CN 30-7

CLASSIFICATION NOTESNo. 30.7

FATIGUE ASSESSMENT OF SHIP STRUCTURES

JUNE 2010DET NORSKE VERITASVeritasveien 1, NO-1322 Hvik, Norway Tel.: +47 67 57 99 00 Fax: +47 67 57 99 11

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, prop-erty and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancyservices relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out researchin relation to these functions.Classification NotesClassification Notes are publications that give practical information on classification of ships and other objects. Examples of de-sign solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some componentsare given as interpretations of the more general rule requirements.All publications may be downloaded from the Societys Web site http://webshop.dnv.com/global/.The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note.This edition replaces the October 2008 edition of Classification Note 30.7.

Main ChangesThe following topics have been included or changed: A table of stress reduction factors to be used if principal stress direction is parallel with the weld line, is included. Analysis guidance for bent hopper knuckle type is included. Guidance on post weld treatment for low cycle fatigue is included. The validity of the S-N curve is elaborated. It is states that the curves is also valid for duplex, and austenitic steels.The electronic pdf version of this document found through http://www.dnv.com is the officially binding version Det Norske Veritas

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Classification Notes - No. 30.7, June 2010Page 3

CONTENTS

1. GENERAL................................................................. 51.1 Introduction..................................................................51.2 Validity of Classification Note ...................................51.3 Methods for fatigue analysis........................................51.4 Guidance to when a detailed fatigue analysis can be

omitted .........................................................................61.5 Definitions ...................................................................61.6 Symbols and abbreviations ..........................................72. ANALYSIS OF FATIGUE CAPACITY ............... 92.1 Introduction..................................................................92.2 Fatigue damage accumulation .....................................92.3 Fatigue analysis methodology and calculation of

stresses ......................................................................102.4 S-N curves .................................................................112.5 Effect of corrosive environment ................................132.6 Fatigue damage from multiple loading conditions ....133. FATIGUE ANALYSIS OF SHIPS........................ 143.1 General.......................................................................143.2 Oil tankers..................................................................143.3 Gas carriers ................................................................143.4 Bulk carriers...............................................................153.5 Container Ships .........................................................163.6 Roll on / Roll off- and Car carriers............................174. SIMPLIFIED FATIGUE CALCULATIONS ...... 174.1 General.......................................................................174.2 Calculation procedure................................................174.3 Long term distribution of stresses .............................174.4 Definition of stress components ................................184.5 Calculation of stress components ..............................184.6 Combination of stresses.............................................184.7 Cumulative damage ...................................................195. SIMPLIFIED STRESS ANALYSIS ..................... 205.1 General.......................................................................205.2 Hull girder bending....................................................205.3 Bending of girder systems .........................................205.4 Local stiffener bending ..............................................205.5 Local plate bending....................................................226. SIMPLIFIED WAVE LOAD

CALCULATIONS .................................................. 226.1 General.......................................................................226.2 Wave induced hull girder bending moments .............236.3 External pressure loads ..............................................236.4 Internal pressure loads due to ship motions...............246.5 Ship accelerations and motions .................................257. SPECTRAL FATIGUE CALCULATIONS......... 267.1 General.......................................................................267.2 Cumulative damage ...................................................267.3 Component stochastic analysis ..................................277.4 Full stochastic analysis ..............................................288. WAVE LOADING BY DIRECT

CALCULATIONS .................................................. 298.1 General ......................................................................298.2 Hydrodynamic modelling ..........................................298.3 Transfer functions......................................................298.4 The long-term distribution ........................................299. FINITE ELEMENT ANALYSIS .......................... 319.1 Finite element models................................................319.2 Load cases..................................................................329.3 Global hull analysis ...................................................339.4 Cargo hold analysis....................................................339.5 Frame and girder models ...........................................359.6 Local structure models...............................................359.7 Stress concentration models ......................................36

10. CALCULATION OF HOT SPOT STRESS BY FINITE ELEMENT ANALYSIS.......................... 36

10.1 Stress field at a welded detail .................................... 3610.2 FE modelling ............................................................. 3710.3 Derivation of hot spot stress...................................... 3710.4 Derivation of stress at read out points 0.5t and 1.5t .. 3810.5 Hot spot S-N curve.................................................... 3810.6 Derivation of effective hot spot stress from FE

analysis ...................................................................... 4210.7 Procedure for analysis of web stiffened cruciform

connections ............................................................... 4210.8 Hot spot stress concept for simple connections ........ 4410.9 Verification of analysis methodology ....................... 4411. IMPROVEMENT OF FATIGUE LIFE

BY FABRICATION............................................... 4511.1 General ...................................................................... 4511.2 Weld toe grinding...................................................... 4511.3 TIG dressing .............................................................. 4511.4 Hammer peening ....................................................... 4512. REFERENCES ....................................................... 46

APPENDIX ASTRESS CONCENTRATION FACTORS ..................... 47

APPENDIX BFATIGUE DESIGN TABLES.......................................... 72

APPENDIX CEXAMPLE OF APPLICATION - SIMPLIFIED CALCULATION METHOD ............................................ 75

APPENDIX DSIMPLIFIED LOADS FOR DIRECT STRENGTH ANALYSIS ......................................................................... 88

APPENDIX ESIMPLIFIED CALCULATION OF THE COMBINED LONGITUDINAL STRESS IN SHIPS WITH LARGE HATCH OPENINGS......................................................... 89

APPENDIX FWORKMANSHIP AND LINK TO ANALYSIS PROCEDURES.................................................................. 92

APPENDIX GS-N CURVE FATIGUE DAMAGE EXPRESSIONS .... 94

APPENDIX HUNCERTAINTIES IN FATIGUE LIFE PREDICTIONS ................................................................. 95

APPENDIX ILOW CYCLE FATIGUE ................................................. 97

APPENDIX JWAVE INDUCED HULL GIRDER VIBRATIONS .. 107

APPENDIX KDERIVATION OF EFFECTIVE HOT SPOT STRESS ........................................................................... 108DET NORSKE VERITAS

Classification Notes - No. 30.7, June 2010 Page 4DET NORSKE VERITAS


1. General1.1 Introduction

1.1.1 Fatigue cracks and fatigue damages have been known to shipdesigners for several decades. Initially the obvious remedy wasto improve detail design. With the introduction of higher ten-sile steels (HTS-steels) in hull structures, at first in deck andbottom to increase hull girder strength, and later on in localstructures, the fatigue problem became more imminent.

1.1.2 In the DNV Rules for Classification of Ships, the material fac-tor f1, which gives the ratio of increase in allowable stresses asa function of the material yield point was initially introducedin 1966. The factor is varying with the yield point at a lowerthan linear rate in order to give some (but insufficient) contri-bution to the general safety against fatigue fracture of highertensile steels. However, during recent years a growing numberof fatigue crack incidents in local tank structures made fromHTS steels have demonstrated that a more direct control of fa-tigue is needed.

1.1.3 This Classification Note is intended to give a general back-ground for the rule requirements for fatigue control of shipstructures, and to provide detailed recommendations for suchcontrol. The aim of the fatigue control is to ensure that all partsof the hull structure subjected to fatigue (dynamic) loadinghave adequate fatigue life. Calculated fatigue lives, calibratedwith the relevant fatigue damage data, may give the basis forthe structural design (steel selection, scantlings and local de-tails). Furthermore, they can form the basis for efficient in-spection programs during fabrication and throughout theservicelife of the structure.

1.1.4 To ensure that the structure will fulfil its intended function, fa-tigue assessment, supported where appropriate by a detailedfatigue analysis, should be carried out for each individual typeof structural detail subjected to extensive dynamic loading. Itshould be noted that every welded joint and attachment or oth-er form of stress concentration is potentially a source of fatiguecracking and should be individually considered.

1.2 Validity of Classification Note

1.2.1 This Classification Note includes procedures for evaluation offatigue strength, but not limited to, for the following:

steel ship structures excluding high speed light crafts foundations welded to hull structures any other areas designated primary structures on the draw-

ings of ship structures attachment by welding to primary ship structures, such as

double plates, etc.

The procedures do not include provisions for taking directlyinto account effect on the fatigue strength by wave inducedhull vibrations. Guidance on how to take into account the fa-tigue effect of wave induced vibrations for full body vesselsunder North Atlantic and world wide wave conditions based onfull scale measurements is however presented in Appendix J Wave induced hull girder vibrations. The same fatigue effectby wave induced vibrations is suggested to be considered alsofor other ships types, in lieu of relevant available data. The ad-ditional fatigue effect of wave induced vibrations on specificroutes of operation may be predicted based on weather data for

Guidance on how to take into account the effect on fatiguestrength by low cycle fatigue (repeated yielding), e.g. as occur-ring during the cargo ballast loading cycles is presented inAppendix I Low cycle fatigue. This Classification Note may be adapted for modification toexisting ship structures, subject to the limitations imposed bythe original material and fabrication techniques.This Classification Note is valid for C-Mn steels, duplex andsuper duplex steels and austenitic steels with yield stress lessthan 500 MPa.

