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GUIDANCE NOTES ON

SPECTRAL-BASED FATIGUE ANALYSIS FORFLOATING PRODUCTION, STORAGE ANDOFFLOADING (FPSO) SYSTEMS

(FOR THE ‘SFA’ OF ‘SFA (years)’ CLASSIFICATION NOTATION)

JANUARY 2002

American Bureau of ShippingIncorporated by Act of Legislature ofthe State of New York 1862

Copyright 2002American Bureau of ShippingABS Plaza16855 Northchase DriveHouston, TX 77060 USA

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ABS GUIDANCE NOTES ON SPECTRAL-BASED FATIGUE ANALYSIS FOR FPSO SYSTEMS . 2002 iii

Foreword

This Guide provides information about the optional classification notation, ‘Spectral FatigueAnalysis’ – SFA or SFA (years) – which is available to qualifying ship-type “Floating ProductionInstallations” (FPIs). This type of offshore installation is usually referred to as a “Floating Storage andOffloading (FSO) System” or “Floating Production, Storage and Offloading (FPSO) System”, and“FPSO” is the term that will be used herein to denote these ship-type Floating ProductionInstallations. Also this guidance document is referred to herein as “this Guide”.

Chapter 1, Section 3 of the ABS Guide for Building and Classing Floating Production Installations(FPI Guide) contains descriptions of the various basic and optional classification notations available.Chapter 4, Section 2 of the FPI Guide gives the specific design and analysis criteria applicable toship-type FPIs (FSOs, FPSOs, etc.). In case of any conflict between this Guide and the FPI Guide,the latter has precedence.

This Guide is issued January 2002. Users of this Guide are welcomed to contact ABS with anyquestions or comments concerning this Guide. Users are advised to check with ABS that this versionof the Guide is current.

ABS GUIDANCE NOTES ON SPECTRAL-BASED FATIGUE ANALYSIS FOR FPSO SYSTEMS . 2002 1

GUIDANCE NOTES ON

SPECTRAL-BASED FATIGUE ANALYSIS FORFLOATING PRODUCTION, STORAGE ANDOFFLOADING (FPSO) SYSTEMS

CONTENTSSECTION 1 Introduction .......................................................................... 3

1 Purpose and Applicability...................................................... 3

3 Background ........................................................................... 4

5 Areas for Fatigue Strength Evaluation .................................. 4

7 Detailed Contents of this Guide ............................................ 6

FIGURE 1 Schematic Spectral-based Fatigue AnalysisProcedure for FPSOs .................................................. 7

SECTION 2 Establishing Fatigue Demand.............................................. 9

1 Introduction............................................................................ 9

3 Stress Range Transfer Function ........................................... 9

5 Base Vessel Loading Conditions .......................................... 9

7 Combined Fatigue from Multiple Base Vessel LoadingConditions ........................................................................... 10

9 Transit Cases ...................................................................... 10

SECTION 3 Environmental Conditions ................................................. 11

1 General................................................................................ 11

3 Environmental Data............................................................. 11

5 Wave Spreading.................................................................. 11

SECTION 4 Motion Analysis and Wave-induced Loads ...................... 13

1 General................................................................................ 13

3 Still-Water Loads ................................................................. 13

5 Essential Features of Spectral-based Analysis of Motionand Wave Load ................................................................... 14

5.1 General Modeling Considerations ...................................14

5.3 Diffraction-Radiation Methods .........................................14

2 ABS GUIDANCE NOTES ON SPECTRAL-BASED FATIGUE ANALYSIS FOR FPSO SYSTEMS . 2002

SECTION 5 Wave-induced Load Components......................................15

1 General................................................................................ 15

3 External Pressure Component ............................................ 15

3.1 Total Hydrodynamic Pressures....................................... 15

3.3 Intermittent Wetting......................................................... 15

5 Internal Tank Pressure Component .................................... 16

7 Loads from the Motions of Discrete Masses....................... 16

SECTION 6 Loading for Global Finite Element Method (FEM)Structural Analysis Model ..................................................17

1 General................................................................................ 17

3 Number of Load Cases ....................................................... 17

5 Mooring Loads..................................................................... 17

7 Equilibrium Check ............................................................... 18

SECTION 7 Structural Modeling and Analysis......................................19

1 General................................................................................ 19

3 Areas for Fatigue Strength Evaluations .............................. 19

5 3-D Global Analysis Modeling ............................................. 19

7 Analyses of Local Structure................................................. 20

7.1 General ........................................................................... 20

7.3 FPSO Specific Structural Details .................................... 20

9 Hot Spot Stress Concentration............................................ 20

FIGURE 1 Definition of Hot Spot Stress ..................................... 20

SECTION 8 Fatigue Strength..................................................................21

1 General................................................................................ 21

3 S-N Data.............................................................................. 21

SECTION 9 Fatigue Life (Damage) Calculation and AcceptanceCriteria .................................................................................23

1 General................................................................................ 23

3 Acceptance Criteria ............................................................. 23

APPENDIX 1 Basic Design S-N Curves ...................................................25

APPENDIX 2 Outline of a Closed Form Spectral-based FatigueAnalysis Procedure.............................................................27

1 General................................................................................ 27

3 Key Steps in Closed Form Damage Calculation................. 27

5 Closed Form Damage Expression ...................................... 30


S E C T I O N 1 Introduction

1 Purpose and Applicability

The fatigue strength criteria for the classification of an FPSO are given primarily in Chapter 4,Section 2 of the FPI Guide. A brief description of the background and objectives for these fatiguecriteria is given in Subsection 1/3, below.

In addition to fatigue strength criteria for ABS’s classification purposes, the Owner/Operator maywish to apply more extensive Spectral-based Fatigue Analysis (SFA) techniques to the FPSO’sstructural systems. It may be an added objective of these Spectral-based Fatigue Analyses todemonstrate longer target fatigue lives than those minimally required for the classification of anFPSO.

The term, ‘more extensive,’ means that the Spectral-based Fatigue Analysis technique, rather than theSafeHull Fatigue Assessment technique (see Subsection 1/3) (a Permissible Stress Range method), isused to verify the adequacy of the fatigue lives of the critical locations in the structural system. TheSafeHull Fatigue Assessment technique is still to be employed in the overall design and analysis effortfor the structure. The results of the fatigue assessment should be used in the selection of areas forwhich the Spectral-based Fatigue Analyses will be done.

