CHAPTER

6

6.1 INTRODUCTION

This chapter discusses the structural limits in Section III NBand Section VIII Div 2 as related to specific structural failuremodes considered applicable to pressure vessel and pipingdesign. The rules and requirements for Section III NB andSection VIII Div 2 are based on the design by analysis philoso-phy addressing specific structural failure modes of structural col-lapse, rupture, instability, fatigue, and progressive deformation.Beam, plate, and shell theory have been used in the past to developdesign analysis methods. These methods are giving way to finiteelement analysis (FEA) methods that are commonplace in engi-neering practice today. This chapter discussed ways to use FEAto show compliance with the ASME Code structural design lim-its. The applicability of linear versus non-linear analysis assump-tions are discussed relative to the failure mode being addressed.Examples are given with guidelines on use of current tools toaddress these failure modes. Comments on the direction fordevelopment of new tools are given. Also discussed is the devel-opment of fracture mechanics methods to address ductile andbrittle fracture failure modes as required in Appendix G, inSection XI, and often in the context of Section III NB designrequirements. Comments are provided on the limitations ofdeterministic assessments as made in the current Section III NBassessment with respect to new initiatives into reliable designmethods based on probabilistic concepts.

For simplicity, the following five terms are frequently used:

(1) Code: 2007 Edition of ASME Boiler and Pressure Vessel(B&PV) Code.

(2) Code Committee: ASME Boiler and Pressure Committeeand Subcommittees that write the rules.

(3) Criteria Document : “Criteria of the ASME B&PV DesignCode by Analysis, Sections III and VIII, Division 2”, TheAmerican Society of Mechanical Engineers, 1969.

(4) NB: Subsection NB of Section III of the 2007 Edition of theASME B&PV Code, Class 1 Components, Rules forConstruction of Nuclear Power Plant Components, July 1,2007*.

(5) Section VIII Div 2: 2007 Edition of ASME B&PV CodeSection VIII Division 2, Alternate Rules for Constructionof pressure Vessels, July 1, 2007.

(6) Section XI: 2007 Edition of ASME B&PV Code SectionXI, Rules for Inservice Inspection of Nuclear Power PlantComponents, July 1, 2007.

(7) FE, FEA, EP-FEA, Finite Element, Finite ElementAnalysis, Elastic-Plastic Finite Element Analysis.

The original edition of Section III addressed only Class 1 ves-sels and did not have Subsection NB. Thus, when this chapterrefers to the original edition, it uses the term Section III. The useof Subsection NB refers to the 2007 edition. The Criteria docu-ment was originally issued in 1963.

The Criteria Document was upgraded in 1969 to includeSection VIII Division 2 design by analysis. The focus of thischapter is on the design by analysis rules of NB. Although thedesign limits in NB are considered essentially the same as in the2007 edition of Sc VIII Div 2, there are now a number of compu-tational differences Sc III NB and Sc VIII Div 2 that are signifi-cant. It will be noted when the analytic procedures between thetwo sections deviate.

The original Criteria Document relegated possible failuremodes of erosion, corrosion, and environmental effects to materi-als selection. Service experience has shown that long term expo-sure to light-water reactor (LWR) environments does more dam-age to structural materials than originality thought. In addition,long time irradiation exposure has been found to produce unex-pected degradation of the fracture toughness of pressure vesselsteels. Accordingly, additional steps have been needed to monitorthese effects by in-service inspections and surveillance materialstesting to assure safe long term operation of nuclear pressure ves-sels. This chapter also provides comments on procedures avail-able through use of the finite element methods to assure long termsafe operation of nuclear pressure vessels.

6.1.1 Scope for Chapter 6 The content for the design and construction of Class 1 pressure

vessels is primarily covered in Subsection NB, but is also

SUBSECTION NB—CLASS 1 COMPONENTS

Greg L. Hollinger1

* This article was developed used the 1998 edition, and the article applies to later editions unless otherwise noted.1 John Hechmer was the auther of this chapter for the first edition.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 1

2 • Chapter 6

addressed in parts of Subsection NCA (General Requirements forDivision 1 and Division 2) and also in the Subsection, Division 1Mandatory and Non-Mandatory Appendices. The major focus ofthis chapter is limited to Article NB-3000, with major signifi-cance on NB-3200 (Design by Analysis) and on NB-3300 (VesselDesign). Application of the FEA to brittle fracture analysis is lim-ited to the non-mandatory procedures in Appendix G and thefatigue crack growth procedures in Section XI.

Most of the rules and requirements for analysis are covered inNB-3200 and NB-3300. The 2007 version of Section VIII Div 2provides much more detail on using FEA for structural designcalculations and those methods will be discussed only as theyrelate and offer insight to methods applicable to NB.

Paragraphs 6.1.2, 6.1.3, and 6.1.4 give background informa-tion of design philosophy, fundamental basis, and principles ofpressure vessel design. Section 6.2 presents an overview of thedesign process including the fundamentals from the 1969Criteria Document and the interaction with the other disciplines.Sections 6.3 through 6.6 primarily address NB-3200 and NB-3300, and Section 6.7 utilizes various parts of NB and itsAppendices. Section 6.8 discusses use of FEA with brittle fractureand crack growth procedures recommended in Sc III Appendix Gand Section XI.

6.1.2 Design Philosophy The goal of Section III of the B&PV Code and specifically the

structural design limits of NB is to provide the safest possible pres-sure vessel and piping components for nuclear service. This philos-ophy is put into practice by applying elements of good design start-ing with material selection, mechanical design, high levelmanufacture and fabrication standards, quality assurance standards,installation, in-service testing, over-pressure relief, and certifiedcompliance of standards regulations by certified inspections andASME plant stampings. The overall driving issue for constructioncomponents for nuclear service is that a catastrophic failure or rup-ture of a nuclear pressure vessel is not acceptable. To achieve this,the elements of the design process mentioned above all go hand-in-hand to produce the required ultimate safe plant operation. Theterm “high quality” in the context of a nuclear pressure vessel isthen one that complies with all of the elements of construction of anuclear power plant: design, manufacture, fabrication, qualityassurance, in-service testing, and operational controls.

Specifically, NB addresses structural design limits for pressurevessel and piping components intended for nuclear power plantswhere the consequence of failure is considered to be a threat tothe health and safety of the public. Thus the design philosophy ofSc III NB is to provide structural limits that insure very safe plantoperation with highest reliability and little threat to public healthand safety.

The goal of all Code books such as Sections I, IV, and VIII isto produce pressure vessel and piping components that operatesafely for their intended purpose. The design factors and con-struction rules for all books are determined based on the conse-quence of failure for the industry in which such equipment is tobe used. Usually the consequence of failure is judged to be morelimiting for components intended for nuclear rather than non-nuclear service. The overall objective of Section III then is to pro-duce plant components for nuclear service with the highest quali-ty of construction and inspection that are verified throughconservative analysis procedures and design limits.

This high quality is obtained through design in compliancewith the structural design limits of NB, high quality construction

rules, and quality assurance rules to qualify that the component isin compliance with the rules. For example, NB-1110(a) (Aspectsof Construction Covered by These Rules) states the following:

Subsection NB contains rules for material, design, fabrication,examination, testing, overpressure relief, marking, stamping, andpreparation of reports by the Certificate Holder of items which areintended to conform to the requirements for Class 1 construction.

To obtain the desired level of safety and quality, design andconstruction must be considered a singular effort. Therefore, thedesigner must interface with and be cognizant of all of the afore-mentioned disciplines. The rules for each of these disciplinesmust be met, and the designer must ensure that the design andbuild approaches are consistent. Thus the philosophy for estab-lishing the design rules of Sc III NB is that all disciplines of con-struction, analysis, quality assurance, and in-service inspectionare applied consistently to produce a high nuclear power plantpressure vessel and piping component that complies with thehighest safety requirements in service.

Structural design analysis plays a role in this process by assur-ing these elements are in place and each given appropriate atten-tion. For example, it is meaningless for a designer to size a vesselneglecting pre-service flaws if the quality assurance and materialselection is not sufficient to produce a vessel with adequate flawtolerance for the anticipated pre-service flaws. The philosophy ofNB is that the materials allowed for nuclear service and the qualityassurance levels required deliver such a product. It is alsoassumed that the fabricator assembles the equipment properly andthat the proper Code inspectors assure sufficient high quality finalproducts.

6.1.3 Fundamental Basis The current Section III Subsection NB covers the same scope

as in the original version of NB. The fundamental basis for theanalysis can be found in the Criteria Document. Although writtenin the 1960s, the Criteria Document is still relevant to the funda-mental basis underlying the structural design limits applied inSection III NB. The Criteria Document states, “The need for designrules for such vessels led to the preparation of Section III . . .” Inaddition, the Criteria Document establishes the differencesbetween the rules for Section III and those for other Code pres-sure vessels by stating the following:

The design criteria of Section III . . . differ from those ofSection I and Division 1 of Section VIII in the following respects:

(a) use the maximum shear stress (Tresca) theory of failure . . ., (b) require a detailed calculation and classification of all stress-

es and the application of different stress limits to differentclasses of stresses . . . ,

(c) require calculation of thermal stresses and gives allowablevalues for them . . . ,

(d) consider the possibility of fatigue failure and give rules forits prevention. . . .

Thus the NB design has specific requirements and acceptancecriteria.

Items (b), (c), and (d) of the preceding list indicate that a sub-stantial increase in stress analysis is required by NB relative torequirements for other pressure vessels. The Criteria suggests thatClass 1 vessels need a complete, thorough assessment of thestresses to ensure that failure will not occur from the variousfailure modes. Thus, the required analyses are major additions forensuring high quality of the product. The Criteria states thefollowing:

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 2

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 3

Because of the prominent role played by stress analysis indesigning vessels by the rules of Section III . . . and becauseof the necessity to integrate the design and analysis efforts,the procedure may be termed “design by analysis.”

The term, design by analysis, is often interpreted backwards—that is, the interpretation is that if the analysis indicates that thedesign is acceptable, it is. The true intent is that the analyses helpensure that high quality is reached. Thus, stress analysis is addedto the “NB rules for all of the disciplines . . . and their interaction”in an effort to reach high quality.

In the search for high quality, the Criteria Document definesfour different types of failure modes: bursting and gross distortionfrom a single application, progressive distortion from cyclic appli-cation, crack initiation from fatigue damage, and instability. Asdiscussed in later sections, the intent of the design analysisrequirements in Section III is to provide suitable design marginagainst these failure modes.

6.1.4 Summary of Principles of Pressure VesselDesign

In summary, the key considerations used to establish high qual-ity pressure vessel and piping design are the following:

(1) The overall goal is to produce vessel & piping componentswith the highest quality of construction.

(2) High quality is obtained through interaction of the four ele-ments of good design; meeting structural design limits,complying with construction rules, employing good fabrica-tion, performing quality assurance, and evoking in-serviceinspection schedules.

(3) Meeting the NB rules for all of the elements of good designand ensuring that their application is interactively consis-tent will produce Class 1 high-quality pressure vessels.

(4) High quality is designed and built into the pressure vesseland not in the paperwork supporting the design.

(5) NB has specific analytical requirements and criteria that iscalled “design by analysis”.

(6) NB provides protection against failure modes of burstingand gross distortion from a single load application, pro-gressive distortion from cyclic application, crack initiationfrom fatigue damage, and instability.

6.2 DESIGN

Structural analysis is one of the elements of good design that isa major part of the Section III design process. However, as men-tioned above, analysis is just one of the elements of good design.The role of analysis is to alert the designer of design deficienciesthat can be fixed before construction. The experience of manyyears of successful pressure vessel operation is a positive consider-ation for obtaining good design. Understanding the interactionsbetween materials, environments, mechanical and thermal loads asaided by other disciplines is critical for every part of every pres-sure vessel design. This section addresses these considerations.

6.2.1 Fundamentals of Good Design Good design starts with the lessons learned from years of oper-

ating vessels—namely, what works and what results in failures.Non-nuclear plants are often operated over long periods of timewith little or no oversight because any loss of product is an

economic issue rather than a safety issue. Nuclear plants are oper-ated for relatively short periods of time with very close opera-tional controls. In addition, many more non-nuclear plants areoperating than nuclear vessels. Consequently there are more leaksand failures in non-nuclear plants than nuclear plants. Eventhough the design and construction acceptance standards are dif-ferent between a non-nuclear and nuclear vessel, the service expe-rience from non-nuclear vessels can still provide insights that canbe applied to all pressure vessels in the understanding of whatworks and what fails. To the extent that the construction used forthese vessels is consistent with the NB rules and requirements, theexperience factor is directly applicable. Understanding and usinglessons learned from applicable service experience is a significantpart of good design.

New design features and fabrication processes are important foradvancing the technology. Obviously, these new features may devi-ate from past designs sufficiently that the application of lessons-learned from those existing design is of limited value. However,there are probably design and fabrication details that do have someintrinsic similarity with previous designs that allow application ofgeneral best-practices to the new design. For example, if the newgeometry precludes a full nondestructive examination (NDE), thepotential for failure is increased. However, there may be an experi-ence base for this type of condition that includes the geometry andloading. New designs and fabrication processes can therefore beassessed for quality over the required analyses.

In recent years the interaction between design and the otherdisciplines appears to be improving. This improvement seems tohave grown from the NASA approach to design and build, theFord Taurus multidiscipline teams, and the Japanese quality con-trol teams. Before these entities, a common approach was to haveeach discipline “do its own thing,” with reports or memos sent outto the other disciplines. It is foolhardy to assume that another dis-cipline will understand the expectations of the designer. Forexample, manufacturing may decide to put a weld at a discontinu-ity, which is allowed to have a reduced NDE as well as anincrease of the stresses in the weld. The analysis may show thislocation to have a high cyclic stress. The construction configura-tion may require an additional fatigue strength reduction factorfor which the designer did not consider. Putting welds in highstress locations is not good design. High-quality welding and fullNDE produce high quality; lacking these does not produce gooddesign for Class.

The term high quality is subjective. It may be more reasonableto establish “bad quality” or, rather, what practices or configura-tions should cause concern. For good design of high-quality ves-sels, the controlling locations (relative to failure) should be evalu-ated relative to operating experience, and the designer mustensure that the construction is fully consistent with the design.

6.2.2 Theory—Criteria Overview The objective is to produce pressure vessel and piping compo-

nents that do not fail within their expected lifespan. The CriteriaDocument establishes and discusses the significant failure modesapplicable to pressure vessels and piping—that is, the modes thatare most likely to cause a failure. The Criteria Document statesthe following:

The various possible modes of failure which confront the pres-sure vessel designer are:

(1) Excessive elastic deformation including elastic instability. (2) Excessive plastic deformation.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 3

4 • Chapter 6

(3) Brittle fracture. (4) Stress rupture/creep deformation (inelastic). (5) Plastic instability—incremental collapse. (6) High strain—low-cycle fatigue. (7) Stress corrosion. (8) Corrosion fatigue.

Items (2), (5), and (6) are the failure modes that require thatanalysis be addressed. Item (1) is generally related to functionalrequirements or the potential for buckling in thin structures. Item(3) is generally addressed in the material toughness but includessome simplified analyses, such as those presented in the Non-Mandatory Appendices. Item (4) addresses high-temperature ves-sels and has substantial requirements related to analysis that werenot part of the original Section III and are not therefore addressedin the Criteria. Items (7) and (8) are the responsibility of theOwner; however, to ensure a high-quality vessel, the designermust understand and address the potential for corrosion damageunder the guidance of the Owner.

For Items (2), (5), and (6), the Criteria document establishesthe failure modes of bursting and gross distortion from a singleload application (discussed in Section 6.4); progressive distortionfrom cyclic application (discussed in Section 6.5); and crack initi-ation from fatigue damage (discussed in Section 6.6), respectively(as was previously stated).

Previously, four new approaches to design analysis were pre-sented. One was that there be a full analysis, about which theCriteria states “require a detailed calculation and classification ofall stresses and the application of different stress limits to differ-ent classes of stresses. . . .” This approach required that a stresslimit be applied to each stress type, each of which, in turn, repre-sented a failure mode. Turning this around, each of the three prin-cipal failures—Items (2), (5), and (6)—must be related to a stresstype, and the design margin must be established. The Criteriaaddresses this matter as “the setting of allowable stress valuesrequired dividing stresses into categories and assigning differentallowable values to different groups of categories.” The stress cat-egories were then established in the Criteria.

The categories and subcategories chosen were as follows:

(a) Primary Stress(1) General primary membrane stress (2) Local primary membrane stress (3) Primary bending stress

(b) Secondary Stress (c) Peak Stress

The Criteria continues to define the relationship along with anexpansion of the failure mode definition:

The potential failure modes and various stress categories arerelated to the Code provisions as follows:

(a) The primary stress limits are intended to prevent plasticdeformation and to provide a nominal factor of safety onductile burst pressure.

(b) The primary plus secondary stress limits are intended toprevent excessive plastic deformation leading to increme-nal collapse, and to validate the application of elastic analy-sis when performing the fatigue evaluation.

(c) The peak stress limit is intended to prevent fatigue failureas a result of cyclic loadings.

(d) Special stress limits are provided for elastic and inelasticinstability.

The items in the preceding list are discussed in detail inSections 6.4 – 6.7. Presently it is sufficient to show the relation-ships of category, failure mode, and Code designation as follows:

(1) primary stress: ductile bursting and plastic deformationfrom a single load application, Pm, Pb, and PL;

(2) primary-plus-secondary stress: excessive plastic deforma-tion leading to incremental collapse and used for validatingthe fatigue evaluation, P � Q; and

(3) fatigue: crack initiation, Sa.

Another of the four new approaches to design analysis is theapplication of the maximum shear stress (Tresca) theory of failurerather than the use of the maximum stress theory. It has beenknown for many years that the shear theory is more accurate thanthe maximum stress theory in terms of failure, especially for dis-tortion from plastic response of the material. Admittedly, theshear theory is more difficult to apply than the stress theory, butthe shear theory is also less conservative because of its improvedaccuracy.

The distortion energy theory (e.g., von Mises criteria) was alsoconsidered based on its better accuracy and less conservatismthan the shear theory. The Criteria addresses this fact by statingthe following:

Most experiments show that the distortion energy theory iseven more accurate than the shear theory, but the sheartheory was chosen because it is a little more conservative, itis easier to apply, and it offers some advantages in someapplications of the fatigue analysis.

With current capabilities (e.g., computers), the Criteria basesfor approaches are not as meaningful as they were in the 1960s.However, NB still requires the use of shear theory for elasticanalysis. For plastic analysis, NB does not preclude the use of thedistortion energy theory for establishing yield in the three-dimensional condition. (Details on plastic analysis are addressedin Section 6.7.) The key here is that the shear theory (Tresca) isthe basis for determining the allowable stresses.

6.2.3 Roles of Materials, Welding, NDE, and OtherForms of Design—Construction Interfaces

Although the major focus of Chapter 6 is stress analysis, theinterface between design and construction has a major impact onthe quality of the vessels. The disciplines of most importance arematerials, welding, and NDE. Subsection NB includes rules forthe following: Materials (NB-2000); Fabrication and Installation(NB-5000); Examination (NB-6000); Overpressure Protection(NB-7000); and Nameplates, Stamping, and Reports (NB-8000).

These sections of NB primarily give rules for constructionbut also give rules for design. The forthcoming paragraphsdiscuss some interactions between design and materials, welding,and NDE.

(a) Material Both the base metal and the weld metal constitutematerial. Although most companies use a small number of materi-als for their construction of pressure vessels, there are differencesbetween the materials used, especially relative to weld-ability andNDE. All materials are not equal, though they may have the samenominal yield and ultimate strengths. For example, plates canhave laminations but forgings do not, which limits the use of platesin some applications. Another example is the impact of the materialthickness, for in thick parts, the toughness will decrease in thethrough-thickness direction, whereas the toughness is established at

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 4

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 5

the quarter-thickness depth—possibly creating problems for theDesigner if the part is thick in some places (e.g., for reinforce-ment) and thin in an area of transition to a thinner part. For one tounderstand the characteristics of a specific material, he or sheshould review the appropriate material as presented in Parts A, B,C, and D of Section II (Materials of the Code).

Most NB pressure vessels are made of carbon or low-alloysteels with austenitic cladding on the inside surface. However,stainless steels and inconels are sometimes used for nozzles andpiping. The characteristics of carbon and low-alloy steels arequite consistent with each other, including welds; stainless steelsand inconel material, on the other hand, are not very consistent,particularly so at high temperatures. Even within stainless steelsand inconel material, however, inconsistencies occur, especiallybetween base metal and weld metal. The accuracy of a designanalysis can be affected by such inconsistencies. When the designis for a pressure-only loading (primary stresses), the accuracy isexpected to be high primarily because the material remains elas-tic. However, for thermal loads (including thermal gradients), theaccuracy will decrease. If the mechanical plus thermal stresses(primary-plus-secondary stresses) exceed the yield strength, theinaccuracy can be significant—that is, as the stresses increaseover the yield strength, the accuracy decreases. When these inter-actions between material occur, the designer must assess thepotential for hidden problems during operation.

(b) Welding This activity may present potential problems forthe designer and caused by a wide range of processes evenwithin the various types of welds. The weld geometry may alsocause problems. Unfortunately, the basic design for the vesselis often completed before the welding engineers establish theweld type, process, and geometries. Thus the designer mustassume that common practices will be used, then follow up asthe welding engineers make the final decisions. The majorproblems arising from weld type, process, and geometries arethe following:

(1) effect of the geometry on the fatigue-strength reductionfactors;

(2) effect of the weld type or process on the number and size offlaws;

(3) the capability to obtain high-quality NDE; (4) surface finish—as-welded versus machined; (5) weld material properties versus the adjacent base metal; (6) effect of the residual stresses in the weld and its heat-affected

zone; (7) effect of the environment on the weld type; and (8) impact of postweld heat treatment.

NB-4240 and 4250 give weld geometry information—probablythe most important part of the weld geometry issue. Some of theconfigurations are very consistent with the quality of the basemetal; others are susceptible to notches at the weld–base metaljuncture. Experience indicates that fatigue damage is most likelyto occur at this location and superimposing a notch increases theprobability. The notch is not consistent with high quality.

Welding and NDE have a major interface. The weld geometry canhave a major impact on the quality of the NDE. In reviewing theplans of the weld engineers, the design should consider the impacton the NDE, especially if the weld is in a high-stress location.

Another consideration is repair welds in both the weld metaland in the base metal. Obviously, the issue of weld repairs occurswell after design, but a designer is needed to view a repair’simpact. Most weld repairs can be accepted by using a standard

approach. For major repairs and repairs in high stress locations,however, a team review is appropriate.

(c) NDE Nondestructive examination is a critical discipline forensuring high quality. NDE for base metal is primarily defined bythe material requirements covered in Section II of the Code. Forwelds, NDE is defined within NB. Three subsections within NBdefine the requirements: specifically, NB-5200 for required exam-ination for welds based on the categories defined in the weldingsubsection; NB-5300 for the acceptance standards; and NB-5400for examination after hydrostatic tests. Details on applying NDEare given in Section V of the Code. The variations that areallowed in the requirements affect the location, size, and orienta-tions of indications that are not rejectable by the NDE procedureor are not found by the NDE. Thus, the NDE application definesthe potential for flaws existing in the weld, where flaw is definedas an undetected notch that can cause significant damage to theproduct.

Based on the hypothesis that NDE has a major role in predict-ing the fatigue life of pressure vessels, a defined relationshipbetween NDE and fatigue strength reduction factors (FSRF) isnecessary. Even though the relationship should apply to both basemetal and weld metal, the NDE for base metal is reasonably con-sistent and produces high quality, whereas NDE for weld metal isvariable, depending on its application. Thus, the focus and poten-tial impact of NDE is on welds.

There have been relationships studied and developed for therole of NDE relative to applying an FSRF. The Welding ResearchCouncil (WRC) Bulletin 432 [1] has developed one of these rela-tionships. A matrix of FSRF was developed based on weld type(full-penetration, partial-penetration, and fillet welds) versus theNDE that is applied. The NDE methods that are included are radi-ographic testing (RT), ultrasonic testing (UT), magnetic-particletesting (MT), dye-penetrant testing (PT), and visual testing (VT).The first two methods are volumetric examinations; the remainingthree are surface examinations. Seven combinations of volumetricand surface examinations are defined; thus seven levels of FSRFare defined. Therefore, the matrix gives the designer a basis forassessing the impact of the NDE on the fatigue life.

Although NB does not define NDE versus fatigue quality, thedesigner is responsible for the quality of the vessel. It is wellestablished that fatigue damage originates at notches, and NDE isintended to detect flaws and allow their removal. The differentNDE techniques have different detection capabilities for differenttypes and locations of flaws. This leads to levels of quality as afunction of which NDE techniques are applied. Thus, the designershould understand the impact of having a full versus partial NDEand taking responsibility for the quality.

6.2.4 Reliability Design MethodsThe concept of using subjective methods such as reliability in a

design scenario was not contemplated when the Criteria for NBwas being formulated. The philosophy of the Code that forms thebasis documented in the Criteria Document is based on determin-istic methods with appropriate safety margins. Current Codemethods do not allow judgments regarding the effect on safetythat accompanies relaxation of a safety margin. Code safety mar-gins are based on judgment, past service experience, and practicaldesign considerations. When the safety factors are relaxed, all onecan say is that the design is probably less safe.

