RECOMMENDED PRACTICEDET NORSKE VERITASDNV-RP-C203FATIGUE DESIGN OF OFFSHORE STEEL STRUCTURESAPRIL 2008Comments may be sent by e-mail to rules@dnv.comFor subscription orders or information about subscription terms, please use distribution@dnv.comComprehensive information about DNV services, research and publications can be found at http://www.dnv.com, or can be obtained from DNV, Veritas-veien 1, NO-1322 Hvik, Norway; Tel +47 67 57 99 00, Fax +47 67 57 99 11. Det Norske Veritas. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, including pho-tocopying and recording, without the prior written consent of Det Norske Veritas.Computer Typesetting (FM+SGML) by Det Norske Veritas.Printed in NorwayIf any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation to such personfor his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compen-sation shall never exceed USD 2 million.In this provision "Det Norske Veritas" shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalf of DetNorske Veritas.FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, prop-erty and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancyservices relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out researchin relation to these functions.DNV Offshore Codes consist of a three level hierarchy of documents: Offshore Service Specifications. Provide principles and procedures of DNV classification, certification, verification and con-sultancy services. Offshore Standards. Provide technical provisions and acceptance criteria for general use by the offshore industry as well asthe technical basis for DNV offshore services. Recommended Practices. Provide proven technology and sound engineering practice as well as guidance for the higher levelOffshore Service Specifications and Offshore Standards.DNV Offshore Codes are offered within the following areas:A) Qualification, Quality and Safety MethodologyB) Materials TechnologyC) StructuresD) SystemsE) Special FacilitiesF) Pipelines and RisersG) Asset OperationH) Marine OperationsJ) Wind TurbinesO) Subsea SystemsAmendments and Corrections This document is valid until superseded by a new revision. Minor amendments and corrections will be published in a separatedocument normally updated twice per year (April and October). For a complete listing of the changes, see the Amendments and Corrections document located at: http://webshop.dnv.com/global/, under category Offshore Codes.The electronic web-versions of the DNV Offshore Codes will be regularly updated to include these amendments and corrections.DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008ChangesPage 3Main changes April 2008 TheprincipalstressdirectioninFigure2-2ischangedfrom 60 to equations combining stress normal to the weldand shear stress when fatigue cracking along the weld toeis the most likely failure mode and a function of maximumprincipal stress when the main stress direction is more par-allel to the weld. Some guidance on how to consider principal stress direc-tionrelativetotheweldtoewithrespecttoselectionofS-N curve is included in the commentary section. Guidanceonderivationofaneffectivethicknesstobeused together with the S-N curve for cast joints subjectedto some bending moment over the thickness is given. The 0 in equations for stress concentration factors for buttweldsinpipelinesisremovedduetoratherstricttoler-ances used in pipeline fabrication and it can not be docu-mentedthatalargetolerance 0isembeddedintheS-Ndata used in design. A commentary section on stress concentration factors fordetailsinpipelinesandcylindricaltankswithstresscyclingmainlyduetointernalpressureisincluded.Thisincludescircumferentialweldsandlongitudinalweldsinpipes. The section on grouted joints is extended to include jointswiththeannulusbetweentubularmembersfilledwithgrout such as joints in jacket legs with insert piles. Stress concentration factors at circumferential butt weldsin tubulars subjected to axial load are included for thick-ness transitions on inside and for welds made from outsideonly. Some printing errors have been corrected and some of thetexts have been revised to improve readability.DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 4ChangesDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 5CONTENTS1. INTRODUCTION.................................................. 71.1 General .....................................................................71.2 Validity of standard.................................................71.2.1 Material............................................................................... 71.2.2 Temperature........................................................................ 71.2.3 Low cycle and high cycle fatigue ....................................... 71.3 Methods for fatigue analysis...................................71.4 Definitions ................................................................71.5 Symbols.....................................................................82. FATIGUE ANALYSIS BASED ON S-N DATA . 92.1 Introduction .............................................................92.2 Fatigue damage accumulation..............................102.3 Fatigue analysis methodology and calculation of Stresses ...........................................102.3.1 General.............................................................................. 102.3.2 Plated structures using nominal stress S-N curves ........... 102.3.3 Plated structures using hot spot stress S-N curves............ 112.3.4 Tubular joints ................................................................... 112.3.5 Fillet welds........................................................................ 122.3.6 Fillet welded bearing supports.......................................... 122.4 S-N curves ..............................................................122.4.1 General.............................................................................. 122.4.2 Failure criterion inherent the S-N curves.......................... 122.4.3 S-N curves and joint classification ................................... 122.4.4 S-N curves in air ............................................................... 132.4.5 S-N curves in seawater with cathodic protection ............. 142.4.6 S-N curves for tubular joints............................................. 152.4.7 S-N curves for cast nodes ................................................. 162.4.8 S-N curves for forged nodes ............................................. 162.4.9 S-N curves for free corrosion ........................................... 162.4.10 S-N curves for base material of high strength steel .......... 162.4.11 S-N curves for stainless steel ............................................ 162.4.12 S-N curves for small diameter umbilicals ........................ 162.4.13 Qualification of new S-N curves based on fatigue test data................................................................. 172.5 Mean stress influence for non welded structures ...........................................172.6 Effect of fabrication tolerances ............................182.7 Design chart for fillet and partial penetration welds .......................................................................182.8 Bolts ........................................................................182.8.1 General.............................................................................. 182.8.2 Bolts subjected to tension loading.................................... 182.8.3 Bolts subjected to shear loading...................................... 182.9 Pipelines and risers................................................182.9.1 General.............................................................................. 182.9.2 Combined eccentricity for fatigue analysis of seamless pipes................................................................... 192.9.3 SCFs for pipes with internal pressure............................... 192.10 Guidance to when a detailed fatigue analysis can be omitted...............................................................203. STRESS CONCENTRATION FACTORS........ 203.1 Stress concentration factors for plated structures ....................................................203.1.1 General.............................................................................. 203.1.2 Stress concentration factors for butt welds....................... 203.1.3 Stress concentration factors for cruciform joints.............. 203.1.4 Stress concentration factors for rounded rectangular holes ................................................ 213.1.5 Stress concentration factors for holes with edge reinforcement .................................................................... 223.1.6 Stress concentration factors for scallops........................... 223.2 Stress concentration factors for ship details .......233.3 Tubular joints and members................................ 233.3.1 Stress concentration factors for simple tubular joints ...... 233.3.2 Superposition of stresses in tubular joints ........................ 233.3.3 Tubular joints welded from one side ................................ 243.3.4 Stiffened tubular joints ..................................................... 243.3.5 Grouted tubular joints....................................................... 253.3.6 Cast nodes......................................................................... 253.3.7 Stress concentration factors for tubular butt weld connections ....................................................................... 253.3.8 Stress concentration factors for stiffened shells ............... 273.3.9 Stress concentration factors for conical transitions .......... 273.3.10 Stress concentration factors for tubulars subjected to axial force ......................................................................... 293.3.11 Stress concentration factors for joints with square sections.................................................................. 293.3.12 Stress concentration factors for joints with gusset plates . 304. CALCULATION OF HOT SPOT STRESS BY FINITE ELEMENT ANALYSIS........................304.1 General ................................................................... 304.2 Tubular joints........................................................ 304.3 Welded connections other than tubular joints ... 314.3.1 Stress field at a welded detail ........................................... 314.3.2 FE modelling .................................................................... 314.3.3 Derivation of stress at read out points 0.5 t and 1.5 t ....... 314.3.4 Derivation of hot spot stress ............................................. 314.3.5 Hot spot S-N curve ........................................................... 324.3.6 Derivation of effective hot spot stress from FE analysis.. 324.3.7 Limitations for simple connections .................................. 324.3.8 Verification of analysis methodology............................... 335. SIMPLIFIED FATIGUE ANALYSIS ...............345.1 General ................................................................... 