Rationally-Based Fatigue Design of Tankers (Owen Hughes and Paul Franklin

8/13/2019 Rationally-Based Fatigue Design of Tankers (Owen Hughes and Paul Franklin

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THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS,,,.e

.> ..; and;,+,,,,,,,/ THE SHIP STRUCTURE COMMllTEEPaper p resented a t the Ship S tructures Sympos ium 93

Sheraton National Hotel , Arl ington, Virginia, Novembw 16-17, 1993

Rationally-Based Fatigue Design of TankersOwen Hughesi and Paul Franklin*

1Professor of Ocean Structures, Aerospace and Ocean Engineering, Virginia Tech,Blacksburg, Virginia

2Graduate Student, Aerospace and Ocean Engineering, Virginia Tech,Blacksburg, Virginia

AbstractTanker fatigue cracking has caused concern for the entiremarine industry including operators, regulators and clas-sif ication societies. In response to this concern, variousresearchers have been developing improved means forevaluating structural fatigue. The authors have developeda practical rationally-based fatigu~ design method whichis sufficiently rapid and efficient to be a part of preliminarys~ctural design. This is important because if fatigue isnot adequately addressed at this stage, no amount of detaildesign will be able to correct or makeup for this inade.quacy. The method consists of fiv~ basic steps: specifyinga realistic wave environment, generating a hydrodynamicship-wave interaction model, computing cyclic nominalstress due to waves and ship motions, using S-N data topredict fatigue life, and using stictural optimization toresize the scantlings such that the desired fatigue life isobtained.The paper describes the method and explains the similarit-ies and the differences with other approaches. Examplecalculations involving a TAPS tanker are presented whichvalidate the method, and which also demonstrate theimportance of both local and overall structure response.The examples show that the heretofore unexplained fa-tigue cracking of midheight side Iongitudinals is causedby the local pulsating pressure due to waves and shipmotions. This demonstrates clearly that fatigue analysisand design must include response to local panel pressure.Other fatigue analysis methods do not propmly accountfor this effect.

IntroductionShips operating in various wave climates are subject tocyclic loads beyond those quasi-static or empirical loadsnormally considered during the design process. In thepast, calculation of cyclic loadings has generally beenbeyond the means of marine designers. However, the

current state-of-the-art in numerical methods and rela-tively affordable computer hardware has eased this limi-tation.

Background - TAPS Tanker FatigueThe significance of fatigue cracking in ship structure andthe urgent need for adequate fatigue design techniques isillustrated by the problems which have arisen in tankersemployed on the TAPS route. In the US Coast GuardsStructural Casualty Study of April 27,1988 [1] the TAPStankers were identified as a population of ships withapparently inadequate fatigue resistance. The study re-ported that during the period 1984 to 1988, 59 of docu-mented structural failures in US flag vessels over 10000tons occurred in the 13 of the population that served theTAPS route. A close-up investigation of the TAPS tank-ers [2, 3] reported at least 16 Class 1 fractures (fracturesin the oil fwatertight boundary or large fractures in otherstmctural members) several of which led to significantpollution incidence. With respect to the existing state-of-the-art, the Coast Guard report of June, 1990 [2] notes:Generally, fatigue evaluation is an extremely complexanalysis . .. . Fatigue evaluations are riot yet a common andpractical component in the design process. The proposedmethod is aimed squarely at rectifying this situation.Need for Practical, Rationally-Based,

Preliminary Fatigue DesignTraditional rule-based structural design is not valid whenconsidering new and different ship types, and may not bevalid when operating conditions for a ship are not in thetypical range. Thus there is a need for a rationally-baseddesign method, where the actual anticipated load environ-ment is used to analyze a specific structural design. Inrecognition of this, the American Bureau of Shipping hasrecently developed, Liu et al [4], a new (and optional)design procedure, the Dynamic Load Approach (DLA), tobe used in conjunction with the Rules.

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Ship Structures Symposium 93Further justification for rationally-based design ariseswhen cyclic loading and the resulting fatigue failures areconsidered. Currently most fatigue contiol efforts arefocused on careful design of connection details and qualitycontrol of welds. Such practices are intended to limit thestress concentration factor (SCF) in the region of a con-nection. However, the stress level at a connection, andthus the resulting fatigue damage, is the product of twoquantities: the SCF and the cyclic stress field that is actingin the region of the connection; i.e., the member stress.The stiess field (both static and cyclic) is determined bypreliminary design which establishes the scantlings of allof the principal structural members. If the preliminarydesign does not deal adequately with fatigue, the cyclicstress field in the principal shuctural members will be toolarge, and no amount of detail design will be able to corrector makeup for this inadequacy. Thus there is a paramountneed for an efficient method for considering fatigue as apart of preliminary design, and that is the purpose of theproposed method.In recent years the need has been made even more acuteby an increase in the number of fatigue failures due toincreased use of high yield steels. Because of the higherstatic strength of such steels, safety authorities have d-allowedhigher levels of total stress, but this means largervalues of cyclic stress as well as static slress. Fatiguestrength is separate from yield stress, and in some casesfatigue sixength actually decreases with an increase inyield stress. Therefore even though the SCF maybe keptat the same value, any increase in the cyclic stress willclearly increase the occurrence of fatigue problems.Also, aswill be shown herein, many of these recent fatiguefailures are due, not to simple hull girder bending, butrather to the fluctuating panel pressures acting on the shiphull. However, such pressures can only be obtained bydirect calculation and are therefore beyond the capabilitiesof Rule-based design.

Elements of the Proposed MethodThe basic elements of the proposed method for fatigueanalysisldesign can be reduced to five steps:1) Specifying a realistic wave envirorunent.2) Using a hydrodynamic model to calculate the fluctuat-

ing panel pressures due to waves and ship motions.3) Calculating the cyclic nominal stresses due to the

ships structural response (both overall and local)to such pressures.

4) Using S-N data and statistics to assess the fatigue lifeof the current design.

5) Incorporating the fatigue performance as an addi-tional constraint in a structural optimization pro-gram, so that the new scantlings will satisfy fatiguerequirements, in addition to all other strength re-quirements.

