Question on application of ASME B31.1 flex factors for elbows 4

[ZippyDDoodah]

Our company is starting to do more piping design and analysis, and as a structural engineer who will be involved with this work, I want to be sure that I understand what's going on as much as possible. In this context, I have a couple of questions for you pipe stress engineering 'veterans':

1) How is the flexibility factor k from Appendix D supposed to be applied for elbows? Is it treated as a reduction factor to the moments of inertia (EI) of the elbow pipe/frame section or what?

2) I can't get a definitive answer from our piping engineer or from the software documentation as to what our pipe stress analysis software is doing internally with regards to modeling elbows. We have a 2 year old version of AutoPipe and also a prepaid run version of Caesar II. Would anyone happen to know if these programs analytically treat elbows as curved elements, multiple segments of straight pipe section to create the curve, or whether they treat it as just two pipe frame sections intersecting? Because the answer to that question would make a difference.

I understand that both programs automatically determine flexibility factors and SIFs, but results would be different, depending on whether the pipe/frame elements are true curved elements and also depends heavily on how well the pipe elements account for torsion.

3) Turning on the water in my garden hose tells me that Bourdon effects might be a consideration, yet the B31.1 code does not address this effect from what I can find. Our piping stress software gives vague references to their Bourdon calculations which are offered as an option, not a default. From your experience, are Bourdon effects "typically" important in carbon steel piping? If yes, how do you account for them?

4) Last couple of questions which don't have anything to do with the title of this post - If there is a SIF required for concentric reducers in B31.1, why not a SIF for eccentric reducers? This makes no sense to me. Also, since reducers are non-pipe components, aren't they typically fabricated with thicknesses which would make them stronger than the connecting pipe? If so, why would B31.1 require a SIF for reducer components?

Thanks in advance for any advice that you all might offer.

 

[MJCronin]

Zippy.....


Your questions are well worded and precise. (Much better than the typical broken, jumbled-up mess that is offered here)

I suggest that you consider reviewing the information available and reposting your question on

http://www.coade.com.

Question #3 I can answer.... when Bourdon effects are to be considered is outlined in ASME B31.3 regarding "thin walled piping. The COADE "CAESAR-II" software can be configured to consieder these effects.

Question #4 - Eccentric reducers - CARSAR-II offers a methodology. They are typically modelled as concentric (for the SIF) and a "jog" in the geometry is ignored

To the best of my recollection


MJC

 

[ZippyDDoodah]

MJCronin,

Thank you for your kind reply. I may well end up asking this question on Coade's forum. It's a little unsettling how little information I've been able to find regarding code approved methods for analytical modeling of elbows and the application of flexibility factors given how the elbow is modeled (curved element? handling of torsion? theory behind it?) would have a significant impact on calculated results.

Regarding the Bourdon effect, our piping engineer has given me the reference to what Caesar II uses. It's not a codified equation, but a citation from a pressure vessel guidebook written by John Harvey. AutoPipe appears to use a different equation. I realize that rigorous modeling of pressure effects using beam elements is approximate, but I was hoping there would be more information and guidelines available assuming that Bourdon effects could be an important consideration in the design. I looked at B31.3 as you suggested, but there's no reference to Bourdon effect except for casual mention of it in Appendix S with no recommended equation that I could find. Did I miss something?

Thanks for the suggestion on modeling eccentric reducers, however, my main concern has to do with the assumptions being made with regards to reducer section properties, wall thickness in particular. As a non-pipe component/fitting, wouldn't the reducer typically/often be fabricated with a thicker wall thickness than connecting pipe and therefore be stronger than the connecting pipe? If so, what's the underlying justification for the concentric reducer SIF, and why does the ASME B31.1 code address SIF calculations for concentric reducers but not eccentric reducers? From what you've suggested, it seems that engineers use the concentric reducer SIF when analyzing eccentric reducers. Is this correct?

Anyway, my questions on the Bourdon effect and treatment of reducers is of interest, but lower priority compared to my need to understand what should be the proper analytical approach to modeling elbows in a piping model. As an engineer who is new to pipe stress analysis, some of my questions may seem basic to the more experienced piping engineers, but I haven't been able to get clear answers to some of these questions from B31.1 code book or from the piping engineers that I work with. That's why I'm posting on this forum.

