B31.3 describes unbalanced systems as those with strains not well distributed or excessive. Some characteristics of unbalanced systems are "Highly stressed small size pipe runs in series with large or relatively stiff pipe runs', and "a local reduction in size or wall thickness...".

B31.3 also states that "If unbalanced cannot be avoided, the designer shall use appropriate analytical methods..."

Is a correctly applied Caesar analysis considered an "appropriate analytical method" or is FEA necessary to appropriately examine an unbalanced system?

Hi Ken,

Basically, the Code is telling us that the larger (and stiffer) "main" piping will "carry" the smaller (less stiff) branch piping with it as the larger piping deflects under various loadings. The Code would warn us that higher stresses might occur in the smaller branch piping. Deflections that may result in acceptable stresses (the moment multiplied by the SIF and divided by the section modulus of the pipe) in the larger piping could result in excessive stresses in the smaller piping. Obviously, the section modulus of the piping with the smaller diameter and/or smaller wall thickness will be less. So, for the same moment, the calculated stresses will be higher.

In some piping system analyses it might be judged "reasonable" by an experienced piping engineer to "uncouple" much smaller (than the "main" system) branches from the "main" piping system for analysis. That is to say the experienced piping engineer would essentially disregard the smaller attached branches in modeling the system (defining an appropriate SIF at the attachment point but not including the attached branch). In these cases, the experienced piping engineer must know that the larger diameter "main" piping would be much stiffer than the much smaller diameter branch piping, and would take the decision that an "approximate" analysis is sufficient for his/her purposes. However the piping engineer MUST then look at the resulting calculated deflections at the branch attachment locations and be certain that the branch has enough flexibility to accommodate these deflections. If the branch is restrained in any way at locations close to the branch attachment point, it may be subjected to excessive stresses (at, e.g., the branch attachment point and at the restraint). If all the piping in the system is of the same diameter/wall thickness, the distribution of forces and moments will be more "even" or "balanced" and whatever local yielding is necessary to effect "shakedown" will be distributed throughout the system over the first several loading cycles. Then (after shakedown) the system response of the slightly "deformed" piping will be elastic and linear. In the case of local overstrains in the smaller diameter/wall thickness branches, the alternating (with loading cycles) strains might never shake down and the branch may fail due to ratcheting. If the rigorous Caesar II analysis calculates stresses in the branches that are greater than (or very near to) the Code maximum allowable stress (stress range) the piping engineer would be prudent in redesigning for additional flexibility in the branches at issue. If the branch piping is constructed of socket welding fittings, the issue of appropriate SIF's (and appropriate post construction NDE) at the fillet welds must be addressed as these are frequent locations for fatigue problems. Also, if the piping system is modified in the future, it would be prudent to look at the resulting "new" deflections at the branch attachment points to ascertain that these will cause no "new" problems to the branches.

If the piping engineer accurately models the entire piping system with CAESAR II, including the all the branches (with appropriate boundary conditions and all the appropriate loading combinations), it will be "a correctly applied Caesar II analysis". Remember, that Caesar II IS a finite element program - all the finite elements in the model are beam elements. A "correctly applied Caesar II analysis" is a rigorous analysis and is certainly in my view, an "appropriate analytical method".

You can find more discussion of "uncoupling" here:

http://www.coade.com/cgi-local/ultimatebb.cgi?ubb=get_topic;f=1;t=001013

There may be times when some piping system components will experience local stresses that exceed those that would be calculated by beam theory (e.g., local stresses in the pipe wall where trunnions are attached to support (restrain) the pipe). In these cases it might be appropriate to develop an FEA model using shell elements or 3-dimensional "brick" elements to determine the local bending stresses acting in the wall of the component. The Code will never intentionally limit the engineer from applying a higher degree of rigor in the analysis.

There is an EPRI guide - (NGIG-05, EPRI Guidelines for Piping System Reconciliation) that addresses the acceptable dimensional (et. al.) differences between "as designed" and "as built" piping system. I think (I may not be correct in this) that this may be the document that is the basis for some company's acceptance of a "virtual anchor" to terminate long small diameter branches some distance from the "main" piping. The Code would warn that this should be done only with prudent engineering judgement.

Of course, all of the above is just my opinion and not necessarily that of ASME or any of the ASME Code Committees

Regards, John.

John -

Your prompt helpful response was due a quicker reply from me...I've wanted to think about all that you wrote and do a bit of reading.

What you have written helps a great deal to clearify several issues. I benefit from your thinking out loud style of writting, as I expect other readers do too.

I think I understand the code input with respect to branch runs. And your link to the thread on decoupling helps add perspective too.