The first two steps are distinct specialty areas within oceanengineering and have been implemented using recentadvances in those specialties. The hydrodynamics modelproduces a frequency bastd transfer function relating unitamplitude waves to panel pressures. A rapid and efficientmethod for whole-ship finite element analysis is then usedto convert the transfer function ofpmssure per unit-ampli-tude-wave to stress per unit-amplitude-wave. Then eachindividual wave spectrum, of the set of wave spectradefining the lifetime wave environment, is multiplied bythe stress transfer function to calculate a set of responsespectra. These response spectra define the lifetime cyclicstress response of the ship, from which the fatigue damagecan be calculated. In a design situation, if the fatiguedamage is unacceptable, then the optimization processwould resize the scantlings so that the cyclic nominalstresses give a satisfactory-fatigue life.This s~ction gives a brief summary of the overall proce-dure. A more complete development of the method isgiven in Hughes and Franklin [5].Wave EnvironmentThe procedures used to establish the TAPS tanker routewave environment are somewhat different from thoseassociated with wave-height vs. wave-period scatter dia-grams currently contained in oceanographic atlases. Thefollowing is a brief review of the methods developed byBuckley [6, 7]. The actual data used for the TAPS exam-ple is given in an Appendix to Hughes and Franklin [5].Long-term wave height spectra measured by NOAAocean buoys have provided the seaway and wind data usedto define two distinct wave climates along the TAPStanker operating route. The large NOAA data base hasbeen characterized in the following manner. For signifi-cant wave height (H~O)class intervals of 1 meter individ-ual wave spectrum energy density ordinates have beenaveraged to define a single long-term Climatic WaveSpectrum (CWS). The overall analysis procedure uses theCWS as the basic load input.For computational ease, each CWS has been approxi.mated by an Ochi 3 parameter wave spectrum formula-tion. In Appendix A of Hughes and Franklin [5], thevarious wave spectra are thus defined by significant waveheight together with the characteristic modal periodTP andspectrum shape parameter 1 for the wave climate in-volved. Given the Ochi (3P) spectrum formulation, the

and for fatigue design: wave energy density is defined as a function of frequency

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Hughes and Franklin on Fatigue Designas required for determination of the response spectrum ofinterest.Buckley has performed this procedure for the two gener-alized wave climates through which the TAPS routepasses: West Coast Long Period and Northern High Lati-tude. Also computed by Buckley from the NOAA buoydata is the probability distributions for wave heading andsea state. For the four NOAA buoys nearest the TAPStanker route he sorted sustained wind direction data intoeight heading sectors. After assuming the wave headingand the direction of the sustained wind were equivalent,the probabilities for various ship headings relative to wavedirection were computed. Also for each buoy, the wavedata were sorted into 12 class intervals, ranked by severityfi-orn H. = 0.5 m to 10.0 m, and the probability ofooccurrence of each wave height was computed.

Hydrodynamics

The hydrodynamic modeling of the interaction betweenthe ship and the seaway is one of the main challenges inany analytical approach for assessing fatigue damage.Currently the common approach towards calculating shipmotions and hull girder loading is strip theory. Striptheory is reasonably accurate for calculating cumulativeresponses such as motions and hull girder forces, but itcannot provide accurate values for pressures acting onlocal structure.

A recent improvement over strip theory is the linear3-dimensional hydrodynamic technique. This techniquesolves the flow problem using a fully 3-dirnensiomd pan-elized model of the hull, rather than prismatic strips. Thesolution therefore has increased accuracy, especially for aship with forward speed. The linearity assumptions arevalid for nearly all of a ships operating conditions andlead to computationally efficient solutions. Linearity as-sumptions are not accurate during extreme storm condi-tions, but because of the relative infrequency of theseconditions the associated cumulative fatigue damag~ isrelatively small. The great value of linear 3-dimensionaltheory for this research effort is that it provides panelpressures, which are often crucial to obtaining membercyclic stress to the required degree of accuracy.Hydrodynamic modeling for the current project is per-formed using the Small Amplitude Motion Program(SAMP) written by Dr. Woei-Min Lin of SAIC Incorpo-rated. SAMP is a linear 3-dimensional ship motions andloads program. It produces pressure values for individualpanels and also calculates hull girder bending moment andshear force. SAMP is thus well suited for fatigu~ analysis.

Calculation of Transfer Function forCyclic Stresses

The next step of the analysis procedure is to generate a setof transfer functions, H2 o (fc), between a unit amplitudewave at encounter frequency f, and the cyclic stress levelin the member of interest. The individual transfer func-tions in the set correspond to the various structural loadtypes (hull girder or panel pressures) and tanker operatingconditions.Each specific type of load has its own subset of transferfunctions. For the relatively low speed TAPS tankers, theprimary loads relating to fatigue are hull girder bendingand local wave induced panel pressure fluctuations. Eachload based subset of transfer functions has its own subsetof h-ansfer functions for every operating condition of theship, The operating conditions consist of permutations ofsuch variables as ship speed (V,tiP),heading relative to thewaves (G), and draft. The service life of the TAPS tankerscan be described by the following operating conditionvariables.

v~fip = constant of 15 knotsDraft = either Loaded or Ballast

@ = Eight 45 sectorsThere are thus 16 distinct operating conditions (and 16transfer functions) in each load based subset (hull girderand panel pressures) and consequently a total of 32 trans-fer functions between unit amplitude waves and stressresponse must be generated. Such transfer functions arecomputed by using panel pressure output from the hydro-dynamic analysis as a load input to a global finite elementmodel of the ship. The proposed method uses the MAES-TRO program for this, because it rapidly generates awhoIe ship model and obtains accurate values of therepresentative or field stresses in all principal stmcturalmembers (but not hotspot stresses). This procedure cor-rectly accounts for the complex three-dimensional natureof both the loading and the structure, which cannot beaccounted for by simple beam theory.Calculation of Cyclic Stress Response

SpectrumOnce the stress transfer function H: (fW)for each principalmember has been obtained, the computation of the re-sponse spectra S= (fC)is a relatively simpl@ process. Themost important step is to convert both H: (fw)and the wavespectra SW(fW)o wave encounter frequency, fe. The re-sponse spectrum is then simply their product.

