RECOMMENDED PRACTICE DET NORSKE VERITAS DNV-RP-C203 FATIGUE DESIGN OF OFFSHORE STEEL STRUCTURES APRIL 2008 Since issued in print (April 2008), this booklet has been amended, latest in October 2008. See the reference to “Amendments and Corrections” on the next page.
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RECOMMENDED PRACTICE
DET NORSKE VERITAS
DNV-RP-C203
FATIGUE DESIGN OF OFFSHORE STEEL STRUCTURES
APRIL 2008
Since issued in print (April 2008), this booklet has been amended, latest in October 2008. See the reference to “Amendments and Corrections” on the next page.
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Offshore 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 Systems
Amendments and Corrections This document is valid until superseded by a new revision.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.
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Changes – Page 3
Main changes April 2008
— The principal stress direction in Figure 2-2 is changedfrom 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-tion relative to the weld toe with respect to selection ofS-N curve is included in the commentary section.
— Guidance on derivation of an effective thickness to beused together with the S-N curve for cast joints subjectedto some bending moment over the thickness is given.
— The δ0 in equations for stress concentration factors for buttwelds in pipelines is removed due to rather strict toler-ances used in pipeline fabrication and it can not be docu-mented that a large tolerance δ0 is embedded in the S-Ndata used in design.
— A commentary section on stress concentration factors fordetails in pipelines and cylindrical tanks with stresscycling mainly due to internal pressure is included. Thisincludes circumferential welds and longitudinal welds inpipes.
— The section on grouted joints is extended to include jointswith the annulus between tubular members filled withgrout 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 VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 4 – Changes see note on front cover
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 5
CONTENTS
1. 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.....................................................................8
2. 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 ...............................................................20
3. 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 .......23
3.3 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 . 30
4. CALCULATION OF HOT SPOT STRESS BY FINITE ELEMENT ANALYSIS........................ 30
4.1 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............................... 33
5. SIMPLIFIED FATIGUE ANALYSIS ............... 345.1 General ................................................................... 345.2 Fatigue design charts ............................................ 345.3 Example of use of design charts........................... 38
6. FATIGUE ANALYSIS BASED ON FRACTURE MECHANICS................................ 39
7. IMPROVEMENT OF FATIGUE LIFE BY FABRICATION ................................................... 39
7.1 General ................................................................... 397.2 Weld profiling by machining and grinding ........ 397.3 Weld toe grinding.................................................. 407.4 TIG dressing .......................................................... 407.5 Hammer peening ................................................... 40
APP. A CLASSIFICATION OF STRUCTURAL DETAILS............................................................................ 47
A.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 ....... 52
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 6 see note on front cover
A.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 ......................... 66
APP. B SCF’S FOR TUBULAR JOINTS ..................... 68
B.1 Stress concentration factors for simple tubular joints and overlap joints ..................................................... 68
APP. C SCF’S FOR PENETRATIONS WITH REINFORCEMENTS ....................................................... 78
C.1 SCF’s for small circular penetrations with reinforcement............................................................ 78
C.2 SCF’s at man-hole penetrations ............................. 100C.3 Results .................................................................... 101
APP. D COMMENTARY ............................................. 115
D.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 side 121D.10 Comm. 4.1 The application of the effective
notch stress method for fatigue assessment of structural details ..................................................... 121
D.11 Comm. 4.3.8 Verification of analysis methodology for FE hot spot stress analysis................................ 123
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 7
1. Introduction1.1 GeneralThis Recommended Practice presents recommendations inrelation to fatigue analyses based on fatigue tests and fracturemechanics. Conditions for the validity of the RecommendedPractice are given in section 1.2.The aim of fatigue design is to ensure that the structure has anadequate fatigue life. Calculated fatigue lives also form thebasis for efficient inspection programmes during fabricationand the operational life of the structure.To ensure that the structure will fulfil its intended function, afatigue assessment, supported where appropriate by a detailedfatigue analysis, should be carried out for each individualmember, which is subjected to fatigue loading. See also section2.10. It should be noted that any element or member of thestructure, every welded joint and attachment or other form ofstress concentration, is potentially a source of fatigue crackingand should be individually considered.
1.2 Validity of standard
1.2.1 MaterialThis Recommended Practice is valid for steel materials in airwith yield strength less than 960 MPa. For steel materials inseawater 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.
1.2.2 TemperatureThis Recommended Practice is valid for material temperaturesof up to 100°C. 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 tomean strength capacity. The reduced resistance in the S-Ncurves can be derived by a modification of the log as:
1.2.3 Low 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.
1.3 Methods 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 analysismay alternatively be based on fracture mechanics. If thefatigue 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-culations based on fracture mechanics, it should be docu-mented that there is a sufficient time interval between time ofcrack detection during in-service inspection and the time ofunstable 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 when
establishing 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 thestress range history contributing most significantly to thefatigue damage should be most carefully evaluated. See alsoAppendix D, Commentary, for guidance. It should be noted that the shape parameter h in the Weibulldistribution 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 thefatigue damage is calculated based on closed form solutionswith an assumption of a Weibull long term stress range distri-bution, a shape parameter to the safe side should be used.
1.4 DefinitionsClassified structural detail: A structural detail containing astructural discontinuity including a weld or welds, for whichthe 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-ular stress fluctuation with constant magnitudes of stressmaxima and minima.Crack propagation rate: Amount of crack propagation duringone stress cycle.Crack propagation threshold: Limiting value of stress inten-sity factor range below which the stress cycles are consideredto be non-damaging.Eccentricity: Misalignment of plates at welded connectionsmeasured 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.Fatigue resistance: Structural detail’s resistance againstfatigue actions in terms of S-N curve or crack propagationproperties.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.Design Fatigue Factor: Factor on fatigue life to be used fordesign.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 atthe hot spot (also known as geometric stress or structuralstress).Local nominal stress: Nominal stress including macro-geo-metric effects, concentrated load effects and misalignments,disregarding the stress raising effects of the welded joint itself.
(1.2.1)
(1.2.2)
263T T10372.1T10239.00376.1R −− ⋅−⋅−=
TRT RLogmaLogaLog +=
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 8 see note on front cover
Local notch: A notch such as the local geometry of the weldtoe, including the toe radius and the angle between the baseplate surface and weld reinforcement. The local notch does notalter the structural stress but generates non-linear stress peaks.Macro-geometric discontinuity: A global discontinuity, theeffect of which is usually not taken into account in the collec-tion of standard structural details, such as large opening, acurved part in a beam, a bend in flange not supported by dia-phragms or stiffeners, discontinuities in pressure containingshells, 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.Miner sum: Summation of individual fatigue damage ratioscaused 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 stresswhich exceeds the linearly distributed structural stress at alocal notch.Notch stress: Total stress at the root of a notch taking intoaccount the stress concentration caused by the local notch.Thus the notch stress consists of the sum of structural stressand non-linear stress peak.Notch stress concentration factor: The ratio of notch stress tostructural stress.Paris’ law: An experimentally determined relation betweencrack growth rate and stress intensity factor range.Palmgren-Miner rule: Fatigue failure is expected when theMiner 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 partof a component, linearly distributed across the thickness asassumed 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.Stress intensity factor: Factor used in fracture mechanics tocharacterise the stress at the vicinity of a crack tip.Stress range: The difference between stress maximum andstress 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.the number of ranges exceeding a particular magnitude ofstress 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-tural details. The effects of a structural discontinuity are (i)concentration of the membrane stress and (ii) formation of sec-ondary bending stress.Structural stress: A stress in a component, resolved taking into
account the effects of a structural discontinuity, and consistingof membrane and shell bending stress components. Alsoreferred to as geometric stress or hot spot stress.Structural stress concentration factor: The ratio of hot spot(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-lar stress fluctuation with stress ranges (and amplitudes) ofvariable magnitude.
1.5 Symbols
C material parameterD accumulated fatigue damage, diameter of chordDFF Design Fatigue FactorDj cylinder diameter at junctionE Young’s modulusF fatigue lifeI moment of inertia of tubulars Kmax Kmin
maximum and minimum stress intensity factors respectively
Kw stress concentration factor due to weld geometryΔK Kmax - KminL length of chord, length of thickness transitionN number of cycles to failureNi number of cycles to failure at constant stress range
ΔσiN axial force in tubularR outer radius of considered chord, reduction factor
on fatigue lifeSCF stress concentration factorSCFAS stress concentration factor at the saddle for axial
load SCFAC stress concentration factor at the crown for axial
loadSCFMIP stress concentration factor for in plane moment SCFMOP stress concentration factor for out of plane
momentRa surface roughnessRT reduction factor on fatigue resistanceT thickness of chordTe equivalent thickness of chordTd design life in secondsQ probability for exceedance of the stress range ΔσA crack depthai half crack depth for internal cracks
intercept of the design S-N curve with the log N axis
e-α exp(-α)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 parameterni number of stress cycles in stress block ino is the number of cycles over the time period for
which the stress range level Δσo is definedtref reference thickness
a
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 9
2. Fatigue Analysis Based on S-N Data2.1 IntroductionThe 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.Additional stresses resulting from fabrication tolerances forbutt 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. Guidanceon finite element modelling and hot spot stress derivation ispresented 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 design lives, different Design Fatigue Fac-tors and different plate thickness.The following fatigue cracking failure modes are considered inthis document (see also Figure 2-1):
— Fatigue crack growth from the weld toe into the basematerial.In welded structures fatigue cracking from weld toes intothe base material is a frequent failure mode. The fatiguecrack 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 with
the purpose of achieving a reliable design with respect tothis failure mode.
— Fatigue crack growth from the weld root through the filletweld.Fatigue cracking from root of fillet welds with a crackgrowth through the weld is a failure mode that can lead tosignificant consequences. Use of fillet welds should besought avoided in connections where the failure conse-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 canhardly be avoided and it is also efficient for fabrication.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-ure for this failure mode is of a similar magnitude asfatigue 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-ment of the weld toe is required the connection willbecome 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 inthe components or from small surface defects/irregulari-ties. The specified design procedure in this document isconsidered to provide reliable connections also withrespect to this failure mode.
a) Fatigue crack growth from the weld toe into the base material
b) Fatigue crack growth from the weld root through the filletweld
T plate thickness, thickness of brace member tc cone thicknesstp plate thicknessQ Weibull scale parameterΓ gamma functionη usage factorα the slope angle of the cone; α = L/Dβ d/Dδ eccentricityδ0 eccentricity inherent in the S-N curveγ R/Tνo average zero-up-crossing frequencyν Poisson’s ratioσlocal local stress σnominal nominal stress σhot spot hot spot stress or geometric stressσx maximum nominal stresses due to axial forceσmy σmz
maximum nominal stresses due to bending about the y-axis and the z-axis
Δσ stress rangeΔσ0 stress range exceeded once out of n0 cyclesτ t/T, shear stress
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 10 see note on front cover
c) Fatigue crack growth from the weld root into the section under the weld
d) Fatigue crack growth from a surface irregularity or notchinto the base materialFigure 2-1Explanation of different fatigue failure modes
2.2 Fatigue damage accumulationThe fatigue life may be calculated based on the S-N fatigueapproach under the assumption of linear cumulative damage(Palmgren-Miner rule).When the long-term stress range distribution is expressed by astress histogram, consisting of a convenient number of con-stant stress range blocks Δσi each with a number of stress rep-etitions ni the fatigue criterion reads:
where
Applying a histogram to express the stress distribution, 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 integration
method as the position of the integration points may have a sig-nificant influence on the calculated fatigue life dependent onintegration method.See also section 5 for calculation of fatigue damage usingdesign charts.Reference is made to commentary section for derivation offatigue damage calculated from different processes.
2.3 Fatigue analysis methodology and calculation of Stresses
2.3.1 GeneralFatigue analysis may be based on different methodologiesdepending on what is found most efficient for the consideredstructural detail. Different concepts of S-N curves are devel-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 2.3.3
for plated structures and in section 2.3.4 for tubular joints.— Notch stress S-N curve that is not used in the main part of
this 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 thatcan be derived by classical theory such as beam theory. In asimple plate specimen with an attachment as shown in Figure4-1 the nominal stress is simply the membrane stress that isused for plotting of the S-N data from the fatigue testing. Anexample of fatigue design using this procedure is shown in thecommentary section (Example with fatigue analysis of adrum).Hot spot stress is understood to be the geometric stress createdby the considered detail. (The notch stress due to the local weldgeometry is excluded from the stress calculation as it isassumed 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-tion that it is only necessary to consider the ranges of cyclicstresses in determining the fatigue endurance (i. e. meanstresses are neglected for fatigue assessment of welded con-nections).
2.3.2 Plated structures using nominal stress S-N curvesThe joint classification and corresponding S-N curves takesinto account the local stress concentrations created by thejoints themselves and by the weld profile. The design stresscan 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 forfatigue design would be the tensile stress, σnominal. For theweld 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 σnominal, 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 axis
m = 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 Δσiη = usage factor
= 1 / Design Fatigue Factor from OS-C101 Section 6 Fatigue Limit States.
( ) ησ ≤∑ Δ⋅=∑===
mk
iii
k
i i
i naN
nD
11
1
a
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 11
stress is derived as
σlocal shall be used together with the relevant S-N curves Dthrough 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 theweld toe, it becomes conservative to use the principle stressrange together with a classification of the connection for stressrange normal to the weld toe as shown in Figure 2-3. As theangle between the principal stress direction and the normal tothe weld, ϕ, is increased further, fatigue cracking may nolonger 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-sented in commentary D.4 Comm. 2.3.2 Plated structuresusing nominal stress S-N curves.
2.3.3 Plated structures using hot spot stress S-N curvesFor detailed finite element analysis of welded plate connec-tions other than tubular joints it may also be convenient to usethe alternative hot spot stress for fatigue life assessment, seesection 4.3 for further guidance. A relation between nominal
stress and hot spot stress may be defined as
where SCF is structural stress concentration factor normallydenoted 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.
2.3.4 Tubular joints For a tubular joint, i. e. brace to chord connection, the stress tobe used for design purpose is the range of idealised hot spotstress 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 as
where
Figure 2-2Explanation of local stresses
(2.3.1)nominallocal σSCFσ = (2.3.2)
(2.3.3)
SCF = stress concentration factor as given in section 3.3.
nominalspothot σSCFσ =
nominalspothot σSCFσ =
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 12 see note on front cover
Figure 2-3Fatigue cracking along weld toe
Figure 2-4Fatigue cracking when principal stress direction is more parallelwith weld toe
2.3.5 Fillet weldsThe relevant stress range for potential cracks in the weld throatof load-carrying fillet-welded joints and partial penetrationwelded joints may be calculated as:
where the stress components are explained in Figure 2-5.The total stress fluctuation (i.e. maximum compression andmaximum tension) should be considered to be transmittedthrough the welds for fatigue assessments.
Figure 2-5Explanation of stresses on the throat section of a fillet weld
2.3.6 Fillet welded bearing supportsWhere support plating below bearings are designed with filletwelded connection, it should be verified that fatigue crackingof the weld will not occur. Even though the joint may berequired to carry wholly compressive stresses and the platesurfaces may be machined to fit, the total stress fluctuationshould be considered to be transmitted through the welds forfatigue assessment.If it is assumed that compressive loading is transferred throughcontact, it should be verified that the contact will not be lostduring the welding. The actual installation condition includingmaximum construction tolerances should be accounted for.
2.4 S-N curves
2.4.1 GeneralThe fatigue design is based on use of S-N curves, which areobtained from fatigue tests. The design S-N curves which fol-lows are based on the mean-minus-two-standard-deviationcurves for relevant experimental data. The S-N curves are thusassociated with a 97.6% probability of survival.
2.4.2 Failure criterion inherent the S-N curvesMost of the S-N data are derived by fatigue testing of smallspecimens in test laboratories. For simple test specimens thetesting 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. For details with the same calculated damage, the initiationperiod of a fatigue crack takes longer time for a notch in basematerial than at a weld toe or weld root. This also means thatwith a higher fatigue resistance of the base material as com-pared with welded details, the crack growth will be faster inbase 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 areal structure where some redistribution of stress is morelikely, this means that this failure criterion corresponds to acrack size that is somewhat less than the plate thickness.The tests with tubular joints are normally of a larger size.These joints also show larger possibility for redistribution ofstresses 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.As these tests are not very different from that of the actualbehaviour in a structure, this failure criterion for S-N curvesfor tubular corresponds approximately to the thickness at thehot spot (chord or brace as relevant).
2.4.3 S-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.
Each construction detail at which fatigue cracks may poten-tially develop should, where possible, be placed in its relevantjoint class in accordance with criteria given in Appendix A. Itshould be noted that, in any welded joint, there are severallocations 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 stressdirection
Weldtoe
Section
Fatigue crack
ϕPrincipal stress
direction
Weldtoe
Section
Fatigue crack
//τΔ //τΔ //τΔ ⊥Δσ
//σΔ //σΔ //σΔ
Principal stressdirection Weld
toe
Section
Fatigue crack
ϕPrincipal stress
direction Weldtoe
Section
Fatigue crack
//τΔ //τΔ //τΔ//σΔ //σΔ //σΔ
⊥Δσ
2//
22w Δτ0.2ΔτΔσΔσ ++= ⊥⊥
σ ττ
Throatsection
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 13
itself. Each location should be classified separately.The basic design S-N curve is given as
where
The 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-erence is made to Appendix D, Commentary. The thicknesseffect is accounted for by a modification on stress such that thedesign S-N curve for thickness larger than the reference thick-ness reads:
where
In general the thickness exponent is included in the designequation to account for a situation that the actual size of thestructural 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 testedsuch as e. g. design of mooring systems with a significantlarger number of chain links in the actual mooring line thanwhat the test data are based on. Then the size effect should becarefully considered using probabilistic theory to achieve areliable design, see Appendix D, Commentary.
2.4.4 S-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 cycleregion the maximum stress range is that of the B1 curve asshown in Figure 2-6. However, for offshore structures sub-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 Δσ
Δσ = 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 axis
tref = 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
σlogmalogNlog Δ−=
loga
s2alogalog −=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
k
refttΔσlogmalogNlog
loga
t = thickness through which a crack will most likely grow. t = tref is used for thickness less than tref
k = 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 = 5.0
Fatigue limit at 10 7 cycles *)
Thickness exponent k Structural stress concentration embedded in
the detail (S-N class), ref. also equation (2.3.2)
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 14 see note on front cover
Figure 2-6S-N curves in air
2.4.5 S-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.
10
100
1000
1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08
Number of cycles
Stre
ss ra
nge
(MPa
)
B1B2CC1C2DEFF1F3GW1W2W3
Table 2-2 S-N curves in seawater with cathodic protectionS-N curve N ≤ 10 6 cycles N > 10 6 cycles
m2= 5.0
Fatigue limit at 10 7 cycles*)
Thickness exponent k Stress concentration in the S-N detail as derived by the hot
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 15
Figure 2-7S-N curves in seawater with cathodic protection
2.4.6 S-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 protection
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 16 see note on front cover
2.4.7 S-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.For cast nodes with a stress gradient over the thickness areduced effective thickness may be used for assessment ofthickness effect. The effective thickness to be used in equation(2.4.3) can be calculated as:
Where
S0 = 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 = 0.15
2.4.8 S-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.
2.4.9 S-N curves for free corrosionS-N curves for free corrosion, i.e. without corrosion protec-tion, are given in Table 2-3. See also Commentary section for consideration of corrosionprotection of connections in the splash zone and inside tanks inFPSOs.
2.4.10 S-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 anda surface roughness equal Ra = 3.2 or better the followingdesign S-N curve can be used for fatigue assessment of thebase material
In air a fatigue limit at 2·106 cycles at a stress range equal 235MPa can be used. For variable amplitude loading with onestress 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).For seawater with cathodic protection a constant slope S-Ncurve should be used. (The same as for air to the left of 2·106cycles, 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)
2.4.11 S-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.
2.4.12 S-N curves for small diameter umbilicalsFor fatigue design of small diameter pipe umbilicals (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 assessment
where
(2.4.4)
Table 2-3 S-N curves in seawater for free corrosionS-N curve
t = actual thickness of the umbilicaltref = 1.0 mm
LogSNLog 70.4446.17 −=
10
100
1000
10000 100000 1000000 10000000 100000000
Number of cycles
Stre
ss ra
nge
(MPa
) Air
Seawater with cathodic protection
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
>
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
≤
25.0
7
25.0
7
*0.5143.17
10
*5.3100.14
:10
ref
ref
ttSLogNLog
Nforand
ttSLogNLog
NFor
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 17
A normal good fabrication of the umbilicals is assumed asbasis for this design S-N curve. The welds on the inside andoutside 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 weldsthe acceptance criteria shall be according to ASME B31.3,chapter IX high pressure service girth groove. Dye penetrantshall be used as a surface test in addition to visual inspectionwhen relevant indications, as defined by ASME VIII div. 1,app.4. are found by X-ray.The S-N curve is based on fatigue testing of specimens sub-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 umbilicals
2.4.13 Qualification of new S-N curves based on fatigue test dataFor qualification of new S-N data to be used in a project it isimportant that the test specimens are representative for theactual fabrication and construction. This includes possibilityfor relevant production defects as well as fabrication toler-ances. The sensitivity to defects may also be assessed by frac-ture mechanics.
