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Platform pipeline-subsea technology fatigue design

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  • 1. Platform, Pipeline and Subsea Technology Fatigue DesignPlatform, Pipeline and Subsea Technology– Fatigue Design 1
  • 2. 1 INTRODUCTION ....................................................................................................... 32 STRUCTURAL FATIGUE......................................................................................... 3 2.1 THE NATURE OF FATIGUE LOADING ........................................................................ 3 2.2 FATIGUE BEHAVIOUR OF STRUCTURAL DETAILS ..................................................... 8 2.3 FATIGUE OF WELDED STRUCTURES ....................................................................... 12 2.3.1 Stress Concentrations..................................................................................... 12 2.3.2 Weld Defects................................................................................................... 15 2.3.3 Residual Stress................................................................................................ 16 2.4 FURTHER FACTORS AFFECTING WELD FATIGUE .................................................... 19 2.4.1 Effect of Steel Strength ................................................................................... 19 2.4.2 Effect of Plate Thickness ................................................................................ 20 2.4.3 Effect of Environment ..................................................................................... 20 2.4.4 Effect of Welding Method ............................................................................... 20 2.5 PREDICTING FATIGUE LIFE UNDER VARIABLE AMPLITUDE LOADING.................... 21 2.6 FATIGUE OF TUBULAR JOINTS ................................................................................ 24 2.7 FATIGUE OF OTHER STRUCTURAL DETAILS ........................................................... 34 2.8 WELD FATIGUE LIFE IMPROVEMENT TECHNIQUES................................................. 343 FATIGUE ANALYSIS .............................................................................................. 36 3.1 DETERMINISTIC FATIGUE ANALYSIS ...................................................................... 36 3.2 SPECTRAL FATIGUE ANALYSIS............................................................................... 37 3.3 RELATIVE MERITS OF DETERMINISTIC AND SPECTRAL FATIGUE ANALYSIS .......... 404 RISK BASED FATIGUE ANALYSIS AND INSPECTION PLANNING ........... 435 REFERENCES .......................................................................................................... 47 5.1 BOOKS ................................................................................................................... 47 5.2 STANDARDS ........................................................................................................... 47 5.3 RESEARCH REPORTS AND PAPERS .......................................................................... 47Platform, Pipeline and Subsea Technology– Fatigue Design 2
  • 3. 1 IntroductionThis section of the unit describes the phenomenon of structural fatigue, and discusses theapproaches used to design and maintain structures against fatigue failure. It is organizedinto three sections: the first provides a general background to structural fatigue, the seconddiscusses methods of fatigue analysis used in the design of offshore structures, and thethird provides an introduction to risk-based approaches and inspection philosophies.2 Structural FatigueIn the context of engineering, fatigue is the process by which a crack can form and thengrow under repeated or fluctuating loading.The magnitude of the fluctuating loading required to induce fatigue cracking may be muchless than that required to cause failure under a single application of the load. Inparticular, it may be much less than the load corresponding to the allowable staticdesign stress.While some types of structure may be able to tolerate extensive cracking withoutcompromising their load-carrying capacity, other structures may be prone to suddencollapse or excessive deflection if a crack is allowed to progress to some critical size.The initiation and growth of fatigue cracks depends on the number of load cycles,regardless of whether these cycles occur in quick succession, or there are significantperiods of time between them. Fatigue performance is therefore often expressed as a life(or period of time before failure) under a particular loading regime. An importantcorollary of this is that fatigue is a cumulative process.2.1 The Nature of Fatigue LoadingThe definitions commonly used to describing individual fatigue loading cycles are shownin Figure 2-1. Note carefully the definition of stress range which is important in thefatigue analysis of welded structures.Another parameter which is sometimes used to describe fatigue loading cycles is theStress Ratio, which is defined commonly as the lower limit stress/upper limit stress, orsimply as: Minimum Stress Stress Ratio  (1) Maximum StressFigure 2-1 shows constant amplitude loading, however, in practice the majority ofengineering structures are subjected to some type of variable amplitude, or randomloading. Some general examples are shown in Figure 2-2.Platform, Pipeline and Subsea Technology– Fatigue Design 3
  • 4. Figure 2-1: Definition of parameters describing constant amplitude fatigue loading cycles. Figure 2-2: Some general examples of random loading on engineering structures.Platform, Pipeline and Subsea Technology– Fatigue Design 4
  • 5. Some examples of loads which contribute to fatigue damage may be:  Loads induced during fabrication or construction.  Loads induced during transportation.  Loads induced during installation (e.g. pile driving)  In-place loads induced by waves, current and wind.  Pressure variations (for pipelines and pressure vessels).  Temperature variations.  Weight variations (or live loads).  Vortex induced vibrations.  Machinery induced vibrations.In the case of fixed and floating offshore platforms it is usually the in-place environmentalloads due to waves which contribute mostly to fatigue damage.Figure 2-3 shows the stress variation in the joint of an offshore platform due to waveloading. Unsurprisingly the stress variation follows the water surface elevation, i.e. thestress fluctuations are associated directly with waves. Figure 2-3: Example of stress variation in a joint of a fixed offshore platform.Figure 2-2 and Figure 2-3 show examples of random fatigue loading described in the timedomain. It is also possible to represent a time series of water surface elevations (andassociated fatigue loads) as the sum of a number of sinusoidal wave components, by aFourier series: N x(t )   ai cos( i t   i ) (2) i 1Where ai is the amplitude and i is the frequency of the ith wave component. i representsa phase anglePlatform, Pipeline and Subsea Technology– Fatigue Design 5