ABS is to be consulted and is to agree on the structural locations that are to be subjected to theSpectral-based Fatigue Analysis. Preferably this should occur after the SafeHull Fatigue Assessmenthas been completed.

In recognition of the appropriate, additional use of Spectral-based Fatigue Analysis, ABS will grantthe optional classification notation SFA or SFA (years).

The SFA notation means that the design fatigue life is the 20-year, minimum value requiredin the Rules and the FPI Guide.

The SFA (years) notation means that the design fatigue life value is greater than theminimum value of 20 years, and that the value in the parenthesis, is the design fatigue lifeused. Typical values of life range between 25 to 50 years in 5-year increments.

It should be understood that only one minimum design life value is applied to the entire structuralsystem. The fatigue life value refers to the target value set by the designer, and not the valuecalculated in the analysis. The calculated values are usually much higher than the target valuesspecified for design.

For structural locations required by the FPI Guide to have additional factors applied to the minimumtarget life (say, due to safety critical function or difficulty of inspection, see, for example, 5-4/13 ofthe FPI Guide), the required minimum fatigue life for these locations is the minimum target fatiguelife being applied to entire structure multiplied by the additional factor.

Section 1 Introduction 1


3 Background

The classification criteria to be applied in the design and analysis of an FPSO are given in the ABSFPI Guide. The fatigue strength criteria contained in the FPI Guide are modifications and extensionsof the fatigue strength criteria given in the ABS Rules for Building and Classing Steel Vessels (theSteel Vessel Rules). The modifications primarily reflect the site-specific environmental loadings,mooring restraints and operational loadings and service of an FPSO compared to a tanker that isengaged in unrestricted ocean service. The extensions reflect the additional need to consider moreareas of the structure for fatigue strength evaluations. The most notable of these additional areas are,as applicable, the areas adjacent to and the mooring turret structure itself, critical intersectionsbetween the deck mounted equipment supports and the hull’s deck structure and the connections of‘FPSO Specific Structural Details’. The FPI Guide’s fatigue criteria also include factors by which theminimum design fatigue life of 20 years is to be increased because of ‘criticality’ and ‘inspectability’considerations for some areas of the structure.

In the Steel Vessel Rules applied to tankers, design and analysis for fatigue strength is usuallyaccomplished through a combination of methods. Designers commonly make primary use of, what isreferred to as the SafeHull ‘Fatigue Assessment’ technique (Reference: Steel Vessel Rules Appendix5-1-A1). This is a ‘designer-oriented’, permissible stress range approach that is readily applied to alarge portion of the fatigue-critical structural details of a tanker’s hull structure. This technique wasderived considering ‘unrestricted ocean service’ environmental loadings (due to waves) and a designfatigue life of 20 years.

The Steel Vessel Rules do not preclude the imposition of requirements by ABS to demonstrate theadequacy of fatigue strength of structural components by additional or other techniques that includethe Spectral-based Fatigue Analysis methods. Indeed, there is commonly the need to performSpectral-based Fatigue Analysis of tanker details, which are beyond the range of applicability of thepermissible stress range fatigue assessment approach. Furthermore, the tanker owner or designer isfree to increase the target fatigue lives of some or all of the structural components above the 20-yearminimum value, which is recognized by the optional classification notation, FL (years), in the SteelVessel Rules and the FPI Guide. Therefore the incidental or supplementary use of Spectral-basedFatigue Analysis methods is not a reason to grant the SFA (years) notation.

The development of the fatigue strength criteria for an FPSO, as contained in the ABS FPI Guide isan extension of the scope and philosophy of the tanker Rule approach. Using the EnvironmentalSeverity Factor approach described in Appendix 1 of the FPI Guide, the SafeHull Fatigue Assessmentapproach is modified for use in the site-specific design regime of an FPSO. But as mentioned, for anFPSO, other locations that are beyond the ordinary scope of applicability of the Fatigue Assessmentapproach are to be analyzed using other fatigue analysis techniques such as the Spectral-based FatigueAnalysis approach described herein.

5 Areas for Fatigue Strength EvaluationThe main reference for areas that should be evaluated for fatigue strength in the hull structure is foundin 5-1-A1/3.3 of the Steel Vessel Rules. See also Subsection 7/7.

For convenience, the “Guidance on Locations” contained in the mentioned referenced Paragraph ofthe Steel Vessel Rules for the hull structure is repeated below.



{This text is excerpted from Appendix 5-1-A1 of the ABS Steel Vessel Rules}

3.3 Guidance on Locations (1995)

As a general guidance for assessing fatigue strength for a tanker, the following connections andlocations should be considered:

3.3.1 Connections of Longitudinal Stiffeners to Transverse Web/Floor and to TransverseBulkhead

/3.3.13.3.1(a) 2 to 3 selected side longitudinals in the region from the 1.1 draft to about 1/3 draft inthe midship region and also in the region between 0.15L and 0.25L from F.P. respectively

3.3.1(b) 1 to 2 stiffeners selected from each of the following groups:

Deck longitudinals, bottom longitudinals, inner bottom longitudinals andlongitudinals on side longitudinal bulkheads

One longitudinal on the longitudinal bulkheads within 0.1D from the deck is to beincluded

For these structural details, the fatigue assessment is to be first focused on the flange of thelongitudinal at the rounded toe welds of attached flat bar stiffeners and brackets, as illustratedfor Class F item 2) and Class F 2 item 1) in 5-1-A1/Table 1.

Then, the critical spots on the web plate cut-out, on the lower end of the stiffener as well asthe weld throat are also to be checked for the selected structural detail. For illustration see5-1-A1/11.3.2 and 5-1-A1/11.3.3(a), 5-1-A1/11.3.3(b) and 5-1-A1/11.3.3(c)

Where the stiffener end bracket arrangements on two sides of a transverse web are different,both configurations are to be checked.

