ssc-81symp19 - Ship Structure Committee

O ,*C”’%*THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERSOne World Tmde Center, Suite 1369, New York, N.Y. 1004S*.$‘% ?epem to be presented at Extreme Loads Response SYmPOSi urn~ ~Arli”@a”, VA, October 1%20, 1981:?+ 0 ●.3O.,ti, . #oApplication of Loading Predictions to Ship StructureDesign: A Comparative Analysis of MethodsDonaki Liu, Hsao Chen and Faith Lee,American Bureau of Shipping, New York, NYABSTRACTThis paper reviews two statistical/probabilistic methods, the well-kno”nlong-term exceedance probability predictionand Ochi 1s extreme value apDroach,and compares results with the methodembodied in the current ABS Rules forpredicting a ship!s dynamic verticalbending moment. Numerical calculationsare performed for a sample tanke~ usingthe three different methods. Structuralresponses are also analyzed, applyingdifferent dynamic bending moments andthe still-water bending moment to afinite element structural modelNumerical results for the sampletanker indicate that Lewis t long-termexceedance prediction for 20-25 years ofshiu service time (Drobabilitv level10-t .‘) is quite Cotipa.rablet: Ochi, sprobable extreme value. The two theoreticalresults are also shown to be inclose agreement with the nominal dynamicbenGlng moment specified in the ABSRules requirements . The stress valueobtained from the structural analysisbased on Lewis 7 dynamic bending momentat 10-’ .‘ is comparable to the ABS requirednominal permissible sti-ess.Ochit s design extreme value of verticalbending moment, incorporating a!IriskDarameter,~ of 0 .01=10-2 for thesample ship closely agrees with COPre S_pending exceedance prediction at a probabilitylevel of 10-7. 6X10-2.10-9 6 .The stress value for this case is hiEherthan the nominal permissible stress ~equiredby the ABS Rules. This would indicatethat if the design extreme verticalbending moment is used as the basisfor the design of the ship girder structure,a higher permissible stress levelshould be established.INTRODUCTIONEver since St. Denis and Piersonpublished their well-known paper [1]*almost thirty years ago for handling the* Number in brackets designates referenceat end of paper,motions of ships in a confused sea, varioustheoretical procedures have beendeveloped foI predicting the ship, s responsesduring its service time. Ingeneral, the theoretical methods fallinto two categories : One is a loruz-termprediction of-the probability “of e~c&edingdifferent response levels, where theRoot-Mean-Squa?e values of ship responseare employed. Works by Jasper [2], Nordenstrom[3] , Band [4] and Lewis [5] forexample, are in this category. The othercategory consists of the work by Ochi[6, 7], where the extreme value theory isused. The longitudinal strength requirementsof classification socie;ies a;egenerally developed on the basis of serviceexperience, using a probabilisticaPPrOach to the determination of loads.POT example, the theoretical procedureused by ABS in the development of itsrequirements employs the long-term exceedanceapproach developed by Band andLewis .The approach employed by the classificationsocieties for establishingRules requirements of ship longitudinalstrength can be considered as semiprobabilisticsince loads are predictedby a probabilistic method, but strength(permissible stress) is deterministic.Since va~ious methods are often used inDractice. a brief review of the 10nx -~erm exchedance prediction of Lewis;Ochi 7s ext~eme value approach, and themethod involved in the .40S Rules isgiven in the following.Lewis [5] examined the 30-minuterecords of midship bending st?ess obtainedevery 4 hours from the c4-s-B5cargo ships Wolverine — — State and Hoosier= in several years 1 service In theNo?th Atlantic He found that the individualdata samples fitted closely tothe Raylei Eh distribution. Furthermore.dividing ail the stress data into weathergroups , the mean square values ofavailable stress samples in each weathergroup we~e found to follow the normaldistribution. Consequently, Band [4]suggested a.probability model where thetwo aforementioned distributions wereassumed to apply to a much larger “population”(or quantity of data) Hence,249I