 

[JohnBreen]

http://www.scribd.com/doc/12793145/Tecnhical-Changes-ASME-2004-PIPING-FLEXIBILITY

http://mydocs.epri.com/docs/public/000000000001012078.pdf

http://www.ndt.net/article/wcndt2004/pdf/petrochemical_industry/130_iimura2.pdf

http://www.coade.com/newsletters/dec93.pdf

http://www.iasmirt.org/SMiRT16/F1431.PDF

http://files.asme.org/asmeorg/Governance/Volunteer/CareerSeries/9677.pdf

http://files.asme.org/asmeorg/Governance/Volunteer/CareerSeries/9655.pdf

 

[ZippyDDoodah]

Mr. Breen,

Thanks for all the useful information. I did a quick read of your links which I'll delve into later in more detail, but I still haven't found what the analytical basis is for analyzing elbow elements in pipe stress programs. The Coade newsletter link you provided made mention of a curved beam. In my experience, not all curved beam/frame elements are equal, with differences in how torsion is accounted for. But assuming that it's a curved beam element points me in the right direction.

My main concern was what analytical assumptions were being made by the ASME B31.1 code in applying the flexibility factors to elbows modeled with beam elements. Results could be very different, depending on how the elbow is handled internally. The B31.1 code does not appear to give any specific guidance as to how the elbows are to be analyzed. Once I have a better understanding of what the piping programs are doing, then I'll be able take it further.

thanks again

 

[prex]

1)The flexibility factor for elbows accounts for a phenomenon that is not treated by the theory of curved beams : the ovalization of the circular section of pipe. The factor multiplies the curvature in the expression curvature=M/EI, so you are correct in your assumption. To be noted that the same factor k is used for in plane bending as it is for out of plane, though one would expect a difference: I guess that this is a result of the research work conducted in the past on the subject.
2)I guess that your softwares (when I was doing piping calculations, those did not exist...) are all using the approach of compliance matrices for elbows that you can find in Crocker's Piping Handbook (again, a quite outdated reference...): shear and torsional deformations should not be accounted for (but I guess that the software documentation should be clear on that, if examined in depth).
3)The Bourdon effect gives rise to secondary or deformation controlled stresses, that should be treated as expansion stresses (though I agree that codes are not telling you how to handle them). I'm not sure to recall correctly, but I think that the code I've been using in a far past (SAP...) had an option to turn on the Bourdon effect, and the resulting stresses were not always negligible. However as the code does not address them, I would say that you are entitled at neglecting them.
4)The fact that the SIF for an eccentric reducer is not given in the code, does not mean in any way that you can take it as 1: you are required to adopt a correct value and have it approved by the inspector, if any. Personally I wouldn't adopt the SIF for a concentric reducer with the same diameters; the SIF corresponding to the maximum slope of wall should be used. I agree that, as SIF's are commonly determined inside the softwares, you should know what they do, or calculate with a SIF of 1 and make yourself the verification.
Of course the SIF accounts for the fact that local bending stresses exist in a conical transition, that do not exist in a straight cylinder, so your consideration of thicknesses is not to the point.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[JohnBreen]

ZippyDDoodah

Exactly as Prex says - the in-plane moment deformation of a pipe bend (elbow) causes varying degrees of cross section ovalization. As the extreme fiber moves closer to the pipe center line (the minor axis shortens) the section modulus is affected. The section becomes more flexible in that plane. Obviously this cross section ovalization happens to a lesser degree at branch connections (the degree depending upon the axis on which the moment is acting) and at least to some degree in straight pipe sections loaded with a bending moment. The increase in the ratio between the diameters of the major and minor axes will result in additional flexibility about one axis until the section collapses in structural instability.

Of course the flexibility comes at the price of increasing stress and this is why the ASME B31 Pressure Piping Codes tie the Stress Intensification Factors (SIF's) closely to the Flexibility Factors. The Codes have had to have "band-aids" applied to these factors through the years to address the way in which adjacent flanges (or other such geometric stiffeners) retard the ovalization in the curved sections. Similar "band-aids" were applied to address the stiffening effect of internal pressure in large diameter relatively thin wall pipe bends.