I think I am more struggling with the second part of the code statement regarding "a local reduction in size or wall thickness". I'm thinking about a larger diameter run of pipe that has an even larger pipe segment(silencer) for a portion of the run, but also has smaller diameter components to fit up a control valve. So, there several size reductions/increases and even a heavier wall downstream to help with noise abatement. The changes in size and wall thickness occurs in series, not as a branch run.

Will a properly modeled Caesar analysis be sufficient in this case? Are some of the section modulus ratios helpful hear too, to evaluate whether to employ a shell or brick FEA analysis? (Sorry not to clarify in my initial inquiry that I meant shell/brick and not beam FEA.)

I find the EPRI guides fairly inaccessible to me. The one you referenced is $10k, and there are only 3 libraries worldwide that I could find that have it, so my interlibrary request will probably not be fullfilled. I see that EPRI's reconciliation guideline is based on WRC 316, which is much more accessible to me, but apparently is much open to wide ranging interpretation, hence, the EPRI guideline.

Regards,
- Ken

Hi Ken,

Thank you for expanding your description of the system at issue. It is certainly an "interesting" system. In reading your original post again I can see that I did not fully grasp the situation that you are addressing.

There are (at least) two ways of looking at any piping system. One way is from the point of view of the designer and another way is from the point of view of the structural analyst. Obviously, it is often the case that both tasks are addressed by the same piping engineer. On the other hand, today the “designer” is often the person who is responsible for the “layout” of the system and for developing the AutoCAD drawings or the Inventor model.

B31.1 Paragraph 119.3 would warn the designer that in a system in which there are significant variations in the relative flexibility of the piping components it is possible to unknowingly design “strain concentrators” into the system such that the more flexible components may be subjected to local strains that could result in permanent plastic deformation (and potentially, failure) due to elastic follow up. Paragraph 119.3 provides a few examples of design features that should be avoided by the designer if possible. If “the designer” drafts a system in which there are significant variations in the relative flexibility of components that are in series and immediately adjacent to each other, there could be “a problem” at the point of mutual attachment (weld line) of the two components (it will be the stress analyst’s job to quantify “the problem” in terms of calculated stresses (stress ranges)). The competent designer will understand that it is good practice to avoid abrupt transitions in pipe diameter (section modulus); however, defining “abrupt transitions” is not an easy task. Certainly, using a series of Standard B16.9 welding reducers might ameliorate the problem of abrupt transitions. Using B16.9 reducers (of the appropriate schedule) also assures that pressure design will be adequate. Such design (one or more reducers) might also (slightly) ease the job of the stress analyst as there is at least some guidance in the B31 Codes for determining the stress intensification factors (SIF’s) to be used with reducers in the analysis.

Ah, stress intensification factors! It is essential to use the correct SIF’s. From the point of view of the stress analyst, it is important to recognize at the outset of planning the analysis model that when we use the rules of B31 we are not always calculating true elastic bending stresses. The B31 beam bending equation (generally) defines the calculated stress as the resultant moment times the SIF, divided by the component nominal section modulus. If the SIF (usually as defined by B31.1 Appendix “D”) is greater than 1.0 the equation calculates an “effective bending stress” that can conveniently be compared to Code defined allowable stresses (stress ranges). A recent thread discussed SIF’s et. al. Go here:

http://www.coade.com/cgi-local/ultimatebb.cgi?ubb=get_topic;f=1;t=001304;p=1#000012

You might also want to review John C. Luf’s article in this newsletter:

http://www.coade.com/newsletters/jun00.pdf

I think a properly modeled CAESAR II analysis will always be the first step in the evaluation of designs of this type. The key is to accurately model the flexibility of the individual components that comprise the system and to include the appropriate SIF’s at the points where the strain concentrations will occur. An analysis model with an appropriate level of attention to detail (including correct flexibilities) will accurately determine the distribution of forces and moments over the entire system and for most of the components in the system the (beam model) analysis will provide accurately calculated stresses for comparison to Code maximum allowable stresses (stress ranges). Again, the validity of the stress calculations would depend upon applying the correct SIF’s. An analysis that includes an accurate model of an inexpertly “designed” system will tell the analyst and the “designer” that he/she has “problems”. This of course will require modifications to the design.

The first place to look for SIF’s is in B31.1 Appendix “D”. If you can’t find SIF’s for the components that you are using in Appendix “D”, you would have to use finite element method to determine them (see the cited references for an explanation of what must be considered to obtain SIF’s that can be used in a B31 analysis). Stresses calculated this way would be compared to B31 maximum allowable stresses (stress ranges). Alternately, the calculated forces and moments from the beam model could be applied to a 3D FEA model and the stresses calculated could be compared to allowable stresses from the ASME B&PV Code, Section VIII, Division 2.