It is recommended to perform fatigue testing of at least 15specimens in order to establish a new S-N curve. At least threedifferent stress ranges should be selected in the relevant S-Nregion such that a representative slope of the S-N curve can bedetermined.Reference is made to IIW document no IIW-XIII-WG1-114-03 for statistical analysis of the fatigue test data. Normallyfatigue test data are derived for number of cycles less than 107.It should be noted that for offshore structures significantfatigue damage occurs for N ≥ 107 cycles. Thus how to extrap-olate the fatigue test data into this high cycle region is impor-tant in order to achieve a reliable assessment procedure. Inaddition to statistical analysis one should use engineeringjudgement based on experience for derivation of the S-N datain this region. It is well known that good details where fatigueinitiation contribute significantly to the fatigue life show amore 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.Also the probability of detecting defects during a productionshould be kept in mind in this respect. The defects that nor-mally can be detected by an acceptable probability are nor-mally larger than that inherent in the test specimens that areproduced to establish test data for a new S-N curve.
2.5 Mean 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. The calculated stress range obtained may be multi-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-tion
where
Figure 2-11Stress range reduction factor to be used with the S-N curve for base material
σt = maximum tension stressσc = maximum compression stress
ct
ct
σσσσ
++= 6.0fm
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 18 see note on front cover
2.6 Effect of fabrication tolerancesNormally larger fabrication tolerances are allowed in realstructures 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 resultingfrom normal fabrication tolerances should be included in thefatigue design. Special attention should be given to the fabri-cation tolerances for simple butt welds in plates and tubulars asthese give the most significant increase in additional stress.Stress concentration factors for butt welds are given in section3.1.2 and at tubular circumferential welds in section 3.3.7.
2.7 Design chart for fillet and partial penetration weldsDesign should be performed such that fatigue cracking fromthe 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 defectsby NDE in fillet/partial penetration welds. Such connectionsshould therefore not be used in structural connections of signif-icant importance for the integrity.
Figure 2-12Welded connection with partial penetration weld
Figure 2-13Weld geometry with probability of root failure equal toe failure
2.8 Bolts
2.8.1 GeneralA 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.
2.8.2 Bolts subjected to tension loadingConnections where the pretensioned bolts are subjected todynamic axial forces should be designed with respect tofatigue taking into account the stress range in the bolts result-ing from tension and compression range. The stress range inthe 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.
2.8.3 Bolts subjected to shear loading For bolts subject to shear loading the following methodologymay be used for fatigue assessment. The threads of the boltsshould 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 from
where Δσ = shear stress based on shaft area of bolt.
2.9 Pipelines and risers
2.9.1 GeneralWelds in pipelines are normally made with a symmetric weldgroove with welding from the outside only. The tolerances arerather strict compared with other structural elements witheccentricity less than 0.1 t or maximum 3 mm (t = wall thick-ness). The fabrication of pipelines also implies a systematicand standardised NDE of the root area where defects are mostcritical. Provided that the same acceptance criteria are used forpipelines with larger wall thickness as for that used as refer-ence thickness (25 mm), a thickness exponent k = 0 may beused 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.For weld grooves that are not symmetrical in shape a stressconcentration for the weld root due to maximum allowableeccentricity 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.This stress concentration factor can also be used for fatigueassessments 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 used for fatigue assessment ofthe inside. The membrane stress in the considered sectionshould be used for calculation of local bending stress over thethickness together with stress concentration factor from equa-tion (2.9.1).
0
0.2
0.4
0.6
0.8
1
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2ai/tp
h/t p
tp = 50 mm
tp = 25 mm
tp = 12 mm
tp = 6mm
Weld toe failure
Weld root failure
logN = 16.301-5.0log Δσ (2.8.1)
(2.9.1)Dtm /etδ3
1SCF −+=
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 19
2.9.2 Combined eccentricity for fatigue analysis of seam-less pipesFor welded pipes it is ovality that normally will govern theresulting eccentricity. Thus the effect of tolerances can simplybe added linearly.For seamless pipes it is realised that the thickness tolerancecontributes 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 (δm = δTot) canbe obtained as:
where
Reference is made to DNV-OS-F101 Section 6 Clause E1200for measurements of tolerances.
2.9.3 SCFs for pipes with internal pressureReference is made to commentary for stress concentration fac-tors for other details in pipelines and cylindrical tanks withstress cycling mainly due to internal pressure.
(2.9.2)
δThickness = (tmax - tmin)/2δOvality = Dmax - Dmin if the pipes are supported such that
flush outside at one point is achieved (no pipe centralising)
δOvality = (Dmax - Dmin)/2 if the pipes are centralised dur-ing construction
δOvality = (Dmax - Dmin)/4 if the pipes are centralised dur-ing construction and rotated until a good fit around the circumference is achieved
22OvalityThicknessTot δδδ +=
Table 2-4 Classification of welds in pipelinesDescription
Tolerance requirement S-N curve Thickness exponent k SCFWelding Geometry and hot spot
Single side
δ ≤ min (0.15t, 3 mm) F1 0.00 1.0
δ > min (0.15t, 3 mm) F3 0.00 1.0
Single sideon backing
δ ≤ min (0.1t, 2 mm) F 0.00 1.0
δ > min (0.1t, 2 mm) F1 0.00 1.0
Single side D 0.15 Eq. (2.9.1)
Double side D 0.15 Eq. (2.9.1)
Hot spot
Hot spot
Hot spot
Hot spot
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 20 see note on front cover
2.10 Guidance 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 2-2 for seawater with cathodic protection. For Design FatigueFactors larger than 1 the allowable fatigue limit should alsohere 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.The use of the fatigue limit is illustrated in Figure 2-14. Adetailed fatigue assessment can be omitted if the largest stresscycle is below the fatigue limit. However, in the example inFigure 2-15 there is one stress cycle Δσ1 above the fatiguelimit. This means that a further fatigue assessment is required.This also means that the fatigue damage from the stress cyclesΔσ2 has to be included in the fatigue assessment.
Figure 2-14Stress cycling where further fatigue assessment can be omitted
Figure 2-15Stress cycling where a detailed fatigue assessment is required
3. Stress Concentration Factors3.1 Stress concentration factors for plated structures
3.1.1 GeneralA stress concentration factor may be defined as the ratio of hotspot stress range over nominal stress range.
3.1.2 Stress 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:
whereδm is eccentricity (misalignment) and t is plate thickness, seeFigure 3-9. δ0 = 0.1 t is misalignment inherent in the S-N data for buttwelds. 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:
where
See also Figure 3-8.
3.1.3 Stress concentration factors for cruciform jointsThe stress concentration factor for cruciform joint at platethickness ti may be derived from following formula:
where
The other symbols are defined in Figure 3-1.
Figure 3-1Cruciform joint
(3.1.1)
N
S
Δσ1
Fatigue limit
Stress cycling
N
S
Δσ1
Fatigue limit
Stress cycling
N
S
Δσ1
Δσ2
Fatigue limit
Stress cycling
N
S
Δσ1
Δσ2
Fatigue limit
Stress cycling
t)δ(3
1SCF 0m δ−+=
(3.1.2)
δm = maximum misalignment δt = ½ (T− t) eccentricity due to change in thickness.
Note: This applies also at transitions sloped as 1:4.δ0 = 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)
δ = (δm + δt) is the total eccentricityδ0 = 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)
( )
⎥⎦
⎤⎢⎣
⎡+
−++=
5.1
5.10m
1
61SCF
tTt
t δδδ
⎟⎟⎠
⎞⎜⎜⎝
⎛+++
−+=
4
34
3
33
2
32
1
31
i
02 )(61SCF
lt
lt
lt
ltl
ti δδ
l3
l4
l2 l1
t2 t1
t3
t4
δ
l3
l4
l2 l1
t2 t1
t3
t4
δ
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 21
3.1.4 Stress concentration factors for rounded rectangular holes Stress concentration factors for rounded rectangular holes aregiven in Figure 3-2.Where there is one stress raiser close to another detail beingevaluated with respect to fatigue, the interaction of stress
between these should be considered. An example of this is awelded 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 holes
Line for calculation of stressLine for calculationof stress
r
x
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 22 see note on front cover
3.1.5 Stress concentration factors for holes with edge rein-forcementStress concentration factors for holes with reinforcement aregiven in Appendix C.Fatigue cracking around a circumferential weld may occur atseveral locations at reinforced rings in plates depending ongeometry 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. Thenσhot spot = σp
2) 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 σ1 is thecrack driving stress.Then σhot spot = σ1Also the region at crown position to be checked.Then σhot spot = σn
3) Fatigue cracking from the weld root (Stiff reinforcementwith small fillet weld size). See Figure 3-4c.
For fillet welds all these positions should be assessed withrespect to fatigue. For full penetration welds the first twopoints should be assessed.
Figure 3-4Potential fatigue crack locations at welded penetrations
All these potential regions for fatigue cracking should beassessed 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 (σhot 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 (σhot spot in Figure 3-4b). Potential fatigue cracking from the weld rootAt some locations of the welds there are stresses in the platetransverse to the fillet weld, σn, and shear stress in the plateparallel with the weld τ//p see Figure 3-4c. Then the fillet weldis designed for a combined stress obtained as
where
The total stress range (i.e. maximum compression and maxi-mum tension) should be considered to be transmitted throughthe welds for fatigue assessments. Reference is also made toAppendix 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.
3.1.6 Stress concentration factors for scallopsReference is made to Figure 3-5 for stress concentration fac-tors for scallops.The stress concentration factors are applicable to stiffenerssubject 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)
σp
Fillet weld
σ1
InsertTubular
n
45°
ασ
σn
45°
τ p
(3.1.4)
t = plate thicknessa = throat thickness for a double sided fillet weld
2//
2 2.02 pnw at τσσ Δ+Δ=Δ
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 23
Figure 3-5Stress concentration factors for scallops
3.2 Stress concentration factors for ship detailsStress concentration factors for ship details may be found in“Fatigue 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 thenotch stress concentration factor due to the weld geometry,Kw, from the analysis, as this factor is accounted for in the D-curve).
3.3 Tubular joints and members
3.3.1 Stress concentration factors for simple tubular jointsStress concentration factors for simple tubular joints are givenin Appendix B.
3.3.2 Superposition of stresses in tubular jointsThe stresses are calculated at the crown and the saddle points,see Figure 3-6. Then the hot spot stress at these points isderived by summation of the single stress components fromaxial, in-plane and out of plane action. The hot spot stress maybe higher for the intermediate points between the saddle andthe crown. The hot spot stress at these points is derived by alinear interpolation of the stress due to the axial action at thecrown and saddle and a sinusoidal variation of the bending
stress 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 σx, σmy and σmz are the maximum nominal stresses dueto axial load and bending in-plane and out-of-plane respec-tively. SCFAS is the stress concentration factor at the saddle foraxial load and the SCFAC is the stress concentration factor atthe crown. SCFMIP is the stress concentration factor for inplane 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 B
SCF = 1.27 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 B
For scallops without transverse welds, the SCF at point B will be governing for the design.
A
B
150
35
B
A
A
B
35
120 120
1035
B
A
(3.3.1)
mzMOPmyMIPxASAC8
mzMOPxAS7
mzMOPmyMIPxASAC6
myMIPxAC5
mzMOPmyMIPxASAC4
mzMOPxAS3
mzMOPmyMIPxASAC2
myMIPxAC1
σSCF221σSCF2
21σ)SCF(SCF
21σ
σSCFσSCFσ
σSCF221σSCF2
21σ)SCF(SCF
21σ
σSCFσSCFσ
σSCF221σSCF2
21σ)SCF(SCF
21σ
σSCFσSCFσ
σSCF221σSCF2
21σ)SCF(SCF
21σ
σSCFσSCFσ
+++=
+=
+−+=
−=
−−+=
−=
−++=
+=
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 24 see note on front cover
Figure 3-6Geometrical definitions for tubular joints
Figure 3-7Superposition of stresses
Influence functions may be used as an alternative to the proce-dure given here to calculate hot spot stress. See e.g. “Com-bined Hot-Spot Stress Procedures for Tubular Joints”, ref. /24/and “Development of SCF Formulae and Generalised Influ-ence Functions for use in Fatigue Analysis” ref. /2/.
3.3.3 Tubular joints welded from one sideThe root area of single-sided welded tubular joints may bemore critical with respect to fatigue cracks than the outsideregion connecting the brace to the chord. In such cases, it isrecommended that stubs are provided for tubular joints wherehigh fatigue strength is required, such that welding from thebackside can be performed.Failure from the root has been observed at the saddle positionof tubular joints where the brace diameter is equal the chord
diameter, both in laboratory tests and in service. It is likely thatfatigue cracking from the root might occur for rather low stressconcentrations. Thus, special attention should be given tojoints other than simple joints, such as ring-stiffened joints andjoints where weld profiling or grinding on the surface isrequired 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 considerationmay be made for X-joints with diameter ratio β ≤ 0.90. Forother joints and for simple tubular X-joints with β > 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, Commentary
3.3.4 Stiffened tubular jointsEquations for joints for ring stiffened joints are given in“Stress Concentration Factors for Ring-Stiffened TubularJoints”, ref. /3/. The following points should be noted regard-ing the equations:
— The derived SCF ratios for the brace/chord intersectionand the SCF's for the ring edge are mean values, althoughthe degree of scatter and proposed design factors aregiven.
— Short chord effects shall be taken into account where relevant.— For joints with diameter ratio β ≥ 0.8, the effect of stiffen-
ing is uncertain. It may even increase the SCF.— The maximum of the saddle and crown stress concentra-
tion factor values should be applied around the wholebrace/chord intersection.
— The following points can be made about the use of ringstiffeners in general:
Axial load
z
x y1 23
45678
In-plane Out-of-planebending moment bending moment
N MIP MOP
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 25
— Thin shell FE analysis should be avoided for calculating theSCF if the maximum stress is expected to be near the brace-ring crossing point in the fatigue analysis. An alternative isto use a three-dimensional solid element analysis model.
— 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, and will probably only be detected afterthrough thickness cracking, at which the majority of thefatigue life will have been expired. These areas shouldtherefore be considered as non-inspectable unless moresophisticated inspection methods are used.
3.3.5 Grouted tubular joints
3.3.5.1 GeneralGrouted joints have either the chord completely filled withgrout (single skin grouted joints) or the annulus between thechord and an inner member filled with grout (double skingrouted joints). The SCF of a grouted joint depends on loadhistory and loading direction. The SCF is less if the bondbetween the chord and the grout is unbroken. For model testingof grouted joints the bond should be broken prior to SCF meas-urements. Due to the grout the tensile and compressive SCFmay 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).
3.3.5.2 Chord filled with groutThe grouted joints shall be treated as simple joints, except thatthe chord thickness in the γ term for saddle SCF calculation forbrace and chord shall be substituted with an equivalent chordwall thickness given by
where D and T are chord diameter and thickness respectively.The dimensions are to be given in mm.Joints with high β or low γ ratios have little effect of grouting.The benefits of grouting should be neglected for joints withβ > 0.9 or γ ≤ 12.0 unless documented otherwise.
3.3.5.3 Annulus between tubular members filled with groutFor joints where the annulus between tubular members arefilled with grout such as joints in legs with insert piles, 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 by
where T is chord thickness and Tp is thickness of insert pile.
3.3.6 Cast nodesIt is recommended that finite element analysis should be usedto determine the magnitude and location of the maximumstress range in castings sensitive to fatigue. The finite elementmodel should use volume elements at the critical areas andproperly model the shape of the joint. Consideration should begiven to the inside of the castings. The brace to casting circum-ferential butt weld (which is designed to an appropriate S-Ncurve for such connections) may be the most critical locationfor fatigue.
3.3.7 Stress 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 suchthat any thickness transitions are placed on the outside (seeFigure 3-8). For this geometry, the SCF for the transitionapplies 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 beclassified as concentricity (difference in tubular diameters),differences in thickness of joined tubulars, out of roundnessand centre eccentricity, see Figure 3-10 and Figure 3-11. Theresulting eccentricity may be conservatively evaluated by adirect summation of the contribution from the differentsources. The eccentricity due to out of roundness normallygives the largest contribution to the resulting eccentricity δ.It is conservative to use the formula for plate eccentricities forcalculation of SCF at tubular butt welds. The effect of thediameter in relation to thickness may be included by use of thefollowing formula, provided that T/t ≤ 2:
where
This formula also takes into account the length over which theeccentricity is distributed: L, ref. Figure 3-9 and Figure 3-8.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 andthe weld is made from both sides, equation (3.3.4) may beapplied 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(5DTe +=
pTT 45.0Te +=
(3.3.4)
δ0 = 0.1 t is misalignment inherent in the S-N data
(3.3.5)
α-0t e
tT1
1t
)6(1SCF βδδδ
⎟⎠⎞
⎜⎝⎛+
−++= m
β⎟⎠⎞
⎜⎝⎛+
⋅=
tT1
1tD
1.82Lα
β 1.5 1.0
Log Dt----⎝ ⎠⎛ ⎞
--------------------– 3.0
Log Dt----⎝ ⎠⎛ ⎞ 2
----------------------------+=
α-t e
tT1
1t
)6(1SCF βδδ
⎟⎠⎞
⎜⎝⎛+
−−= m
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 26 see note on front cover
may 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 weld
Figure 3-9Section through weld
In 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 thatwork is checked by non-destructive examination. It may bedifficult 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-ated by fracture mechanics such as described in BS 7910“Guidance on Methods for Assessing the Acceptability of
Flaws in Fusion Welded Structures”, ref /7/. Therefore, if afabrication 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 stressfor fatigue assessment of the outside weld toe. The nominalstress on the inside should be used for assessment of fatiguecracks initiating from the inside.
(3.3.6)α-t e
tT1
1t
61SCF βδ
⎟⎠⎞
⎜⎝⎛+
+=
t
tT
L
σδ
nominal
41
axisNeutral
Inside
Outside
t
D
L
δm
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 27
Figure 3-10Geometric sources of local stress concentrations in tubular buttwelds
Figure 3-11Geometric sources of local stress concentrations in tubular buttwelds
3.3.8 Stress concentration factors for stiffened shellsThe stress concentration at a ring stiffener can be calculated as
where
Due to less stress on the inside it is more efficient to place ringstiffeners on the inside of shell, as compared with the outside.In addition, if the shell comprises longitudinal stiffeners thatare 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 shell
3.3.9 Stress concentration factors for conical transitionsThe stress concentration at each side of unstiffened tubular-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):
where
A A
Section A-Aa) Concentricity
t
t
δm
A A
b) Thickness Section A-A
T
t
δ = ½ (T-t)t
A
Section A-Ac) Out of roundness
A
t
t
δm
δm
δm
A A
Section A-Ad) Center eccentricity
δ
t
t
mmδ
(3.3.7)
Ar = area of ring stiffener without effective shellr = radius of shell measured from centre to mean shell
thicknesst = thickness of shell plating
for 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 thicknessα = the slope angle of the cone (see Figure 3-13)
rArt1.56t1α
shell theof inside for theα
0.541SCF
shell theof outside for theα
0.541SCF
+=
−=
+=
( )ν1tr b
−
tanαt
)t(tDt0.61SCF 2
cj ++=
tanαt
)t(tDt0.61SCF 2
c
cj ++=
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 28 see note on front cover
The stress concentration at a junction with ring stiffener can becalculated as
where
A ring stiffener may be placed centric at the cone junction.Then the butt weld should be grinded and NDE examinedbefore the ring stiffener is welded.If a ring stiffener is placed a distance δe away from the inter-section lines, an additional stress concentration should beincluded to account for this eccentricity:
where
where
where
If a ring stiffener with a flange is used the effect of the flangeshould be included when calculating the moment of inertiaabout 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).A full penetration weld connecting the ring stiffener to thetubular 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 thicknessα = 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)
r
j
r
j
r
j
r
j
r
j
A
tD1.10t1β
andjunction,diameterlargerinsidetheatβ1tanα
At0.91D
0.541SCF
junctiondiameterlargeroutsidetheatβ1tanα
At0.91D
0.541SCF
junctiondiametersmallerinsidetheatβ1tanα
At0.91D
0.541SCF
junctiondiametersmalleroutsidetheatβ1tanα
At0.91D
0.541SCF
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−+=
⎟⎟⎠
⎞⎜⎜⎝
⎛+−=
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
53 )(
681
1tan31
cj
e
ttD
ItSCF
++
+=αδ
))2
(12
(
)()2
(5.012
22
23
yhhht
ttythbtbI
r
sc
−+
++−++=
(3.3.13)
h = height of ring stiffenertr = thickness of ringstiffenerb = effective flange width calculated as
(3.3.14)
bttth
ttbt
hthy
cr
cr
)(2
)()2
(2
++
+++=
ecj ttDb δ++= )(78.0
Ds
DL
ts
tL
α
.
tC
Ds
D L
ts
t L
α
δtc e
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 29
Figure 3-14Notations for calculation of moment of inertia
3.3.10 Stress 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 dueto a resulting global bending moment, see Figure 3-16. Theeccentricity due to co-linearity is a function of axial tension inthe tubular and is significantly reduced as the axial force isincreased by tension. Assuming that the moment M resultsfrom an eccentricity δN where pretension is accounted for inthe analysis, the following derivation of a stress concentrationfactor is performed:
where the stress concentration factor is:
where δN is eccentricity as function of the axial force N and Dis outer diameter. The eccentricity for two elements is indi-cated in Figure 3-16. With zero tension the eccentricity is δ.With an axial tension force N the eccentricity becomes:
where
The formula for reduction in eccentricity due to increased axialforce can be deduced from differential equation for thedeflected 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 issystematic or random, ref. Figure 3-15. In the first case, theerrors must be added linearly, in the second case it may be
added quadratically.