S0 (f.)= H: (f.) SW(f,) (1)

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Ship Structures Symposium 93

Computation of Fatigue DamageThe response spectra of the previous paragraph have, ingeneral, a Weibull distribution. Known statistical proper-ties of the Weibull distribution can be invoked and corn.bined with the appropriate S-N curves to compute afatigue damage ratio, q. The fatigue damage ratio is adesign oriented measure of fatigue life: a q of 1.0 or largeris a predictor of fatigue failure. The proposed fatiguedesign method uses the S-N curves of the British WeldingInstitute [8], which are already used by many ship andoffshor~ structure approval bodies such as the AmericanBureau of Shipping [9], Det norske Veritas [10] and theUK Department of Energy [11]. The joint classificationsystem associated with these curves empirically includesthe stress concentration factor (SCF) which occurs as theresult of a welded joint.As shown in [5], for a Weibull distribution of stressamplitudes the fatigue damage ratio is

The s~mbols in the above equation are defined at the endof the papm.Several studies have shown that peak values of hull girderbending in tankers follow a Weibull distribution with k =0.7 to 1.0 [12, 13]. Equation(2), with an appropriate valueof k, is therefore implemented for the hull girder bendingload set.

In contrast, the stress amplitudes due to panel pressurtifollow the Rayleigh distribution. Panel pressures are dueto the sum of many sinusoidal waves and a large numberof harmonic ship motions. Therefore from the centrallimit theorem the panel pressures themselves follow aGaussian process. It is also reasonable to assume that thefluctuations of panel pressure are narrow banded (crossthe mean pressure level between each peak value) andhave a mean value close to zero. Consequently the cyclicstresses due to panel pressures also have a Gaussiandistribution and a mean value close to zero. For such aprocess the peak values follow the Rayleigh distribution.This distribution is simply a special form of the Weibulldistribution with parameters of k = 2 and &= O. Hence forpressure-derived stresses the fatigue damage ratio is

(3)The total fatigue damage ratio for a particular structuralmember is the sum of the fatigue damage ratios for eachresponse spectrum. For the purposes of this paper it willbe convenient and informative to keep the various loading

conditions initially separate and report a distinct damageratio for each (i.e..., hull girder bending, qhb, and panelpressnre fluctuations, ~pp). In any case, when the totalfatigue damag~ ratio equals or exceeds 1.0, the relevantmember is considered to have failed.

Satisfying Fatigue Requirements as a Partof Preliminary Design

The final step in the method is to incorporate the require-ment of satisfactory fatigue performance, as measured bythe damage ratio, as another of the constraints in an overallstructural optimization process. In this way the memberscantlings will automatically be resized such that theirnominal slm ses will give a lifetime damage ratio thatsatisfies the specific factor of safety against fatigue. Si-multaneously, the optimization process also resizes thescantlings so as to satisfy all other design constraints,notably avoiding all structural failures and fulfilling alldesigner-specified constraints, such as fabrication re-quirements.This optimization process, and also a whole-ship finiteelement analysis and a rigorously thorough failure analy-sis (examining all failure types for all members) alreadyexist in the form of the MAESTRO computer program forpreliminary structural design. It is a proven technology,having been used by many designers for many years. Itsdesign method can be summarized as follows:1) For every possibl~ failure mode, and for all members

and load cases, calculate the current load effects,Q (stresses etc.) and the corresponding failure (orother limit) values of those load effects, QL.

2) Setup a mathematical optimization problem in whichtho constraints are y Q S Q~, where dy is the prod-uct of any number of partial safety factors, eachof which accounts for the probabilities of the var-ous loads and failure modes, the degree of serious-ness of the latter, and the various uncmtainties(especially in predictions).

3) For any designer. specified measure of merit, such asa nondimensional combination of cost and weight,solve the optimization problem using dual level se-quential linear programming.

It should be noted that we are hem dealing only withpreliminary design, the purpose of which is to obtainsatisfactory nominal cyclic stresses. The fatigue analysispresumes certain types of structural details and degrees ofweld quality. Therefore it is still necessary that the detaildesign should pay careful attention to both of these al-im-portant aspects of fatigue design.

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Comparison with Other MethodsDavid Taylor Research CenterApproximately a decade ago Sikora et al (14) outlined aprocedure in use at DTRC for performing fatigue analysisof ships. Their paper uses experimentally and empiricallyderived tiansfer functions to relate hull girder bendingmoment to unit amplitude waves. The transfer fimctionsare then multiplied by known wave spectra to compute aseries of bending moment response spectra and their re-spective probability density functions. From the prob-ability density functions a histogram of cyclic stressamplitude vs. the number of cycles for which the stressvalue is exceeded was created. Sikora et al then demon-strated how to directly apply the Pahngren-Miner cumul-ative fatigue damage theory to the histogram in order tocompute fatigue life.The fatigue analysis presented here differs horn the ap-proach of Sikora et al. in four significant areas. First ofall, physical modeling and extensive tank tinting of theship are not required. Secondly, the analysis is not limitedto overall ship quantities such as hull girder bending.Thirdly, several well known statistical procedures can bcimplemented to streamline and improve the fatigue darr-age calculation. Finally, a specific set of widely availableS-N curves is incorporated.American Petroleum InstituteA second existing source of guidance for analyzing fatiguein ocean structures is the American Petroleum Institute(API), which devotes a chapter in its RP-2A [15] to fatigueanalysis. The API RP-2A outlines a basic fatigue methodfor offshore stmctures. The technique includes recom-mendations for the wave climate description, dynamicmodeling of the stmcture, development of the stress trans.fer function and calculation of the fatigue damage ratio.The API recommendations are limited in generality; theyconsider only open-framed platforms consisting of tubularmembers. The recommendations are also limited inscope; [15] is a publication of recommended practices anddoes not specify analysis procedures in detail.Structural Maintenance ProjectVery recently a Joint Industry Project titled th~ StructuralMaintenance Project or SMP, based at the University ofCalifornia at Berkeley, published a series of volumesentitled Structural Maintenance for New and ExistingShips [16]. The Berkeley SMP, as the name implies, is abroadly based study on the structural maintenance ofexisting ships. Under this maintenance theme it addressescorrosion, fatigue, structural monitoring and repair man-agement. Its fatigue analysis method differs from thosepreviously mentioned in that it is mainly intended for theanalysis of existing ships rather than tlw design of newships.