an ideal cumulative distribution ofstresses (or bending moments) could beconstructed for each weather group bysumming up all of the many Rayleighdistributions and integrating to differentstress (or bending moment ) level BThe total cununulative distribution couldthen be obtained by combining all of theindividual cumulative distributions onthe basis of the actual percentage oftime each weathe~ group would be-encoun–tered by ships in service, and on thebasis of average weather on some particularroute such as the NoFth AtlantlcLittle and Lewis [8] further evaluatedthe idealization of statistical dataagainst the stress data collected fmmnfive ships with about 3-1/2 years * service. These five ships consisted offour tankers and one bulk ca’?ie?, andare 754.6 to 1076 feet in length. Inaddition, Lewis introduced the so-calledH-family wave spectra which were selectedIn a random fashion from those givenby Pierson, et .al [9] . The H-familywave data consists of fine weathergroups in accordance with significantwave heights 10, 20, 30, 40 and 48.zfeet . With the exception of the lastgroup which contains 12 spectra, allother groups contain 10 spectra.In contrast to Lewis , approach,Ochi [7] first analyzed wave data collectedat Stations P.,B, C, D, I, J andK in the North Atlantic, and then derivedtwo families of wave spect~a oftwo- and six- parameter, Perspectively,which can be considered to represent the‘ImeanNorth Atlantict! sea conditionsBoth the two– and six- pa~ameter spectralfamily consists of 18 different seaseverities (significant wave heights) .But the numbers of wave spectra in eachsea severity of the two families aredifferent . In the two-parameter family,for each significant wave height the~eare nine spectra. The six-parameterfamily has eleven spectra for each .slgnificantwave height . FOY dynamic loadprediction, Ochi introduced an apprmachbased on extreme value theory. Thispredicts the highest response expectedin a shipv s lifetime by calculating theshort-term extreme value for the mostsevere sea condition expected. Ochialso developed a long-term extreme valuemethod where the frequency of varioussea severities , as well as other facto~~including wane spectral shapes, shipspeeds, and heading angles, are weightedaccording to their occum.ence during theship!s service life time. This approachis similar but not identical with theLewis method.Prior to 1975, the basic concept ofABS Rules requi~ements fop p~ima~y, longitudinalstrength of the hull girderwas to prescr-ibe for each individualship a b~ section modulus based onits main geometric characteristics. Therequired section modulus amidships was250then specified in terms of the basicsection modulus and the maximum stillwaterbending moment in the governingloaded condition. With this sectionmodulus the maximum primary bendingstress in the hull zirder. which can beproduced when the m;ximum’possible longitudinalbending moment is Imposed onthe ship could not exceed a nominal permissiblestress level, which varied withship length. The requirements for longitudinalstrength In the above describedform were successfully applied toships for many years . Since 1975, ABSRules strength requirements have beenpresented in a different format, inorder to accommodate the recent findingsobtained from the long–term dynamic orwave load studies . For the purpose ofship longitudinal strength evaluation,ABS now employs the long-term responseprediction method suggested by Band andLewis to generate a long-tepm response- which Is used as a basis for extendingthe existing ABS Rule.? to largerships . The new requirements are specifiedIn terms of the nominal still-waterand wave-induced vertical bending momentsStress limits are then sDecifiedin conjunction with the longitudinalstrength requirements .In view of the different assumptionsand different approaches employedin the above two theoretical methods fordetermining extreme loads, it is of interestIn this paper eo investigate theship structural response for the dynamicwave loads which are determined bv eachof the different methods, and to ;ompare;~lm~;ith those given in the latest ABSShip structural response subjectto different loads at different Drob -ability/confidence levels will aiso becalculated, using a simplified finiteelementstructural model of a sampleship No attempt is made to compare orcorrelate the theories pertaining to thedifferent approaches. Mathematical derivationsand proofs are avoided, withthe exception of those necessary forpresentation of the related topicsEvaluation and m?rification of the assumptionsin”olved in developing thedifferent methods can be found in otherpublished literature. This paper beginswith a summary of eq”atio”s and formulasassociated with the three different methodsfor determining loads under consideration.It is followed by a SUIWlaPyof the H-family and the six-parameterwave suectral data. Theoretically calculateildynamic loads based on th; sewave spectra, and the mathematicalstructural model of the sample ship arethen presented. In the remainder ofthis paper, computed structural resultsof’ the sample ship, and concluding remarksare given. It is the authors 8 hopethat through the numerical example, somelight can be shed on the application ofthe different statistical/probabilisticmethods for the evaluation of ship—.