  • 6. This concept is shown in Figure 2-4. This permits the random loads to be described in thefrequency domain by an energy spectrum, S() which is defined as: 1 ai2 S(ω i )  2 (2) ωwhere i is a discrete frequency, and ai is the amplitude of the cycles in the frequencyband . These definitions are further illustrated in Figure 2-5. This definition of a loadspectrum can be useful in spectral fatigue analysis, which will be discussed in a latersection of these notes. Figure 2-4: The relationship between time domain and frequency domain representation of ocean waves. Figure 2-5: A random load x(t) and its energy spectrum, S().Platform, Pipeline and Subsea Technology– Fatigue Design 6
  • 7. Spectra are sometimes described as either broad-banded or narrow-banded and theseconcepts are shown in Figure 2-6. In a broad-banded process, a number of smaller cyclesare superimposed on larger cycles, and these smaller cycles may not pass through themean level. By contrast, in a narrow-banded process most cycles pass through the meanvalue. Figure 2-6: Definition of narrow-band and broad-band load spectra.A further important point is that fatigue loads reflect the dynamic behaviour of thestructure. If a structure is excited at close to its natural frequency, dynamic amplificationof the loads must be accounted for. A simple way that is sometimes used to correct theresults of a quasi-static structural analysis to account for dynamics is to assume that thestructure behaves as a single degree of freedom system. A Dynamic Amplification Factor(DAF) is simply applied to the stresses calculated in the quasi-static analysis. The DAF isa function of the system damping and the closeness of the frequency of the excitationforce and the natural frequency of the structure. It may be calculated according to thefollowing equation, and the relationship between the DAF and damping, and the excitationfrequency is shown in Figure 2-7. Figure 2-7: Relationship between Dynamic Amplification Factor (DAF), damping ratio() and /N.Platform, Pipeline and Subsea Technology– Fatigue Design 7
  • 8. 1 DAF  (3) 1     2  ζ   2 2 2where   ω ωNand  is the damping ratio,  is the frequency of the excitation force, N is the natural frequency of the structure (assuming a single degree of freedom system).For sway of fixed offshore platforms, a commonly used damping ratio in fatigue analysisis  = 0.02.For dynamically sensitive structures, or sections of structures, a more rigorous approach isoften required. An excellent reference is Barltrop and Adams (1991).2.2 Fatigue Behaviour of Structural DetailsIn describing the fatigue behaviour of engineering structures, the focus is frequently onstructural details. This is because fatigue cracking is highly localized. Therefore, inengineering design the fatigue behaviour of each detail must be considered under theaction of local loads.Fortunately, there is now a considerable body of test data covering a wide range ofstructural details. Figure 2-8 shows a butt welded specimen being tested under constantamplitude loading in a hydraulically powered fatigue test machine. Data from these typesof test form the basis for fatigue analysis. The data is usually presented as an S-N curve,which plots Stress Range on the ordinate (y axis) and Number of Cycles to Failure (on alogarithmic scale) on the abscissa (x axis). An example is given in Figure 2-9.It is worthwhile noting the wide range of scatter in the test results (an order of magnitudein cycles to failure in some cases!). Therefore, Design S-N curves usually represent themean line minus 2 standard deviations to obtain a suitably conservative estimate of thenumber of cycles to fatigue failure.Some S-N curves include an endurance limit, or stress level below which fatigue failurewill not occur irrespective of the number of loading cycles applied to the specimen (seeFigure 2-10). To a large extent this is a consequence of the method of fatigue testing. Thecorrect method of dealing with small amplitude load cycles in the fatigue analysis ofwelded structures remains the subject of ongoing research. However, there is increasingevidence that endurance limits should be ignored, particularly for structuressubjected to variable amplitude loading in corrosive environments. However, someengineering guidelines make a compromise by suggesting S-N curves with different slopein the low stress region. Some examples of these are provided later in these notes.Platform, Pipeline and Subsea Technology– Fatigue Design 8
  • 9. Figure 2-8: Constant amplitude fatigue test of a butt welded specimen.Platform, Pipeline and Subsea Technology– Fatigue Design 9
  • 10. Figure 2-9: Fatigue test data for butt welded specimens.Platform, Pipeline and Subsea Technology– Fatigue Design 10
  • 11. Stress Endurance Limit S0 Number of Cycles Figure 2-10: The endurance limit represents the stress level below which fatigue failure will not occur in a constant amplitude fatigue test.One important shortcoming in describing fatigue behaviour using an S-N curve is that thepoint of “failure” is not always clearly defined. For example, it may be the point at whicha detectable crack initiates, the point at which a crack proceeds through the full thicknessof a plate, or the point at which a structural specimen breaks in half.A more physically correct approach is to describe the propagation of a crack under cyclicloading using fracture mechanics techniques. Unfortunately, a discussion of fracturemechanics techniques is beyond the scope of this course, however, there are numeroustexts on this subject (a good introduction is the book by Broek (1986)). Furthermore,British Standard 7910 provides an excellent engineering guidance for assessing flaws andcracks in engineering structures using fracture mechanics techniques (also known asEngineering Critical Analysis).Platform, Pipeline and Subsea Technology– Fatigue Design 11
  • 12. 2.3 Fatigue of Welded StructuresWelded joints are particularly susceptible to fatigue failure. Figure 2-11 compares thefatigue performance of welded specimens with plain steel specimens and specimenscontaining holes. Figure 2-11: S-N Curves comparing the fatigue behaviour of welded specimens with plane plate and notched specimens.There are three major factors which contribute to the susceptibility of welded joints tofatigue failure: 1. As joints, welds are subjected to both the stress concentration caused by their location at structural discontinuities, and the stress raising effect of the weld shape itself. 2. Due to the nature of the welding process they are likely to contain defects which act as fatigue crack initiators. 3. High tensile residual stresses frequently exist in the vicinity of the weld as a result of shrinkage during solidification and cooling of the weld metal.These reasons are all important, and influence the way in which engineers carry outfatigue analysis of welded structures, and ultimately design against fatigue failure. Theyare therefore discussed in more detail in the following sections.2.3.1 Stress ConcentrationsThere are two important sources of stress concentration which contribute to thesusceptibility of welded joints to fatigue cracking.Platform, Pipeline and Subsea Technology– Fatigue Design 12