Figure 3-15Colinearity or angle deviation in pipe segment fabrication, I = Systematic deviation, II = random deviation
Figure 3-16Eccentricity due to co-linearity
3.3.11 Stress concentration factors for joints with square sectionsStress concentration factors for T- and X- square to squarejoints may be found in “Proposed Revisions for Fatigue Designof Planar Welded Connections made of Hollow Structural Sec-tions”, ref. /27/.Stress concentration factors for Y- and K square to squarejoints may be found from “IIW Fatigue Rules for TubularJoints”. These stress concentration factors may be usedtogether 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:
These 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 = Young’s modulus
h
t
b
α
tc
tr
x x
y h
t
b
α
tc
tr
x x
y
( ) SCFttDπ
Nσ−
=
tD41SCF N
−+= δ
klkltanh
N δδ =
EIN
N
N
δN
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 30 see note on front cover
3.3.12 Stress concentration factors for joints with gusset platesInsert gusset plates are sometimes used in joints in topsidestructures 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-ficult to document the fatigue capacity for fatigue crackingstarting from the weld root. In dynamic loaded structures it isrecommended to shape the gusset plate in such a way that asmooth 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 perform finite element analysis if the geometry issignificantly different from that shown in Figure 3-17b. Thestress concentration factors in Table 3-1 are derived from finiteelement analysis using shell elements. Then the hot spot stresscan be combined with the D-Curve. The stress concentrationfactor for tubular member is simply derived by scaling theresults from that of RHS by π/4 for the same thickness. Usingshell elements for such analysis provides conservative stressconcentration factors as compared with use of three-dimen-sional elements with modelling also of the fillet weld. (It ishere 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 geometry
4. Calculation of hot spot stress by finite ele-ment analysis4.1 GeneralFrom detailed finite element analysis of structures it may bedifficult to evaluate what is “nominal stress” to be usedtogether with the S-N curves, as some of the local stress due toa detail is accounted for in the S-N curve.In many cases it may therefore be more convenient to use analternative approach for calculation of fatigue damage whenlocal stresses are obtained from finite element analysis.It is realised that it is difficult to calculate the notch stress at aweld due to a significant scatter in local weld geometry anddifferent types of imperfections. This scatter is normally moreefficiently accounted for by use of an appropriate S-N curve.In this respect it should also be mentioned that the weld toeregion has to be modelled with a radius in order to obtain reli-able results for the notch stress.If a corner detail with zero radius is modelled the calculatedstress will approach infinity as the element size is decreased tozero. The modelling of a relevant radius requires a very fineelement mesh, increasing the size of the computer model. The notch stress concept may be used in special cases whereother methods are not found appropriate, see Appendix D,Commentary.Hence, for design analysis a simplified numerical procedure isused in order to reduce the demand for large fine mesh modelsfor the calculation of SCF factors:
— The stress concentration or the notch factor due to the welditself is included in the S-N curve to be used, the D-curve.
— The stress concentration due to the geometry effect of theactual detail is calculated by means of a fine mesh modelusing shell elements (or solid elements), resulting in a geo-metric SCF factor.
This procedure is denoted the hot spot method.It is important to have a continuous and not too steep, changein the density of the element mesh in the areas where the hotspot stresses are to be analysed.The geometry of the elements should be evaluated carefully inorder to avoid errors due to deformed elements (for examplecorner angles between 60° and 120° and length/breadth ratioless than 5 are recommended).The size of the model should be so large that the calculatedresults are not significantly affected by assumptions made forboundary conditions and application of loads.It should be noted that the hot spot concept cannot be used forfatigue checks of cracks starting from the weld root of fillet/partial penetration welds. A fillet weld should be checked sep-arately considering the stresses in the weld itself, ref. section2.3.5.
4.2 Tubular jointsThe stress range at the hot spot of tubular joints should be com-bined with the T-curve.Analysis based on thick shell elements may be used. In thiscase, the weld is not included in the model. The hot spot stressmay be determined as for welded connections.More reliable results are obtained by including the weld in themodel. This implies use of three-dimensional elements. Herethe Gaussian points, where stresses are calculated, may beplaced from the weld toe (r = radius of consideredtubular and t = thickness). The stress at this point may be useddirectly in the fatigue assessment.
Table 3-1 Stress concentration factors for joints with gusset plateGeometry SCFRHS 250x16 with favourable geometry of gusset plate 2.9RHS 250x16 with simple shape of gusset plate 3.8Ø250x16 with favourable geometry of gusset plate 2.3Ø250x16 with simple shape of gusset plate 3.0
10TYP.
40TYP.
tr1.0
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 31
4.3 Welded connections other than tubular joints
4.3.1 Stress field at a welded detailDue to the nature of the stress field at a hot spot region thereare questions on how to establish the hot spot stress, see Figure4-1. The notch effect due to the weld is included in the S-Ncurve and the hot spot stress is derived by extrapolation of thestructural stress to the weld toe as indicated in Figure 4-1. It isobserved that the stress used as basis for such an extrapolationshould be outside that affected by the weld notch, but closeenough to pick up the hot spot stress.
4.3.2 FE modellingThe following guidance is made to the computation of hot spotstresses with potential fatigue cracking from the weld toe withlocal models using the finite element method.Hot spot stresses are calculated assuming linear materialbehaviour and using an idealized structural model with no fab-rication-related misalignment. The extent of the local modelhas to be chosen such that effects due to the boundaries on thestructural detail considered are sufficiently small and reasona-ble boundary conditions can be formulated.In plate structures, three types of hot spots at weld toes can beidentified as exemplified in Figure 4-3:
a) at the weld toe on the plate surface at an ending attachment b) at the weld toe around the plate edge of an ending attach-
mentc) along the weld of an attached plate (weld toes on both the
plate and attachment surface).
Models with thin plate or shell elements or alternatively withsolid elements are normally used. It should be noted that on theone hand the arrangement and type of elements have to allowfor steep stress gradients as well as for the formation of platebending, and on the other hand, only the linear stress distribu-tion in the plate thickness direction needs to be evaluated withrespect to the definition of hot spot stress.The following methods of modelling are recommended.The simplest way of modelling is offered by thin plate andshell elements which have to be arranged in the mid-plane ofthe structural components, see also Figure 4-4. 8-noded elements are recommended particularly in case ofsteep stress gradients. Care should be given to possible stressunderestimation especially at weld toes of type b) in Figure 4-3. Use of 4-noded elements with improved in-plane bendingmodes is a good alternative. The welds are usually not modelled except for special caseswhere the results are affected by high local bending, e. g. dueto an offset between plates or due to a small free plate lengthbetween adjacent welds such as at lug (or collar) plates. Here,the weld may be included by transverse plate elements havingappropriate stiffness or by introducing constrained equationsfor coupled node displacements. A thickness equal 2 times the thickness of the plates may beused for modelling of the welds by transverse plates.For 4-node shell elements with additional internal degrees offreedom for improved in plane behaviour and for 8-node shellelements a mesh size from t x t up to 2 t x 2 t may be used.Larger mesh sizes at the hot spot region may provide non-con-servative results. (For efficient read out of element stresses andhot spot stress derivation a mesh txt is in general preferred atthe hot spot region).An alternative particularly for complex cases is offered bysolid elements which need to have a displacement functionallowing steep stress gradients as well as plate bending withlinear stress distribution in the plate thickness direction. Thisis offered, e. g., by isoparametric 20-node elements (with mid-
side nodes at the edges) which mean that only one element inplate thickness direction is required. An easy evaluation of themembrane and bending stress components is then possible if areduced integration order with only two integration points inthe thickness direction is chosen. A finer mesh sub-division isnecessary particularly if 8-noded solid elements are selected.Here, at least four elements are recommended in thicknessdirection. Modelling of the welds is generally recommendedand easily possible as shown in Figure 4-5.For modelling with three dimensional elements the dimensionsof the first two or three elements in front of the weld toe shouldbe chosen as follows. The element length may be selected tocorrespond to the plate thickness. In the transverse direction,the plate thickness may be chosen again for the breadth of theplate elements. However, the breadth should not exceed the“attachment width”, i. e. the thickness of the attached plateplus 2 x the weld leg length (in case of type c: the thickness ofthe web plate behind plus 2 x weld leg length). The length ofthe elements should be limited to 2 t. In cases where three-dimensional elements are used for the FEmodelling it is recommended that also the fillet weld is mod-elled to achieve proper local stiffness and geometry. In order to capture the properties of bulb sections with respectto St Venant torsion it is recommended to use several three-dimensional elements for modelling of a bulb section. If inaddition the weld from stiffeners in the transverse frames ismodelled the requirements with respect to element shape willlikely govern the FE model at the hot spot region.
4.3.3 Derivation of stress at read out points 0.5 t and 1.5 tThe stress components on the plate surface should be evaluatedalong the paths shown in Figure 4-4 and Figure 4-5 and extrap-olated to the hot spot. The average stress components betweenadjacent elements are used for the extrapolation. Recommended stress evaluation points are located at distances0.5 t and 1.5 t away from the hot spot, where t is the plate thick-ness at the weld toe. These locations are also denoted as stressread out points. If the element size at a hot spot region of size txt is used, thestresses may be evaluated as follows:
— In case of plate or shell elements the surface stress may beevaluated at the corresponding mid-side points. Thus thestresses at mid side nodes along line A-B in Figure 4-2may be used directly as stress at read out points 0.5 t and1.5 t.
— In case of solid elements the stress may first be extrapo-lated from the Gaussian points to the surface. Then thesestresses can be interpolated linearly to the surface centre orextrapolated to the edge of the elements if this is the linefor hot spot stress derivation.
For meshes with 4-node shell elements larger than t x t it is rec-ommended to fit a second order polynomial to the elementstresses in the three first elements and derive stresses forextrapolation from the 0.5 t and 1.5 t points. An example of thisis shown schematically in Figure 4-6. This procedure may beused to establish stress values at the 0.5 t and 1.5 t points. For8-node elements a second order polynomial may be fitted tothe stress results at the mid-side nodes of the three first ele-ments and the stress at the read out points 0.5 t and 1.5 t can bederived.
4.3.4 Derivation of hot spot stressTwo alternative methods can be used for hot spot stress deriva-tion: method A and method B. Method AFor modelling with shell elements without any weld includedin the model a linear extrapolation of the stresses to the inter-section line from the read out points at 0.5t and 1.5t from the
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 32 see note on front cover
intersection line can be performed to derive hot spot stress. For modelling with three-dimensional elements with the weldincluded in the model a linear extrapolation of the stresses tothe weld toe from the read out points at 0.5t and 1.5t from theweld toe can be performed to derive hot spot stress.The notations for stress components are shown in Figures 2-3and 2-4.The effective hot spot stress to be used together with the hotspot S-N curve is derived as
where
α = 0.90 if the detail is classified as C2 with stress parallelto the weld at the hot spot, ref. Table A-3.
α = 0.80 if the detail is classified as C1 with stress parallelto the weld at the hot spot, ref. Table A-3.
α = 0.72 if the detail is classified as C with stress parallelto the weld at the hot spot, ref. Table A-3.
The first principal stress is calculated as
and
The equation for effective stress is made to account for the sit-uation with fatigue cracking along a weld toe as shown in Fig-ure 2-3 and fatigue cracking when the principal stress directionis more parallel with the weld toe as shown in Figure 2-4.
Method BFor modelling with shell elements without any weld includedin the model the hot spot stress is taken as the stress at the readout point 0.5t away from the intersection line. For modelling with three-dimensional elements with the weldincluded in the model the hot spot stress is taken as the stressat the read out point 0.5t away from the weld toe.The effective hot spot stress is derived as
where α, Δσ1 and Δσ2 are explained under method A.The equation for effective stress is made to account for the sit-uation with fatigue cracking along a weld toe as shown in Fig-ure 2-3 and fatigue cracking when the principal stress directionis more parallel with the weld toe as shown in Figure 2-4.
4.3.5 Hot spot S-N curveIt is recommended to link the derived hot spot stress to the D-curve.
4.3.6 Derivation of effective hot spot stress from FE analy-sisAt hot spots with significant plate bending one might derive aneffective hot spot stress for fatigue assessment based on thefollowing equation:
where
The reduction factor on the bending stress can be explained byredistribution of loads to other areas during crack growth whilethe crack tip is growing into a region with reduced stress. Theeffect is limited to areas with a localised stress concentration,which occurs for example at a hopper corner. However, in acase where the stress variation along the weld is small, the dif-ference in fatigue life between axial loading and pure bendingis much smaller. Therefore it should be noted that it is not cor-rect to generally reduce the bending part of the stress to 60 per-cent. This has to be restricted to cases with a pronounced stressconcentration (where the stress distribution under fatigue crackdevelopment is more similar to a displacement controlled situ-ation than that of a load controlled development).
4.3.7 Limitations for simple connectionsIt should be noted that the definition of the stress field throughthe plate thickness in section 4.3.1 implies that the describedhot spot stress methodology is not recommended for simplecruciform joints, simple T-joints in plated structures or simplebutt joints that are welded from one side only. Analyzing suchconnections with for example shell elements would result in ahot spot stress equal the nominal stress. This is illustrated bythe shell model shown in Figure 4-7. For stresses in the direc-tion normal to the shell (direction I) there will be no stress flowinto the transverse shell plating as it is represented only by oneplane in the shell model. However, it attracts stresses for in-plane (direction II) shown in Figure 4-7.As the nominal stress S-N curve for direction I is lower thanthat of the D-curve, it would be non-conservative to use the hotspot concept for this connection for direction I while it wouldbe acceptable for direction II at position “a”. Thus, the nominalstress approach is recommended used for direction I at position“c” as also the nominal stress can be easily derived for analysisof these connections.It should also be noted that it is for these joints (butt welds andcruciform joints) that fabrication tolerances are most importantand need to be considered in a fatigue assessment.The described hot spot concept linked to the D-curve is givingacceptable results as soon as there is a bracket behind the trans-verse plate as shown in Figure 4-3 acting with its stiffness inthe direction of I (Figure 4-7).The reader should also be made aware of another case that islinked to the same problem. When analysing a brace with asimple ring stiffener the hot spot stress will include the effectof decreased stress on the inside and increased stress on theoutside due to the circumferential stiffness of the ring. How-ever, the ring will not attract stress normal to its plane. There-fore, a lower S-N curve than D has to be used, see Tables of S-N classification. From a finite element analysis using shell ele-ments the largest stress at the node at the ring stiffener shouldbe used as nominal stress. This is important at an outside ringstiffener in order to include the bending stress in the shell dueto its deformed shape, ref. Figure 3.3. Ref. also fatigue analysisof the drum in Appendix D, Commentary. In a case that a longitudinal stiffener is ended at a circumferen-tial ring stiffener the described procedure using S-N curve Dwill again be working.
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 33
4.3.8 Verification of analysis methodologyThe analysis methodology may be verified based on analysisof details with derived target hot spot stress. Such details withtarget hot spot stress are shown in Appendix D, Commentary.
Figure 4-1Schematic stress distribution at a hot spot
Figure 4-2Example of derivation of hot spot stress
Figure 4-3Different hot spot positions
Figure 4-4Stress extrapolation in a three-dimensional FE model to the weldtoe
Figure 4-5Stress extrapolation in a three-dimensional FE model to the weldtoe
Stress evaluation plane
Notch stress
Hot spot stress
Membrane stress
Attachmentplate
t
Fillet weld
Notch stress
t/2 3t/2
Stress
Hot spot stressSurface stress
Attachment plate
Fillet weld
Attachment plate
Fillet weld
AA
Nominal stressNominal stress
Intersectionline
Hot spot
1
4 3
2
A
0.5 t
Gaussian integrationpoint
1
4 3
2
1.5 t
Extrapolatedhot spot stress
B
Intersectionline
Hot spot
1
4 3
2
A
0.5 t
Gaussian integrationpoint
1
4 3
2
1.5 t
Extrapolatedhot spot stress
B
Intersectionline
Hot spot
1
4 3
2
A
0.5 t
Gaussian integrationpoint
1
4 3
2
1.5 t
Extrapolatedhot spot stress
B
Intersectionline
Hot spot
1
4 3
2
A
0.5 t
Gaussian integrationpoint
1
4 3
2
1.5 t
Extrapolatedhot spot stress
B
c
cb
a
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 34 see note on front cover
Figure 4-6Derivation of hot spot stress for element size larger than t x t
Figure 4-7Illustration of difference to attract stresses normal to and in planeof a shell element model
5. Simplified fatigue analysis5.1 GeneralThe long term stress range distribution may be presented as atwo-parameter Weibull distribution
where
Δσ 0 is the largest stress range out of n0 cycles.When the long-term stress range distribution is defined apply-ing Weibull distributions for the different load conditions, anda one-slope S-N curve is used, the fatigue damage is given by
where
Use of one slope S-N curves leads to results on the safe side forcalculated fatigue lives (with slope of curve at N < 106 - 107cycles).For other expressions for fatigue damage see Appendix D,Commentary.
5.2 Fatigue design chartsDesign charts for steel components in air and in seawater withcathodic protection are shown in Figure 5-1 and Figure 5-2respectively. These charts have been derived based on the twoslopes S-N curves given in this RP. The corresponding numer-ical values are given in Table 5-2 and Table 5-3.These design charts have been derived based on an assumptionof an allowable fatigue damage η = 1.0 during 108 cycles (20years service life which corresponds to an average period of6.3 sec). For design with other allowable fatigue damages, η,the allowable stress from the design charts should be reducedby factors derived from Table 5-4 and Table 5-5 for conditionsin air and Table 5-6 and Table 5-7 for conditions in seawaterwith cathodic protection.The fatigue utilisation factor η as a function of design life and
(5.1.1)
t 5 t 6 t4 t3 t2 t0Distance from hot spot
Hot spot stress
Second order polynomial
0.5 t 1.5 t
Results from FE analysis
t 5 t 6 t4 t3 t2 t0Distance from hot spot
Hot spot stress
Second order polynomial
0.5 t 1.5 t
Results from FE analysis
ca
I II
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−=
h
qΔσexp)Q(Δσ
Q = probability for exceedance of the stress range Δσh = Weibull shape parameterq = Weibull scale parameter is defined from the stress
range level, Δσ 0, as:
(5.1.2)
(5.1.3)
Td = design life in secondsh = Weibull stress range shape distribution parameterq = Weibull stress range scale distribution parameterν0 = average zero-crossing frequency
= gamma function. Values of the gamma function
are listed in Table 5-1.
Table 5-1 Numerical values for Γ (1+ m/h)h m = 3.0 h m = 3.0 h m = 3.0
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 35
design fatigue factor (DFF) is given in Table 5-8.The stresses derived here correspond to the reference thick-ness. For thickness larger than the reference thickness, anallowable extreme stress range during 108 cycles may beobtained as
where
Figure 5-1Allowable extreme stress range during 108 cycles for components in air
(5.2.1)k
⎟⎠⎞
⎜⎝⎛=
ttσσ ref
tref0,t0,
k = thickness exponent, see section 2.4 and Table 2-1, Table 2-2 and Table 2-3
σ0,tref = allowable stress as derived from Table 5-2 and Table 5-3
Table 5-2 Allowable extreme stress range in MPa during 108 cycles for components in airS-N curves Weibull shape parameter h
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 36 see note on front cover
Figure 5-2Allowable extreme stress range during 108 cycles for components in seawater with cathodic protection
Table 5-3 Allowable extreme stress range in MPa during 108 cycles for components in seawater with cathodic protectionS-N curves Weibull shape parameter h
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 38 see note on front cover
5.3 Example of use of design chartsThe allowable stress range in the deck structure of a FPSO isto be determined. The maximum thickness of the steel plates is 35.0 mm. FromDNV Classification Note No. 30.7 a Weibull shape parameterequal 0.97 is determined. It is assumed that details with a clas-sification F3 is going to be welded to the deck structure. The design life of the FPSO is 25 years and the operator wouldlike to use a Design Fatigue Factor equal 2. The detail is in air environment. Then by a linear interpolation
of stress ranges for h-values 0.90 and 1.0 in Table 5-2 for S-Ncurve F3 is obtained:199.6 - (199.6 - 169.0) ((0.97 - 0.90)/(1.0 - 0.90)) = 178.18 MPa.This corresponds to an allowable stress for 20 years design lifeand a DFF equal 1. Then from Table 5-8 an utilisation factor ηequal 0.40 is obtained for 25 years service life and a DFF equal2.0.Then from Table 5-5 a reduction factor is obtained by linearinterpolation between the factors for h-values 0.90 and 1.0 forη = 0.40. The following reduction factor is obtained:
Table 5-6 Reduction factor on stress to correspond with utilisation factor η for B1 and B2 curves in seawater with cathodic protection Fatigue damage
Table 5-7 Reduction factor on stress to correspond with utilisation factor η for C - W3 curves in seawater with cathodic protectionFatigue damage utilisation η
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 39
0.779 + (0.785-0.779) ((0.97 - 0.90)/(1.0 - 0.90)) = 0.783.Thus the allowable stress range for a 25 mm thick plate isobtained as 178.18·0.783 = 139.55. The thickness exponent for a F3 detail is k = 0.25 from Table2-1.Then the allowable stress range for the 35 mm thick plate isobtained as: 139.55·(25/35) 0.25 = 128.29 MPa.