When there is a change in wall thickness and a change in diameter it can be effectively addressed in the design by including B16.9 reducers with the appropriate SIF's (see B31.1 Appendix "D"). A rule of thumb that is sometimes used suggests that if the length of the reducer is near to or less than the diameter of the larger adjacent pipe, the reducer can be modeled as a single section of pipe having an average diameter and average wall thickness (the thought here is that this method will result in about the right flexibility). Since this is a false geometry, care must be taken to apply the SIF's at the attachment nodes associated with the true diameters and wall thicknesses of the pipes adjacent to the reducer (this to get the stress calculation correct). To calculate the SIF’s for reducers to be applied in the CAESAR II model you will have to know the “cone angle” and this varies from manufacturer to manufacturer (it is not standardized by B16.9).

From the standpoint of the designer, due consideration should be given to wall thickness changes at adjacent components. Where there is a change in wall thickness at a point of connection of two pipes of the same diameter, it is prudent to note on the drawing that the matching end of the pipe with the larger wall thickness should be "line bored" with a taper to avoid wall thickness "miss-match" at the weld line (note that the minimum required thickness for pressure design must be maintained). There will be some degree of stress intensification at such welds and this invites a thorough reading of B31.1 paragraph 127.4.2 with attention to subparagraph 127.4.2 (C). Of course, B31.1 Appendix "D", Table D-1 (regarding butt welds with "miss-match") is also to be referenced. I think that if we can get the SIF's right the beam model will provide accurate calculated effective stresses.

In summary, I think that if you can develop an accurate CAESAR II beam model, including realistic component flexibilities, realistic loadings, realistic boundary conditions and accurate SIF’s (for the stress calculations), the requirement for an "appropriate analytical method" will have been met.

And again, all of this is just my opinion and not necessarily that of ASME or any of the ASME Code Committees.

Regards, John.

Hello John et. al.,

Reducer SIFS a favorite annoyance of mine. In fact B31.1 gives a formula for SIFS for CONCENTRIC reducers only! Apparently the comittee must feel the more abrupt geometry of an eccentric reducer is of no concern!

However for a real eye opener the origin of the formula in B31.1 is an old ancient WRC bulletin put together by Dr. Rodabaugh. The good Dr. being pragmatic points out with dry, pointed humor, that the critical angle of the reducer is not standardized. That is, the ASME/ ANSI standard the fittings are manufactured to controls end to end length and pipe diameters soley, the critical tangent lengths which set the angle are not part of a standard!

The other intersting thing is that in his fatigue tests the reducer itself never cracked!!!! Due to the heavier wall required to insure pressure retention after forging. What cracked was the pipe attached to the reducer in the area next to the weld cap on the butt weld!!!!!!

So thats all I have to say about reducers!!! No I don't recall the bulletin number I have a copy laying around somewhere???!!!!!

Another consideration is the modelling technique used for branches Rich Ay had a dandy newletter on this subject.... http://www.coade.com/newsletters/dec98.pdf

It is possible when modeling large diameter headers and small diameter branches that are short to grossly underestimate the actual or I should say the code stresses on the branch! When modeling from work point node to work point node you are giving the branch much more flexibilty than it really has.

The WRC document John refers to is WRC-285.

Regarding unbalanced systems and strain concentration...

Flexibility analyses, such as is performed using CAESAR, are based on the assumption of elastic behavior. This assumption is valid for most systems although the displacement stress may be over the material yield strength because the allowable stress criteria is designed to result in shake down to elastic behavior.

In an unbalanced system, it is possible that only one local section of the system may be yielding, or creeping, while the remainder of the system is elastic. Under that condition, considering plasticity, the local region could form a plastic hinge and take a much greater proportion of the thermal strain in the system than is calculated by elastic analysis. Note that if the local region remains at a stress below yield, this will not occur (one approach to making sure this does not occur for the system you have described).

So, in answer to your question, the precautionary wording in the code warns about conditions when elastic analysis, such as performed using CAESAR, provide unconservative calculations of local strains, and thus an unconservative prediction of fatigue life. A similar concern exists with respect to creep and elastic followup.

For those that happen to have my book, see 8.7.

Thanks Chuck... In similiar vein it may not always be a wise idea to design welded attachemnts using a higher thermal fatiuge type allowable. For thermal strains.

Thermal strains do not always behave as one would like!

It has taken until now to read and study the many references suggested. I am hopeful to still get two more by library loan.

John B. thanks for tremendously helpful input. John L. and Richard, I'm still not completely sure how to handle the reducers, but your input has helped me make gains. I plan to use Chuck's input from has book to keep Sus & Exp stresses below S(h), which looks difficult to achieve but is a goal to work toward.

The input and reference resources offered in this thread have met my need to understand what unbalance is and the various tasks and tools needed to evaluate an unbalanced section of a piping system. Again, thanks very much, as without input like this, dispair & frustration would be too constant a companion.

I think I worked for this company at one time "dispair & frustration"....