1.3 Methods for fatigue analysis

1.3.1 Fatigue design may be carried out by methods based on fatiguetests (S-N data) and estimation of cumulative damage (Palm-gren - Miners rule).

1.3.2 The long term stress range distribution is a fundamental re-quirement for fatigue analysis. This may be determined in var-ious ways. This Classification Note outlines two methods forstress range calculation:

1) A postulated form of the long-term stress range distribu-tion with a stress range based on dynamic loading as spec-ified in the rules.

2) Spectral method for the estimation of long-term stressrange.

In the first method a Weibull distribution is assumed for thelong term stress ranges, leading to a simple formula for calcu-lation of fatigue damage. The load effects can be derived di-rectly from the ship rules. The nominal stresses have to bemultiplied by relevant stress concentration factors for calcula-tion of local hotspot stresses before entering the S-N curve.The second method implies that the long-term stress range dis-tribution is calculated from a given (or assumed) wave climate.This can be combined with different levels of refinement ofstructural analysis. Thus a fatigue analysis can be performed based on simplifiedanalytical expressions for fatigue lives or on a more refinedanalysis where the loading and the load effects are calculatedby numerical analysis. The fatigue analysis may also be per-formed based on a combination of simplified and refined tech-niques as indicated by the diagonal arrows in Figure 1-3.

1.3.3 The requirement to analysis refinement should be agreed uponbased on

experience with similar methods on existing ships andstructural details with respect to fatigue

consequences of a fatigue damage in terms of serviceproblems and possible repairs.

In general, the simplified method for fatigue life calculation isassumed to give a good indication as to whether fatigue is asignificant criterion for design or not. The reliability of the cal-culated fatigue lives is, however, assumed to be improved byrefinement in the design analysis.

1.3.4 It should further be kept in mind that real fatigue lives are afunction of workmanship related to fabrication and corrosionprotection. Therefore, to achieve the necessary link betweenthe calculated and the actual fatigue lives for ships, the fabri-cation has to be performed according to good shipbuildingDET NORSKE VERITAS

the route, as available. practice with acceptance criteria as assumed in the calculation.

Classification Notes - No. 30.7, June 2010 Page 6

1.4 Guidance to when a detailed fatigue analysis can be omitted

1.4.1 A detailed fatigue analysis can be omitted if the largest hot spotstress range for actual details in air or cathodic protected envi-ronment is less than the fatigue limit at 107 cycles. The use of the fatigue limit is illustrated in Figure 1-1. A de-tailed fatigue assessment can be omitted if the largest stress cy-cle is below the fatigue limit. However, in the example inFigure 1-2, there is one stress cycle 1 above the fatigue lim-it. This means that a further fatigue assessment is required.This also means that the fatigue damage from the stress cycle2 has to be included in the fatigue assessment and the sum-mation of fatigue damage presented in this document should beused.

Figure 1-1Stress cycling where further fatigue assessment can be omitted

Figure 1-2Stress cycling where a detailed fatigue assessment is required

1.5 Definitions

1.5.1 Classified structural detail: A structural detail containing astructural discontinuity including a weld or welds, for whichthe nominal stress approach is applicable, and which appear intables of many fatigue design standards such as CSR for Tank-er Structures and DNV-RP-C203, also referred to as a standardstructural detail. Each classified detail is defined to belong toone S-N curve. This means that the K-factor for this detail isincluded in the S-N curve.Constant amplitude loading: A type of loading causing a reg-ular stress fluctuation with constant magnitudes of stress maxi-ma and minima.Crack propagation rate: Amount of crack propagation duringone stress cycle.Crack propagation threshold: Limiting value of stress intensi-ty factor range below which the stress cycles are considered tobe 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-

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 stress rangemagnitude required 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 details resistance against fatigueactions in terms of S-N curve or crack propagation properties.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.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.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, the ef-fect of which is usually not taken into account in the collectionof standard structural details, such as large opening, a curvedpart in a beam, a bend in flange not supported by diaphragmsor stiffeners, discontinuities in pressure containing shells, ec-centricity 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 a lo-cal notch.Notch stress: Total stress at the root of a notch taking into ac-count the stress concentration caused by the local notch. Thusthe notch stress consists of the sum of structural stress and 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 (Fracturemechanics).Palmgren-Miner rule: Fatigue failure is expected when theMiner sum reaches unity.Rainflow counting: A standardised procedure for stress range

N

S

1

Fatigue limit

Stress cycling

N

S

1

Fatigue limit

Stress cycling

N

S

1

2

Fatigue limit

Stress cycling

N

S

1

2

Fatigue limit

Stress cyclingDET NORSKE VERITAS

tion and/or by the growth of cracks. counting.


Shell bending stress: Bending stress in a shell or plate like partof a component, linearly distributed across the thickness as as-sumed 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 discreet in a certain number of blocks.Stress range exceedance: A tabular or graphical presentationof the cumulative frequency of stress range exceedance, i.e. thenumber of ranges exceeding a particular magnitude of stressrange in stress history. Here frequency is the number of occur-rences.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 intoaccount the effects of a structural discontinuity, and consistingof membrane and shell bending stress components. Also re-ferred 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 classificationnote the shorter notation: Stress concentration factor due togeometry (Kg) is used.Variable amplitude loading: A type of loading causing irregu-lar stress fluctuation with stress ranges (and amplitudes) ofvariable magnitude.

1.6 Symbols and abbreviations

1.6.1 The following general symbols are used in this ClassificationNote:

A Cross sectional areaB Greatest moulded breadth of ship measured at the sum-

mer waterline

CB Block coefficient =Cw Wave coefficient as given in DNV Rules for Ships Pt.3

Ch.1. D Moulded depth of ship, confer DNV Rules for Ships

Pt.3 Ch.1 Sec.1 D Fatigue damageF() Weibull distributionH() Transfer functionHs Significant wave heightI Moment of inertia K Stress concentration factor Kg Geometric stress concentration factorKn Un-symmetrical stiffeners with lateral loading stress

concentration factorKte Eccentric tolerance stress concentration factor (normal-

ly plate connections)Kt Angular mismatch stress concentration factor (normal-

ly plate connections)

RULELBT025.1

L Rule length of ship in m, confer DNV Rules for Ships Pt.3 Ch.1 Sec.1.

Lpp Length between perpendicularsM MomentMwo Wave induced vertical momentMH Wave induced horizontal momentQ () Probability level for exceedance of stress range

Wave spectrum

Stress response spectrum

Td Design lifeTact Draught actualT vessel mean moulded summer draught Tz Zero crossing period Z Section modulus

S-N fatigue parameter

a Local / global load combination factorb Local / global load combination factorbf Flange width ai Acceleration in direction I f1 Material factor as specified in the Rules

Pt.3 Ch.1 Sec.1 fe Environmental reduction factor fm Mean stress reduction factor fr Factor for calculation of load effects at 10-4 probability

level g Acceleration of gravity (=9.81 m/s2)h Weibull shape parameterho Basic Weibull shape parameterhw Web heightl Stiffener lengthlog( ) 10th logarithm ln( ) Natural logarithm m S-N fatigue parametermn Spectral moment of order np Lateral pressure pij Occurrence probability of sea condition i and heading jps Sailing rate = fraction of design life at seaq Weibull scale parameters Stiffener spacingt Plate thicknesstp Plate thicknesstf Flange thicknesstw Web thickness tn Net plate thickness d Deformationvij Zero crossing frequency in short-term condition i, j Wave frequency vo Long-term average zero up-crossing frequency Correlation coefficient Stress amplitude 2 Secondary stress amplitude 3 Tertiary stress amplitude produced by bending of plate

elements between longitudinal and transverse frames/stiffeners

nominal Nominal stress amplitude, e.g. stress derived from beam element or finite element analysis

Fatigue usage factor Moulded displacement in tonnes in salt water (density

1.025 [t/m3] on draught T Stress range

S ( )S ( )

aDET NORSKE VERITAS

Kw Weld geometry stress concentration factor


Figure 1-3

g Global stress rangel Local stress range h Nominal stress range due to horizontal bending v Nominal stress range due to vertical bending ( ) Gamma function [-]

Simplified Analysis

Direct Analysis

Long Term Stress Distribution

Sec. 4.3

Fatigue Damage Calculation

Sec. 4.7

Rule Loads Ch. 6

Long Term Load

Distribution

Stress Components

Ch. 5

Combination of Stresses Sec. 4.6

SCF: K-factors App. A

FE Model of detail

Sec. 9.5-9.6

Interchangeable Results

Interchangeable Results

Fatigue Damage Calculation

App. G

Local Stress Transfer Functions for stress

components Sec. 7.3

Full Stochastic Fatigue Analysis

Sec. 7.4

Stress Component based Stochastic

Fatigue Analysis Sec. 7.3

Equivalent Long Term Stress Distribution (Weibull param.)