  • 13. The first source of stress concentration is due to the location of welds at structuraldiscontinuities where there are changes in geometry and stiffness. This leads to a localincrease in stress at locations within the joint, and these are sometimes referred to as “hotspots”. Misalignment of joints can also lead to secondary bending moments which canincrease stresses locally.The concept of hot spot stress concentration is illustrated in Figure 2-12. Figure 2-12: Example of hot spot stresses in a tubular nodal joint.Platform, Pipeline and Subsea Technology– Fatigue Design 13
  • 14. The second source of stress concentration is the shape of the weld itself. A notch isformed by the toe of the weld and this location is by far the most common initiation sitefor fatigue cracking in welded structures. However, the root of partial penetration weldsand defects introduced during the welding process also represent notches, and thereforepotential fatigue initiation sites. Some examples of fatigue crack initiation sites in weldsare shown in Figure 2-13 while the influence of the toe radius and flank angle on thefatigue performance of butt welds is shown in Figure 2-14. (a) (b) (c) Figure 2-13: Fatigue crack initiation sites: (a) at the toe of a butt weld, (b) at the toe of a butt weld containing porosity, (c) at a lack of penetration defect. Percent reduction in fatigue strength Figure 2-14: Influence of flank angle and toe radius on the reduction in fatigue strength of butt welded joints.Platform, Pipeline and Subsea Technology– Fatigue Design 14
  • 15. The influence of weld shape and defects on fatigue behaviour emphasizes the importanceof weld quality in achieving adequate fatigue performance of welded joints. Particularcare should be taken with weld quality when joints are subjected to fatigue loading.Another important point is that S-N curves for welded joints are based on experimentaldata from fatigue tests on welded structural details. Therefore the stress concentration dueto the weld itself is included implicitly in the S-N curve and does not need to beconsidered separately. The stress range on the ordinate (y axis) of the S-N curves ofwelded details refers to the local, or hot spot stress. This stress must be calculated as partof any fatigue analysis.2.3.2 Weld DefectsThe complexity of the welding process often leads to defects occurring in, or adjacent to,the weld metal. These may be macroscopic defects (such as lack of fusion between weldmetal and parent plate, cracking, inclusions, or porosity) which are commonly detectedusing conventional non-destructive examination techniques. It is common practice toexamine critical welds in structures to ensure that any defects present are below anacceptable level.However, even in “sound” welds a range of microscopic defects may occur. These arecommonly encountered at the weld toe where melted weld metal meets unmelted parentmetal and surface oxides. The rapid cooling of this zone promotes materialheterogeneities and the formation of a range of microscopic defects which may includeporosity, slag inclusions and sharp undercuts. These defects coincide with the stressconcentration of the weld and may ultimately become the initiation sites of fatigue cracks.The nature of these defects is shown diagrammatically in Figure 2-15. Intrusions at weld toe approx 0.1-0.15 mm deep Figure 2-15: Microscopic intrusions at the toe of a “sound” weld.Platform, Pipeline and Subsea Technology– Fatigue Design 15
  • 16. 2.3.3 Residual StressThe contraction of weld metal during solidification and cooling is responsible for theintroduction of “locked-in” residual stresses in welded structures. These stresses existindependent of external loading. Therefore they will be balanced within the structure; inother words there is a system of tensile and compressive components of stress which is inequilibrium.Two systems of residual stress may be produced in a welded structure: global reactionstresses which affect members as a whole, and localized residual stresses in the vicinity ofjoints.The concept of global reaction stresses is shown in Figure 2-16. Here the assemblyprocedure may introduce an overall distribution of stresses within the structure. In thesimplest cases, tension in some members will be balanced by compression in others. Tensile load in brace balanced by compression load in adjacent members Girth weld completed after adjacent welds Figure 2-16: Concept of global reaction stresses.The concept of localized residual stresses is shown in Figure 2-17 and Figure 2-18. Mostwelded joints have sufficient external restraint to lead to tensile residual stresses of similarmagnitude to the material yield stress in the vicinity of the joint.Platform, Pipeline and Subsea Technology– Fatigue Design 16
  • 17. Figure 2-17: Formation of residual stress as a result of welding: (a) expected longitudinal shrinkage of “unrestrained” weld; (b) longitudinal shrinkage of restrained weld. Figure 2-18: Typical residual stress distribution in a welded joint.From the viewpoint of the analysis of welded structures the most important residualstresses are the localized stresses in the joint. To understand the implications of high localPlatform, Pipeline and Subsea Technology– Fatigue Design 17
  • 18. tensile residual stress on fatigue, consider Figure 2-19 which shows an alternating fatigueload applied to a welded joint. It is well established that, all other things being equal,compressive stress does not contribute to fatigue crack initiation or propagation.Therefore only the tensile part of the loading cycle contributes to fatigue failure.However, if a tensile residual stress of yield stress magnitude is present at the weld, thiscombines with the fatigue load to give the stress cycle shown in Figure 2-19(b). Here anelastic-perfectly plastic material behaviour has been assumed so that the stress cycle variesfrom the yield stress downwards. In this instance the entire stress range is tensile andtherefore damaging from the viewpoint of fatigue. Figure 2-19: When the residual stress is equivalent to a tensile yield stress the actual stress range will vary from yield stress downwards, regardless of the nominal stress ratio.Therefore, the significance of welding residual stress is that even compressive loadsapplied to a structure may lead to a net tensile fatigue stress in the vicinity of the welds.For this reason it is the stress range which is usually most important in determiningthe fatigue behaviour of welded joints.Localized residual stresses can be relieved to some extent by Post Weld Heat Treatment(PWHT). This involves heating the joint in an oven to approximately 600C for a periodof some hours. The yield stress of the steel is reduced by the heating and this allowsrelaxation of the locked-in stresses. Some fatigue analysis guidelines make allowance fora limited benefit from PWHT. If in doubt, a conservative approach is to ignore anybeneficial effects which may arise from PWHT.Platform, Pipeline and Subsea Technology– Fatigue Design 18