The concept of reliability design is to consider the probabilityof events, the uncertainty in design and manufacture, and the con-sequence of failure to establish a balanced design that does not

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 5

6 • Chapter 6

weigh one aspect too highly at the expense of another. Such meth-ods were not possible in the 1960’s due to the computationalintensity required to perform the analysis. With high-speed com-puters and large memory capacity, these calculations are now notonly possible but being required in some regulatory sectors.

Reliability design methods have progressed beyond researchtopics to the point where application textbooks and tutorial coursesare offered by the ASME for use in design. Two such documentsare the work of Andrews and Moss on “Reliability and Riskassessment” Reference [24] and an application handbook pub-lished by ASME titled “Risk-Based Methods for Equipment LifeManagement” Reference [25]. The fact that these methods arenow beign taught as pratical methods for use in design suggeststhat implementation into the ASME Code is not far behind.

The largest uncertainty in the design process is the number andseverity of the design transients expected in the course of thedesign life. On the other hand, one might require a higher level ofreliability for an event that is expected to occur during the courseof plat service as opposed to one that might occur. Clearly, theconsequence of failure enters in as loss of primary water coolantmay have very serious consequences whereas loss of function of areplaceable component has an altogether different consequence.The concept of a high quality design now can take on a quantita-tive aspect so that a design agency can establish target reliabilityfactors given the likelihood of the event and the consequence of afailure.

As this chapter is being written, a new article is being devel-oped for Section III implementing reliability design into theCode. Consideration of all the failure modes required by the Codeis a formidable task for reliability design to be effective. However,reliability can help address the risk-benefit decisions required inthis new world of international competitiveness where a relax-ation of safety related factors can allow construction of a moreaffordable plant. Although outside of the discussion of this chap-ter, reliability methods are going to be developed and will becomean asset useful in mechanical design. For that reason, future workon bringing this technology into ASME Code regulation is war-ranted.

6.2.5 Probability Risk Assessment NB does not discuss probabilistic risk assessment methods

(PRA). This technology is required by the United States NuclearRegulatory Commission for assessment of loss of coolant acci-dents and is a mainstay in Section XI of the Code. PRA is basedon fracture mechanics methodologies to assess the effect of piperuptures and the accompanied rapid cooling of the reactor vesselto maintain a coolable nuclear core.

It is evident that introduction of brittle fracture procedures intothe design methodology of NB could promote better performanceof future plants in the event of a loss-of-coolant accident.Currently, NB relies on material selection to assure the initialmaterial has adequate toughness to tolerate any pre-service flawssuch that they will be benign to fatigue growth. This stanceshould be re-evaluated in light of recent information on the effectsof thermal aging, irradiation exposure, and environmental effectson fatigue.

6.2.6 Defense-in-Depth Defense-in-depth refers to building redundant safety features

into a plant to improve the safety posture of the plant in the eventof an accident. Instrument errors, operator errors, componentmalfunctions, and any other myriad of events can occur in

un-expected orders. A plant must be designed to accommodatesome reasonable consideration of multi-event failures and combatthem with redundancy to mitigate their effect. In this regard, relia-bility design methodology can come into play.

6.3 ANALYSIS

Subsection NB rules do not establish tools for doing the analy-ses with one exception: the basic thickness for cylinders andspheres. Equations are supplied in NB-3324.1 and NB-3324.2;NB-3324 (Tentative Pressure Thickness) makes these equationsmandatory:

The following formulas are given as an aid to the designer fordetermining a tentative thickness for use in the design. Theyare not to be construed as formulas for acceptable thicknesses.However, except in local regions (NB-3221.2), the wall thick-ness shall never be less than that obtained from the formulasin NB-3324.1 and NB-3324.2. . . .

The Criteria document establishes that the intent of the primarystress limits is to prevent plastic collapse. The Criteria documentsstates that “the choice of the basic stress intensity limits . . . wasaccomplished by the application of limit design theory . . .”. Thusthe primary stress limits ensure the allowable loads on a compo-nent provide an appropriate margin to the lower bound limit theload.

The designer has the responsibly to qualify the methods, mod-els, and assumptions used in the analysis. This qualification is tobe stated in the “Certification Holder” documentation. The use ofthe general structural analysis tools based on equilibrium, com-patibility, and linear elastic materials are accepted as qualifiedmethods. This implies that the accepted deformations are small,that the structural response is predominately elastic, and that theinternal stresses remain in equilibrium with external forces.

The Criteria document also establishes that the Tresca failureor strength criterion be used to deal with multi-axial stress states.It was generally accepted then and so today that the von Misescriterion is more accurate than the Tresca criterion. However, theTresca criterion was selected for the Code because it is a little betmore conservative, it is easier to apply, and offers some advan-tages in fatigue analysis.

Today the situation is different in that virtually all computercodes use the von Mises yield criterion as the bases for the elas-tic-plastic algorithms used in the programs. One of the reasons forthis is that the normal to the yield surface is unique at all pointson the surface for von Mises whereas it is not in the Tresca due tothe presence of sharp corners in the Tresca yield surface.However, Tresca still affords advantages in evaluating present dayunderstanding of fatigue damage mechanisms still as will be dis-cussed later.

Stating these ideas seems obvious but it does provide the basicprogression of analysis methods that have historically followedcompliance of fundamental strength of materials methods asallowed by computational capability. In the 1960’s and earlier,structural analysis was based on formulas derived from beam the-ory, theory of plates and shells, and linear elastic materials. Thesemethods combined in what is known as “discontinuity analysis”provided these early designers sufficient stress analysis capabilityto show compliance with the Code allowable stress limits. Themethod became an industry standard as computer technologyadvanced to the point that structural analysis software packages

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 6

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 7

using various beam, plate and shell elements were widely avail-able. Still, to implement discontinuity analysis methods requiredmany simplifying engineering assumptions on geometry, bound-ary conditions, and materials to setup a complete pressure vesseland piping thermal-structural analyses.

During the 1990’s significant advances were made in the soft-ware packages implementing Finite Element Analysis (FEA)methods based on solid element formulations. This method makespossible elastic and elastic-plastic (EP) solutions of three-dimen-sional (3D) general continuum thermal structural analysis widelyavailable. With sufficient computer capability, the 3D FEAmethod relieves the structural analyst from making many of thesimply fining assumptions necessary to complete a discontinuityanalysis. Assumptions regarding stress concentrations due to pen-etrations, friction boundary conditions, 3D load effects, and amyriad of other structural and loading features that here-to-forerequired simplified techniques are now being considered.

Today, very fast computers with large data storage capabilityare available at the desktop of virtually every engineer. This low-cost, very high powered computing capability along withimproved geometric and boundary value modeling tools has madeFEA computer programs the standard tool for structural analysis.It is becoming so simple to use that handbook stress formulas tra-ditionally the standard in the past are now relegated to checkingtools for the FEA results. It turns out that FEA is rapidly becom-ing simpler, easier, faster, and less error prone than making a sim-plifying assumption, looking up a formula, and running a solu-tion.

Section 6.3.1 provides a brief history of development the Codeanalytic tools. Subsequent sections discuss use of elastic 3D FEAresults and application of EP-FEA as it is emerging as an alternatemethod to meet the intent of the structural design limits of theCode.

6.3.1 Analysis Methods As discussed above, when Section III was first released in 1963

the discontinuity method was the most common method used forstress analysis. This method is still part of Subsection NB asAppendix A, Article 6000 (Discontinuity Stresses). A-6110,Scope, states the following:

Pressure vessels usually contain regions where abruptchanges in geometry, material, or loading occur. Theseregions are known as discontinuity areas and the stressesassociated with them are known as discontinuity stresses. Thediscontinuity stresses are required to satisfy the compatibilityof deformations of these regions.

The preceding paragraph, combined with the equations ofNB3324, Tentative Pressure Thickness ensures that all of the pri-mary stress limits and the primary plus secondary stress limits areadequately addressed. Even though many plant components usedin the nuclear industry are thick and involve complicated 3Dgeometries, the accuracy of discontinuity analysis was consideredadequate for Section III stress limits. Because the discontinuitymethod is still a part of Subsection NB, it is still considered ade-quate. It was expected then and is expected now that any non-conservative inaccuracy in the discontinuity method is covered bythe design margins.

Today, the FEA has become the standard method of choice.There are many excellent finite element analysis (FEA) computerprograms. ABAQUS [19], ANSYS [18], MARC[20], and

NASTRAN[21] are samples of commercially available programs.The ASME has short courses available on use of FEA in pressurevessel and piping design, References [x-z]. This very active com-mercial world-wide business in FEA software development coupledwith the high-speed computers has made FEA available on everydesigner’s desktop and has dramatically changed pressure vesseland piping design practices. Those calculations that were impossi-ble a few years ago are now routine. However, the basic output of asolid element FEA program is stress or strain at a point in the struc-ture and not what are called stress resultants computed from forcesand moments available from beam, plate, and shell elements.

The difficulty with application of the FEA result of stress-at-a-point to assess a pressure vessel to the Section III subsectionNB rules is that NB is written in terms of beam, plate, and shellstress results. The membrane and membrane-plus-bending desig-nations used throughout NB are based on membrane and bendingstress resultants. In solid-element FEA results there is no conceptof primary stress, secondary stress, membrane, or bending stress.To couch the FEA results in terms of the current Code allowablestress limits requires what is called post-processing and itinvolves a process called stress-linearization.

The 2007 edition of Section III NB does not have a codifiedversion of stress linearization while the 2007 version of SectionVIII Div 2 does. Section 6.3.2 and 6.3.3 provides a discussion and6.3.3 provide guidelines for using Section VIII Div 2 rules con-tained in Annex 5.A: Linearization of Stress Results for StressClassification. Section 6.3.4 discusses use of elastic-plastic FEA(EP-FEA) for the satisfaction of stress limits in NB.

It is interesting that the design margins built into the Codestress limits are considered in part to deal with the analytic inac-curacies of the stress analysis methods. As mentioned above thesemargins were determined in 1963 when NB was written. A solidelement 3D FEA model is usually considered more accurate thana discontinuity analysis yet the design margins have not beenadjusted to reflect this anticipated increase in accuracy. The inher-ent analysis assumptions that is not addressed by FEA is theapplicability of elastic analysis and the fundamental assumptionsregarding material homogeneity, isotropy, failure criteria, geome-try assumptions based on manufacturing tolerances, thermalboundary conditions and the like. The FEA model is based on allof these assumptions and although the solution for the problemdefined might be more accurate, it must be recognized that theproblem definition is a significant source of error that is coveredby the required margins built into the Code stress limits.

6.3.2 Use of the FEA As mentioned above, there are many FEA programs available

today and they all have their strengths and weaknesses. The deci-sion on which program to use is often made by availability ratherthan capability as all programs today are very good. The first stepin choosing a program is to determine the purpose of the analysisand then pick the program that is designed to solve that problem.For example, a program that is intended to compute a limit-load isnot appropriate for use in solving a buckling problem. Many ofFEA programs are multi-purposed and have libraries of elementsto choose from that perform well for certain jobs. For that reasonmost analysts become more comfortable with one particularmulti-purpose FEA program and will use their preference for allof their analyses if possible. It must be kept in mind that it is theuser’s responsibility to demonstrate that the methods, models, andassumptions used are qualified for the design analysis at hand.When using a multi-purpose FEA code, that involves justifying

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 7

8 • Chapter 6

the choice of element from the library of elements that is mostappropriate for the failure mode being evaluated. With that caveat,it is acceptable to use any verified FEA program to show compli-ance with Code design requirements.

The second issue concerns development of the FEA model.FEA results are sensitive to finite element type, mesh placement,and mesh refinement. Solid element FEM application focuses onaccurate modeling of the geometry and loading. The tendency isto use the most accurate element types and apply a high refine-ment of those types in the controlling areas. Numerical problemsoften occur when using nonrectangular elements or elements hav-ing high-aspect ratios (length-to-width ratio), the latter tending tooccur at discontinuities and notches. These types of meshes candecrease the accuracy of the stresses, depending on the severity ofthe element distortion from rectangular or the element type itself.The modeling for shell elements has the same issues, the focus ofwhich is still refinement in the controlling areas and aspect ratios.However, controlling areas and aspect ratios are not as critical asthey are for solid elements. Most companies who do design (pri-marily the Code Stampholders) run test cases to determine theaccuracy of the various element types to determine their refine-ment and aspect ratio requirements.

FEA methods are numerical and all have inaccuracies that mustbe understood and minimized. The first step in modeling is todetermine those regions where high stress or strain gradients areexpected and if accurate solutions are needed in that area. If thearea is such that the geometry cannot be controlled by manufac-turing difficulties (e.g., uncontrolled weld surface) then approxi-mations need to be made. The FEA model should be developedwith the controlling features in mind so that the mesh can be con-centrated as necessary depending on the failure mode in question.Oftentimes, analysts will generate the model before making goodestimates of the controlling location and the accuracy required.This approach often causes a decrease in accuracy, but it also mayincrease the model size (i.e., the number of elements), whichcauses an increase in analysis time and cost and sometimes makesassessing potential errors difficult.

Modeling for evaluating fatigue is significantly different frommodeling for primary stress. Primary stress evaluations are aimedat obtaining the burst pressure or plastic collapse of a structure.Such failure modes are governed by limit load analysis and rela-tively crude meshes are required as one is seeking a stress distrib-ution where the stresses are below yield and in equilibrium withexternal forces. Fatigue analysis on the other hand is seeking thehistory of the strain that is converted to alternating pseudo-stressat each point in the body since the fatigue damage model used inthe Cod is based on alternating strain at a point. Evaluating strainat notches and for nonlinear thermal gradients such as a thermalshock can be very difficult requiring highly refined meshes. Theappropriate refinement depends on the severity of the notch or thethermal gradient, which must be studied to determine if the refine-ment is sufficient for the accuracy required.

Modeling for EP analysis is not any different than modeling forelastic analysis except that greater refinements may be necessaryfor the same level of accuracy—an increase in refinement is not amajor difference when the analysis is for primary applied loads.However, for fatigue, the difference in refinement can be signifi-cant, depending on the geometry. It is important to consider thatalternating strain converted to alternating pseudo-stress at eachpoint is the appropriate FEA output for assessing fatigue whetherEP or elastic analysis is used. Section 6.6 discusses Code fatiguerules and how FEA can be used for that assessment.

6.3.3 Guidelines for FEA The 2007 edition of Sc VIII Div 2 gives guidelines for using

the results of solid-element FEA results to assess Code structuraldesign limits. The first paper published on linearization methodswas by Gordon [12]. Since then there have been several papersincluding a study within the Pressure Vessel Research Council(PVRC) to develop a consistent set of guidelines. The studyproduced two PVRC reports: the Phase 1 Report, “ThreeDimensional Stress Criteria,” in 1991 [2] and the Phase 2 Report,“PVRC 3D Stress Criteria, Guidelines for Application,” in 1997[3]. Finally, a combined report was issued in 1999 as the WeldingResearch Council (WRC) Bulletin 429 (WRC-B 429), entitled“3D Stress Criteria Guidelines for Application” [4].

Short courses supported by the ASME and presented in pastASME PVP Conferences are of interest. Kalnins and Reinhardt[15] and Gordon and Sauve [23] are two examples. The B&PVCode Committee Subgroup on Design Analysis sponsored anactivity that developed linearization methods and guidelines thatbuilt on the procedures and guidelines provided in WRC-429. Therecommended guidelines published in the 2007 Section VIII Div2 Annex 5.A are based on all of this work.

It is important to recognize that there are two aspects ofassessing Code stress limits; stress classification and categoriza-tion. In Code language, classification usually refers to rules forconstructions such as Class 1 or Class 2 items. These are definedin NCA-2000. NB stress limits apply to Class 1 construction.However, in evaluation of stress limits, classification refers todetermining membrane and bending stress components and cate-gorizing them as primary or secondary. Stress ClassificationLines are lines through a structure over which membrane andbending stresses are evaluated. Stress linearization cannot deter-mine if a membrane or bending stress is in the primary or sec-ondary stress category. An analyst must determine that fromother considerations. The following guidelines provide some ofthese considerations.

There are certain basic ideas that must be considered beforeFEA models are developed and before the results of the models areprocessed. Sections 6.3.3.1`through 6.3.3.5 set the background forthe stress-linearization methods discussed in Section 6.3.3.6. Theseguidelines and considerations are taken from the 2007 Section VIIIDiv 2 Annex 5.A.

6.3.3.1 Guideline 1: Analysis for Purpose The intent of anyanalysis and especially FEA is to evaluate specific failure modesrepresenting a threat to structural performance of the design. TheCode provides protection agains burst or rupture by the generalprimary membrane stress (Pm), gross deformation by the primarylocal stress (PL), plastic collapse by the primary-plus-bendingstress (PL � Pb), and cyclic failures by the primary-plus-secondarystress range (P � Q) and fatigue. An FEA model should be gener-ated to provide accurate membrane and bending stresses to evaluatePm, Pl, Pb and (P � Q) stresses. Fatigue analysis requires accuratelocal or peak stresses. Membrane and bending stresses areobtained from FEA by linearization of the stress distributions cal-culated by solid-element FEA.

6.3.3.2 Guideline 2: Calculating Primary ComponentStresses For most pressure vessel and piping components, generalprimary membrane stress, Pm, can be adequately evaluated usingCode-provided equations basd on discontinuity analysis. FEA withstress linearization can be used but separating primary from sec-ondary is difficult when on total stress is known. For shell cross

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 8

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 9

sections, a simple equation (e.g., P/A or 6M/t2) is usually adequate.Elastic FEA is an appropriate tool for calculating PL, PL Pb, and P � Q when instructural elements such as beams, plates, andshells can be isolated using strength of materials, free-body dia-gram methods. This is typically very hard to do with thick 3Dstructures such as thick nozzles. In these case, a limit load analy-sis is most appropriate for primary assessment using a EP-FEAcode with an elastic perfectly plastic stress-strain curve. Thestrength parameter for the EP-FEA analysis should be Sm.

6.3.3.3 Guideline 3: Definition of Stress Classification Lines(SCL) and Planes (SCP) SCLs and SCPs are used to represent thebreak-points for free-body diagrams in a discontinuity analysis. In3D FEA applications they are used as lines or planes through thestructure where the membrane and bending stresses are needed forPm, PL, PL � Pb, and P � Q evaluations. This guideline defines theSCL and SCP and the basis for their application, as well as therules for calculating membrane and bending stresses. The basicidea of stress classification is to identify stress resultants whenmultiplied by the appropriate section modulus (e.g., area or c/I)gives a force or moment on the section. An SCL is intended to rep-resent a plane over which a stress resultant per unit depth producesa force or moment that produces equilibrium on a cross-section. In3D structures, appropriate SCPs are often hard to identify and sousually SCLs are used in design analysis. The stress distribution ofa typical SCL is shown in Fig. 6.1; from this stress distribution,membrane and bending stresses are developed. Figure 6.2 is usedto define the SCL.

6.3.3.4 Guideline 4: Gross Structural Discontinuity LocationFor Primary Stress Evaluation. SCLs for primary membrandand membrane-plus-bending stresses are typically located at grossstructural discontinuities. Gross structural-discontinuity loca-tions are those for which the failure modes of burst and gross dis-tortion (Pm) and/or plastic collapse (PL � Pb) are likely to occur.

FIG. 6.1 COMPONENT STRESS DISTRIBUTION ALONGTHE SCL [4]

FIG. 6.2 DEFINING THE SCL

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 9

10 • Chapter 6

A gross structural discontinuity may be at the juncture of twobasic structural features such as a pipe and a nozzle for whichequilibrium cannot be achieved if the juncture would fail or grosslydeform. For example, an SCL for primary stress evaluation is notintended to pass through the crotch of the nozzle as equilibriumwould be maintained by adjacent material. These SCLs are alsoused to evaluse PL as that failure mode is to prevent gross defor-mations that can only happen at these locations.

6.3.3.5 Guideline 5: Local Structural Discontinuity LocationThe local location addresses the location and orientation of theSCL-SCP through the root of a sharp notch or at the surface of apenetration that may be within a basic structural limit. Local loca-tions are the sites of local failures such as fatigue crack initiationof brittle fracture. These SCLs are used to evaluate P � Q to vali-date fatigue analyses. Often fatigue strength reduction factors andfatigue penalty factors are applied to the linearized stresses at theselocations.

6.3.3.6 Guideline 6: Linearized Stress Definition Linearizedstresses (membrane-plus-bending) are stresses represented by lin-ear distributions which develop the same net forces and momentson a section as the actual stress distribution. The intent is not to useany mathematical procedure to fit a variable to a linear function butrather to compute a stress distribution that is the linear equivalentto the actual stress distribution. The use of equilibrium is the mea-sure used for stress linearization.

The membrane and bending stresses are calculated from thecomponent stresses, not principal stresses. The symbols Pm, PL,Pb, and Q do not represent single quantities but rather sets of sixquantities representing the six stress components Snn, Sll, Stt, tnl, tlt,tnt where n, l, and t are the normal, out-of-plane, and tangent coor-dinates of the SCL or SCP. From these quantities, the principalstresses are calculated and finally the maximum principal stressdifference to compare to the limit. Figure 6.1 is a simplification ofthe concepts presented here. Annex 5.A of Section VIII providesexpanded figures of this process.

6.3.3.7 Guideline 7: Validity of SCLs There is no quantitativebasis upon to base SCL location and orientation. It is up to the ana-lyst to judiciously place the SCL to provide the required result. Ina 3D structure this can be very difficult. Annex 5.A of Section VIIIprovides several guidelines to follow that can help with thisprocess.

(1) For fatigue evaluations, SCLs should be started normal tothe surface where the highest principal stress differencerange exists.

(2) For primary evaluations, SCLs should be placed normal tothe mid-plane of the minimum thickness or at the cross-section where plastic-collapse is suspected.

(3) SCLs should be oriented normal to the contour lines of thestress component of highest magnitude. This is typicallyonly possible at a few points across a SCL as the principalstress directions rotate with position. Starting the SCL nor-mal to the surface location where the largest principal stressexists is a good start.

(4) The normal stresses should be monotonically increasing ordecreasing along the cutline. This is often not possible forSCLs at local structural discontinuity locations.

(5) The tnt should be parabolic. This will not be possible if theSCL is not normal to both surfaces and the mid-plane.

However, if the distribution is significantly non-parabolic,then the SCL is probably not valid.

6.3.3.8 Guideline 8: Calculating Principal Stresses, StressIntensities, and Ranges Principal stresses are calculated usinglinearized component stresses—that is, based on component (Sij)membrane and bending stresses. All six component stresses areused for calculating membrane principal stresses. For bending,only two of the component stresses are used; there is no shear“bending stress” as well as no through-thickness “bending stress.”For P � Q, ranges of stress component from which principal stressdifference ranges are computed. Section VIII Division 2 Annex5.A provides for both a stress-based linearization process andprocess based on nodal point forces. Whenever possible, SCLshould be oriented along node lines and the nodal force balancemethod used for stress linearization. Annex 5.A also presents thestructural stress method of Dong (zzz) for a method to use withweldments. It is very important that the mesh be set-up correctlyfor this method to be effective.

6.3.3.9 Guideline 9: Stress Classification Lines and PlanesUse of the SCL for evaluation of membrane and bending stresses(for the PL � Pb and P � Q elastic limits) is appropriate for mostgeometries, especially shell geometries that are analyzed asaxisymmetric. Some particular geometries are conducive to use ofthe SCP. The example geometries include actual (readily defined)planes for stress classification. Thus, the use of SCP is appropriatewhen the geometry has a well-defined plane that can be directlyrelated to the failure mode of loss-of-equilibrium or gross defor-mation if yielding would occur.

6.3.3.10 Guideline 10: Application of the FEA This guidelineincludes the following six fundamental applications:

(1) The modeling techniques must be adequate for the level ofaccuracy needed for the stresses to be computed as accu-rately as needed for the application.

(2) The location of any nodes needed for the postprocessor todefine the start and end of the SCL is important. The FEAnodes must be suitably located at the controlling locations(i.e., at the discontinuity of fatigue limiting location).

(3) An SCL or SCP may originate or end at a singularitybecause the integration of the loads along the line or on theplane based on equilibrium and thus accounts the stress dis-tribution including the singularity.

(4) The use of FEA to evaluate primary stresses at discontinu-ities can result in significant secondary stresses being con-sidered primary. An equilibrium or limit-load type of analy-sis is likely to produce more accurate results.

(5) It is not necessary to evaluate “every location” just becausestresses are computed there. It is important for the analystto focus on the failure locations based on the flow of thestresses or load bearing cross-sections.

(6) Contour plots of von Mises stress are useful in identifyinglocations of potentially high fatigue usage factors. SCLsshould be placed through these locations.

(7) EP-FEA limit load analysis can be very useful to identifycritical SCLs as it clearly identifies the limit locations forprimary stress. A EP-FEA model using a realistic cyclicstress strain curve can also help identify deformation limit-ing locations as well as location where fatigue issues arelikely to occur.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 10

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 11

6.4 PRIMARY STRESS LIMITS

This section presents a discussion of the intent of the primarystress limits in the Code. Consideration is given to the definitionsin the Code and the discussion in the Criteria document. The dis-cussion is provided in the context of EP-FEA and limit-load capa-bilities now available to the analyst.