3.3.2 Shell, Bottom, Inner Bottom or Bulkhead Plating at Connections to Webs or Floors(for Fatigue Strength of Plating) 5

-1-A1/3.3.23.3.2(a) 1 to 2 selected locations of side shell plating near the summer LWL amidships andbetween 0.15L and 0.25L from F.P. respectively

3.3.2(b) 1 to 2 selected locations in way of bottom and inner bottom amidships

3.3.2(c) 1 to 2 selected locations of lower strakes of side longitudinal bulkhead amidships

3.3.3 Connections of the Slope Plate to Inner Bottom and Side Longitudinal BulkheadPlating at the Lower Cargo Tank Corners

one selected location amidships at transverse web and between webs, respectively

For this structural detail, the value of fR, the total stress range as specified in 5-1-A1/9.1, is tobe determined from fine mesh FEM analyses for the combined load cases, as specified forZone B in 5-1-A1/7.5.2.

3.3.4 End bracket Connections for Transverses and Girders

1 to 2 selected locations in the midship region for each type of bracket configuration

3.3.5 Other Regions and Locations

Other regions and locations, highly stressed by fluctuating loads, as identified from structuralanalysis

{Above text excerpted from Appendix 5-1-A1 of the ABS Steel Vessel Rules}



7 Detailed Contents of this GuideSpectral-based Fatigue Analysis is a complex and numerically intensive technique. As such, there ismore than one variant of the method that can be validly applied in a particular case. ABS does notwish to preclude the use of any valid variant of a Spectral-based Fatigue Analysis method by ‘overspecifying’ the elements of an approach. However, there is a need to be clear about the basicminimum assumptions that are to be the basis of the method employed and some of the key detailsthat are to be incorporated in the method to produce results that will be acceptable to ABS. For thisreason, most of the remainder of this Guide is a presentation on these topics.

As for the main assumptions underlying the Spectral-based Fatigue Analysis method, these are listedbelow:

i) Ocean waves are the source of the fatigue inducing stress range acting on the structuralsystem being analyzed.

ii) In order for the frequency domain formulation and the associated probabilistically-basedanalysis to be valid, load analysis and the associated structural analysis are assumed to belinear. Hence, scaling and superposition of stress range transfer functions from unit amplitudewaves are considered valid.

iii) Non-linearities, brought about by non-linear roll motions and intermittent application of loadssuch as wetting of the side shell in the splash zone, are treated by correction factors.

iv) Structural dynamic amplification, transient loads and effects such as springing areinsignificant for a typical FPSO hull structure and hence use of quasi-static finite elementanalysis is valid, and the fatigue inducing stress variations due to these types of load effectscan be ignored.

Also, for the particular method presented in Appendix 2, it is assumed that the short-term stressvariation in a given sea-state is a random narrow-banded stationary process. Therefore, the short-termdistribution of stress range can be represented by a Rayleigh distribution.

The key components of the Spectral-based Fatigue Analysis method for the selected structurallocations can be categorized into the following components:

Establish Fatigue Demand

Determine Fatigue Strength or Capacity

Calculate Fatigue Damage or Expected Life.

These analysis components can be expanded into additional topics as follows, which become thesubject of particular Sections in the remainder of this Guide.

The topic, “Establish Fatigue Demand” is covered in Sections 2 to 7. The topics of “DetermineFatigue Strength or Capacity” and “Calculate Fatigue Damage or Expected Life” are the subjects ofSections 8 and 9, respectively. Reference can be made to Section 1, Figure 1 for a schematicrepresentation of the Spectral-based Fatigue Analysis Procedure.

In this Guide, a purposeful effort is made to avoid complicating formulations, which will detract fromthe concepts being presented. The most complex formulations are those relating to the calculation offatigue damage resulting from the predicted stress range. These formulations are presented inAppendix 2 of this Guide. It is often at this formulation level that valid variations of a method may beintroduced, and for that reason, it is emphasized that the contents of the Appendix 2 are mainlyprovided to illustrate principle, rather than as mandatory parts of the Spectral-based Fatigue method.



FIGURE 1Schematic Spectral-based Fatigue Analysis Procedure for FPSOs

(For Each Location or Structural Detail)

Determine Still-waterLoads and Check

EquilibriumSee 4/3

Perform Analysis ofVessel Motion and

Wave Induced LoadsSection 4

Obtain and Verify SiteEnvironmental Data

Section 3

Establish FatigueDemand

Sections 2 thru 7

Establish On-siteFatigue Strength

Section 8

Calculate Fatigue dueto Transit Cases(s)

See 2/9

Obtain Net FatigueStrength and Apply

Rule RequiredSafety Factors

Do for eachBase Vessel

Load ConditionSee 2/5

For each Heading Angle and Wave Freq.See 2/3

Calculate RAOs for -External Hydrodynamic PressureInternal Tank PressureAccelerations of Discrete Masses

Section 5

Assemble Load Cases for StructuralAnalysis and Check Dynamic Equilibrium

Section 6

Perform Structural Analysis to ObtainStress Range Transfer Function

Section 7

Calculate Fatigue DamageSection 9

also e.g. See Appendix 2

Calculate combined Fatigue Damagefrom Multiple Base Vessel Load Cases

See 2/7

InputMooringLoads

See 6/5

COMPAREExpected Strength

To Be GreaterThan or Equal toExpected Damage


S E C T I O N 2 Establishing Fatigue Demand

1 Introduction

Sections 2 through 7 address the procedures used to estimate the fatigue demand at a structurallocation that is the object of the fatigue strength evaluation.

3 Stress Range Transfer Function

With ocean waves considered the main source of fatigue demand, the fundamental task of a spectralfatigue analysis is the determination of the stress range transfer function, Hσ(ω|θ), which expresses

the relationship between the stress at a particular structural location and wave frequency (ω) and waveheading (θ).

It is preferred that a structural analysis is carried out at each frequency, heading angle, and ‘BaseVessel Loading Condition’ (see Subsection 2/5) employed in the spectral analysis, and that theresulting stresses are used to generate the stress transfer function directly.

Normally, the frequency range to be used is 0.2 to 1.80 radians/second, in increments not larger than0.1 rad/s. However, depending on the characteristics of the response, it may be necessary to considera different frequency range. The wave heading range is 0 to 360 degrees, in increments not larger than30 degrees.