345.2 Fatigue design charts ............................................ 345.3 Example of use of design charts........................... 386. FATIGUE ANALYSIS BASED ON FRACTURE MECHANICS................................397. IMPROVEMENT OF FATIGUE LIFE BY FABRICATION...................................................397.1 General ................................................................... 397.2 Weld profiling by machining and grinding ........ 397.3 Weld toe grinding.................................................. 407.4 TIG dressing .......................................................... 407.5 Hammer peening................................................... 408. EXTENDED FATIGUE LIFE............................419. UNCERTAINTIES IN FATIGUE LIFE PREDICTION......................................................419.1 General ................................................................... 419.2 Requirements to in-service inspection for fatigue cracks......................................................... 4410. REFERENCES.....................................................44APP. A CLASSIFICATION OF STRUCTURAL DETAILS............................................................................47A.1 Non-welded details...................................................47A.2 Bolted connections ...................................................48A.3 Continuous welds essentially parallel to the direction of applied stress.........................................49A.4 Intermittent welds and welds at cope holes..............51A.5 Transverse butt welds, welded from both sides .......52DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 6A.6 Transverse butt welds, welded from one side ..........55A.7 Welded attachments on the surface or the edge of a stressed member .......................................................56A.8 Welded joints with load carrying welds ...................60A.9 Hollow sections ........................................................63A.10 Details relating to tubular members .........................66APP. B SCFS FOR TUBULAR JOINTS .....................68B.1 Stress concentration factors for simple tubular joints and overlap joints .....................................................68APP. C SCFS FOR PENETRATIONS WITH REINFORCEMENTS.......................................................78C.1 SCFs for small circular penetrations with reinforcement............................................................78C.2 SCFs at man-hole penetrations .............................100C.3 Results ....................................................................101APP. D COMMENTARY.............................................115D.1 Comm. 1.2.3 Low cycle and high cycle fatigue.....115D.2 Comm. 1.3 Methods for fatigue analysis ...............115D.3 Comm. 2.2 Combination of fatigue damages from two dynamic processes ..........................................115D.4 Comm. 2.3.2 Plated structures using nominal stress S-N curves......................................116D.5 Comm. 2.4.3 S-N curves........................................117D.6 Comm. 2.4.9 S-N curves and efficiency of corrosion protection ...............................................119D.7 Comm. 2.9.3 SCFs for pipes with internal pressure .....................................................119D.8 Comm. 3.3 Stress concentration factors ................121D.9 Comm. 3.3.3 Tubular joints welded from one side121D.10 Comm. 4.1 The application of the effective notch stress method for fatigue assessment of structural details .....................................................121D.11 Comm. 4.3.8 Verification of analysis methodology for FE hot spot stress analysis................................123D.12 Comm. 5 Simplified fatigue analysis.....................129DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 71.Introduction1.1GeneralThisRecommendedPracticepresentsrecommendationsinrelation to fatigue analyses based on fatigue tests and fracturemechanics.ConditionsforthevalidityoftheRecommendedPractice are given in section 1.2.The aim of fatigue design is to ensure that the structure has anadequatefatiguelife.Calculatedfatiguelivesalsoformthebasisforefficientinspectionprogrammesduringfabricationand the operational life of the structure.To ensure that the structure will fulfil its intended function, afatigue assessment, supported where appropriate by a detailedfatigueanalysis,shouldbecarriedoutforeachindividualmember, which is subjected to fatigue loading. See also section2.10.Itshouldbenotedthatanyelementormemberofthestructure, every welded joint and attachment or other form ofstress concentration, is potentially a source of fatigue crackingand should be individually considered.1.2Validity of standard1.2.1MaterialThis Recommended Practice is valid for steel materials in airwithyieldstrengthlessthan960MPa.Forsteelmaterialsinseawater with cathodic protection or steel with free corrosionthe Recommended Practice is valid up to 550 MPa.This Recommended Practice is also valid for bolts in air envi-ronment or with protection corresponding to that condition ofgrades up to 10.9, ASTM A490 or equivalent.This Recommended Practice may be used for stainless steel.1.2.2TemperatureThis Recommended Practice is valid for material temperaturesof up to 100C. For higher temperatures the fatigue resistancedata may be modified with a reduction factor given as:where T is given in C (Derived from figure in IIW documentXII-1965-03/XV-1127-03). Fatigue resistance is understood tomeanstrengthcapacity.ThereducedresistanceintheS-Ncurves can be derived by a modification of the log as: 1.2.3Low cycle and high cycle fatigueThis Recommended Practice has been produced with the pur-pose of assessing fatigue damage in the high cycle region. Seealso Appendix D, Commentary. 1.3Methods for fatigue analysisThe fatigue analysis should be based on S-N data, determinedby fatigue testing of the considered welded detail, and the lin-ear damage hypothesis. When appropriate, the fatigue analysismayalternativelybebasedonfracturemechanics.Ifthefatigue life estimate based on S-N data is short for a componentwhere a failure may lead to severe consequences, a more accu-rate investigation considering a larger portion of the structure,or a fracture mechanics analysis, should be performed. For cal-culationsbasedonfracturemechanics,itshouldbedocu-mented that there is a sufficient time interval between time ofcrackdetectionduringin-serviceinspectionandthetimeofunstable fracture.All significant stress ranges, which contribute to fatigue dam-age, should be considered. The long term distribution of stressranges may be found by deterministic or spectral analysis, seealso ref. /1/. Dynamic effects shall be duly accounted for whenestablishing the stress history. A fatigue analysis may be basedon an expected stress history, which can be defined as expectednumber of cycles at each stress range level during the predictedlife span. A practical application of this is to establish a longterm stress range history that is on the safe side. The part of thestressrangehistorycontributingmostsignificantlytothefatiguedamageshouldbemostcarefullyevaluated.SeealsoAppendix D, Commentary, for guidance. ItshouldbenotedthattheshapeparameterhintheWeibulldistribution has a significant impact on calculated fatigue dam-age. For effect of the shape parameter on fatigue damage seealso design charts in Figure 5-1 and Figure 5-2. Thus, when thefatiguedamageiscalculatedbasedonclosedformsolutionswith an assumption of a Weibull long term stress range distri-bution, a shape parameter to the safe side should be used.1.4DefinitionsClassifiedstructuraldetail:Astructuraldetailcontainingastructuraldiscontinuityincludingaweldorwelds,forwhichthe nominal stress approach is applicable, and which appear inthe tables of this Recommended Practice. Also referred to asstandard structural detail.Constant amplitude loading: A type of loading causing a reg-ularstressfluctuationwithconstantmagnitudesofstressmaxima and minima.Crack propagation rate: Amount of crack propagation duringone stress cycle.Crackpropagationthreshold:Limitingvalueofstressinten-sity factor range below which the stress cycles are consideredto be non-damaging.Eccentricity:Misalignmentofplatesatweldedconnectionsmeasured transverse to the plates.Effective notch stress: Notch stress calculated for a notch witha certain effective notch radius.Fatigue deterioration of a component caused by crack initia-tion and/or by the growth of cracks.Fatigue action: Load effect causing fatigue.Fatigue damage ratio: Ratio of fatigue damage at considerednumber of cycles and the corresponding fatigue life at constantamplitude loading.Fatigue life: Number of stress cycles at a particular magnituderequired to cause fatigue failure of the component.Fatigue limit: Fatigue strength under constant amplitude load-ing corresponding to a high number of cycles large enough tobe considered as infinite by a design code.Fatigueresistance:StructuraldetailsresistanceagainstfatigueactionsintermsofS-Ncurveorcrackpropagationproperties.Fatigue strength: Magnitude of stress range leading to partic-ular fatigue life.Fracture mechanics: A branch of mechanics dealing with thebehaviour and strength of components containing cracks.DesignFatigueFactor:Factoronfatiguelifetobeusedfordesign.Geometric stress: See hot spot stress.Hot spot: A point in structure where a fatigue crack may initi-ate due to the combined effect of structural stress fluctuationand the weld geometry or a similar notch.Hot spot stress: The value of structural stress on the surface atthehotspot(alsoknownasgeometricstressorstructuralstress).Localnominalstress:Nominalstressincludingmacro-geo-metriceffects,concentratedloadeffectsandmisalignments,disregarding the stress raising effects of the welded joint itself.(1.2.1)(1.2.2)2 6 3TT 10 372 . 1 T 10 239 . 0 0376 . 