6. Fatigue analysis based on fracture mechanicsFracture mechanics may be used for fatigue analyses as sup-plement to S-N data.Fracture mechanics is recommended for use in assessment ofacceptable defects, evaluation of acceptance criteria for fabri-cation and for planning in-service inspection.The purpose of such analysis is to document, by means of cal-culations, that fatigue cracks, which might occur during serv-ice life, will not exceed the crack size corresponding tounstable fracture. The calculations should be performed suchthat the structural reliability by use of fracture mechanics willnot be less than that achieved by use of S-N data. This can beachieved by performing the analysis according to the follow-ing procedure:
— crack growth parameter C determined as mean plus 2standard deviation
— a careful evaluation of initial defects that might be presentin the structure when taking into account the actual NDEinspection method used to detect cracks during fabrication
— use of geometry functions that are on the safe side— use of utilisation factors similar to those used when the
fatigue analysis is based on S-N data.
As crack initiation is not included in the fracture mechanicsapproach, shorter fatigue life is normally derived from fracturemechanics than by S-N data.In a case that the results from fracture mechanics analyses can-not directly be compared with S-N data it might be recom-mended to perform a comparison for a detail where S-N dataare available, in order to verify the assumptions made for thefracture mechanics analyses.The initial crack size to be used in the calculation should beconsidered in each case, taking account of experienced imper-fection or defect sizes for various weldments, geometries,access and reliability of the inspection method. For surfacecracks starting from transitions between weld/base material, acrack depth of 0.5 mm (e.g. due to undercuts and microcracksat bottom of the undercuts) may be assumed if other docu-mented information about crack depth is not available.It is normally, assumed that compressive stresses do not con-tribute to crack propagation. However, for welded connectionscontaining residual stresses, the whole stress range should beapplied. Only stress components normal to the propagationplane need to be considered.The Paris’ equation may be used to predict the crack propaga-tion or the fatigue life:
where
The stress intensity factor K may be expressed as:
where
See BS 7910, ref. /7/, for further guidelines related to fatigueassessment based on fracture mechanics.
7. Improvement of Fatigue Life by Fabrica-tion7.1 GeneralIt should be noted that improvement of the toe will not improvethe fatigue life if fatigue cracking from the root is the mostlikely failure mode. The considerations made in the followingare for conditions where the root is not considered to be a crit-ical initiation point. Except for weld profiling (section 7.2) theeffect from different improvement methods as given in the fol-lowing can not be added.Reference is made to IIW Recommendations, on post weldimprovement with respect to execution of the improvement.
7.2 Weld profiling by machining and grindingBy weld profiling in this section is understood profiling bymachining or grinding as profiling by welding only is not con-sidered to be an efficient mean to improve fatigue lives.In design calculations, the thickness effect may be reduced toan exponent 0.15 provided that the weld is profiled by eithermachining or grinding to a radius of approximately half theplate thickness, (T/2 with stress direction as shown in Figure7-2 B).Where weld profiling is used, the fatigue life can be increasedtaking account of a reduced local stress concentration factor. Areduced local stress due to weld profiling can be obtained asfollows. When weld profiling is performed, a reduced hot spot stresscan be calculated as
where α and β are derived from equations (7.2.2) and (7.2.3)respectively.
For description of geometric parameters see Figure 7-1.The membrane part and the bending part of the stress have tobe separated from the local stress as
where
(6.1.1)
ΔK = Kmax - KminN = Number of cycles to failurea = crack depth. It is here assumed that the crack depth/
length ratio is low (less than 1:5)
( )mΔKCdNda =
C, m = material parameters, see BS 7910, ref. /7/
(6.1.2)
σ = nominal stress in the member normal to the crackg = factor depending on the geometry of the member and
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 40 see note on front cover
If a finite element analysis of the considered connection hasbeen performed, the results from this can be used directly toderive membrane stress and bending stress.For cruciform joints and heavy stiffened tubular joints it maybe assumed that the hot spot stress is mainly due to membranestress. For simple tubular joints it may be assumed that the hot spotstress in the chord is due to bending only.The reduced local stress in equation (7.2.1) is to be usedtogether with the same S-N curves as the detail is classified forwithout weld profiling. (It is assumed that R/T = 0.1 withoutweld profiling for a plate thickness T = 25 mm).In addition the fatigue life can be increased taking account oflocal toe grinding, reference is made to Section 7.3. However,the maximum improvement factor from grinding only shouldthen be limited to a factor 2 on fatigue life.
Figure 7-1Weld profiling of cruciform joint
7.3 Weld toe grindingWhere local grinding of the weld toes below any visible under-cuts is performed the fatigue life may be increased by a factorgiven in Table 7-1. In addition the thickness effect may bereduced to an exponent k = 0.20. Reference is made to Figure7-2. Grinding a weld toe tangentially to the plate surface, as atA, will produce only little improvement in fatigue strength. Tobe efficient, grinding should extend below the plate surface, asat B, in order to remove toe defects. Grinding is normally car-ried out by a rotary burr. The treatment should produce asmooth concave profile at the weld toe with the depth of thedepression penetrating into the plate surface to at least 0.5 mmbelow the bottom of any visible undercut (see Figure 7-2). Thegrinding depth should not exceed 2 mm or 7% of the platethickness, whichever is smaller.In general grinding has been used as an efficient method forreliable fatigue life improvement after fabrication. Grindingalso improves the reliability of inspection after fabrication andduring service life. However, experience indicates that it maybe a good design practice to exclude this factor at the designstage. The designer is advised to improve the details locally byother means, or to reduce the stress range through design andkeep the possibility of fatigue life improvement as a reserve toallow for possible increase in fatigue loading during the designand fabrication process, see also DNV-OS-C101 Design ofSteel Structures, section 6.It should also be noted that if grinding is required to achieve aspecified fatigue life, the hot spot stress is rather high. Due togrinding a larger fraction of the fatigue life is spent during theinitiation of fatigue cracks, and the crack grows faster after ini-tiation. This implies use of shorter inspection intervals duringservice life in order to detect the cracks before they become
dangerous for the integrity of the structure.For grinding of weld toes it is recommended to use a rotary ballshaped burr with typical diameter of 12 mm.
Figure 7-2Grinding of welds
7.4 TIG dressingThe fatigue life may be improved by TIG dressing by a factorgiven in Table 7-1.Due to uncertainties regarding quality assurance of the weld-ing process, this method may not be recommended for generaluse at the design stage.
7.5 Hammer peeningThe fatigue life may be improved by means of hammer peen-ing by a factor given in Table 7-1.
However, the following limitations apply:
— Hammer peening should only be used on members wherefailure will be without substantial consequences, ref. OS-C101 Design of Steel Structures, Section 6.
— Overload in compression must be avoided, because theresidual stress set up by hammer peening will bedestroyed.
— It is recommended to grind a steering groove by means ofa rotary burr of a diameter suitable for the hammer head tobe used for the peening. The peening tip must be smallenough to reach weld toe.
Due to uncertainties regarding workmanship and quality assur-ance of the process, this method may not be recommendablefor general use at the design stage.
Weld ProfilingT
Rϕ
Table 7-1 Improvement on fatigue life by different methods Improvement method
Minimum specified yield strength
Increase in fatigue life (factor on life) 1)
GrindingLess than 350 MPa 0.01fy Higher than 350 MPa 3.5
TIG dressingLess than 350 MPa 0.01fy Higher than 350 MPa 3.5
Hammer peening 3) Less than 350 MPa 0.011fy Higher than 350 MPa 4.0
1) The maximum S-N class that can be claimed by weld improve-ment is C1 or C depending on NDE and quality assurance for execution see Table A-5 in Appendix A.
2) fy = characteristic yield strength for the actual material.3) The improvement effect is dependent on tool used and work-
manship. Therefore, if the fabricator is without experience with respect to hammer peening, it is recommended to perform fatigue testing of relevant detail (with and without hammer peening) before a factor on improvement is decided.
Depth of grinding shouldbe 0.5mm below bottomof any visible undercut.BA
σ σ
T
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 41
8. Extended fatigue lifeAn extended fatigue life is considered to be acceptable andwithin normal design criteria if the calculated fatigue life islonger than the total design life times the Fatigue Design Fac-tor.Otherwise an extended life may be based on results from per-formed inspections throughout the prior service life. Such anevaluation should be based on:
1) Calculated crack growth.Crack growth characteristics; i. e. crack length/depth asfunction of time/number of cycles (this depends on type ofjoint, type of loading, and possibility for redistribution ofstress).
2) Reliability of inspection method used.Elapsed time from last inspection performed.It is recommended to use Eddy Current or Magnetic Parti-cle Inspection for inspection of surface cracks starting athot spots.
For welded connections that are ground and inspected forfatigue cracks the following procedure may be used for calcu-lation of an elongated fatigue life. Provided that grindingbelow the surface to a depth of approximately 1.0 mm is per-formed and that fatigue cracks are not found by a detailedMagnetic Particle Inspection of the considered hot spot regionat the weld toe, the fatigue damage at this hot spot may be con-sidered to start again at zero. If a fatigue crack is found, a fur-ther grinding should be performed to remove any indication ofthis crack. If more than 10% of the thickness is removed bygrinding, the effect of this on increased stress should beincluded when a new fatigue life is assessed. In some cases asmuch as 30% of the plate thickness may be removed by grind-ing before a weld repair is resorted to. This depends on type ofjoint, loading condition and accessibility for a repair.It should be noted that fatigue cracks growing from the weldroot of fillet welds can hardly be detected by NDE. Also, thefatigue life of such regions can not be improved by grinding ofthe surface.It should also be remembered that if renewal of one hot spotarea is performed by local grinding, there are likely other areasclose to the considered hot spot region that are not ground andthat also experience a significant dynamic loading. The fatiguedamage at this region is the same as earlier. However, also thisfatigue damage may be reassessed taking into account:
— the correlation with a ground neighbour hot spot regionthat has not cracked
— an updated reliability taking the reliability of performedin-service inspections into account as discussed above.
9. Uncertainties in Fatigue Life Prediction9.1 GeneralLarge uncertainties are normally associated with fatigue lifeassessments. Reliability methods may be used to illustrate theeffect of uncertainties on probability of a fatigue failure. Anexample of this is shown in Figure 9-1 based on mean expecteduncertainties for a jacket design from ”Reliability of Calcu-lated Fatigue Lives of Offshore Structures”, ref. /17/. From Figure 9-1 it might be concluded that a design modifica-
tion to achieve a longer calculated fatigue life is an efficientmean to reduce probability of a fatigue failure.The effect of scatter in S-N data may be illustrated by Figure9-2 where the difference between calculated life is shown formean S-N data and design S-N data (which is determined asmean minus 2 standard deviations).The effect of using Design Fatigue Factors (DFF) larger than1.0 is shown in Figure 9-3. This figure shows the probabilityof a fatigue failure the last year in service when a structure isdesigned for 20 years design life. Uncertainties on the mostimportant parameters in the fatigue design procedure areaccounted for when probability of fatigue failure is calculated.This figure is derived by probabilistic analysis where theuncertainty in loading is included in addition to uncertaintiesin S-N data and the Palmgren-Miner damage accumulationrule. (The loading including all analyses of stress is assumednormal distributed with CoV = 25%, Standard deviation = 0.20in S-N data that is assumed normal distributed in logarithmicscale and the Palmgren-Miner is assumed log normal distrib-uted with median 1.0 and CoV = 0.3). The same figure also shows the accumulated probability offailure the service life as function of DFF. The accumulatedprobability of failure is independent of design life (and neednot be linked to 20 years service life.An expected long term stress range is aimed for in the designresponse analysis. A Design Fatigue Factor equal 1.0 implies aprobability of a fatigue crack during service life equal 2.3 %due to the safety in the S-N curve if uncertainties in otherparameters are neglected. Reference is made to Figure 9-3 which shows accumulatedprobability of a fatigue failure as function of years in servicefor different assumptions of uncertainty in the input parame-ters. This figure shows the results for DFF = 1.0. The left partof this figure corresponding to the first 20 years service life isshown in Figure 9-4.One may achieve results for other values of DFFs by multipli-cation of the time scale on the abscissa axis by the actual DFFthat is considered used.Figure 9-4 and Figure 9-5 shows accumulated probability offatigue failure for uncertainty in S-N data corresponding to astandard deviation of 0.20 in log N scale. A normal distributionin logarithmic scale is assumed. The uncertainty in Miner sum-mation is described as log normal with median 1.0 and CoVequal 0.30. Other uncertainties are load and response assumedas normal distributed with CoV 15-20% and hot spot stressderivation also assumed as normal distributed with CoV equal5-10%.Calculated fatigue life forms the basis for assessment of prob-ability of fatigue cracking during service life. Thus, it implic-itly forms the basis for requirement to in-service inspection,ref. also section 9.2. For details showing a short fatigue life atan early design stage, it is recommended that the considereddetails are evaluated in terms of improvement of local geome-try to reduce its stress concentration. At an early design stageit is considered more cost efficient to prepare for minor geo-metric modifications than to rely on methods for fatigueimprovement under fabrication and construction, such asgrinding and hammer peening.Design Fatigue Factors for different areas should be defined inCompany specifications to be used as a contract document forconstruction.
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 42 see note on front cover
Figure 9-1Calculated probability of fatigue failure as function of calculated damage
Figure 9-2Effect of scatter in S-N data on calculated fatigue life
0.000000001
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
0 0.2 0.4 0.6 0.8 1 1.2
Calculated fatigue damage
Prob
abili
ty o
f fat
igue
failu
re
020406080
100120140160180200
200 250 300 350 400
Maximum allowable stress range in MPa
Cal
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fatig
ue li
fe in
yea
rs
Design S-N dat a (mean minus 2 st andard deviat ions)
Mean S-N dat a
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 43
Figure 9-3Fatigue failure probability as function of design fatigue factor
Figure 9-4Accumulated probability of fatigue crack as function of service life for 20 years design life
0.00001
0.0001
0.001
0.01
0.1
1 2 3 4 5 6 7 8 9 10Design Fatigue Factor
Failu
re p
roba
bilit
y Accumulated Probability
Annual Probability
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 50 100 150 200Time in service (years)
Acc
umul
ated
pro
babi
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of fa
tigue
failu
re
Uncertainty in S-N-Curve only
Uncertainty in S-N, Miner,CoVnom = 0.15, CoVhs = 0.05Uncertainty in S-N, Miner,CoVnom = 0.20, CoVhs = 0.05Uncertainty in S-N, Miner,CoVnom = 0.15, CoVhs = 0.10Uncertainty in S-N, Miner,CoVnom = 0.20, CoVhs = 0.10
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 44 see note on front cover
Figure 9-5Accumulated probability of through wall fatigue crack as function of service life for 20 years calculated fatigue life (Left part from Figure 9-4)
9.2 Requirements to in-service inspection for fatigue cracksUncertainties associated with fatigue life calculation normallyimply that some in-service inspection for fatigue cracks will berequired during service life depending on consequence of afatigue failure and calculated fatigue life. Figure 9-5 may beused for a first estimate of time to a first inspection based onthe lower graph in this figure if normal uncertainties are asso-ciated with the fatigue life calculation. Figure 9-5 is derived fora calculated fatigue life equal 20 years. For other calculatedfatigue lives (Lcalc) the numbers on the abscissa axis can bescaled by a factor f = Lcalc/20 for estimate of time to firstrequired inspection. If a fatigue crack is without substantial
consequences an accumulated probability of 10-2 may be con-sidered acceptable and from Figure 9-5 it is not requiredinspection the first 6 years. If the consequence of a fatiguecrack is substantial the accumulated probability of a fatiguefailure should be less than 10-4 and from Figure 9-5 an inspec-tion would be required after 2 years. (Normally a calculated fatigue life significantly longer than 20years would be required for a large consequence connectionduring design).After a first inspection the time interval to the next inspectioncan be estimated based on fracture mechanics and probabilisticanalysis taking the uncertainty in the inspection method intoaccount.
10. References
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10 2 4 6 8 10 12 14 16 18 20
Time in service (years)
Accu
mul
ated
pro
babi
lity
of fa
tigue
failu
re
Uncertainty in S-N curve only
Uncertainty in S-N, Miner, Stress:CoVnom = 0.15, CoVhs = 0.05
Uncertainty in S-N, Miner, Stress:CoVnom = 0.20, CoVhs = 0.05
Uncertainty in S-N, Miner,Stress:CoVnom = 0.15, CoVhs = 0.10
Uncertainty in S-N, Miner, Stress:CoVnom = 0.20, CoVhs = 0.10
/1/ Classification Note No 30.7 Fatigue Assessment of Ship Structures. Det Norske Veritas 2003.
/2/ Efthymiou, M.: Development of SCF Formulae and Generalised Influence Functions for use in Fatigue Analysis. Recent Developments in Tubular Joint Tech-nology, OTJ’88, October 1988, London.
/3/ Smedley, S. and Fischer, P.: Stress Concentration Fac-tors for Ring-Stiffened Tubular Joints. Fourth Int. Symp. on Tubular Structures, Delft 1991. pp. 239-250.
/4/ Lotsberg, I., Cramer, E., Holtsmark, G., Løseth, R., Olaisen, K. and Valsgård, S.: Fatigue Assessment of Floating Production Vessels. BOSS’97, July 1997.
/5/ Eurocode : Design of steel structures. Part 1-1: General rules and rules for buildings. February 1993.
/6/ Guidance on Design, Construction and Certification. HSE. February 1995.
/7/ BS7910:1999. Guide on Methods for Assessing the Acceptability of Flaws in Fusion Welded Structures. BSI.
/8/ Van Wingerde, A. M. Parker, J. A. and Wardenier, J.: IIW Fatigue Rules for Tubular Joints. Int. conf. on Per-formance of Dynamic Loaded Welded Structrues, San Francisco, July 1977.
/9/ Gulati, K. C., Wang, W. J. and Kan, K. Y.: An Analyt-ical study of Stress Concentration Effects in Multibrace Joints under Combined Loading. OTC paper no 4407, Houston, May 1982.
/10/ Gurney,T.R.: Fatigue Design Rules for welded Steel Joints, the Welding Institute Research Bulletin. Vol-ume 17, number 5, May 1976.
/11/ Gurney, T. R.: The Basis for the Revised Fatigue Design Rules in the Department of Energy Offshore Guidance Notes. Paper No 55.
/12/ Berge, S.: Effect of Plate Thickness in Fatigue Design of Welded Structures. OTC Paper no 4829. Houston, May 1984.
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 45
/13/ Buitrago, J. and Zettlemoyer, N.: Fatigue of Welded Joints Peened Underwater. 1997 OMAE, ASME 1997.
/14/ Stacey, A., Sharp, J. V. and Nichols, N. W.: Fatigue Performance of Single-sided Circumferential and Clo-sure Welds in Offshore Jacket Structures. 1997 OMAE, ASME.
/15/ Pilkey, W. D.: Peterson’s Stress Concentration Factors. Second Edition. John Wiley & Sons. 1997.
/16/ Haagensen, P. J. and Maddox, S. J.: IIW Recommenda-tions on Post Weld Improvement of Steel and Alumin-ium Structures. Doc. XIII-1815-00. Revision 5 July 2004.
/17/ Lotsberg, I., Fines, S. and Foss, G.: ”Reliability of Cal-culated Fatigue Lives of Offshore Structures”, Fatigue 84, 2nd Int. Conf. on Fatigue and Fatigue Thresholds, 3-7 September 1984. Birmingham.
/18/ Haagensen, P. J.,Slind, T. and Ørjasæter, O.: Scale Effects in Fatigue Design Data for Welded and Unwelded Components. Proc. Ninth Int. Conf. On Off-shore Mechanics and Arctic Engineering. Houston, February 1990.
/19/ Berge, S., Eide, O., Astrup, O. C., Palm, S., Wästberg, S., Gunleiksrud, Å. and Lian, B.:Effect of Plate Thick-ness in Fatigue of Welded Joints in Air ans in Sea Water. Steel in Marine Structures, edited by C. Noor-hook and J. deBack Elsevier Science Publishers B.V., Amsterdam, 1987, pp. 799-810.
/20/ Razmjoo, G. R.: Design Guidance on Fatigue of Welded Stainless Steel Joints. OMAE 1995.
/21/ Madsen, H. O., Krenk, S. and Lind, N. C. (1986) Meth-ods of Structural Safety, Prentice-Hall, Inc., NJ.
/22/ Marshall, P. W.: API Provisions for SCF, S-N, and Size-Profile Effects. OTC Paper no 7155. Houston, May 1993.
/23/ Waløen, Å. Ø.: Maskindeler 2, Tapir, NTNU (In Nor-wegian).
/24/ Buitrago, J., Zettlemoyer, N. and Kahlish, J. L.: Com-bined Hot-Spot Stress Procedures for Tubular Joints. OTC Paper No. 4775. Houston, May 1984.
/25/ Lotsberg, I.: Stress Concentration Factors at Circum-ferential Welds in Tubulars. Journal of Marine Struc-tures, January 1999.
/26/ VDI 2230 Part 1: Systematic Calculation of High Duty Bolted Joints. Verein Deutsche Ingenieure, August 1988.
/27/ Van Wingerde, A.M., Packer, J.A., Wardenier, J., Dutta, D. and Marshall, P.: Proposed Revisions for Fatigue Design of Planar Welded Connections made of Hollow Structural Sections. Paper 65 in "Tubular Structures V," Ed. M.G. Coutie and G. Davies, 1993 E & FN spon.