6.4.1 Code and Criteria Primary Stress Definitions As defined in NB-3213.8 (Primary Stress),

Primary stress is any normal stress or a shear stress devel-oped by an imposed loading which is necessary to satisfy thelaws of equilibrium of external and internal forces andmo-ments. The basic characteristic of a primary stress is that it isnot self-limiting. Primary stresses which considerablyexceed the yield strength will result in failure, or at leastingross distortion.

Primary stresses result from an applied mechanical load, suchas a pressure load. Equilibrium occurs when the applied (external)load is balanced within the material (internal). The judgment ofhaving reached equilibrium is based on a single (monotonic) load-ing condition and a lowerbound limit load. The Code rules arebased on a maximum load that, if exceeded, will result in failure.The “gross distortion” is defined as the failure mode in thepreceding definition. Thus, primary stresses are limited to a maxi-mum load; the maximum stress caused by the maximum load isthe yield stress. Exceeding the limit load (using limit load analy-sis) causes gross deformation, noted as “not self-limited” in thedefinition.

The self-limiting concept relates to deformation-controlledstrain rather than load-controlled strain. The self-limiting strainrelates to plasticity-produced deformation—that is, the appliedload causes plasticity and produces a specific deformation orstrain rather than a specific equilibrium stress. For example, athermal (load) gradient produces strains that are controlled by adeformation. When the deformation is reached, the load has beenbalanced. For cyclic conditions, the self-limiting condition willproduce a hysteresis loop for the loading and unloading condition.Assuming that nonhardening materials are used, the non-self-limiting condition produces collapse or ratchet (assumingthat cycling occurs). For cyclic-hardened materials, the elasticstress will increase until equilibrium is reached. The primarystress definition, however, is based on perfect-plasticity (i.e., nohardening), which is appropriate when the rules are being appliedto both cyclic-hardening and -softening materials.

The NB-3213.8 definition continues by stating the following:“A general primary membrane stress is one which is so distributedin the structure that no redistribution of the load occurs as a resultof yielding.” This phrase separates the failure modes for generalmembrane stress from local membrane stress. It thus relegatesgross distortion to general primary stress (no redistribution) andexcessive plastic deformation to local primary membrane stress(redistribution of load).

The Criteria document expands one’s understanding with thefollowing statement:

In a structure as simple as a straight bar in tension, a load-producing yield stress, Sy, results in “collapse.” If the bar isloaded in bending, collapse does not occur until the load hasbeen increased by a factor known as the “shape factor” of the

cross section; at that time a “plastic hinge” is formed. . . .When the primary stress in a rectangular section consists of acombination of bending and axial tension, the value of thelimit load depends on the ratio between the tensile and bend-ing loads.

The Criteria document uses the term collapse as the failuremechanism. Combining the Criteria definition with the NB-3213.8definition, the intent is to preclude collapse from occur-ring fromgeneral primary membrane-plus-bending stress (Pm � Pb) and canbe interpreted as failure by exceeding the ultimate strength orwhen perfect-plasticity is assumed (a plastic modulus of zero) asfailure by gross plastic deformation because the yield strength isexceeded. However, it is relating general primary membranestress and primary bending stress (Pm � Pb) to plastic collapse orrelating to the maximum allowable mechanical load. Combiningthe Criteria definition with the NB-3213.8 definition can alsorelate to a redistribution condition, the intent of which is to pre-clude excessive plastic deformation from occurring because oflocal primary membrane-plus-bending stresses (PL � Pb).

A recent JPVT paper [5], developed within the Code Subgroupon Design Analysis, defines primary stress as the following:

Primary stresses are those that can cause ductile rupture or acomplete loss of load-carrying capability due to plastic col-lapse of the structure upon a single application of load. Thepurpose of the Code limits on primary stress is to preventgross plastic deformation and to provide a nominal factor ofsafety on the ductile burst pressure.

This definition is consistent with the Code and Criteriadefinitions and extends the understanding of the mechanism forfailure conditions to “ductile rupture” and “plastic collapse.” Thegross plastic deformation as the failure mode is maintained, but italso adds the concept of ductile burst. The following paragraphdiscusses the differences between the two failure conditions.

The three terms applied to failure are burst, collapse (grossplastic deformation), and excessive plastic deformation. The termburst should be interpreted to mean a separation of the materialfrom a single-load application—for example, the bursting of aballoon. Pressure vessel failures have occurred from burst primar-ily during hydrotest or after many years of operation. All of thesefailures resulted from a condition that was not included in thedesign analysis, such as cracks caused by fatigue, the environ-ment, or degraded material properties. Thus, the design marginfor burst is not directly related to design analysis. In addition, thedesign margin relates to experience, and the burst failure moderelates to the ultimate tensile stress.

Historically, the Code has undergone reductions of the designmargin for burst failures. In the past, and for certain types of ves-sels, the design margin was a factor of 5 on the ultimate tensilestress. During World War II, however, the design margin wasreduced to 4 to reduce the amount of steel used in production andalso because experience indicated that the design margin of 5 wasoverly conservative. Recently, the design margin for Section VIII,Division 1, was reduced to 3.5—again based on the excellentexperience of operating vessels. Thus, the design margin on theultimate tensile stress is based on experience.

Reductions in design margins are also justifiable for hydrotest.The purpose of hydrotest is to ensure that the vessel has been con-structed without major errors in, for example, its design, material,welding, and NDE. Hydrotest failures have occurred, but their

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 11

12 • Chapter 6

cause can be defined and shown as related to major errors indesign or construction. Similarly, burst failures that occur aftermany years of operation are not related to the design and con-struction requirements of the Code. However, because such burstfailures are normally related to undefined operating conditions,construction errors can be their cause. The burst failure mode islogically related to experience; consequently, the design andanalysis requirements of the Code do not address the burst failuremode except for the requirement that design margins be based onultimate tensile strength.

The following criteria are presented for primary membrane andbending stress:

(1) bursting relates to major operating damage not defined inthe construction process and considered by applying adesign margin to the ultimate tensile stress;

(2) the design margin for the ultimate tensile stress is based onexperience;

(3) the failure mode related to the ultimate tensile stress can berupture or collapse;

(4) limit load theory controls the allowable load when theallowable stress is based on the yield strength;

(5) failure modes constitute gross (large area) or excessive(redistribution) plastic deformation when failure is basedon the yield strength; and

(6) using both the ultimate tensile strength and the yieldstrength to establish the allowable stress precludes grossplastic deformation, collapse, and burst.

6.4.2 Basis for Primary Stress Requirements Based on the definitions discussed previously, the general pri-

mary membrane stress-plus-primary bending stress (Pm � Pb)limits relate to the lesser of the ultimate tensile stress or theyield stress. The local primary membrane stress-plus-primarybending stress (PL � Pb) relate only to the yield strength. Thefailure modes are as follows: burst, collapse, gross plastic defor-mation, and excessive plastic deformation. The intent for thedesign margin is to ensure elastic behavior or applying a designmargin that ensures elastic behavior. Page 10 of the Criteriastates the following:

Nevertheless, unless stated specifically otherwise, it isexpected that calculations be made on the assumption of elas-tic behavior.

Therefore, the limits for the primary stresses, Pm, Pb, PL � Pb,are set to ensure elastic behavior.

Elastic behavior is ensured by precluding through thicknessyielding. Page 5 of the Criteria states the following:

If a primary stress exceeds the yield strength of the materialthrough the entire thickness, the prevention of failure isentirely dependent on the strain-hardening properties of thematerial.

As used by the Code, materials will strain harden for a singleapplication, causing permanent plastic deformation and strain,and is considered unacceptable for across-the-board design whencyclic conditions occur and if the material is undefined.Adjustments are made for specific materials known to have a highlevel of strain hardening, such as stress limits for stainless steelsthat allow strain hardening.

In support of using both yield and ultimate strength in estab-lishing stress limits, page 9 of the Criteria states the following:

In assigning allowable stress values to a variety of materialswith wide varying ductilities and widely varying strain-hardening properties, the yield strength alone is not asufficient criterion. In order to prevent unsafe designs inmaterials with low ductility and in materials with high yield-to-tensile ratios, the Code has always considered both theyield strength and the ultimate tensile strength in assigningallowable stresses.

The focus of the Criteria is to ensure that materials with lowductility have an allowable stress limit less than the yield stress(with the design margin). When Section III was initiated, almostall of the materials with high yield-to-tensile (ultimate strength)ratios had low ductility. Since then, however, materials with highyield-to-tensile ratios have been developed to have high levels ofductility. The intent still applies—that is, low ductility materialsneed allowable stresses that are less than those based on the yieldstress—but to ensure safety the focus is to base the allowablestresses on the yield strength.

The basic allowable stress is Sm; for ferritic materials, this is thelesser of one-third of the ultimate tensile strength or two-thirds ofthe yield strength (austenitic have a different criteria that are dis-cussed later in this chapter). The design margin is established as 1.5for (Pm � Pb). Page 7 of the Criteria shows a figure (Fig. 2, DesignMargin for Pm � Pb; given here as Fig. 6.3) and states the following:

FIG. 6.3 DESIGN MARGIN FOR PM � PB

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 12

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 13

Figure 2 was used to choose allowable values, in terms of theyield stress for general primary membrane stress, Pm, and pri-mary membrane-plus-bending stress, Pm � Pb. It may be seenthat limiting Pm to ( ) Sy and Pm � Pb to Sy provides adequatesafety. The safety factor is not constant for all combinationsof tension and bending, but a design rule to provide a uniformsafety factor would be needlessly complicated.

Figure 6.1 is a classical approach to defining through-thicknessyielding. The “design limits” shown in the figure have been main-tained for design (Level A) and, by default, service limits (Level B).(See NCA-2142.4 for “Levels.”) The design limits are reduced forLevels C and D.

As discussed previously, the local primary membrane stress(PL) differs from the general primary membrane stress in thatlocal membrane stress produces load redistribution, whereas thegeneral membrane stress does not have this capability. Page 5 ofthe Criteria states the following:

It (local primary membrane stress) is self-limiting and whenit exceeds yield, the external load will be resisted by otherparts of the structure, but this shift may involve intolerabledistortion. . . .

Thus, the PL � Pb is considered to be primary. Because of theability to redistribute the applied load, the stress limit is set as theyield strength—1.5Sm. It is noted that the primary bending stress(Pb) limit is 1.5Sm. which is the same as PL. These limits are read-ily verified by limit load (plastic) analysis. Using a geometry andloading where PL controls, the limit load will be about 1.5 greaterthan the yield strength—that is, 1.5Sm. Therefore, the design mar-gin for PL � Pb is 1.5 with the acceptance of minor permanentdeformation.

Austenitic materials substantially strain harden for both monot-onic and cyclic loading. Consequently, the austenitic materialswill not ratchet after a few cycles. Page 9 of the Criteria states thefollowing:

These materials have no well-defined yield point but havestrong strain-hardening capabilities so that their yieldstrength is effectively raised as they are highly loaded. Thismeans that some permanent deformation during the first load-ing cycle may occur; however, the basic structural integrity iscomparable to that obtained with ferritic materials.

The allowable basic stress (Sm) for austenitic material thereforehas a somewhat different definition than discussed previously forferritic materials. The basic allowable limit (Sm) changes its valuewith temperature: up to 100�F, two-thirds of the nominal yieldstrength controls, but above 100�F, Sm may increase to 0.9Sy butnot exceed the Sm value at 100�F. It is noted that for austeniticmaterial, by using Sy as the maximum stress, a limit load analysisgives a lower allowable load than the current Code rules produce.

6.4.3 Calculations for Limits NB-3214 (Stress Analysis) defines the required analyses and

states the following:

A detailed stress analysis of all major structural componentsshall be prepared in sufficient detail to show that each of thestress limitations of NB-3220 (Stress Limits for Other thanBolts) and NB-3230 (Stress Limits for Bolts) is satisfied

23

when the component is subjected to the loading of NB-3110(Loading Criteria).

The level of stress analysis is therefore substantial, the effort ofwhich may appear to be enormous. However, the original NBattempted to simplify this level of effort; NB-3214 states thefollowing:

As an aid to the evaluation of these stresses, formulas andmethods for the solution of certain recurring problems havebeen placed in Appendix A.

Effectively applying these formulas and methods requires studyand the development of some simple procedures, after which therequired effort becomes rather simple. These “formulas and meth-ods” relate to an interaction or to discontinuity-type analyses,whereas the FEM is the common approach for analyses. From thisperspective, most of Appendix A is not relevant to today’s analy-ses. To effectively use FEM for developing additional procedures,the analyst must study the FEA theories and methods.

The limits that are required for Pm, PL, and Pb in the designeffort are presented in Fig. NB-3221-1 (Stress Categories andLimits of Intensity for Design Conditions), given here as Fig. 6.4.Note (2) of the original figure states the following:

The symbols Pm, PL, and Pb do not represent single quantities,but rather sets of six quantities representing the six stresscomponents st, sl, sr, tlt, tlr, and trt.

This note can be somewhat misleading, as it can be taken out ofcontext. The failure theories are all based on the shear theory of fail-ure, sometimes referred to as Tresca theory, so the limits on stresses(Pm, PL, and Pb) are based on the maximum shear stress. Calculatingthe maximum shear stress starts with the six (membrane and bend-ing) component stresses that are used to calculate the three principalstresses, which in turn are used to calculate the three stress differ-ences. The maximum of the three stress differences is designated asthe stress intensity discussed in more detail in Section 6.4.4.

NB-3300 (Vessel Design) gives several rules on design, two ofwhich involve analyses. The first one, NB-3324 (Tentative PressureThickness), is discussed here; the second, NB-3330 (Openings andReinforcement), is discussed later. NB-3324 states the following:

The following formulas are given as an aid to the designer fordetermining a tentative thickness for use in the design. Theyare not to be construed as formulas for acceptable thickness-es. However, except in local regions (NB-3221.2), the wall-thickness of a vessel shall never be less than that obtainedfrom the formulas in NB-3324.1 and NB3324.2. . . .

The third sentence of the preceding definition clearly requiresthat the equations define the minimum thickness for cylindricalshells (NB-3324.1) and spherical shells (NB-3324.2). In addition,it also allows a reduction to the minimum thickness for local areas(NB-3221.2) that relate to PL. The NB-3324 equations are consis-tent with Pm requirements); in fact, the equations can be rewrittenfor solving for the stress intensity (Pm) by replacing Sm with Pm,and also for a given thickness (t). For example, the equation forthe cylinder becomes the following:

Pm � (PR/t) � 0.5P (6.1)

where

P � design pressure R � inside radius

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 13

14 • Chapter 6

Based on the Code equations, it is therefore mandatory that Pm

be met except in defined local areas. This requirement cannot beoverridden by plastic analysis (discussed later).

The NB-3330 (Openings and Reinforcement) rules are notmandatory in the sense that the designer can use these rules or perform an analysis that shows that all stress limits are met.NB-3331 (a), under General Requirements for Openings, statesthe following:

For vessels or parts thereof which meet the requirements ofNB-3222.4(d) (Analysis for Cyclic Operation, ComponentsNot Requiring Analysis for Cyclic Service), analysis showingsatisfaction of the requirements of NB-3221.1, NB-3221.2,NB-3221.3, and NB-3222.2 in the immediate vicinity of theopenings is not required for pressure loading if the rules ofNB-3330 are met.

By rewording it backwards, NB-3331(a) states that analysis isnot required for Pm (NB-3221.1), PL (NB-3221.2), PL � Pb

(NB-3221.3) and P � Q (NB-3222.2) if the fatigue life is accept-able based on the simplified fatigue analysis [NB-3222.4(d)].

NB-3331(b) extends this fact by not requiring analysis for Pm, PL,and PL � Pb if NB-3330 is applied, even if the simplified fatigueanalysis is not met. NB-3331(b) also allows deletion of analysisfor P � Q if additional checks are met. The use of NB-3330 over-rides the analysis for primary stress limits and also for P � Q lim-its if additional checks are met.

Reversing the requirement, NB-3331(c) allows the full analysisto override the use of NB-3330. It states that “if it is shown byanalysis that all the stress requirements have been met, the rulesof NB-3330 are waived.” Thus, the designer has the option to usea full analysis or the NB-3330 procedures.

Currently, the FEM is the common tool for analysis related toPL and PL � Pb requirements. The failure mode is excessive plas-tic deformation, and the controlling stress is expected to occur inthe vicinity of a discontinuity. For all mechanical loads, the mem-brane stress is considered the primary stress. For the majority ofgeometries and loads, however, the bending stress is consideredthe secondary stress, examples of which are presented in TableNB-3217.1 (Classification of Stress Intensity in Vessels for SomeTypical Cases), given here as Fig. 6.5. In general, bending stressesare primary when the moment is applied to the total section—for

FIG. 6.4 HOPPER DIAGRAM FOR LIMITS ON PM, PL AND PB (Source: Fig. NB-3221-1, Subsection NB of the ASME B&PV Code)

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 14

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 15

example, the whole cylinder or a flat plate. Table NB-3217.1 pre-sents the following two considerations for bending that is consid-ered primary when it is expected to be secondary:

(1) What geometries require the bending stress to be treated asprimary stress?

(2) What is the accuracy of the approach or uncommon geome-tries?

Note (2) of the aforementioned table is an example of when thebending stress must be considered primary stress rather than theexpected secondary designation. Note (2) states the following:

If the bending moment at the edge is required to maintain thebending stress in the middle to acceptable limits, the edgebending is classified as Pb. Otherwise, it is classified a Q.

Note (2) generally applies to the juncture of a shell to flat-head or flange, but may include other geometries. In subsectione. Examples, the shell to flat-head geometry is discussed indetail.

The concept that the membrane stress is primary and the bend-ing stress is secondary is a simplification, for the reality is that themajority of the membrane stress is primary and the majority ofthe bending stress is secondary. The simplification gives accept-able accuracy when the juncture discontinuity is nominal (e.g., acylinder to sphere). As the severity of the discontinuity increases,the accuracy of the simplification decreases (e.g., a cylinder to aflat-head or even a relatively flat-formed–head to cylinder). Whenthe FEA model includes the full geometry (e.g., cylinder and flat-head), the Note (2) “edge” refers to the discontinuity juncture. Thebending stress (or moment) at this juncture automatically reduces

FIG. 6.5 CLASSIFYING STRESSES (Source: Table NB-3217-1, Subsection NB of the ASME B&PV Code)

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 15

16 • Chapter 6

the bending stress at the center of the flat-head. If yielding occursat the discontinuity from the combined membrane and bendingstresses, the bending stress at the center of the flat-head willincrease and may exceed 1.5Sm . Thus, in an elastic analysis, themembrane-plus-bending stress, from FEA, must be limited to1.5Sm, which is the assumed initiation of yielding. This conditioncan be demonstrated by limit load analysis.

The accuracy of the “simplified approach” for uncommongeometries is difficult to assess. The safe way is to assume that allFEA bending stress is in the primary category. If eliminating theunnecessary conservatism is important, the design should bedeveloped by a plastic or limit analysis (NB-3228). Other meth-ods exist for eliminating the unnecessary conservatisms; these areknown as simplified plastic analyses and include the equilibriumanalysis, the generalized local stress–strain method and redistribu-tion nodes, and the elastic compensation method. Some finite ele-ment programs allow adjustment of the boundary conditions atthe discontinuity-to-transfer load, but not for maintaining defor-mation. For the common geometries (e.g., nozzle-to-cylinderjunctures), however, the guidelines given in Table NB-3217.1 areappropriate.

6.4.4 Calculation of Stress Intensity NB-3215 (Derivation of Stress Intensity) presents the

sequence of steps from component stresses to stress intensity.Although the paragraphs include both primary (Pm, PL, or PL � Pb)and primary-plus-secondary (P � Q) stress intensity, the presen-tation focuses on the primary stress intensities (it addresses asingle load). The primary-plus-secondary stress intensity (P � Q)is related to a stress range (it addresses two loadings). The fun-damental steps for determining the stress intensity are appropri-ate to both types of stress intensity, but the P � Q requiresadditional steps (discussed in Section 6.5.2) to account for thestress range.

The Pm, PL, or PL � Pb symbols are developed from componentstresses, the three normal component stresses, and three shearcomponent stresses. These component stresses are membranestresses and/or bending stresses—that is, they represent athrough-thickness (linear) stress distribution, either membrane orbending. (The steps to calculate and apply the membrane andbending stresses are discussed in Section 6.7.4.) The three princi-pal stresses are then developed from the six component stresses,and the three stress differences are developed from the three

FIG. 6.5 (CONTINUED)

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 16

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 17

principal stresses, the maximum of which is defined as the stressintensity—that is, the appropriate of Pm, PL, or PL � Pb.

The following paragraphs discuss key points in the six steps[(a)–(e)] for determining the stress intensity, with quotationstaken directly from NB-3215. However, the reader is advised to review the full paragraph before applying the steps in ananalysis.

(a) At the point on the component which is being investi-gated, choose an orthogonal set of coordinates, such astangential, longitudinal, and radial, and designate them bysubscripts. . . .

The orthogonal coordinates should be consistent with the localgeometry, not a random set and not necessarily the global set. Themembrane and bending stresses are based on a through-thicknessstress distribution, and the coordinates should be consistent withthis, for it is critical for FEA and complex geometries.

(b) Calculate the stress component for each type of loading towhich the part will be subjected, and assign each set of stressvalues to one or a group of the following categories. . . .

The categories are listed as Pm, PL, Pb, Pe, Q, and F. These sixcategories have somewhat different procedures from the othercategories. The Pm should require only the three normal compo-nent stresses, with the calculation based on the applied load, andexcept for specific applied shear (torsion) loads there should beno shear component stress. Both PL and Pb are also expected tobe dominated by the normal component stresses but are likely tohave a component shear stress. However, if there are significantcomponent shear stresses without having an applied torsionload, the coordinate choice is probably the cause and should bereevaluated. The Pe may have both normal and shear componentstresses, including torsion. When the piping enters the vessel atan angle (not perpendicular to the vessel centerline), the stressdistributions can be very complex (including the shear stresses)and extra studying may be required for establishing the appro-priate coordinates. The Q is a subset of P � Q; thus it need notbe considered independent of the primary stresses. The F is astrange term with mixed definitions; the NB states that “NB-3217 provides guidance for this step.” It is called PeakStress and is used in the fatigue analysis. The reference to NB-3217 points to NB-3216 (Derivation of Stress Differences),used in the fatigue rules and that can be used in determining thestress intensity for P � Q. (The fatigue procedure is discussedlater in this chapter.)

(c) For each category, calculate the algebraic sum of the(stress) values. . . .

This is the calculation of the membrane and bending compo-nent stresses. Accomplishing this calculation can be complex; it istherefore addressed in detail in Section 6.7.

(d) Translate the stress components . . . into principal stresses . . . .

There are various routines for this calculation. For axisymmet-ric geometries, the translations are based on the Mohr’s Circleapproach. For three-dimensional conditions, the calculations aremore complex, but procedures are available and have even beenprogrammed for spreadsheets.

(e) Calculate the stress differences. . . . The stress intensity S is the largest absolute value of [the stress differences].

A stress difference is one principal stress minus a secondprincipal stress—that is, Sij � Si � SJ; thus, there are three stressdifferences.

A note to NB-3215 requires that the membrane stress be calcu-lated using the component stress distribution. The bending stressshould also be calculated by the component stress distribution,which is required for thermal stress distribution in a footnote toNB-3213.13 (Thermal Stress). A procedure for this calculation ispresented and discussed in Section 6.7. The NB-3215 note statesthe following:

Membrane stress intensity is derived from the stress componentaveraged across the thickness of the section. The averaging shallbe performed at the component level in (b) and (c) above.

As previously stated, NB uses the maximum shear stress theory(Tresca criterion) for defining the strength theory. Page 3 of theCriteria presents the mathematics used for relating the maximumshear stress to the term stress intensity. It states the following:

The maximum shear stress at a point is defined as one-half ofthe algebraic difference between the largest and the smallestof the three principal stresses. Thus, if the principal stressesare s1, s2, and s3, and s1 � s2 � s3 (algebraically), the max-imun shear stress is ( ) (s1 � s3).

This maximum shear stress can be readily shown by a Mohr’sCircle where the principal stresses are plotted on the stress line(no shear stress), the controlling Mohr’s Circle is based on s1 � s3

(maximum distance along the stress line), and the shear stress isthe radius of the circle—thus ( ) (s1 � s3).

The maximum shear stress theory of failure states that yieldingin a component occurs when the maximum shear stress reachesa value equal to the maximum shear stress at the yield point ina tensile test. In the tensile test, at yield, s1 � Sy, s2 � 0, and s3 � 0; therefore the maximum shear stress is Sy �2. Thereforeyielding in the component occurs when ( ) (s1 � s3) � ( ) Sy.