5 Base Vessel Loading ConditionsThe Base Loading Conditions relate to the probable variations in loading that the hull structure of theFPSO will experience during its on-site service life and for the transit case(s). The main parametersdefining a Base Loading Condition are tank loading/ballast arrangements, hull draft and trim, andsignificant variations in topside equipment loads. These parameters have a direct influence on the‘static’ stress components of the hull’s response, but they also affect the wave-induced cyclic stressrange experienced at a structural location. Two direct ways that this influence is felt are first in themagnitudes and distributions of masses and restoring forces in the determination of global and localaccelerations and rigid body displacements, which in turn affect the wave-induced load effectsemployed in the structural analysis. Secondly, the variation of draft affects the areas of the hull,which will be subjected to direct external pressures, and the magnitude and distribution of thesepressures.

Section 2 Establishing Fatigue Demand 2


7 Combined Fatigue from Multiple Base Vessel LoadingConditions

Because of the variability in Base Vessel Loading Conditions and its effects on the fatigue strengthpredictions, it is necessary to consider more than one base case in the fatigue analysis. As a minimumfor the analysis of post-installation on-site conditions, two cases are to be modeled and used in theSpectral-based Fatigue Analysis process. The two required cases are ones resulting from, andrepresenting, the probable deepest and shallowest drafts, respectively that the vessel is expected toexperience during its on-site service life.

Note: Suggested Approach: In some (so-called ‘Closed Form’) formulations to calculate fatigue demand, the fraction of thetotal time on-site for each Base Vessel Loading Condition is used directly. In this case, potentially useful information aboutthe separate fatigue damage from each vessel loading condition is not obtained. Therefore, it is suggested that the fatiguedamage from each vessel loading condition be calculated separately. Then the ‘combined fatigue life’ is calculated as aweighted average of the reciprocals of the lives resulting from considering each case separately. For example, if two baseloading conditions are employed, and the calculated fatigue life for a structural location due to the respective base vesselloading conditions are denoted L1 and L2, and it is assumed that each case is experienced for one-half of the FPSO’s on-siteservice life, then the combined fatigue life, LC is:

LC = 1/[0.5(1/L1)+ 0.5(1/L2)].

As a further example, if there were three base vessel loading conditions L1, L2, L3 with exposure time factors of 40, 40 and20 percent, respectively; then the combined fatigue life, LC is:

LC = 1/[0.4(1/L1) + 0.4(1/L2) + 0.2(1/L3)].

9 Transit CasesThe fatigue demand arising from anticipated FPSO transit cases (usually only the FPSO voyage to theinstallation site) is to be determined.

Note: As in the previous Note, it is suggested that the fatigue demand produced by the transit case(s) be calculatedseparately.

The extent to which fatigue analysis is to be performed for the transit cases associated with an FPSOwith a classification notation Disconnectable (see FPI Guide 1-3/5.1) will be specially considered.


S E C T I O N 3 Environmental Conditions

1 General

Spectral-based Fatigue Analysis uses environmental data for ocean waves that are given in a ‘wavescatter’ diagram format. The wave data consist of a number of ‘cells’ that represent the probability ofoccurrence of specific ‘sea states’. Each cell effectively contains three data items, namely

i) the significant wave height, Hs, (typically in meters),

ii) the characteristic wave period (in seconds), and

iii) the probability of occurrence of the sea state.

Additionally, data on the long-term directionality of waves at the installation site are needed for thefatigue analysis. The wave scatter diagram data are ‘normalized’ to a base period of time, usually one-year. In this case, the annual number of stress cycles, fatigue Damage per year and fatigue Life inyears as the reciprocal of the annual fatigue Damage are determined directly.

3 Environmental DataIn the context of Spectral-based Fatigue Analysis, the subject of environmental data is heavily focusedon wave data. However, reference is to be made to Section 3 of the ABS FPI Guide, which requiresthe submission of authoritative documentation concerning all of the pertinent environmental data usedin design. Data related to wind and current for some installation sites may have important effects onthe FPSO’s heading angles with respect to incident waves, and the hull’s interaction with the mooringsystem.

Further, for an FPSO receiving the classification notation Disconnectable (see FPI Guide 1-3/5.1)and the SFA notation, special attention needs to be paid to adjusting the data in the wave scatterdiagram to reflect the wave climates actually to be experienced by the FPSO while exposed toconditions up to the disconnection and possible sheltering of the FPSO.

5 Wave SpreadingThe subject of wave energy spreading is to be addressed in the authoritative report addressing theenvironmental data to be used in the design, as required in Section 3 of the FPI Guide. Typically, thecosine squared spreading function may be used to simulate the short-crestedness of the ocean waves.


S E C T I O N 4 Motion Analysis and Wave-inducedLoads

1 GeneralThis Section gives general criteria on the parameters to be obtained from the vessel motion analysisand the calculation of wave-induced load effects. In the context of a Spectral-based Fatigue Analysis,the main objective of motion and load calculations is the determination of Response AmplitudeOperators (RAOs), which are mathematical representations of the vessel responses and load effects tounit amplitude sinusoidal waves. The motion and load effects RAOs are to be calculated for ranges ofwave frequencies and wave headings, as indicated in Subsection 2/3.

Aside from vessel motions, the other wave-induced load effects that need to be considered in theSpectral-based Fatigue Analysis of an FPSO are the external wave pressures, internal tank pressuresdue to tank fluid accelerations, inertial forces on the masses of structural components and significantitems of equipment and mooring loads. Additionally, there may be situations where partial models ofthe FPSO’s structural system are used. In such a case, hull-girder shear forces and bending momentsare to be determined to appropriately represent the boundary conditions at the ends of the partialmodels.

Note: Fatigue damage due to the sloshing of fluid in partially filled tanks is not within the scope of the SFA classificationnotation. However, the designer is encouraged to perform and submit such calculations if deemed important for the FPSO.

3 Still-Water LoadsThe motion and load calculations are to be performed with respect to static initial conditionsrepresenting the vessel geometry, loadings, etc. (see Subsection 2/5). With the input of hull loadings,the hull girder shear force and bending moment distributions in still water are to be computed at asufficient number of transverse sections along the hull’s length, in order to accurately take intoaccount discontinuities in the weight distribution. A recognized hydrostatic analysis program is to beused to perform these calculations. By iteration, the convergence of the displacement, LongitudinalCenter of Gravity (LCG) and trim should be checked to meet the following tolerances:

Displacement: + 1%

Trim: + 0.5 degrees

Draft:

Forward + 1 cm

Mean + 1 cm.