  • 19. 2.4 Further Factors Affecting Weld FatigueThere are a number of other factors which have some influence on the fatigue behaviourof welded joints and are usually taken into account during fatigue analysis. These aredescribed in this section.2.4.1 Effect of Steel StrengthOne of the most useful features of steel is that its mechanical properties can besignificantly altered through alloying and heat treatment. Up to a certain limit, the fatiguestrength of smooth steel specimens increases proportionally with tensile strength.However, this relationship does not hold for welded joints. Figure 2-20 shows fatigue testresults for welded specimens made from steels ranging in tensile strength from 438 to 753MPa. The test results fall within a relatively narrow scatter band and there is nocorrelation between ultimate tensile strength and fatigue strength.Therefore, if an engineering design is limited by its fatigue performance, using ahigher strength steel will not improve the situation. Figure 2-20: Effect of steel ultimate tensile strength on fatigue behaviour (note: 1 tons/in2 = 15.44 MPa).Platform, Pipeline and Subsea Technology– Fatigue Design 19
  • 20. 2.4.2 Effect of Plate ThicknessIt has generally been observed that, all other things being equal, increasing plate thicknessresults in a decrease in fatigue performance. Figure 2-21 shows the results of fatigue testson welded specimens in bending. Although the reason for the thickness effect is notuniversally agreed, one suggestion has been that thinner plates have a higher stressgradient, and therefore the driving force behind fatigue crack growth decreases morerapidly than in thick plates. Most design codes and standards which deal with fatiguedesign include a correction for the thickness effect. Figure 2-21: Fatigue test results showing the influence of plate thickness.2.4.3 Effect of EnvironmentA corrosive environment, such as seawater, may have the effect of accelerating the growthof fatigue cracks, and therefore reducing overall fatigue performance. The presence of acorrosive environment also effectively removes the endurance limit on the S-N curve.Cathodic protection reduces the impact of this detrimental effect to some extent.In the case of offshore structures different S-N curves are usually specified depending onthe prevailing corrosion conditions. It is important to note at this point that cathodicprotection is ineffective for joints in the splash zone where electrolyte presence is notcontinuous. These joints exist under effectively free corrosion conditions.2.4.4 Effect of Welding MethodThere is very little evidence to suggest that, among common welding techniques, differentwelding methods produce intrinsically different fatigue strengths in welded joints. IfPlatform, Pipeline and Subsea Technology– Fatigue Design 20
  • 21. anything, manual welding techniques produce welds with marginally better fatigueperformance compared with automatic welds.2.5 Predicting Fatigue Life Under Variable Amplitude LoadingIt has already been discussed how S-N curves are generated from laboratory tests carriedout under constant amplitude fatigue conditions. However, it has also been pointed outthat most engineering structures are subject to random, variable amplitude loading. It istherefore necessary to have a method of estimating the fatigue life under a variableamplitude loading regime, but still use S-N curves generated under constant amplitudeloading.The method that has achieved the broadest acceptance is the Palmgren-Miner linearcumulative damage hypothesis, commonly known as Miner’s Rule. This states that ni n1 n2 n3 N    N1 N 3 N 3  ... D (4) iwhere n1, n2,… are the number of cycles that stresses 1, 2,… are applied to the joint, andN1, N2,… are the corresponding numbers of cycles to failure of a similar joint underconstant amplitude loading at those stresses. D is a constant that represents theaccumulated fatigue “damage” of the joint. If D = 1.0, the rule may be restated that,under variable amplitude loading, the basic damage fraction caused by each separateloading cycle is equal to that caused by a single cycle of the corresponding constantamplitude loading, and that failure occurs when the sum of these basic damage fractionsreaches unity.This concept is shown diagrammatically in Figure 2-22. 1 2 3 Figure 2-22: Definition of Miner’s rule.Platform, Pipeline and Subsea Technology– Fatigue Design 21
  • 22. Figure 2-23 shows a comparison of Miner’s Rule with typical experimental fatigue testresults under variable amplitude loading. It can be seen that a Miner’s summation (ordamage accumulation, D) =1.0 is the most likely result corresponding to failure, however,there is considerable variation in the results. 0.35 Frequency of Occurrence 0.3 0.25 0.2 Corresponding lognormal distribution 0.15 0.1 0.05 0 0 1 2 3 4 5 6 7 8 9 Miners Sum Figure 2-23: Comparison of calculated Miner’s summation and variable amplitude test results.There may be instances where a method of turning a time series of stresses into a numberof discrete stress cycles is required. A complete discussion of the various methodsavailable is beyond the scope of this course, however it is worth mentioning that theRainflow, or Reservoir method of cycle counting has gained the broadest acceptance. Adiscussion of this technique can be found in British Standard BS 7608:1993. In manyinstances, the fatigue loads in offshore structures are already grouped in a manner which isconducive to fatigue analysis using Miner’s Rule. An example of this is the waveoccurrence table shown in Figure 2-24.An alternative is the wave height exceedance diagram of Figure 2-25 which shows Waveheight on the ordinate (y axis), and the number of waves exceeding a particular waveheight on the abscissa (x axis).An important corollary of the Miner’s Rule calculation is that a large number of smallstress cycles can be as equally damaging as a few large cycles. It is therefore important tobe able to carry out the Miner’s Rule calculation in order to determine just how damaginga given loading spectrum really is.Platform, Pipeline and Subsea Technology– Fatigue Design 22
  • 23. Figure 2-24: Wave occurrence table for fatigue analysis (25 year period).Platform, Pipeline and Subsea Technology– Fatigue Design 23
  • 24. 16.0 North West Shelf (typical) 14.0 Central North Sea (typical) Gulf of Mexico (design) Significant Wave Height, H sig (m) 12.0 10.0 Central North Sea 8.0 6.0 North West Shelf 4.0 (shallow water) 2.0 0.0 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Number of Waves Exceeding H sig per year Figure 2-25: Wave height exceedance diagram.2.6 Fatigue of Tubular JointsThe vast majority of fixed offshore platforms are constructed from a space frame oftubular joints. Considerable research effort has therefore been directed towardcharacterizing the fatigue performance of this particular class of welded joint.Where tubulars are butt jointed to form members, any eccentricity between adjacenttubulars can lead to the development of secondary bending moments in response to axialloads in the member. For the purposes of fatigue analysis this may be accounted for byassigning a Stress Concentration Factor (SCF) which, when multiplied by the nominalaxial stress in the member, describes the increased local stress in the vicinity of the weldedjoint, i.e. local = SCFnominal (5)The various sources of geometric stress concentration which may be encountered in atubular butt weld are shown in Figure 2-26. For butt welded tubular members, thefollowing formula for eccentricities in flat plates provides a conservative estimate of theSCF at the joints: 3( m ) SCF  1  (6) tPlatform, Pipeline and Subsea Technology– Fatigue Design 24