Combining the two quotes and simplifying the equation, we see that

(S1� S3) � Sy (6.2)

The preceding equation shows one of the three stress differ-ences; the other two are (s3 � s2) and (s2 � s1). The maximumabsolute stress difference is the stress intensity. In conclusion, theCriteria states the following:

In order to avoid the unfamiliar and unnecessary operation ofdividing both the calculated and the allowable stresses by twobefore comparing them, a new term called “equivalent inten-sity of combined stress” or, more briefly, “stress intensity,”has been used. The stress intensity is defined as twice themaximum shear stress and is equal to the largest algebraicdifference between any two of the three principal stresses.Thus the stress intensity is directly comparable to strengthvalues found from tensile tests.

6.4.5 Examples Two examples of primary stress are presented: a cone–cylinder

assembly (Fig. 6.4) and a flat-head attached to a cylinder

12

12

12

12

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 17

18 • Chapter 6

(Fig. 6.6). The cone–cylinder is expected to fail at one of the twodiscontinuities because the PL � Pb limit is exeeded. If the failureoccurs in one of the two cylinders away from the discontinuity, thecause is “exceeding Pm stress limit.” However, the flat-head-cylinderassembly is expected to fail at the center of the flat-head or at theflat-head–cylinder discontinuity rather than in the cylinder awayfrom the discontinuity. Failure at the flat-head center is caused byexceeding the Pb limit, whereas failure at the discontinuity iscaused by exceeding the PL � Pb limit. The following paragraphsdiscuss these two geometries in terms of equilibrium analysis,which is consistent with the Code definition of a primary stress—that is, “to satisfy the laws of equilibrium.”

The cone–cylinder consists of three shells: a large-end cylinder,a small-end cylinder, and a conical shell connecting both cylin-ders (Fig. 6.4). This arrangement generates structural discontinu-ities at both ends of the conical section and the correspondingcylinder end. In a sense, the conical section is a continuous dis-continuity because the hoop (circumferential) and meridional(axial) membrane stresses change along the midplane of the coni-cal section. The conical section as well as the cylinders can besized as free bodies; Figs. 6.6(a) and (b) show two approaches.

The internal forces are caused by pressure on the inside surfacesof the cone and cylinders and axially in the cylinders, assuming aclosed-end geometry. The forces are used to calculate the general

primary membrane stresses (Pm). The hoop (membrane) stresses arecalculated using the following standard equation:

Hoop � PR/(t cos f ) (6.3)

where

P � pressure R � inside radius at the location of interest t � thickness f � cone axis angle

cos f � 1.0 for the cylinders

The meridional stresses must also be calculated. The membranestresses can be calculated using standard equations, an approachthat produces general primary membrane stresses (Pm).

The PL � Pb limits must be met as well. Either of the twoapproaches presented in Figs. 6.4(a) and (b) can be used. Fig. 6.6(a)has no bending in the cylinders, but there is a bending momentproduced in the cone that changes the hoop membrane stresses.Therefore a primary bending stress is to be considered in thegeometry. In Fig. 6.6(b), on the other hand, the bending stress isnoted in the cylinder. The approach presented in Fig. 6.6(b) isnormally more simple and less conservative than the approachpresented in Fig. 6.6(a), but in either approach, the controllinglocation is expected to be in the cone at the small end.

The foregoing discussion is based on equilibrium analyses andis intended to give one a better understanding of the stress types.An FEA can also be used; however, even when the FEA is to beused, the simple equations shown previously should be used toensure that Pm limits are met. The FEA is to be used to demon-strate that the PL � Pb limits are met. It is expected that the PL � Pb stresses will control the design (rather than Pm) and thatthe small end is controlling. When using the FEA, the bendingstresses are considered secondary (or deformation-controlled)stresses—a valid assumption, though it may be nonconservativefor large-cone angles (e.g., greater than 30 deg.) In addition tomeeting the PL � Pb limit (1.5Sm), NB controls the distance overwhich 1.1Sm may occur. NB-3213.10 (Local Primary MembraneStress) states the following:

A stressed region may be considered local if the distance overwhich the membrane stress exceeds 1.1Sm does not extend inthe meridional direction more than 1.0SQRT(Rt) where R isthe minimum mid-surface radius of curvature and t is the min-imum thickness in the region considered.

This is interpreted as requiring the distance to be met in bothdirections, that is, a 1.0SQRT(Rt) distance in both the cone andthe cylinder.

The requirement of 1.0SQRT(Rt) distance in both directionsrelates to the attenuation of the stresses at the juncture. If the shellis very stiff at the juncture of the cone, the full 1.0SQRT(Rt) dis-tance would be required in the cone direction. However, if thecylinder and cone have the same stiffness, a lesser distance in bothdirections would be acceptable, but it is inappropriate to right rulesfor the distance of various geometries because of the complexity ofthe various design options. The appropriate approach is to designby the limit load analysis. The PL � Pb limit (1.5Sm) is directlyrelated to the plastic analysis. The PL allows for redistribution ofthe load, similar to what occurs in the plastic analysis, and when theload reaches the point where there is a through-thickness yieldstress, the load redistributes to the adjacent material and continues

FIG. 6.6 CONE–CYLINDER ASSEMBLY [4]

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 18

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 19

until the plastic zone has increased to its limits (i.e., the plastic zonebecomes a plastic hinge). This process is shown in Fig. 6.7, a sup-port skirt of a simple two-part cylinder loaded axially from the bot-tom in supporting the vessel. Thus, the attenuation rules are appro-priate for any geometry, but the limit load analysis will give a moreaccurate and less conservative design.

The flat-plate example geometry consists of the flat plate andthe shell (e.g., a cylinder) joined by a ring element; a typicalshell–plate assembly is shown in Fig. 6.8. The NB design of a flatplate is controlled by Pb, and all bending stresses in the plate areprimary. Although it must be considered in the analysis, the mem-brane stress in the plate is normally small relative to the bendingstress; thus, the discussion of the primary stresses is focused onthe bending stress. The thickness of the plate is determined by thePm � Pb limit. However, three approaches for calculating the con-trolling primary stresses (Pb) are used:

(1) simply supported–plate model; (2) assembled-geometry model; and (3) intermediate-constraint model.

6.4.5.1 Simply Supported–Plate Model The plate and the ring-plus-cylinder, shown in Fig. 6.9(a), can be sized independently.The plate is supported simply and the applied pressure only pro-duces bending stresses (hoop and radial), which are Pb. The ringshell can be analyzed as a single element or separated into two ele-ments. Assuming the single-element approach is used, the cylinderhas Pm away from the ring and PL (at the ring juncture); the bend-ing stress at the ring juncture is a secondary stress (Q). The load ispressure on the cylinder, but there may be pressure on the ringdepending on how the modeling junctures are set. The ring mayhave hoop-bending stresses that are primary, but there is no pri-mary membrane. Of the three approaches, the latter produces thethickest plate.

FIG. 6.7 CONE CYLINDER: PLASTIC ZONE AT LIMIT LOAD [4]

FIG. 6.8 FLAT PLATE ATTACHED TO A CYLINDER [4]

FIG. 6.9 FLAT-PLATE GEOMETRIES: DESIGNAPPROACHES [4]

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 19

20 • Chapter 6

6.4.5.2 Assembled Geometry Model This approach is consis-tent with the use of the FEA. The model includes the plate, ring,and cylinder as a continuous geometry, as noted in Fig. 6.9(b). Thebending in the plate is constrained by the stiffness of the ring andcylinder. The full model with pressure applied remains continuousto ensure the load transfer (primary stress requirement) and defor-mation (secondary stress requirement). This approach reduces thebending in the plate, thereby reducing the required thickness. Forthis model, all bending and membrane stresses are treated as pri-mary; the controlling location is expected to be at the ring–cylinderjuncture, which ensures that the shell provides the assumed con-straint to the plate. If yielding occurs in the ring or cylinder, on theother hand, constraint to the plate would be reduced, therebyincreasing the bending stresses in the plate. Therefore, the assem-bled geometry reduces the plate thickness of the simply supported–plate approach, but it changes the bending stresses at thering–cylinder juncture from secondary to primary stresses.

6.4.5.3 Intermediate Constraint Model This model, as noted inFig. 6.9(c) is based on equilibrium analysis; its constraint is appliedto the plate by an assumed, realizable moment, the maximum beingthe full constraint of the ring and cylinder. The moment is applied toboth the plate and the ring, reducing the primary bending stresses inthe plate and increasing the primary bending stresses in the ring (rel-ative to the simply supported-plate approach). The ring–cylinderassembly can be analyzed as a single element or separated into twoelements. (The more accurate way is to separate the ring from thecylinder.) If the ring stresses from the assumed moment (hoop-bending stress) meet the bending (Pb) limits, the design is accept-able. The cylinder stresses are obtained by the Pm equations. If thering stresses do not meet the Pb limits, another assumed, realizablemoment can be applied at the ring–cylinder juncture and used in theanalysis of both the ring and cylinder. If the NB limits are not met,the thickness in one of the three elements must be increased.Therefore, the intermediate-constraint approach reduces the platethickness of the simply supported–plate approach and can eliminatePb from the ring–cylinder juncture.

6.5 PRIMARY-PLUS-SECONDARY STRESSLIMITS

The term P � Q is defined as the primary-plus-secondary stressintensity range and is addressed in this section—why it is neces-sary and how to apply it. In terms of membrane and bendingstress, the P � Q is developed without separating the primary andsecondary stresses. The secondary stress (Q) is also defined, as isits relation to ratchet and fatigue. Two procedures for calculatingP � Q (i.e., the stress intensity) are presented, and the impact ofthermal stresses is discussed for definition and application. The P � Q limit is intended to preclude ratchet and to ensure accuracyin the fatigue procedure. If the P � Q limit is not met, NB pre-sents an additional procedure for evaluating the potential ratchetand defining a penalty factor for the fatigue analysis.

6.5.1 Theory and Criteria Basis NB-3222.2 (Primary-Plus-Secondary Stress Intensity) defines

P � Q as the following:

This stress intensity is derived from the highest value at anypoint across the thickness of a section of the general or localprimary membrane stress, plus primary bending stress plussecondary stresses, produced by the specified service pressure

and other specified mechanical loads and by general thermaleffects associated with normal Service Conditions. The allow-able value of the maximum range of this stress intensity is 3Sm.

A simple way to view P � Q is the membrane-plus-bendingstress range (through the thickness at any location within thecomponent) for all applied loads. Thus, P � Q can be calculatedwithout separating the types of stresses, that is, Pm, PL, Pb, and Q.The P � Q includes all applied operating loads—mechanical,thermal, and expansion—applied in normal operation (i.e., LevelsA and B). Although the title does not state it, the P � Q is a rangeof stress that occurs from one loading condition to a second load-ing condition (calculation methods for P � Q are discussed laterin this chapter). The use of 3Sm as the limit is a simplifiedapproach; in theory, twice yield stress (2Sy) is the appropriatelimit (also to be discussed later).

A definition of secondary stress is given in both the Criteriadocument and NB. Page 5 of the Criteria states the following:

Secondary stress is a stress developed by the self-constraintof a structure. It must satisfy an imposed strain pattern ratherthan being in equilibrium with an external load. The basiccharacteristic of a secondary stress is that it is self-limiting.Local yielding and minor distortions can satisfy the disconti-nuity conditions of thermal expansion which cause the stressto occur.

Thus, the major characteristic of the secondary stress is that itis a strain-controlled condition—the applied load is balanced by astrain distortion rather then by an equilibrium of stresses. Theresulting strain is translated to be a stress in the analysis.

The required P � Q limit is related to fatigue and ratchet; itsintent is to ensure that the stress ranges respond elastically. Page 6of the Criteria states the following:

The primary-plus-secondary stress limits are intended to pre-vent excessive plastic deformation leading to incremental col-lapse, and to validate the application of elastic analysis whenperforming the fatigue evaluation.

Thus, the P � Q limits ensure that the cycling of a load rangeresults in elastic response of the material. This is known as (elas-tic) shakedown. When the initial cycles produce plasticity(exceeding Sy), some permanent plastic deformation will occur;after a few cycles, however, the condition becomes elastic fromthe generation of residual stresses. NB-3213.34 (Shakedown)states the following:

Shakedown of a structure occurs if, after a few cycles of loadapplication, ratcheting ceases. The subsequent structuralresponse is elastic, or elastic-plastic, and progressive incre-mental inelastic deformation is absent.

Page 8 of the Criteria gives a simple example for the stress-strain response, an example of which includes a figure that isgiven in this chapter as Fig. 6.10. Part (a) of this figure shows thecycling condition when the membrane-plus-bending range isgreater than Sy but less than 2Sy. The stress increases until theyield stress is reached (O–A); then, only the strain increases bymeans of plastic response until the maximum strain is reached(A–B). When the load is removed, the stress-strain curve returns tothe zero strain (B–C); the load reduction produces a compressivestress, resulting from residual stresses. In the next cycle, the strain

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 20

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 21

and the stress from the applied load follow the straight line (C–B)and the cycle produces no plastic reaction (i.e., the stresses areelastic through the full cycle). The primary stresses in the P � Q must be elastic for shakedown to occur, so the residualstresses are generated by the deformation stresses (Q).

In part (b) of the figure, the 2Sy is exceeded, shakedown is notreached (assuming no material hardening), and ratchet and/orplastic cycling occurs. The plastic cycling must be addressed inthe fatigue analysis, but as long as the 2Sy is met, ratchet will bean acceptable amount and the elastic fatigue analysis procedure isacceptable. The approaches for including plastic cycling in ratchetand fatigue are discussed in Section 6.5.4.

Figure 6.8 is a simple approach to understanding the theory. Instudying hysteresis curves generated by cyclic loadings, thestress–strain curves are not as simple as those shown in Fig. 6.10.Assuming the case of Fig. 6.10(a), the hysteresis loops will showhardening and multiple loops as the material shakes down(asymptotically) to an elastic response. Each material will have itsown hysteresis loops, and the final amount of permanent plasticdeformation is dependent on the material.

To summarize, page 8 of the Criteria states the following:

It (twice the yield stress) determines the borderline betweenloads which, when repetitively applied, allow the structure to“shake down” to elastic action and loads which produce plas-tic action each time they are applied.

Thus, the P � Q limit defines the stress level for elastic actionbased on through-thickness (membrane-plus-bending) stress.Also, it assumes that exceeding the P � Q limit produces plasticcycling. Therefore, the assumption of elastic behavior is justified

even though the yield strength is exceeded, for elastic response isthe condition in all load cycles subsequent to shakedown.

6.5.2 Application Section 6.4.4 discusses the fundamental, sequential steps from

component stress to stress intensity. The discussion, based on NB-3215, also presents the fundamental procedure for primarystresses. The procedure for P � Q (stress intensity range) is thesame as that for primary stresses except that P � Q is a range ofstresses (the D stresses caused by two load sets), whereas primarystress intensities relate to a single load set (monotonic loading), sothe procedure is adjusted for “range.” NB-3215 is directed to pri-mary stresses, and NB-3216 is directed to P � Q and fatiguewhere range of stresses are required.

NB-3216 gives two procedures for calculating the stress differ-ences: NB-3216.1 (Constant Principal Stress Direction) and NB-3216.2 (Varying Principal Stress Direction). The ConstantDirection and Varying Direction refer to the orthogonal coordinates;specifically, the directions of the principal stresses for every loadcase are the same (constant) versus different (variable). By using theNB-3216.1 procedure, the three stress differences are calculated foreach load case; thus, the procedure is the same as that used for theprimary stress differences. NB-3216.1(c) (Alternating StressIntensity) presents the final step for P � Q; it states the following:

Determine the extremes of the range through which eachstress difference Sij fluctuates and find the absolute magnitudeof this range for each Sij. Call this magnitude Srij and let Saltij � 0.5Srij.

The second sentence of the preceding quotation is directed tofatigue, whereas P � Q is the maximum of “the absolute magni-tude” of the three stress differences (Srij). Even though the stressintensity is an absolute (no sign of ���), the calculation for P � Q must be based on stress differences with a plus or minussign—that is, the two sets of stress differences must maintaintheir direction (���) until the stress ranges of stress differencesare established.

The weakness in the NB-3216.1 (Constant Principal StressDirection) procedure is that the two sets of principal stress coordi-nates must be the same. This condition was very common whenthe geometry models were simplified in the interaction analysesprocedure (e.g., constant-thickness shell at a discontinuity), buttoday’s FEA locations for analysis are often not at a constant-thickness shells. Consequently, the principal stress directions(coordinates) are likely to be different for each load case; for thatreason, NB-3216.2 is the appropriate procedure.

The NB-3216.2 approach is to range each of the six componentstresses producing component stress ranges. For fatigue, the rangeis done at a single point; for P � Q, however, the process is morecomplex because the P � Q requires a through-thickness compo-nent stress distribution that, in turn, requires multiple stress pointsthrough the thickness. Each point has two sets of six ranged com-ponent stresses; all the points use the same orthogonal set of coor-dinates. The following steps for calculating membrane and bendingstresses, principal stresses, and stress differences are the same asthose of the Constant Principal Stress Direction procedure exceptthat they are developed by using stress ranges (membrane andbending stress range, principal stress range, and stress differencerange—sometimes called delta stresses). Thus, the process is todetermine the six component stress ranges at each stress pointthrough the thickness and then calculate the membrane and bending

FIG. 6.10 SHAKEDOWN FOR P � Q

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 21

22 • Chapter 6

stress ranges, the three principal stress ranges, and the three stressdifference ranges. The maximum stress difference range is thestress intensity.

6.5.3 Thermal Loads Stresses produced by thermal loads are always secondary or

peak stresses. Thermal stresses occur when the temperature of thematerial is changing and producing a thermal gradient. The natureof the thermal gradient can produce a through-thickness stress ora local stress. NB-3213 states the following:

Thermal stress is a self-balancing stress produced by a nonuni-form distribution of temperature or by differing thermalcoefficients of expansion. Thermal stress is developed in a solidbody whenever a volume of material is prevented from assum-ing the size and shape that it normally should under a change intemperature. For the purpose of establishing allowable stresses,two types of thermal stress are recognized, depending on thevolume or area in which distortion takes place. . . .

The second sentence is critical, for when a thermal gradientoccurs, the geometry can be divided into small cubes of material,each representing a temperature. The “thermal coefficient of expan-sion” attempts to expand the cube locally and radially (hoop effect),and the adjacent cubes, representing different temperatures, willattempt to expand for the same reason as well. However, because thematerial is continuous with limits on local and total expansion, thecubes push one another, which prevents them from expanding aspredicted by the “thermal coefficient of expansion.” A strain istherefore put on each cube, producing self-balancing stresses. Anexample is as follows: during the heating of the vessel, a through-thickness thermal gradient (linear or nonlinear) will occur in theshell. Each cube of material is at a different temperature andattempts to expand depending on its temperature, but it is con-strained (decreased or increased) by adjacent cubes.

The third sentence of the foregoing quotation states that twotypes of conditions occur because of thermal gradients. These twoconditions are described as having a distortion of the structure orhaving (almost) no distortion. NB-3213.13(a) and (b) define theseconditions as follows:

(a) General thermal stress is associated with distortion ofthestructure in which it occurs.

(b) Local thermal stress is associated with almost completesuppression of the differential expansion and thus producesno significant distortion.

Item (b) of the preceding quotation uses the term almost completesuppression, which raises issues. From a practical standpoint, item(b) has no distortion, but mathematically distortion may exist. Forexample, a hot vessel can undergo a thermal shock (a rapid decreasein the temperature of the fluid within the vessel), causing a veryrapid decrease in the surface temperature but no change in thethrough-thickness temperature. The shell thickness with “no temper-ature change” will constrain the small amount of material with thereduced temperature. However, if a full-through-thickness assess-ment is used to determine the membrane-plus-bending stress pro-duced by the thermal shock, the mathematics would produce somechange (albeit extremely small) in the through-thickness stresses.These stresses, though, are ignored by NB as nonsignificant.

Another consideration is the continuation of thermal shock so thata significant through-thickness gradient occurs. The initial thermalshock produces a peak stress (fatigue concern), the maximum of

which occurs very early in the shock. If the thermal shock continues,however, the membrane-plus-bending stresses increase and becomesignificant. The secondary (Q) stresses may produce some “distor-tion of the structure.” It is noted that the maximum peak stress andthe maximum secondary stress do not occur simultaneously in theevent, so they do not superimpose. The general thermal stress,because it is a secondary stress (Q), is included in the P � Q.

NB-3213.13 also gives categories of thermal distribution typesthat result in stresses. Three examples for both general thermalstresses (secondary stresses) and local thermal stresses (peakstresses) exist.

The categories for general thermal distribution with Q are thefollowing:

(1) The temperature changes in the axial or meridional direc-tion, requiring a nonlinear temperature distribution toproduce stresses.

(2) The temperature changes between two adjacent parts of thevessel—for example, a nozzle having a different temperature than the adjacent shell.

(3) A through-thickness thermal distribution, which may belinear or nonlinear, but only the membrane-plus-bendingstress (generated by the distribution) is Q.

The categories for local thermal distribution with peak stressesare the following:

(1) There is a hot spot on the surface of the vessel. For exam-ple, there is a thermal sleeve that produces a slight openingas it vibrates, allowing a small, periodic flow into the cham-ber and producing a cycling thermal shock over a verysmall material area.

(2) A through-thickness stress distribution produces a totalthermal stress on the surface. The total stress minus themembrane plus bending stress gives the peak stress. Themagnitude of the peak stress is a function of the nonlinearnature of the distribution.

(3) Cladding material produces a nonlinear stress distributionfrom the differences of the coefficient of expansionbetween the cladding and the base metal, even when thetemperature is the same in both materials.

NB-3213.13 gives examples of the three categories of localthermal distribution with peak stresses. They match the threeentries in the preceding list (only worded differently) as follows:

(1) the stress in a small hot spot in a vessel wall; (2) the difference between the actual stress and the equivalent

linear stress resulting from a radial temperature distributionin a cylindrical shell; and

(3) the thermal stress in a cladding material which has acoefficient of expansion different from that of the base metal.

It is noted that thermal gradients are more likely to include bothgeneral and local distributions at the same time and also that mul-tiple categories occur simultaneously. Consequently, the analyst isnot dealing with singular conditions, so to address this, he or shemust focus on the calculation of membrane-plus-bending stressesand total stresses for the P � Q and fatigue analysis, respectively.

6.5.4 Thermal Expansion in Piping Systems Piping systems have a unique set of stresses because of the

thermal expansion of the piping and the constraint of the piping(supports), as exemplified by NB-3213.19 (Expansion Stress) that

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 22

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 23

states, “Expansion stresses are those resulting from restraint offree-end displacement of the piping system.”

Fig. NB-3222-1 [Stress Categories and Limits of StressIntensity for Level A and Level B Service Limits (HopperDiagram)] shows that expansion stresses (Pe) are secondarystresses. This figure defines Pe as follows:

Stresses which result from the constraint of free-end dis-placement. Considers effect of discontinuities but not localstress concentration (not applicable to vessels).

The fundamental view is that a piping system is attached to avessel at both ends of the piping run. It is assumed that vessels areso stiff that they act as a full constraint (zero displacement and rota-tion). Even if the constraint is not full (e.g., analysis that includesthe vessel), the vessels are expected to produce a high constraint,for which piping supports can also be designed to have. The tem-perature of the piping is relatively constant during operation (lowthrough-thickness gradient), and the piping attempts to expand axi-ally to match the temperature coefficient of expansion. The vesselsat both ends do not allow the full expansion as a function of thevessel stiffness, producing axial strains. If the piping system is astraight run (no bends) and the vessels give full constraint, thestrain/in. can be defined by the coefficient of expansion and thestrain can be translated to the stress. Normally, piping runs havebends, which decrease the axial strains but cause bending withinthe piping bends. The expansion stresses and the bending stressesmust be considered in the secondary stresses.

The rules for thermal expansion are well defined in the threesubsets to NB-3624 (Thermal Expansion and Contraction Loads).These rules and their comments are as follows:

Loadings, Displacements, and Restraints. The design of thepiping system shall take into account the forces and momentsresulting from thermal expansion and contraction, equipmentdisplacements and rotations, and the restraining effects ofhangers, supports, and other localized loadings.

The preceding quotation confirms the need to address both theaxial constraint and any bending or torsion that occurs from thebends in the piping system. It also confirms the need to addressthe impact of supports even if their capability to constrain the pip-ing is inadequate.

Analysis of Thermal Expansion and Contraction Effects. Theanalysis of the effects of thermal expansion and contraction iscovered in NB-3672.

NB-3670 (Special Piping Requirements) expands on therequirements for piping, one set of which is NB-3672 (Expansionand Flexibility). NB-3672 presents a considerable number ofadditional issues including rules that address sources of loads notdefined previously, failures from overstress or overstrain, leakageat joints, detrimental distortion, material properties, unit thermalexpansion range, flexibility calculations, methods of analysis,basic assumptions, and the use of cold-springing.

Provisions for Rapid Temperature Fluctuation Effects. Thedesigner shall provide for unusual thermal expansion andcontraction loads caused by rapid temperature fluctuations.

This requirement defines that analysis must include what hap-pens during a change in operation. Rapid changes have a moresevere impact than slow changes. The steady-state condition is

expected to be the controlling condition for global expansionstresses, but rapid changes are likely to control local areas(fatigue issue).