/28/ DNV Offshore Standard. OS-C101 Design of Steel Structures
/29/ Lotsberg, I., and Rove, H.: Stress Concenteration Fac-tors for Butt Welds in Stiffened Plates.OMAE, ASME 2000.
/30/ IIW. Fatigue Design of Welded Joints and Compo-nents. Recommendations of IIW Joint Working Group XIII-1539-96/XV-845-96. Edited by A. Hobbacher Abington Publishing, 1996, The International Institute of Welding.
/31/ Fricke, W. (2001), “Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs and Ships Based on Round-Robin FE Analyses”. Proc. 11th ISOPE, Stavanger. Also Int. J. of Offshore and Polar Engineering. Vol. 12, No. 1, March 2002.
/32/ Lotsberg, I. (2004), “Recommended Methodology for Analysis of Structural Stress for Fatigue Assessment of Plated Structures”. OMAE-FPSO'04-0013, Int. Conf. Houston.
/33/ Lotsberg, I. and Larsen, P. K.: Developments in Fatigue Design Standards for Offshore Structures. ISOPE, Stavanger, June 2001.
/34/ Bergan, P. G., Lotsberg, I.: Advances in Fatigue Assessment of FPSOs. OMAE-FPSO'04-0012, Int. Conf. Houston 2004.
/35/ Sigurdsson, S., Landet, E. and Lotsberg, I. , “Inspection Planning of a Critical Block Weld in an FPSO”. OMAE-FPSO'04-0032, Int. Conf. Houston, 2004.
/36/ Storsul, R., Landet, E. and Lotsberg, I. , “Convergence Analysis for Welded Details in Ship Shaped Struc-tures”. OMAE-FPSO'04-0016, Int. Conf. Houston 2004.
/37/ Storsul, R., Landet, E. and Lotsberg, I., “Calculated and Measured Stress at Welded Connections between Side Longitudinals and Transverse Frames in Ship Shaped Structures”. OMAE-FPSO'04-0017, Int. Conf. Hou-ston 2004.
/38/ Lotsberg, I., “Fatigue Design of Welded Pipe Penetra-tions in Plated Structures”. Marine Structures, Vol 17/1 pp. 29-51, 2004.
/39/ Lotsberg, I., “Fatigue Capacity of Fillet Welded Con-nections subjected to Axial and Shear Loading”. IIW Document no XIII-2000-03 (XV-1146-03).
/40/ Lotsberg, I., “Recommended Methodology for Analy-sis of Structural Stress for Fatigue Assessment of Plated Structures”. OMAE-FPSO'04-0013, Int. Conf. Houston 2004.
/41/ Lotsberg, I. and Sigurdsson, G., “Hot Spot S-N Curve for Fatigue Analysis of Plated Structures”. OMAE-FPSO'04-0014, Int. Conf. Houston 2004.
/42/ Lotsberg, I and Landet, E., “Fatigue Capacity of Side Longitudinals in Floating Structures”. OMAE-FPSO'04-0015, Int. Conf. Houston 2004.
/43/ Urm, H. S., Yoo, I. S., Heo, J. H., Kim, S. C. and Lots-berg, I.: “Low Cycle Fatigue Strength Assessment for Ship Structures”. PRADS 2004.
/44/ Kim, W.S. and Lotsberg, I., “Fatigue Test Data for Welded Connections in Ship Shaped Structures” OMAE-FPSO'04-0018, Int. Conf. Houston 2004.
/45/ Maddox, S. J. “Key Development in the Fatigue Design of Welded Constructions”, Portewin Lecture IIW Int. Conf. Bucharest, 2003.
/46/ Kristofferesen, S. and Haagensen, P. J.: ”Fatigue Design Criteria for Small Super Duplex Steel Pipes”, Proceedings OMAE Vancouver, 2004.
/47/ Berge, S., Kihl, D., Lotsberg, I., Maherault, S., Mik-kola, T. P. J., Nielsen, L. P., Paetzold, H., Shin, C. –H., Sun, H. –H and Tomita, Y.: Special Task Committee VI.2 Fatigue Strength Assessment. 15th ISSC, San Diego, 2003.
/48/ Chen, W. and Landet, E. (2001), “Stress Analysis of Cut-outs with and without Reinforcement”. OMAE Rio de Janeiro.
/49/ Choo, Y.S. and Zahidul Hasan, M. (2004), “Hot Spot Stress Evaluation for Selected Connection Details”. OMAE-FPSO'04-0028. Int. Conf. Houston.
/50/ Fricke, W., Doerk, O. and Gruenitz, L. (2004), “Fatigue Strength Investigation and Assessment of Fillet-Welds around Toes of Stiffeners and Brackets. OMAE-FPSO'04-0010. Int. Conf. Houston.
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 46 see note on front cover
/51/ Radaj, D., Sonsino, C. M. and Fricke, W.: (2006): Fatigue Assessment of Welded Joints by Local Approaches. Woodhead Publishing in Materials.
/52/ Ranestad Kaase, G. O.: “Finite Element Analysis of SCF in Stiffener to Plate Connections”, Pre-Project Thesis, Marine Structures NTNU 2002.
/53/ DNV-OS-F201 Dynamic Risers. 2001./54/ DNV-OS-F101 Submarine Pipeline Systems./55/ Schneider, C. R. A. and Maddox, S. J. : “Best Practice
Guide on Statistical Analysis of Fatigue Data". Doc. IIW-XIII-WG1-114-03.
/56/ Hobbacher, A.: IIW document XII-1965-03/XV-1127-03 Recommendations for Fatigue Design of Welded joints and Components. July 2004.
/57/ ASME B.31.4, Code for Pressure Piping, Chapter IX./58/ Lotsberg, I., Background for Revision of DNV-RP-
C203 Fatigue Analysis of Offshore Steel Structures. OMAE 2005-67549. Int. Conf. Halkidiki, Greece, June 2005.
/59/ Wästberg, S.; Salama, M. Fatigue Testing and Analysis of Full Scale Girth weld Tubulars. OMAE2007-29399.
/60/ DNV-OS-401 Fabrication and Testing of Offshore Structures. April 2005.
/61/ Lotsberg, I.: Fatigue Design of Plated Structures using Finite Element Analysis. Journal of Ships and Offshore Structures. 2006 Vol. 1 No 1 pp. 45-54.
/62/ Lotsberg, I and Landet, E., "Fatigue Capacity of Side Longitudinals in Floating Structures". Marine Struc-tures, Vol 18, 2005, pp. 25-42.
/63/ Lotsberg, I., "Fatigue Capacity of Fillet Welded Con-nections subjected to Axial and Shear Loading". Pre-sented at OMAE in Hamburg, 4 - 9 June 2006. OMAE paper no 2006 - 92086. Also in Journal of Offshore and Arctic Engineering.
/64/ Lotsberg, I. "Recent Advances on Fatigue Limit State Design for FPSOs", Journal of Ships and Offshore Structures, 2007 Vol. 2 No. 1 pp. 49-68.
/65/ Lotsberg, I. and Holth, P. A.: Stress Concentration Fac-tors at Welds in Tubular Sections and Pipelines. Pre-sented at OMAE 2007. OMAE paper no 2007-29571. 26th International Conference on Offshore Mechanics and Arctic Engineering, San Diego, California, June 2007. Also IIW document no XIII-2159-07.
/66/ Lotsberg, I., Rundhaug, T. A., Thorkildsen, H., Bøe, Å. and Lindemark, T.: Fatigue Design of Web Stiffened Cruciform Connections. Presented at PRADS 2007.
/67/ Lotsberg, I.: Stress Concentration Factors at Welds in Pipelines and Tanks subjected to Internal Pressure. In Journal of Marine Engineering 2008.
/68/ Sele, A., Collberg, L., Lauersen, H.: Double Skin Grout Reinforced Joints, Part Project One and Two. Fatigue Tests on Grouted Joints. DNV-Report No 83-0119.
/69/ Lotsberg, I.: Fatigue Design Criteria as Function of the Principal Stress Direction Relative to the Weld Toe. OMAE 2008-57249. To be presented at OMAE 2008 Estoril, Portugal.
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 47
APPENDIX A CLASSIFICATION OF STRUCTURAL DETAILS
A.1 Non-welded details
Table A-1 Non-welded detailsNotes on potential modes of failureIn plain steel, fatigue cracks will initiate at the surface, usually either at surface irregularities or at corners of the cross-section. In welded construction, fatigue failure will rarely occur in a region of plain material since the fatigue strength of the welded joints will usually be much lower. In steel with boltholes or other stress concentrations arising from the shape of the member, failure will usually initiate at the stress concentration. The applied stress range shall include applicable stress concentration factors arising from the shape of the member. Reference is made to section 2.4.10 for non-welded components made of high strength steel with a surface finish Ra = 3.2 or better.Detail category
Constructional details Description Requirement
B1 1.
2.
1. Rolled or extruded plates and flats2. Rolled sections
1. to 2.
— Sharp edges, surface and rolling flaws to be improved by grind-ing.
— For members that can acquire stress concentrations due to rust pitting etc. curve C is required.
B2 3. 3. Machine gas cut or sheared material with no drag lines
3.
— All visible signs of edge discon-tinuities should be removed.
— No repair by weld refill.— Re-entrant corners (slope <1:4)
or aperture should be improved by grinding for any visible defects.
— At apertures the design stress area should be taken as the net cross-section area.
C 4. 4. Manually gas cut material or material with machine gas cut edges with shal-low and regular draglines.
4.
— Subsequently dressed to remove all edge discontinuities
— No repair by weld refill.— Re-entrant corners (slope <1:4)
or aperture should be improved by grinding for any visible defects.
— At apertures the design stress area should be taken as the net cross-section area.
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 48 see note on front cover
A.2 Bolted connections
Table A-2 Bolted connectionsDetail category
Constructional details Description Requirement
C1 1. 2. 1. Unsupported one-sided connec-tions shall be avoided or else effects of eccentricities shall be taken into account when calculat-ing stresses.
2. Beam splices or bolted cover plates.
1. and 2.
— Stresses to be calculated in the gross section.
— Bolts subjected to reversal forces in shear shall be designed as a slip resistant con-nection and only the members need to be checked for fatigue.
3. 3. Bolts and threaded rods in ten-sion.
3.
— Tensile stresses to be calculated using the tensile stress area of the bolt.
— For preloaded bolts, the stress-range in the bolt depends upon the level of preload and the geometry of the connection, see e.g. “Maskindeler 2”, ref. /23/.
F1 Cold rolled threads with no fol-lowing heat treatment like hot gal-vanising
W3 Cut threadsSee Section 2.8.3
4. Bolts in single or double shear.Fitted bolts and normal bolts without load reversal.
Thread not in shear plane.The shear stress to be calculated on the shank area of the bolt.
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 49
A.3 Continuous welds essentially parallel to the direction of applied stress
Table A-3 Continuous welds essentially parallel to the direction of applied stressDetail category
Constructional details Description Requirement
Notes on potential modes of failure.With the excess weld material dressed flush, fatigue cracks would be expected to initiate at weld defect locations. In the as welded condition, cracks may initiate at start-stop positions or, if these are not present, at weld surface ripples.General comments
a) Backing stripsIf backing strips are used in these joints, they must be continuous. If they are attached by welding, such welds must also comply with the relevant joint classification requirements (note particularly that tack welds, unless subsequently ground out or covered by a continuous weld, would reduce the joint to class F)
b) Edge distanceAn edge distance criterion exists to limit the possibility of local stress concentrations occurring at unwelded edges as a result, for example, of undercut, weld spatter, or accidental overweave in manual fillet welding (see also notes in Table A-7). Although an edge distance can be specified only for the “width” direction of an element, it is equally important to ensure that no accidental undercutting occurs on the unwelded corners of, for example cover plates or box girder flanges. If undercutting occurs it should subsequently be ground smooth.
C 1.
2.
1. Automatic welds carried out from both sides. If a specialist inspec-tion demonstrates that longitudi-nal welds are free from significant flaws, category B2 may be used.2. Automatic fillet welds. Cover plate ends shall be verified using detail 5. in Table A-8
1. and 2.
— No start-stop position is per-mitted except when the repair is performed by a spe-cialist and inspection carried out to verify the proper exe-cution of the repair.
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 50 see note on front cover
C1 3.
4.
3. Automatic fillet or butt welds car-ried out from both sides but con-taining stop-start positions.4. Automatic butt welds made from one side only, with a backing bar, but without start-stop positions.
4.
— When the detail contains start-stop positions use cate-gory C2
C2 5. Manual fillet or butt welds.6. Manual or automatic butt welds carried out from one side only, particularly for box girders
6.
— A very good fit between the flange and web plates is essential. Prepare the web edge such that the root face is adequate for the achievement of regular root penetration with out brake-out.
C2 7. Repaired automatic or manual fil-let or butt welds
7.
— Improvement methods that are adequately verified may restore the original category.
Table A-3 Continuous welds essentially parallel to the direction of applied stress (Continued)Detail category
Constructional details Description Requirement
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 51
A.4 Intermittent welds and welds at cope holes
Table A-4 Intermittent welds and welds at cope holesDetail category
Constructional details Description Requirement
E 1. 1.Stitch or tack welds not sub-sequently covered by a con-tinuous weld
1.
— Intermittent fillet weld with gap ratio g/h ≤ 2.5.
F 2. 2.Ends of continuous welds at cope holes.
2.
— Cope hole not to be filled with weld material.
3. 3.Cope hole and transverse butt weld.
3.
— For butt weld in material with cope hole advice on fatigue assessment may be found in 3.1.6.
— The SCFs from 3.1.6 may be used together with the D-curve.
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 52 see note on front cover
A.5 Transverse butt welds, welded from both sides
Table A-5 Transverse butt welds, welded from both sidesDetail category
Constructional details Description Requirement
Notes on potential modes of failureWith the weld ends machined flush with the plate edges, fatigue cracks in the as-welded condition normally initiate at the weld toe, so that the fatigue strength depends largely upon the shape of the weld overfill. If the overfill is dressed flush, the stress concentration caused by it is removed, and failure is then associated with weld defects.Design stressesIn the design of butt welds that are not symmetric about the root and are not aligned, the stresses must include the effect of any eccentricity (see section 3.1 and 3.3).With connections that are supported laterally, e.g. flanges of a beam that are supported by the web, eccentricity may be neglected.C1 1.
2.
3.
1.Transverse splices in plates flats and rolled sections2.Flange splices in plate girders.3.Transverse splices in plates or flats tapered in width or in thick-ness where the slope is not greater than 1:4.
1. and 2.
— Details 1. and 2. may be increased to Category C when high quality welding is achieved and the weld is proved free from significant defects by non-destructive examination (it is assumed that this is fulfilled by inspection category I).
1., 2. and 3.
— All welds ground flush to plate surface parallel to direction of the arrow.
— Weld run-off pieces to be used and subsequently removed, plate edges to be ground flush in direction of stress.
— All welds welded in horizon-tal position in shop.
41
4
1
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Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 53
D 4.
5
6.
4.Transverse splices in plates and flats.5.Transverse splices in rolled sec-tions or welded plate girders6.Transverse splices in plates or flats tapered in width or in thick-ness where the slope is not greater than 1:4.
4., 5. and 6.
— The height of the weld con-vexity not to be greater than 10% of the weld width, with smooth transitions to the plate surface.
— Welds made in flat position in shop.
— Weld run-off pieces to be used and subsequently removed, plate edges to be ground flush in direction of stress.
Table A-5 Transverse butt welds, welded from both sides (Continued)Detail category
Constructional details Description Requirement
41
4 1
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 54 see note on front cover
E 7. 7.Transverse splices in plates, flats, rolled sections or plate girders made at site.(Detail category D may be used for welds made in flat position at site meeting the requirements under 4., 5. and 6 and 100 % MPI of the weld is performed.)
7.
— The height of the weld con-vexity not to be greater than 20% of the weld width.
— Weld run-off pieces to be used and subsequently removed, plate edges to be ground flush in direction of stress.
8. 8.Transverse splice between plates of unequal width, with the weld ends ground to a radius.
8.:
— The stress concentration has been accounted for in the joint classification.
— The width ratio H/h should be less than 2.
F1
F3
Table A-5 Transverse butt welds, welded from both sides (Continued)Detail category
Constructional details Description Requirement
41
4 1
0.16hr ≥
11.0hr
≥
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 55
A.6 Transverse butt welds, welded from one side
Table A-6 Transverse butt welds, welded from one sideNotes on potential modes of failureWith the weld ends machined flush with the plate edges, fatigue cracks in the as-welded condition normally initiate at the weld toe, so that the fatigue strength depends largely upon the shape of the weld overfill. If the overfill is dressed flush, the stress concentration caused by it is removed, and failure is then associated with weld defects. In welds made on permanent backing strip, fatigue cracks most likely initiate at the weld metal/strip junction.By grinding of the root after welding this side of the welded connection can be categorised to C1 or C; ref. Table A-5.Design stressesIn the design of butt welds that are not symmetric about the root and are not aligned, the stresses must include the effect of any eccentricity (see section 3.1 and 3.3).With connections that are supported laterally, e.g. flanges of a beam that are supported by the web, eccentricity may be neglected.Detail category
Constructional details Description Requirement
W3 1. 1.Butt weld made from one side only and without back-ing strip.
1.With the root proved free from defects larger than 1-2 mm (in the thickness direc-tion) by non-destructive testing, detail 1 may be categorised to F3 (it is assumed that this is fulfilled by inspection category I). If it is likely that larger defects may be present after the inspection the detail may be downgraded from F3 based on fatigue life calculation using fracture mechanics. The analysis should then be based on a rel-evant defect size.
F 2. 2.Transverse butt weld on a temporary or a permanent backing strip without fillet welds.
G 3. 3.Transverse butt weld on a backing strip fillet welded to the plate.
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 56 see note on front cover
A.7 Welded attachments on the surface or the edge of a stressed member
Table A-7 Welded attachments on the surface or the edge of a stressed memberDetail category
Constructional details Description Requirement
Notes on potential modes of failureWhen the weld is parallel to the direction of the applied stress, fatigue cracks normally initiate at the weld ends. When the weld is transverse to direction of stressing, cracks usually initiate at the weld toe; for attachments involving a single, as opposed to a double, weld cracks may also initiate at the weld root. The cracks then propagate into the stressed member. When the welds are on or adjacent to the edge of the stressed member the stress concentration is increased and the fatigue strength is reduced; this is the reason for specifying an “edge distance” in some of this joints (see also note on edge distance in Table A-3).
1.
2.
1.Welded longitudinal attachment
2. Doubling plate welded to a plate.
1. and 2. The detail category is given for:
— Edge distance ≥ 10mm— For edge distance < 10 mm
the detail category shall be downgraded with one S-N-curve
E l ≤ 50 mmF 50 < l ≤ 120 mmF1 120 < l ≤ 300 mmF3 l > 300 mm
3. 3. Longitudinal attachment welded to transverse stiffener.
E l ≤120 mmF 120 < l ≤ 300 mmF1 l > 300 mm
l
l
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E 4.r > 150 mm
4. Longitudinal fillet welded gusset with radius transition to plate or tube; end of fillet weld reinforce-ment (full penetration); length of reinforcement weld > r.
4. Smooth transition radius r formed by initially machining or gas cut-ting the gusset plate before weld-ing, then subsequently grinding the weld area parallel to the direc-tion of the arrow so that the trans-verse weld toe is fully removed.
5. 5.Gusset plate with a radius welded to the edge of a plate or beam flange.
5. The specified radius to be achieved by grinding.
E
F
F1
F3
G
Table A-7 Welded attachments on the surface or the edge of a stressed member (Continued)Detail category
Constructional details Description Requirement
r r
150mmr ,Wr
31 ≥≤
31
Wr
61 <≤
61
Wr
101 <≤
101
Wr
161 <≤
161
Wr
251 <≤
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 58 see note on front cover
6.
7.
6.Gusset plate welded to the edge of a plate or beam flange.7. Flange welded to another flange at crossing joints.
6. and 7:The distance l is governing detail category for the stress direction shown in sketch. For main stress in the other beam the distance L will govern detail category.
G l ≤ 150 mmW1 150 < l ≤ 300 mmW2 l > 300 mm
Table A-7 Welded attachments on the surface or the edge of a stressed member (Continued)Detail category
Constructional details Description Requirement
l
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 59
8.
9.
10.
8.Transverse attachments with edge distance ≥ 10 mm9.Vertical stiffener welded to a beam or a plate girder. 10. Diaphragms of box girders welded to the flange or web
9.
— The stress range should be calculated using principal stresses if the stiffener termi-nates in the web.
8., 9. and 10. The detail category is given for:
— Edge distance ≥ 10 mm— For edge distance < 10 mm
the detail category shall be downgraded with one SN-curve
E t ≤ 25 mmF t > 25 mm
11. 11. Welded shear connector to base material.