  • 25. A more sophisticated and less conservative method of evaluating the stress concentrationfactor in butt jointed members can be found in DNV-Recommended Practice C203, alongwith guidance for joints in pipelines. Figure 2-26: Sources of geometric stress concentration in butt welded tubular members.Where tubular members such as jacket braces and legs intersect, a complex geometry iscreated. In these cases the stress distribution around the joint is not uniform due to thecomplexity of the localized geometry. Considerable effort has been spent investigatingstress concentration factors to be used with tubular joints such as those shown in Figure2-27. The methods used have included strain gauging and load testing scale models,photoelastic testing, and detailed finite element modelling. These activities have resultedin the availability of parametric equations which are suitable for the analysis of a range ofcommonly encountered tubular joints. A comprehensive discussion of this subject may befound in HSE (1997).Appendix A provides the parametric equations due to Efthymiou (1988), which areprobably now the most widely used of their type. The SCFs for T and Y joints are definedonly at the “crown” and “saddle” locations (refer back to Figure 2-12 for the definition ofthese locations). Therefore there must be some method of interpolation so that the SCFsat the intermediate points can be calculated. The conventional method is to linearlyinterpolate the SCFs for axial loading, while the SCFs associated with in-plane and out-of-plane loading are sinusoidally distributed. This concept is shown in Figure 2-28.Platform, Pipeline and Subsea Technology– Fatigue Design 25
  • 26. Figure 2-27: Geometric parameters describing welded tubular joints.When carrying out the interpolation described above it is important to understand that theSCFs calculated using parametric equations for tubular joints should be used only with thenominal member stresses. In the case of axial SCFs, the nominal member axial stressshould be used in conjunction with the calculated SCF, while in the case of bending SCFs,the maximum (outer fibre) bending stress should be used in conjunction with the relevantbending SCF. 3 2 4 1 5 8 6 7 Figure 2-28: Recommended distribution factors for SCFs in T & Y joints.Platform, Pipeline and Subsea Technology– Fatigue Design 26
  • 27. Stresses due to axial, in-plane bending and out-of-plane bending loads may be added usingthe principle of superposition. The following formula is useful:HSS  SCFaxS  SCFaxC  SCFaxS   θ 90σ ax     SCFipC  sin θ σ ip  (7)   SCFopS  cos θ σ op  where HSS is the hot spot stress SCFaxS is the axial SCF at the saddle point SCFaxC is the axial SCF at the crown point SCFipC is the in-plane bending SCF at the crown point SCFopS is the out-of-plane bending SCF at the saddle point ax is the nominal axial stress ip is the nominal (maximum) in-plane bending stress op is the nominal (maximum) out-of-plane bending stress  is the angle around the joint measured from the saddle (see diagram below). Crown 90  Saddle 0 Figure 2-29: Definition of  in hot spot stress calculation equation.Note that this method of interpolating the axial SCFs only works in the first quadrant (i.e.for  between 0 and 90 degrees) Symmetry should be used to determine the interpolatedaxial SCFs in the other quadrants.The fatigue behaviour of tubular joints has been characterized by numerous fatigue tests,and typical results are shown in Figure 2-30. From tests such as these, suitablyPlatform, Pipeline and Subsea Technology– Fatigue Design 27
  • 28. conservative design S-N curves can be derived. As an example, Figures 231 to 233show the design S-N curves for tubular joints published in the UK Health and SafetyExecutive’s (HSE) guidance on the design, construction and certification of offshoreinstallations. Different curves are shown for fatigue of joints in air, under free corrosionconditions in seawater, and in seawater with cathodic protection. These S-N curves mayalso be expressed mathematically as: log10 ( N )  log10 ( K1 )  m log10 ( S B ) (8)where N is the predicted number of cycles to failure under stress range SB, K1 is a constantand m is the inverse slope of the S-N curve. Details of the basic design S-N curves aregiven in Table 1 below. S0 and N0 represent the point where the slope of the S-N curvechanges, see Figure 2-34.The HSE design S-N curves apply to all joints with plate thicknesses of 16 mm or less.For thicker joints, a thickness correction applies to take account of the thickness effect onwelded joints discussed previously. The thickness correction can be incorporated into themathematical expression of the S-N curves in the following manner:  SB  log10 ( N )  log10 ( K1 )  m log10    t t q  (9)  B where tB is the reference thickness, = 16 mm t is the thickness of the member under consideration q is the thickness exponent factor, = 0.3 and all other constants are defined as before.Platform, Pipeline and Subsea Technology– Fatigue Design 28
  • 29. Figure 2-30: Experimental results for 16mm thick tubular joints tested in air. Table 1: Details of thee basic S-N curves in HSE Guidance. Welded Plates Tubular JointsPlatform, Pipeline and Subsea Technology– Fatigue Design 29
  • 30. Figure 2-31: Basic HSE design S-N curves for welded tubular joints and plates in air.Platform, Pipeline and Subsea Technology– Fatigue Design 30
  • 31. Figure 2-32: Basic HSE design S-N curves for welded tubular joints and plates in seawater – free corrosion.Platform, Pipeline and Subsea Technology– Fatigue Design 31
  • 32. Figure 2-33: Basic HSE design S-N curves for welded tubular joints and plates in seawater – cathodic protection.Platform, Pipeline and Subsea Technology– Fatigue Design 32
  • 33. Stress Point where slope of S-N curve changes S0 N0 Number of Cycles Figure 2-34: Definition of S0 and N0 on dual slope S-N curve.It is important to note that different offshore design codes have subtle differences in theelements of fatigue analysis. There are slight differences in S-N curves, thicknesscorrections, and the required fatigue design life. Once a particular fatigue design codeis adopted, it should be followed consistently, and in its entirety.A good example of the differences between design codes is the required fatigue designlife. The API offshore design code, RP2A, requires that the calculated fatigue life be atleast twice the design life of the structure, whereas the HSE guidance requires that thecalculate fatigue life be at least equal to the design life (however, a more conservative S-Ncurve is used in the latter case). The Norwegian offshore structural design code (NorsokStandard N-004, 1998) suggests an even more sophisticated approach where the calculateddesign lives also depend on the accessibility of the joint for inspection and repair, and thisis described in Table 2. Note that a design fatigue factor of 10 means that the calculatedfatigue life must be at least 10 times the design life of the structure. Table 2: Design fatigue factors (from Norsok Standard N-004, 1998). Access for Inspection and RepairClassification of structuralcomponents based on No access, or in the Accessibledamage consequence splash zone Below Splash Zone Above Splash ZoneSubstantial Consequences 10 3 2Without Substantial 3 2 1ConsequencesPlatform, Pipeline and Subsea Technology– Fatigue Design 33