1 R =T RTR Log m a Log a Log + =DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 8Local notch: A notch such as the local geometry of the weldtoe,includingthetoeradiusandtheanglebetweenthebaseplate surface and weld reinforcement. The local notch does notalter the structural stress but generates non-linear stress peaks.Macro-geometricdiscontinuity:Aglobaldiscontinuity,theeffect of which is usually not taken into account in the collec-tionofstandardstructuraldetails,suchaslargeopening,acurved part in a beam, a bend in flange not supported by dia-phragmsorstiffeners,discontinuitiesinpressurecontainingshells, eccentricity in lap joints.Macro-geometric effect: A stress raising effect due to macro-geometry in the vicinity of the welded joint, but not due to thewelded joint itself.Membrane stress: Average normal stress across the thicknessof a plate or shell.Minersum:Summationofindividualfatiguedamageratioscaused by each stress cycle or stress range block according toPalmgren-Miner rule. Misalignment: Axial and angular misalignments caused eitherby detail design or by fabrication.Nominal stress: A stress in a component, resolved, using gen-eral theories such as beam theory.Nonlinear stress peak: The stress component of a notch stresswhichexceedsthelinearlydistributedstructuralstressatalocal notch.Notchstress:Totalstressattherootofanotchtakingintoaccountthestressconcentrationcausedbythelocalnotch.Thusthenotchstressconsistsofthesumofstructuralstressand non-linear stress peak.Notch stress concentration factor: The ratio of notch stress tostructural stress.Parislaw:Anexperimentallydeterminedrelationbetweencrack growth rate and stress intensity factor range.Palmgren-Minerrule:FatiguefailureisexpectedwhentheMiner sum reaches unity. Reference is also made to Chapter 9on uncertainties).Rainflow counting: A standardised procedure for stress rangecounting.Shell bending stress: Bending stress in a shell or plate like partofacomponent,linearlydistributedacrossthethicknessasassumed in the theory of shells.S-N curve: Graphical presentation of the dependence of fatiguelife (N) on fatigue strength (S).Stress cycle: A part of a stress history containing a stress max-imum and a stress minimum.Stressintensityfactor:Factorusedinfracturemechanicstocharacterise the stress at the vicinity of a crack tip.Stressrange:Thedifferencebetweenstressmaximumandstress minimum in a stress cycle.Stress range block: A part of a total spectrum of stress rangeswhich is discretized in a certain number of blocks.Stress range exceedances: A tabular or graphical presentationof the cumulative frequency of stress range exceedances, i. e.thenumberofrangesexceedingaparticularmagnitudeofstress range in stress history. Here frequency is the number ofoccurrences.Stress ratio: Ratio of minimum to maximum value of the stressin a cycle.Structural discontinuity: A geometric discontinuity due to thetype of welded joint, usually found in tables of classified struc-turaldetails.Theeffectsofastructuraldiscontinuityare(i)concentration of the membrane stress and (ii) formation of sec-ondary bending stress.Structural stress: A stress in a component, resolved taking intoaccount the effects of a structural discontinuity, and consistingofmembraneandshellbendingstresscomponents.Alsoreferred to as geometric stress or hot spot stress.Structuralstressconcentrationfactor:Theratioofhotspot(structural) stress to local nominal stress. In this RP the shorternotation: Stress concentration factor (SCF) is used.Variable amplitude loading: A type of loading causing irregu-larstressfluctuationwithstressranges(andamplitudes)ofvariable magnitude.1.5SymbolsC material parameterD accumulated fatigue damage, diameter of chordDFF Design Fatigue FactorDjcylinder diameter at junctionE Youngs modulusF fatigue lifeI moment of inertia of tubulars Kmax Kmin maximum and minimum stress intensity factors respectivelyKwstress concentration factor due to weld geometryK Kmax - KminL length of chord, length of thickness transitionN number of cycles to failureNinumber of cycles to failure at constant stress range iN axial force in tubularR outer radius of considered chord, reduction factor on fatigue lifeSCFstress concentration factorSCFASstress concentration factor at the saddle for axial load SCFACstress concentration factor at the crown for axial loadSCFMIPstress concentration factor for in plane moment SCFMOPstress concentration factor for out of plane momentRasurface roughnessRTreduction factor on fatigue resistanceT thickness of chordTeequivalent thickness of chordTddesign life in secondsQ probability for exceedance of the stress range A crack depthaihalf crack depth for internal cracksintercept of the design S-N curve with the log N axise-exp(-)g gap = a/D; factor depending on the geometry of the member and the crack.h Weibull shape parameter, weld sizek number of stress blocks, exponent on thicknessl segment lengths of the tubularm negative inverse slope of the S-N curve; crack growth parameterninumber of stress cycles in stress block inois the number of cycles over the time period for which the stress range level o is definedtrefreference thicknessaDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 92.Fatigue Analysis Based on S-N Data2.1IntroductionThe main principles for fatigue analysis based on fatigue testsare described in this section. The fatigue analysis may be basedon nominal S-N curves for plated structures when appropriate.Additionalstressesresultingfromfabricationtolerancesforbutt welds and cruciform joints should be considered when thefabrication tolerances exceed that inherent the S-N data. Ref-erence is made to sections 3.1 and 3.3.When performing finite element analysis for design of platedstructures it is often found more convenient to extract hot spotstress from the analysis than that of a nominal stress. Guidanceonfiniteelementmodellingandhotspotstressderivationispresented in section 4.3. The calculated hot spot stress is thenentered a hot spot S-N curve for derivation of cycles to failure.Also here additional stresses resulting from fabrication toler-ances for butt welds and cruciform joints should be considered.For design of simple tubular joints it is standard practice to useparametric equations for derivation of stress concentration fac-tors to obtain hot spot stress for the actual geometry. Then thishot spot stress is entered a relevant hot spot stress S-N curvefor tubular joints.Results from performed fatigue analyses are presented in sec-tion 5 in terms of design charts that present allowable stressesas function of the Weibull shape parameter. The basis for thedesign charts is that long term stress ranges can be describedby a two parameter Weibull distribution. The procedure can beused for different designlives, differentDesign FatigueFac-tors and different plate thickness.The following fatigue cracking failure modes are considered inthis document (see also Figure 2-1): Fatiguecrackgrowthfromtheweldtoeintothebasematerial.In welded structures fatigue cracking from weld toes intothebasematerialisafrequentfailuremode.Thefatiguecrack is initiated at small defects or undercuts at the weldtoe where the stress is highest due to the weld notch geom-etry. A large amount of the content in this RP is made withthe purpose of achieving a reliable design with respect tothis failure mode. Fatigue crack growth from the weld root through the filletweld.Fatiguecrackingfromrootoffilletweldswithacrackgrowth through the weld is a failure mode that can lead tosignificantconsequences.Useoffilletweldsshouldbesoughtavoidedinconnectionswherethefailureconse-quences are large due to less reliable NDE of this type ofconnection compared with a full penetration weld. How-ever, in some welded connections use of fillet welds canhardlybeavoidedanditisalsoefficientforfabrication.The specified design procedure in this document is consid-ered to provide reliable connections also for fillet welds. Fatigue crack growth from the weld root into the sectionunder the weld.Fatigue crack growth from the weld root into the sectionunder the weld is observed during service life of structuresin laboratory fatigue testing. The number of cycles to fail-ureforthisfailuremodeisofasimilarmagnitudeasfatigue cracking from the weld toe in as welded condition.There is no methodology that can be recommended used toavoid this failure mode except from using alternative typesof welds locally. This means that if fatigue life improve-mentoftheweldtoeisrequiredtheconnectionwillbecome more highly utilised and it is also required to makeimprovement for the root. This can be performed using afull penetration weld along some distance of the stiffenernose. Fatigue crack growth from a surface irregularity or notchinto the base material.Fatigue cracking in the base material is a failure mode thatis of concern in components with high stress cycles. Thenthe fatigue cracks often initiate from notches or grooves inthecomponentsorfromsmallsurfacedefects/irregulari-ties.Thespecifieddesignprocedureinthisdocumentisconsideredtoprovidereliableconnectionsalsowithrespect to this failure mode.a) Fatigue crack growth from the weld toe into the base materialb) Fatigue crack growth from the weld root through the filletweldT plate thickness, thickness of brace member tccone thicknesstpplate thicknessQ Weibull scale parametergamma function usage factor the slope angle of the cone; = L/D d/D eccentricity0eccentricity inherent in the S-N curve R/Toaverage zero-up-crossing frequency Poissons ratiolocallocal stress nominalnominal stress hot spothot spot stress or geometric stressxmaximum nominal stresses due to axial forcemy mz maximum nominal stresses due to bending about the y-axis and the z-axis stress range0stress range exceeded once out of n0 cycles t/T, shear stressDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 10c) Fatigue crack growth from the weld root into the section under the weldd)Fatiguecrackgrowthfromasurfaceirregularityornotchinto the base materialFigure 2-1Explanation of different fatigue failure modes2.2Fatigue damage accumulationThefatiguelifemaybecalculatedbasedontheS-Nfatigueapproachundertheassumptionoflinearcumulativedamage(Palmgren-Miner rule).When the long-term stress range distribution is expressed by astresshistogram,consistingofaconvenientnumberofcon-stant stress range blocks i each with a number of stress rep-etitions ni the fatigue criterion reads:whereApplyingahistogramtoexpressthestressdistribution,thenumber of stress blocks, k, should be large enough to ensurereasonable numerical accuracy, and should not be less than 20.Due consideration should be given to selection of integrationmethod as the position of the integration points may have a sig-nificant influence on the calculated fatigue life dependent onintegration method.Seealsosection5forcalculationoffatiguedamageusingdesign charts.Referenceismadetocommentarysectionforderivationoffatigue damage calculated from different processes.2.3Fatigue analysis methodology and calculation of Stresses2.3.1GeneralFatigueanalysismaybebasedondifferentmethodologiesdepending on what is found most efficient for the consideredstructuraldetail.DifferentconceptsofS-Ncurvesaredevel-oped and referred to in the literature and in this RP. It is thusimportant that the stresses are calculated in agreement with thedefinition of the stresses to be used together with a particularS-N curve. Three different concepts of S-N curves are defined: Nominal stress S-N curve that is described in section 2.3.2. Hot spot stress S-N curve that is described in section 2.3.3for plated structures and in section 2.3.4 for tubular joints. Notch stress S-N curve that is not used in the main part ofthis RP. (A notch stress S-N curve is listed in the commen-tary that can be used together with finite element analysiswhere the local notch is modelled by an equivalent radius.This approach is foreseen used only in special cases whereit is found difficult to reliably assess the fatigue life usingother methods).Nominal stress is understood to be a stress in a component thatcanbederivedbyclassicaltheorysuchasbeamtheory.Inasimple plate specimen with an attachment as shown in Figure4-1thenominalstressissimplythemembranestressthatisused for plotting of the S-N data from the fatigue testing. Anexample of fatigue design using