Hello again Ken,

First of all, I think your questions are very good. It is never my intention to show disrespect to you; on the contrary, your postings on this board indicate that you have given and are continuing to give uncommonly good in-depth thought to piping design. I applaud you. Some of what I will write here is actually aimed at people who lurk and do not pose their own questions. Please accept in advance my apologies for any tone of harshness that might creep into my opinions.

You surely did provide some very important references: "von Karman/Hovgaard/Beskin/Markl basis for developing the fatigue stresses in fittings". The publications by these fellows also give you the chain of logic that leads to the methods used in the B31 Codes for calculating flexibility factors. Mr. Rodabaugh describes the von Karman flexibility and stress index equations on pp 7-22 - 7-25 of TID25553.

Q1. "I find it interesting that the 2PD of straight pipe diameters for intersection runs does not also apply to the intersection branch. Would not the flexibility of the intersection be affected by a stiffer element close on the branch as well as close on the run?"

Yes it will. Again, a suite of equations would be required to calculate the flexibilities inherent in all the possible branch connection geometries. If they are to use linear elastic theory they would have to be approximate. In absence of better data (there still does not appear to be a theory developed that will support simple parametric linear approximation for calculating FF's for generic branch connections) the Codes use a FF of 1.0 (in concert with the Markl developed SIF's). This will be conservative for static analyses and perhaps not so conservative for dynamic analyses. However, the use of these Code rules has proven to be adequate for assuring acceptable service life of branch connections (if ductile materials are used and very significant creep (and creep-fatigue interaction) is not included in the service life).

"I don’t see any code equations using k, so is it used in the linear elastic beam theory equations?"

Yes. The FF is used in the development of the system stiffness matrix (the Code prescribed FF for branch connections is 1.0). The effect of the FF's on the stiffness matrices will affect the calculation of the forces and moments. The calculated forces and moments are used in the Code equations for calculating the various stresses (stress ranges). The Code stress equations apply the SIF's that result from the increased flexibility.

Q1. Why does it take such extensive and time-consuming analysis to complete a stress analysis now, when 20-30 years ago it was done quickly with simple methods?

Why do we do this at all? Because the building codes of the States and Provinces require it (and therefore it is the law). It is the law, because it has proven to be a good set of minimum requirements for piping design.

20 - 30 years ago (mid 70's) we took more time to do the work and the results were not as accurate as they are now (and the systems that we designed, for the most part, proved to be satisfactory). If someone in the business thinks we are doing more now than was called for (required) in the mid-'70's, their memory is faulty. Before then, before computers were generally available, some so-called design firms (drafting shops actually) were taking chances with the health and safety of a lot of people ("just do it like we did on the previous contract"). It took me (and I presume everybody else who did it correctly) much more time to evaluate the stresses in piping systems using "square corner technique" and "Flex-Anal" charts than is now required to do the same systems using CAESAR II.

Q2. "I can show you dozens of steam piping systems where the tees have other fittings, flanges, or valves welded directly to them. Why were those systems successfully accomplished then, and I can assure you no shell/brick finite element analysis or prototype was built to prove the tees were okay, but you need these methods to accomplish the same now?"

Because for the very large majority of piping systems it is not necessary (albeit in a few designs it will be necessary - not very many) to do shell/brick finite element analysis or to build prototypes to assure that the systems will provide adequate service life. The (fatigue) rules in the Code books have been in use in one form or another since 1955 and they have served us well. If the piping engineer understands the design parameters and gives due attention to the system being designed and performs professionally in developing a representative analysis model and diligently applying the Code rules, there is a good likelihood that the piping system will provide adequate service life. We have all heard horror stories of piping system failures and presumably we have all applied "lessons learned" (from the root cause analyses) to our designs. I can assure that the Code Committees have done so.

Q3. "Such systems are still working today, decades later. Do you hear of tees failing in carbon steel steam piping? The code is overly conservative and highly specified with no benefit over the designs of decades ago."

Actually, I have seen more branch connections fail due to pressure pulsation (typically in feed water and condensate piping) than I have seen in steam and process lines. Today, some generators are trying to INCREASE the plant design pressure and run closer to theoretical stress limits in an effort to reduce the kilowatt-hour-to-cost ratio. In the last 10 years I have seen many plants being run near or above the Code (stress) pressure limit in their feed water and condensate piping. When I think about that in context with what I know about erosion-corrosion, I am glad that I have been so lucky that my hearing loss is my only enduring personal plant injury.

The B31 Code is what it is - in many jurisdictions it is the law. If it is someone’s stated judgment that the B31 Code is OVERLY conservative and highly specified with no benefit over the designs of decades ago, that person is speaking out of ignorance. We have learned from doing and we have used hard-won wisdom to DECREASE conservatism where it can appropriately be decreased (e.g., in some cases higher allowable stresses and "f" factors greater than one).

Q4. “The code is not precluding designs that do not reproduce these end conditions…” (John B.) No, it is not precluding such designs, but doesn’t provide an answer within the code as to whether a very common piping fit-up is okay or not. Why was it okay by code to weld other fittings/flanges/valves to tees decades ago (agreed the code does not, per se, state it can not be done so now), but now says “may require special consideration”, read “the SIFs may be higher, may be lower”, so the code can not tell me whether that tee that I’m looking at right here in this 20 year old station is okay or not? Tees are often fitted to other fittings/flanges/valves, so would not share the perspective that such configurations are a small percentage of systems that are evaluated."

"doesn’t provide an answer within the code as to whether a very common piping fit-up is okay or not."

It is not the Code's charter to list every construct that would represent adequate design/construction. The Code is not a design manual. The Code provides a finite set of design rules based upon the experiences and knowledge of thousands of past and present Code Committee members. Some Codes provide warnings regarding using certain constructs in specific types of systems and services ( e.g., B31.1 Chapter II, Part 6 - I guess these are examples of "don't do it").