Aft + 1 cm

LCG: + 0.1% of length

SWBM: + 5%

Section 4 Motion Analysis and Wave-induced Loads 4


Additionally, the longitudinal locations of the maximum and the minimum still-water bendingmoments and, if appropriate, that of zero SWBM should be checked to assure proper distribution ofthe SWBM along the vessel’s length.

5 Essential Features of Spectral-based Analysis of Motionand Wave Load

5.1 General Modeling Considerations

The representation of the hull should include the masses of the topside equipment and their supportingstructure. The model is also to consider the interaction with the mooring system, and as appropriate,the effects of risers, the effects of the Dynamic Positioning system and the operations of offloading orsupport vessels. The motion analysis should appropriately consider the effect of shallow water onvessel motions. There is also to be sufficient compatibility between the hydrodynamic and structuralmodels so that the application of fluid pressures onto the finite element mesh of the structural modelcan be done appropriately.

For the load component types and structural responses of primary interest, analysis softwareformulations derived from linear idealizations are deemed to be sufficient. However, the use ofenhanced bases for the analysis, especially to incorporate non-linear loads (for example hullslamming) is encouraged, if this proves to be necessary for the specific design being evaluated. Theadequacy of the employed calculation methods and tools is to be demonstrated to the satisfaction ofABS.

5.3 Diffraction-Radiation Methods

Computations of the wave-induced motions and loads are to be carried out using appropriate, provenmethods. Preference should be given to the application of seakeeping analysis codes utilizing three-dimensional potential flow based diffraction-radiation theory. All six degrees-of-freedom rigid-bodymotions of the vessel are to be accounted for, and effects of water depth are to be considered. Thesecodes, based on linear wave and motion amplitude assumptions, make use of boundary elementmethods with constant or higher order sink-source panels over the entire wetted surface of the hull, onwhich the hydrodynamic pressures are computed.


S E C T I O N 5 Wave-induced Load Components

1 General

Wave-induced loads on a buoyant structure are complicated because in addition to producing directforces (e.g. wave pressures on the external surface of the hull), there are indirect force componentsproduced by the rigid body motions of the vessel. The motions result in inertial forces and rotationalcomponents of the (quasi-statically considered) loads. These two motion-related load components arereferred to below as the ‘inertial’ and ‘quasi-static’ load components. For a moored, buoyant structuresuch as an FPSO, added complexity arises from the mooring system, which produces reaction loadcomponents.

The treatment of the various load and motion effects is typically done through the use of their real andimaginary parts that are employed separately in structural analyses. In a physical sense, the real andimaginary parts correspond to two wave systems that are 90 degrees out of phase relative to eachother.

The following Subsections list the primary wave-induced load components that are to be consideredin the Spectral-based Fatigue Analysis of an FPSO. Using the methods and calculation tools that aredescribed in Section 4, the Response Amplitude Operators (RAOs) for the listed components are to beobtained.

3 External Pressure Component

3.1 Total Hydrodynamic Pressures

The total hydrodynamic pressure is to include the direct pressure components due to waves and thecomponents due to hull motions. The components of the hydrodynamic pressure are to be determinedfrom the model and calculation procedure mentioned in Section 4.

3.3 Intermittent Wetting

Ship motion analysis based on linear theory will not predict the non-linear effects near the meanwaterline due to intermittent wetting. In actual service, this phenomenon is manifested by a reductionin the number of fatigue cracks at side shell plating stiffeners located near the waterline compared tothose about 4 or 5 bays below. To take into account pressure reduction near the mean waterline due tothis non-linearity, the following reduction factor can be used:

RF = 0.5[1.0 + tanh(0.35d)]

where d is the depth in meters of the field point below the still-water waterline.

The pressure distribution over a hydrodynamic panel model may be too coarse to be used directly inthe structural FEM analysis. Therefore, as needed, the pressure distribution is to be interpolated (3-Dlinear interpolation) over the finer structural mesh.

Section 5 Wave-induced Load Components 5


5 Internal Tank Pressure ComponentAs stated in Subsection 5/1, the vessel motion related internal tank pressure is composed of quasi-static and inertial components. The quasi-static component results from the instantaneous roll andpitch of the vessel. The inertial component is due to the acceleration of the fluid caused by vesselmotion in six degrees of freedom. The vessel motion should be obtained from analysis performed inaccordance with Section 4.

The internal tank pressure (quasi-static + inertial) for each of the tank boundary points is calculated bythe following:

P = Po + ρht {[(gx + ax)2 + (gy + ay)

2 + (gz + az)2]}0.5

where

P = total internal tank pressure at a tank boundary point

Po = value of the pressure relief valve setting

ρ = density of the fluid cargo or ballast

ht = total pressure head defined by the height of the projected fluid column in thedirection to the total acceleration vector

ax, ay, az = longitudinal, lateral, and vertical motion wave-induced accelerations relative tothe vessel’s axis system at a tank boundary point.

gx,,gy,,gz = longitudinal, lateral, and vertical instantaneous gravitational accelerations relativeto the vessel’s axis system at a tank boundary point.

The internal pressure at the tank boundary points are to be linearly interpolated and applied to all thenodes of the structural analysis model defining the tank boundary.

7 Loads from the Motions of Discrete Masses

Vessel motions produce loads acting on the masses of ‘lightship’ structure and equipment. There arequasi-static and inertial components, which can be obtained in the following manner. The motioninduced acceleration, At, is determined for each discrete mass from the formula:

At = (R x θ) ω2 + a

where

R = distance vector from the hull’s CG to the point of interest

θ = rotational motion vector

x = cross product between the vectors

a = translation acceleration vector

ω = relevant frequency

Using the real and imaginary parts of the complex accelerations calculated above, the motion-inducedload is computed by:

F = m (At )

where m is the discrete mass under consideration.

The real and imaginary parts of the motion-induced loads from each discrete mass in all threedirections are calculated and applied to the structural model.


S E C T I O N 6 Loading for Global Finite ElementMethod (FEM) Structural AnalysisModel

1 General

For each heading angle and wave frequency at which the structural analysis is performed (seeSubsection 2/3), two load cases corresponding to the real and imaginary parts of the frequency regimewave-induced load components are to be analyzed. Then, for each heading angle and wave frequency,the frequency-dependent wave-induced cyclic stress range transfer function, Hσ(ω|θ), is obtained forthe Base Vessel Loading Condition.