Sec. 5.2

FE Model of Ship Sec. 9.3-9.4

Load Transfer Functions

Sec. 8.3

Calculation of hotspot stress

Ch. 10 DET NORSKE VERITAS

Flow diagram over possible fatigue analysis procedures


2. Analysis of Fatigue Capacity 2.1 Introduction

2.1.1 The main principles for fatigue analysis based on fatigue testsare described in this section.The fatigue analysis may be based on hot spot stress S-Ncurves for welded plated structures. The hot spot stress at a weld toe is defined as the geometricstress that includes stress rising effects due to structural dis-continuities and presence of attachments, but excluding the lo-calised stress due to the presence of the weld itself. Guidance on finite element modelling and hot spot stress deri-vation is presented in Section 6. The calculated hot spot stressis then entered a hot spot stress S-N curve for derivation of cy-cles to failure. Additional stresses resulting from fabricationtolerances for butt welds and cruciform joints should be con-sidered when the fabrication tolerances exceed that inherentthe S-N data. Reference is made to section for stress concen-tration factors in Appendix A.Results from performed fatigue analyses are presented in Ap-pendix B in terms of allowable stress ranges as function of theWeibull shape parameter. The basis for the allowable stressranges is that long term stress ranges can be described by a twoparameter Weibull distribution. The following fatigue cracking failure modes are considered inthis document (see also Figure 2-1):

Fatigue crack growth from the weld toe into the base ma-terialIn 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 classificationnote is made with the purpose of achieving a reliable de-sign with respect to this failure mode.

Fatigue crack growth from the weld root through the filletweldFatigue cracking from root of fillet welds with crackgrowth through the weld is a failure mode that can lead tosignificant consequences. Use of fillet welds should beavoided in connections where the failure consequences arelarge due to less reliable NDE of this type of connectioncompared with a full penetration weld. However, in manywelded connections use of fillet welds can hardly beavoided and it is also efficient for fabrication. The speci-fied design procedure in this document is considered toprovide reliable connections also for fillet welds.

Fatigue crack growth from the weld root into the sectionunder the weldFatigue crack growth from the weld root into the sectionunder the weld is observed during service life of structuresand is also observed in laboratory fatigue testing. Thenumber of cycles until failure for this failure mode is ofsimilar magnitude as fatigue cracking from the weld toe.There is no methodology recommended used to avoid thisfailure mode except from using alternative types of weldslocally. This means that if fatigue life improvement of theweld toe is required the connection will become morehighly utilised and it is also required to make improvementfor the root. This can be performed using full penetrationweld along some distance of the stiffener nose.

Fatigue crack growth from a surface irregularity or notchinto the base materialFatigue 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 in

ties. The specified design procedure in this document isconsidered to provide reliable connections also with re-spect to this failure mode.

a) Fatigue crack growth from the weld toe into the base ma-terial

b) Fatigue crack growth from the weld root through the filletweld

c) Fatigue crack growth from the weld root into the sectionunder the weld

d) Fatigue crack growth from a surface irregularity or notchinto the base material

Figure 2-1Explanation of different fatigue failure modes

2.2 Fatigue damage accumulation

2.2.1 The fatigue life under varying loading is calculated based onthe S-N fatigue approach under the assumption of linear cumu-lative damage (Palmgren-Miners rule). The total damage thestructure is experiencing may be expressed as the accumulateddamage from each load cycle at different stress levels, inde-pendent of the sequence in which the stress cycles occur.The design life assumed in the fatigue assessment of ships isnormally not to be taken less than 20 years. The accumulatedfatigue damage is not to exceed a usage factor of 1.0. The ac-ceptance criterion is related to design S-N curves based onmean- minus-two-standard-deviations curves for relevant ex-perimental data.

2.2.2 When the long-term stress range distribution is expressed by astress histogram, consisting of a convenient number of con-DET NORSKE VERITAS

the components or from small surface defects/irregulari- stant amplitude stress range blocks i each with a number of


stress repetitions ni the fatigue criterion reads

where

Applying a histogram to express the stress distribution, thenumber of stress blocks, k, is to be large enough to ensure rea-sonable numerical accuracy, and should not be less than 20.Due consideration should be given to selection of integrationmethod as the position of the integration points may have a sig-nificant influence on the calculated fatigue life dependent onintegration method.

2.2.3 Expressions for fatigue damage based on long term stress dis-tributions defined through Weibull distributions and short termRayleigh distribution within each sea state are given in Appen-dix C.

2.3 Fatigue analysis methodology and calculation of stresses

2.3.1 The procedure for fatigue analysis is based on the assumptionthat it is only necessary to consider the ranges of cyclic stressesin determining the fatigue endurance. However, some reduc-tion in the fatigue damage accumulation can be credited whenparts of the stress cycle range are in compression.It should be noted that in welded joints, there may be severallocations at which fatigue cracks can develop, e.g. at the weldtoe in each of the two parts joined, at the weld ends, and in theweld itself. Each potential location should be considered sepa-rately.

2.3.2 When the potential fatigue crack is located in the parent mate-rial at the weld toe, the relevant local hot spot stress is the rangeof maximum principal stress adjacent to the potential crack lo-cation with stress concentrations being taken into account.This stress concentration is due to the gross shape of the struc-ture. As an example, for the welded connection shown in Fig-ure 2-2a), the relevant local hot spot stress for fatigue designwould be the tensile stress, . For the weld shown in Figure 2-2b), the stress concentration factor for the local geometry mustin addition be accounted for, giving the relevant hot spot stressequal to Kg, where Kg is the stress concentration factor due to

the hole. The maximum principal stress range within 45 of the normalto the weld toe should be used for the analysis.

Figure 2-2Explanation of local hot spot stresses

2.3.3 The maximum principal stress is considered a significant pa-rameter for analysis of fatigue crack growth. When the princi-pal 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 the an-gle between the principal stress direction and the normal to theweld, , is increased further, fatigue cracking may no longerinitiate along the weld toe, but may initiate in the weld andgrow normal to the principal stress direction as shown in Fig-ure 2-4. This means that the notch at the weld toe does no long-er significantly influence the fatigue capacity and a higherallowable hot spot stress applies for this stress direction. Moreguidance on this effect of stress direction relative to the weldtoe as shown in Figures 2-3 and 2-4 when using finite elementanalysis and hot spot stress S-N curves is presented in Appen-dix K.

Figure 2-3Fatigue cracking along weld toe

D = accumulated fatigue damage

, m = S-N fatigue parametersk = number of stress blocksni = number of stress cycles in stress block iNi = number of cycles to failure at constant stress range i = usage factor. Accepted usage factor is defined as = 1.0

( )==

==k

1i

mii

k

1i i

i n1Nn

Da

a

Principal stress

direction

Weldtoe

Section

Fatigue crack

////

Principal stress direction

Weldtoe

Section

Fatigue crack

////

//

//DET NORSKE VERITAS


Figure 2-4Fatigue cracking when principal stress direction more parallelwith weld toe

2.3.4 For fatigue analysis of regions in the base material not signifi-cantly affected by residual stress due to welding, the stressrange may be reduced dependent on whether the cycling stressis tension or compression. Mean stress means the static hotspot stress including relevant stress concentration factors. Thecalculated stress range may be multiplied with the reductionfactor fm before entering the S-N curve, see also Figure 2-5:

where

For variable amplitude stresses can be taken as the stressrange at 10-4 probability level of exceedance.

Figure 2-5Stress range reduction factor that may be used with S-N curve forbase material

2.3.5 Residual stresses due to welding and construction are reducedover time as the ship is subjected to external loading. If it islikely that a hot spot region is subjected to a tension force im-

stress range for fatigue analysis can therefore be reduced dueto the mean stress effect also for regions affected by residualstresses from welding. The following reduction factor on thederived stress range may be applied for welded joints:

2.4 S-N curves

2.4.1 The fatigue design is based on use of S-N curves which are ob-tained from fatigue tests. The design S-N curves which followare based on the mean-minus-two-standard-deviation curvesfor relevant experimental data. The S-N curves are thus asso-ciated with a 97.6% probability of survival.