this procedure is shown in thecommentarysection(Examplewithfatigueanalysisofadrum).Hot spot stress is understood to be the geometric stress createdby the considered detail. (The notch stress due to the local weldgeometryisexcludedfromthestresscalculationasitisassumed to be accounted for in the corresponding hot spot S-Ncurve. The notch stress is defined as the total stress resultingfrom the geometry of the detail and the non-linear stress fielddue to the notch at the weld toe).Derivation of stresses to be used together with the different S-N curves are described in more detail in the following section.The procedure for the fatigue analysis is based on the assump-tionthatitisonlynecessarytoconsidertherangesofcyclicstressesindeterminingthefatigueendurance(i.e.meanstressesareneglectedforfatigueassessmentofweldedcon-nections).2.3.2Plated structures using nominal stress S-N curvesThejointclassificationandcorrespondingS-Ncurvestakesintoaccountthelocalstressconcentrationscreatedbythejointsthemselvesandbytheweldprofile.Thedesignstresscan therefore be regarded as the nominal stress, adjacent to theweld under consideration. However, if the joint is situated in aregion of stress concentration resulting from the gross shape ofthe structure, this must be taken into account. As an example,for the weld shown in Figure 2-2 a), the relevant local stress forfatiguedesignwouldbethetensilestress,nominal.Fortheweld shown in Figure 2-2 b), the stress concentration factor forthe global geometry must in addition be accounted for, givingthe relevant local stress equal to SCF nominal, where SCF isthe stress concentration factor due to the hole. Thus the local(2.2.1)D = accumulated fatigue damage = intercept of the design S-N curve with the log N axism = negative inverse slope of the S-N curvek = number of stress blocksni= number of stress cycles in stress block iNi= number of cycles to failure at constant stress range i = usage factor= 1 / Design Fatigue Factor from OS-C101 Section 6 Fatigue Limit States.( ) = == =mkii ikiiina NnD1 11aDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 11stress is derived aslocalshallbeusedtogetherwiththerelevantS-NcurvesDthrough G, dependent on joint classification.The maximum principal stress is considered to be a significantparameter for analysis of fatigue crack growth. When the prin-cipal stress direction is different from that of the normal to theweldtoe,itbecomesconservativetousetheprinciplestressrange together with a classification of the connection for stressrange normal to the weldtoeasshown in Figure 2-3.As theangle between the principal stress direction and the normal totheweld,,isincreasedfurther,fatiguecrackingmaynolonger initiate along the weld toe, but may initiate in the weldand grow normal to the principal stress direction as shown inFigure 2-4. This means that the notch at the weld toe does nolonger significantly influence the fatigue capacity and a higherS-N curve applies for this stress direction. More guidance on this for use of nominal S-N curves is pre-sentedincommentaryD.4Comm.2.3.2Platedstructuresusing nominal stress S-N curves.2.3.3Plated structures using hot spot stress S-N curvesFordetailedfiniteelementanalysisofweldedplateconnec-tions other than tubular joints it may also be convenient to usethealternativehotspotstressforfatiguelifeassessment,seesection4.3forfurtherguidance.Arelationbetweennominalstress and hot spot stress may be defined aswhereSCFisstructuralstressconcentrationfactornormallydenoted as stress concentration factor.The effect of stress direction relative to the weld toe as shownin Figures 2-3 and 2-4 when using finite element analysis andhot spot stress S-N curve is presented in section 4.3.4.2.3.4Tubular joints For a tubular joint, i. e. brace to chord connection, the stress tobeusedfordesignpurposeistherangeofidealisedhotspotstress defined by: the greatest value of the extrapolation of themaximum principal stress distribution immediately outside theregion effected by the geometry of the weld. The hot spot stressto be used in combination with the T-curve is calculated aswhereFigure 2-2Explanation of local stresses(2.3.1)nominal local SCF = (2.3.2)(2.3.3)SCF = stress concentration factor as given in section 3.3.nominal spot hot SCF =nominal spot hot SCF =DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 12Figure 2-3Fatigue cracking along weld toeFigure 2-4Fatigue cracking when principal stress direction is more parallelwith weld toe2.3.5Fillet weldsThe relevant stress range for potential cracks in the weld throatofload-carryingfillet-weldedjointsandpartialpenetrationwelded joints may be calculated as:where the stress components are explained in Figure 2-5.Thetotalstressfluctuation(i.e.maximumcompressionandmaximumtension)shouldbeconsideredtobetransmittedthrough the welds for fatigue assessments.Figure 2-5Explanation of stresses on the throat section of a fillet weld2.3.6Fillet welded bearing supportsWhere support plating below bearings are designed with filletwelded connection, it should be verified that fatigue crackingoftheweldwillnotoccur.Eventhoughthejointmayberequiredtocarrywhollycompressivestressesandtheplatesurfacesmaybemachinedtofit,thetotalstressfluctuationshould be considered to be transmitted through the welds forfatigue assessment.If it is assumed that compressive loading is transferred throughcontact,itshouldbeverifiedthatthecontactwillnotbelostduring the welding. The actual installation condition includingmaximum construction tolerances should be accounted for.2.4S-N curves2.4.1GeneralThefatiguedesignisbasedonuseofS-Ncurves,whichareobtained from fatigue tests. The design S-N curves which fol-lowsarebasedonthemean-minus-two-standard-deviationcurves for relevant experimental data. The S-N curves are thusassociated with a 97.6% probability of survival.2.4.2Failure criterion inherent the S-N curvesMostoftheS-Ndataarederivedbyfatiguetestingofsmallspecimensintestlaboratories.Forsimpletestspecimensthetesting is performed until the specimens have failed. In thesespecimens there is no possibility for redistribution of stressesduring crack growth. This means that most of the fatigue life isassociated with growth of a small crack that grows faster as thecrack size increases until fracture. Fordetailswiththesamecalculateddamage,theinitiationperiod of a fatigue crack takes longer time for a notch in basematerial than at a weld toe or weld root. This also means thatwithahigherfatigueresistanceofthebasematerialascom-paredwithweldeddetails,thecrackgrowthwillbefasterinbase material when fatigue cracks are growing. For practical purpose one defines these failures as being crackgrowth through the thickness.When this failure criterion is transferred into a crack size in arealstructurewheresomeredistributionofstressismorelikely,thismeansthatthisfailurecriterioncorrespondstoacrack size that is somewhat less than the plate thickness.Thetestswithtubularjointsarenormallyofalargersize.Thesejointsalsoshowlargerpossibilityforredistributionofstresses as a crack is growing. Thus a crack can grow throughthe thickness and also along a part of the joint before a fractureoccur during the testing. The number of cycles at a crack sizethrough the thickness is used when the S-N curves are derived.Asthesetestsarenotverydifferentfromthatoftheactualbehaviourinastructure,thisfailurecriterionforS-Ncurvesfor tubular corresponds approximately to the thickness at thehot spot (chord or brace as relevant).2.4.3S-N curves and joint classificationFor practical fatigue design, welded joints are divided into sev-eral classes, each with a corresponding design S-N curve. Alltubular joints are assumed to be class T. Other types of joint,including tube to plate, may fall in one of the 14 classes spec-ified in Table 2-1, Table 2-2 and Table 2-3, depending upon: the geometrical arrangement of the detail the direction of the fluctuating stress relative to the detail the method of fabrication and inspection of the detail.Eachconstructiondetailatwhichfatiguecracksmaypoten-tially develop should, where possible, be placed in its relevantjoint class in accordance with criteria given in Appendix A. Itshouldbenotedthat,inanyweldedjoint,thereareseverallocations at which fatigue cracks may develop, e. g. at the weldtoe in each of the parts joined, at the weld ends, and in the weld(2.3.4)Principal stressdirectionWeldtoeSectionFatigue crackPrincipal stressdirectionWeldtoeSectionFatigue crack// // // // // // Principal stressdirectionWeldtoeSectionFatigue crackPrincipal stressdirectionWeldtoeSectionFatigue crack// // // // // // 2//2 2w 0.2 + + = ThroatsectionDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 13itself. Each location should be classified separately.The basic design S-N curve is given aswhereThe fatigue strength of welded joints is to some extent depend-ent on plate thickness. This effect is due to the local geometryof the weld toe in relation to thickness of the adjoining plates.See also effect of profiling on thickness effect in section 7.2. Itis also dependent on the stress gradient over the thickness. Ref-erenceismadetoAppendixD,Commentary.Thethicknesseffect is accounted for by a modification on stress such that thedesign S-N curve for thickness larger than the reference thick-ness reads:whereIngeneralthethicknessexponentisincludedinthedesignequationtoaccountforasituationthattheactualsizeofthestructural component considered is different in geometry fromthat the S-N data are based on. The thickness exponent is con-sidered to account for different size of plate through which acrack will most likely grow. To some extent it also accounts forsize of weld and attachment. However, it does not account forweld length or length of component different from that testedsuchase.g.designofmooringsystemswithasignificantlargernumberofchainlinksintheactualmooringlinethanwhat the test data are based on. Then the size effect should becarefullyconsideredusingprobabilistictheorytoachieveareliable design, see Appendix D, Commentary.2.4.4S-N curves in airS-N curves for air environment are given in Table 2-1 and Fig-ure 2-6. The T curve is shown in Figure 2-8. In the low cycleregionthemaximumstressrangeisthatoftheB1curveasshowninFigure2-6.However,foroffshorestructuressub-jected to typical wave and wind loading the main contributionto fatigue damage is in the region N > 106 cycles and the bilin-ear S-N curves defined in Table 2-1 can be used.