Hughes and Franklin on Fatigue DesignFor this same reason, the method presented herein alsodiffers from that of the SMP. The most significant differ-ences between the two projects are:1)

2)

3)

4)

SMP uses less precise wave data, based on Marsdensquares, whereas for the TAPS tankers we use themore accurate climatic data fi-om the NOAA wavebuoys located directly along the TAPS route.For hydrodynamic analysis SMP uses strip theory in-stead of a 3-D panel method.SMP uses local FE analysis of specific joints and cor-responding hotspot stxesses in the fatigue analysis,in conjunction with either hotspot S-N curves orfi-acture mechanics for failure criteria. In contiast,our method usm the aforementioned joint classifica-tion system and S-N curves.The tankers studied by SMP did not include anywhich had axtensive cracking of side longitudinalat the midheight of the ship.

The first difference is primarily an issue of availability.The improved wave data from NOAA buoys and the workBuckley has done to convert the raw data into a usableengineering format is quite recent and is not yet widelyavailable. Even when published, Buckleys data will belimited to those ocean areas for which NOAA buoy dataexists (primarily North American coastal waters). Unfor-tunately the wave directionality for the published Marsdensquares data is not sufficiently differentiated by waveheight to correctly allow for specific trade routes.The second difference may also be considered an issu~ ofavailability. Efficient 3-D panel based hydrodynamicprograms, while certainly a large improvement over stripmethods, are relatively new. Indeed the early version ofSAMP which was used for the calculations in this reportdid not have an allowance for roll darnping. Futurecalculations will be performed using the current versionof SAMP, which does include roll damping and severalother improvements to streamline calculations.The use of local FE analysis on specific joints is animportant step in analyzing existing structure, especiallywhen concerns of continued crack growth arise. Howeversuch a process is computationally quite intense and is, asof yet, still too cumbersome for design techniques.Similarly, failure criteria consisting of hotspot S-N curvesor fi-acture mechanics are appropriate for analyzing exist-ing, problematic structure, but have drawbacks in terms ofa design m~thod. One of the Iargmt difficulties withhotspot S-N curves is that no widely accepted collectionappears to exist. The SMP team conceded as much whenthey took non-hotspot curves and scaled them accordingto engineering judgment. As for fractare mechanics, this

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Ship Structures Symposium 93is again a rather complicated amdysis best suited forexamining known problem areas.Finally, when it came to performing specific examplecalculations, SMP chose to analyze a group of ships whichdid not contain a large number of documented failures ofthe midheight side longitudinal. As such, a comparisonof the relative importance of panel pressures and hullgirder bending stress was not a subject in the SMP study.American Bureau of ShippingABS has recently published a design document Guide forthe Fatigue Strength Assessment of Tankers 9 , whichsets forth a simplified method for fatigue assessment. TheGuide implicitly includes the same basic elements as thefatigue analysis methods described above; the scope ofthese implicit elements is summarized in the Guidespreface, ... considered in the derivation of the criteria are:the Palmgren-Miner linear damage model, S-N curvemethodologies, a long term sea environment repre-sentative of the North Atlantic Ocean (which is to beconsidered for unrestricted service classification), and anominal vessel service life of 20 years. However, be-cause the derivation of the Guide simplifies, condensesand combines these elements, it also limits the fatigueassessment in terms of both accuracy and flexibility. TheGuide addresses this concern and recommends that moreelaborate analysis methods are required in cases where theapplicability of the derivation is in question.At the 1992 SNAME annual meeting Liu et al [4] pre-sented a paper describing ABSs Dynamic Load Ap-proach, including a case study involving a more rigorousfatigue analysis than that of the Guide. Although thefatigue calculations of the case study are only brieflydescribed, they appear to be essentially the same as thefirst four st~ps of our method: wave data (in this caseobservational wave data from the North Atlantic), a hy-drodynamic motion and loads analysis, finite elemtmtanalysis to obtain stress tiansfer functions, and S-N dataplus long-term statistics to calculate lifetime fatigue dam-age. However there are two aspects in which we believeour method is more accurate: the wave data and thetreatment of cyclic stress due to local panel response.The Walden wave data used in the ABS case study is basedon weather ship observations from two specific weatherstations. ABS did not attempt to model the actual operat-ing environment for the tanker studied, but simply useddata from an extreme environment in the North Atlantic.Thus for two reasons the authors prefer Buckleys wavedata over Waldens: they have greater confidence in wavedata derived from NOAA buoy measurements thanstrictly observational data, and Buckleys wave data per-mits the analysis to use the actual lifetime wave environ-ment of the TAPS tankers.

As for the computation of the stress transfer function, Muet al [4] used the midship vertical bending moment (VBM)to characterize the p~ak value, the shape and the statisticsof the frequency response function for all types of stressand for all of th~ structural members studied. While thissimplifies the computation, such an approach is not validfor those structural responses not dominated by VBM orfor members far from midships.Most of the structural members in a ships hull incur twotypes of cyclic stress: one due to hull girder bending andone due to direct response to the local cyclic pressures dueto wave and ship motions. This paper contains threefindings regarding these two stress types:1) In some regions of the hull the local pressure induced

stresses contribute significantly to, and even domi-nate, fatigue accumulation.

2) Example 2 (Figures 8 and 11) will show that the trans-fer fanctions of these two stress types have very dif-ferent shapes.

3) The statistical properties of the two stress disti=ibu-tions are also different, as was shown in equations2 and 3.

In the AIM nmthod these two types of stress are combinedand are processed together. The third stop of their methodhas two levels: a whole-ship finite element analysis usinga wave load corresponding to the frequency of the peakvalue of the midship VBM transfer function, and local finemesh analyses. The combining of the stress types occurswhen local pressures and nodal displacements fiorn thewhole-ship analysis are applied to the fine mesh modelsto generate a corresponding peak value of the memberstress. The tiansfer function for the combined stress isthen constructed by assuming that it has the same shapeas the transfer function for the midship VBM. Then in thefourth step, since the stresses have been combined, thepressure-induced stress is treated as if it had the samestatistical properties as the hull girder stress.Nevertheless, in the four basic steps that constitute fatigueanalysis, the ABS method and the method presentedherein share the same philosophy and approach. Thedistinction is that our method also provides for fatiguedesign; it has a fifth step in which the results of the fatigueanalysis become additional constraints in a structural op-timization process, in which the member scantlings areresized such that their nominal cyclic stresses give asatisfactory fatigue performance, while also satisfying allother comtiaints. In fact, we believe that optimization iscrucial for this approach to fatigue because it not onlyguides, but also automates the entire process. Without itthe process takes on a trial and error nature and becomes

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Hughes and Franklin on Fatigue Designso tedious and lengthy that it could not be done within the static load is not appropriate because it does not meet thecost and time constraints of preliminary design. requirements of the hydrodynamic loading.