2.4.2 The S-N curves are applicable for normal and high strengthsteels used in construction of hull structures.The S-N curves for welded joints include the effect of the localweld notch. They are also defined as hot spot S-N curves. Thusthese S-N curves are compatible with calculated stress thatdoes not include the notch stress due to the weld. This also means that if a butt weld is machined or grind flushwithout weld overfill a better S-N curve can be used. Refer-ence is e. g. made to DNV-RP-C203.

2.4.3 The basic design S-N curve is given as

with S-N curve parameters given in Table 2-1 and Table 2.2.

where

For unprotected joints in sea water the S-N curve I presentedin Table 2-1 shall be reduced by a factor of 2 on fatigue life.

t = tension stress

=

c = compression stress

=

Principal stress

direction Weldtoe

Section

Fatigue crack

////

Principal stress direction Weld

toe

Section

Fatigue crack

////

//

//

ct

ctm

6.0f +

+=

+

02max static

02min static

Reductionfactor fm

TensionCompression

1.0

0.6

m = /2- m = /2 m = 0

Reductionfactor fm

TensionCompression

1.0

0.6

m = /2- m = /2 m = 0

N = predicted number of cycles to failure for stress range = stress range m = negative inverse slope of S-N curve

= intercept of log N-axis by S-N curve

a = is constant relating to mean S-N curves = standard deviation of log N;

= 0.20

Table 2-1 S-N parameters for air or with cathodic protection S-N Curve Material N 107 N > 107

m m

I Welded joint 12.164 3.0 15.606 5.0III Base Material 15.117 4.0 17.146 5.0

Table 2-2 S-N parameters base material for corrosive environmentS-N Curve Material m

ct

ctm

7.0f +

+=

= logmlogNlog a

log a

s2aloglog =a

loga log a

logaDET NORSKE VERITAS

plying local yielding at the considered region, the effective IV Base material 12.436 3.0


2.4.4 Most 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. The initiation of a fatigue crack takes longer time for a notchin base material than at a weld toe or weld root. This alsomeans that with a higher fatigue resistance of the base materialas compared with welded details, the crack growth will be fast-er in base material when fatigue cracks are growing. For practical purpose one defines the failures in test data as be-ing crack growth though the thickness.When this failure criterion is transferred into a crack size in areal structure where some redistribution of stress is more like-ly, this means that this failure criterion corresponds to a cracksize that is somewhat less than the plate thickness.

2.4.5 The fatigue strength of welded joints is to some extent depend-ent on plate thickness and on the stress gradient over the thick-ness. Thus for a thickness larger than 25 mm, the S-N curve inair reads

where t is thickness (mm) through which the potential fatiguecrack will grow. This S-N curve in general applies to all typesof welds except butt-welds with the weld surface dressed flushand small local bending stress across the plate thickness. Thethickness effect is less for butt welds that are dressed flush bygrinding or machining. Also a less severe S-N curve can beused if the weld notch is removed by machining. Reference ismade to DNV-RP-C203 if needed.

2.4.6 The S-N curves given in Table 2.1-2 are developed for princi-pal stresses acting normal to the weld and should be used to-gether with the maximum stress range within 45 of thenormal to the weld as explained in 2.3.2. If the governing stress direction is parallel with the weld direc-tion a stress reduction factor KP should be used on the principalstress range before entering stress into the SN curve. The stressreduction factor will depend on the quality of the weld, Table2-3. Alternatively the procedure of effective hot spot stress de-scribed in 2.3.3 and Appendix K may be used.

Figure 2-6

2.4.7 For Duplex and Super Suplex steel one may use the same S-Ncurve as for C-Mn steels. Also for austenitic steel one may use

= logm25tlog

4mlogNlog a

10

100

1000

10000 100000 1000000 10000000 100000000 1000000000

Number of cycles

Stre

ss ra

nge

(MP

a)

I

III

IV

Table 2-3 Stress reduction factor KPStress reduc-tion factor KP

Figure Description Require-ment

0.72 1. Automatic welds carried out from both sides.

1. No start-stop posi-tion is per-mitted except when the repair is performed by a special-ist and in-spection carried out to verify the proper exe-cution of the repair.

0.80 2.Automatic fil-let or butt welds carried out from both sides but con-taining stop-start positions.

3.Automatic butt welds made from one side only, with a backing bar, but without start-stop posi-tions.

3. When the detail con-tainsstart-stop positions use Kp = 0.90

0.90 4. Manual fillet or butt welds.

5. Manual or automatic butt welds carried out from one side only, par-ticularly for box girders

6. Repaired au-tomatic or manual fillet or butt welds

5.A very good fit between theflange and web plates is essential. Prepare the web edge such that the root face is adequate for the achieve-ment of reg-ular root penetration with out brake-out.6.Improve-ment meth-ods that are adequately verified may restore the original category.DET NORSKE VERITAS

S-N curves the same S-N curve as for C-MN steels.


2.5 Effect of corrosive environment

2.5.1 It is recognised that the fatigue life of steel structures is consid-erably shorter in freely corroding condition submerged in seawater than in air, i.e. in dry indoor atmosphere such as commonlaboratory air. For steel submerged in sea water and fully ca-thodically protected, approximately the same fatigue life as indry air is obtained. An intact coating system will also protect the steel surfacefrom the corrosive environment, so that the steel can be con-sidered to be as in dry air condition.The basic S-N curve for welded regions in air is only to be ap-plied for joints situated in dry spaces, for joints in cargo oiltanks or joints in ballast tanks effectively protected against cor-rosion. For joints efficiently protected only a part of the designlife and exposed to corrosive environment the remaining part,the fatigue damage may be calculated as a sum of partial dam-ages according to 2.5.2.For joints in freely corroding conditions submerged in sea wa-ter the basic S-N curve for welded joints in air are to be re-duced by a factor 2 on fatigue life.

2.5.2 For coated ballast tanks the fatigue strength may be assessedwith the S-N curve in air for the effective corrosion protectionperiod. The effective corrosion protection period is taken to bethe specified design life of the vessel minus five years (TD-5).Corrosive environment is to be used for the remaining fiveyears of the specified design life.For uncoated cargo oil tanks and coated cargo oil tanks, S-Ncurves in air may be used for the specified design life.For dry cargo holds, fuel oil tanks, void spaces, cofferdam, andhull external surfaces, the S-N curve in air may normally beused for the specified design life.

2.5.3 Global stress components may be calculated based on grossscantlings. Local stress components should be calculatedbased on reduced scantlings, i.e. gross scantlings minus corro-sion addition tk as given in Table 2-3. (The corrosion additionspecified below is similar to that specified in the Rules [1]).

2.6 Fatigue damage from multiple loading condi-tions

2.6.1 Depending on the required accuracy of the fatigue evaluationit may be necessary to divide the design life into a number oftime intervals due to different loading conditions and limita-tions of the corrosion protection. For example, the design lifemay be divided into one interval with good corrosion protec-tion and one interval where the corrosion protection is morequestionable for which different S-N data should be used. Eachof these intervals should be divided into that of loaded and bal-last conditions.

2.6.2 The combined fatigue damage, D, and the corresponding fa-tigue life, T, in multiple loading conditions and non-corrosiveand corrosive environment can be calculated as follows:

1) Calculate the fatigue damage for non-corrosive environ-ment equal to the design life, Tdesign, of the vessel, DInAir:

wherei = loading condition no. i = 1 to npi = fraction of the lifetime operating under loading condi-tion i

2) Calculate the fatigue damage for corrosive environmentequal to the design life, Tdesign, of the vessel, DCorrosive:

3) The combined fatigue damage for the design life of thevessel is calculated as:

The corresponding fatigue life is calculated as:

Table 2-4 Corrosion addition tk in mmTank/hold region LocationInternal members and plate boundary between spaces of the given category

Within 1.5 m below weather deck tank or hold top

Elsewhere

Ballast tank1) 3.0 1.5Cargo oil tank only 2.0 1.0 (0)2)Hold of dry bulk cargo carriers 4) 1.0 1.0 (3)5)Plate boundary between given space categories

Within 1.5 m below weather deck tank or hold top

Elsewhere

Ballast tank 1) / Cargo oil tank only 2.5 1.5 (1.0) 2)Ballast tank 1) / Hold of dry bulk cargo carrier 4)

2.0 1.5

Ballast tank 1) / Other category space 3)

2.0 1.0

Cargo oil tank only / Other catego-ry space 3)

1.0 0.5 (0) 2)

Hold of dry bulk carrier 4) / Other category space 3)

0.5 0.5

1) The term ballast tank includes also combined ballast and cargo oil tanks, but not cargo oil tanks which may carry water ballast according to Regulation 13 (3), of MARPOL 73/78, see Rules

2) The figure in bracket refers to non-horizontal surfaces.3) Other category space denotes the hull exterior and all spaces oth-

er than water ballast and cargo oil tanks and holds of dry bulk cargo carriers.