There have been many discussions on this particular forum regarding the "Olde Classic Books" of our "trade" and you will be well served if you can find a copy of the out-of-print (by many years) tome that was published by M.W Kellogg Company and entitled "Design of Piping Systems".

There have also been many papers and WRC Bulletins written by E.C.Rodabaugh in which he expands on this topic (ANYTHING written by Mr. Rodabaugh is more than worth the time it takes to read and digest it. Early in the previous nuclear power generation "boom" the Regulatory people commissioned a "literature search" to pull together as much of this fundamental piping knowledge as was possible. This work was also done by Mr. Rodabaugh (although he did MUCH more in this volume than a "literature search" with a resulting bibliography) and the result is an out-of-print (and treasured by those who have a copy)government publication with the government's cryptic file number "TID-25553". It is a very good read.

http://www.iasmirt.org/SMiRT16/F1984.PDF

http://paginas.fe.up.pt/demegi/Avaliacao/Paper QMelo.pdf

http://www.iasmirt.org/SMiRT16/F1431.PDF

http://www-personal.umich.edu/~hmourad/PDF/MS_Thesis.pdf

http://paginas.fe.up.pt/~ptcastro/LMadureira.pdf

http://www.hpmsl.neu.edu/content/2009Papers/Thin-walled structures - 2009.pdf

Regards, John.

 

[JohnBreen]

ZippyDDoodah

There are some other interesting things for you to look at:

The ASME B31 Code for Pressure Piping, B31.3, Process Piping does not require the use of SIF's at reducers but since the B31.1 (power Piping) Code essentially says that the largest that the range of SIF's for reducers is less than 2.0 that is the SIF magnitude used by most conservative stress analysts. Note that the B31.1 Code and the B31,3 Code provide some (not all that you may need) SIF's and Flexibility Factors in Appendices "D" (the SIF equations are presented there). The Codes tell you that you may use these SIF's or you may use more accurate SIF's if you have that information. To see how theses SIF's are applied you must look at the equations in the main text of the B31 Codes). Essentially these equations are of the classic beam bending form of Stress = SIF * Bending moment (M) / the section modulus (Z).

The software uses curved beam elements but then they must also apply the FF's to address the ovality that occurs in curved pipe when bending moments are applied. Bourdon effects are not often an issue in metallic piping but may become important in large diameter relatively thin wall pipe with relatively high pressure.

The SIF's used in the B31 Codes are the result of work done by A.R.C. Markl and his colleagues at Tube Turns Company in the late 1940's and early 1950's. Several technical papers resulted from this testing work. Tube turns printed those papers in the back of their (out-of-print) book "Piping Engineering".

http://www.4shared.com/file/24763967/a08fc247/Piping_Engineering.html?s=1

When these new fatigue rules were fist introduce to the B31.1 Code in the 1955 edition, there were some books written to explain the basic concepts.

http://www.scribd.com/doc/15454461/Spielvogel-Piping-Stress-Calculatons-Simplified

It is very important to understand that the rules and equations in the B31 Codes do not have us calculating "true elastic stresses". The SIF's in the equations result in the calculation of "equivalent stresses" (the piping Codes in the ASME B&PV Section III Code uses Stress Intensifiers that are almost twice those of the B31 Codes).

You are discovering the fact that the SCIENCE piping system analysis is significantly different that analysis of other irregularly shaped space frames. Wait until you get into the ART of designing pipe supports - especially those supporting piping close to strain sensitive equipment.

Regards, John.