6.5.5 When P � Q Is Exceeded In previous discussions, it was shown that the stress limit for

P � Q (twice the yield stress) determines the borderline betweenloads that (when cycled) allow the structure to “shake down” toelastic action and loads that produce plastic action each time theyare applied. The following question arises: “What happens to thematerial if the P � Q limit is not met?” Not meeting the limitcreates the potential for two conditions: ratcheting (cyclic growthof the structure leading to collapse) and nonconservatism of theNB fatigue-required procedure. Exceeding the P � Q limit pro-duces plastic cycling within the material—it is a physical reality,not a theoretical condition. This section addresses the issue byusing the rules in NB-3222.5 (Thermal Stress Ratchet), NB-3228.5 (Simplified Elastic–Plastic Analysis), and NB-3228.4(Shakedown Analysis). The following paragraphs espouse anelasticity view—that hardening or softening effects are not con-sidered in predicting the need for shakedown, ratchet, or plasticstrain cycling.

Ratchet starts when the stress exceeds the proportional limit.As discussed previously, cycling will produce residual stressesfollowed by elastic cycling. If shakedown to an elastic conditionoccurs, ratchet will not occur. If the stresses increase from theproportional limit to the defined yield strength, some distortiondue to ratchet will occur. However, it is assumed that shakedownto an elastic condition will occur for all materials allowed withinNB. If the applied stresses are at the yield strength, shakedown isexpected to occur within 20–100 cycles (material dependent) withan acceptable level of ratchet. If the stresses increase to twice theyield strength, shakedown depends on cyclic hardening of thematerial. If the material responds to cyclic softening, some ratchetis expected to occur. If the cyclic stress-strain curve shows hard-ening, some ratchet will occur during the shakedown process.Because shakedown will occur, therefore, the potential for someratchet is acceptable within the NB rules.

As previously discussed, P � Q limit is 3Sm, not the 2Sy dis-cussed previously. For perhaps all of the materials that producecyclic softening, Sm is based on one-third of the ultimate strengthrather than on the yield strength. Consequently, the P � Q limit(3Sm) is less than 2Sy, and there is an allowance for some cyclicsoftening, but the ratchet will be minimal. If the stresses exceed theP � Q limit, both softening and hardening materials will ratchet.For the softening material, however, ratchet will occur continuously;the hardening materials will ratchet until shakedown occurs, but thelevel of ratchet is unknown. Even if this ratchet is found to beacceptable relative to the operation of the vessel, it has an impacton the fatigue, discussed later in the chapter.

The rules in NB-3222.5 present an elastic procedure for deter-mining whether ratchet will occur based on the work by D. R.Miller [6]. This procedure was also developed by using cylindri-cal shell without any discontinuities or axial gradients, with accu-racy that is acceptable for through-thickness gradient in cylinders(e.g., long piping runs); the accuracy at discontinuities, however,is questionable and probably overly conservative. Plastic analysisis a more accurate, reliable approach; its accuracy is primarilydependent on the accuracy of the cyclic stress–strain curve.However, it is important to understand that the level of ratchetdepends on the number of cycles. If the number is low, ratchetwill not be problematic, though fatigue might still be as such.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 23

24 • Chapter 6

NB-3228.5 addresses the increased fatigue damage that canoccur from ratchet—that is, the plastic cycling that occurs withratchet. NB-3228.5 states the following:

The 3Sm limit on the range of primary-plus-secondary stressintensity (NB-3222.2) may be exceeded provided that therequirements of (a) through (f ) . . . are met.

NB-3228(a) and (b) are the key requirements for acceptanceand for calculating the increased damage in fatigue; it uses theterm Ke as a multiplier in the fatigue procedure. Item (a) states thefollowing:

The range of primary-plus-secondary membrane-plus-bendingstress intensity, excluding thermal bending stresses, shall be� 3Sm.

Item (a) means that the P � Q limit must be met when the ther-mal bending stress is deleted from P � Q—that is, the modified(no thermal bending) P � Q must be met in addition to applyingKe to the fatigue analysis.

Item (b) of NB-3228.5 presents the equations for calculatingKe for the fatigue analysis. It also defines the term Sn, which isused in the equations. Sn is defined as the “range of primary-plus-secondary stress intensity.” Thus it includes the thermalbending.

The following quotations represent items (c)–(f) of NB-3228.5.A brief statement regarding the significance of the items is alsoprovided.

Item (c) is exemplified by the following:

The rest of the fatigue evaluation stays the same as requiredin NB-3222.4, except that the procedure of NB-3227.6 neednot be used.

NB-3222.4 (Analysis for Cyclic Operation) defines the fatigueprocedures. NB-3227.6 (Application of Elastic Analysis forStresses Beyond the Yield Strength) defines the application ofPoisson’s ratio to peak thermal stresses in a fatigue analysis. Thisis discussed, in some detail, in Sections 6.6 and 6.7.

Item (d) is exemplified by the following:

The component meets the thermal ratchet requirements ofNB-3222.5.

(NB-3222.5 was discussed previously.) Item (e) is exemplified by the following:

The temperature does not exceed those listed in Table NB-3228.5(b)-1 for various classes of material.

Table NB-3228.5(b)-1 presents values for terms used in the Ke

equations and sets the maximum temperature for operationsexceeding the P � Q limit (e.g., 700�F for carbon steel); if theoperating temperature exceeds this temperature limit, NB-3228.5cannot be used.

Item (f) is exemplified by the following:

The material shall have a specified minimum yield strength tospecified minimum tensile strength ratio of less that 0.80.

This global approach is to ensure that the material exceedingthe P � Q limit is ductile. Materials having ultimate tensilestresses that are only minimally greater than their yield stresshave the potential for low ductility. Thus, NB-3228.5 cannot beused for low ductile materials.

When the P � Q limit is exceeded, plastic cycling is assumedto occur until there is shakedown to an elastic condition. As previ-ously stated, plastic cycling is likely to cause ratchet, and theresulting plastic strains are not included in the fatigue analysisprocedure. NB-3228.4 presents three requirements for whichshakedown can be assumed for thermal stress ratchet and for pro-gressive distortion of nonintegral connections—a topic that is dis-cussed in detail in Section 6.7.6. As stated previously, elasticanalysis assumes that ratchet occurs when the P � Q limit with-out thermal bending is exceeded.

6.6 FATIGUE

There is an industry-wide consensus that the NB Section III S-N fatigue approach has provided a safe design against failure.This approach to fatigue evaluation is based on fatigue curves ofstress versus number of cycles (designated as S-N curves). Thetest data were originally developed over 35 yr. ago from smooth,base metal specimens tested in air at room temperature. Thefatigue design curves were obtained or “adjusted” from the meanfailure curves by applying a design factor. For both ferritic andaustenitic S-N curves, the design factor was the more conservativeof 20 on cycles or 2 on stress (2&20). More recent data have dis-covered that the 2&20 do not adequately account for primaryreactor environments at low-strain rates. Recent testing confirmsthat 2&20 is adequate for ferritic material in low-oxygenated pri-mary water but not for high-oxygenated water. Data foraustenitics produces a reduced design factor at low strain rates inboth low and high oxegenated water. There is also a less than afacor of 2 on stress for austenitic materials in air. These deficien-cies are being considered now (2008) by Code Committees andare mentioned here as a caution.

The inclusion of fatigue as a potential failure mechanism wasintended to increase the reliability of reactor vessel performance.It was the intent of the authors that the fatigue rules be applied to“new” construction [7]; such rules, however, were not intendedfor the reevaluation of existing components. Stated another way,the procedures were intended to evaluate fatigue performancebased on a set of assumed “design” conditions, for actual opera-tion of nuclear reactor systems would not be fully known to thedesigner or manufacturer. It was also intended that the analyseswould produce conservative fatigue life usage (not necessarily anactual prediction of fatigue life).

6.6.1 Basis Over the years, the use of NB fatigue analysis rules has become

somewhat nebulous regarding their original intent. The originalSection III, created in 1963, incorporated fatigue as a failuremode, thereby providing a rationale for reducing the basic (primarystresses) design safety factor from 4 to 3. At that time, Section Iand Section VIII used the design factor of 4 for defining theallowable stress. Thus, the basic allowable stress, Sm is based par-tially on the introduction of fatigue analysis in the rules. Also atthat time, none of the books of the ASME B&PV Code had rulesfor fatigue analysis. The intent for Section III was for fatigueanalysis to be used, not so much to quantitatively predict fatiguelife but to demonstrate that the fatigue usage factor for the antici-pated life of the vessel was less than 1.0 for normal operatingtransients. A rigorous application of fatigue evaluation was clear-ly not the intent of the Section III fatigue rules. The major conser-vatism is that actual plant operational transients have less severity

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 24

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 25

and fewer cycles than design assumptions; therefore, the SectionIII analysis procedures are conservative.

The Criteria document is the source for the aforementionedbasis; it established the need and purpose for the development ofnew fatigue curves. Page 10 of the Criteria states the following:

One of the important innovations in Section III . . . as com-pared to Section I . . . is the recognition of fatigue as a possi-ble mode of failure and the provision of specific rules for itsprevention. . . . In pressure vessels, however, the number ofstress cycles applied during the specified life seldom exceeds1E5 and is frequently only a few thousand. Therefore, inorder to make fatigue analysis practical for pressure vessels,it was necessary to develop some new concepts not previouslyused in machine design.

The following paragraphs discuss the fundamental rules and thebasis for their acceptance.

Subsection NB provides fatigue evaluation methodology forpressure boundary components and also provides requirements forfabrication and NDE of these components. The design, fabrication,and inspection requirements are altogether intended to provide asafe, reasonably long life for their respective pressure boundarycomponents (i.e., the three technologies together ensure safety fromfatigue failure). Although Section III has been revised many times,the general fatigue evaluation procedures have remained essentiallyunchanged since their 1963 introduction into Section III.

The basis of the NB fatigue assessment procedures is thatfatigue damage, caused by cyclic loading, is cumulative and thatthe summation of this damage during component life does notexceed 1.0. Fatigue damage is defined by a usage factor. A partialusage factor is obtained by the ratio of (ni Ni). The term Ni is thenumber of allowable cycles at a given stress level obtained fromthe appropriate fatigue curve, whereas the term ni is the cycles tobe applied during the operating life of the vessel as according tothe design requirements. When there are multiple operating con-ditions, each operation generates a partial usage factor. A cumula-tive usage factor (CUF), known as the Palmgren–Minor lineardamage relationship, is obtained by adding the multiple partialusage factors. Page 18 of the Criteria states the following:

Other hypotheses for estimating cumulative fatigue damagehave been proposed and some have been shown to be moreaccurate than the linear assumption. Better accuracy could be obtained, however, only if the sequence of the stress cyclewere known in considerable detail, and this information is notapt to be known with any certainty at the time the vessel isbeing designed. Tests have been shown [6] that the linearassumption is quite good when cycles of large and small stressmagnitude are fairly evenly distributed throughout the life ofthe member, and therefore this assumption was considered tocover the majority of cases with sufficient accuracy.

The [6] in the preceding Criteria quotation is a reference towork by Baldwin et al. (ref. [8] in this chapter).

The development of the S-N curves are discussed in detail laterin this section. The following paragraphs present an overview ofthe fatigue procedure and its basis.

Fatigue damage is quantified in terms of the alternating stressintensity (Sa), which is one-half the difference between the maxi-mum and minimum cyclic (Tresca) stresses at the point of interestin the component. The equation is as follows:

(6.4)Sa =

1

2 (Smax - Smin)

This equation is consistent with the (Tresca) shear theory offailure in assessing primary and primary-plus-secondary stresslevels. Cyclic life (Ni) at a given alternating stress is determinedfrom the appropriate material design life curves given in Figs. I-9.1–I-9.5 of Appendix I to Section III.

As stated previously, the pressure vessels used in nuclear reac-tor plants are more likely to be subjected to low-cycle fatigue (a strain-controlled damage mechanism) than high-cycle fatigue(a load-controlled damage mechanism), which simplified thedevelopment of the original fatigue curves. Fatigue data for steelsused in reactor systems were developed from small, smooth speci-mens tested in air under strain-controlled conditions. Fatiguefailure curves were obtained by two steps, the first of whichencompassed multiplying the test-generated strain (Det � 2) byYoung’s modulus to obtain the stress amplitude (Sa) as presentedin equation (6.5). The second step involved the development of“best-fit” mean curves (normally called the failure curve) throughthe available data.

(6.5)

A design curve was developed from the failure curve. The pro-cedure is to apply two reduction factors: one for the data fromdeformation-controlled tests, the other for load-controlled data.

Then, these two reduced curves are blended into a single curvecalled the design curve.

The fatigue failure curve includes test data obtained well abovethe yield strength of the material; thus it is based on plasticityrather than elasticity. Because the alternating stress for the fatigueanalysis is expected to be derived from a linear-elastic calculation,strain ranges greater than the yield strain result in pseudoelasticstress (Sa) when converted from the test data. The suitability ofthis approach is addressed in the development of the analysis pro-cedure—to be presented later.

In 1963, it was well known that mean stresses (the average ofthe maximum and minimum stresses used for the stress range)had an impact on fatigue damage if the stress range was load con-trolled rather than deformation controlled. The mean stress effectswere conservatively included in the fatigue curve by lowering the best-fit failure curve according to an interpretation of theModified Goodman Diagram (see pages 12 and 13 of the Criteria),which produces a worst-case assumption for the mean stresseffect.

6.6.2 Analysis Two sets of rules—NB-3216 (Derivation of Stress Differences)

and NB-3222.4 (Analysis for Cyclic Operation)—are discussed indetail in this section. Additional rules for fatigue analysis are pre-sented in a simple manner.

6.6.2.1 NB-3216 (Derivation of Stress Differences) This topicwas discussed in Section 6.5.2 for developing the primary-plus-secondary stress intensity range (P � Q). The process is thesame for fatigue except that the stresses are at a point rather thanfor a membrane-plus-bending through-thickness stresses. In addi-tion, the final step in the process defines the alternating stress (Salt)that is used in the fatigue, whereas P � Q uses the full range.

The fatigue procedure of NB-3222.4 starts with the derivationof stress differences. The procedure for the development of thestress differences (NB-3216) addresses both the varying principalstress direction and the constant principal stress direction, both ofwhich generate stress difference ranges. For the constant direction

Sa = EDet /2

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 25

26 • Chapter 6

approach, NB-3216.1(c) (Alternating Stress Intensity) presentsthe final step for both P � Q and fatigue; it states the following:

Determining the extremes of the range through which eachstress difference Sij fluctuates and find the absolute magnitudeof this range for each Sij. Call this magnitude Srij and let Salt ij

0.5Srij.

Thus, the procedure develops the alternating stress to be usedin the fatigue analysis, but the precise wording for this procedureis generally suitable only for single operating conditions. Formultiple loadings, the range is based on the maximum and mini-mum stress differences, as determined when considering all of theoperating conditions.

The final step in NB-3216.2(e) (Varying Principal StressDirection) also defines the stress difference ranges and the alter-nate stresses; it states the following:

(e) Determine the stress differences S12 � s1 – s2, S23 � s2 – s 3, and S3l � s3 – s1 versus time for the com-plete cycle and find the largest absolute magnitude of any stressdifference at any time. The alternating stress intensity Salt isone-half of this magnitude.

Thus, both procedures (constant and variable direction) developalternating stresses that are used in the fatigue curves for deter-mining the allowable cycles. The fatigue curves use the term Sa

rather than Salt.

6.6.2.2 NB-3222.4 (Analysis for Cyclic Operation) presentsthe rules and the procedures for obtaining the CUF. Its subsectionsinclude (a) Suitability for Cyclic Condition; (b) Peak StressIntensity; (c) Conditions and Procedures; (d) Components NotRequiring Analysis for Cyclic Service; and (e) Procedure forAnalysis for Cyclic Loading.

Subsection (a) Suitability for Cyclic Condition This subsectiongives an overview of rules. Specifically, it directs the analyst toNB-3232.3(b) for “fatigue of high-strength bolts”, which modifiesthe procedure for areas that are specific to bolts and studs such asthe fatigue-strength reduction factor to be used for bolts and thebolt-thread design. For the most part, the general fatigue analysisrules—NB-3222.4(e) (Procedure for Analysis for CyclicLoading)—are included for bolts. Also, this subsection states that“the possibility of thermal stress ratchet shall be investigated,”which is a restating of the requirement. Other parts of this subsec-tion also restate requirements.

Subsection (b) Peak Stress Intensity This subsection limits thefatigue analysis to normal service conditions (i.e., Levels A and Bbut not C and D). It restates the role of thermal stresses and notchesand also restates that the maximum total stresses (primary, sec-ondary, and peak) are to be used in the fatigue analysis.

Subsection (c) Conditions and Procedures This subsection dis-cusses some theory on the relationship between the modified testdata (mean stress effect and the design margin) and the calculatedstresses. It explains the similarity between the fatigue curves useof Sa and the analysis use of Salt (discussed later in detail).

Subsection (d) Components Not Requiring Analysis for CyclicService This subsection presents a simplified procedure for thefatigue analysis. It defines six criteria that, if met, do not requirethe full analysis to be performed. The Criteria document, begin-ning on page 18, presents a background theory on how these ruleswere established. The simplified fatigue procedure may be usedrather than the rigorous fatigue analysis as presented inSubsection (e) if all six requirements are met. These simplified

requirements are considered conservative for the following threereasons:

(1) the peak stress used in the evaluation is 6Sm for pressureloading (where Sm is the design stress intensity) and 4EaDTfor thermal loading;

(2) every cycle for the life of the component is assumed to bee-qual to the most severe pressure or thermal stress cycle; and

(3) the component is not subject to a significant number of cycles.

Subsection (e) Procedure for Analysis for Cyclic Loading pre-sents the full fatigue analysis. The initial paragraph presents fourgeneral items as follows:

The determination shall be made on the basis of the stressesat a point . . . the allowable stress cycles shall be adequate forthe specified Service Loading at every point . . . Only thestress differences due to service cycles as specified in theDesign Specifications need to be considered . . . Compliancewith these requirements means only that the component issuitable from the standpoint of possible fatigue failure. . . .

The first two items are requirements; specifically, the stress at asingle point must be used in the analysis and the CUF limit of 1.0must be met. The second and third items are somewhat relax-ations; specifically, only service loads (normal operation) are sub-ject to fatigue analysis and only the cycles (numbers) specified inthe Design Specifications need to be considered. The fourth itemrestates that cyclic loadings can produce damage in addition togenerating fatigue cracks. These items are important to considerin understanding the overall requirements for cyclic analyses.

Subsection (e) has five subsections as follows:

(1) Stress Differences. (2) Local Structural Discontinuities. (3) Design Fatigue Curves. (4) Effect of Elastic Modulus. (5) Cumulative Damage.

The subsection Stress Differences states the following:

For each condition of normal service, determine the stress dif-ferences and alternating stress intensity Sa in accordance withNB-3216.

Thus, the rules of NB-3216 (Derivation of Stress Differences)apply. The stress difference ranges are determined, consisting ofthe three stress differences produced by primary membrane andbending stresses-plus-secondary (self-limiting) stresses-plus-peak(stress concentration and thermal skin) stresses. The stress differ-ences are defined as follows:

S12 �s1 � s2 S23 � s2 � s3 S31 � s3 � s1 (6.6)

where

s1, s2, and s3 � the principal stresses

The stress difference ranges are developed and the maximum ofthese ranges are used in the fatigue analysis.

The subsection Local Structural Discontinuities addresses stressconcentrations (effect of notches on the local stress), including those“determined from theoretical, experimental, or photoelastic studiesor numerical stress analysis techniques.” This is a requirement tofully address the stress concentration effect on the alternating stress-es. The numerical stress analysis techniques can be interpreted toinclude the finite element (FE) approach. An FE analysis (FEA) can

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 26

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 27

produce a very accurate total stress and thus define which stressesand their impact on the stress from a notch and the location on thatnotch (e.g., membrane and bending stresses have differentconcentrations, which occur at the deepest point on the notch anddecrease as the location moves away from the deepest point).

The subsection Local Structural Discontinuities also allows theuse of the fatigue strength reduction factor (FSRF) in lieu of usinga stress concentration factor (SCF). The FSRF will normally givea lower value than the SCF. There is one limitation on the use ofFSRF, however: it may not be used “for high-strength alloy steelbolting”—addressed in NB-3232.3(c) in Fatigue Analysis ofBolts. Additional discussions of the SCF and FSRF are given inSection 6.7.1 of this chapter.

The final sentence of the Local Structural Discontinuitiessubsection allows the maximum FSRF to be 4.0. This relaxationis acceptable “except for the case of cracklike defects andspecified piping geometries for which specific values are given inNB-3680.” Other rules state that cracklike defects are not accept-able and must be repaired. Thus, FSRF � 4.0 is a maximum forany acceptable notch except for certain piping requirements.

The subsection Design Fatigue Curves directs the analyst to theAppendix (Section III, Division 1) for the figures that contain the applicable (per material) fatigue design curves. It also addressesthe applicability and the use of linear interpolation if a figure includesmultiple curves. The figures are discussed in detail in Section 6.6.3.

The subsection Effect of Elastic Modulus (E) presents amodification for Salt based on temperature. Each fatigue curve isdeveloped from strains by multiplying the strain by an elastic mod-ulus. For example, the fatigue curve for carbon steel (Fig. I-9.1) isdefined by E � 30 106 psi, but the operating temperature mayproduce a modulus less than that of this equation. A ratio of the twomoduli will produce a ratio that is greater than 1.0. The Salt must bemultiplied by the ratio, thus producing a modified and increased Salt

that is called Sa by the S-N curve. This adjustment allows the testdata to be consistent with the operating temperature.

The subsection Cumulative Damage gives six steps for reach-ing the CUF. These steps assume that there are multiple loadcases and are presented concisely in the following list:

(1) Designate the number of cycles for each operating cycle(transient). (A “transient” is defined as the full cycle of aloading condition, such as start-up and shutdown.)

(2) Associate each alternating stress with the appropriate cycles. (3) Go to the appropriate fatigue curve; then determine the

allowable cycles for each alternating stress. (4) Determine a partial usage factor for each alternating stress

by dividing the designated cycles by the allowable cycles. (5) Calculate the CUF by adding all the partial usage factors. (6) Compare the CUF to 1.0; if less than 1.0, the analysis is

complete.

Alternating stresses are determined on a cross-transient (operating-cycle) basis to maximize their value—that is, the “cross-transient”procedure requires the range be based on the maximum stress dif-ference minus the minimum stress difference of all the transients.However, the maximum range is based on the following threestress differences or ranges:

S12R � S12max � S12min S23R � S23max�S23min S31R

� S31max S31min (6.7)

The cross-transient approach causes difficulty in determining Salt,especially when the procedure of variable principal stress directionis used. When multiple transients exist, the analyst must define the

maximum and minimum stress difference for each transient. Thistask is rather easy when the constant principal stress directionapproach is used because the range is the last step (i.e., the maxi-mum and minimum stress differences are determined before calcu-lating the range). When the varying principal stress directionapproach is used, however, neither the maximum nor minimumstress difference for a transient is known (i.e., S12R, S23R, and S31R

are determined directly from principal stress ranges). Thus, thevarying principal stress direction needs an additional procedure (ofwhich there are many) to define the maximum and minimum stressdifference for each transient and their direction (plus or minus).

Once the maximum stress difference range based on all thetransients is established, the number of cycles associated with itcan be determined as represented in step (2) of the preceding list.Assuming that the maximum and the minimum contributing stressdifferences are from different transients, each having differentnumbers of cycles, the lesser of these two transients (maximum orminimum) are the appropriate cycles for this Salt. For example,assume that the “minimum contributing stress difference” hasfewer cycles than the “maximum contributing stress difference.”The cycles for that range are those from the “maximum contribut-ing stress difference.” The fatigue damage from the “maximumcontributing stress difference” from the “maximum minus mini-mum” range is now completed, so the maximum stress differenceis not considered in the additional Salt evaluations. For the “mini-mum contributing stress difference,” the initial cycles are reducedby those already applied and the new number of cycles shall beused for additional Salt evaluation. An example of this is given in aNote that follows step (1) in the Cumulative Damage subsection.

As each Salt is developed and the associated cycles are defined,the allowable cycles from the appropriate fatigue curve can bedetermined and a partial usage factor can be calculated (whichmay also require the adjustments for establishing Sa from Salt).The process is continued until all cycles for all transients areincluded in partial usage factors. The final step is the summationof the partial usage factors to obtain the total usage factor (CUF)for comparison with the limit of 1.0.

As mentioned previously, establishing Sa from Salt requires themodulus (E) adjustment; Sa is used in the S-N curve and Salt definesthe maximum stress difference range. This transfer (Salt to Sa) alsorequires an adjustment factor when an FSRF or the P � Q factor(Ke) are appropriate. (The FSRF is discussed in NB-3213.17.) TheKe is required when the P � Q limit is not met. The Code recog-nizes that allowing membrane-plus-bending stresses to exceed theyield stress can cause strain concentration that is not included in anelastic analysis. If the P � Q limit is not satisfied, the appropriateKe is applied to Sa before fatigue curve is entered. (The develop-ment of Ke is discussed in Section 6.5.5.)