"Why was it okay by code to weld other fittings/flanges/valves to tees decades ago .... but now says “may require special consideration”, read “the SIFs may be higher, may be lower”.

There has been no "rule change" here; the advisory note was added for information. The Codes tell the designer that if the designer has better data the designer should use the better data. In the case stated, the note at issue intends to make the designer aware that when components are used in close proximity such that the stiffness of a branch connection might be affected (and consequently the SIF may be affected), the designer should give additional design consideration to the construct. One of the possible "additional considerations" might comprise the application of knowledge of many years of successful service of similar constructs in other piping systems (i.e., engineering). The Code does not pretend to provide specific design assistance or rules for every design challenge. It is the responsibility of the piping engineer to satisfy him/herself, that the design is adequate. Perhaps (my opinion) that the assumption is that the piping engineer is educated in piping engineering and is willing to apply that education (albeit, here in this forum we are frequently provided with evidence to the contrary).

".....so the code can not tell me whether that tee that I’m looking at right here in this 20 year old station is okay or not"?

Correct, the Code cannot do this (and it does not attempt to). And, it is not in the Codes charter to do so. To get to the "whether that tee that I’m looking at right here in this 20 year old station is okay or not" point, one would evaluate the remaining life fraction of the component while applying fresh structural analysis data. Also, a prudent amount of new nondestructive evaluation would be required to make an assessment - e.g., what is/are the remaining wall thickness(es), are there any surface indications of fatigue cracking and surface replication to establish the degree of creep damage.

Q5 "....What good is a code that doesn’t address common piping arrangements other to say you need to go to another code or conduct special analysis to know if the system is will not fail..."

I would suggest that Codes that were and are being used around the world to provide guidance in the design of many, many successful piping systems (and were used as the basis of the development of other county’s piping Codes) have demonstrated that they are of SOME value (?). Upon reflection, I think that your interpretation - "...other (than) to say you need to go to another code or conduct special analysis to know if the system is will not fail..." - is an inaccurate overstatement. The Code does not mandate that you go to any other Code (except for external pressure design) or that you conduct any other special analyses (except for "unlisted components" pressure design). Ken, would you rather that the phrase "...may require special consideration" NOT appear in the Code? The Committee that included that phrase did so simply to inform the Code user that under the stated circumstances the SIF's provided in Appendix "D" might not be accurate. It just waves a flag and says "think about this while persuing your engineering responsibilities". Reference is made to paragraph 319.3.6.

".........Here’s what I am finding on these steam stations with tees that don’t meet Table D300, Note 13..."

Ken, some of what you have said seems to imply that you are interpreting the Code such that not having at least two diameters of straight run pipe on each side of the branch centerline is a violation of the Code rules. Appendix D, Table D300, Note 13, does not imply that branch connection not having at least two diameters of straight run pipe on each side of the branch centerline are a violation of Code rules. Rather, it says (in my opinion) that the SIF's at the branch connection, calculated by the equations in Appendix "D" might not be accurate in such a construct. There is no "...requirement..." stated on note 13.

Appendix "D" provides guidance for piping system analysis based upon the limited testing done by Markl's team. It is "for what it is worth"; anyone having better data should use it. Ken, would you suggest that it would be a better Code if Appendix "D" were deleted? With all due respect, is there an attitude of "well if the collective piping Codes cannot be totally comprehensive and perfect in all areas of piping design then they are of no value at all"? The body of research work (theoretical and experimental) is out there. TID25553 gives all the right references (later documents have supplemented those references). It cannot be expected that the Codes reprint all the underlying theory or reprint even the references to these works. Taken as a whole, the entire body of research work is not sufficient to cover all the design issues that we will encounter. Code Committee members would be the first to tell the world that the Codes are a distillation of the best knowledge that we have (albeit incomplete and imperfect) for piping design. In my view, that does not invalidate the worth of the B31 Codes for Pressure Piping.

"...But the switchover between one leg of the station to another have stresses of 500 to 700% of the allowable stress..."

Yes, "tie-in piping" between two or more units in the same power plant often seem to exhibit indications of "less than good" analysis. Sometimes I wonder if there has been ANY analysis of these "tie-in line". The design team responsible for each of the units seem to abdicate responsibility for the "tie-in lines" ("its not in OUR scope"). As you point out, the problem is often found in the analyses of the various modes of operation - some units "coming up" and other units "going down" or into "hot stand-by". Some full cycles and many partial cycles especially when base-loaded units are placed into "peaking" service.

Most plant owners are now looking at the remaining useful life of their units so that they may know which "critical components" will have to be replaced and in what order (this will affect the projected cost per kilowatt-hour of various stations and will dictate what plants are put into "cold stand-by"). Some plant owners have placed the "major pieces of equipment" in their "critical component" programs but ignored the high energy piping. They may find out the hard way that the piping systems' most likely mode of failure is low cycle high stress (the data shown over on the extreme left of the S-N "curve") due to inadequately evaluated "modes of operation". Some will see the value of having an engineer tell them that their piping systems are in trouble.

"....how can I learn more about how the Flexibility Factor, k, factors..."

At the risk of being repetitive, begin with the "Markl Papers". Sift through the TID25553 references (some of these will be tough to find). Then there are selected WRC bulletins and a wealth of Oak Ridge National Laboratories (ORNL) reports. Read the John Brock written section on flexibility analysis in the Fifth Edition (it was dropped in subsequent editions) of Reno King's Piping Handbook.

Again, my apologies for any unintended Luf-isms found in the above. Also, all of this is just my opinion and not the opinion of ASME international or any ASME Code Committee.

Best regards, John.