 

[ZippyDDoodah]

Thanks for the replies, and particular thanks to Mr. Breen for the links and advice. Many/most of those links were more advanced than what I'm looking for now, albeit with much appreciated theoretical background. They will certainly be of value later on when I'm ready to take more steps. I'll also thank Mr. Breen for his comment on use of Bourdon pressure effect, in that it doesn't always have a significant effect in steel pipe applications

As stated in my 1st post, I'm at the basic level, looking to understand what is required for application of flexibility factors, and when taking on a new challenge in a well traveled area like piping engineering, I like to follow Ronald Reagan's advice to "trust but verify". At this point, I'm not concerning myself with "why" the B31 flexibility factors (k) or SIF formulas are what they are, I'm looking to understand how the code mandated flex factors should be properly applied. The B31.1 code is very explicit with instructions on how to calculate flexibility factors for elbows, but once one has calculated a flex factor of say, 10, how should that be properly handled? In my 1st post, I asked whether this should be treated analytically as a reduction factor to the EI. I assume the answer, based on note (2) of App. D in the B31.1 code, is "yes", and my analytical testing of my FE / Structural software versus piping programs so far seems to verify that this is the standard operating procedure.. but I've seen no clear-cut answer.

Unfortunately the B31.1 code doesn't appear to indicate how the elbows should be modeled analytically. Most of the engineers I've spoken with seem to assume that there is some standard template methodology for proper analysis curved beam elements. Ok then, if that's the case (and so far I'm not buying that the handling of curved elements is standard), is the flexibility of a curved beam element "double counting" the intended application of the B31.1 flex factors based on Markl's research or whatever the basis? I haven't seen a clear answer to that question yet. A reduction to the moments of inertia of an "elbow" element would yield different results depending on whether that elbow was modeled as a flexible curved element or if it was modeled as an "L" intersection of pipe frame elements. I realize that the code is a guide and not a step-by-step recipe, but I would have expected more details in B31.1 on the intended handling of elbows.

I've run some tests and I'm becoming more comfortable with the analytical procedures used by our AutoPipe and Caesar II pipe stress programs. I think it's problematic that these piping programs cannot generate a moment diagram or account for P-delta effects (or beam shear? or nonprismatic elements?), but they do seem to offer other advantages with their temperature dependent material libraries and reporting.

Regarding the science vs art, that observation pretty much nails it. Lots of subjective and yes, 'artistic' judgement, hopefully based on experience and an understanding of the physics of the problem, is what makes a good engineer. I believe my structural engineering background may be of value in some of that pipe support design Mr. Breen mentions. It will be a different environment for me in which loads on flanges and sensitive equipment so often govern the design of the piping system and support structures, but then again, in our structural designs we have 'non-stress' serviceability checks on deflections and foundation loads that we have to deal with, as science vs economic constructability with many unknowns is a constant issue with most practicing structural engineers.

 

[prex]

I already answered above your question about the use of the flexibility factor.
However I see that a misunderstanding might arise from what you state: it is not true in fact that the flexibility factor may be used to reduce the product EI. The correct statement is that the flexibility factor is introduced in the basic equation for beams in bending:
curvature = kM/EI
The two are not equivalent, as they might appear at a first glance. However to understand this you should study a book treating the compliance (or flexibility or stiffness) of piping elements: in short, that's beacause Poisson effects and shear deformation mess up with bending deformation.
Kellogg, as mentioned by John, was THE reference in a far past (it included a method, with a system of tables, for manually calculating the flexibility of piping systems!), Crocker (5th Ed.) is another old reference, but also more modern handbooks certainly include this topic. I don't think that the treatment has changed from the times of Kellogg (and I was wrong: the shear deformation is included in the standard treatment).
Crocker, in the 5th Ed., had a clear treatment of Bourdon effect ('Effect of Pressure on Free Expansion'): here you have the 7th Ed. Piping Handbook

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

 

[ZippyDDoodah]

Thanks prex, a star for your good suggestions. And sorry for missing your earlier comment on the EI. I'm not sure exactly what you mean in your followup comments regarding reduction of kM/EI vs EI relating to frame elements, but I get the gist that the bending stiffness of elbow elements needs to be reduced by the FF. A FF of 10 would reduce the EI by 90%, for example. I agree entirely with your observation on the FF bending stiffness reduction being the same for out of plane as it for in plane not making sense. Like you said, there may be some other research behind that.

I was able to obtain a copy of the Kellogg book you and Mr. Breen mentioned. That's exactly the kind of resource I was looking for to help me get started. I got more useful advice in this forum than I ever expected. Thanks again for your suggestions.