Discussion of TAPS FatigueBefore demonstrating the fatigue analysis method, we willstep back and look at the trends which have developed inthe fracture data for one class of ship. The USCG reportof May 1991 [3] reported that the Atigun Pass class wassubject to fractures in both the side longitudinal and inthe bottom longitudinal (in way of limber holes). For thisstudy we examined a summary, prepared for the USCG,of the side longitudinal fractures in one of the Atigun Passtankers. The graphical representation of this data, Figures1 and 2, may at first seem rather inexplicable, but actuallythe fractures occur mainly in patterns for which goodengineering reasons can be presented.Until now fatigue in longitudinal members has been cus-tomarily associated with the cyclic stresses due to hullgirder bending. Hence the most intriguing anomaly in thedata, which has not heretofore been adequately explained,is that some (indeed many) of the cracks are located at ornear the ships neutral axis. Since hull girder bendingstresses are negligible at such a location, there must besome other significant cause or source of fatigue damage.It will be shown (in Example 3) that the cause of thiscracking is the pulsating hydrodynamic pressure on theships hull due to waves and ship motions.A second anomaly is the large difference in tlm number ofside longitudinal fractures between the port side (210) andthe starboard side (296). This has frequently been attrib-uted to the direction of travel during cargo and ballastvoyages. The weattmrside (exposed to seas fi-omthe west)during the more heavily loaded cargo voyage is the stm-board side of the ship. While this is correct, we would liketo offer a more complete explanation.During cargo voyages the waterline of the Atigun Passtankers is approximately at longitudinal 44. Such water-line longitudinal are most heavily affected by local pul-sating pressures. Conversely in a ballast voyage thesesame tankers ride approximately 15 feet higher in thewater. The waterline is then in the vicinity of longitudinal38. The higher longitudinal on the port side are thereforesubject to less pulsating pressure. The data reflects thisreality with a stxong grouping of fi-actures on the starboardside from longitudinal 39 to 45. Using similar logic itmight be expected to see a grouping of fractures on theport side from longitudinal 34 to 40. This however doesnot occur, and the reason is that such longitudinal arelarger, having been sized in proportion to the hydrostaticload, and consequently they have smaller fluctuatingstress values. This shows, incidentally, that the customarylinear sizing of longitudinal based purely on the hydro-

When looking at the same starboard side data a thirdpattern appears which again at first seems to be an anom-aly, Longitudinal 41,44 and even 46 are within the highrisk zone and indeed have a poor Ilacture history attmnsverse bulkheads, but are remarkably tlte of fracturesat other frames. The explanation for this phenomenon isfound by comparing the connection detail between longi-tudinal 44 and a web frame, Figure 3, with a typicallongitudinal to web frame detail, Figure 4, and finally thetypical longitudinal to transverse bulkhead detail, Fig-ure 5.It is apparent that the large brackets used in L41, L44 andL46 (Figure 3), reduce the susceptibility of these longitu-dinal to fatigue. These large brackets have been creditedas being both an improved fatigue design detail (soften-ing the SCF) and with shortening the effective span (andthus reducing stress levels at the connection). But a morecomplete and convincing explanation can be obtained byexamining the bending moment distribution in a typicalside longitudinal segment between transverse frames,which is that of a clamped beam as shown in Figure 6.The bending moment and thus stress at the end of thebracket, the location most likely to generate a fatiguefracture, is almost exactly zero and therefore little or nofatigue damage will occur. We would like to suggest thatthis very beneficial geometric arrangement should be usedwherever possible in structural design. In contrast, thesmaller brackets used in the details shown in Figures 4 and5 have their edges, and thus the SCF, at locations of muchhigher bending stress. These smaller brackets are there-fore much more susceptible to fatigue damage.It is worth noting that all of the patterns discussed hereinrequixe consideration of fluctuating panel pressures. Anydesign or analysis technique which ignores panel pres-sures would fail to predict neutral axis fatigue cracking, astarboarcL/port fatigue difference or a differentiation be-tween the bracket connections. Similarly, any techniquewhich treats the local pressure-induced stress in the samemanner as hull girder stress would not be able to correctlyassess or quantify these three phenomena.

In the following section we will present four exampleanalyses in order to quantify some of these fracture pat-terns. The example calculations will look at both panelpressure fluctuations for side shell longitudinal and hullgirder bending stresses for the lower longitudinal and thebottom shell structure. Due to time and funding con-straints the example calculations are not comprehensive,but they serve to illustrate the proposed analysis methodand demonstrate its capabilities.

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Example CalculationsThe four example calculations presented herein am basedon an Atigun Pass class tanker operating on the TAPSroute. The analyses are limited to only one buoy location(out of four; hence corresponding to 1/4 of the shipsvoyage life) and only one operating condition (out of 16:8 headings and 2 loading conditions). A complete mmly-sis would therefore repeat the following procedures a totalof 64 times.The following data, describing a February 1992 voyagefrom Valdez to San Francisco will be used for all examplecalculations [17].