Additional rules for fatigue are available to the analyst inNB-3338 (Fatigue Evaluation of Stresses in Openings) (nozzle-to-shellgeometry). The rules for NB-3338 present three analysis proceduresfor developing fatigue stresses, including the stress concentrationcaused by the opening: The analytical methods, which utilize NB-3222.4 (Analysis for Cyclic Operation) rules; the experimentalStress Analysis, which is based on test data; and the stress indexmethod, which is the focus and developed before the initialSection III but still permitted by NB. The development of this lattermethod was based on pressure; therefore, its accuracy is acceptable.However, when other loads are included (e.g., thermal gradients),the accuracy becomes suspect.

There are also procedures for piping and valves. For piping,NB-3650 (Analysis of Piping Products) for Class 1 piping presents

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 27

28 • Chapter 6

mostly design-by-formula rules. Using these simplified fatiguerules for Class 1 piping is in lieu of using NB-3200, which coversthe rules for reactor vessels. If the NB-3650 design-by-formularules are not met, the piping can be assessed by the NB-3200design-by-analysis rules, which are found specifically in NB-3216(Derivation of Stress Differences) and NB-3222.4 (Analysis forCyclic Operation). Fatigue for openings, piping, and valves arenot discussed further in this chapter.

6.6.3 The S-N Curve A typical S-N curve (fatigue design curve) is shown in Fig. 6.11.

This figure is a duplication of Fig. I-9.1 (Design Fatigue CurvesFor Carbon, Low-Alloy, and High-Tensile Steel For MetalTemperatures Not Exceeding 700�F), found in Section III, Division1 Appendices. It addresses two curves: one for materials with anultimate tensile strength (UTS) of less than 80 ksi, the other formaterials with 130 ksi � UTS � 115 ksi. The figure allows inter-polation for materials with UTS between 80 and 115 ksi. The twocurves cover most of the ferritic materials used in Class 1 vessels.

The curves plot stress (Sa) versus (allowable) cycles and extend10–1,000,000 (1E1–1E6) cycles and 580 ksi–12.5 ksi for Sa. At10 cycles, Sa � 580 ksi, which is a factor of 7 over the UTL and10 greater than the expected yield strength (Sy) of 50 ksi or less.From a design perspective, one might expect P � Q to equal 2Sy

and a notch effect to be a factor of 4. Thus the maximum factor is2 4 � 8, which is a factor of 1.25 below the factor of 10.Geometries combined with normal operating conditions (Levels Aand B) should never produce stresses of this level. For abnormal

operating conditions (Levels C and D), the number of cyclesshould be less than 10; these conditions do not require inclusionin a fatigue analysis. In the overview, there is therefore no needfor extrapolation below 10 cycles.

At 1E6 cycles, Sa � 12.5 ksi. Because this is an alternatingstress, the stress range is 25 ksi. At 1E6, the design factor appliedto the failure curve is 2, making the expected stress for failure be50 ksi; this is the yield strength (room temperature) for the com-mon material with a UTS of 80 ksi. Thus the failure curve stresslevel matches the yield strength and, in theory, no damage shouldbe expected. However, the 50 ksi yield is a maximum for this setof materials. For example, carbon steel could have a yieldstrength as low as 35 ksi. The vast majority of Class 1 vessels arebuilt with materials having ULT � 80 ksi and Sy 50 ksi, and theactual yeild property is expected to be significantly greater.Therefore the 1E6 cycles are often considered endurance levels,but NB does not allow this assumption. The use of these curves isbased on the minimum required properties.

Figure 6.9 shows that the two curves cross each other at about50 ksi and 5E3 cycles. The lower strength material has moreallowable cycles at the high Sa values and less at the lower Sa

values. For example, if the material has minimum UTL of 80 ksiand an Sy of 50 ksi, the “dashed” curve shown in the figure shouldbe used even if the material as received has an Sy � 60 ksi. Theductility is important in fatigue properties of the material, espe-cially at high stress levels. At low levels, however, strength ismore likely to control the fatigue damage. Ductility is related tomaterials, but strength is related to how the material is fabricated.

FIG. 6.11 A TYPICAL S-N CURVE (Source: Fig. 1-9.I, Section III, Division 1 of the ASME B&PV Code)

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 28

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 29

Therefore, it is appropriate to associate a material having definedproperties to a curve rather than matching actual properties.

The Criteria document presents two sets of data from ferriticmaterial and fatigue failure curves (found in Fig. 10, page 16 ofthe document, and given here as Fig. 6.12), which were used todevelop the original fatigue design curves. The data is for carbonsteel and for low-alloy steels, for which the data showsinsignificant differences; thus a single curve was used for thesetwo materials. The Criteria document also has a figure used forthe stainless steel data.

Since their development more than 35 yr. ago, additional testdata has been obtained. For the ferritic S-N curves, superimposingthe new data on the original data does not significantly change thebest-fit failure curve (this data is presented in Fig. 6.13). Foraustenitics, superimposing the new data reduces the best-fit fail-ure curve. The austenitic S-N curve has also been modified forcycles greater than (but not under) 1E6, which reduces the designfactor for the austenitic S-N curve to less than 2 and 20.

The design curve is developed by applying two sets of factorsto the failure curve, thus generating two new curves. One factor is2 on stress, and the other is 20 on cycles. The two curves werethen blended into a smooth curve. The factor of 20 on cycles con-trols the blended curve in the low-cycle (deformation-controlled)regime (i.e., below about 1E5 cycles), whereas the factor of 2 isfor load control that occurs in the high-cycle regime. This reduc-tion is made after the adjustment for the mean stress effect and,consequently, the design factor is often referred to as 2&20.

The factor of 2&20 was based on engineering judgment thatrecognized that test data were obtained from small, smooth speci-mens and were used to predict the fatigue behavior of large com-ponents. In the high-cycle regime, in which a factor on cycles ismeaningless, the factor of 2 on stress was established to achieve asimilar margin as the 20 factor on cycles.

The 2&20 factor was originally justified by full-sized vesseltests and also by acknowledging unknowns in the fatigue testingand analytic procedure. The full-sized vessel tests were performedby pressure cycling at room temperature. Page 20 of the Criteria

presents this data as Fig. 12, which is given here as Fig. 6.14. Itshows that no failures occurred before the design curve, althoughthere are a few data points where cracks initiated close to thedesign curve. In general, the data shows that there were nothrough-thickness cracks in less than a factor of 3 on cycles.

The “acknowledging of unknowns” has been discussed foryears. The original “acknowledgment” included data scatter, sizeeffect, surface finish, etc. Studies and discussions have greatlyextended this list (see Table 6.1). In addition, work continues todefine a more accurate design factor. In general, studies indicatethat the 2&20 is conservative. Based on a review of available lit-erature, the conditions with known impact and definable valuesare presented in Table 6.2. The effect of the pure water environ-ment used for the primary fluid in a nuclear plant may also have asignificant impact. Until this environmental issue is resolved, areduction in the 2&20 design factor is inappropriate; in the inter-im, however, the designer should accept the full size tests as notedin Fig. 6.12 as the basis of design curve adequacy.

6.7 SPECIAL PROCEDURES

This section discusses six areas in which the Code presentsfundamental procedures, but does not reveal some of the detailsnecessary for a full analysis. The following discussions expand onthe Code fundamentals by presenting guidelines for a singularview of acceptable procedures that are consistent with the originalintent for Section III and consistent with the current rules. Someof the discussions relate to the FEA and, specifically, areas inwhich the FEA model uses solid (continuum) elements.

6.7.1 Notches It is well established that fatigue damage originates at notches

and defects. The NB rules for NDE are intended to eliminatedefects (defect is defined as a flaw that can produce significantfatigue damage). However, notches occur in all vessels, and theirimpact on fatigue damage must be considered in the analysis. The

FIG. 6.12 FATIGUE DATA FOR ORIGINAL FAILURE CURVES

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 29

30 • Chapter 6

responsibility for accurately including the notch effect is withinthe domain of the analyst.

A notch is defined as any geometric or material (local) disconti-nuity that causes a stress or strain concentration that decreases the fatigue life. The word “notch” implies a surface condition, but near-surface inhomogeneities are of interest as well. Two

approaches for addressing stress concentrations are discussed: thestress concentration factor (SCF) and the fatigue strength reduc-tion factor (FSRF).

Notches can be categorized as blunt or sharp. Blunt notches havea definable geometry usually dominated by a definable radius,whereas sharp notches are more severe than blunt notches and are

FIG. 6.13 UPDATED FATIGUE DATA FOR FERRITICS

FIG. 6.14 TEST DATA FOR JUSTIFICATION OF THE 2&2O FACTOR

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 30

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 31

characterized by early initiation of a fatigue crack. Table 6.3 cate-gorizes notches as design, fabrication, and operation; it presents keyinformation for each category as well. The rules of NB do notaddress the third category (operation notches); considerations forassessing the remaining two notch categories include the following:

(1) An FSRF is applied to the alternating stress (Salt or Sa) whenit is developed from theory or test data, but it may beapplied to component stresses when they are developedfrom an SCF or when the orientation of the notch is known-to be one-dimensional.

(2) Peak thermal stresses (through-thickness gradient) are notconcentrated by notches, for they result from a local tem-perature constraint rather than stress flow.

(3) An SCF is normally applied to design notches. If the fabri-cation notch has a definable geometry, it can be modeledand the SCF determined by using an FE.

(4) If the geometry of a fabrication notch cannot be defined, anFSRF must be developed.

(5) If the NDE is not able to define the flaw as planar or round-ed, or if it could possibly be characterized as planar, theflow should be evaluated as planar.

The SCF is defined as Smax/Snom, where Smax is the total stress ata point and snom is the local membrane-plus-bending stress. TheSCF is applied to a component stress. The FSRF, caused by anotch, is defined as follows:

(6.8)

where

Sa� the applied alternating stress for a smooth specimen Sa � the applied alternating stress for the notched specimen

FSRF = S¿a/Sa

TABLE 6.1 CONDITIONS AFFECTING THE DESIGN MARGINS

Title Subject Condition (Description or Comment)

Basic Metal — Ingot size and amount or reduction Material working direction, heat treatment, and chemistry Grain size impact on S-N

Fabrication effects Surface finish Value in current design factor versus RMS/RHR Hot/cold work Surface preparation: work hardening Mechanical/electrochemical polishing Fabrication surface conditioning: cleaning Weld repair Unbonded cladding Oxide buildup Blending of notches

Residual stress: from fabrication — After PWHT process or from operation Cladding impact

Exceeding 3Sm

Crack closure during crack growth

NDE Number, size, and distribution of inhomogeneities Analytic Notches FSRF/SCF values and methods of application

Constraint Plane strain versus plane stress; biaxial loading Miners’ Rule History effects with plasticity

Tresca versus Mises Max. mean stress effect

Environment Water versus air versus vacuum Temperature effects Cladding: singularity, residual stress, and plasticity Differentiating SCF versus FSRF: Application Penalty factors for exceeding P � Q limit Accuracy of stress analysis

Testing Material type: plate, forging, and weld Specimen orientation with respect to working direction Material heat treatments and chemistry Specimen heating (especially in high-cycle fatigue) Temperature effect on life

Size effect Specimen size and shape

TABLE 6.2 CONTROLLING CONDITIONS FOR THE DESIGN MARGIN

(1) Convert mean failure curve to curve for 5% probability of cracking

(2) Size effect (3) Surface flaws and notches (finish) (3) Loading sequence with Linear Damage Rule (4) Multiaxial stress field

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 31

32 • Chapter 6

In the test data, produces a lower cyclic life than Sa pro-duces. Thus the FSRF is a function of the geometry. Both the no-notch geometry (Sa) and the notched geometry ( ) are both testedusing the same material and geometry except for the notch. Usingthe failure curve for this material, both Sa and Sa are determinedand FSRF � /Sa is calculated. The FSRF is appropriate to theS-N point defined by Sa cycles. The FSRF will vary as a functionof cyclic life, for it is a maximum at the endurance limit (generallyconsidered as 1E6 cycles for ferritic materials) and approaches1.0 at the high-stress (low-cycle) limit.

There are functions that allow the translation of an SCF into anFSRF. (Using the FSRF will produce an increase in the cycliclife.) Applying the FSRF to the component stress versus applyingit to the alternating stress (Sa) depends on the geometry—that is,defined notch geometry or not able to define.

SCFs are associated with elastic conditions, whereas FSRFs aremore appropriate for stress levels (Smax) above Sy. In the elasticregime, the SCF and FSRF should be close to the same value fordefining the fatigue life (i.e., SCF � FSRF within the generalaccuracy of the fatigue analysis procedure). Both the SCF andFSRF relate to crack initiation and, in this sense, their values areequal in the elastic range. If a crack initiates, the damage mecha-nism is crack growth that theoretically does not relate to an SCFor FSRF. If the stresses exceed the yield strength, the FSRF willgive less fatigue damage than the SCF.

If an elastic FEA is used, the SCF is automatically included inthe results if an adequately refined modeling is used. If the analystmust superimpose an SCF (e.g., the grid refinement is inade-quate), the procedure for applying an SCF has weaknesses, exam-ples of which are as follows:

(1) Many notch geometries do not have theoretical or hand-book solutions. Thus, the analyst relies on such methods asapproximating the SCF from similar geometries, photoe-lastic studies, and FEA predictions.

S¿a

S¿a

S¿a(2) The analyst must develop the membrane-plus-bending

stress before applying the SCF, and the thermal peak stressesmust be superimposed after applying the SCF.

(3) A single SCF is applied at all locations on the notch sur-face, whereas the stress concentration actually varies alongthe notch surface.

In summary, locations containing notches should always be con-sidered for fatigue analysis. The approach to addressing the impact ofnotches are not fully defined in NB but are important to the analysis.The responsibility for the analysis of notches belongs to the analyst.

6.7.2 Welds The vast majority of fatigue failures in pressure vessels and

piping have occurred in a weld or at the weld-to-base metal inter-face. The majority of these welds are fillet welds, which the NBrules limit to low-stress locations. However, other vessels and pip-ing (e.g., those of Section I and Section VIII, Division 1) allowfillet welds in many applications. Also, the NB rules have a higherlevel of inspection (NDE) and more rules for weld developmentthan other pressure vessels and piping. These built-in rulesenhance the quality and, consequently, NB fatigue procedures arenot transferable to non-NB vessels.

Vessels constructed under the rules of NB have an excellentfatigue record for both base and weld metal. Thus, welds and basemetal have equivalent fatigue quality. However, their responses toapplied cyclic loading are different. The following paragraphsaddress the differences (embodied in ten issues) in fatigue consid-erations for welds relative to base metal. The fatigue design pro-cedure for welds should provide guidance on these differences.

(1) Determination of the FSRF The determination of the FSRFmust be developed by using specimens of the same geometries,materials, and procedures as those used for the actual productionweldments. The tests should be run as load- or deformation-controlled, depending on how the actual component is loaded.

TABLE 6.3 SOURCES OF NOTCHES

Type of Notch Description

Design notch: A planned design condition caused by the nature of the product or by material requirements (e.g., blend radius and bimetal interface).

Examples Changes in shell thickness, shell penetrations, and blend/fillet radii at discontinuities. Condition Geometry can be defined in the design phase and included in the design analysis (e.g.,

FEA model), and is part of the fabrication-inspection requirements (e.g., minimum blend radius).

Evaluation Using the S-N fatigue procedure, obtain the total stress from FEA or apply SCF to membrane and bending component stresses.

Fabrication notch: Geometry local discontinuities caused by manufacturing requirements or processes. Examples Partial-penetration welds, nonremoved backing straps, as-welded condition, tooling

marks, and exposed porosity. Condition Notch geometry may be definable through fabrication mock-ups, but geometry is not

modeled for accurate local stresses in FEA. Evaluation Define SCF or FSRF and the procedure for applying in S-N fatigue.

Operation notch: Surface geometry discontinuities caused by load cycling or aggressive environment, or not detected by shop NDE.

Examples Corrosion pitting, heat cracking, fretting, or NDE indications found inservice. Condition The size and shape may not be fully definable. Evaluation Severe (planar geometry): Define an assumed crack that approximates the depth of the

notch and perform a crack growth analysis. Blunt (rounded geometry): Define a geometric shape and conservatively estimate its FSRF/SCF.

Perform S-N fatigue analysis.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 32

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 33

The elastic SCF may be used in place of the FSRF, but it can beconservative—perhaps excessively so.

(2) Low-Cycle and High-Cycle Fatigue Application to theFSRF The FSRF can be established for every “number-of-cycles”level and is expected to be a maximum at the endurance limit,decreasing as the stress increases. For the experimental determi-nation of the FSRF, enough specimens should be available to testthe range of design stresses determined to be important in theapplication. The variable FSRF may be used for the matchingstress level. If data are not developed for the full range of designstresses, the maximum FSRF (the value determined for the 1E6cycle limit) may be used over the full stress range.

(3) The Role of NDE Procedures The weld fatigue test speci-men used to generate an FSRF must match the worst-case qualityof the pressure vessel weld, including the probability of the exis-tence of flaws. This is especially important for surface conditionsbecause fatigue damage normally initiates at the surface. If practi-cal, the test specimen should receive the same NDE as thatrequired by NB for the component.

(4) As-Welded Surface Finishes The as-welded condition isexpected to have a higher roughness (e.g., measured by RHR)than base metal. The experimental determination of FSRF toaccount for surface dressing procedures and physical profiles ofthe as-welded components should be included in the develop-ment. Grinding to make the surface suitable for certain NDE pro-cedures will improve the weld fatigue quality.

(5) The Effect of Yield Strength Variations (MetallurgicalNotch) A weld is part of a weldment that consists of multiplematerials with various yield strengths. When the load exceeds theyield strength, strain is likely to concentrate in the material withthe lowest yield strength. Thus, the yield strength of the weldshould be greater than that of the other (base metal) materials inthe weldment. In analyses, the yield strength of weld metal is nor-mally considered equal to the equivalent base metal minimumyield strength, but in reality the weld yield strength is normallyhigher than that of the equivalent base metal. Therefore, theexpected yield strengths should be used for determining thepotential for local strain concentration.

(6) Residual Stresses Because uncertainty of the level of resid-ual stresses, the NB rules apply the strategy of assuming the“worst effect” of mean stress on the fatigue behavior. Thus, the S-N curve that includes the “worst effect” of mean stress andresidual stresses from welding are conservatively addressed forthe fatigue analysis. However, residual stresses affect corrosion,including stress corrosion cracking [see issue (9)].

7) Weld Surface Geometry (Process/Procedure) The mostcommon fatigue damage site is the weld toe, which is caused byundercuts and intrusions. The potential for these conditionsrelates to the weld process and procedure. The fatigue designapproach for welded joints should include guidelines for thewelding process and procedure. The current NB requirementsshould be reevaluated relative to design expectations (i.e., theworst weld toe notch). It is noted that NDE requirements shouldpreclude flaws (notches) at the weld toe if the weld process andprocedure is adequately developed and applied.

(8) Effects of Environment on S-N Fatigue The response of theweld metal to the environment (e.g., corrosion) cannot be predictedsimply from studies on the base metal. Their responses are weld-ment attributes that can affect environmental fatigue damage;thus, the weldment it requires attention over that of the basemetal. Such attributes include composition, microstructure, surfacefinish, and residual stresses. The current environmental databaseon welds is weak.

(9) Stress-Corrosion Cracking Some austenitic materials (baseand welds) are susceptible to cracking. The design procedure forwelded joints should include an evaluation of the potential forcracking. For weld metals susceptible to cracking, welding para-meters and sequences should be chosen to minimize sensitizationof the various weld zones—particularly near crevices. Whereverpossible, sensitive welds should be designed with geometries freeof sharp notches.

(10) Postweld Heat Treatment The requirements for postweldheat treatment (PWHT) are detailed in NB-4600 (Heat Treatment).The PWHT performs the following two functions:

(1) softening of the material, and (2) reduction of residual stresses.

These benefits apply to both the heat-affected zone and theweldment-fusion zone.

6.7.3 Controlling Locations for Assessment The discontinuity or interaction analysis were common proce-

dures when Section III was initially released in 1963. This proce-dure focused on such readily defined elements as cylinders, par-tial spheres, tapered shells, and cone shells. In addition, itrequired the elements to be continuous at the junctures (i.e., theadjoining elements had the same displacement and rotation). Thedefined equations ensured the continuous material and also deter-mined the loads (forces and moments), from which the stresses atthe junctures were calculated. Thus, the discontinuity proceduredetermined the stresses that would be used in the comparison tothe stress limits (PL, PL � Pb, and P � Q). This simplicity fordetermining the controlling stresses was totally changed when theFEA became the commonly applied procedure. The FEA sub-stantially increased the complexity for defining the controllinglocation.

The FEA procedure (continuum elements) has the followingtwo features that cause most of the increase in complexity overthat of the discontinuity procedure:

(1) the change in the role and definition of the elements, and (2) the completeness of the model defining the geometry.

Regarding item (1) of the preceding list, the finite elements canbe of any size or shape as long as they cover the whole geometrywith multiple elements placed meridionally and through the thick-ness. The stresses are calculated for each element at integrationpoints. Consequently, a single element does not produce a forceor moment that defines the membrane or bending stresses, respec-tively, so when continuum elements are used, the FEA requires aprocedure for determining the membrane and bending stressesbased on the stresses in multiple finite elements.

Regarding item (2), the more completeness of the geometrymodel also produces an increase in complexity. The discontinuityprocedure used clearly defines geometries as the elements anddoes not include nonelement features such as blend radii. TheFEA can and normally does include these features in the model.The result is a complex through-thickness set of finite elements.Figure 6.15 shows a complex finite element distribution in anozzle-to-shell geometry, with the nozzle being at an angle to theshell. This capability to accurately model the full geometryrequires a special procedure to define the controlling location formembrane and bending stresses.

The following paragraphs discuss the features for a suitableprocedure and are divided into two parts: global locations andlocal locations.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 33

34 • Chapter 6

The global location is expected to be at a discontinuity for thefailure modes, PL � Pb and P � Q; Pm is evaluated away from anydiscontinuity (i.e., it is not of “local concern” for the failure modeit addresses). Normally the global location is at the juncture of twobasic discontinuity-type elements. Sometimes, however, one of thebasic elements responds to the loads as a ring (it rotates, but doesnot bend); these are called “transition” elements, and the other ele-ments are called “structural” elements. There are cases, such as acone–cylinder juncture, that do not contain a transition element,but for which the global location is still expected to be in the vicin-ity of the juncture of the two adjacent structural elements.

Membrane-plus-bending stresses are evaluated in structuralelements, not in transition elements. Although the controllinglocation is expected to be at the juncture of the two discontinuity-type elements, the controlling location may be some distancefrom the juncture (in all likelihood, however, it will be close tothe juncture). If the controlling location is not at the juncture ofstructural and transition elements, it will be in the structuralelement; however, for complex geometries (as noted in Fig. 6.13),it can be very difficult to define the juncture, in which case under-standing the definition for the two element types is important.

A basic structural element is a pressure-containing shape, such asa cylindrical shell, spherical head, or flat (cover) plate in which oneor two of the three principal stresses (hoop and meridional) are sig-nificant. An element that connects two basic structural elements is atransition element. As stated previously, the controlling location isnot within a transition element. Evaluation in transition elementsmay be limited to fatigue crack initiation (SN) and crack propagation(da/dN)—that is, an evaluation of the NB elastic limits for PL,PL � Pb, and Q—need not be made in transition elements. Thebasis for the exclusion of transition elements comes from theoriginal development that was based on interaction (discontinuity)analysis. It is overly conservative to force the limits to be satisfiedwherever such internal forces and moments have little structuralphysical significance. Transition elements are normally transitionrings. The geometry of the ring cross section can be described as aquadrilateral; blend radii may need to be deleted to obtain four sides.Of the four sides, two adjacent sides will have traction loads (e.g., aplate–shell juncture ring is restrained by the plate-bending momentand by the axial load in the shell, both of which are on adjacent sides.

The local location primarily addresses the orientation of athrough-thickness stress distribution. If blend radii are included in

the model, the local location and its orientation must beaddressed. For this and similar cases, criteria should be appliedfor establishing locations and orientations. To accomplish thistask requires a through-thickness stress distribution that is repre-sented as a line and called a stress classification line (SCL). Theguidelines are presented as six steps (in order of importance) inTable 6.4. These guidelines are also discussed in depth in WRC-B429 [4].

There may be geometry and load combinations where criteria(4), (5), and (6) cannot be met in the region of interest. For thiscondition, criteria (3) controls. Deviations from the criteria areacceptable if the FE grid or software limitations cause such devia-tions. However, if the SCL is not perpendicular to the midline, thechoice of local location or orientation is probably invalid.

To summarize, the procedure validates that the stress limits aremet at discontinuities and in the structural element (global view).The precise location is obtained by ensuring that the through-thickness stress distributions are theoretically correct—that is,they are linear or parabolic depending on whether they are normalcomponents or shear components, respectively. The WRCBulletin 429 provides more details for this development.

6.7.4 Calculating Membrane-Plus-Bending Stresses Except for fatigue, the stress intensity limits (Pm, PL, Pb, and

P � Q) require the calculation of the membrane and the bendingstresses. These are through-thickness stresses (i.e., the membranestress is constant from the inside surface to the outside surface ofthe shell or plate and the bending stress is a linear stress from theinside to the outside of the shell or plate). For many geometriesand loadings, FEA through-thickness stress gradients are nonlin-ear. Therefore, a procedure is required to translate a nonlinearstress gradient into a linear gradient.