4) Hold of dry bulk cargo carriers refers to the cargo holds of ves-sels with class notations Bulk Carrier and Ore Carrier

5) The figure in bracket refers to lower part of main frames in bulk carrier holds.

=

=n

1ii,InAiriInAir DpD

==

==n

iiAiri

n

iiCorrosiveiCorrosive DpDpD

1,

1, 2

designCorrosive

design

designInAir T

DT

TDD 5

5 +=

InAir

design

DT

T =DET NORSKE VERITAS

if


else

where Tdesign-5 is the effective corrosion protection period.

3. Fatigue Analysis of Ships3.1 General

3.1.1 Fatigue damages are known to occur more frequently for someship types and categories of hull structure elements. The fatiguelife is in particular related to the magnitude of the dynamic stresslevel, the corrosiveness of the environment and the magnitudeof notch- and stress concentration factors of the structural de-tails, which all vary depending on ship type and structure con-sidered. The importance of possible fatigue damage is related tothe number of potential damage points of the considered type forthe ship or structure in question and to its consequences.

3.1.2 A major fraction of the total number of fatigue damages onship structures occurs in panel stiffeners on the ship side andbottom and on the tank boundaries of ballast- and cargo tanks.However, the calculated fatigue life depends on the type ofstiffeners used, and the detail design of the connection to sup-porting girder webs and bulkheads. In general un-symmetricalprofiles will have a reduced fatigue life compared to symmet-rical profiles unless the reduced effectiveness of the un-sym-metrical profile is compensated by an improved design for theattachment to transverse girder webs and bulkhead structures.

3.1.3 The dynamic wave loading on the hull varies with the draughtand load distribution and it is therefore necessary to considermore than one loading condition in the fatigue evaluation. De-pending on the ship type 2-3 loading conditions representingthe most frequently used loaded and ballast conditions are nor-mally sufficient. The fraction of the lifetime operating undereach loading conditions should reflect the operational tradingpattern of the ship.

3.2 Oil tankers

3.2.1 Structural elements in oil tankers being of possible interest forfatigue evaluation are listed in Table 3-1. For vessels intended for normal, world wide trading the frac-tion of design life in the fully loaded cargo and ballast condi-

tions, pn, may be taken from Table 3-2.

3.3 Gas carriers

3.3.1 Structural elements being of possible interest for fatigue eval-uation of gas carriers are listed in Table 3.3. For vessels intended for normal, world wide trading the frac-tion of design life in the fully loaded cargo and ballast condi-tions, pn, may be taken from Table 3.4.

)5( designInAir

design TDT

Corrosive

InAirdesign

InAir

designdesign D

DTDT

TT

++= 55

Table 3-1 TankersStructure member

Structural detail Load type

Side-, bot-tom- and deck plating and longitudi-nals

Butt joints, deck open-ings and attachment to transverse webs, trans-verse bulkheads, hopper knuckles and intermedi-ate longitudinal girders

Hull girder bending, stiff-ener lateral pressure load and support deformation

Transverse girder and stringer structures

Bracket toes, girder flange butt joints, curved girder flanges, knuckle of inner bottom and sloped hopper side and other panel knuck-les including intersec-tion with transverse girder webs. Single lug slots for panel stiffeners, access and lightening holes

Sea pressure load com-bined with cargo or ballast pressure load

Longitudi-nal girders of deck and bottom structure

Bracket termination's of abutting transverse members (girders, stiff-eners)

Hull girder bending, and bending / deformation of longitudinal girder and considered abutting mem-ber

Table 3-2 Fraction of time at sea in loaded and in ballast conditionVessel type TankersLoaded condition 0.425Ballast condition 0.425

Table 3-3 Gas carriersStructure member Structural detail Load typeSide-, bottom- and deck plating and longitudinals

Butt joints, deck open-ings and attachment to transverse webs, trans-verse bulkheads, hopper knuckles and intermedi-ate longitudinal girders

Hull girder bending, stiffener lateral pres-sure load and support deformation

Transverse girder and stringer structures

Inner hull knuckles in-cluding intersection with transverse girder webs. Single lug slots for panel stiffeners, ac-cess and lightening holes

Sea pressure load combined with cargo or ballast pressure load

Longitudinal girders of deck, side and bottom structure

Inner hull knuckles at intersection with trans-verse BHDs.

Hull girder bending, and bending / defor-mation of longitudi-nal girder and considered abutting member

Tank supports Tank supporting struc-ture in general

Hull girder bending, cargo and sea pres-sure loadsDET NORSKE VERITAS


(*) Fraction of time values should be according to latest ver-sion of DNV Ship Rules. Current values for gas carriers refersto DNV Ship Rules, July 2008 issue.

3.4 Bulk carriers

3.4.1 Structural elements in the bulk carriers being of possible inter-est for fatigue evaluation are listed in Table 3-6 and Table 3-7For vessels intended for normal trading the fraction of the frac-tion of the design life in loaded and ballast conditions, pn, may

be taken from Table 3-5.

(*) Panamax vessel as defined in Classification Note 31.1Sec.1.2.1.

Table 3-4 Fraction of time at sea in loaded and in ballast conditionVessel type Gas carriers (*)Loaded condition 0.45Ballast condition 0.40

Table 3-5 Fraction of time in different conditionsVessel type Bulk carri-

ers larger than Pan-amax (*)

Panamax bulk carri-ers and smaller (*)

Vessels in-tend to carry ore cargoes mostly

Ore carrier

Alternate condition

0.25 0 0.5 0

Homogenous condition

0.25 0.5 0 0.5

Ballast condition

0.35 0.35 0.35 0.35DET NORSKE VERITAS


3.4.2

erations need to be considered, see 6.4.1. The appropriate den-sity and pressure height for bulk cargoes should specially beconsidered to give a hold mass according to Table 3-8. If mass-es specified in the submitted loading conditions are greaterthan those in Table 3-8, the maximum masses shall be used forfatigue strength calculations.

3.4.3 The draught for the loaded conditions shall be taken as thescantling draught. The draught for the ballast condition shallbe taken as the ballast draught given in the loading manual, or0.35T if the loading manual is not available (where T is scant-ling draught).

3.4.4 For bottom and inner bottom longitudinals the effect of relativedeflections and double hull bending shall be taken into accountat locations where this effect is significant. The relative defor-mations are to be obtained by a direct strength analysis.

3.5 Container Ships

3.5.1 Structural elements in the cargo area being of possible interestfor fatigue evaluation of container ships are listed in Table 3-9.

Table 3-6 Bulk CarriersStructure member Structural detail Load typeHatch corners Hatch corner Hull girder bending,

hull girder torsional de-formation

Hatch side coaming

Termination of end bracket

Hull girder bending

Main frames End bracket termina-tions, weld of main frame web to shell for un-symmetrical main frame profiles

External pressure load, ballast pressure load as applicable

Longitudinals of hopper tank and top wing tank

Connection to trans-verse webs and bulk-heads

Hull girder bending, sea- and ballast pres-sure load

Double bottom longitudinals1)

Connection to trans-verse webs and bulk-heads

Hull girder bending stress, double bottom bending stress and sea-, cargo- and ballast pressure load

Transverse webs of double bottom, hopper and top wing tank

Slots for panel stiff-ener including stiff-ener connection members, knuckle of inner bottom and sloped hopper side including intersec-tion with girder webs (floors). Single lug slots for panel stiff-eners, access and lightening holes

Girder shear force, and bending moment, sup-port force from panel stiffener due to sea-,cargo- and ballast pressure load

1) The fatigue life of bottom and inner bottom longitudinals of bulk carriers is related to the combined effect of axial stress due to hull girder- and double bottom bending, and due to lateral pressure load from sea or cargo.