ship = 15 knotsDraft = 50 ft

Light Ship = 24707 LTDisplacement = 168956 LT

Lcg (from A.P.) = 456.16 ftVCg (above keel) = 40.73 ft

Example 1: Panel Pressure,Lower Side Longitudinal L32

Longitudinal 32 is in the lower side shell approximately163 above the bilge. Because longitudinal 32 is in theside shell and at a significant distance from the hullsneutral axis, it is reasonable to expect fatigue damage dueto both panel pressure fluctuations and hull girder bend-ing. We examine the welded joint between the outer edgeof the web of the side longitudinal and the flat bar bracketat a typical web frame (see Figure 4). The first examplecalculation computes the contribution of local pressurefluctuations to fatigue damage. Example 2 will examinefatigue damage due to hull girder bending at this samelocation. Since the purpose is simply to illustrate themethod, both calculations are done for only one heading.Pressure Transfer FunctionA single transfer function, H2(f), is required for thiscalculation. Due to the emmgy content of the wave envi-ronment a transfer function throughout the range, fW= 0.04to 0.15 Hz is sufficient. The panel geometry used for thehydrodynamic analysis uses 165 panels to describe thesubmerged portion of the hull. The panel identified asSurface 5, Station 6, Waterline 3, encompasses the loca-tion of longitudinal 32 and frame 54. Time histories ofpanel pressures are calculated for a series of regular wavesusing the linear hydrodynamics program S.AMP. TheSAMP runs use the following parameters:

fw = 0.04,0.0601015 Hz.?.Wave Amplitude = 390 inFrom each time history (see Hughes and Franklin (5)) theamplitude of the steady state pressure fluctuation for thepanel of interest is extracted and the quantity

is plotted against wave frequency. The result is Figure 7,a transfer function for panel pressure.Stress Transfer FunctionFor the relatively low frequency pressure fluctuationsnormally considered, a static stress analysis is sufficient.The overall fatigue analysis method proposed herein nor-mally uses MAESTRO on a PC or workstation to rapidlygenerate a whole ship structural model, and obtain repre-sentative or field stresses in all principal structuralmembers (but not hotspot stresses). This enables theanalyst to accurately assess member field stresses for agiven load with the assurance that the local boundayconditions are complete and correct. However, even thissimple PC-based analysis was not required for the sideIongitudinals considered herein, because each segmentbetween transverse frames is nothing more than a clampedbeam subjected to a uniform distributed load. Therefore,stress levels in the outer edge of the web were calculatedusing beam theory, allowing for the asymmetry of theflange. The resulting transfer function

is given by Figure 8.The steep decay of Figures 7 and 8 is primarily due to thefiequmcy dependence of the pressure values within anocean wave. The pressure distribution with depth, p(y),for an undisturbed linear wave is given as

P(y) = pga exp ()a sin(wt)g

Therefore, especially for higher frequency waves, there isa substantial decay in pressure at a depth y beneath themean water line.Wave SpectrumThe TAPS Tankm route and the location of the four buoyswhich have been chosen to describe the wave environmentarn shown in Figure A-1 of Appendix A of Hughes andFranklin [5]. The length of the route defined by each buoywas scaled from the map and divided by total route lengthto compute the location probabilities in Table 1.

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Hughes and Franklin on Fatigue Design

Buoy P(loc)46001 0.3246004 0.2646005 0.1446002 0.28

Table 1Location ProbabilityThe wave spectra for the buoys are calculated based onthe Ochi parameters given in Appendix A [5]. Shown inFigure 9 are. both the wave and encounter frequencyspectia for Buoy 46002 at H. = 4.0 m. Such an overlaid.plot demonstrates the importance of the encounter fre-quency modification.Response SpectrumFor each sea state of concern, H~ = 1.0 to 13.0 m, theo@msfer function FI~is multiplied by the respective wavespectrum SW(fe).The spectral moments, mOand ml, of theresult ing response spectrum S= (fC) are then calculated.As an illustration of the intermediate results a singleresponse spectrum is given in Figure 10.Damage RatioThe damage ratio, ~, is calculated by combining theresponse spectral moment, ~ with the parameters C andm (which describe a S-N curve) in Equation (16). Thevalues of C and m are based on the joint classificationsystem of the Welding Insti tute [8]. For the bracketed endconnection of the side shell longitudirmls to the transverse

web frame, Figure 4, the joint type is 4.2 and the classifi-cation is G. The S-N curve parameters am thus, C =1.738x1018 and m = 3.0. The operating lifetime used inthe example is Tli~,= 20 years and the probabili ty associ-ated with each response spech-a is calculated in Table 2.The response spectrum probabilitim of Table 2, the spec-tral moments and the fatigue strength parameters are allcombined to compute the fatigue damage ratio of a singlespectrum. Table 3 shows the contribution to q for 11different sea states and for each of the example calcula-t ions performed in this section. Each contribution repre-sents only the damage accumulated during a single seastate, location, draft, heading and speed combination.

Example 2: Hull Girder Bending,Lower Side Longitudinal L32

This example demonstrates the technique used to calcu-late fatigue damage due to hull girder bending at the samelocation as in Example 1. The resulting damage can thusbe algebraically added to the results from the panel pres-sure analysis. The operating condition for this example isagain: loaded, forward speed of 15 knots and head seas.The wave spectra are also identical. The transfer functionfor this particulw operating condition is given in Figure11.To demonstrate the difference between hull girder andpanel pressure response, we examine Figures 8 and 11which give the frequency response transfer function ofstress in a side shell longitudinal due to both. The stressimmsfer function for V13M has a distinct peak which is aresult of the hulls response to the integration of many

Hm p(v~hip) P(@) P(Draft) p(HrnO) P(loc) P(RSP)1.0 1.0 .055 0.5 .1905 .28 1.47 x 10-32.0 1.0 .0615 0.5 .3171 .28 2.73 X 10-33.0 1.0 .1055 0.5 .2323 .28 3.43 x 10-34.0 1.0 ,123 0.5 .1455 .28 2.51 x 10-35.0 1.0 .1005 0.5 .0667 .28 9.39 x 10-46.0 1.0 .0925 0.5 .0278 .28 3.60 X 10-47.0 1.0 099 0.5 .0113 .28 1.57x 10-48.0 1.0 .077 0.5 .0042 .28 4.53 x 1059.0 1.0 .056 0.5 .0028 .28 2.20 x 10-510.0 1.0 0.00 0.5 .0007 .28 0.0

>10.0 1.0 0.00 0.5 ,0007 .28 0.0

Table 2Response Spectra Probabilities for Buoy 46002, @ = 180 and Draft= 600 in

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qHmo L32 Panel L23 Hull L43 Panel Bottom Bottom