Note (2) to NB-3213.13 states the following for the linearizedstress:

Equivalent linear stress is defined as the linear stress distrib-ution which has the same net bending moment as the actualdistribution.

FIG. 6.15 EXAMPLE OF A COMPLEX FINITE-ELEMENTGRID

TABLE 6.4 CRITERIA FOR LOCAL LOCATIONS

(1) Only address structural elements, not transition elements.Safety margins cover potential inaccuracies in this approach.

(2) The SCL orientation should be perpendicular to the stressflow. Some times, this may be too difficult to apply.

(3) In lieu of step (2), the SCL orientation should be perpendicu-lar to the midline of the geometry. This is expected to closelymatch step (2).

(4) Hoop and meridional component stress distribution should belinear except for the effects of the stress concentration fromnotches and thermal peak stresses. If this is not met, a previ-ous step has been violated.

(5) The stress distribution should be linear for the component ofstress parallel to the direction of the SCL, with the surfacestresses equal to the boundary stress (e.g., compressive pres-sure). When the SCL is not perpendicular to the surface, thisrequirement may not be met.

(6) The through-thickness, shear stress distribution should beparabolic, and the stresses should be low relative to thenormal hoop and meridional stresses. When the SCL is notperpendicular to the surface, either (the distribution or themagnitude) requirement may be difficult to attain.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 34

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 35

This wording is interpreted as the bending moment that mustbe determined, and the bending stress must be calculated usingthe bending moment. There have been significant discussionsabout whether this interpretation precludes linearizing the stressdistribution directly in determining the bending stress. One groupof engineers experienced with the Code reached a consensus thatthe total force and the bending moment must be calculated andused to obtain the membrane and bending stress. This group alsorewrote the Note (2) of NB-3213.13 as follows:

Linearized stresses (membrane-plus-bending) are stresses rep-resented by linear distributions which develop the same netforces and moments on a section as the total stress distribution.

This rewrite is more clear and comprehensive than its predeces-sor. The WRC Bulletin 429 (PVRC, 1998) recommends that thisrevised wording replace the current wording.

Thus the overview is as follows:

(1) The linearized stresses (i.e., membrane and bending stress-es) are calculated from the component stresses, not fromprincipal stresses.

(2) The linearized stresses are based on internal forces andmoments for explicitly computing membrane (p/a) andbending (6m/t2 ) stresses; they are not obtained by arbitrar-ily fitting a straight line through the stress distribution(stress versus distance) curve for each component of stress.

Appropriate steps for applying the approach in the precedinglist are presented in Table 6.5.

6.7.5 Poisson’s Ratio for Peak Thermal Stresses As discussed previously, fatigue assessment uses elastic analy-

sis; however, local thermal stress may require an adjustment. NB-3227.6 (Applications of Elastic Analysis for Stresses Beyond theYield Strength) gives a procedure for the adjustment, referencingNB-3213.13(b) for the definitions of local thermal stresses. (Thelatter was discussed previously in Section 6.5.3.) The adjustmentis described in NB-3227.6(b) as follows:

In evaluating stresses for comparison with fatigue allowables,all stresses except those which result from local thermalstresses . . . shall be evaluated on an elastic basis.

The adjustment is therefore applied only to the local thermalstress.

The local thermal stress results from a rapid change in the con-tained fluid. For example, assume that the pressure boundary andthe fluid are at stable temperatures. When the fluid temperaturechanges, the temperature of the pressure boundary starts tochange and continues to change until it reaches (approximately) thetemperature of the fluid. During this interval, the differencebetween the surface temperature and the average through-thicknesstemperature increases until its maximum delta temperature isreached, which produces the maximum local thermal stress.Following this condition, the local thermal (surface) stressdecreases as the through-thickness temperature gradient increases.As the temperature gradient increases, the P � Q increases, andeventually the temperature gradient reaches its maximum. It willthen begin decreasing, and the through-thickness temperature willapproach that of the fluid.

The adjustment is made to the surface stress when the differ-ence between the surface temperature and the average tempera-ture is at a maximum. Conservatism in the adjustment occurswhen the maximum surface stress is superimposed on the P � Q;in fact, the maximum surface (local) thermal stress occurs at atime different from that of the thermal gradient’s effect on reach-ing the maximum P � Q. Another consideration results from theadjustment procedure being developed when the common toolwas the discontinuity or interaction analysis. In that procedure, itwas common to calculate the maximum local thermal stress inde-pendent of the membrane and bending stresses from a through-thickness thermal gradient. Thus it was simple to apply the adjust-ment to the maximum local thermal stress and then superimposeit on the P � Q from the discontinuity analysis.

With this in mind, the NB procedure is defined as the following:

In evaluating local thermal stresses, the elastic equations shallbe used, except that the numerical value substituted forPoisson’s ratio shall be determined from the expression:

n � 0.5 � 0.2(Sy / Sa), but not less than 0.3

where

Sa � value obtained from the applicable design fatigue curve(Fig. I-9.0) for the specific number of cycles of the con-dition being considered

Sy � yield strength of the material at the mean value of thetemperature of the cycle

The NB procedure presumes that the adjustment of Poisson’sratio is based on the ratio of stress above the yield stress to theyield stress. For this presumption to be true, the procedureassumes that P � Q is at its limit. Also, the total stress is at itslimit for the number of cycles (i.e., the definition of Sa relates it to

TABLE 6.5 PROCEDURE FOR LINEARIZED STRESSES

(1) Map and/or interpolate nodal-point FE stresses onto the SCL(see Fig. 6.15). Note: sij from FEA or other methods aremapped or interpolated onto “sample points” or “stress sam-ple cubes” along the SCL. These are “total” componentstresses; they are used in the linearization process.Guidelines for this step are as follows: (a) use enough sample points to accurately predict the load

distribution; (b) all six component stresses are included (for three-

dimensional cases); and (c) the component stresses are oriented relative to the SCL.

(2) Develop the load distribution through the thickness (seeFig.6.16). Each stress point represents a cube that produces aload on each face, producing load distributions for each com-ponent stress along the SCL.

(3) Integrate each load distribution to obtain the total load (p)and the area it represents.

(4) Calculate the average (membrane) stress (each componentstress) using the simple equation (p/a).

(5) Subtract the membrane stress from the total stress, point bypoint. (a) This only needs to be done for the two normal compo-

nent stresses that are perpendicular to the SCL (faces 2and 3 in Fig. 6.16, nominally, the hoop and meridionalcomponent stresses).

(b) This produces a moment stress distribution. (6) Develop the moment load distribution through the thickness. (7) Integrate the moment load distribution to obtain the moment

on the cross section. (8) Calculate the bending stress by a simple equation (M/Z or

6m/t2)

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 35

36 • Chapter 6

the number of cycles that will occur). These are both conservativeassumptions. The mathematics are that as Sa increases, thePoisson’s ratio (n) increases until it (the asymptote) reaches 0.5.When the adjusted n is calculated, it is applied to the actual localthermal peak stress (S) as follows:

Sadj � S[(1 � n)/(1 � nadj)] (6.9)

where the subscript “adj” denotes “adjusted.”

As stated previously, the foregoing procedure was developedassuming that discontinuity or interaction analyses were the meth-ods of choice. With today’s use of FEA, the current NB approachadds difficulty to the normal process. For this reason, and alsobecause of the resulting unnecessary conservatism, various groupswithin the Code are evaluating suggested methods for use withFEA. The fundamental and accurate step is to apply the Poisson’sratio adjustment to that part of the total stress range exceeding theyield strength, while at the same time demonstrating that thisabove yield stress can be related to local thermal stress. It isexpected that this new procedure will soon be added to NB.

6.7.6 Plasticity Currently, there are multiple studies on using plasticity in

design and analysis. Both the Code and the PVRC have subcom-mittees that are developing new NB rules. It is expected that thenew rules, and expansion of the current rules, will be added toNB. The following discussions are based on the 1998 version ofNB; future study of the NB subsection requires an understandingof the changes to the 1998 version. The 2007 version of SectionVIII Division 2 codifies the recommendation of the PVRC as willbe discussed later.

When one designs by plastic analysis, his or her key concernsshould be unacceptable levels of deformation, ratcheting, andcyclic plastic strain. Deformation has two conditions to address:customer-defined limits and a design condition that requires alimit on deformation. For example, a condition that develops aleak path is a design condition. Deformation is defined in NB-3213.20 (Deformation) as follows:

Deformation of a component part is an alteration of its shapeor size.

A customer-defined limit is addressed in NB-3222.6 (Defor-mation Limits) as follows:

Any deformation limits prescribed by the Design Specifica-tions shall be satisfied.

The assumption is that the customer has written the DesignSpecifications and has included the limit; thus, meeting therequirement is mandatory. Deformation can be caused by eitheran elastic or a plastic design procedure.

Ratcheting, defined in NB-3213.33 (Ratcheting), is generallyassociated with plasticity. Under certain cyclic conditions, thevessel can expand with each cycle until shakedown occurs or itcan expand continuously if shakedown does not occur. The termsof shakedown and inelasticity are defined in NB-3213.34(Shakedown) and NB-3213.21 (Inelasticity), respectively. Eachterm is defined as the following:

Ratcheting is a progressive incremental inelastic deformationor strain which can occur in a component that is subject tovariations of mechanical stress, thermal stress, or both.

Shakedown of a structure occurs if, after a few cycles of loadapplication, ratcheting ceases. The subsequent structuralresponse is elastic, or elastic–plastic, and progressive incre-mental inelastic deformation is absent. Elastic shakedown isthe case in which the subsequent response is elastic.

Inelasticity is a general characteristic of material behavior inwhich the material does not return to its original shape andsize after removal of all applied loads. Plasticity and creep arespecial cases of inelasticity.

As stated in the preceding definition, ratcheting (i.e., progres-sive incremental inelastic deformation or strain) is therefore anunacceptable condition; indeed, it is considered a failure mode.The Criteria document calls this condition plastic instability–incremental collapse (page 4, 5). However, elastic-plastic shake-down can be acceptable, although it produces cyclic plastic strainthat is addressed within the fatigue procedure.

Inelasticity for conditions below the creep region are addressedas plasticity. NB-3213.23 (Plasticity) defines this term as follows:

Plasticity is a special case of inelasticity in which the materialundergoes time-independent nonrecoverable deformation.

Thus, plasticity addresses all noncreep conditions in which theyield strength is exceeded for mechanical loads (primary loadssuch as pressure) or to twice yield for mechanical-plus-thermalloads (cyclic operation). These conditions are in lieu of the elasticfailure modes with their limits defined by Pm, Pb, PL, and Q—theseare defined by the average strain through the thickness of thematerial. In addition, plasticity addresses the permanent total(cyclic) strain at a point (fatigue analysis). As elastic analysis usesthe yield strength as the controlling material property, plasticanalysis uses the lowerbound stress–strain curve. For the non-cyclic conditions (primary loads), the material will harden; forcyclic conditions, on the other hand, the material can be a harden-ing or a softening condition.

When plasticity is used in an analysis, there are two approaches:plastic analysis and limit analysis. The first term is defined byNB-3213.24 (Plastic Analysis) as follows:

Plastic analysis is that method which computes the structuralbehavior under given loads considering the plasticity character-istics of the materials (stress–strain curve), including strain hard-ening and the stress redistribution occurring in the structure.

Note that the preceding definition assumes strain hardening,which is valid only for the noncyclic primary loads. The interpre-tation of this phrase for cyclic conditions is difficult, for it can beaddressing only primary loads (noncycling) or it can be assumingthat cyclic softening materials are not included in the NB-allowedmaterials. However, the Code does not define the cyclic-softenedmaterials. The rational assumption is that NB allows plasticanalysis if only cyclic hardening material is used.

The second term is defined by NB-3213.27 (Limit Analysis)that refers to it as a special case of plastic analysis and also pre-sents the differences between it and plastic analysis. The basicdifference is that limit analysis assumes an “ideally plastic”stress–strain curve, whereas plastic analysis uses a hardeningcurve. The term ideally plastic means that no strengthening afterthe yield strength is reached—that is, the stress–strain curve is flat(zero modulus) after the yield strength is reached. The limitanalysis will produce stress (load) redistribution to a lesser extentthan plastic analysis because of the hardening.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 36

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 37

The limit analysis also recognizes two theories: the lowerboundapproach and the upperbound approach. The first is “associatedwith a statically admissible stress field”; the second, “associatedwith a kinematically admissible velocity field.” The NB discus-sions and rules for the use of limit analysis appear to be directedto the lowerbound approach—the tone that the tone that theCriteria uses as well when it discusses the basis for the designmargins for elastic stress limit.

6.7.6.1 Applying Plastic Analysis The rules for applying plas-tic analysis can be difficult to interpret. For example, the first para-graph of NB-3228.3 (Plastic Analysis) is worded similarly (but notquite the same) as NB-3213.24 (Plastic Analysis), presented in thefore-going paragraphs. The wording should be identical, or elseone of the two paragraphs should be deleted. However, the firstparagraph of NB-3228.3 should address using the methods ofsmall deformation versus large deformation. It does state that theplastic analysis “may include strain hardening or change in geom-etry, or both”— a small phrase can be interpreted as allowing largedeformation. The current definition of collapse, in “CollapseLoad” of NB-3213.25 (Plastic Analysis), would probably precludeany significant benefit for the large-deformation approach for NBferritic materials. However, for the austenitic materials (e.g., stain-less steels), the use of large deformation could be significant, andin addition, for many geometries such as flat plates, the permanentdeformation could produce a significant change in geometry. Theinterpretation is that the small deformation should be used unlessthe large deformation produces an acceptable new geometry (i.e.,allowable deformation).

Another example of difficult interpretation occurs in NB-3228.3 (Plastic Analysis), the second paragraph of which statesthe following:

The limits of General Membrane Stress Intensity (NB-3221.1) . . . need not be satisfied at a specific location if it canbe shown that the specified loadings do not exceed two-thirdsof the plastic analysis collapse load. . . .

However, the final sentence of the paragraph states the fol-lowing:

The design shall satisfy the minimum wall-thickness require-ments.

At one place, the paragraph implies that the basic thicknessobtained by Pm need not be met if plastic analysis is performed,whereas the paragraph’s last sentence implies that Pm must bemet. The appropriate interpretation is that Pm must be met unlessthe violation is limited to “a specific (local) location,” which inreality changes a “general membrane” to a “local membrane”stress intensity. One should refer to NB-3213.8 (Primary Stress),which states, “A general primary stress is one which is so distrib-uted in the structure that no redistribution of the load occurs as aresult of yielding.” Thus, plastic analysis requires a basis andadditional rules to allow it to supersede the elasticity definition ofthe minimum shell-thickness.

The “Collapse Load” of NB-3213.25 (Plastic Analysis) definesthe limit or design margin for the use of plastic analysis. It gives astep-by-step procedure sometimes known as the double-angleapproach. This procedure is also applied to NB-3228.2(Experimental Analysis), but it includes a figure to show themethod (see Division 1, Appendix II-1430). A review of thefigure, reproduced here as Fig. 6.16, should more readily explainthe double-angle approach. To better understand the impact, the

double-angle approach should be applied to a common ferriticmaterial and an austenitic material by using monatomic stress-straincurves. It is expected that the ferritic material will show very littleimprovement in allowable applied load compared to an elasticallydetermined allowed load. The austenitic material may show aneven greater impact.

The use of the term collapse load is often criticized, for a col-lapse in the material does not occur at the double-angle load. Inother words, the term of collapse load is inappropriate, but it doesdefine the design margin. The actual failure mode is defined inNB-3213.26 (Plastic Instability Load) and states the following:

The plastic instability load for members under predominatelytensile or compressive loading is defined as that load at whichunbounded plastic deformation can occur without an increasein load. At the plastic instability load, the true stress in thematerial increases faster than hardening can accommodate.

The plastic instability relates to the ultimate tensile stress undermost conditions. Plastic instability seems similar to “collapse,”but NB uses “collapse” to denote the double-angle definition.

FIG. 6.16 PLASTIC ANALYSIS METHOD FOR DESIGN LIMITWITH DARKENED ELEMENTS INDICATING PLASTICITY

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 37

38 • Chapter 6

The rules and discussion in NB-3228.4 (Shakedown Analysis)can be difficult to interpret, in part because of the overlappingwording with other section. The initial sentence seems to estab-lish the intent of the section as allowing plastic analysis results forshell ratcheting and nonintegral connections to override therequirements of elastic analysis. The first paragraph states the fol-lowing:

The limits on Thermal Stress Ratchet in Shell (NB-3222.5)and Progressive Distortion on Nonintegral Connections (NB-3227.3) need not be satisfied at a specific location, if, at thelocation, the procedure of (a) through (c) . . . are used.

Item (a) states the following:

In evaluating stresses for comparison with the remainingstress limits, the stresses shall be calculated on an elasticbasis.

Saying this backwards, elastic analysis is used for all requiredlimits except those that will be addressed in the second require-ment. Thus item (a) requires that elastic limits be met except forthe specific exceptions that appear in item (b).

Item (b) allows plastic analysis for overriding the limits on PL, P � Q, ratcheting, and progressive distortion of nonintegralconnections. Thus, Pm and Pb must be met on an elastic basis as aminimum—NB-3221.2 (Local Membrane Stress Intensity), NB-3222.2 (Primary-Plus-Secondary Stress Intensity), NB-3222.5(Thermal Stress Ratchet), and NB-3227.3 (Progressive Distortionon Nonintegral Connections). The first is a repeat of paragraphNB-3228.3 (Plastic Analysis); the second is not previously statedelsewhere and applies to cyclic analysis; the third and fourth areboth repeats of the first paragraph of subsection NB-3228.4. Notethat the title for NB-3222.5 is “Thermal Stress Ratchet” ratherthan “Thermal Stress Ratchet in Shell,” for the rules and discus-sion of NB-3222.5 are actually for shells. There are significantdisagreements on the interpretation. A reasonable starting point isthat NB-3228.3 applies to primary loads (i.e., monotonic loading),whereas NB-3228.4 applies to cyclic conditions. The overview isas follows:

(1) Pm and Pb must be met on an elastic basis, as a minimum; (2) PL, P � Q, ratcheting, and progressive distortion of non-

integral connections may override the elastic limits whenusing plastic analysis; and

(3) shakedown is not an issue for primary loads because of thehardening of monotonic stress–strain curve.

Item (b) also states that shakedown requirements need not besatisfied for Thermal Stress Ratchet and for ProgressiveDistortion of Nonintegral Connections if the following aresatisfied:

(1) the yield to ultimate strength ratio is less than 0.70, and (2) the plastic analysis produces a maximum accumulated plas-

tic strain at a point that does not exceed 5.0%.

These rules appear to require that plastic shakedown must bedemonstrated. One way to show this is by a hysteresis curve thatgenerates total plastic strain. When shakedown is shown, the pri-mary-plus-secondary loads, ratchet in shell, and progressive dis-tortion will be shown as acceptable as well.

Item (c) of NB-3228.4 does not seem to apply to the first para-graph, for it covers plastic analysis for fatigue (i.e., the discussiondoes not directly relate to shakedown). It states the following:

In evaluating stresses for comparison with fatigue allowables,the numerically maximum principal total strain range shall bemultiplied by one-half the modulus of elasticity of the mater-ial . . . at the mean value of the temperature.

The preceding quotation defines the rule that the total plasticstrain be converted to elastic stress by using the elastic modulusand includes the use of only the maximum principal strain in theconversion. It also defines the elastic modulus as based on themean temperature of the cycle.

To summarize, the procedure for plastic analysis allows that itcan override the need to meet the fundamental limits of PL, PL � Pb,and P � Q, as well as the limits for specific rules such as NB-3222.5 and NB-3227.3. However, general ratcheting must be eval-uated by cyclic analysis and must meet the defined limits.Ratcheting is not expected for NB materials when the appliedload is load-control (e.g., by pressure or other mechanical load),nor is it expected for fatigue because of the notches or thermalshock (except when continuous in a long shell). Ratcheting mustbe considered when the plasticity extends through the thickness ofthe vessel and average (membrane) strain (through-thickness) isgreater than twice the (von Mises) yield strain. Plastic analysiscan be applied to load-controlled, load-controlled-plus-deforma-tion-controlled, and fatigue; moreover, any combination of thesethree is acceptable without using plasticity for the others.

6.7.6.2 Applying Limit Load Analysis Limit load was dis-cussed previously to the extent of NB-3213.27 (Limit Analysis)and presents the use of a nonhardening stress-strain curve as wellas two approaches: lowerbound and upperbound. “LimitedLoad–Collapse Load” of NB-3213.28 Limit Analysis extends theprocedure by defining “collapse” for limit load, which is differentthan the definition used for plastic analysis. It is defined as follows:

The methods of limit analysis are used to compute the maxi-mum load that a structure assumed to be made of ideally plas-tic material can carry. At this load, which is termed the col-lapse load, the deformation of the structure increases withoutbond.

This definition applies to both the lowerbound and the upper-bound approaches. It becomes specific when it is applied to eitherlower- or upperbound procedure. The next definition is given inNB-3213.29 (Collapse Load—Lowerbound), which states the fol-lowing:

If, for a given load, any system of stresses can be found whicheverywhere satisfies equilibrium, and nowhere exceeds thematerial yield strength, the load is at or below the collapseload. This is the lowerbound theorem of limit analysis whichpermits calculations of a lowerbound to the collapse load.

This definition actually pertains to an elastic concept—that is,the “equilibrium,” which allows the load to be distributed to pre-clude exceeding the yield stress, can be applied in elasticity. Inthe limit analysis, favorable and realizable redistribution doesoccur as the yield stress is reached at one location and the remain-ing load is distributed to adjacent locations. For example, acone–cylinder geometry, when loaded by pressure, will reach theyield stress first at the cone-cylinder juncture. Then, the load willredistribute through the thickness at the juncture and subsequentlyredistribute away from the juncture along the cone and also alongthe cylinder. At some point, the geometry will not allow any addi-tional distribution; for such geometry, the distance is too far from

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 38

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 39

the juncture, and limit analysis–type collapse occurs. If a plot ismade of pressure versus strain (or deformation), the curve isvirtually flat (horizontal) until collapse, where the curve almostinstantly becomes vertical. This process is known as lowerboundcollapse.

The rules for applying the lowerbound limit load are presentedin NB-3228.1, which addresses the overriding elastic limits inaddition to giving a definition for yield stress and the design mar-gin (it also addresses other concerns). Its first sentence is as fol-lows:

The limits on General Membrane Stress Intensity (NB-3221.1),Local Membrane Stress Intensity (NB-3221.2), and PrimaryMembrane-plus-Bending Stress Intensity (NB-3221.3) neednot be satisfied at a specific location if it can be shown bylimit analysis that the specified loadings do not exceed two-thirds of the lowerbound collapse load.

The last sentence, as it pertains to the plastic analysis, requiressatisfying “the minimum wall-thickness” regardless of the limitanalysis. Thus, the general membrane stress intensity (Pm) is notoverridden by the limit analysis; in fact (and different from plasticanalysis), if the limit analysis is correctly performed, the result(allowable load and shell-thickness) should be the same as anelastic analysis would give for Pm. The application is applicableto local membrane stresses—that is, the application is appropriateat global discontinuities. In addition, the sentence sets the design-margin as 1.5.

The second sentence of NB-3228.1 states the following:

The yield strength to be used in these calculations is 1.5Sm.

The use of 1.5Sm for the yield strength is conservative if the Sm

is based on the ultimate tensile stress rather than on the yieldstrength. This fact is consistent with the elastic analysis safetymargin; the same logic is not applied to plastic analysis. Theinconsistency can be interpreted in many ways, so for plasticanalyses, the analyst should consider using the 1.5Sm as the yieldstrength for the stress-strain curve. Doing so assumes that theelastic part of the stress–strain curve is linear.

The next two sentences of NB-3228.1 address excessive plas-ticity as follows:

The use of 1.5Sm for the yield strength of those materials ofSection II, Part D, Subpart 1, Tables 2A and 2B to which Note(2) . . . is applicable, may result in small permanent strainsduring the first few cycles of loading. If these strains are notacceptable, the yield strength to be used shall be reducedaccording to the strain-limiting factors of Section II, Part D,Subpart 1, Table Y-2.

Section II addresses the material; Part D, the material proper-ties; Subpart 1, the stress tables (i.e., the allowable stresses for thesections and classes); and Tables 2A and 2B, the Sm values for fer-rous materials and nonferrous materials, respectively. The concernis that the limit load may produce “small permanent strains” thatare not acceptable. Assuming that yield stress is 1.5Sm, Table Y-2presents a factor that, when applied to the yield strength, willreduce the permanent strain. Thus the reduced yield strength(�1.5Sm) is used in a (limit load) reanalysis to produce an accept-able permanent strain.

The sentences of NB-3228.1 address concerns for the impactof design by limit load analysis on the fatigue analysis, ratchet-ing behavior, and buckling behavior. These sentences state thefollowing:

When two-thirds of the lowerbound collapse load is used, theeffects of plastic strain concentrations in localized areas ofthe structure such as the points where hinges form must beconsidered. The effects of these concentrations of strain onthe fatigue behavior, ratcheting behavior, or buckling behav-ior of the structure must be considered in the design.