  • 34. 2.7 Fatigue of Other Structural DetailsIn addition to tubular joints there are, of course, a wide range of other types of weldedstructural details which occur in offshore structures. These include attachments such asladders and boat landings, standard weld details in the topsides structure, and ship detailsin FPSOs and other floating production systems. Where these joints are subjected tofluctuating loading, their fatigue performance must also be assessed.Fortunately, there are a range of design standards and guidelines which describe the S-Ncurves and analysis methodologies for a range of commonly encountered structural details.These guidelines include: British Standard 7608:1993 and DNV Recommended Practice RP-C203 (2001) which provide guidance for the analysis of a range of common structural details, some of which might typically be found in platform topside structures. DNV Class Note 30.7 (1998) which provides guidance on stress concentration factors and design S-N curves for a range of ship structural details which might typically be found in FPSOs and other offshore structures made up from stiffened panels.2.8 Weld Fatigue Life Improvement TechniquesBecause of the susceptibility of welded joints to fatigue failure, there have been numeroustechniques developed to improve their behaviour. Gurney (1979) provides acomprehensive coverage of the different methods which have been tested.However, in practice, the most widely used methods for improving the fatigue behaviourof welded joints are toe grinding and peening.Toe grinding involves using either a disc, or rotary burr grinder to reduce the stressconcentration at the toe of the weld as shown in Figure 2-35. To be most effective, toegrinding should extend 0.5–1.0 mm into the parent plate to remove any small undercuts orintrusions which may act as fatigue crack initiators.Peening involves impacting the surface of the weld with a pneumatic hammer fitted with arounded tool. This induces a compressive residual stress which retards fatigue crackinitiation. Peening is usually directed towards the toe of the weld and this may have theadded benefit of also improving the shape of the weld toe.The relative benefits of toe grinding and peening are shown in Figure 2-36. Despite thesignificant benefits which can be achieved through these techniques, they are timeconsuming and costly, and skill is required to achieve consistently good results. It is forthese reasons that these techniques are rarely considered in the design of welded joints(that is, joints are usually designed so that improvement techniques are not relied upon toachieve satisfactory performance). However, they are sometimes used as an addeddefence against fatigue failure in critical welds.Platform, Pipeline and Subsea Technology– Fatigue Design 34
  • 35. Methods of improving the fatigue performance of a joint at the design stage includemodifying the joint geometry to reduce local stresses, or replacing the welded tubular jointwith a cast node. Using a casting is an expensive option, but may be cost effective forparticularly complex joints. 0.5 mm min Figure 2-35: It is recommended that toe grinding extend below the plate surface to remove weld defects. Figure 2-36: Comparison of grinding, peening and some other weld improvement techniques on the fatigue performance of fillet welded specimens.Platform, Pipeline and Subsea Technology– Fatigue Design 35
  • 36. 3 Fatigue AnalysisThere are two common approaches in the fatigue analysis of offshore structures. Perhapsthe most popular is analysis in the time domain, commonly known as deterministicfatigue analysis. However, as will be discussed in a later section, there can be someadvantages carrying out fatigue analysis in the frequency domain, and this type of analysisis called a stochastic, or spectral fatigue analysis.The deterministic and spectral approaches to fatigue analysis are described in thefollowing sections, and the relative advantages of each are compared.3.1 Deterministic Fatigue AnalysisDeterministic fatigue analysis requires fatigue loads to be expressed as a finite number ofdiscrete events. An example of this was provided in Figure 2-24 where a discrete numbersof waves of varying height and period are provided over a 25 year period.The subsequent deterministic fatigue analysis is best summarised as a series of steps:1. All the physical phenomena which are likely to contribute to fatigue of a structure over its entire life need to be identified. In the case of offshore structures these may include loads imposed during construction, transportation, live loads due to machinery, and, perhaps most importantly, in-place environmental loads due to waves, current and wind. It must be recognized that the stresses at any potential fatigue failure site in the structure will be different for waves coming from different directions and this must be accounted for in the analysis.2. The physical phenomena need to be translated into loads on structural members. The use of specialized offshore structural computer analysis packages can often be used for this step. The effect of dynamics should also be accounted for.3. Loads in structural members need to be translated into localized joint stresses. Member loads must firstly be translated into member stresses and, in the case of tubular joints, hot spot stress concentration factors can be used to determine the localized stresses at various points around the joint. Typically 8 locations around the joint on both the chord and brace would be considered. Remember that it is the stress range which is important in determining fatigue behaviour, and so the maximum and minimum hot spot stresses need to be determined.4. A S-N curve describing the relevant structural detail must be chosen. Appropriate codes and standards provide a range of S-N curves.5. A Fatigue Damage calculation must be carried out using Miner’s Rule. The calculation must be carried out for expected loads over the design lifetime of the structure. Remember that Miner’s Rule is cumulative, therefore the fatigue damage due to one set of loads can be added directly to the fatigue damage caused by other loads. In particular the fatigue damage may be summed for each wave direction.Platform, Pipeline and Subsea Technology– Fatigue Design 36