Pressure Girder Pressure Longitudinal Longitudinal~1.0 4.59 x 10-6 2.43 X 10-6 6.25 X 10-4 3.68 X 10-5 1.01 x 10-52.0 1.08 X 10-4 7.22 X 10-5 1,06 X 10-2 1.09x 10-3 2.99 X 10-43.0 1.84 X 10-4 1.64 X 10-4 1.01x 10-2 2.48 X 10-3 6.79 X 10-44.0 4.56 X10-4 4.61 X 10-4 1.91 x 10-2 6.98 X 103 1.91 x 10-35.0 4.29 X10-4 4,52 X 10-4 1.47x 102 6.84 X 10-3 1.87 X 10-36.0 3.4 x 10-4 3.59 x 10-4 1.01x 102 5,44 x 10-3 1.49x 10-37.0 2,72 X10-4 2.82 X 10-4 7.11 X1O-3 4.27 X 10-3 I. I7X1O-38.0 1.32 X 104 1.33x 10-4 3.11 XI O-3 2.01 x 10-3 5.49 x 10-49.0 9.93 x 10-5 9.66 X 10-5 2.16 x10-3 1.46 X 10-3 4.00 x 10-410.0 0.00

>10.0 0.00Total 2.03 X 10-3 2.02 x 10-3 7.75 x 10-2 3.06 X 10-2 8.37 X 103

Table 3Fatigue Damage Ratios for Buoy 46002, @= 180 and Draft= 600 in

* Basic Drain Hole*In way of Butt-Weld

panel pressures distributed over the entire hull. In contrastthe transfer function for the localized response to panelpressure fluctuation is dominated by the pressure distribu-tion within the incident wave. Because the basic natureand shape of the two transfer function are quite different,it is impossible to accurately derive the function for panelpressure by scaling the function for midship V13M.As in Example 1, the joint type is 4.2, the class is G andtie S-N curve parameters are: C = 1.738x101~ andm = 3.0. The fatigue damage ratio for each sea state issummarized in Table 3. Again the total from Table 3represents the contribution to the fatigue damage ratio dueto hull girder bending for a single operating condition anda single buoy location. A complete analysis would pro-ceed to evaluate all other operating headings as well aseach buoy location, but as explained earlier, it is not yetpossible to obtain results for all headings.

Example 3: Panel Pressure,Midheight Side Longitudinal L43Longitudinal 43 is located approximately at the shipsdesign water line and thus panel pressures do not decay asquickly, in comparison to longitudinal 32, with wavefrequency. Therefore the frequency range of the analysismust extend beyond the earlier example. It should also benoted that longitudinal 43 is designed for a smaller hydro-

static head than longitudinal 32 and accordingly a smallercross sectional area is used. The result is higher stressesin longitudinal 43 for equivalent panel pressures. Figure12 shows the encounter frequency transfer function ofouter web stress for both longitudimds 32 and 43.The stress value for longitudinal 32 starts at a relativelylow value and decays to an insignificant quantity withinthe frequency range of significant wave energy, Thetransfer function for longitudinal 43 however, starts at alarge value and remains significant throughout the fre-quency range. The fatigue analysis for longitudinal 43 isperformed in an identical manner to that shown for longi-tudinal 32. The joint type and class are again 4.2 and Grespectively. The pertinent data for the calculation isgiven in Table 3.The final result of Table 3 is a damage ratio of 0.078, ormore than 75 times the darnage due to pressure in longi-tudinal 32 for the same operating condition. This value isfor 1 out of 64 lifetime operating conditions and thereforerepresents a significant contribution towards a possiblefatigue failure. For both longitudinal 32 and 43 otherheadings involve much more rolling, and rolling cantypically increase the time-varying dynamic componentof pressure on a ships side by a factor of two or more,depending on the degree of rolling. Thus for the full setof operating conditions the value of 0.078 will be magni-fied not just by 64 but more likely by some value between

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Hughes and Franklin on Fatigue Design100 and 150, and possibly even larger. Ifit is 100 then thelifetime (20 year) fatigue darnage ratio becomes 7.8,which means a crack would appear in only 2017.8 = 2.6operating or approximately 4 calendar years*. Thisagrees very well with the actual fatigue cracking historyof the example ship, and thus provides good validation ofthe proposed method.It is also important to note that longitudinal 43 is near theships neutral axis. Any analysis procedure which reliesexclusively on hull girder bimding would predict little orno fatigue damage to such a member. TMs example showsthat fatigue darnage due to panel pressures can be quitesignificant, and that fatigue analysis must consider thedynamic panel pressures due to waves and ship motions,including roll.

Example 4: Bottom Longitudinal;Web to Plating Weld

The bottom longitudinal of the TAPS tankers have alsobeen subject to fatigue cracking. Such cracks have tendedto occur in the region of drain holes in the Iongitudinals,as shown in Figure 13. There are two types of drain holes,as shown in Figure 14.The basic drain hole is an oval cut-out. The oval maintainsthe continuity of the web-to-plating weld (joint type 4. lb,weld class F2), but creates a stress concentration factor ofapproximately 2.0 at the longitudinal weld. In the way oferection butt welds the oval is interrupted, leaving a gapin the longitudinal weld. The gap eliminates the SCF inthe web plating, but degrades the joint type to 4.2, weldclass G.For bottom structure hull girder bending stresses are large.In contrast the wave-induced pressures have attenuated toa quite small value and therefore the cyclic stresses due tolocal panel response are also small and do not contributeto fatigue.Example 4a: Basic Drain HoleThe stress transfer function for a bottom longitudinal inthemgion of a basic drain hole is given in Figure 15. Table3 summarizes the fatigue damag~ ratio calculation.Example 4b: Erection Butt-Weld DrainHoleAgain the stress transfer function is given in Figure 16 anda summary of the fatigue darnage ratio calculation is againgiven in Table 3.