(2.4.1)N = predicted number of cycles to failure for stress range = stress range m= negative inverse slope of S-N curve= intercept of log N-axis by S-N curve(2.4.2)a = constant relating to mean S-N curves = standard deviation of log N. (2.4.3)m = negative inverse slope of the S - N curve= intercept of log N axistref = reference thickness equal 25 mm for welded connec-tions other than tubular joints. For tubular joints the reference thickness is 32 mm. For bolts tref = 25 mm log m a log N log =logas 2 a log a log = =kreftt log m a log N loglogat = thickness through which a crack will most likely grow. t = tref is used for thickness less than trefk= thickness exponent on fatigue strength as given in Table 2-1, Table 2-2 and Table 2-3.k = 0.10 for tubular butt welds made from one sidek= 0.25 for threaded bolts subjected to stress variation in the axial direction.Table 2-1 S-N curves in airS-N curve N 10 7 cycles N > 10 7 cycles m2 = 5.0Fatigue limit at 10 7 cycles *)Thickness exponent k Structural stress concentration embedded in the detail (S-N class), ref. also equation (2.3.2)m1 B1 4.0 15.117 17.146 106.97 0B2 4.0 14.885 16.856 93.59 0C 3.0 12.592 16.320 73.10 0.15C1 3.0 12.449 16.081 65.50 0.15C2 3.0 12.301 15.835 58.48 0.15D 3.0 12.164 15.606 52.63 0.20 1.00E 3.0 12.010 15.350 46.78 0.20 1.13F 3.0 11.855 15.091 41.52 0.25 1.27F1 3.0 11.699 14.832 36.84 0.25 1.43F3 3.0 11.546 14.576 32.75 0.25 1.61G 3.0 11.398 14.330 29.24 0.25 1.80W1 3.0 11.261 14.101 26.32 0.25 2.00W2 3.0 11.107 13.845 23.39 0.25 2.25W3 3.0 10.970 13.617 21.05 0.25 2.50T 3.0 12.164 15.606 52.63 0.25 for SCF 10.00.30 for SCF >10.01.00*) see also section 2.102loga1logaDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 14Figure 2-6S-N curves in air2.4.5S-N curves in seawater with cathodic protectionS-N curves for seawater environment with cathodic protectionare given in Table 2-2 and Figure 2-7. The T curve is shown inFigure 2-8. For shape of S-N curves see also comment in 2.4.4.1010010001.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08Number of cyclesStress range (MPa)B1B2CC1C2DEFF1F3GW1W2W3Table 2-2 S-N curves in seawater with cathodic protectionS-N curve N 10 6 cycles N > 10 6 cyclesm2= 5.0Fatigue limit at 10 7 cycles*)Thickness exponent k Stress concentration in the S-N detail as derived by the hot spot methodm1B1 4.0 14.917 17.146 106.97 0B2 4.0 14.685 16.856 93.59 0C 3.0 12.192 16.320 73.10 0.15C1 3.0 12.049 16.081 65.50 0.15C2 3.0 11.901 15.835 58.48 0.15D 3.0 11.764 15.606 52.63 0.20 1.00E 3.0 11.610 15.350 46.78 0.20 1.13F 3.0 11.455 15.091 41.52 0.25 1.27F1 3.0 11.299 14.832 36.84 0.25 1.43F3 3.0 11.146 14.576 32.75 0.25 1.61G 3.0 10.998 14.330 29.24 0.25 1.80W1 3.0 10.861 14.101 26.32 0.25 2.00W2 3.0 10.707 13.845 23.39 0.25 2.25W3 3.0 10.570 13.617 21.05 0.25 2.50T 3.0 11.764 15.606 52.63 0.25 for SCF 10.0 0.30 for SCF >10.01.00*) see also 2.102loga1logaDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 15Figure 2-7S-N curves in seawater with cathodic protection2.4.6S-N curves for tubular jointsS-N curves for tubular joints in air environment and in seawa-ter with cathodic protection are given in Table 2-1, Table 2-2and Table 2-3.Figure 2-8S-N curves for tubular joints in air and in seawater with cathodic protection1010010001.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08Number of cyclesStress range (MPa)B1B2CC1C2DEFF1F3GW1W2W311010010001,00E+04 1,00E+05 1,00E+06 1,00E+07 1,00E+08 1,00E+09Number of cyclesStress range (MPa)Seawater with cathodic protectionIn airDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 162.4.7S-N curves for cast nodesIt is recommended to use the C curve for cast nodes. Tests maygive a more optimistic curve. However, the C curve is recom-mended in order to allow for weld repairs after possible castingdefects and possible fatigue cracks after some service life. Theprobability of a repair during service life depends on accumu-lated fatigue damage. Reference is made to section 9.1 and Fig-ure 9-3 which indicates fatigue failure probability as functionof Design Fatigue Factor.For cast nodes a reference thickness tref = 38 mm may be usedprovided that any possible repair welds have been ground to asmooth surface.Forcastnodeswithastressgradientoverthethicknessareducedeffectivethicknessmaybeusedforassessmentofthickness effect. The effective thickness to be used in equation(2.4.3) can be calculated as:WhereS0= hot spot stress on surfaceSi= stress 38 mm below the surface, under the hot spot tactual= thickness of cast piece at considered hot spot meas-ured normal to the surfacete= effective thickness. te shall not be less than 38 mm.k= thickness exponent = 0.152.4.8S-N curves for forged nodesFor forged nodes the B1 curve may be used for nodes designedwith a Design Fatigue Factor equal to 10. For designs with DFFless than 10 it is recommended to use the C-curve to allow forweld repair if fatigue cracks should occur during service life.2.4.9S-N curves for free corrosionS-Ncurvesforfreecorrosion,i.e.withoutcorrosionprotec-tion, are given in Table 2-3. SeealsoCommentarysectionforconsiderationofcorrosionprotection of connections in the splash zone and inside tanks inFPSOs.2.4.10S-N curves for base material of high strength steelThe fatigue capacity of the base material is depending on thesurface finish of the material and the yield strength.For high strength steel with yield strength above 500 MPa andasurfaceroughnessequalRa=3.2orbetterthefollowingdesignS-Ncurvecanbeusedforfatigueassessmentofthebase materialIn air a fatigue limit at 2106 cycles at a stress range equal 235MPacanbeused.Forvariableamplitudeloadingwithonestress range larger than this fatigue limit a constant slope S-Ncurve should be used. Reference is also made to section 2.10.(The mean S-N curve is given by Log N = 17.770 4.70 LogS).ForseawaterwithcathodicprotectionaconstantslopeS-Ncurve should be used. (The same as for air to the left of 2106cycles, see Figure 2-9). If requirements to yield strength, sur-face finish and corrosion protection are not met the S-N curvespresented in sections 2.4.4, 2.4.5 and 2.4.9 should be used. Thethickness exponent k = 0 for this S-N curve.Figure 2-9S-N curve for high strength steel (HS curve)2.4.11S-N curves for stainless steelFor Duplex and for Super Duplex steel one may use the sameclassification as for C-Mn steels.Also for austenitic steel one may use the same classification asfor C-Mn steels. 2.4.12S-N curves for small diameter umbilicalsForfatiguedesignofsmalldiameterpipeumbilicals(outerdiameter in the range 10 -100 mm) made of super duplex steelwith a yield strength larger than 500 MPa with thicknesses inthe range 1.0 to 10 mm the following S-N curve can be usedfor fatigue assessmentwhere(2.4.4)Table 2-3S-N curves in seawater for free corrosionS-N curveFor all cycles m = 3.0Thickness exponent kB1 12.436 0B2 12.262 0C 12.115 0.15C1 11.972 0.15C2 11.824 0.15D 11.687 0.20E 11.533 0.20F 11.378 0.25F1 11.222 0.25F3 11.068 0.25G 10.921 0.25W1 10.784 0.25W2 10.630 0.25W3 10.493 0.25T 11.687 0.25 for SCF 10.00.30 for SCF >10.0kiactual eSSt t/ 10 =a log(2.4.5)(2.4.6)t = actual thickness of the umbilicaltref= 1.0 mmLogS N Log 70 . 4 446 . 17 =10100100010000 100000 1000000 10000000 100000000Number of cyclesStress range (MPa) Air Seawater with cathodic protection => =25 . 0725 . 07* 0 . 5 143 . 1710* 5 . 3 100 . 14: 10refrefttS Log N LogN for andttS Log N LogN ForDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 17AnormalgoodfabricationoftheumbilicalsisassumedasbasisforthisdesignS-Ncurve.Theweldsontheinsideandoutside of the pipes should show a smooth transition from theweld to the base material without notches and/or undercuts. Adetailed NDE inspection for each connection is assumed. The NDE methods are visual inspection and X-ray. For singlepass welds, no indications are acceptable. For multipass weldstheacceptancecriteriashallbeaccordingtoASMEB31.3,chapter IXhighpressure servicegirthgroove.Dyepenetrantshall be used as a surface test in addition to visual inspectionwhenrelevantindications,asdefinedbyASMEVIIIdiv.1,app.4. are found by X-ray.TheS-Ncurveisbasedonfatiguetestingofspecimenssub-jected to a mean stress up to 450 MPa.The given S-N curve is established from test specimens that arenot prestrained from reeling. However, based on a few test datawith prestrained specimens it is considered acceptable to usethe S-N curve also for umbilicals that have been reeled. Thusthis S-N curve applies also when number of cycles under reel-ing is less than 10 and strain range during reeling is less than2%.Figure 2-10S-N curves for small diameter pipe for umbilicals2.4.13Qualification of new S-N curves based on fatigue test dataFor qualification of new S-N data to be used in a project it isimportantthatthetestspecimensarerepresentativefortheactualfabricationandconstruction.Thisincludespossibilityforrelevantproductiondefectsaswellasfabricationtoler-ances. The sensitivity to defects may also be assessed by frac-ture mechanics.Itisrecommendedtoperformfatiguetestingofatleast15specimens in order to establish a new S-N curve. At least threedifferent stress ranges should beselected in the relevant S-Nregion such that a representative slope of the S-N curve can bedetermined.ReferenceismadetoIIWdocumentnoIIW-XIII-WG1-114-03forstatisticalanalysisofthefatiguetestdata.Normallyfatigue test data are derived for number of cycles less than 107.Itshouldbenotedthatforoffshorestructuressignificantfatigue damage occurs for N 107 cycles. Thus how to extrap-olate the fatigue test data into this high cycle region is impor-tantinordertoachieveareliableassessmentprocedure.Inadditiontostatisticalanalysisoneshoulduseengineeringjudgement based on experience for derivation of the S-N datain this region. It is well known that good details where fatigueinitiationcontributesignificantlytothefatiguelifeshowamore horizontal S-N curve than for less good details where thefatigue life consists mainly of crack growth. Reference is alsomade to S-N curves with different slopes shown in this chapter. It should also be remembered that for N 107 cycles there isadditional uncertainty due to variable amplitude loading. Thisis an issue that should be kept in mind if less conservative S-Ncurves than given in this RP are aimed for by qualifying a newS-N curve.Alsotheprobabilityofdetectingdefectsduringaproductionshouldbekeptinmindinthisrespect.Thedefectsthatnor-mallycanbedetectedbyanacceptableprobabilityarenor-mallylargerthanthatinherentinthetestspecimensthatareproduced to establish test data for a new S-N curve.2.5Mean stress influence for non welded structuresFor fatigue analysis of regions in the base material not signifi-cantly affected by residual stresses due to welding, the stressrange may be reduced if part of the stress cycle is in compres-sion. This reduction may e.g. be carried out for cut-outs in the basematerial.Thecalculatedstressrangeobtainedmaybemulti-plied by the reduction factor fm as obtained from Figure 2-11before entering the S-N curve.The reduction factor can be derived from the following equa-tionwhereFigure 2-11Stress range reduction factor to be used with the S-N curve for base material10100100010000 100000 1000000 10000000 100000000 1000000000Num berof cycle sStress range (MP(2.5.1)t= maximum tension stressc= maximum compression stressc tc t ++=6 . 0fmDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 182.6Effect of fabrication tolerancesNormallylargerfabricationtolerancesareallowedinrealstructures than that accounted for in the test specimens used toderive S-N data, ref. DNV OS-C401; Fabrication and Testingof Offshore Structures. Therefore, additional stresses resultingfromnormalfabricationtolerancesshouldbeincludedinthefatigue design. Special attention should be given to the fabri-cation tolerances for simple butt welds in plates and tubulars asthesegivethemostsignificantincreaseinadditionalstress.Stress concentration factors for butt welds are given in section3.1.2 and at tubular circumferential welds in section 3.3.7.2.7Design chart for fillet and partial penetration weldsDesignshouldbeperformedsuchthatfatiguecrackingfromthe root is less likely than from the toe region. The reason forthis is that a fatigue crack at the toe can be found by in-serviceinspection while a fatigue crack starting at the root can not bediscovered before the crack has grown through the weld. Thusthe design of the weld geometry should be performed such thatthe fatigue life for cracks starting at the root is longer than thefatigue life of the toe. Figure 2-13 can be used for evaluationof required penetration. The notation used is explained by Fig-ure 2-12.It should be added that it is difficult to detect internal defectsbyNDEinfillet/partialpenetrationwelds.Suchconnectionsshould therefore not be used in structural connections of signif-icant importance for the integrity.Figure 2-12Welded connection with partial penetration weldFigure 2-13Weld geometry with probability of root failure equal toe failure2.8Bolts2.8.1GeneralA bolted joint connection subjected to dynamic loading shouldbe designed with pretensioned bolts. The pretension should behigh enough to avoid slipping after relevant loss of pretensionduring service life. 2.8.2Bolts subjected to tension loadingConnectionswherethepretensionedboltsaresubjectedtodynamicaxialforcesshouldbedesignedwithrespecttofatigue taking into account the stress range in the bolts result-ingfromtensionandcompressionrange.Thestressrangeinthe bolts may be assessed based on e.g. Maskindeler 2, ref. /23/, or Systematic Calculation of High Duty Bolted Joints,ref. /26/.For S-N classification see Table A-2 of Appendix A.2.8.3Bolts subjected to shear loading For bolts subject to shear loading the following methodologymaybeusedforfatigueassessment.Thethreadsof theboltsshould not be in the shear plane. The methodology may be usedfor fitted bolts or for normal bolts without load reversal. Theshear stress to be calculated based on the shank area of the bolt.Then number of cycles to failure can be derived fromwhere = shear stress based on shaft area of bolt.2.9Pipelines and risers2.9.1GeneralWelds in pipelines are normally made with a symmetric weldgroove with welding from the outside only. The tolerances areratherstrictcomparedwithotherstructuralelementswitheccentricity less than 0.1 t or maximum 3 mm (t = wall thick-ness).Thefabricationofpipelinesalsoimpliesasystematicand standardised NDE of the root area where defects are mostcritical. Provided that the same acceptance criteria are used forpipelineswithlargerwallthicknessasforthatusedasrefer-encethickness(25mm),athicknessexponentk=0maybeused for hot spot at the root and k = 0.15 for the weld toe. Pro-vided that these requirements are fulfilled, the detail at the rootside may be classified as F1 with SCF = 1.0, ref. Table 2-4. TheF-curve and SCF = 1.0 may be used for welding on temporarybacking, ref. Table 2-4. Reference is made to Table 2-4 for other tolerances and weld-ing from both sides.Forweldgroovesthatarenotsymmetricalinshapeastressconcentrationfortheweldrootduetomaximumallowableeccentricity should be included. This stress concentration fac-tor can be assessed based on the following analytical expres-sion:where notations are shown in Figure 3-9.Thisstressconcentrationfactorcanalsobeusedforfatigueassessments of the weld toes, ref. also Table 2-4.The nominal stress on the outside of the pipe should be usedfor fatigue assessment of the outside and the nominal stress onthe inside of the pipe should be usedfor fatigue assessment ofthe inside.00.20.40.60.811.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12ai/tph/tptp = 50 mmtp = 25 mmtp = 12 mmtp = 6mmWeld toe failureWeld root failurelogN = 16.301-5.0log (2.8.1)(2.9.1)D t m /et 31 SCF+ =DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 192.9.2Combined eccentricity for fatigue analysis of seam-less pipesForweldedpipesitisovalitythatnormallywillgoverntheresulting eccentricity. Thus the effect of tolerances can simplybe added linearly.Forseamlesspipesitisrealisedthatthethicknesstolerancecontributes by a similar magnitude to the resulting eccentricity.A resulting tolerance to be used for calculation of stress con-centration factor using equation (2.9.1)with (m = Tot) canbe obtained as:whereReference is made to DNV-OS-F101 Section 6 Clause E1200for measurements of tolerances.2.9.3SCFs for pipes with internal pressureReference is made to commentary for stress concentration fac-torsforotherdetailsinpipelinesandcylindricaltankswithstress cycling mainly due to internal pressure.(2.9.2)Thickness= (tmax - tmin)/2Ovality= Dmax - Dmin if the pipes are supported such that flush outside at one point is achieved (no pipe centralising)Ovality= (Dmax - Dmin)/2 if the pipes are centralised dur-ing constructionOvality= (Dmax - Dmin)/4 if the pipes are centralised dur-ing construction and rotated until a good fit around the circumference is achieved2 2Ovality Thickness Tot + =Table 2-4Classification of welds in pipelinesDescriptionTolerance requirement S-N curve Thickness exponent k SCFWelding Geometry and hot spotSingle side min (0.15t, 3 mm) F1 0.00 1.0 > min (0.15t, 3 mm) F3 0.00 1.0Single sideon backing min (0.1t, 2 mm) F 0.00 1.0 > min (0.1t, 2 mm) F1 0.00 1.0Single side D 0.15Eq. (2.9.1)Double side D 0.15Eq. (2.9.1)Hot spotHot spotHot spotHot spotDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 202.10Guidance to when a detailed fatigue analysis can be omittedA detailed fatigue analysis can be omitted if the largest localstress range for actual details defined in eq. (2.3.1) is less thanthe fatigue limit at 107 cycles in Table 2-1 for air and Table 2-2forseawaterwithcathodicprotection.ForDesignFatigueFactorslargerthan1theallowablefatiguelimitshouldalsohere be reduced by a factor (DFF) -0.33. For definition of DFF see OS-C101 ref. /28/.Requirements to detailed fatigue analysis may also be assessedbased on the fatigue assessment charts in Figure 5-1 and Figure5-2.TheuseofthefatiguelimitisillustratedinFigure2-14.Adetailed fatigue assessment can be omitted if the largest stresscycleisbelowthefatiguelimit.However,intheexampleinFigure2-15thereisonestresscycle1abovethefatiguelimit. This means that a further fatigue assessment is required.This also means that the fatigue damage from the stress cycles2 has to be included in the fatigue assessment.Figure 2-14Stress cycling where further fatigue assessment can be omittedFigure 2-15Stress cycling where a detailed fatigue assessment is required3.Stress Concentration Factors3.1Stress concentration factors for plated structures3.1.1GeneralA stress concentration factor may be defined as the ratio of hotspot stress range over nominal stress range. 3.1.2Stress concentration factors for butt weldsThe eccentricity between welded plates may be accounted forin the calculation of stress concentration factor. The followingformula applies for a butt weld in an unstiffened plate or for apipe butt weld with a large radius: wherem is eccentricity (misalignment) and t is plate thickness, seeFigure 3-9. 0=0.1tismisalignmentinherentintheS-Ndataforbuttwelds. See DNV-OS-C401 for fabrication tolerances.The stress concentration for the weld between plates with dif-ferent thickness in a stiffened plate field may be derived fromthe following formula: whereSee also Figure 3-8.3.1.3Stress concentration factors for cruciform jointsThestressconcentrationfactorforcruciformjointatplatethickness ti may be derived from following formula: whereThe other symbols are defined in Figure 3-1.Figure 3-1Cruciform joint(3.1.1)NS1Fatigue limitStress cyclingNS1Fatigue limitStress cyclingNS12Fatigue limitStress cyclingNS12Fatigue limitStress cyclingt) ( 31 SCF0 m + =(3.1.2)m= maximum misalignment t= (T t) eccentricity due to change in thickness. Note: This applies also at transitions sloped as 1:4.0= 0.1 t is misalignment inherent in the S-N data for butt welds. See DNV-OS-C401 for fabrication tolerances.T = thickness of thicker platet = thickness of thinner plate(3.1.3) = (m + t) is the total eccentricity0= 0.3 ti is misalignment embedded in S-N data for cruci-form joints. See DNV-OS-C401 for fabrication toler-ances.ti= thickness of the considered plate (i = 1, 2)li= length of considered plate (i = 1, 2)( )+ ++ =5 . 15 . 10 m161 SCFtTtt + + ++ =434333232131i02) ( 61 SCFltltltltlti l3l4l2l1t2 t1t3t4 l3l4l2l1t2 t1t3t4 DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 213.1.4Stress concentration factors for rounded rectangular holes Stress concentration factors for rounded rectangular holes aregiven in Figure 3-2.Wherethereisonestressraiserclosetoanotherdetailbeingevaluatedwithrespecttofatigue,theinteractionofstressbetweentheseshouldbeconsidered.Anexampleofthisisawelded connection in a vicinity of a hole. Then the increase instress at the considered detail due to the hole can be evaluatedfrom Figure 3-3. Some guidelines on effect of interaction of different holes canbe found in Peterson's Stress Concentration Factors, /15/).Figure 3-2Stress concentration factors for rounded rectangular holesFigure 3-3Stress distribution at a hole01234560 0,1 0,2 0,3 0,4 0,5 0,6r / bSCFrb/a=1.5b/a=1.0b/a=0.5b/a=0.25b/a=2.0ab0.000.200.400.600.801.001.201.401.601.802.002.202.402.602.803.001.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00Relative distance from centre of hole x/rRelative stressr Stress directionx/rLine for calculation of stressLine for calculationof stressrxDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 223.1.5Stress concentration factors for holes with edge rein-forcementStressconcentrationfactorsforholeswithreinforcementaregiven in Appendix C.Fatigue cracking around a circumferential weld may occur atseverallocationsatreinforcedringsinplatesdependingongeometry of ring and weld size.1) Fatigue cracking transverse to the weld toe in a region witha large stress concentration giving large stress parallel tothe weld (Flexible reinforcement). See Figure 3-4a. Thenhot spot = p2) Fatigue cracking parallel to the weld toe (Stiff reinforce-ment with large weld size). See Figure 3-4b. Fatigue crackinitiating from the weld toe. The principal stress 1 is thecrack driving stress.Then hot spot = 1Also the region at crown position to be checked.Then hot spot = n3) Fatigue cracking from the weld root (Stiff reinforcementwith small fillet weld size). See Figure 3-4c.Forfilletweldsallthesepositionsshouldbeassessedwithrespecttofatigue.Forfullpenetrationweldsthefirsttwopoints should be assessed.Figure 3-4Potential fatigue crack locations at welded penetrationsAllthesepotentialregionsforfatiguecrackingshouldbeassessed in a design with use of appropriate stress concentra-tion factors for holes with reinforcement.For stresses to be used together with the different S-N curvessee section 2.3.Potential fatigue cracking transverse to the weld toeFor stresses parallel with the weld the local stress to be usedtogether with the C curve is obtained with SCF from AppendixC (hot spot in Figure 3-4a). Potential fatigue cracking parallel with the weld toeFor stresses normal to the weld the resulting hot spot stress tobe used together with the D curve is obtained with SCF fromAppendix C (hot spot in Figure 3-4b). Potential fatigue cracking from the weld rootAt some locations of the welds there are stresses in the platetransversetothefilletweld,n,andshearstressintheplateparallel with the weld //p see Figure 3-4c. Then the fillet weldis designed for a combined stress obtained aswhereThetotalstressrange(i.e.maximumcompressionandmaxi-mum tension) should be considered to be transmitted throughtheweldsforfatigueassessments.ReferenceisalsomadetoAppendix C for an example.Equation (3.1.4) can be outlined from equation (2.3.4) and theresulting stress range is to be used together with the W3 curve.The basic stress in the plate as shown in Figure 3-4 is derivedfrom Appendix C.3.1.6Stress concentration factors for scallopsReference is made to Figure 3-5 for stress concentration fac-tors for scallops.Thestressconcentrationfactorsareapplicabletostiffenerssubject to axial loads. For significant dynamic pressure loadson the plate these details are susceptible to fatigue cracking andother design solutions should be considered to achieve a properfatigue life.a)b) c) pFillet weld1InsertTubularn45n45p(3.1.4)t = plate thicknessa = throat thickness for a double sided fillet weld2//22 . 