  • 37. 6. The fatigue life of each detail (or hot spot) of interest can be compared with the design life after appropriate factors of safety have been accounted for.3.2 Spectral Fatigue AnalysisSpectral fatigue analysis recognizes the underlying random nature of the wave heightoccurrence table (as given in Figure 2-24) and models the process statistically.It has already been discussed in S ection 2.1 of these notes that a random series (of forexample wave heights) may be expressed as an energy spectrum. Figure 2-5 isreproduced below:The energy of a harmonic wave is proportional to the square of its amplitude, and theenergy in each frequency band is given by the following equation: 1 ai2 S (ω i )  2 (10) ωUsing Fourier analysis techniques, a random process such as a wave history may berepresented by a superposition of a large number of sinusoidal components. If onecomponent of the excitation process is given by x(t )  ai  cos(ω i t   i ) (11)then the component of the response at the same frequency is given by y (t )  Tω  x(t ) (12)Platform, Pipeline and Subsea Technology– Fatigue Design 37
  • 38. This provides the definition of the transfer function, T(). The excitation process istypically the wave height spectrum. The response function is typically the hot spot stressrange at a particular joint location.The energy spectrum of the response may therefore be related to the energy spectrum ofthe excitation by using the relationship S y (ω)  Tω  S x (ω) 2 (13)The relationship between the excitation spectrum, the response spectrum and the transferfunction is illustrated in Figure 3-1. Figure 3-1: The transfer function T(f) relates the excitation spectrum Sx(f) and the response spectrum Sy(f).The excitation and response functions, as well as the transfer functions may equally beexpressed as functions of frequency in Hz, instead of radians/sec. The definition of thetransfer function would then be given by: S y ( f )  T f   S x ( f ) 2 (14)where f represents frequency expressed in Hz. The remainder of this section of the noteswill assume that the functions are expressed in Hz. In passing, it is important to note thatcare should be taken to properly define the shape of the loading spectrum and transferfunction, particularly around the natural frequencies of the structure.Once a fatigue stress spectrum has been developed (i.e. a plot of Sy( f )) then the fatiguedamage may be calculated by firstly calculating the zero and second order moments of thestress spectrum.The moments of an energy spectrum are defined as:Platform, Pipeline and Subsea Technology– Fatigue Design 38
  • 39.  m n   S x  f   f n df (15) 0Therefore the zero order moment is:  m 0   S x  f df (16) 0and this represents the area under the spectral curve.The second order moment is:  m 2   S x  f   f 2 df (17) 0In practice, these integrals can be evaluated by numerical integration using for examplethe trapezoid rule. This concept is shown in Figure 3-2. Figure 3-2: Definition of zero order and second order moments of response spectrum.For a narrow-banded process, and where the frequency in the response spectrum isexpressed in Hz, the mean zero upcrossing period may be approximated as: m0 Tz  (18) m2Platform, Pipeline and Subsea Technology– Fatigue Design 39
  • 40. [ Note that this equation will be slightly different if the input, output and stress transferfunctions are expressed in rad/sec. rather than Hz. ]The number of stress cycles, n, in a total time of T seconds is therefore given by: T n (19) TzThe complete derivation of spectral fatigue damage under a narrow banded process isbeyond the scope of this course. Interested readers are referred to Barltrop and Adams(1990). However, assuming that the stress range within each short term seastate can bedescribed by the Rayleigh distribution, the fatigue damage for each seastate may becalculated as: m 2 (8m 0 ) m 2  2  m  D T      (20) m0 K  2 where T is the time period in seconds m0, m2 are the zero and second order spectral moments (defined above) m and K are constants describing the S-N curve (see Section 2.6 of these notes)   is the incomplete gamma function: ( g )   x ( g 1) e x dx 0The fatigue damage may be summed linearly over all seastates and all wave directions. IfT is the number of seconds in 1 year, then the fatigue life of the hot spot in years will be1/D. The spectral fatigue analysis approach is illustrated schematically in Figure 3-3.3.3 Relative Merits of Deterministic and Spectral Fatigue AnalysisAn important aspect of spectral fatigue analysis is that, via the transfer function, it canaccount for dynamic effects more completely than deterministic fatigue analysis.Provided that appropriate software is available to develop the transfer function betweenthe excitation spectrum and the response spectrum spectral analysis is usually morecomputationally efficient than deterministic analysis.However, an important implicit assumption in the development of the transfer function isthat it applies to each wave component irrespective of its amplitude. This means that theremust be a linear relationship between the excitation (wave height) and the response (hotspot stress range). In practice, this is a reasonable approximation for large jacket typestructures in moderate to deep water depth, although effort is sometimes put towardmodifying the transfer functions to account for the non-linear nature of the drag force inMorison’s equation and the non-linear kinematics associated with higher order wavePlatform, Pipeline and Subsea Technology– Fatigue Design 40
  • 41. theories. These effects may be particularly important for smaller structures in shallowwater, and spectral fatigue analysis may not be appropriate.It is also important to recognize that deterministic and spectral fatigue analyses require thewave height distribution to be expressed differently. Deterministic analyses require atable describing the occurrence rate of waves of a specific height and period (such as thatshown in Figure 2-24). Spectral analyses, on the other hand require a table describing theoccurrence rate of individual seastate conditions (described typically by the significantwave height and zero upcrossing period).It should be apparent from the previous sections that both deterministic and spectralfatigue analysis are computationally intensive. In practice, it would be commonplace tocarry out a damage summation for 8 locations on both the brace and chord side of allcritical tubular joints for a range of range of wave heights and periods over 8 directions fora fixed offshore structure. For this reason, specialised offshore analysis packages such asSESAM, SACS and StruCAD*3D all have fatigue analysis modules which carry out thenumerous repetitive calculations required.Despite the convenience of analysis software, a sound understanding of thefundamentals of fatigue remains an essential prerequisite for obtaining reliableresults.Platform, Pipeline and Subsea Technology– Fatigue Design 41
  • 42. Figure 3-3: Frequency domain spectral fatigue analysis.Platform, Pipeline and Subsea Technology– Fatigue Design 42