E Edge distance ≥ 10 mmG Edge distance < 10 mm
Table A-7 Welded attachments on the surface or the edge of a stressed member (Continued)Detail category
Constructional details Description Requirement
t
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 60 see note on front cover
A.8 Welded joints with load carrying welds
Table A-8 Welded joints with load carrying weldsDetail category
Constructional details Description Requirement
Notes on potential modes of failureFailure in cruciform or T joints with full penetration welds will normally initiate at the weld toe. In joints made with load-carrying fillet or partial penetration butt welds, cracking may initiate either at the weld toe and propagate into the plate, or at the weld root and propagate through the weld. In welds parallel to the direction of the applied stress, however, weld failure is uncommon. In this case, cracks normally initiate at the weld end and propagate into the plate perpendicular to the direction of applied stress. The stress concentration is increased, and the fatigue strength is therefore reduced, if the weld end is located on or adjacent to the edge of a stressed member rather than on its surface.Design stressesIn the design of cruciform joints, which are not aligned the stresses, must include the effect of any eccentricity. The maximum value of the eccentricity may normally be taken from the fabrication tolerances. The design stress may be obtained as the nominal stress multiplied by the stress concentration factor due to the eccentricity.F 1. 1.Full penetration butt welded
cruciform joint1.:
— Inspected and found free from sig-nificant defects.
The detail category is given for:
— Edge distance ≥ 10mm— For edge distance < 10mm the
detail category shall be down-graded with one SN-curve
W3 2. 2.Partial penetration tee-butt joint or fillet welded joint and effective full penetration in tee-butt joint. See also section 2.7.
2.:
— Two fatigue assessments are required. Firstly, root cracking is evaluated taking Category W3 for σw. σw is defined in section 2.3.5. Secondly, toe cracking is evaluated by determining the stress range in the load-carrying plates and use Category G.
— If the requirement in section 2.7 that toe cracking is the most likely failure mode is fulfilled and the edge distance ≥ 10mm, Category F1 may be used for partial penetra-tion welds and F3 for fillet welds.
F1 3. 3.Fillet welded overlap joint. Crack in main plate.
3.
— Stress in the main plate to be calcu-lated on the basis of area shown in the sketch.
— Weld termination more than 10 mm from plate edge.
— Shear cracking in the weld should be verified using detail 7.
t < 20 mm
>10 mm
of main plateStressed area
2
1
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 61
W1 4. 4.Fillet welded overlap joint. Crack in overlapping plate.
4.
— Stress to be calculated in the over-lapping plate elements
— Weld termination more than 10 mm from plate edge.
— Shear cracking in the weld should be verified using detail 7.
5. 5.End zones of single or multiple welded cover plates in beams and plate girders. Cover plates with or without frontal weld.
5.
— When the cover plate is wider than the flange, a frontal weld, carefully ground to remove undercut, is nec-essary.
G t and tc ≤ 20 mmW3 t and tc > 20 mmE 6. and 7. 6.
Continuous fillet welds trans-mitting a shear flow, such as web to flange welds in plate girders. For continuous full penetration butt weld in shear use Category C2.7.Fillet welded lap joint.
6.
— Stress range to be calculated from the weld throat area.
7.
— Stress range to be calculated from the weld throat area considering the total length of the weld.
— Weld terminations more than 10 mm from the plate edge.
Table A-8 Welded joints with load carrying welds (Continued)Detail category
Constructional details Description Requirement
tt c
tt
c
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Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 62 see note on front cover
E 8. 8.Stud connectors (failure in the weld or heat affected zone).
8.
— The shear stress to be calculated on the nominal cross section of the stud.
9. 9.Trapezoidal stiffener welded to deck plate with fillet weld or full or partial penetration butt weld.
9.
— For a full penetration butt weld, the bending stress range shall be calcu-lated on the basis of the thickness of the stiffener.
— For a fillet weld or a partial penetra-tion butt weld, the bending stress range shall be calculated on the basis of the throat thickness of the weld, or the thickness of the stiff-ener if smaller.
F
G
Table A-8 Welded joints with load carrying welds (Continued)Detail category
Constructional details Description Requirement
DET NORSKE VERITAS
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A.9 Hollow sections
Table A-9 Hollow sectionsDetail category
Constructional details Description Requirement
B1 1. 1.Non-welded sections
1.
— Sharp edges and surface flaws to be improved by grinding
B2 2. 2.Automatic longitudinal seam welds (for all other cases, see Table A-3)
2.
— No stop /start positions, and free from defects outside the tolerances of OS-C401 Fabrication and Testing of Offshore Structures.
C1 3.Circumferential butt weld made from both sides dressed flush.
3., 4., 5. and 6.
— The applied stress must include the stress concentration factor to allow for any thickness change and for fabrication toler-ances, ref. section 3.3.7.
— The requirements to the corresponding detail category in Table A-5 apply.
D 4.Circumferential butt weld made from both sides.
E 5.Circumferential butt weld made from both sides made at site.
F6.Circumferential butt weld made from one side on a backing bar.
F3 7. 7.Circumferential butt weld made from one side without a backing bar.
7.
— The applied stress should include the stress concentration factor to allow for any thickness change and for fabrication tolerances, ref. section 3.3.7.
— The weld root proved free from defects larger than 1-2 mm.
C1 8. Circumferential butt welds made from one side that are machined flush to remove defects and weld overfill.
8. A machining of the surfaces will reduce the thickness. Specially on the root side material will have to be removed. A reduced thickness should be used for calculation of stress. The weld should be proved free from defects by non-destructive examination (It is assumed that this is fulfilled by Inspection category I). Category C may be achieved; ref. Table A-5.
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 64 see note on front cover
C1 8., 9., 10 and 11. 8.Circumferential butt welds between tubular and conical sections, weld made from both sides dressed flush.
8., 9., 10., and 11.
— The applied stress must also include the stress concentration factor due to the overall form of the joint, ref. section 3.3.9.
— The requirements to the corresponding detail category in Table A-5 apply.D 9.
Circumferential butt welds between tubular and conical sections, weld made from both sides.
E 10.Circumferential butt welds between tubular and conical sections, weld made from both sides made at site.
F 11.Circumferential butt welds between tubular and conical sections, weld made from one side on a backing bar.
F3 12. 12.Circumferential butt welds between tubular and conical sections, weld made from one side without a backing bar.(This classification is for the root. For the outside weld toe see 8-11).
12.
— The applied stress must also include the stress concentration factor due to the overall form of the joint
— The weld root proved free from defects larger than 1-2 mm.
F3 13. 13.Butt welded end to end con-nection of rectangular hollow sections.
13.
— With the weld root proved free from defects larger than 1-2 mm
F 14. 14. Circular or rectangular hol-low section, fillet welded to another section.
14.
— Non load carrying welds. — Section width parallel to
stress direction ≤ 100 mm.— All other cases, see Table A-7
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 66 see note on front cover
A.10 Details relating to tubular members
Table A-10 Details relating to tubular membersDetail category
Constructional details Description Requirement
T 1.Parent material adjacent to the toes of full penetration welded tubular joints.
1.
— The design should be based on the hot spot stress.
F1 2. 2.Welded rungs.
D 3. and 4. 3.Gusseted connections made with full penetration welds.
3.
— The design stress must include the stress concentration factor due to the overall form of the joint.
F 4.Gusseted connections made with fillet welds.
4.
— The design stress must include the stress concentration factor due to the overall form of the joint.
5. 5.Parent material at the toe of a weld attaching a diaphragm to a tubular member.
The nominal design stress for the inside may be determined from section 3.3.8.
E t ≤ 25 mmF t > 25 mm
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E to G, see Table A-7
6. 6. Parent material (of the stressed member) adjacent to the toes of a bevel butt or fillet welded attachments in region of stress concentration.
6.
— Class depends on attachment length (see Table A-7) but stress must include the stress concentration factor due to the overall shape of adjoining structure.
C 7. 7.Parent material to, or weld metal in welds around a pene-tration through a wall of a mem-ber (on a plane essentially perpendicular to the direction of stress)
7.In this situation the relevant stress must include the stress concentration factor due to the overall geometry of the detail.Without start and stop at hot spot region. See also section 3.1.5.
D 8. 8. At fillet weld toe in parent metal around a penetration in a plate.
8.
— The stress in the plate should include the stress concentration factor due to the overall geometry of the detail.
See also section 3.1.5.
W3 9. Weld metal in partial penetra-tion or fillet welded joints around a penetration through the wall of a member (on a plane essentially parallel to the plane of stress).
9.
— The stress in the weld should include an appropriate stress con-centration factor to allow for the overall joint geometry. Reference is also made to Appendix C.See also section 3.1.5.
Table A-10 Details relating to tubular members (Continued)Detail category
Constructional details Description Requirement
C
C
C-C
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 68 see note on front cover
APPENDIX B SCF’S FOR TUBULAR JOINTS
B.1 Stress concentration factors for simple tubular joints and overlap jointsStress concentration factors for tubular joints for joint types T/Y are given in Table B-1, for joint types X in Table B-2, forjoint types K in Table B-3 and Table B-4 and for joint types KTin Table B-5. Stress concentration factors are based on “Devel-opment of SCF Formulae and Generalised Influence Functionsfor use in Fatigue Analysis", ref. /2/.Joint classification is the process whereby the axial force in agiven brace is subdivided into K, X and Y components ofactions corresponding to the three joint types for which stressconcentration equations exists. Such subdivision normallyconsiders all of the members in one plane at a joint. For pur-poses of this provision, brace planes within ±15° of each othermay be considered as being in a common plane. Each brace inthe plane can have a unique classification that could vary withaction condition. The classification can be a mixture betweenthe above three joint types.Figure B-1 provides some simple examples of joint classifica-tion. For a brace to be considered as K-joint classification, theaxial force in the brace should be balanced to within 10% byforces in other braces in the same plane and on the same side
of the joint. For Y-joint classification, the axial force in thebrace is reacted as beam shear in the chord. For X-joint classi-fication, the axial force in the brace is carried through the chordto braces on the opposite side. Figure B-1 c), e) and h) showsjoints with a combination of classifications. In c) 50% of thediagonal force is balanced with a force in the horizontal in a K-joint and 50% of the diagonal force is balanced with a beamshear force in the chord in a Y-joint. In e) 33% of the incomingdiagonal force is balanced with a force in the horizontal in a K-joint with gap 1 and 67% of the incoming diagonal force is bal-anced with a force in the other diagonal in a K-joint with gap2. In h) 50% of the diagonal force is balanced with a force inthe horizontal on the same side of the chord in a K-joint and50% of the diagonal force is balanced with a force in the hori-zontal on the opposite side of the chord in a X-joint.Definitions of geometrical parameters can be found in FigureB-2. A classification of joints can be based on a deterministic anal-ysis using a wave height corresponding to that with the largestcontribution to fatigue damage. A conservative classificationmay be used keeping in mind that:SCFX > SCFY > SCFK.
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 69
Figure B-1 Classification of simple joints
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 70 see note on front cover
Figure B-2 Definition of geometrical parameters.
saddleD
T
crown crown
L
t
d
ΘT
t
d
D
Θ
Ddβ =
D2Lα =
2TDγ =
Ttτ =
T
BRACE A
D
g
d
BRACE B
A
t A
Bt
dB
AΘΘB
Dd
β AA =
Dd
β BB =
Ttτ A
A =Ttτ B
B =
2TDγ =
Dg=ζ
AB
T
t
d
B
A t
BC
D
B
t
C
d
d
B
B
C
CA
A
A C
ΘΘ Θ
g g
Ddβ A
A = Dd
β BB =
Dd
β CC =
Ttτ A
A =Tt
τ BB =
Tt
τ CC =
2TDγ =
Dgζ AB
AB =D
gζ BCBC =
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 71
The validity range for the equations in Table B-1 to Table B-5is as follows:
Reference is made to Section 4.2 if actual geometry is outsidevalidity range.
0.2 ≤ β ≤ 1.00.2 ≤ τ ≤ 1.08 ≤ γ ≤ 324 ≤ α ≤ 40
20° ≤ θ ≤ 90°
≤ ζ ≤ 1.0sinθ
β0.6−
Table B-1 Stress Concentration Factors for Simple Tubular T/Y Joints
Load type and fixity condi-tions SCF equations Eqn. No. Short chord
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 73
Axial load in one brace only Chord saddle:
(18)
Chord crown:(Eqn.6))Brace saddle:
(19)
Brace crown:(Eqn. (7))In joints with short chords (α < 12) the saddle SCFs can be reduced by the factor F1 (fixed chord ends) or F2 (pinned chord ends) where:
Out-of-plane bending on one brace only:
Chord saddle:(Eqn. (10))Brace saddle:(Eqn. (11))
In joints with short chords (α < 12) eqns. (10)and (11) can be reduced by the factor F3 where:
Table B-2 Stress Concentration Factors for Simple X Tubular Joints (Continued)
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 74 see note on front cover
Table B-3 Stress Concentration Factors for Simple Tubular K Joints and Overlap K JointsLoad type and fixity conditions SCF equation Eqn.
no.Short chord correction
Balanced axial load Chord:
(20) None
Brace:
(21) None
Where:C = 0 for gap jointsC = 1 for the through braceC = 0.5 for the overlapping braceNote that τ, β, θ and the nominal stress relate to the brace under considerationATAN is arctangent evaluated in radians
Unbalanced in plane bending Chord crown:(Eqn. (8))(for overlaps exceeding 30% of contact length use 1.2 · (Eqn. (8)))
Out-of-plane bending brace SCFs are obtained directly from the adjacent chord SCFs using:
where SCFchord = (Eqn. 27)) or (Eqn. (28)) (29)
( ) ( )( ) ( ) ( )( )+−−⋅ AC0.5
CAB0.5
BA x0.8-expγβ0.081x0.8-expγβ0.081(10)) (Eqn.
( ) ( )( ) ( )( )+−⋅ AB0.5maxAB
0.5AB 1.3x-expβ2.050.8x-expγβ0.081(Eqn(10))
( ) ( )( ) ( )( )AC0.5maxAC
0.5AC 1.3x-expβ2.050.8x-expγβ0.081(Eqn(10)) −⋅
A
AABAB β
θsinζ1x +=
( )A
ABBCABAC β
θsinβζζ1x
+++=
( ) ( )( ) ⋅−⋅ 1PAB
0.5AB x0.8-expγβ0.081(10)) (Eqn.
( ) ( )( ) +− 2PBC
0.5C x0.8-expγβ0.081
( ) ( )( ) ( )( )+−⋅ AB0.5maxAB
0.5BA x1.3-expβ2.05x0.8-expγβ0.081(10)) (Eqn.
( ) ( )( ) ( )( )BC0.5maxBC
0.5BC x1.3-expβ2.05x0.8-expγβ0.081(10)) (Eqn. −⋅
B
BABAB β
θsinζ1x +=
B
BBCBC β
θsinζ1x +=
2
B
A1 β
βP ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
2
B
C2 β
βP ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
( ) chord40.050.54 SCFβ0.08β0.470.99γτ ⋅+−−−
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 77
Axial load on one brace only Chord saddle:(Eqn. (5))
Chord crown:(Eqn. (6))
Brace saddle:(Eqn. (3))
Brace crown:(Eqn. (7))
Out-of-plane bending on one brace only
Chord SCF adjacent to diagonal brace A:
where
(30)
Chord SCF adjacent to central brace B:
where
(31)
Out-of-plane brace SCFs Out-of-plane brace SCFs are obtained directly from the adjacent chord SCFs using:
(32)
Table B-5 Stress Concentration Factors for Simple KT Tubular Joints and Overlap KT Joints (Continued)
( ) ( )( ) ( ) ( )( )AC0.5
CAB0.5
BA x0.8-expγβ0.081x0.8-expγβ0.081(10)) (Eqn. −−⋅
A
AABAB β
θsinζ1x +=
( )A
ABBCABAC β
θsinβζζ1x
+++=
( ) ( )( ) ⋅−⋅ 1PAB
0.5AB x0.8-expγβ0.081(10)) (Eqn.
( ) ( )( ) 2PBC
0.5C x0.8-expγβ0.081−
B
BABAB β
θsinζ1x +=
B
BBCBC β
θsinζ1x +=
2
B
A1 β
βP ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
2
B
C2 β
βP ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
( ) chord40.050.54 SCFβ0.08β0.470.99γτ ⋅+−−−
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 78 see note on front cover
APPENDIX C SCF’S FOR PENETRATIONS WITH REINFORCEMENTS
C.1 SCF’s for small circular penetrations with rein-forcement
C.1.1 GeneralStress concentration factors at holes in plates with insertedtubulars are given in Figure C-1 - Figure C-14.Stress concentration factors at holes in plates with ring rein-forcement are given in Figure C-16 - Figure C-19.Stress concentration factors at holes in plates with double ringreinforcement given in Figure C-20 - Figure C-23.The SCFs in these figures may also be used for fatigue assess-ments of the welds. Stresses in the plate normal to the weld ,Δσn; and stresses parallel to the weld, Δτ//, in equation 3.1.4may be derived from the stresses in the plate. The total stressrange, Δσw, from equation 3.1.4 (or from equation 2.3.4) isthen used together with the W3 curve to evaluate number ofcycles until failure.
C.1.2 Example of fatigue analysis of a welded penetration in plateA tubular Φ 800 x 15 is used as a sleeve through a deck plateof thickness 20 mm. The tubular will be welded to the deckplate by a double sided fillet weld.Assume Weibull parameter h = 0.90 and that the deck has beendesigned such that S-N class F3 details can be welded to thedeck plate and still achieves a fatigue life of 20 years. FromTable 5-2 a maximum stress range of 199.6 MPa during 108cycles is derived for the F3 detail.Questions asked:
1) Is the fatigue life of the penetration acceptable withrespect to fatigue cracking from the weld toe?
2) How large fillet weld is required to avoid fatigue crackingfrom the weld root?
The following assessment is made: r/tp = 20, tr/tp = 0.75. It isassumed that H/tr = 5. Then from:Figure C-4 SCF = 2.17 applies to position Figure 3-4 a.Figure C-6 SCF = 0.15 applies to position Figure 3-4 c andweld root.Figure C-8 SCF = 1.07 applies to position Figure 3-4 b andweld toe.Figure C-10 SCF = 0.46 applies to position Figure 3-4 b andweld root.Figure C-12 SCF = -0.75 applies to position Figure 3-4 b and
weld toe.A negative SCF value in some of the figures means that theresulting stress is negative at the hot spot for a positive stressin the plate. Thus for fatigue assessment the absolute valueshould be used.The C-curve applies to position Figure 3-4 a.The D-curve applies to weld toes of Figure 3-4 b.The W3-curve applies to weld root of Figure 3-4 c.Check of fatigue cracking at the Figure 3-4 a position:Δσ = Δσ0 x SCF = 199.6 x 2.17 = 433.13 MPa which is justwithin the acceptable value of 445.5 MPa for a C detail, ref.Table 5-2.Check of fatigue cracking at the Figure 3-4 a b position:Δσ = Δσ0 x SCF = 199.6 x 1.07 = 213.57 MPa which is wellwithin the acceptable value of 320.8 MPa for a D detail, ref.Table 5-2.Thus the fatigue life of weld toe is acceptable.The required throat thickness is calculated as follows. FromTable 5-2 a maximum stress range of 128.2 MPa for a W3detail (Weibull shape parameter = 0.90).Then from considerations of equilibrium in direction normal tothe weld toe:
From considerations of equilibrium in direction parallel withthe weld toe:
Then from equation (3.1.4):
From this equation a required throat thickness is a = 4.0 mm forboth sides of the plate. This is a required weld size that is wellbelow the minimum required weld size specified in ship clas-sification rules.