girder longitudinal strength.PROCEDURES OF STATISTICAL/PROBABILISTICMETHODS FOR LOADSThe basic assumption involved inthis approach is that the short-termresponse of a ship in statistically unchangingseas is a nar?ow band process,and is distributed according to the Rayleighdisti-ibution. That is, the probabilitydensity function, f(x), of arandom variable x takes the fo~m:where Pr(Wk) is the probability of encounteringthe k-th weather group,Pr{x~xo Iw~] is the conditional probabilitywhich, in turn, has similar expressionsof the riEht-hand side of eouatior:r(x) = ~exp (-xZ/E)(1)where E>O is the parameter of Raylei&hdistribution for O

where ~=0.572z...... the Eulerqs COnstant, and E is deffned in equation(l). If the random process is narrowband, Ochi and Bolton [6] showed thenumber n In equation (6) can be expressedbywhereMOn= * (.2/.. )1/2 (7)T = timein hours= area under the spectrum of I-an–dom variable considered (meansquare value of ship responsein the present wopk)m,= area under the second momentof random variable considered.Considering the first term on theright hand side of equation (6), a“dusing equation (7), 0chi8s short-termprobable extreme value approach is obtainedas follows :l/2jin . Etn { y3600T(’m/mo)‘1(8)2[Ochi and Bolton further showed thatan extreme value higher than ~n givenby equation (8) would occur with probabilityO .632 for large n. This probabilityvalue is too hich for DTedi ,.. .—.—... .kionpurpos; in practice. Thu ‘“” S , a risk parametera (usually taken to be 0.01) isLntmduced into equation (8). DenotinEthe recently obtained “alue by Yn, “ th~nOchi, s short-term deslm-..extreme v.l I,e.i.e. , the expected highest value in a ‘fleet of (l/a) similar ships, is,.~n .1/2~Ln{ 3600T . (9)[~ q}1In equations (8) and (9) , m. and m, aredefined in equation (7) In addition,T=a=k=E=longest duration of specifiedseas fn hoursrisk parameternumber of encounter with aspecified sea in ship 1s servicetime2mo, if the peak value is asingle amplitude; 8mo for doubleamplitude.Equations (8) and (9) are the basis forthe subsequent sample calculation of theprobable a“d design extreme values.Ochi also developed his own veFsionof the long-term response predictionmethods for the most probable extremevalue and the design extreme value. ‘Theprobability density function of hls longtermresponse is shown as follows :whereZZzEn*pipJpkpfif*(x)~(x) = ijkkEEZZn*P~Pj PkPE ‘ijkkf*(x) =ns(mo), =(m,), =Pi>Pj >Pk,PE=(lo)probability density functionfor short-term response,average numbe F of responseper unit time of short-termresponse,1= ~ (m, )*/(mo)* ,mean square “alue of responsespectrum,second moment of responsespectrum,probabilities of sea condi–tion, wave spectrum, headingangle and ship speed,respectively.The total number, n, of responses expectedin the lifetime of a ship isn = (EZZZn*PiPJPkP1) X T x (Go)’, (11)ijkkwhere T is the total exposure time ofa ship to the sea.The cumulative distribution of thepro bable extreme value, F(~n), can beobtained by integrating equation (10) .The function F(Yn) , as shown by Ochi,has the following relationship with thetotal number, n, of response for alarge n:F(in) 1 -1 =n. (12)[ 1- .For the design extreme ValUe, Yn, equation(12) is also applicable, except thatthe term on the right-hand side should bereplaced by n/a, where a is the riskparameter.Approach in ABS RulesFor the purpose of numerical comparisonwith other methods, only the “er -tical bending moment is considered. Therequired bending moment for ship girderlongitudinal strength evaluation in thecurrent ABS Rules [10] expresses the totalbending moment amidzhipa, Mt3 asfollows :Mt=MSw+Mw, (13)where MSW and Mw are Yespecti”ely the252