  • 43. 4 Risk based fatigue Analysis and Inspection PlanningIt is apparent from the previous discussion that there are several sources of uncertainty, orvariability in fatigue analysis. The practice adopted by most engineers when faced withsuch uncertainty is to adopt conservative approaches (for example using the mean S-Ncurve minus two standard deviations for design). While there is nothing wrong with this,an alternative approach is to consider the uncertainties explicitly along with the inherentconservatisms, and carry out a reliability analysis. The concept behind fatigue reliabilityanalysis is illustrated schematically in Figure 4-1. Here, Tmean represents the best estimateof fatigue life, T represents the standard deviation (or variability) associated with theestimate of fatigue life, and Ts represents the required service life. The shaded areatherefore represents the probability of fatigue failure. Ts Tmean Probability Density T Fatigue Life (Years) Figure 4-1: Concept of fatigue reliability analysis: Tmean and T represent the calculated distribution of fatigue lives, Ts represents the required service life, and the shaded area represents the probability of fatigue failure.A crucial aspect of any engineering reliability assessment is quantifying the uncertaintiesassociated with the analysis. In estimating the fatigue life of welded structures there arethree principal sources of uncertainty:1. Uncertainty in estimating the fatigue loads and hot spot stresses on the structure.2. Uncertainty associated with fatigue test data which is apparent as scatter on the S-N curve (refer back to Figure 2-9).3. Uncertainty associated with the exact value of Miner’s summation which will result in fatigue failure of the joint (refer back to Figure 2-23).Platform, Pipeline and Subsea Technology– Fatigue Design 43
  • 44. A detailed description of the calculation of probability of fatigue failure taking intoaccount the uncertainties listed above is beyond the scope of this course, however,Appendix B provides a general introduction. The calculation can be carried out usingeither S-N data, or by using a fracture mechanics approach.Although Figure 4-1 illustrates the concept of the probability of fatigue failure at the endof a service lifetime, Ts, it is not difficult to imagine that the probability of fatigue failurecan be calculated at other times. This enables the probability of fatigue failure to beplotted as a function of time, an example is shown in Figure 4-2. This figure shows howthe probability of fatigue failure increases with the amount of time that a joint is subjectedto a certain loading environment.An extension of Figure 4-2 also demonstrates one of the important uses of probabilisticfatigue analysis. The results of inspections can be used to update the probability of fatiguefailure using Bayesian statistics. Figure 4-3 illustrates schematically the effect ofinspection after 10 years with no crack being detected. In this way, inspection can be usedto maintain the probability of failure below some acceptable level. The results of theanalysis can also be used to determine optimum inspection intervals on a risk basis. Thisis known as Risk Based Inspection (RBI) planning. 1.0E+00 Probability of Fatigue Failure, PF 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 1.0E-06 1.0E-07 0 5 10 15 20 Service Life (years) Figure 4-2: Typical results of a probabilistic fatigue analysis: Time in Service vs. Probability of Fatigue Failure.Platform, Pipeline and Subsea Technology– Fatigue Design 44
  • 45. 1.0E+00 Probability of Fatigue Failure, PF 1.0E-01 Effect of Inspection at 10 years - no crack detected 1.0E-02 1.0E-03 -4 P F = 2.2 x 10 1.0E-04 1.0E-05 1.0E-06 1.0E-07 0 5 10 15 20 Service Life (years) Figure 4-3: The probability of fatigue failure can be updated through inspection.Another use for probabilistic fatigue analysis is in design optimization studies. Here, thetotal cost of a structure may be defined as: Total Cost = CAPEX + OPEX + RISKEX (21)where CAPEX is capital expenditure, including the cost of fabricating and installing a structure or structural element. OPEX is operating expenditure, including fatigue inspection. RISKEX is risk related expenditure, defined as the probability of failure multiplied by the cost of failure.In many engineering designs there is a trade-off between these types of expenditure.Figure 4-4 shows the results of probabilistic fatigue analysis on a joint in an offshorestructure. Increasing the thickness of the chord in the joint will increase CAPEX,however, this will be offset by decreased OPEX (because the inspection intervals havebeen increased) and decreased RISKEX (because the probability of failure has beenreduced).Platform, Pipeline and Subsea Technology– Fatigue Design 45
  • 46. 1.0E-01 Minimum Joint Probability of Fatigue Failure Design Thickness 1.0E-02 1.0E-03 Increasing Joint 1.0E-04 Thickness = Increasing CAPEX 1.0E-05 Increasing Inspection Interval 41mm = Decreasing OPEX 44mm 47mm 50mm 1.0E-06 0 5 10 15 20 Service Life (years) Figure 4-4: Increasing joint thickness in an offshore structure may increase CAPEX, but may also decrease OPEX and RISKEX.Platform, Pipeline and Subsea Technology– Fatigue Design 46
  • 47. 5 References5.1 BooksAlmar-Naess A. (1985) Fatigue Handbook – Offshore Steel Structures, Tapir, Trondheim.Barltrop N.D.P. and Adams A.J. (1991) Dynamics of Fixed Marine Structures, 3rd Ed.,Butterworth-Heinemann, Oxford.Broek D.B. (1986) Elementary Engineering Fracture Mechanics, 4th Ed., Kluwer,Dordrecht.Gurney T.R. (1979) Fatigue of Welded Structures, 2nd Ed., Cambridge University Press,Cambridge.Maddox S.J. (1991) Fatigue Strength of Welded Structures, 2nd Ed., Abington Publishing,Cambridge.UEG (1985) Design of Tubular Joints for Offshore Structures, UEG.5.2 StandardsAPI (2000) Recommended Practice for Planning, Designing and Constructing FixedOffshore Platforms – Working Stress Design, 21st Ed., American Petroleum Institute.BS 7608:1993 Fatigue Design and Assessment of Steel Structures, British StandardsInstitute.BS 7910:1999 Guide on Methods for Assessing the Acceptability of Flaws in MetallicStructures, British Standards Institute.DNV RP C203 (2001) Fatigue Strength Analysis of Offshore Steel Structures, Det NorskeVeritas.DNV Classification Note 30.7 (1998) Fatigue Assessment of Ship Structures, Det NorskeVeritas.HSE (1990) Offshore Installations: Guidance on Design, Construction and Certification,4th Ed., United Kingdom Department of Energy / Health and Safety Executive.Norsok (1998) Design of Steel Structures, Rev.1, Norsok Standard N-004, NorwegianPetroleum Directorate.5.3 Research Reports and PapersEfthymiou (1988) Development of SCF Formulae and Generalized Influence Functionsfor use in Fatigue Analysis, Offshore Tubular Joints Conference, Surrey UK.HSE (1997) Stress Concentration Factors for Simple Tubular Joints, OffshoreTechnology Report OTH 354, United Kingdom Health and Safety Executive.HSE (1999) Background to New Fatigue Guidance for Steel Joints and Connections inOffshore Structures, Offshore Technology Report OTH 92 390, United Kingdom Healthand Safety Executive.Platform, Pipeline and Subsea Technology– Fatigue Design 47
  • 48. APPENDIX APlatform, Pipeline and Subsea Technology– Fatigue Design 48
  • 49. APPENDIX BPlatform, Pipeline and Subsea Technology– Fatigue Design 49