When inputting the pressure loading components, care is to be taken in the interpolation near regionswhere pressure changes sign.

3 Number of Load CasesThe number of combined load cases for each Base Vessel Loading Condition can be relatively large.When the structural analysis is performed for 33 frequencies (0.2 to 1.80 rad/s at 0.05 increment) and12 wave headings (0 to 360 degree at 30 degree increment), the number of combined Load Cases is792 (considering separate real and imaginary cases). If there are 3 Base Vessel Loading Conditionsthe total number of load cases is (3 ∙ 792) = 2376.

However, a significant reduction in the number of heading angles, hence load cases, to be analyzed ispossible in the ‘on-site’ analysis of an FPSO system with a ‘weathervaning’ turret mooring. Wherejustified by the submitted environmental data, a minimum of 3 heading angles, head-on and 30degrees off either side of head-on, will be considered sufficient. In the absence of submitted data, itmay be assumed that the relative exposure weighting factor for the head-on# direction is 0.70 and 0.15for each of the off head-on directions. In this case, with 3 Base Vessel Loading Conditions thenumber of load cases for analysis is (33 ∙ 2 ∙ 3 ∙ 3) = 594.# Note: The term ‘head-on’ does not imply a stern mounted turret is treated differently.

5 Mooring LoadsMooring loads are primarily elastic reactions resisting the combined effects of wave-induced forcesand motions, and current, wind, etc. effects on the FPSO hull. The effects of mooring can beconsidered in three regimes of hull motion: first-order (wave frequency), second-order (lowfrequency or slowly varying), and steady offset due to wind and wave. These frequency-relatedcomponents are to be obtained using a recognized vessel mooring analysis method.

Section 6 Loading for Global Finite Element Method (FEM) Structural Analysis Model 6


The results of the mooring analysis and the environmental data on the directionality of the prevalentload effects are to be used to establish the mooring loads to be included in the structural analyses ofSection 7. Typically, where the effects of ocean swells are accounted for* in the employed fatigueanalysis method, only the first order (wave frequency) mooring load components need to beconsidered in the spectral-based fatigue analysis.

* Note: The Wirsching rainflow correction is often used for this purpose.

7 Equilibrium CheckThe applied hydrodynamic external pressure and the mooring loads should be in equilibrium with allother loads applied. The unbalanced forces in three global directions for each load case should becalculated and checked. For head sea condition, the unbalanced force should not exceed one percentof the displacement. For oblique and beam sea condition, it should not exceed two percent of thedisplacement. These residual forces could be balanced out by adding suitably distributed inertialforces [so called ‘inertial relief’] before carrying out the FEM structural analysis.


S E C T I O N 7 Structural Modeling and Analysis

1 General

The stress range transfer function, Hσ(ω|θ), for a location where the fatigue strength is to beevaluated, is to be determined by the finite element method (FEM) of structural analysis using a threedimensional (3-D) model representing the entire hull structure, the topside equipment supportstructure and the interface with the mooring system. The Load Cases to be used in the analysis arethose obtained in accordance with Section 6. Special attention is to be paid to the modeling of thestiffness of a turret mooring system and the transmission of mooring loads into the hull.

As necessary to evaluate the fatigue strength of local structure, finer mesh FEM analyses are also tobe performed. Results of nodal displacements or forces obtained from the overall 3-D analysis modelare to be used as boundary conditions in the subsequent finer mesh analysis of local structures.

Specialized fine mesh FEM analysis is required in the determination of stress concentration factorsassociated with the ‘hot-spot’ fatigue strength evaluation procedures (see Subsection 7/9).

Note: Reference should be made to additional ABS Guidance on the expected modeling and analysis of vessel structure; e.g.the ABS Finite Element Analysis Guidance that is provided with the SafeHull software. While there is a significantdifference in the extent of structural model described here and the partial hull model allowed in SafeHull, numerous detailedmodeling considerations are shared; such as expected element types, mesh sizes, dependence between local and globalmodels, etc.

3 Areas for Fatigue Strength EvaluationsRefer to Subsection 1/5 and Paragraph 7/7.3.

5 3-D Global Analysis Modeling

The global structural and load modeling should be as detailed and complete as practicable. For theSpectral-based Fatigue Analysis of a new-build structure, gross scantlings are ordinarily used.

In making the model, a judicious selection of nodes, elements and degrees of freedom is to be made torepresent the stiffness and inertia properties of the hull. Lumping of plating stiffeners, use ofequivalent plate thickness and other techniques may be used to keep the size of the model andrequired data generation within manageable limits.

The finite elements, whose geometry, configuration and stiffness closely approximate the actualstructure, are of three types:

i) truss or bar elements with axial stiffness only

ii) beam elements with axial, shear and bending stiffness, and

iii) membrane and bending plate elements, either triangular or quadrilateral.

Section 7 Structural Modeling and Analysis 7


7 Analyses of Local Structure

7.1 General

More refined local stress distributions should be determined from the fine mesh FEM analysis of localstructure. In the fine mesh models, care is to be taken to represent the structure’s stiffness, as well asits geometry, accurately. Boundary displacements obtained from the 3-D global analysis are to beused as boundary conditions in the fine mesh analysis. In addition to the boundary constraints, thepertinent local loads should be reapplied to the fine mesh models.

7.3 FPSO Specific Structural Details

Reference is to be made to 4-2/15.1, 5-4/13 and 5-4/15 of the ABS FPI Guide, regarding someadditional modeling and analysis considerations for Mooring System/Hull interaction.

9 Hot Spot Stress Concentration

When employing the so-called ‘Hot-Spot’ Stress Approach (for example to determine the fatiguestrength at the toe of a fillet weld), it is necessary to establish a procedure to be followed tocharacterize the expected fatigue strength. The two major parts of the procedure are (a) the selectionof an S-N Data Class (see Section 8) that applies in each situation; and (b) specifying the fine meshFEM model adjacent to the weld toe detail and how the calculated stress distribution is extrapolated tothe weld toe (hot-spot) location. The figure below shows an acceptable method, which can be used toextract and interpret the ‘near weld toe’ element stresses and to obtain a (linearly) extrapolated stressat the weld toe. Element sizes in such cases near the weld toe would be close to the thickness of theplating. When stresses are obtained in this manner the use of the E class S-N data is considered to bemost appropriate.