02p n wat + = DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 23Figure 3-5Stress concentration factors for scallops3.2Stress concentration factors for ship detailsStressconcentrationfactorsforshipdetailsmaybefoundinFatigue Assessment of Ship Structures (CN 30.7), ref. /1/. S-N curve C from this Recommended Practice may be used if theprocedure of CN 30.7 is used to determine the hot spot and Kwstress. S-N curve D from this RP may be used if the procedureof CN 30.7 is used to determine the local stress (Excluding thenotchstressconcentrationfactorduetotheweldgeometry,Kw, from the analysis, as this factor is accounted for in the D-curve).3.3Tubular joints and members3.3.1Stress concentration factors for simple tubular jointsStress concentration factors for simple tubular joints are givenin Appendix B. 3.3.2Superposition of stresses in tubular jointsThe stresses are calculated at the crown and the saddle points,seeFigure3-6.Thenthehotspotstressatthesepointsisderivedbysummationofthesinglestresscomponentsfromaxial, in-plane and out of plane action. The hot spot stress maybehigherfortheintermediate pointsbetweenthesaddleandthe crown. The hot spot stress at these points is derived by alinear interpolation of the stress due to the axial action at thecrownandsaddleandasinusoidalvariationofthebendingstress resulting from in-plane and out of plane bending. Thusthe hot spot stress should be evaluated at 8 spots around the cir-cumference of the intersection, ref. Figure 3-7.Here x, my and mz are the maximum nominal stresses duetoaxialloadandbendingin-planeandout-of-planerespec-tively. SCFAS is the stress concentration factor at the saddle foraxial load and the SCFAC is the stress concentration factor atthecrown.SCFMIPisthestressconcentrationfactorforinplane moment and SCFMOP is the stress concentration factorfor out of plane moment.SCF = 2.4 at point A (misalignment not included)SCF = 1.27 at point B SCF = 1.17 at point A (misalignment not included)SCF = 1.27 at point BSCF = 1.27 at point A (misalignment not included)SCF = 1.27 at point BSCF = 1.17 at point A (misalignment not included)SCF = 1.27 at point BFor scallops without transverse welds, the SCF at point B will be governing for the design.AB15035BAAB35120 1201035BA(3.3.1)mz MOP my MIP x AS AC 8mz MOP x AS 7mz MOP my MIP x AS AC 6my MIP x AC 5mz MOP my MIP x AS AC 4mz MOP x AS 3mz MOP my MIP x AS AC 2my MIP x AC 1 SCF 221 SCF 221 ) SCF (SCF21 SCF SCF SCF 221 SCF 221 ) SCF (SCF21 SCF SCF SCF 221 SCF 221 ) SCF (SCF21 SCF SCF SCF 221 SCF 221 ) SCF (SCF21 SCF SCF + + + =+ =+ + = = + = = + + =+ =DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 24Figure 3-6Geometrical definitions for tubular jointsFigure 3-7Superposition of stressesInfluence functions may be used as an alternative to the proce-duregivenheretocalculatehotspotstress.Seee.g.Com-bined Hot-Spot Stress Procedures for Tubular Joints, ref. /24/andDevelopmentofSCFFormulaeandGeneralisedInflu-ence Functions for use in Fatigue Analysis ref. /2/.3.3.3Tubular joints welded from one sideTherootareaofsingle-sidedweldedtubularjointsmaybemorecriticalwithrespecttofatiguecracksthantheoutsideregionconnectingthebracetothechord.Insuchcases,itisrecommended that stubs are provided for tubular joints wherehighfatiguestrengthisrequired,suchthatweldingfromthebackside can be performed.Failure from the root has been observed at the saddle positionoftubularjointswherethebracediameterisequalthechorddiameter, both in laboratory tests and in service. It is likely thatfatigue cracking from the root might occur for rather low stressconcentrations.Thus,specialattentionshouldbegiventojoints other than simple joints, such as ring-stiffened joints andjointswhereweldprofilingorgrindingonthesurfaceisrequired to achieve sufficient fatigue life. It should be remem-bered that surface improvement does not increase the fatiguelife at the root.Based on experience it is not likely that fatigue cracking fromthe inside will occur earlier than from the outside for simple Tand Y joints and K type tubular joints. The same considerationmaybemadeforX-jointswithdiameterratio0.90.Forother joints and for simple tubular X-joints with > 0.90 it isrecommended that a fatigue assessment of the root area is per-formed. Some guidance on such an assessment can be found inAppendix D, Commentary.Due to limited accessibility for in service inspection a higherdesign fatigue factor should be used for the weld root than forthe outside weld toe hot spot. Reference is also made to Appen-dix D, Commentary3.3.4Stiffened tubular jointsEquationsforjointsforringstiffenedjointsaregiveninStressConcentrationFactorsforRing-StiffenedTubularJoints, ref. /3/. The following points should be noted regard-ing the equations: ThederivedSCFratiosforthebrace/chordintersectionand the SCF's for the ring edge are mean values, althoughthedegreeofscatterandproposeddesignfactorsaregiven. Short chord effects shall be taken into account where relevant. For joints with diameter ratio 0.8, the effect of stiffen-ing is uncertain. It may even increase the SCF. The maximum of the saddle and crown stress concentra-tionfactorvaluesshouldbeappliedaroundthewholebrace/chord intersection. Thefollowingpointscanbemadeabouttheuseofringstiffeners in general:Axial loadzxy12345678In-plane Out-of-planebending moment bending momentNMIPMOPDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 25 ThinshellFEanalysisshouldbeavoidedforcalculatingthe SCF if the maximum stress is expected to be near thebrace-ring crossing point in the fatigue analysis. An alter-native is to use a three-dimensional solid element analysismodel. Ring stiffeners have a marked effect on the circumferentialstress in the chord, but have little or no effect on the longi-tudinal stress. Ring stiffeners outside the brace footprint have little effecton the SCF, but may be of help for the static strength. Failures in the ring inner edge or brace ring interface occurinternally,andwillprobablyonlybedetectedafterthroughthicknesscracking,atwhichthemajorityofthefatiguelifewillhavebeenexpired.Theseareasshouldthereforebeconsideredasnon-inspectableunlessmoresophisticated inspection methods are used.3.3.5Grouted tubular joints3.3.5.1GeneralGroutedjointshaveeitherthechordcompletelyfilledwithgrout(singleskingroutedjoints)ortheannulusbetweenthechordandaninnermemberfilledwithgrout(doubleskingroutedjoints).TheSCFofagroutedjointdependsonloadhistoryandloadingdirection.TheSCFislessifthebondbetween the chord and the grout is unbroken. For model testingof grouted joints the bond should be broken prior to SCF meas-urements.DuetothegroutthetensileandcompressiveSCFmay be different.To achieve a fatigue design that is on the safe side it is recom-mended to use SCF's derived from tests where the bounds arebroken and where the joint is subjected to tensile loading. Thebounds can be broken by a significant tension load. This loadmay be determined during the testing by an evaluation of theforce displacement relationship. (When incrementing the load-ing into a non-linear behaviour).3.3.5.2Chord filled with groutThe grouted joints shall be treated as simple joints, except thatthe chord thickness in the term for saddle SCF calculation forbrace and chord shall be substituted with an equivalent chordwall thickness given bywhere D and T are chord diameter and thickness respectively.The dimensions are to be given in mm.Joints with high or low ratios have little effect of grouting.Thebenefitsofgroutingshouldbeneglectedforjointswith > 0.9 or 12.0 unless documented otherwise.3.3.5.3Annulus between tubular members filled with groutForjointswheretheannulusbetweentubularmembersarefilledwithgroutsuchasjointsinlegswithinsertpiles,thegrouted joints shall be treated as simple joints, except that thechord thickness in SCF calculation for brace and chord shall besubstituted with an equivalent chord wall thickness given bywhere T is chord thickness and Tp is thickness of insert pile.3.3.6Cast nodesIt is recommended that finite element analysis should be usedtodeterminethemagnitudeandlocationofthemaximumstress range in castings sensitive to fatigue. The finite elementmodelshouldusevolumeelementsatthecriticalareasandproperly model the shape of the joint. Consideration should begiven to the inside of the castings. The brace to casting circum-ferentialbuttweld(whichisdesignedtoanappropriateS-Ncurve for such connections) may be the most critical locationfor fatigue.3.3.7Stress concentration factors for tubular butt weld connectionsDue to less severe S-N curve for the outside weld toe than theinside weld root, it is strongly recommended that tubular buttweld connections subjected to axial loading are designed suchthatanythicknesstransitionsareplacedontheoutside(seeFigure3-8).Forthisgeometry,theSCFforthetransitionapplies to the outside. On the inside it is then conservative touse SCF = 1.0. Thickness transitions are normally to be fabri-cated with slope 1:4.Stress concentrations at tubular butt weld connections are dueto eccentricities resulting from different sources. These may beclassifiedasconcentricity(differenceintubulardiameters),differencesinthicknessofjoinedtubulars,outofroundnessand centre eccentricity, see Figure 3-10 and Figure 3-11. Theresultingeccentricitymaybeconservativelyevaluatedbyadirectsummationofthecontributionfromthedifferentsources.Theeccentricityduetooutofroundnessnormallygives the largest contribution to the resulting eccentricity .It is conservative to use the formula for plate eccentricities forcalculationofSCFattubularbuttwelds.Theeffectofthediameter in relation to thickness may be included by use of thefollowing formula, provided that T/t 2: whereThis formula also takes into account the length over which theeccentricityisdistributed:L,ref.Figure3-9andFigure3-8.The stress concentration is reduced as L is increased and or Dis reduced. It is noted that for small L and large D the last for-mula provides stress concentration factors that are close to butlower than that of the simpler formula for plates.The transition of the weld to base material on the outside of thetubular can normally be classified to S-N curve E. If weldingis performed in a horizontal position it can be classified as D.This means that the pipe would have to be rotated during weld-ing.Equation (3.3.4) applies for the outside tubular side shown inFigure 3.8. For the inside the following formula may be used:If the transition in thickness is on the inside of the tubular andtheweldismadefrombothsides,equation(3.3.4)maybeapplied for the inside weld toe and equation (3.3.5) for the out-side weld toe.If the transition in thickness is on the inside of the tubular andthe weld is made from the outside only, the following formulae(3.3.2)(3.3.3)134T)/144 (5D Te+ =pT T 45 . 