Table 3-7 Ore CarriersStructure member Structural detail Load typeUpper deck plating Hatch corners and side

coaming terminationsHull girder bend-ing

Side-, bottom- and deck longitudinals

Butt joints and attach-ment to transverse webs, transverse bulkheads, hatch opening corners and intermediate longitu-dinal girders

Hull girder bend-ing, stiffener lat-eral pressure load and support de-formation

Transverse girder and stringer struc-tures

Bracket toes, girder flange butt joints, curved girder flanges, panel knuckles at intersection with transverse girder webs etc. Single lug slots for panel stiffeners, ac-cess and lightening holes

Sea pressure load combined with cargo or ballast pressure load

Transverse girders of wing tank1)

Single lug slots for panel stiffeners

Sea pressure load (in particular in ore loading con-dition)

1) The transverse deck-, side- and bottom girders of the wing tanks in the ore loading condition are generally subjected to considerable dynamic shear force- and bending moment loads due to large dynamic sea pressure (in rolling) and an increased vertical racking deflection of the transverse bulkheads of the wing tank. The rolling induced sea pressure loads in the ore loading condition will normally exceed the level in the ballast (and a possible oil cargo) condition due to the combined effect of a large GM-value and a small rolling period. The fatigue life evaluation must be considered with respect to the category of the wing tank considered (cargo oil tank, ballast tank or void). For ore-oil carriers, the cargo oil loading condition should be considered as for tankers.

Table 3-8 Hold massOre holds Empty holds

Alternate condition

MHD or MFull accord-ing to Pt.5 Ch.2 Sec.5

Zero

Homogenous condition

MH according to Rules Pt.5 Ch.2 Sec.5

MH according to Rules Pt.5 Ch.2 Sec.5

Table 3-9 Container carriersHull member

Structural detail Load type

Side-and bottom longitudi-nals

Butt joints and attachment to transverse webs, transverse bulkheads and intermediate longitudinal girders

Hull girder bending, torsion1), stiffener lateral pressure load and support deforma-tion

Upper deck Plate and stiffener butt joints, hatch corner curvatures and support details welded on up-per deck for container pedes-tals etc.

Hull girder bending- and torsional warp-ing stress2).

1) Torsion induced warping stresses in the bilge region may be of significance from the forward machinery bulkhead to the for-ward quarter length.

2) The fatigue assessment of upper deck structures must include the combined effect of vertical and horizontal hull girder bend-ing and the torsional warping response. For hatch corners, ad-ditional stresses introduced by the bending of transverse (and longitudinal) deck structures induced by the torsional hull gird-er deformation must be included in the fatigue assessment.

Table 3-10 Fraction of time at sea in loaded and in ballast condition Vessel type Container vesselsLoaded conditions 0.65Ballast conditions 0.20DET NORSKE VERITAS

For bulk and ore cargoes only pressures due to vertical accel-


3.6 Roll on / Roll off- and Car carriers

3.6.1 Structural elements in the cargo area being of possible interestfor fatigue evaluation of Roll on/ Roll off- and Car carriers arelisted in Table 3-11.

For vessels intended for normal, world wide trading, the frac-tion of design life in the homogeneous design load and ballastconditions, pn , may be taken from Table 3-12.

4. Simplified Fatigue Calculations4.1 General

4.1.1 This section outlines a simplified approach to determine thedistributions of long-term stress ranges expressed as Weibulldistributions. Simple formats for combination of global and lo-cal stress components are given to calculate the total stress re-sponse.

4.2 Calculation procedure

4.2.1 A flow chart of the calculation procedure is given in Figure 4-1.

Figure 4-1Flow diagram for simplified fatigue calculations

4.3 Long term distribution of stresses

4.3.1 The long term distribution of stress ranges at local details maybe described by the Weibull distribution

where:

The stress range distribution may also be expressed as

where

Table 3-11 Roll on / Roll off- and Car carriersStructure member Structural detail Load typeSide- and bottom longitudinals

Butt joints and at-tachment to trans-verse webs, transverse bulkheads and intermediate lon-gitudinal girders

Hull girder bending, stiffener lateral pres-sure load and support deformation

Racking constraining girders, bulkheads etc.

Stress concentration points at girder sup-ports and at bulkhead openings

Transverse accelera-tion load1)

1) It should be noted that the racking constraining girders and bulkheads are in many cases largely unstressed when the ship is in the upright condition. Thus the racking induced stresses may be entirely dynamic, which implies that fatigue is likely to be the primary design criterion. For designs which incorpo-rate racking bulkheads, the racking deformations are nor-mally reduced such that the fatigue assessment may be limited to stress concentration areas at openings of the racking bulk-heads only. If sufficient racking bulkheads are not fitted, rack-ing deformations will be greatly increased, and the fatigue assessment of racking induced stresses should be carried out for primary racking constraining members and vertical girder structures over the ship length as applicable.

Table 3-12 Fraction of time at sea in loaded and in ballast conditionVessel type Car carriersLoaded conditions 0.65Ballast conditions 0.20

Q = probability of exceedance of the stress range h = Weibull shape parameterq = Weibull scale parameter, defined as

o = reference stress range value at the local detail exceeded

Hydrodynamic loadsSimplified calculations Ch. 8

Stress responseSimplified calculations: Ch. 5Finite element analysis Ch. 9

Combination of stress componentsSec. 4.6

Long term stress distributionSec. 4.3

Fatigue damage calculationSec. 4.7

( )

=

h

qexpQ

( ) h100

nlnq

=

h1

00 nln

nln

=DET NORSKE VERITAS

once out of no cycles


The Weibull shape parameter may be established from long-term wave load analysis. In lieu of more accurate calculations,the shape parameter may be taken as

where:

The above Weibull shape parameters are based on results fromthe study in [2].For hopper knuckle connections, the Weibull shape parameterfor ship side at the waterline may be used.In lieu of more accurate calculations h0 may, for open type ves-sels, be taken as 1.05 in connection with fatigue assessment ofdeck structure subjected to dynamic torsional stresses.

4.4 Definition of stress components

4.4.1 A schematic illustration of the different load components to beconsidered in fatigue analysis of ship structures are given inFigure 4-2.

4.4.2 The global dynamic stress components (primary stresses)which should be considered in fatigue analysis are

For ships with large hatch openings the also the stress due totorsional wave bending moments should be considered.

4.4.3 The local dynamic stress amplitudes which should be consid-ered are defined as follows

4.4.4 The total local stress amplitudes due to external or internalpressure loads are the sum of individual local stress compo-nents as follows

with local stress components defined as

Figure 4-2Definition of Stress Components

4.5 Calculation of stress components

4.5.1 The stress response in stiffeners and plating mainly subjectedto axial loading due to hull girder bending and local bendingdue to lateral pressures can be calculated based on beam theorycombined with tabulated values of stress concentration factors.Simplified formulas are given in Section 5.

4.5.2 For details with a more complex stress response and/or wheretabulated values of stress concentration factors are not availa-ble, the stress response should be calculated by finite elementanalyses as described in Section 9.

4.6 Combination of stresses

4.6.1 For each loading condition, combined local stress componentsdue to simultaneous internal and external pressure loads are tobe combined with global stress components induced by hullgirder wave bending. The procedures described in the follow-ing are applicable for ships with closed or semi-closed crosssections only. For open type vessels (e.g. container vessels),

no = total number of cycles associated with the stress range level o

For deck longitudinals

For ship side above the waterlineTact


4.6.2 The stress components to be combined are the hot spot stress-es, i.e. stresses including stress concentration factors, K. Theresulting stress concentration factor of a structural detail de-pends on the structural geometry and type of loading.

4.6.3 Dynamic stress variations are referred to as either stress range() or stress amplitude (). For linear responses, the follow-ing relation applies

4.6.4 The combined global and local stress range may be taken as

4.6.5 The combined global stress range may in general be taken as

except for ships with large hatch openings (i.e. container carri-ers and open hatch type bulk carriers) for which torsionalstresses must be included, see Appendix E.

4.6.6 The combined local stress range, l, due to external and in-ternal pressure loads may be taken as

where

The Origin of the coordinate system has co-ordinates (midship,centre line, base line), see Figure 4-3. x, y and z are longitudi-nal, transverse and vertical distance from origin to load pointof considered structural member. It should be noted that the combined local stress range is basedon combination stress amplitudes and the sign of stress has tobe considered. I.e. for each stress component it has to be eval-uated if the applied load causes tension (positive) or compres-sive (negative) stress at the hot spot.

Figure 4-3Coordinate system

4.7 Cumulative damage

4.7.1 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

fe = Reduction factor on derived combined stress range ac-counting for the long- term sailing routes of the ship con-sidering the average wave climate the vessel will be exposed to during the lifetime. Assuming world wide op-eration the factor may be taken as 0.8. For shuttle tankers and vessels that frequently operates in the North Atlantic or in other harsh environments, fe = 1.0 should be used.

fm = Reduction factor on derived combined stress range ac-counting for the effect of mean stresses, see Sections 2.3.4 and 2.3.5.

a,b = Load combination factors, accounting for the correlation between the wave induced local and global stress ranges. (The below factors are based on [2]).

a = 0.6.b = 0.6.l = combined local stress range due to lateral pressure loads. g = combined global stress range.

= stress range due to wave induced vertical hull girder bending.