FIGURE 1Definition of Hot Spot Stress

Peak Stress

Weld Toe "Hot Spot" Stress

Weld Toe

Weld Toe Location

t/2

3t/2

t

t

~~

Weld hot spot stress can be determined from linear extrapolation to the weld toe using calculatedstresses at t/2 and 3t/2 from weld toe. Defining stresses are the principal centroidal stresses at thelocations shown. Description of the numerical procedure is given in 5-1-A1/13.7 of the ABS SteelVessel Rules.


S E C T I O N 8 Fatigue Strength

1 General

The previous Sections of this Guide have addressed establishing the cyclic stress range (demand) forlocations in the structure for which the adequacy of fatigue strength is to be evaluated. The capacity ofa location to resist fatigue damage is characterized by the use of S-N Data, which are described below.Refer to Appendix 1 of this Guide, and Appendix 5-1-A1 of the ABS Steel Vessel Rules, concerningthe S-N Data recommended by ABS.

Using the S-N approach, fatigue strength (capacity) is usually characterized in one of two ways. Oneway is called a nominal stress approach. In this approach, the acting cyclic stress range (demand) isconsidered to be obtained adequately from the nominal stress distribution in the area surrounding theparticular location for which the fatigue life is being evaluated. The other way of characterizingfatigue strength (capacity) at a location is the ‘hot-spot’ approach (see Subsection 7/9). The hot-spotapproach is needed for locations where complicated geometry or relatively steep local stress gradientswould make the use of the nominal stress approach inappropriate or questionable. Reference shouldbe made to 5-1-A1/13 of the Steel Vessel Rules for further explanation and application of these twoapproaches.

3 S-N Data

To provide a ready reference, the S-N Data recommended by ABS are given in Appendix 1 of thisGuide. (Note: source United Kingdom’s Dept of Energy (HSE) Guidance Notes, 3rd Edition.)

There are various adjustments (reductions in capacity) that may be required to account for suchfactors as a lack of corrosion protection (coating) of structural steel and relatively large platethicknesses. The imposition of these penalties on fatigue capacity will be in accordance with ABSpractice for tanker vessels.

There are other adjustments, which could be considered to increase fatigue capacity above thatportrayed by the cited S-N data. These include adjustments for ‘mean stress’ effects, a highcompressive portion of the acting cyclic stress range and the use of ‘weld improvement’ techniques.The first two of these adjustments are not permitted, primarily because they may violate thecalibration and validation that was performed in the development of the recommended fatiguestrength criteria. The use of a weld improvement technique, such as weld toe grinding or peening torelieve ambient residual stress, can be effective in increasing fatigue life. However, credit should notbe taken for such a weld improvement in the design phase of the structure. Consideration for grantingcredit for the use of weld improvement techniques should be reserved for situations arising duringconstruction, operation, or future reconditioning of the structure.


S E C T I O N 9 Fatigue Life (Damage) Calculationand Acceptance Criteria

1 GeneralMathematically, spectral-based fatigue analysis begins after the determination of the stress transferfunction. Wave data are then incorporated to produce stress-range response spectra, which are used todescribe probabilistically the magnitude and frequency of occurrence of local stress ranges at thelocations for which fatigue strength is to be calculated. Wave data are represented in terms of a wavescatter diagram and a wave energy spectrum. The wave scatter diagram consists of sea-states, whichare short-term descriptions of the sea in terms of joint probability of occurrence of a significant waveheight, Hs and a characteristic period.

An appropriate method is to be employed to establish the fatigue damage resulting from eachconsidered sea state. The damage resulting from individual sea states is referred to as ‘short-term’.The total fatigue damage resulting from combining the damage from each of the short-term conditionscan be accomplished by the use of a weighted linear summation technique (i.e. Miner’s rule).

Appendix 2 contains a detailed description of the steps involved in a suggested Spectral-based FatigueAnalysis method that follows the basic elements mentioned above. ABS is to be provided withbackground and verification information that demonstrates the suitability of the analytical methodemployed.

3 Acceptance CriteriaThe required fatigue strength can be specified in several ways primarily depending on the evaluationmethod employed. For the Spectral-based approach it is customary to state the minimum requiredfatigue strength in terms of a Damage ratio (D) or minimum target Life (L). The latter is employed inthis Guide and the FPI Guide.

See Subsection 1/1 regarding target life and reference to additional factors which are to be applied tothe design fatigue life in some situations.


A P P E N D I X 1 Basic Design S-N Curves

Constants for Basic S-N Design Curves

Class K1 m1 K2 m2Std Dev

log10

B 1.013 × 1015 4 1.013 × 1017 6 0.1821

C 4.227 × 1013 3.5 2.926 × 1016 5.5 0.2041

D 1.519 × 1012 3 4.239 × 1015 5 0.2095

E 1.035 × 1012 3 2.300 × 1015 5 0.2509

F 6.315 × 1011 3 9.975 × 1014 5 0.2183

F2 4.307 × 1011 3 5.278 × 1014 5 0.2279

G 2.477 × 1011 3 2.138 × 1014 5 0.1793

W 1.574 × 1011 3 1.016 × 1014 5 0.1846


A P P E N D I X 2 Outline of a Closed Form Spectral-based Fatigue Analysis Procedure

Notes:

(1) This Appendix is referred to in Section 9. It is provided to describe the formulations comprising a Spectral-basedFatigue Analysis approach, which can be employed to satisfy the criteria to obtain the SFA or SFA (years)Classification notation. However, it is often at this formulation level that valid variations of a method may beintroduced, and for that reason, it is emphasized that the contents of this Appendix are mainly provided to illustrateprinciple, rather than to give mandatory steps for the Spectral-based Fatigue method.

(2) The procedure described below considers the use of a wave scatter diagram that represents long-term wave data atthe FPSO’s installation site that have been ‘normalized’ to represent a period of one-year. Where a different baseperiod for the wave scatter diagram is employed the procedure needs to be suitably modified.