0 Te+ =(3.3.4)0= 0.1 t is misalignment inherent in the S-N data(3.3.5) -5 . 20 tetT11t) 6(1 SCF+ ++ = m2.5tT11t D1.82L+ = -5 . 2tetT11t) ( 61 SCF+ =mDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 26may be used for the inside weld root:And equation (3.3.5) may be applied for the outside weld toe.Figure 3-8Preferred transition in thickness is on outside of tubular butt weldFigure 3-9Section through weldIn tubulars, the root side of welds made from one side is nor-mally classified as F3. This requires good workmanship duringconstruction, in order to ensure full penetration welds, and thatworkischeckedbynon-destructiveexamination.Itmaybedifficult to document a full penetration weld in most cases dueto limitations in the non-destructive examination technique todetect defects in the root area. The F3 curve can be consideredto account for some lack of penetration, but it should be notedthat a major part of the fatigue life is associated with the initialcrack growth while the defects are small. This may be evalu-atedbyfracturemechanicssuchasdescribedinBS7910GuidanceonMethodsforAssessingtheAcceptabilityofFlawsinFusionWeldedStructures,ref/7/.Therefore,ifafabrication method is used where lack of penetration is to beexpected, the design S-N curves should be adjusted to accountfor this by use of fracture mechanics.For global moments over the tubular section it is the nominalstress derived at the outside that should be used together withan SCF from equation (3.3.4) for calculation of hot spot stressforfatigueassessmentoftheoutsideweldtoe.Thenominalstressontheinsideshouldbeusedforassessmentoffatiguecracks initiating from the inside.(3.3.6) -5 . 2tetT11t 61 SCF++ =ttTLnominal41axisNeutralInsideOutsidetDLmDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 27Figure 3-10Geometricsourcesof localstressconcentrationsintubular buttweldsFigure 3-11Geometricsourcesof localstressconcentrationsintubular buttwelds3.3.8Stress concentration factors for stiffened shellsThe stress concentration at a ring stiffener can be calculated aswhereDue to less stress on the inside it is more efficient to place ringstiffeners on the inside of shell, as compared with the outside.Inaddition,iftheshellcompriseslongitudinalstiffenersthatare ended, it is recommended to end the longitudinal stiffenersagainst ring stiffeners for the inside. The corresponding com-bination on the outside gives a considerably larger stress con-centration.The SCF = 1.0 if continuous longitudinal stiffeners are used.In the case of a bulkhead instead of a ring, Ar is taken as where tb is the thickness of the bulkhead.Figure 3-12Ring stiffened shell3.3.9Stress concentration factors for conical transitionsThestressconcentrationateachsideofunstiffenedtubular-cone junction can be estimated by the following equations (theSCF shall be used together with the stress in the tubular at thejunction for both the tubular and the cone side of the weld): whereA ASection A-A a) ConcentricityttmA Ab) Thickness Section A-ATt = (T-t)tASection A-A c) Out of roundnessAttmmmA ASection A-A d) Center eccentricityttmm (3.3.7)Ar= area of ring stiffener without effective shellr = radius of shell measured from centre to mean shell thicknesst= thickness of shell platingfor the tubular side (3.3.8)for the cone side(3.3.9)Dj= cylinder diameter at junction (Ds, DL)t = tubular member wall thickness (ts, tL)tc= cone thickness = the slope angle of the cone (see Figure 3-13)rArt 1.56t1 shell the of inside for the0.541 SCFshell the of outside for the0.541 SCF+ = =+ =( ) 1t rbtant) t (t D t 0.61 SCF2c j++ =tant) t (t D t 0.61 SCF2cc j++ =DET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 28The stress concentration at a junction with ring stiffener can becalculated aswhereAringstiffenermaybeplacedcentricattheconejunction.ThenthebuttweldshouldbegrindedandNDEexaminedbefore the ring stiffener is welded.If a ring stiffener is placed a distance e away from the inter-sectionlines,anadditionalstressconcentrationshouldbeincluded to account for this eccentricity: wherewherewhereIf a ring stiffener with a flange is used the effect of the flangeshouldbeincludedwhencalculatingthemomentofinertiaabout the neutral axis x-x shown in Figure 3-14.The stress concentration factor from equation (3.3.11) shall bemultiplied together with the relevant stress concentration fac-tor from equation (3.3.10).Afullpenetrationweldconnectingtheringstiffenertothetubular is often preferred as potential fatigue cracks from theroot of fillet weld into the cylinder can hardly be detected dur-ing in service inspection. If improvement methods are used forthe weld toe the requirement of a full penetration weld will beenhanced.Figure 3-13Cone geometry(3.3.10)Ar= area of ring stiffener without effective shell(3.3.11)Dj= cylinder diameter at junction (Ds, DL)t = tubular member wall thickness (ts, tL)tc= cone thickness = the slope angle of the cone (see Figure 3-13)I = moment of inertia about the X-X axis in Figure 3-14 calculated as(3.3.12)rjrjrjrjrjAt D 1.10t1 and junction, diameter larger inside the at1tanAt 0.91D0.54 1 SCFjunction diameter larger outside the at1tanAt 0.91D0.54 1 SCFjunction diameter smaller inside the at1tanAt 0.91D0.54 1 SCFjunction diameter smaller outside the at1tanAt 0.91D0.54 1 SCF+ = = + =+ =+ + =5 3) (6811 tan 31c jet t DI tSCF+++ = ) )2(12() ( )2( 5 . 0122223yh hh tt t yth btb Irs c ++ + + + =(3.3.13)h = height of ring stiffenertr= thickness of ringstiffenerb = effective flange width calculated as(3.3.14)b t t t ht t bth t hyc rc r) ( 2) ( )2(2+ ++ + +=e c jt t D b + + = ) ( 78 . 0DsDLtstL.tCDsD Ltst LtceDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 29Figure 3-14Notations for calculation of moment of inertia3.3.10Stress concentration factors for tubulars subjected to axial forceThis section applies to tubular sections welded together to longstrings and subjected to axial tension. Tethers and risers of aTLP are examples of such structures.The co-linearity with small angle deviation between consecu-tive fabricated tubular segments results in increased stress duetoaresultingglobalbendingmoment,seeFigure3-16.Theeccentricity due to co-linearity is a function of axial tension inthetubularandissignificantlyreducedastheaxialforceisincreasedbytension.AssumingthatthemomentMresultsfromaneccentricityNwherepretensionisaccountedforinthe analysis, the following derivation of a stress concentrationfactor is performed: where the stress concentration factor is: where N is eccentricity as function of the axial force N and Disouterdiameter.Theeccentricityfortwoelementsisindi-catedinFigure3-16.Withzerotensiontheeccentricityis.With an axial tension force N the eccentricity becomes: whereThe formula for reduction in eccentricity due to increased axialforcecanbededucedfromdifferentialequationforthedeflected shape of the model shown in Figure 3-16. Thus thenon-linearity in terms of geometry is included in the formulafor the stress concentration factor.Judgement should be used to evaluate the number of elementsto be considered, and whether deviation from a straight line issystematicorrandom,ref.Figure3-15.Inthefirstcase,theerrorsmustbeaddedlinearly,inthesecondcaseitmaybeadded quadratically.Figure 3-15Colinearity or angle deviation in pipe segment fabrication, I = Systematic deviation, II = random deviationFigure 3-16Eccentricity due to co-linearity3.3.11Stress concentration factors for joints with square sectionsStressconcentrationfactorsforT-andX-squaretosquarejoints may be found in Proposed Revisions for Fatigue Designof Planar Welded Connections made of Hollow Structural Sec-tions, ref. /27/.StressconcentrationfactorsforY-andKsquaretosquarejointsmaybefoundfromIIWFatigueRulesforTubularJoints.Thesestressconcentrationfactorsmaybeusedtogether with the D-curve.The following stress concentration factors may be used for d/Dw = 1.0, where d = depth and width of brace; Dw = depth andwidth of chord, in lieu of a more detailed analysis for calcula-tion of hot spot stress: Axial: 1.90 In-plane bending: 4.00 Out-of plane bending:1.35These stress concentration factors should be used together withthe F-curve.(3.3.15)(3.3.16)(3.3.17)k = l = segment lengths of the tubularsN = axial force in tubularsI = moment of inertia of tubulars E = Youngs modulushtbtctrx xyhtbtctrx xy( )SCFt t D N=t D41 SCFN+ =klkl tanhN =EINNNNDET NORSKE VERITASRecommended Practice DNV-RP-C203,April 2008Page 303.3.12Stress concentration factors for joints with gusset platesInsertgussetplatesaresometimesusedinjointsintopsidestructures to connect RHS and tubular members. Reference ismade to Figure 3-17. When such connections are subjected todynamic loading a full penetration weld between the memberand the gusset plate is preferred. Otherwise it is considered dif-ficulttodocumentthefatiguecapacityforfatiguecrackingstarting from the weld root. In dynamic loaded structures it isrecommendedtoshapethegussetplateinsuchawaythatasmooth transfer of stress flow from the member into the gussetplate is achieved; ref. Figure 3-17a. Where a reliable fatigue life is to be documented it is recom-mended to performfinite element analysis if the geometry issignificantlydifferentfromthatshowninFigure3-17b.Thestress concentration factors in Table 3-1 are derived from finiteelement analysis using shell elements. Then the hot spot stresscan becombined with the D-Curve. Thestressconcentrationfactorfortubularmemberissimplyderivedbyscalingtheresults from that of RHS by /4 for the same thickness. Usingshellelementsforsuchanalysisprovidesconservativestressconcentrationfactorsascomparedwithuseofthree-dimen-sionalelementswithmodellingalsoofthefilletweld.(Itishere assumed that a fillet weld also can be used on the outsideon a full or partial penetration weld). In a relevant example theresulting SCF using a model with three-dimensional elementswas only 0.70 of that from analysis using a shell model. Thusthe SCFs in Table 3-1 might be further reduced if necessary. a)b)Figure 3-17Joints with gusset plates a) Favourable geometry b) Simple geometry4.Calculation of hot spo