94.2915.06.199min =⋅==Δ SCFalnon σσ
82.9146.06.199min// =⋅== SCFalnop στ
( ) ( )22 82.912.094.292202.281 +=
a
DET NORSKE VERITAS
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C.1.3 SCF’s for small circular penetrations with reinforce-ments
Figure C-1 SCF at hole with inserted tubular. Stress at outer surface of tubular, parallel with weld. H/tr = 2
H
tp
A A
tr
AA
r
tr
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
100
20
10
r/tp
50
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 80 see note on front cover
Figure C-2 SCF at hole with inserted tubular. Stress at outer surface of tubular, parallel with weld. H/tr = 5
H
tp
A A
tr
AA
r
tr
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
r/tp
100
50
10
20
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 81
Figure C-3 SCF at hole with inserted tubular. Stress in plate, parallel with weld. H/tr = 2
H
tp
A A
tr
AA
r
tr
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
r/tp
100
50
20
10
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 82 see note on front cover
Figure C-4 SCF at hole with inserted tubular. Stress in plate, parallel with weld. H/tr = 5
H
tp
A A
tr
AA
r
tr
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
100
50
20
10
r/tp
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 83
Figure C-5 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 2
H
tp
A A
tr
AA
r
tr
0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
tr/tp
SCF
r/tp
100
50
20
10
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 84 see note on front cover
Figure C-6 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 5
H
tp
A A
tr
AA
r
tr
0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
tr/tp
SCF
r/tp
100
50
20
10
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 85
Figure C-7 SCF at hole with inserted tubular. Principal stress in plate. H/tr = 2
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 87
Figure C-9 SCF at hole with inserted tubular. Shear stress in plate. H/tr = 2
H
tp
A A
tr
AA
r
tr
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
tr/tp
SCF
r/tp
100
50
20
10
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 88 see note on front cover
Figure C-10 SCF at hole with inserted tubular. Shear stress in plate. H/tr = 5
H
tp
A A
tr
AA
r
tr
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
tr/tp
SCF
r/tp
100
50
20
10
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 89
Figure C-11 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 2
H
tp
A A
tr
AA
r
tr
-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
10
50
100
20
r/tp
r/tp
10
20
100
50
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 90 see note on front cover
Figure C-12 SCF at hole with inserted tubular. Stress in plate, normal to weld. H/tr = 5
H
tp
A A
tr
AA
r
tr
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.0 0.5 1.0 1.5 2.0
tr/tp
SCF
10
100
50
20
r/tp
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 91
Figure C-13 SCF at hole with ring reinforcement. Max stress concentration
R
B A AtR
tp
A A
Kg
3.0
3.1
3.2
3.3
3.4
3.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
Kg
tR/tp
0.5
1.5
1.0
The following relation applies(a = throat-thickness): tR/tp a/tR 0.5 0.71 1.0 0.40 1.5 0.33
SC
F
3.0
3.1
3.2
3.3
3.4
3.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
Kg
tR/tp
0.5
1.5
1.0
The following relation applies(a = throat-thickness): tR/tp a/tR 0.5 0.71 1.0 0.40 1.5 0.33
SC
F
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 92 see note on front cover
Figure C-14 SCF at hole with ring reinforcement. Stress at inner edge of ring
R
B A AtR
tp
A A
Kg
1.5
2.0
2.5
3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF
tR/tp
0.5
1.5
1.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 93
Figure C-15 SCF at hole with ring reinforcement. Stress in plate, parallel with weld
tRtp
A A
R
B A A
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.2 0.4 0.6 0.8
B/R
SCF tR/tp
0.5
1.5
1.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 94 see note on front cover
Figure C-16 SCF at hole with ring reinforcement. Shear stress in weld
tRtp
A A
R
B A A
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF
tR/tp
0.5
1.5
1.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 95
Figure C-17 SCF at hole with ring reinforcement. Stress in plate, normal to weld
tRtp
A A
R
B A A
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0.0 0.2 0.4 0.6 0.8
B/R
SCF
0.5
1.5
1.0
tR/tp
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 96 see note on front cover
Figure C-18 SCF at hole with double ring reinforcement. Stress at inner edge of ring
tRtp
A A
R
B A A
1.5
2.0
2.5
3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF
tR/tp
0.5
1.5
1.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 97
Figure C-19 SCF at hole with double ring reinforcement. Stress in plate, parallel with weld
tRtp
A A
R
B A A
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF
tR/tp
0.5
1.51.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 98 see note on front cover
Figure C-20 SCF at hole with double ring reinforcement. Shear stress in weld
tRtp
A A
R
B A A
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF
tR/tp
0.5
1.5
1.0
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 99
Figure C-21 SCF at hole with double ring reinforcement. Stress in plate, normal to weld
tRtp
A A
R
B A A
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B/R
SCF 0.5
1.5
1.0
tR/tp
The following relation applies: tR/tp throat-thickness 0.5 3.5 1.0 4.0 1.5 5.0
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 100 see note on front cover
C.2 SCF’s at man-hole penetrations
C.2.1 GeometryThe following hole geometries are considered see also FigureC-22:
1) Circular cut-out with diameter = 600 mm2) Rectangular cut-out 600 x 800 mm with rounded corner R
= 300 mm3) Rectangular cut-out 600 x 1200 mm with rounded corner
R = 300 mm
Figure C-22 Cut-out geometry
For the three cut-out geometry six different edge reinforce-ments are applied, see Figure C-23. The reinforcement detailsare described below, see also Figure C-23:
(A) Cut-out alone (no reinforcement) (Figure C-23 (A))(B) Cut-out with inserted plate (15 mm thick, 300 mm
wide) around the edge (Figure C-23 (B))(C) Cut-out with double side reinforcement 50 mm away
from the edge (Figure C-23 (C))
(D) Cut-out with single side reinforcement 50 mm awayfrom the edge (Figure C-23 (D))
(E) Cut-out with double side reinforcement 100 mm awayfrom the edge (Figure C-23 (E))
(F) Cut-out with single side reinforcement 100 mm awayfrom the edge (Figure C-23 (F))
Stress concentrations factors are presented for the hot-spotsmarked in Figure C-23.
Figure C-23 Cut-out, reinforcement and hot-spot positions
For geometry (D) and (F), the maximum stresses of the bottomor the top surface in the 20 mm plate at the cut-out edge are
given in the plots. For the other geometry the stresses are sym-metrical about the mid-plane of the plate.
The stresses in the longitudinal and the transverse directionsare applied separately but are combined with shear stress. Theshear stress is varied between zero and up to the value of thenormal stress.
C.2.3 Stress Concentration Factor DefinitionThe definition of the stress concentration factors presented forcut-outs are the maximum principal stress divided by the nom-inal normal stress, σx or σy, (not the nominal principal stress).The maximum principal stress in the hot-spot is selected as themaximum of |σ1| and |σ2|.The stress concentration factor (Kg) is then:
C.3 ResultsIn general, stress concentration factors are given at 5 points(see Figure C-23) except for the cases shown in Figure C-23(A) and (B). The following should be noted:
— Maximum principal stresses are parallel to the weld toe(hot-spots 2 to 5) with only one exception:for double reinforcement and point 2 (see Figure C-23,(C)and (E)), the maximum principal stress is normal to theweld toe.
( ))(
21)(,
;max
yxyxgK
σσσ
=
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 102 see note on front cover
C.3.1 SCFs for Point 1, ref. Figure C-23
Figure C-24 Circular Cut-out Ø = 600 mm, σx and τ
Figure C-25 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
A1
B1
C1
D1
E1
F1
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
A1
B1
C1
D1
E1
F1
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 103
Figure C-26 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
Figure C-27 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σy and τ
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
A1
B1
C1
D1
E1
F1
1.50
2.50
3.50
4.50
5.50
6.50
7.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
A1
B1
C1
D1
E1
F1
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 104 see note on front cover
Figure C-28 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σy and τ
C.3.2 SCFs for Point 2, ref. Figure C-23
Figure C-29 Circular Cut-out Ø = 600 mm, σx and τ stresses for C and E are normal to the weld
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
A1
B1
C1
D1
E1
F1
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
B2
C2
D2
E2
F2
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 105
Figure C-30 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
Figure C-31 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
B2
C2
D2
E2
F2
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
B2
C2
D2
E2
F2
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 106 see note on front cover
Figure C-32 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
Figure C-33 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
B2
C2
D2
E2
F2
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
B2
C2
D2
E2
F2
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 107
C.3.3 SCFs for Point 3, ref. Figure C-23
Figure C-34 Circular Cut-out Ø = 600 mm, σx and τ
Figure C-35 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
B3
C3
D3
E3
F3
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
B3
C3
D3
E3
F3
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 108 see note on front cover
Figure C-36 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
Figure C-37 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σy and τ
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
B3
C3
D3
E3
F3
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σ
Kg=
σ1m
ax/ σ
y
B3
C3
D3
E3
F3
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 109
Figure C-38 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σy and τ
C.3.4 SCFs for Point 4, ref. Figure C-23
Figure C-39 Circular Cut-out Ø = 600 mm, σx and τ
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
B3
C3
D3
E3
F3
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
C4
D4
E4
F4
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 110 see note on front cover
Figure C-40 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
Figure C-41 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
1.50
1.70
1.90
2.10
2.30
2.50
2.70
2.90
3.10
3.30
3.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
C4
D4
E4
F4
1.50
2.00
2.50
3.00
3.50
4.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/ σx
Kg=
σ1m
ax/ σ
x
C4
D4
E4
F4
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 111
Figure C-42 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σy and τ
Figure C-43 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σy and τ
1.00
1.50
2.00
2.50
3.00
3.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
C4
D4
E4
F4
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
C4
D4
E4
F4
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 112 see note on front cover
C.3.5 SCFs for point 5, ref. Figure C-23
Figure C-44 Circular Cut-out Ø = 600 mm, σx and τ
Figure C-45 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σx and τ
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
C5
D5
E5
F5
1.50
2.00
2.50
3.00
3.50
4.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
C5
D5
E5
F5
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 113
Figure C-46 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σx and τ
Figure C-47 Rectangular Cut-out with Rounded Corners: 600 x 800 mm, σy and τ
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
3.80
4.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σx
Kg=
σ1m
ax/ σ
x
C5
D5
E5
F5
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
C5
D5
E5
F5
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 114 see note on front cover
Figure C-48 Rectangular Cut-out with Rounded Corners: 600 x 1200 mm, σy and τ
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
τ/σy
Kg=
σ1m
ax/ σ
y
C5
D5
E5
F5
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 115
APPENDIX D COMMENTARY
D.1 Comm. 1.2.3 Low cycle and high cycle fatigueFatigue strength assessment of offshore structures is normallyunderstood to be the capacity due to high cycle fatigue loading. High cycle loading is normally understood to be cycles of morethan 10 000. For example stress response from wave actionshows typically 5 · 106 cycles a year. A fatigue assessment ofresponse that is associated with number of cycles less than 10000 is denoted low cycle fatigue.This Recommended Practice has been produced with the pur-pose of assessing fatigue damage in the high cycle region. Thespecified S-N curves are shown in the graphs above 104 cycles.Typical S-N test data are derived for number of cycles between104 and 5 · 106 cycles. However, the S-N curves can be linearlyextrapolated to fewer cycles for practical use in a fatigueassessment.High cycle fatigue analysis is based on calculation of elasticstresses that are used in the assessment.Low cycle fatigue is associated with load reversals that implysignificant yielding at the hot spot. Therefore calculated strainis often used as a parameter to account for non-linear materialbehaviour when low cycle fatigue is considered. Offshore structures are normally designed for other limit statessuch as the Ultimate Limit State (ULS). Then a load and mate-rial coefficient is used in design to achieve sufficient safety.Even if stresses due to local notches are not accounted for in anULS design the assessment of ULS imply that the actual strainranges during an ULS loading is limited and that a furtherassessment of low cycle fatigue is not required. Thus fordesign of offshore structures in the North Sea it has not beenpractice to analyse the structures specifically for low cyclefatigue.However, it should be mentioned that low cycle fatigue isfound to be of concern in some local areas in ship structuresdue to loading and unloading. The reason for this is that shipstructures in general show a much higher utilisation in ULSthan offshore structures.If required, a proposed design methodology for low cyclefatigue can be found in the paper: “Low Cycle Fatigue StrengthAssessment for Ship Structures” ref. /43/. FPSOs are rathersimilar structures with similar loading and unloading as tank-ers; therefore low cycle fatigue may be an issue to consider forthese structures depending on procedure used for loading andunloading.
D.2 Comm. 1.3 Methods for fatigue analysisImportant part of action history The contribution to fatigue damage for different regions of aWeibull distribution is shown in Figure D-1 for fatigue damageequal 1.0 (and 0.5) for a 20-year period. The calculation isbased on a Weibull long term stress range distribution withshape parameter h = 1.0 (in the range that is typical for a semi-submersible and an S-N curve with slope m = 3.0 for N < 107
and m = 5.0 for N > 107 cycles (Typical S-N curve for air con-dition).It is noted that the most important part of the long-term stressrange is for actions having a probability of exceedance in therange 10-3 to 10-1. This corresponds to log n = 5-7 in Figure D-1.
Figure D-1 Relative fatigue damage in Weibull distribution of stress ranges
D.3 Comm. 2.2 Combination of fatigue damages from two dynamic processesBackgroundIn some design cases one fatigue damage is calculated for onedynamic process. Then another fatigue damage for the samehot spot is calculated for another dynamic process. Then thequestion arises on how to calculate the resulting fatigue dam-age for the considered hot spot. It is non-conservative to sim-ply add the two fatigue damages together.An example of such a design situation is swell response of anFPSO that also is subjected to wave response.Another example may be wave response of a floating platformthat also may be subjected to wind response on a flare towerthat are giving stress cycling at the same hot spot in the struc-ture. In many cases it is practical to calculate the fatigue dam-age for each of these processes separately as the design maybelong to different engineering contracts.When a detailed stochastic analysis of the complete structuralsystem is performed for each of the dynamic processes a moreaccurate combined stress response can be calculated before theS-N curve is entered and the fatigue damage is calculated. Ref.for example DNV-OS-E301 Position Mooring, June 2001.In the following a simple method for derivation of resultingfatigue damage from two processes is presented. This method-ology is based on information of mean zero up-crossing fre-quency in addition to the calculated fatigue damages for eachof the processes.Combined fatigue damage for one slope S-N curveCombined fatigue damage for the responses shown in FigureD-2 can be obtained as
(1)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 1 2 3 4 5 6 7 8 9
log nR
elat
ive
fatig
ue d
amag
e
Relative damage h = 1.0 and D = 1.0
Relative damage h = 1.0 and D = 0.5
mmmDD
DD⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+−=
/1
2
2
/1
1
12
1
21 )1(
ννν
νν
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 116 see note on front cover
where
The combined fatigue damage is based on the assumption thateach of the fatigue damages D1 and D2 are derived based on aone slope S-N curve. The equation is derived based on analogywith Rainflow stress range counting.
Figure D-2 Sketch showing high and low frequency response and combinedresponse
Combined fatigue damage for two-slope S-N curvesFor two-sloped S-N curves it is questioned if equation (1) canbe used for calculation of resulting fatigue damage.The S-N curves in air have a transition in slope from m = 3.0to m = 5.0 at 107 cycles.
For a long term stress range distribution with Weibull shapeparameter h = 1.0, 20 years service life, and a fatigue damageequal 1.0 the major contribution to fatigue damage occursaround 107 cycles. Approximately half the damage occurs atnumber of cycles below 107 cycles and the other half above107 cycles. For lower fatigue damage than 1.0, which is thecase in order to have acceptable resulting fatigue damage whenconsidering two processes, the main contribution to fatiguedamage will be at the S-N line with slope m = 5.0. Thus, in order to have a methodology that is safe one shoulduse a slope m = 5.0 in equation (1) if the fatigue damages forthe two processes have been calculated based on this two-slopeS-N curve.An alternative to this is to calculate the fatigue damage forprocess no 2 with a straight S-N curve with slope m = 3.0. Thenequation (1) can be used with D1 calculated from a two-slopeS-N curve and with m = 3.0.
D.4 Comm. 2.3.2 Plated structures using nominal stress S-N curvesThe fatigue capacities of welded connections are dependent onthe principal stress range direction relative to the weld toe. Thefollowing guidance is based on assessment of fatigue test data.Figure D-3 a) and b) are intended used for nominal stress anal-yses.The selection of E or F curve for ϕ = 0° depends on thicknessof attachment as presented in Table A-7 in Appendix A. Forother ϕ values see Table D-1.Figure D-3 c) can be used together with the hot spot stressmethodology in general.In general the stress range in both the two principal directionsshall be assessed with respect to fatigue.
D1 = calculated fatigue damage for the high frequency response
D2 = calculated fatigue damage for the low frequency response
ν1 = mean zero up crossing frequency for the high fre-quency response
ν 2 = mean zero up crossing frequency for the low frequency response
m = inverse slope of the S-N curve = 3.0.
Table D-1 Classification of details and selection of S-N curveAngle ϕ in Figure D-3
Detail classified as F for stress direction nor-
mal to the weld
Detail classified as E for stress direction nor-
mal to the weld
S-N curve when using the hot spot stress
methodology0 - 30 F E D30 - 45 E D C245 - 60 D C2 C260 - 75 C2 C2 C2*75 - 90 C2* C2* C2*
* A higher S-N curve may be used in special cases. See Table A-3 for fur-ther information.
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 117
a) Detail classified as F for stress direction normal to theweld (See Table D-1 for ϕ)
b) Detail classified as E for stress direction normal to theweld (See Table D-1 for ϕ)
c) S-N curve when using the hot spot stress methodology(See Table D-1 for ϕ)
Figure D-3 Classification of details and selection of S-N curve
D.5 Comm. 2.4.3 S-N curvesSize effectThe size effect may be explained by a number of differentparameters:
— thickness of plate – which is explained by a more severenotch with increasing plate thickness at the region wherethe fatigue cracks are normally initiated
— attachment length – which is explained by a more severenotch stress due to more flow of stress into a long attach-
ment than a short— volume effect – which for surface defects can be explained
by increased weld length and therefore increased possibil-ity for imperfections that can be initiated into fatiguecracks.
It might be added that some authors group all these 3 effectsinto one group of “thickness effect” or size effect. In this Rec-ommended Practice, the thickness exponent is assumed tocover the first item in the list above and partly the second,although also an increased attachment length reduces the S-Nclass as shown in Appendix 1 of this Recommended Practice.Examples of the third effect and how it can be accounted for inan actual design is explained in more detail in the following.Reference may also be made to /12/, /19/ and /18/ for morebackground and explanation of the thickness effect.Test specimens used for fatigue testing are normally smallerthan actual structural components used in structures. The cor-respondence in S-N data depends on the stress distribution atthe hot spot region. For traditional tubular joints there is onelocal hot spot region, while at e. g. circumferential welds ofTLP tethers there is a length significantly longer than in the testspecimens having the similar order of stress range. Crackgrowth is normally initiated from small defects at the transitionzone from weld to base material. The longer the weld, thelarger is the probability of a larger defect. Thus, a specimenhaving a long weld region is expected to have a shorter fatiguelife than a short weld. This can be accounted for in an actualdesign by probabilistic analysis of a series system, ref. e. g.“Methods of Structural Safety” ref. /21/. Weld length in atether system is one example where such analysis should beconsidered to achieve a reliable fatigue design. A mooring lineconsisting of chains is another example where reliability meth-ods may be used to properly account for the size effect or sys-tem effect. The system effect for the S-N curves in this RP has been inves-tigated using reliability methods. The results are expressedanalytically below.The length of weld and number of similar connections sub-jected to the same stress range should be assessed based onengineering judgement. If a tether system is subjected to adynamic axial force without significant bending the assess-ment becomes simple as all welds will be subjected to the samestress range. As soon as there is some bending over the diam-eter of the tether there will likely be some hot spots at someconnections that are subjected to a larger stress range than theother connections. Then only the regions with the most severestress ranges need to be included for weld length and numberof connections.For threaded bolts, the stress concentration at the root of thethreads increases with increasing diameter. Based on fatiguetests, it is recommended to use k = 0.25 which can be assumedto include size effects both due to the notch itself, and due toincreased length of notch around circumference with increaseddiameter. The thickness exponent may be less for rolledthreads. Thus for purpose made bolts with large diameters, itmay be recommendable to perform testing of some bolts toverify a fatigue capacity to be used for design. It should beremembered that the design S-N data is obtained as meanminus 2 standard deviation in a log S-log N diagram.S-N curve with thickness effectThe design S-N curve with thickness effect included is givenby:Curve part (1), see Figure D-4
C2C2
F F
φ
EEDD
Principal stress direction
Weldtoe
Section
C2C2
F F
φ
EEDD
Principal stress direction
Weldtoe
Section
C2C2
E E
f
DD
Principal stress direction
Weldtoe
Section
C2C2
E E
f
DD
Principal stress direction
Weldtoe
Section
C2C2
D D
φPrincipal stress
direction
Weldtoe
Section
C2C2
D D
φPrincipal stress
direction
Weldtoe
Section
(2)−⎟⎟⎠
⎞⎜⎜⎝
⎛−= loglogaloglog 111 m
ttkmNref
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 118 see note on front cover
Part (2) of the curve is established assuming continuity atN1=106 or 107 cycles depending on the S-N curve is given forseawater with cathodic protection or in air is given by
where is for S-N curve without thickness effect included.log is given in Table 2-1, 2-2 and 2-3.Part (2) of the S-N curve can also be written on a standard form
where
S-N curve with system effect and thickness effectThe design S-N curve with system effect and thickness effectincluded is given by:Curve part (1), see Figure D-4
where
Part (2) of the curve is established assuming continuity atN1=106 or 107 cycles depending on the S-N curve is given forseawater with cathodic protection or in air is given by
with
where is for S-N curve without thickness effect included.log is given in Table 2-1, 2-2 and 2-3.
Figure D-4 Typical S-N curve with thickness effect included
(3)
(4)
(5)
(6)
σΔ−⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−+= logloglog1aloglog 221
1
21
1
2 mttkmN
mm
mm
Nref
1a1a
σΔ−⎟⎟⎠
⎞⎜⎜⎝
⎛−= loglogaloglog 222 m
ttkmNref
11
21
1
22 log1alogalog N
mm
mm
⎟⎟⎠
⎞⎜⎜⎝
⎛−+=
σΔ−⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟
⎟⎠
⎞⎜⎜⎝
⎛−= logloglog1.0aloglog 111 m
ttkmn
ll
Nref
sref
weld
lweld = length of weld subjected to the same stress rangelref = reference length corresponding to typical length of
weld in tested specimen used for derivation of S-N curve. = 100 mm may be used.
ns = number of similar connections subjected to the same stress range
(7)
(8)
σΔ−⎟⎟⎠
⎞⎜⎜⎝
⎛−= loglogaloglog 222 m
ttkmNref
11
21
1
22 log1log1.0alogalog N
mm
nll
mm
sref
weld⎟⎟⎠
⎞⎜⎜⎝
⎛−+⎟
⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
1a1a
10
100
1000
1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08
Number of cycles
Stre
ss ra
nge
(MP
a)
2
1
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 119
Link to S-N curves in other design codesThe relationship between S-N curves in this document andthose given by IIW, ref. /30/, Eurocode 3, ref. /3/, for air envi-ronment is given in Table D-1. It should be noted that the cor-respondence between S-N curves in this document and IIWrelates only to number of cycles less than 5·106 in Eurocode 3.
