle is greater than when the pipe is in axial tension.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[ONENGINEER]

1503-44, my apology for the typo on hoop stress calculation for 0.5" wall thickness. I am yet to understand your last post better if I can be assured that the attached design method is principally correct. Thank you again.

 

[1503-44]

Personally I would show the stress ratio for each check, something like this,
29899/63000 = 0.47 < 1.00 OK

It shows you or someone making a quick review what degree of safety the design has, rather than making them do the math.



A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[ONENGINEER]

Thanks 1503-044. I am keen to understand the pipeline design process with reference to HDD projects. While easier to visualize the functioning of the hoop and longitudinal stresses, the functioning of shear stresses are difficult to imagine. I hope I can learn then being on this platform now.

 

[1503-44]

What generally helps a little is that shear stresses are usually maximum where bending stresses are minimum.

"Just for fun" ...
Try a working backwards exercise. A reverse beam analysis. Draw a number of points in a not so linear line. Connect the dots with a cubic spline curve. Assume that cubic spline represents a pipeline's deflected position. Now try to determine the bending moment at each point of the curve. It's proportional to the derivative of the spline at any point. Now from that, try to determine the shear at every point. That's the derivative of the bending moment curve. Now from the shear diagram, try to determine the load. Load is the derivative of the shear diagram. Assume the load is generally a nonlinear distributed load applied by the soil to the pipe. You can add a concentrated "hard spot" load or two, if it helps. It's not going to be completely accurate, as a few constants go missing from time to time, but it will give you some interesting thoughts about how a pipe gets bent into unusual shapes.


A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[ONENGINEER]

There are two formulations on bending stress, i.e.

σ = ED/2R
σ = Mc/I

Could someone explain how the two are connected together. I hope no body blames me for not knowing this simple structural engineering question.