The use of limit analysis does not ensure that other analyses(e.g., fatigue) are acceptable, especially when the other analysesare conducted with elastic methods. Although the rules make theconcerns mandatory (as exemplified by the words that state “mustbe considered”), guidelines are not provided. As a minimum, theanalyst must ensure that no hinges, as defined by NB-3213.30(Plastic Hinge), have been generated. A simple definition is “anoccurrence of through-thickness yielding”; nonetheless, additionalguidelines should be developed.

Experimental analyses are also acceptable for inelastic analy-ses, and their rules are presented in NB-3213.32 (Test CollapseLoad). With today’s emphasis on FEA, the use of experimentalanalysis is not anticipated for design.

6.7.6.3 Application of Thermal Stress Ratchet The term thermalstress ratchet occurs in the plastic analysis discussions, and some-times the term in shells is included. The full term, thermal stressratchet in shells, is related to NB-3222.5, which is an elastic analy-sis, and defines a procedure for assessing ratchet. However, the pro-cedure is based on thermal shock in long shells: for example, pipingwithout discontinuities. Page 21 of the Criteria states the following:

The problem of potential thermal ratchet growth has beendescribed by Miller . . . this paper provides the basis for theCode rules.

NB-3222.5 is therefore not accurate, especially at discontinu-ities. Therefore, the analyst should directly address the potentialfor ratchet for all conditions except for the long shell subject tothermal shock. (This subject is also discussed in Section 6.5.5.)

6.7.6.4 Fatigue—Plastic Analysis This topic was discussedpreviously in item (c) of NB-3228.4 (Shakedown Analysis). It hasinput for plastic analysis for fatigue; specifically, it states the fol-lowing:

In evaluating stress for comparison with fatigue allowables,the numerically maximum principal total strain range shall bemultiplied by one-half the modulus of elasticity of the mater-ial . . . at the mean value of the temperature of the cycle.

Thus the following three requirements are addressed:

(1) the total strain range, as determined by plastic analysis,must be used;

(2) the maximum principal strain is converted to the stress forfatigue; and

(3) the mean temperature of the cycle is used for establishing Sa.

Items (1) and (3) are standard for elastic fatigue analysis. Item (2) states that one-half of the principal stress can be used to enterthe S-N curve, which could be inappropriately interpreted as con-verting the full maximum principal strain to a principal stress andcalculate the stress difference and Sa from the stress difference touse in the S-N curve. However, the plastic analysis directly gener-ates the maximum strain range; therefore, the translation to stressgives the appropriate pseudostress (i.e., the stress difference) andis the appropriate stress for entering the S-N curve.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 39

40 • Chapter 6

6.7.6.5 Study Items Many issues related to inelastic analysis arenot addressed in NB. Most of these issues are being studied withinthe Code and the PVRC, and a few were mentioned earlier in thischapter. To obtain accurate results from inelastic analyses, the ana-lyst must understand and address the issues not addressed in NB.What follows is a sampling of the issues that are being studied.

6.7.6.5.1 The Rules Must Define Which of the Yield StressCriteria Will Be Used and Apply the Criteria to Both the Limitand Plastic Analyses The current rules set the yield stress as 1.5times the allowable stress. Thus, the applied yield stress can bebased on the ultimate tensile stress divided by 3 times 1.5 (i.e., theultimate tensile stress divided by 2). The analysis yield stress canbe much lower than the actual yield stress. Currently, this approachis specific for limit load but not specific to plastic analysis.

6.7.6.5.2 Define the Role of Su/3 in Inelastic Analysis,Establish the Basis, and Ensure Consistency of Rules BetweenElastic and Inelastic Requirements Plastic analysis eliminatesthe Su / 3 stress limit. Even if the yield stress is designated as Su / 3,the stress-strain curve will overpower it. If plastic analysis canoverride the Su/ 3 limit, why should elastic not match it? Thechange would be to base Sm only on yield stress or at least reducethe SF on ultimate to 2.0 and base P � Q on twice-yield, not 3Sm.

6.7.6.5.3 Should the Rules Be the Same for NB and Division 2?Should Interpreted, Current Rules for Basic Shell ThicknessBe Maintained or Should Inelastic Results Be Allowed toControl? Code-defined rules for inelastic analysis require maintraining the basic elastic calculated thickness for shells. NB andSection VIII, Division 2 rules differ in defining what shells areincluded. NB includes cylinders and hemispherical heads, which isconsistent with limit analysis and perhaps conservative for plasticanalysis.

6.7.6.5.4 Define Values and, If Appropriate, Their Impact onStrain or Deformation Limits The current NB rules includedirect safety factors that need to be confirmed or revised. Limitanalysis has a 1.5 on collapse. Plastic analysis uses the doubleelastic slope, the reduction of which impacts permanent plasticanalysis.

6.7.6.5.5 Revisit the Definitions and Revise for PlasticAnalysis if Appropriate Definitions (elastic) for primary and sec-ondary stress are based on loads and displacements. Thesedefinitions may not be consistent with plastic analysis. The inelas-tic rules separate analyses into three areas: load-controlled, load-controlled-plus-deformation-controlled, and fatigue. The inelasticareas should have clear definitions. The elastic PL is no longer rel-evant in limit load analysis, which may also be true for Pm and Pb

for limit and plastic analysis. The definition of Q is strictly elasticrelative to P � Q limit.

6.7.6.5.6 Determine when Monotonic or Cyclic Stress-StrainCurves Should Be Used; Determine if Credit Should Be Takenfor Hardening Is monotonic or cyclic stress–strain curves appro-priate to either or both primary design or cyclic analysis?According to the current definition, monotonic appears to beappropriate for primary loads. Cyclic matches the concerns thatdefine P � Q loads and fatigue. Is hardening by primary load per-mitted in the fatigue analysis? Note that both analyses may not beinelastic analysis.

6.7.6.5.7 Will Mises or Tresca Be Required or Will theOption Be Open? Should Mises Be Used in Fatigue Analysesand Tresca Used for Strains? Current and available FE programsuse von Mises rather than Tresca to define yielding. Mises is supposedly more accurate and less conservative than Tresca. Pastanalyses using inelastic methods (limit load and elastic–plastic)were probably based on Mises. Mises may have been used for pri-mary loads and primary-plus-secondary loads, though not forfatigue.

6.7.6.5.8 Determine the Roles for Small- and Large-StrainApproaches Formulations: Should large or small deformation theory be used? Small deformation seems to be more suitable forfatigue concerns. Should the use of small or large deformation becontractual? Does material ductility affect which approach shouldbe used? Can the small-strain be nonconservative relative to large-strain approach?

6.7.6.5.9 Determine the Need for Strain Limits and DefineValues Where Appropriate Plastic analysis produces strain levelsthat are a function of the geometry, the impact of which variesfrom minimal for cylinders to high for plates. Acceptable strainlevels must be defined with the basis definition or judgment usedas the choice. Two sets of rules/guidelines for both noncyclic andcyclic applications may be required.

6.7.6.5.10 For a Bilinear Curve, Rules for the Yield Stressand Plastic Modulus Must Be Set For plastic analysis, the kneeof the stress-strain curve is expected to control. If a bilinear curveis used, there are different results.

6.7.6.5.11 Develop Guidelines Appropriate for Defining theLocations For plastic analysis, the location of maximum strainshould control. The location may differ for ratchet and fatigue.

6.7.6.5.12 Should the Current Worst Case–Type Combiningfor Strain Range Be Continued? Strains from multiple loads arepath-dependent and impact the strain range.

6.7.7 Sizing Vessels Using Limit Analysis WRC Bulletin 464 [9] describes sizing of vessels using modern

limit analysis. The ASME Boiler and Pressure Vessel Code pro-vides several, and the sizing by limit analysis is one of them. Withlimit analysis, the sizing can be achieved by closed-form formu-las, equilibrium relations of free bodies, and finite-element lower-bound analyses. When coupled with a finite-element computercode, a lowerbound analysis is an effective tool for the sizing ofany vessel or its components. Limit analysis addresses the designobjective of preventing gross plastic deformation with an agreed-upon design margin. The procedure is simple and straightforward.If a lowerbound to the limit load is established that is equal to orgreater than the design loading, the objective is achieved. Adesign based on limit analysis also protects the vessel againstburst by tensile plastic instability (ductile rupture), but with adesign margin that depends on geometry, loading, and material.The sizing of vessels by limit analysis is applicable to vesselsmade of any material that is permitted for Section III-Class 1 andSection VIII-Division 2 construction.

Design by limit analysis represents a proven design technologyfor sizing structures. It is based on the concept of maintainingequilibrium of the model of the structure, and, by doing so, it pro-tects the real structure against the onset of gross plastic deformation,

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 40

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 41

which is a recognized concern in the operation of pressurevessels.

Limit analysis is an effective tool for sizing vessels of allgeometries and materials that are permitted for Section III-Class 1and Section VIII-Division 2 vessels. These guidelines show howto make use of it. The objective is to determine the gross dimen-sions of a vessel, which are those that affect its limit load. Theyexclude those that have little or no effect on the limit load, such assmall holes, fillets, and corner radii.

Standard FE codes do not calculate limit loads. They only cal-culate lower bounds to the limit loads. According to the theory oflimit analysis, the lowerbound analysis requires an elastic-perfectlyplastic material model and a geometrically linear algorithm thatsatisfies equilibrium in the undeformed state.

These guidelines address the following questions:

1 What is a Limit Load? 2 How to calculate it by plastic FEA? 3 How does it work for a real design problem?

6.7.8 Piping Stress Indices Using (Finite-ElementAnalysis)

WRC Bulletin 472 [10] presents results of research on deter-mining piping stress indices using FEA. The qualification ofClass 1 and 2 piping systems to the requirements of ASMESection III requires the evaluation and limitation of primarystresses. For moment loadings this is achieved with the use of B2 stress indices. The first part of the bulletin reviews the back-ground and history of the B2 indices and suggests a procedure fordeveloping these indices. The suggested procedure is based uponthe use of nonlinear FEA. The second part is focused on examin-ing existing data for straight pipe and 2” schedule 40 elbows. Theexisting data consists of both test and FEA data. The objective wasto demonstrate that the FEA methodology can simulate the nonlin-ear behavior of elbows and straight pipe. A new procedure forrepresenting the material properties was developed. Using the newprocedure the nonlinear response of the elbows and pipe weresimulated more accurately than previously published results. Thethird part uses the FEA methodology to predict the global behav-iors of thin-walled elbows subjected to in-plane bending. Newtests were performed which served as the basis of this part of thestudy. It was determined that if the weld is included in the model,the results are significantly improved. The fourth part addressesthe out-of-plane loading behavior of piping elbows. New experi-mental data was developed and the corresponding FEA wasperformed. There is excellent agreement between the FEAmethodology and the test results. The general conclusion is thatthe methodology described in this document can be used to accu-rately develop B2 stress indices for piping components.

6.7.9 Environmental Fatigue WRC Bulletin 487 [11] describes the activities of the PVRC

Steering Committee on Cyclic Life and Environmental Effects(CLEE) and the PVRC Working Group S-N Data Analysis. Thisreport presents the PVRC recommendations to the ASME Boardon Nuclear Codes and Standards (BNCS) concerning neededmodifications to the ASME fatigue analysis procedure. The pro-posed modifications will account for the effect of the environmenton the fatigue properties of the pressure boundary materialsConsidering all well-characterized, available data, PVRC hasdrawn the following major conclusions: (1) ASME Section IIIshould adopt a procedure such as proposed in Section 7 of this

report to apply an environmental correction factor, Fen, to lifefractions calculated using the existing ASME S-N design curveswhen anticipated operating conditions are sufficiently severe thatit is necessary to account for environmental effects. (2) ASMESection XI should adopt a procedure such as proposed in a draftcode case in Section 7 of this report and apply the environmentalcorrection factor, Fen, to life fractions calculated using the exist-ing ASME S-N design curves when it is necessary to account forenvironmental effects. (3) The Fen models are shown to workwell in predicting the effect of the coolant environments on the lowcycle fatigue properties of stainless steel. The low cycle fatigueinformation on stainless steel in air, collected by the PVRC to per-form the evaluation, does not appear to support the ASME meandata line for stainless steel, and more data are needed to adequatelyunderstand behavior. The conclusions are based on two princi-ples: (1) The environmental correction factors can be determinedusing equations developed either by Argonne National Laboratoryor by MITI’s investigators in Japan. While these equations aresomewhat different; in real situations, they are expected to givesimilar results, within the bounds of experimental error and oper-ating uncertainties. (2) The factor of 20 on life, originally used inthe development of the fatigue design curves to account for uncer-tainties, is adequate to account for reductions in fatigue life due tothe environment under well controlled operating conditions.Under those conditions, provision for further reductions in fatiguelife due to the environment is not essential. The PVRC hasreviewed the ASME Section III Fatigue Analysis procedure todetermine what modifications are needed to take into account theeffects of the coolant environment on the S-N fatigue properties.In per-forming this review, the PVRC evaluated the followingareas: (1) The margins used in the development of the Section IIIprocedure. (2) Laboratory data used in the development of theSection III procedure. (3) Laboratory fatigue data on smooth speci-mens in simulated reactor coolant environments. (4) Models topredict the S-N properties in Light Water Reactor (LWR) coolantenvironments of the pressure boundary materials. (5) Laboratorydata on structural tests conducted in water environments.

The recommended use of Fen does require the computation ofstrain rate. At the moment the only method suggested is to dividethe alternating strain by the time for the strain cycle in question.There has been limited discussion of using explicit FEA results tocompute Fen when hold-time, and cycle-superposition is evolved.

6.8 ELASTIC-PLASTIC FEA

Section VIII Div 2 Part 5 now includes provisions for usingEP-FEA as alternative to the traditional elastic analysis methodsdiscussed above. Paragraph 5.2.4 discusses EP-FEA methods forprotection against plastic collapse, 5.3.3 for using EP-FEA todetermine protection against local failure, 5.5.4 for using EP-FEAfor assessing fatigue limits, and 5.5.7 for using EP-FEA forassessing ratchet limits.

These methods are brief and short on detail mainly because EP-FEA is still not used in everyday engineering offices. The follow-ing discusses these is methods.

6.8.1 Protection Against Plastic CollapseThis procedure is based on computation of a limit load for the

structure using EP-FEA. The previous discussions in this chapterdocumented that the primary stress limits are intended to estimatea lower bound limit load from elastic analysis results. Modern

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 41

42 • Chapter 6

FEA programs now offer the opportunity to compute the lowerbound limit load directly using EP-FEA. There is little doubt thatif such tools were available in the 1950’s the Code stress allow-able stress limits would simply said compute the lower boundlimit load and place a margin of 1.5 against plastic collapse.

This is achieved in most EP-FEA programs by using an elastic-perfectly plastic material stress-strain curve and setting thestrength parameter to the material allowable Sm. Since Sm is thelower of 2Sy/3 or Sult/3, there is a built in margin of 3 on burst and1.5 against plastic collapse.

Typically the FEA mesh can be reasonably crude for this calcu-lation as shown by Jones and Holliday [22]. The problem is runby incrementing the loads until non-convergence is achieved. Thenon-convergence is an indication that instability has beenachieved denoting plastic collapse. If the loads so obtained aremore than the required design loads, the structure is acceptable.

Some geometries that may have large deformations before col-lapse may required large strain, large deflection analysis to obtaina valid solution. Typically these geometries are prone to elasticinstabilities as well. A ellipsoidal-to-cylinder juncture of certainradius-to-thickness ratios is an example of such a structure thatcan require non-linear geometry assumptions. Typically, however,small-strain and small-deflection assumptions are appropriate forthis calculation.

6.8.2 Protection Against Local FailureSection VIII Div 2 step 5.3.3 requires that the triaxial strain be

limited by local strain that is calculated based on an estimate ofconstraint. Table 5.5 of Section VIII gives the load cases to con-sider and Table 5.7 provides the material properties to computethe local strain allowable.

Sc III NB does not have this limit. Little experience is availablefor calculating this limit.

6.8.3 Protection Against Failure From CyclicLoading

Sc VIII Div 2 paragraph 5.5.4 details the use of the 2Sy methodof Kalnins [13] to use EP-FEA for fatigue analysis. There is noexplicit reference in Sc III NB for the use of the 2Sy method sothe methods in 5.5.4 of Sc VIII are an excellent source of materialon this method.

There are a number of points that are not detailed in the proce-dure that are worth noting. First is the temperature dependence ofthe cyclic stress-strain curve. The method suggests using a cyclicstress-strain curve at the average temperature of the cycle.Typically each point in the structure will be at a different averagetemperature so the EP-FEA program must have the ability to firstaverage the temperature of the cycle and then select the correctcurve on a point-by-point basis.

The second difficulty is processing the results. In elastic stress-based methods, typically a fatigue strength reduction factor isplaced onto the linearized stress to obtain the alternating stress foruse in fatigue evaluations. In the 2Sy method, a peak strain ampli-tude is calculated based on EP-FEA results. It is not clear how todo this for sharp notches. It is suggested here that a minimumnotch-root dimension and FEA mesh be established that allows anelastically calculated strain at the tip of the sharp notch to be cal-culated that is equal to E*Salt where E is Young’s modulus andSalt is the elastically calculated alternating stress obtained usingthe fatigue strength reduction factor. That minimum dimensionand the mesh is then used in the EP-FEA model. Fatigue assessment

is completed by using the peak strain calculated directly from the2Sy EP-FEA results.

The question of what strain to use in a fatigue analysis is alsoan issue. The paper by Reinhardt [16] is a notable reference inthis regard.

An example of using EP-FEA in fatigue assessments is avail-able in Jones and Adams [17]. An incremental EP-FEA analysisand the 2Sy method were used to analyze a cylinder-to-plate junc-ture comparing the results to the experimental results.

6.9 REFERENCES

1. WRC 432, Hechmer, J. L., and Kuhn, E. J. III.(1998). “Fatigue-Strength Reduction Factor for Welds Based on NDE,” WeldingResearch Council, Bulletin 432, New York.

2. Hechmer, J. L., and Hollinger, G. L., “Three-Dimensional StressCriteria,” Grants 89-16 and 90-13, PVRC Phase 1 Report, ThePressure Vessel Research Council, New York, Sept. 12, 1991.

3. Hechmer, J. L., and Hollinger, G. L., “3D Stress Criteria, Guidelinesfor Application,” Grant 91-14, PVRC Phase 2 Report, The PressureVessel Research Council, New York, Aug. 1997.

4. WRC 429, Hechmer, J. L., and Hollinger, G. L. (1998). “3D StressCriteria, Guidelines for Application,” Welding Research Council,Bulletin 429, New York.

5. Pastor, T. P., and Hechmer, J. L., “ASME Task Group Report onPrimary Stress,” Journal of Pressure Vessel Technology, Trans. of theASME, Feb. 1997.

6. Miller, D. R., “Thermal Stress Ratchet Mechanisms in PressureVessels,” Trans. of the ASME, Vol. 81, Series D, No. 2, 1959.

7. Cooper, W. E., “The Initial Scope and Intent of the Section III FatigueDesign Procedure,” presented at the PVRC Workshop onEnvironmental Effects on Fatigue Performance, Clearwater Beach,FL, Jan. 20, 1992.

8. Baldwin, E. E., Sokol, G. J., Coffen, L. F. Jr., “Cyclic Strain FatigueStudies on AISI Type 347 Stainless Steel,” ASTM Proc., Vol. 57, p.567, 1975.

9. WRC Bulletin 464, Kalnins, Artus, Guidelines for Sizing of Vesselsby Limit Analysis Welding Research Council Bulletin 464, ISSN:0043-2326, ISBN: 1-58145-471-6, Library of Congress Catalog CardNumber: 85-647116, The Welding Research Council, New York, NY,August, 2001.

10. WRC Bulletin 472, Matzen, Vernon C. and Ying Tan, Using FiniteElement Analysis to Determine Piping Elbow Bending Moment(B2) Stress Indices, ISSN: 0043-2326, ISBN: 1-58145-479-1, Libraryof Congress Catalog Card Number: 85-647116, The WeldingResearch Council, New York, NY, June, 2002.

11. WRC Bulletin 487, VanDerSluys, PVRC Position onEnvironmental Effects on Fatigue Life in LWR Applications,ISSN: 0043-2326, ISBN: 1-58145-494-5, Library of CongressCatalog Card Number: 85-647116, The Welding Research Council,New York, NY, December, 2003.

12. J. L. Gordon, “OUTCUR: An Automated Evaluation of Two-Dimensional Finite Element Stresses According to ASME Section IIIStress Requirements,” ASME Paper 760-WA/PVP-16, presented atthe 1976 ASME Winter Annual Meeting in New York, NY.

13. Kalnins, A. “Twice-Yield Method for Assessment of Fatigue Causedby Fast Thermal Transient According to 2007 Section VIII-Division 2of ASME B&PV Code”, PVP2008-61397, ASME PVP Conference,July 2008.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 42

COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 43

14. Kalnins, A., “STRESS CLASSIFICATION LINES STRAIGHTTHROUGH SINGULARITIES, PVP2008-61746, ASME PVPConference, July 2008.

15. A. Kalnins & W. Reinhardt, “ASME PVP Division Tutorial SeriesPlastic Analysis in Pressure Vessel Design, Part 2: Sizing of a Vesselby Limit Analysis, and Cyclic Loading,” Tutorial PVPD-32 ASMEPVP Conference July 2007.

16. W. Reinhardt, “Strain Measures for Fatigue Assessment UsingElastic-Plastic FEA,” July 17–21, ASME PVP Conference, PVP2005-71547.

17. Jones, D. P. and Adams, S. A., “Fatigue Analysis Round Robin ofNozzle-to-Plate Juncture; Results of Analytic-Test Comparison,”2008 ASME PVP Conference July 2008.

18. ANSYS, Inc. Southpointe; 275 Technology Drive; Canonsburg, PA15317.

19. ABAQUS FE Code, Version 6.1, Hibbiott, Karlsson, and Sorensen,Inc., Pawtucket, R.I.

20. MSC Software Corporation; 2 MacArthur Place; Santa Ana, CA92707 USA.

21. Sang H. Lee, “MSC/NASTRAN Nonlinear Analysis,” The MacNeal-Schwendier Corporation, Los Angeles, CA 90041.

22. Jones, D. P. and J. E. Holliday, “Elastic-Plastic Analysis of the PVRCBurst Disk Tests with Comparison to the ASME CODE PrimaryStress Limits,” PVP Vol. 383, Pressure Vessel and Piping Codes andStandards, 1999, ASME PVP Conference 1999.

23. J. L. Gordon and R. G Sauve, “Introduction to Finite ElementAnalysis,” July 2004. PVPD Tutorial Series, PVPD-43.

24. J. D. Andrews and T. R. Moss, Reliability and Risk Assessment,Second Edition, ASME Press, 2002.

25. Risk-Based methods for Equipment Life Management; An ApplicationHandbook; A Step-by-Step Instructional Manual with SampleApplications, ASME International, Three Park Avenue, NY, NY, CRDVol. 41, 2003.

26. R. E. Peterson, Stress Concentration Factors, John Wiley & Sons,New York, 1974.

6.10 SUMMARY OF CHANGES

Summary of Changes from 2007 Code Section III Division 1,Subsection NB Class 1 Components (page xxix) are extractedbelow from the 2007 Code. For details readers are suggested toconsult the Code.

SUMMARY OF CHANGES

The 2007 Edition of this Code contains revisions in addition to the 2004 Edition with 2005 and 2006 Addenda. The revisions are identifiedwith the designation 07 in the margin and, as described in the Foreword, become mandatory six months after the publication date of the2007 Edition. To invoke these revisions before their mandatory date, use the designation “2007 Edition” in documentation required by thisCode. If you choose not to invoke these revisions before their mandatory date, use the designation “2004 Edition through the 2006Addenda” in documentation required by this Code.

The BC numbers listed below are explained in more detail in “List of Changes in BC Order” following this Summary of Changes.

Changes given below are identified on the pages by a margin note, 07, placed next to the affected area.Page Location Change (BC Number)

Page Location Change (BC Number)

9 NCA-3126 Added (BC06-315 )

12 NCA-3252 (1) Last sentence of subpara. (a) revised (BC05-1166)

(2) Subsubparagraphs (a)(6) and (a)(7) redesignated as

(a)(7) and (a)(8), respectively (BC05-1166)

(3) New subsubpara. (a)(6) added (BCO5-1166)

27 NCA-3855.3 (1) Subparagraph (c) redesignated as subpara. (d) (BC06-315)

(2) New subpara. (c) added (BC06-315)

43,44 Table NCA-8700-1 Under NS Certificate Holder, Note (10) deleted by errata (BC06-147)

50,53 NCA-9200 Definition of plate-and shelf-type supports added (BC06-748)

NOTE: Volume 57 of the Interpretations to Section III, Divisions 1 and 1, of the ASME Boiler and PressureVessel Code follows the last page of this Edition.

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 43

ASME_Ch06_p001-044.qxd 10/15/08 11:48 AM Page 44