D.6 Comm. 2.4.9 S-N curves and efficiency of corro-sion protectionS-N curve for joints in the splash zoneIn Norway it has been the practice to use seawater S-N curvewith cathodic protection for joints in the splash zone and alarger Design Fatigue Factor (DFF) in the splash zone than inother areas in jacket structures. It is assumed that the joints alsohave a good coating.A high DFF is used because it is considered to be difficult toperform inspection and repair in this area. Increasing the DFFimplies that the probability of a fatigue cracking becomesreduced. For example a DFF = 10 implies that the probabilityof a fatigue crack during the lifetime becomes very small(accumulated probability less than 10-4 and annual less than10-5 the last year in service). Quite a lot of the fatigue life is associated with initiation of afatigue crack and growth of small cracks. The cracks have togrow to some size before the coating is broken. As long as thecoating is not broken the condition corresponds to that of air.The probability of having a fatigue crack that is so large thatthe coating is broken is considered to be low within the majorpart of the design life using a DFF = 10. Based on this it is considered acceptable to calculate fatiguedamage with an S-N curve that is somewhat reduced comparedwith that of air. Then the seawater curve with cathodic protec-tion can be used in lack of documented S-N curves in seawaterin free corrosion for coated joints (in the high cycle regionabove 106 cycles). This recommendation is linked to use of a high DFF and a goodcoating. Then the probability of presence of an open fatiguecrack subjected to free corrosion becomes small in the majorpart of the service life of the platform life as explained above.S-N curve for details in tanks in FPSOsTanks in FPSOs are not designed with the same high DFF asused for splash zone joints in jackets. Also the coating is not sodurable. The coating becomes more brittle with time and it ismost likely to crack at hot spot regions with large strain cycles.In tanks without anodes the efficiency of the coating should be
specially considered.In DNV Classification Note No. 30.7 it is assumed that thecoating is efficient for some years and then the condition is thatof free corrosion. A similar procedure may be used for designof tanks in FPSOs. The time with efficient coating depends ontype and quality of the coating used. Reference is made toDNV Classification Note No. 30.7 for more details.
D.7 Comm. 2.9.3 SCFs for pipes with internal pres-sureThe following sections can be used for fatigue assessment ofpipelines or cylinders used for transportation of gas subjectedto high pressure where low cycle fatigue from loading andunloading are considered.Tapered thickness transitionsFor tapered thickness transitions in pipes and cylinders asshown in Figure D-5 the bending stress over the wall thicknessat the weld is mainly due to the axial stress in the pipe wall.This means that at thickness transitions the stress concentra-tion factors presented in section 3.3.7 can be used directlytogether with the nominal stress in the pipe wall for calculationof hot spot stress at the weld. Nominal stress in the pipe walldue to global bending moment can be calculated based on sec-tion modulus at the mid wall pipe section.
Figure D-5 Tapered thickness transition in pipe or cylinder
Thickness transitions with step in thicknessA transition with a step in thickness from t1 to t2 in a pipe orcylinder as shown in Figure D-6 is considered. It is assumedthat the radius of the pipe or cylinder r » t1. The stress due tothe end cap pressure is calculated as:
The total stress at the inner side and the outer side is calculated as:
This equation can also be written as:
where the stress concentration factor for the inner side is:
Table D-2 DNV notation in relation to Eurocode 3DNV notation IIW and Eurocode 3 notation
B1 160B2 140C 125
C1 112C2 100D 90E 80F 71F1 63F3 56G 50
W1 45W2 40W3 36T
(9)
σt = σa ± σb (10)
(11)
(12)
t2 t1
14
p
t2 t1
14
p
12 trp
a =σ
SCFaa
bat σ
σσσσ =⎟⎟
⎠
⎞⎜⎜⎝
⎛±= 1
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−−+=
2
12 1
1321
ttSCF
νγν
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 120 see note on front cover
and the stress concentration factor for the outer side of the pipe is:
The γ is defined as:
Figure D-6 Thickness transition in pipe or cylinder
Ring stiffeners at supports in storage tanks and at flange con-nections in risersA ring stiffener in a cylinder as shown in Figure D-7 is consid-ered. This applies also to a bolted flange connection that is fre-quently used in risers for oil and gas production, ref. FigureD-8 where the most critical hot spot is found at point B.The stress concentration at a ring stiffener is obtained as:
where the plus sign applies to the inner side and minus to theouter side. This stress concentration includes effect from inter-nal pressure and end cap pressure. It is to be used together withthe nominal stress acting in the axial direction of the pipe walldue to end cap pressure.β is defined as:
With ν = 0.3 for steel the expression for β becomes:
and the stress concentration factor for the inner side becomes:
and the stress concentration factor for the outer side becomes:
Due to the notch of the weld itself the fatigue strength of theweld at the ring stiffener itself becomes less than for the othershell side. As the stress is lesser on the outside than at theinside it is thus recommended to place ring stiffeners on theoutside of a shell structure subjected to internal pressure. Thisis a different conclusion from that of ring stiffeners in tubularmembers subjected to pure external axial force, ref. /25/.
Figure D-7 Ring stiffener on cylinder with internal pressure
Figure D-8 Section through bolted flange connection
Longitudinal welds with bending stress over the pipe wallresulting from out-of-roundness of fabricated pipesThe out-of-roundness of fabricated pipe elements results inincreased stress due to a bending moment over the wall thick-ness, see Figure D-9. The eccentricity due to out-of-roundnessis a function of tension in the hoop direction of the pipe. Thiseccentricity is reduced as the internal pressure is increased andthe hoop tension is increased. Thus the bending stress over thewall thickness is a non-linear function of the internal pressure. It is assumed that the out-of-roundness results in an eccentric-ity δ0 without any hoop tension force from internal pressure.In terms of out of roundness the equation for stress concentra-tion factor can be derived as:
where the out of roundness is defined as δOOR = dmax- dmin,l = πd/8 and λ which is a function of the membrane hoop stressσm is defined as follows:
Tolerance requirements for pipelines are given in DNV-OS-F101 (2001).
(13)
(14)
(15)
(16)
(17)
(18)
(19)
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−−−=
2
12 1
1321
tt
SCFνγ
ν
( )11
22
2
1
5.1
2
121
5.02
5.22
5.22
5.21 −⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+
−+
=tt
tt
tttttγ
t2 t1
p
t2 t1
p
βνν 1
1
)2(312−
−±=SCF
4 2 )1(3
21
νβ
−+=
rA
trt
rAtrt56.1
1+=β
β087.31+=SCF
β087.31−=SCF
(20)
(21)
p
B
p
B
)(tanh5.1
1 llt
SCF OOR λλδ
+=
2
12tE
mσλ =
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 121
Figure D-9 Section through pipe showing out-of-roundness and analysismodel
D.8 Comm. 3.3 Stress concentration factorsReference is made to “An Analytical study of Stress Concen-tration Effects in Multibrace Joints under Combined Loading”,ref. /9/, for further background on this procedure of calculatinga resulting hot spot stress from superposition of stress compo-nents.The formula for SCF at a tubular butt weld can be outlinedbased on theory for thin walled structures, ref. /25/.
D.9 Comm. 3.3.3 Tubular joints welded from one side The fatigue design of the root area of tubular joints weldedfrom one side may be considered as follows:
— Lack of penetration is hard to control by non-destructiveexamination and it is considered more difficult to detectpossible defects at a root area of a tubular joint weldedfrom one side, than for a butt weld welded from one side.
— For butt welds welded from one side the joint may be clas-sified as F3. The defect size inherent in this curve is lessthan 1-2 mm (This defect size may be evaluated by frac-ture mechanics calculations and the calculated value willdepend on plate thickness. A long defect should be consid-ered here with the defect size measured in the thicknessdirection of the tubular). Defect sizes up to 5 mm may bepresent without being detected even with a detailed exam-ination of the root of a tubular joint. A factor for reductionof fatigue life due to a possible large root defect in a tubu-lar joint compared to a butt weld may be evaluated basedon fracture mechanics analysis.
— The stress field at the root may be derived from a finite ele-ment analysis. The crack growth may be assumed to benormal to the direction of the maximum principal stress.The fatigue life is first calculated for an initial defect sizecorresponding to that of the F3 curve: F(Life ai = 1 mm).Then the fatigue life is calculated for an initial defect sizecorresponding to that of a tubular joint welded from oneside: F(Life ai = 5 mm). The fatigue life reduction factor,R, is obtained from equation (22).
— A modified S-N curve below F3 is calculated from equa-tion (23). An S-N curve corresponding to this log a value(or below) may now be used for fatigue life analysis basedon nominal stress at the root as calculated by a detailedfinite element analysis.
— Fatigue cracking from the root is harder to discover by inservice inspection than crack growth from the toe. There-fore, an additional factor on fatigue life should be consid-ered for crack growth from the root.
The following simplified approach for fatigue life assessmentof the weld root may be performed as an alternative procedure:
— As noted above an additional factor on fatigue life shouldbe considered for crack growth from the root.
— Normally the stress on the outside of the brace at the hotspot is larger than at the root area. Hence it is consideredto be conservative to use the brace SCF for evaluation offatigue life at the root. As an approximation the SCF forthe inside can be calculated as
— The fatigue life for the root may now be calculated usingthe W3 curve.
This procedure is applicable for simple tubular joints only.
D.10 Comm. 4.1 The application of the effective notch stress method for fatigue assessment of struc-tural detailsGeneralEffective notch stress is the total stress at the root of a notch,obtained assuming linear-elastic material behaviour. To takeaccount of statistical nature and scatter of weld shape parame-ters, as well as of non-linear material behaviour at the notchroot, the real weld is replaced by an effective one, ref. FigureD-10. For structural steels an effective notch root radius ofr = 1.0 mm has been verified to give consistent results. Forfatigue assessment, the effective notch stress is compared witha common fatigue resistance curve.The method is restricted to welded joints which are expected tofail from the weld toe or weld root. Other causes of fatigue fail-ure, e.g. from surface roughness or embedded defects, are notcovered. Also it is not applicable where considerable stresscomponents parallel to the weld or parallel to the root gapexist.The method is well suited to the comparison of alternativegeometries. Unless otherwise specified, flank angles of 30o forbutt welds and 45° for fillet welds are suggested.The method is limited to thicknesses t ≥ 5 mm. For smallerwall thicknesses, the method has not been verified.In cases where a mean geometrical notch root radius can bedefined, e.g. after certain post weld improvement proceduressuch as grinding, the actual geometrical radius may be used inthe effective notch stress analysis. Then the calculated notchstress should be entered into a relevant S-N curve. Referenceis made to Table A-5 in Appendix A for potential fatigue crackgrowth from ground areas at welded regions.
Figure D-10 Analysis of effective notch stress
Calculation of Effective Notch StressEffective notch stresses or notch stress concentration factors
(22)
(23)
Inflection point
dl = pd/8
Maximum bending moment
Inflection point
dl = pd/8
Maximum bending moment
mm)1aF(Lifemm)5aF(LifeR
i
i
==
=
(R)log11.546alog +=
(24)2.0SCFSCF braceinside −=
Radius=1mm
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 122 see note on front cover
can be calculated by parametric formulae, taken from diagramsor calculated from finite element analysis. The effective notchradius is introduced such that the tip of the radius touches theroot of the real notch, e.g. the end of an un-welded root gap.Calculation of effective notch stress by the finite elementmethod requires that a fine element mesh is used around thenotch region. The effective notch stress to be used togetherwith the recommended S-N curve is the maximum calculatedsurface stress in the notch. This maximum surface stress maybe obtained directly from the nodal stress calculated at the sur-face or from extrapolation of element stresses to the surface. Insome finite element programs it may also be efficient to addbar elements with a small area (negligible area) along the notchsurface. Then the surface stress is finally derived as force in thebar divided by area.The requirement to mesh size is depending on elements used.If elements with quadratic displacement functions are used, aminimum of 4 elements should be used along a quarter of thecircle circumference. If simpler elements are used the meshrefinement should be improved correspondingly. The meshshould be made with regular elements without transition toreduced refinement within the first three element layers fromthe notch surface. An element shape that is close to “quadratic”is preferred.In case of uncertainty about elements ability to provide reliablesurface stress it is recommended to perform a validation of themethodology against a well known case.Notch Stress S-N CurvesThe calculated notch stress should be linked to a notch stressS-N curve for fatigue design as described in Table D-3. The S-N curves are presented as mean minus two standard deviationsin logarithmic S-N format.The thickness effect is assumed accounted for in the calculatednotch stress. Thus a further reduction of fatigue capacity forlarger thicknesses is not required.The S-N curve is presented on the standard form
where
Validation of Analysis MethodologyThe notch stress concept using finite element analysis can bevalidated against a well tested detail that also can be assessedbased on nominal stress approach.A cruciform joint may be selected for analysis as shown in Fig-ure D-11 and Figure D-12.The F curve may be used for fatigue assessment of the weld toeusing the nominal stress approach. Then a target notch stress at the weld root is obtained as 3.17times the nominal stress in the plate.A fillet welded cruciform joint may be selected for analysis asshown in Figure D-13 and Figure D-14. Then the W3 curvemay be used for fatigue assessment of the weld root using thenominal stress approach. The nominal stress in the weld isderived as:
where
Then a target notch stress in the weld root is obtained as 6.25times the nominal stress in the fillet weld.If the calculated stress from validation analyses is far from thetarget values, it is recommended to consider the accuracy ofthe methodology used such as type of element in relation tomesh refinement and read out of notch surface stress.The toe of the same detail would be classified as F3. This resultin a target notch stresses 3.57 times the nominal stress.
Figure D-11 Geometry for validation of analysis procedure for the weld toe
(25)
= intercept of the design S-N curve with the log N axism = negative inverse slope of the S-N curve
Table D-3 Notch stress S-N curvesEnvironment Log Air N ≤ 107 cycles
m1 = 3.0N > 107 cyclesm2 = 5.0
13.358 17.596Seawater with cathodic protection
N ≤ 106 cyclesm1 = 3.0
N > 106 cyclesm2 = 5.0
12.958 17.596Seawater with free corrosion For all N log = 12.880 and m1 = 3.0
mLogSaLogLogN −=
a
a
a
(26)
t = thickness of membera = throat thickness
atw 2/Nominalσσ =
t
t
Nominalσ
45°t/2
t
t
Nominalσ
45°t/2
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 123
Figure D-12 Geometry of the transition from weld to base material to be usedin the analysis
Figure D-13 Detail selected for validation of procedure for root of fillet welds
Figure D-14 Notch to be included in FE model for the weld root
D.11 Comm. 4.3.8 Verification of analysis methodol-ogy for FE hot spot stress analysisSpecimens for verification of analysis methodology are shownin Figure D-15 - Figure D-20. The hot spot stress analysis methodology may be verifiedbased on analysis of these details with derived target hot spotstress.Loading on the specimens for calculation of hot spot stress isshown in Table D-4.The target hot spot stresses for the specified load cases arelisted in Table D-5.A correction factor to be applied to the analyses may be estab-lished if the calculated hot spot stress in general is differentfrom the target hot spot stress. This correction factor isobtained as
r =1mm
t
a t
σ Nominal
t = 16 mma = 8 mm
(27)
Table D-4 Loading on the specimensSpecimen Position of loading Nominal stress1 Stress in the axial direction over
end area equal 0.667 MPa (= 900 mm2)
1.00 MPa
2 Stress in the axial direction over end area equal 0.667 MPa (= 900 mm2)
1.00 MPa
3 Stress in the axial direction over end area equal 0.700 MPa (= 1000 mm2)
1.00 MPa
4 Point load 119 N above bracket in cantilever at a distance 625 mm from the support plate in test rig
Nominal stress at weld toe to be calcu-lated as bending moment calculated in this section divided by the elastic section modulus in this sec-tion. The specified point load is made to provide a nominal stress at this position equal 1.00 MPa.
5 Point load 123 N above bracket in cantilever at a distance 435 mm from the support plate in test rig
6 Stress in the axial direction of plate equal 1.00 MPa
1.00 MPa
CalculatedspotHot
TargetspotHot
σσ
=f
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 124 see note on front cover
Figure D-15 Specimen 1
Table D-5 Target hot spot stress values/stress concentrations linked to the D curve
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 125
Figure D-16 Specimen 2
Figure D-17 Specimen 3
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 126 see note on front cover
Figure D-18a) Specimen 4
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 127
Figure D-18 b) Specimen 4
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 128 see note on front cover
Figure D-19 Specimen 5
DET NORSKE VERITAS
Amended October 2008 Recommended Practice DNV-RP-C203, April 2008see note on front cover Page 129
Figure D-20 Specimen 6 Thickness all plates t = 50 mm.
D.12 Comm. 5 Simplified fatigue analysisWeibull distributed Stress Range and Bi-linear S-N curvesWhen a bi-linear or two-slope S-N curve is used, the fatiguedamage expression is given by
where
For definitions and symbols see also sections 1.4, 1.5 and 5.1.Alternatively the damage may be calculated by a direct inte-gration of damage below each part of the bilinear S-N curves:
where the density Weibull function is given by
S-N curves for air condition are assumed here such that thecrossing point of S-N curves is here at 107 cycles. The stressrange corresponding to this number of cycles is
The left part of S-N curve is described by notation 1, while theright part is described by notation 2.Short term Rayleigh distribution and linear S-N curveWhen the long term stress range distribution is defined througha short term Rayleigh distribution within each short termperiod for the different loading conditions, and a one-slope S-N curve is used, the fatigue criterion reads,
where
The Gamma function, is equal to 1.33 for m = 3.0.
500
1500
500
50
To be welded to test machine
Plate 500x725
Full penetration weld
Partial penetration
Plate 500x500
500
1500
500
50
To be welded to test machine
Plate 500x725
Full penetration weld
Partial penetration
Plate 500x500
500
1500
500
50
To be welded to test machine
Plate 500x725
Full penetration weld
Partial penetration
Plate 500x500
(28)
S1 = Stress range for which change of slope of S-N curve occur
= S-N fatigue parameters for N < 107 cycles (air condition)
= S-N fatigue parameters for N > 107 cycles (air condition)
γ( ) = Incomplete Gamma function, to be found in standard tables
Γ( ) = Complementary Incomplete Gamma function, to be found in standard tables
(29)
(30)
(31)
ηqS
;hm
1γaq
qS
;h
m1Γ
aq
TνDh
12
2
mh
11
1
m
d0
21
≤⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛++⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+=
11 m ,a
22 m ,a
dS(S)N
h),Δσ(S,fTvdS
(S)Nh),Δσ(S,fTv
D0
1
1 Δσ
S 1
0d0S
0 2
0d0 ∫∫ +=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
− h
0h
0
1h
0 h),q(ΔSexp
h),q(ΔShh),Δσf(S,
σσ
1/h0
00
))(ln(nh),q(Δ
σσ
Δ=
(32)
(33)
rij = the relative number of stress cycles in short-term condition i, j
νo = long-term average zero-up-crossing-frequency (Hz)moij = zero spectral moment of stress response process
1m1
71
1 10aS ⎟
⎠⎞
⎜⎝⎛=
η)2m(2r)2mΓ(1
aTν
Dheadings allseastates all
1j1,i
m0ijij
d0 ≤∑⋅+===
)2mΓ(1+
DET NORSKE VERITAS
Recommended Practice DNV-RP-C203, April 2008 Amended October 2008Page 130 see note on front cover
Short term Rayleigh distribution and bi linear S-N curveWhen a bi-linear or two-slope S-N curve is applied, the fatiguedamage expression is given as,
Example Fatigue analysis of a drumA drum used for transportation of equipment is assessed withrespect to fatigue. Reference is made to Figure D-21. The max-imum allowable tension force in the wire on the drum is to bedetermined. There are three different spaces for wire on thedrum, separated by external ring stiffeners 200 × 20 mm. Thering stiffeners are welded to the drum by double sided filletwelds. The highest bending stress in the drum occurs when thewire is at the centre of the drum. Then the reaction force at eachsupport becomes equal P/2 and the maximum bending momentat the highest stressed ring stiffener is Pa/2. When the drum isrotated 180 degrees the bending moment at the same positionis reversed and the range in bending moment is derived as
The section modulus for the drum is calculated as
where D = diameter = 600 mm and t = thickness = 20 mm.Then W = 5114·103 mm3.For the outside of the drum a stress concentration factor is cal-culated from section 3.3.8
The nominal stress at the outside of the drum at the consideredring stiffener is obtained as:
The distance from the drum support to the considered ringstiffener a = 1200 mm.A Design Fatigue Factor of 2 is specified: DFF = 2.
The number of rotations of the drum is not specified and is con-sidered to be uncertain. Therefore a stress range below the con-stant amplitude fatigue limit is aimed for. The detailclassification is found from Table D-7 detail 8: The classifica-tion is E.Then the allowable stress range is obtained from Table 2-1 foran E -detail and from section 2.10 as
Then the maximum tension force is derived as
Figure D-21 Drum for transportation
Comm. 7 Improvement of fatigue life by fabricationReference is made to “Recommendations on Post weldImprovement of Steel And Aluminium Structures”, ref. /16/,for effect of weld improvements on fatigue life. Reference isalso made to “API Provisions for SCF, S-N, and Size-ProfileEffects”, ref. /22/, for effect of weld profiling on thicknesseffect. Reference is made to “Fatigue of Welded Joints PeenedUnderwater”, ref. /13/, for fatigue of welded joints peenedunderwater.