= stress range due to wave induced horizontal hull gird-er bending.

= 2h in general (for tankers and vessels without large hatch openings).= 0.10, average correlation between vertical and hori-zontal wave induced bending stress (from [2]).

= 2

= m0 f

++=

lg

lge a

bmaxf

hgvvh2hg

2vg 2 ++=

vhg

vh

22 22 ++=

= total local stress amplitude due to the dynamic sea pressure loads (tension = positive)

= total local stress amplitude due to internal pressure loads (tension = positive)

= average correlation between sea pressure loads and internal pressure loads ( from [2] )

=

where:

For , z may be taken equal to Tact

Nload = total number load conditions consideredpn = fraction of design life in load condition n, pn 1,

but normally not less than 0.85Td = design life of ship in seconds (20 years = 6.3108

secs.)hn = Weibull stress range shape distribution parameter

for load condition n, see item 3.2qn = Weibull stress range scale distribution parameter

for load condition no = long-term average response zero-crossing fre-

quency

= gamma function

eip

actact TL5zx

B4y

L4x

T10z

21

++

actTz

actTz >

D Ta

p q mh

dn n

m

nn

Nload= + =

01

1( )

( )1 + mDET NORSKE VERITAS

iepiel hn


The Weibull scale parameter is defined from the stress rangelevel, o, as

where n0 is the number of cycles over the time period for whichthe stress range level 0 is defined.In simplified fatigue calculations the zero-crossing-frequencymay be taken as

where L is the ship Rule length in meters.Expressions for fatigue damage applying bi-linear S-N curvesare given in Appendix G.

4.7.2 In addition to the high cycle fatigue induced by waves, the fa-tigue strength could be effected by the repeated yielding as oc-curring during the cargo ballast loading cycles (low cyclefatigue). Guidance on how to account for the effect of com-bined high cycle and low cycle fatigue is given in Appendix I.

5. Simplified Stress Analysis5.1 General

5.1.1 In the following sections simplified formulas for calculating thehot spot stress in stiffeners and plating are presented. The for-mulas are based on simple beam theory combined with stressconcentration factors. The stress concentration factors may bebased on tabulated values given in Appendix A or derived fromlocal finite element analysis as described in Section 10.

5.1.2 The stress formulas may be combined with simplified loadsderived according to Section 6 or serve as basis for determina-tion of stress component factors for a component stochastic fa-tigue analysis as described in 7.3.

5.2 Hull girder bending

5.2.1 The wave induced vertical hull girder stress is given by

where

The corresponding stress range is

5.2.2 In addition to the vertical hull girder stress induced by thewaves, the waves also generally induces hull girder vibrationsthat give rise to additional vertical dynamic stresses in the hullgirder. Guidance on the how to account for the effect of com-bined vertical hull girder stress and wave induced vibrationstress is given in Appendix J. The guidance is intended to beapplied on a voluntary basis.

5.2.3 The wave induced horizontal hull girder stress is given by

where

The corresponding stress range is

5.2.4 For analysis of ships with large hatch openings the combinedlongitudinal stress due to hull girder bending and torsion maybe determined as described in Appendix E.

5.3 Bending of girder systems

5.3.1 Local secondary bending stresses (2) are the results of bend-ing due to lateral pressure of stiffened single skin or doublehull cross-stiffened panels between transverse bulkheads, seeFigure 4-2. This may be bottom or deck structures, sides orlongitudinal bulkheads.

5.3.2 The preferred way of determining secondary stresses is bymeans of FEM analysis or alternatively by 3(2)-dimensionalframe analysis models.

5.3.3 Dynamic secondary bending stresses should be calculated fordynamic sea pressure pe and for internal dynamic pressure pi.The pressures to be used should generally be determined at themid-position for each cargo hold or tank.

5.4 Local stiffener bending

5.4.1 The local bending stress of stiffeners with effective plateflange between transverse supports (e.g. frames, bulkheads)may be approximated by

where

Mwo,s(h) =vertical wave sagging (hogging) bending mo-ment amplitude

| z -n0 | =vertical distance in m from the horizontal neutral axis of hull cross section to considered member

IN =moment of inertia of hull cross-section in m4 about transverse axis

Kg axial =stress concentration factor for considered detail for axial loading

( ) nh/100

nnln

q =

010

14

= log ( )L

[ ] Nswohwoaxialgv InzMMK /105.0 03,, =

MH = horizontal wave bending moment amplitudey = distance in m from vertical neutral axis of hull cross section to member consideredIC =

the hull section moment of inertia about the vertical neutral axis

Kg axial =stress concentration factor for considered detail for axial loading

Kg bending = stress concentration factor for local stiffener bendingKn = stress concentration factor for un-symmetrical stiffen-

ers on laterally loaded panelsM = moment at stiffener support adjusted to hot spot posi-

tion at the stiffener (e.g. at bracket toe)

C3

Haxial gh I/y10MK=

hhg 2=

= rZEIm

KZMKK

s2bending g

snbending gA2

l

p

2r

12s lp=DET NORSKE VERITAS

vv 2= p = lateral dynamic pressure


For stiffener bending stress due to local pressures the follow-ing sign convention applies:

Positive for pressures acting on the stiffener side of thepanel (tension stress at hot spot)

Negative for pressures acting on the plate side of the panel(compression stress at hot spot).

For stress due to relative deflections the sign convention is:

Positive if the displacement (in local stiffener z-direction)at the adjacent frame is less than the displacement at theconsidered frame or bulkhead (tension stress at hot spot)

Negative if the displacement (in local stiffener z-direction) atthe adjacent frame is larger than the displacement at the con-sidered frame or bulkhead (compression stress at hot spot).

Figure 5-1Definition of effective span lengths

= pe for dynamic sea pressure= pi for internal dynamic pressure

s = stiffener spacingl = effective span of longitudinal/stiffener as shown in

Figure 5.1 Zs = section modulus of longitudinal/stiffener with associ-

ated effective plate flange. For definition of effective flanges, see 5.4.3

I = moment of inertia of longitudinal/stiffener with asso-ciated effective plate flange.

m = moment factor due to relative deflection between transverse supports. For designs where all the frames obtain the same deflection relative to the transverse bulkhead, e.g. where no stringers or girders supporting the frames adjacent to the bulkhead exist, m may be taken as 4.4 at the bulkhead. At termination of stiff par-tial stringers or girders, m may be taken as 4.4.When the different deflections of each frame are known from a frame and girder analysis, m should be calculated due to the actual deflections at the frames by using a beam model or a stress concentration model of the longitudinal. A beam model of a longitudinal covering + cargo hold length is shown in Figure 5-3. Normally, representative m may be calculated for side and bottom, using one load condition, accord-ing to

whereM is the calculated bending moment at the bulkhead due to the prescribed deflection at the frames, 1, 2 n. i is the relative support deflection of the longitu-dinal at the nearest frame relative to the transverse bulkhead. The frame where the deflection for each longitudinal in each load condition, , is to be taken, should be used.

=

deformation of the nearest frame relative to the con-sidered frame or bulkhead in the direction of the local stiffener z-direction (see Figure 5-4)

rd rp = moment interpolation factors for interpolation to hot spot position along the stiffener length, see Figure 5-2.

=

=

wherex = distance to hot spot, see Figure 5-2.

EIMm

i

2

=l

r

lx21 ; lx0

pr 0.1x6x6

2

+

ll

; lx0

Single skin configuration

Double skin configuration and transverse bulkheads

Effective bracket length of soft toe brackets

l

x

x

l

x

h/2

h

h/2

l

l

xx

h/2

h

h/2

b bDET NORSKE VERITAS


Figure 5-2Stresses in stiffener

Figure 5-3Beam element model of longitudinal through 6 frame spacings

5.4.2 It is of great importance for a reliable fatigue assessment thatbending stresses in longitudinals caused by relative deforma-tion between supports are not underestimated. The appropriatevalue of relative deformation has to be determined in eachparticular case, e.g. by beam- or element analyses (Classifica-tion Note No. 31.1 and 31.3 show modelling examples).

5.4.3 Effective breadth of plate flanges of stiffeners (longitudinals)in bending (due to the shear lag effect) exposed to uniform lat-eral load can be taken asFor bending at midspan:

For bending at ends:

where

Figure 5-4Stiffener geometry

5.5 Local plate bending

5.5.1 Longitudinal local tertiary plate bending stress amplitude inthe weld at the plate/transverse frame/bulkhead intersection(plate short edge) is midway between the longitudinals givenby

where

Similarly, the transverse stress amplitude at stiffener mid-length (plate long edge) is

For local tertiary plate bending due to local pressures the fol-lowing sign conventions applies:

Positive for pressure acting on the welded side of the plate(tension at hot spot)

Negative for pressure acting on the non-welded side of theplate (compression at hot spot).