Results Summary and ConclusionsSummaryThe examples shown above are summarized in Table 4.The relative importance of local panel pressures and over-all hull girder bending is shown for three different membertypes. One of the most important results of these analysesis to show the importance of local panel pressures infatigue analysis.Examples 1 and 2, which consider a typical longitudinalapproximately 163 above the bilge, report nearly identi-cal fatigue damage due to panel pressure and hull girderbending. Therefore any analysis that only examines hullgirder bending would dangerously overestimate the fa-tigue life by a factor of two.Example 3 continues the theme by considering a longitu-dinal at or near the ships neutral axis. Although a hullgirder analysis would indicate no fatigue darnage, thepanel pressure calculation reveals that such a longitudinalis actually highly susceptible to fatigue damage.The tid examples, 4a and 4b, are the opposite of Exam-ple 3. Here panel pressures are not significant, but hullgirder bending results in high fatigue damage ratios. Themuch higher damage ratio for case 4a vs. case 4b is due tothe SCF of 2.0 used for the basic drain hole.ConclusionsThis report presents a rationally-based method for thefatigue design of ship hulls , which is essentially a synthe-sis of existing (and proven) analysis tools. The reportgives four example calculations for the TAPS tankerswhich demonstrate the methods practicality and suitabil-ity for design. The quantitative results am in excellentagreement with the actual fatigue cracking history forthese ships, thus validating the accuracy of the method.The results also indicate that the heretofore unexplainedcracking in the midheight side Iongitudinals is caused bythe pulsating hydrodynamic pressure on the ships hulldue to waves and ship motions. The proposed method wasable to achieve this result because it is based on fiistprinciples; i.e. direct analysislcalculation of all of theimportant factors regarding ship hull fatigue. It is alsoworth noting the practicality of the method: all of thecomputations required for these examples were performedon a desktop computer.The examples presented herein are incomplete becausethey are performed for only a small portion of the ships

* The value for calendar years is based on a typical value for such tankers of spending 60 of a year at sea. In thiscase: 2.610.6 = 4.3 years.

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Example Member Analysis Location withinLormitudinals Web Damage RatiotI I 1 I1 L32 Panel Pressure IAt bracket butt weld (Fig 3) I 2.03 X 10-3

I I 1 I2 L32 t-lull Girder I At bracket butt weld (Fiu 3) \ 2.02 x 10-33 I L43 I Panel Pressure I At bracket butt weld (Fig 3) I 7.75 x 10-2

4a BL Hull Girder Below drain hole @web/plating weld (Fig 13) 3.06 X 10-24b 13L Hull Girder Edge of drain hole gap @ 8.37 X 10-3web/pIating weld (Fig 13)

TDamage ratio was calculated for 1/64 of the ships operating life. A complete analysis would require repeatingthe process for all combinations of 2 load conditions, 8 headings and 4 buoy locations.

Table 4Summary of Examples

operating life. Nevertheless they demonstrate conclu-sively that a meaningful fatigue analysis requires accuratemodeling of all load types and major segments of a shipsoperating life. Above all, panel prmsures must be in-cluded in any methodology to examine fatigue of a shipsshell structure. To accurately predict such fluctuatingpanel pressures requires a 3-D panel-based hydrodynamicanalysis, including roll motions. Therefore the proposedmdhod will utilize the now available version of SAMPwhich includes roll damping and thus accurate values ofroll motion.

AcknowledgmentsThe authors are grateful to SNAME and the Ship StructureCommittee for their support of this work. We also wishto thank Mr. Alexander Delli Paoli of Exxon Company,International for providing the data neeclad to validate themethod and demonstrate its practicality.

H2 o (f)

fwf.Vsllip@so (f)

SW(f)

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SymbolsTransfer Function of stress per unitamplitude waveWave frequencyWave encounter frequencyShip velocityShip headingStress response spectra

Wave spectra

WISP

cmo

mz

E

N

mkroNRsP

Pmlp rrlpPagcoHmo

fatigue damage ratio for a particularstress response spectralog(C) is the intmcept of the cycles axis ofthe S-N curveZeroth order spectral moment of stressresponseSecond order spectral moment of stressresponseBandwidth parameter defined in terms ofspectial momentsLifetime number of stress cycles (usually108)Negative slope of the S-N curveWeibull parameterGamma functionNumber of lifetime stress cycles for eachresponse spectrumAmplitude of cyclic pressureAmplitude of cyclic stressMass density of sea waterWave amplitudeAcceleration due to gravitywave frequency in radianslsecsignificant wave height


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484746E43424140373635343332313029

5251z464746454443::40393837363332313029

I0 10 20 30 40

No. of FracturesFigure 1

Vertical Distribution of Cracks, Port Side Longitudinal

w 1982 1985 1986 1988 1990 1991

982985986988990

1991

0 10 20No. of Fr~ures

Figure 2Vertical Distribution of Cracks, Stbd.

30 40

Side Longitudinal

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Figure 3Longitudinal 41, 44 and 46 at a Web Frame

k------ 8-8---+ ,Longitudinal 32 ~ 7k-30+4I Web Frame

Flat Bar Bracket ~ EM

Figure 4Typical Longitudinal at Web Frame

Lmgituc6na[ 32 ~, _

1

/

Trans. BHO

Bmcket /

Figure 5Typical Longitudinal at Transverse

\

Bulkhead

x = 45 (See fig. 2)\

:E=E= =l51 101 152 ZozLcxatim alcmgBeam (in)Figure 6Normalized Moment for Clamped Longitudinalbetween Transverse Frames1.0+3

8.-4

6.0e4+.W4

2.0+4

0.0 5+00.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16wve Ff8q~ (Hz)

Figure 7Panel Pressure transfer Function

(S5, Sta 6, WI 3)1200 I1mo di

2

800~ \

:s 600~a Yw = 400

~\

zoo l\ Lo, I I i0.0 0.1 0.2 0.3EmmmterFreqw~w

Figure 8Web (Outer Edge) Stress Transfer Function for

L32 at FR54 Due to Panel Pressure

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Basic Drain Hole Drain Hole in Way of Butt Weldl-lo+ +10-+o T6i 5 JQ-P---,1

Figure 14Bottom Longitudinal Drain Holes

Smm

4ma .

3mm -

Zmm -

lmm.

0.0 0.1 0.2 0.3Encounter Frequen~ (Hz)

Figure 15Stress Transfer Function for Bottom

Longitudinal with SCF = 2.0

0:0 0:1 02 0:3Encounter Frequenq (Hz)

Figure 16Bottom Longitudinal Butt-Weld Drain Hole

Stress Transfer Function

Rationally-Based Fatigue Design of Tankers (Owen Hughes and Paul Franklin

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