1 General

In the ‘short-term closed form’ approach described below, the stress range is normally expressed interms of probability density functions for different short-term intervals corresponding to theindividual cells or bins of the wave scatter diagram. These short-term probability density functionsare derived by a spectral approach based on the Rayleigh distribution method, whereby it is assumedthat the variation of stress is a narrow banded random Gaussian process. To take into account effectsof swell, which are not accounted for when the wave environment is represented by the scatterdiagram, Wirsching’s ‘rainflow correction’ factor is applied in the calculation of short-term fatiguedamage. Having calculated the short-term damage, the total fatigue damage is calculated throughtheir weighted linear summation (using Miner’s rule). Mathematical representations of the steps of theSpectral-based Fatigue Analysis approach just described are given next.

3 Key Steps in Closed Form Damage Calculation

1. Determine the complex stress transfer function, Hσ(ω|θ), at a structural location of interest fora particular load condition. This is done in a direct manner where structural analyses areperformed for the specified ranges of wave frequencies and headings, and the resultingstresses are used to generate the stress transfer function explicitly. See Sections 2 to 7.

2. Generate a stress energy spectrum, Sσ(ω|Hs, Tz, θ), by scaling the wave energy spectrum

Sη(ω|Hs, Tz) in the following manner:

Sσ(ω|Hs, Tz, θ) = |Hσ(ω|θ)|2 ⋅ Sη(ω|Hs, Tz) .................................................................(1)

Appendix 2 Outline of a Closed Form Spectral-based Fatigue Analysis Procedure A2


3. Calculate the spectral moments. The n-th spectral moment, mn, is calculated as follows:

∫∞

σ ωθωω=0

),,|( dTHSm zsn

n .....................................................................................(2)

Most fatigue damage is associated with low or moderate seas, hence confused short-crestedsea conditions must be allowed. Confused short-crested seas result in a kinetic energy spreadwhich is modeled using the cosine-squared approach, (2/π)cos2 θ. Generally, cosine-squaredspreading is assumed from +90 to –90 degree on either side of the selected wave heading.Applying the wave spreading function modifies the spectral moment as follows:

∫ ∑∞ +θ

−θσ θωω⋅θ

π

=0

90

90

2 ),,|(cos2

dwTHSm zsn

n ...........................................................(3)

4. Using the spectral moments, the Rayleigh probability density function (pdf) describing theshort-term stress-range distribution, the zero up-crossing frequency of the stress response andthe bandwith parameter used in calculating Wirsching’s ‘rainflow correction’ are calculatedas follows:

Rayleigh pdf:

−=

2

2

2 2exp)(

σσSS

Sg .............................................................................................(4)

Zero-up crossing frequency:

0

2

2

1

m

mf

π= ..............................................................................................................(5)

Bandwidth Parameter:

40

221mm

m−=ε ..........................................................................................................(6)

where

S = stress range (twice the stress amplitude)

σ = root-mean-square (rms) value of S

m0, m2 and m4 are the spectral moments.

5. Calculate cumulative fatigue damage based on Palmgren-Miner’s rule which assumes that thecumulative fatigue damage (D) inflicted by a group of variable amplitude stress cycles is thesum of the damage inflicted by each stress cycle (di), independent of the sequence in whichthe stress cycles occur:

∑∑==

==totalN

i i

itotalN

ii N

ndD

11

...............................................................................................(7)

where

ni = number of stress cycles of a particular stress range

Ni = average number of loading cycles to failure under constant amplitudeloading at that stress range according to the relevant S-N curve



Ntotal = total number of stress cycles.

Failure is predicted to occur when the cumulative damage (D) over Ntotal loading cyclesexceeds a critical value equal to unity. The short-term damage incurred in the i-th sea-stateassuming an S-N curve of the form N = KS-m is given by:

∫∞

=

0

0 dsgpfSK

TD iii

mi ............................................................................................(8)

where

Di = damage incurred in the i-th sea-state

m, K = physical parameters describing the S-N curve

T = target fatigue life

f0i = zero-up-crossing frequency of the stress response

pi = joint probability of Hs and Tz

gi = probability density function governing S

S = stress range

Summing Di over all the sea-states in the wave scatter diagram leads to the total cumulativedamage, D. Therefore,

[ ]∫ ∑∞

=

0

000 / dsfgpfSK

TfD iii

m .............................................................................(9)

where

D = total cumulative damage

f0 = “average” frequency of S over the lifetime

= Σi pif0i

Introducing the long-term probability density function, g(S), of the stress range as

∑∑

=

iii

iiii

pf

gpf

Sg0

0

)( ...................................................................................................(10)

and NT equal to the total number of cycles in life time = f0T, the expression for totalcumulative damage, D can be re-written as:

∫∞

=

0

)( dSSgSK

ND mT ............................................................................................(11)

The minimum target fatigue life is twenty years. Having calculated the damage, fatigue lifewould then be equal to 20/D. Changing the minimum target fatigue life to higher values isdone accordingly.



5 Closed Form Damage ExpressionFor all one-segment linear S-N curves, the closed form expression of damage, D as given by equation9 is as follows:

∑λ+Γ=i

m mK

TD )12/(2 2/ (m, εi) f0i pi (σi)

m ......................................................................(12)

where

σi = root-mean-square value of S

λ = rainflow factor of Wirsching and is defined as

λ (m, εi) = a(m) + [1 – a(m)][1 – εi]b(m) .............................................................(13)

where

a(m) = 0.926 – 0.033m

b(m) = 1.587m – 2.323

εi = Spectral Bandwidth (eq. 6)

For bi-linear S-N curves where the negative slope changes at point Q = (Sq, 10q) from m to m′ = m +

∆m (∆m > 0) and the constant K changes to K′, the expression for damage as given in equation 12 is asfollows:

∑λ+Γ=i

m mK

TD )12/(2 2/ (m, εi) µi f0i pi (σi)

m ..................................................................(14)

where µi is the endurance factor having its value between 0 and 1 and measuring the contribution of

the lower branch to the damage. It is defined as:

∫

∫∫∞

∆+

′−

−=

0

001

dsgS

dsgSK

KdsgS

im

qS

imm

qS

im

iµ ................................................................................(15)

If g(S) is a Rayleigh distribution, then µi is:

)12/(

),12/()/1(),12/(1

2/

+Γ+′−+−=

∆

m

mm im

iii

νγννγµ ...............................................................(16)

where

νi = (1/2) [Sq/σi]2

γ = incomplete gamma function

= ∫ −= −x

a duuuxa0

1 )exp(),(γ

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