6. Simplified Wave Load Calculations6.1 General

6.1.1 This section outlines a simplified approach for calculation ofdynamic loads. Formulas are given for calculation of globalwave bending moments, external sea pressure acting on the hulland internal pressure acting on the tank boundaries based on thelinear dynamic part of the loads as defined in the Rules [1]. Thedesign loads as defined in the Rules do also includes non-lineareffects such as bow-flare and roll damping, and are not neces-

length of stiffener between zero moment inflection points (at midspan - uniformly

=9

sfor;0.1

9s

for;s6

sin

ss

m

mm

e

l

ll

=3

sfor;67.0

3s

for;s6

sin67.0

ss

e

ee

e

l

ll

length of stiffener at ends, i.e. outside zero moment inflection points

p = lateral pressure= pe for dynamic sea pressure= pi for internal dynamic pressure

s = stiffener spacingtn = net plate thickness

( ) 2/311e = llbf

bg

z

tf

twhw

se

tp

N.A.

zp

zf

( ) Ktsp343.0 2n3 =

( ) Ktsp50.0 2nT3 =DET NORSKE VERITAS

sarily identical with the dynamic loads presented herein.loaded and clamped stiffener)3m ll =


6.1.2 Fatigue damage should in general be calculated for represent-ative loading conditions accounting for the expected operationtime in each of the considered conditions using actualdraughts, Tact, metacentric heights GMact and roll radius of gy-ration, kr,act for each condition.

6.2 Wave induced hull girder bending moments

6.2.1 The vertical wave induced bending moments may be calculat-ed using the bending moment amplitudes specified in the RulesPt. 3, Ch.1[1]. The moments, at 10-4 probability level of exceedance, may betaken as:

where

6.2.2 The horizontal wave bending moment amplitude at 10-4 prob-ability level may be taken as follows (ref. Rules Pt.3, Ch.1 /1/):

where

6.2.3 Wave torsional loads and moments which may be required foranalyses of open type vessels ( e.g. container vessels) are de-

6.3 External pressure loads

6.3.1 Due to intermittent wet and dry surfaces, the range of the pres-sure is reduced above Tact- zwl, see Figure 6-1. The dynamicexternal pressure amplitude (half pressure range), pe, related tothe draught of the load condition considered, may be taken as:

where

The dynamic pressure amplitude may be taken as the largest ofthe combined pressure dominated by pitch motion in head/quartering seas, pdp, or the combined pressure dominated byroll motion in beam/quartering seas, pdr as:

where

Between specified areas ks is to be varied linearly.

Mwo,s = wave sagging amplitudeMwo,h = wave hogging amplitudeCw = wave coefficient

= 0.0792L L < 100 m

= 100 m< L < 300 m

= 10.75 300 m < L < 350 m

= 350 m< L

kwm = moment distribution factor

=1.0 between 0.40L and 0.65L from A.P., for ships with low/moderate speed

= 0.0 at A.P. and F.P. (linear interpo-lation between these values)

fr =factor to transform the load from 10-8 to 10-4 probability level

=

ho =long-term Weibull shape parame-ter

=

L = Rule length of ship (m)

B =Greatest moulded breath of ship measured at the summer waterline (m)

CB =Block coefficient (actual load con-dition data may be used)

Tact = actual draught in considered load conditionsx = distance from A.P. to section consideredL, B, CB, fr = as defined in 6.2.1

(kNm) )7.0C(BLCkf11.0M B2

wwmrs,wo +=

(kNm) CBLCkf19.0M B2

wwmrh,wo =

( )[ ] 23100L30075.10

( )[ ] 23150350L75.10

oh/15.0

)Llog(54.021.2

( ) ( )( ) (kNm) L/x2cos1CB30.0TLf22.0M Bact49rH +=

pd = dynamic pressure amplitude below the waterline

pl =

=

ks =

=

=

Zw = vertical distance from the baseline to the load point= maximum Tact (m)

y = horizontal distance from the centre line to the load point (m)= y, but minimum B/4 (m)

kf = the smallest of Tact and f

f = vertical distance from the waterline to the top of the ships side at transverse section considered (m)= maximum 0.8Cw (m)

= maximum roll angle, simple amplitude (rad) as defined in 6.5.1V = vessel design speed in knotsrp = reduction of pressure amplitude in the surface zone

= 1.0 for z < Tact - zwl

=

= 0.0 for z > Tact + zwl

zwl =distance measured from actual water line (m). In the area of side shell above z = Tact + zwl it is assumed that the external sea pressure will not contribute to fatigue damage

=

)(kN/m prp 2dpe =

)(kN/m 27.0

16210

)(2.175

135

max 2

+++=

++==act

wfBdr

wactldp

d

TzkyCyp

zTB

ypp

p

fws kCk +

( ) 1.5L

V if L

V0.150.8kCk fws >

++

aft and A.P.at C2.53C

BB +

A.P from 0.7L and 0.2Lbetween 3CB

forward and F.P.at C4.03C

BB +

y

wl

wlact

z2zzT + for Tact - zwl < z < Tact + zwl

p3 dTDET NORSKE VERITAS

fined in Appendix E. g4


Figure 6-1Reduced pressure range in the surface region

6.4 Internal pressure loads due to ship motions

6.4.1 The dynamic pressure from liquid cargo or ballast watershould be calculated based on the combined accelerations re-lated to a fixed co-ordinate system. The gravity componentsdue to the motions of the vessel should be included. The dynamic internal pressure amplitude, pi in kN/m2, may betaken as the maximum pressure due to acceleration of the in-ternal mass:

where

Note:

The factor fa is estimated for ships with a roll period TR < 14 sec.,and may otherwise be less for roll induced pressures and forces,see also 4.3.

---e-n-d---of---N-o-t-e---

The accelerations av, at and al are given in 6.5.For the upper part of bulkheads the pressure range due to hor-izontal acceleration may be reduced by a factor rull within adistance zul below the tank top due to the effect of ullage as fol-lows:

where

Note:The above scaling of pressures, by use of the factor fa, is only val-id for fatigue assessment and may be justified as the dominatingfatigue damage is caused mainly by moderate wave heights.

---e-n-d---of---N-o-t-e---

For bulk and ore cargoes, only p1 need to be considered. Theappropriate density and pressure height should be speciallyconsidered.

Figure 6-2Distribution of pressure amplitudes for tankers in the fully loadedcondition.

Figure 6-3Distribution of pressure amplitudes for tankers in ballast condi-tion

pdT = pd at z = Tact = density of sea water

= 1.025 (t/m3)

p1 = pressure due to vertical acceleration (largest pressure in lower tank region)p2 = pressure due to transverse accelerationp3 = pressure due to longitudinal acceleration

= density of ballast, bunkers or liquid cargo, normally not to be taken less than 1.025 (t/m3)xs =

longitudinal distance from centre of free surface of liquid in tank to pressure point considered (m)

ys =transverse distance from centre of free surface of liquid in tank to the pressure point considered (m), see Figure 6-5

hs =vertical distance from point considered to surface inside the tank (m), see Figure 6-5

av = combined vertical acceleration (m/s2)at = combined transverse acceleration (m/s2)al = combined longitudinal acceleration (m/s2)

fa =factor to transform the load effect to probability level 10-4 , when the accelerations are specified at the 10-8 probability level.

= 0.5l/hh = h0 + 0.05

= 2.26 - 0.54log10(L)

)(kN/m xapyaphap

maxfp 2

sl3

st2

sv1

ai

===

=

)(kN/mmax 2

3

2

1

===

=slull

stull

sv

ai

xarp

yarphap

fp

nksballast tafor 1.0

tanksoil cargofor 1.0max ,z2

zhr

ull

ullsull

=

+=

onaccelerati allongitudinfor 43 3

gpzull =

onaccelerati ersefor transv43 2

gpzull =DET NORSKE VERITAS


Figure 6-4Distribution of pressure amplitudes for a bulk carrier in the oreloading condition.

6.5 Ship accelerations and motions

6.5.1 The formula for ship accelerations and motions given beloware derived from the Rules, Ch.1. Pt.3, Sec.4, [1]. The acceler-ation and motions are extreme values corresponding to a prob-ability of occurrence of 10-8.Combined accelerations:

Acceleration components:

Roll motions:

In case the values of roll radius, kr, and metacentric height,GM, have not been calculated for the relevant loading condi-tions, the following approximate values may be used:

Pitch motions:

at = combined transverse acceleration (m/s2)

=

al = combined longitudinal acceleration (m/s2)

=

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CN 30-7