still-water bendin~ moment and waveinducedbending moment . These bendingmoment components are given byandwhereM Sw= CStLZ.5B(Cb + 0.5] (14)Mwcst=~.,,,= c2L2BHeKb+ ~],o,‘k”” + %+-’:‘P”’ + %%+-’>=[0.544110-2,‘b’ -‘b” +“F’”++’” +=[0.275]10-8 ,‘E’”’” - %&l’”-’>He,Meter= 0.0172L+3 .653,=0.0181 L+3. 516,(15)61~L

the H-family are grouped into 5 groupsas shown in Table I. The characteristicsof the average spectrum of each Ofthemfive groups in the H-family are shown‘in Table II. In Figure 1, the spectra. ofone group are displayed.Table I - Percentage of occurrence andnumber of spectra of H–familywave data“,.,, .,.”. , , , , ,,s ,.3,2 ,.0,, 8.s39 ,,.8,0 ,4.,7,m- ,.0,, 3,,5, ,.,,, ,8,,, ,,,830=’. 0.70, 2.,03 ,.,,, , ,18 ,2,,20. 0.,,, ,.57, ,.,,, ,.,,6 ,.5,4.9 0.4s, 1.2,, 2.,,6 ,,,,, , .,,m, 0.44, ,.,,, ,.,,, ,,,,, , ,3,~, 0.507 ,.4,, ,.3,, ,,71, ,,443. 0.,50 0.5,, ,.4,, ,.+O, ,,40,Table II . Characteristics of the a“er -age spectra of the H-familywave dataNotes:Hs‘n“P.= significant wave height inmeters= moments of wave spectrumin metric units, forn=-1,0,1,2,3 and 4= peak frequency in rad/sec.I,‘,gested pe~centage of occurrence by Ochl[7], the significant wave heights andthe durations of the sea states used inthe present work are shown in Table III.The assumed duration of each particula~sea state as shown in this table is .aDproximatelythe same as that in Ochi ~ndMotter [13] , with the exception of thewave group of one meter significant waveheightSlmifica, t . . . .“.,,,, {.,,.,, ),,0,.s2,,,.54.5s.,6.,,.58.,9.5,0.,,1.5,2.5>3.5,4.51s.,,6. ,17.0,.,. t L..sea S,.., (),..,s,,0. ,46.046.046.046,045.,39.836.130.1,4,,17.0Table III - Wave group, percentage ofocc”mence, and duration ofsea state of six-parameterwave familyWithin each significant wave groupof the six-parameter wave family, thei-eare 11 members, of which the most probablespectrum is weighted by a factor of0.50, and each of all othei- spectra isweighted by 0.05. For the significantwave height specified in the above table,spectra are generated using the followingformula~1,,,,.35.,4.,3.33.3Is(o) = >4x.J.+0.25) ‘mj(17)[ 11bTFig. 1 - H–family wave spectra for significantwave height 3.o5metersOchi’s six-parameter wave spectralfamily of the “mean North Atlantic,, consistsof 18 groups in accordance withthe significant wave height. The sug-where r (),.) is a gamma function, andj=l,2 Stan~S fOr the lower and higherfrequency components, r’especti”ely. In .equation (17) , the Parameters HSj , timj,and i are functions of significant “a”eheigh~, and are gi”en in Table IV of Ochi[71. An example of the six-parameterfamily is shown in Figure 2.254

-Fig. 3 - Profiles and tank arrangementof the sample shipFig. 2 - Family of six-parameter wavespectra for significant waveheight 3.50 metersNUMERICAL EXAMPLE OF RESPONSE CALCULATIONAs a numerical examDle, the threedifferent approaches discussed in theprevious sections have been applied toan existing tanke~ for the dynamic verticalbending moment amidships calculationin the fully loaded condition of105,700.00 met~lc tons The hull girderscant ling of this vessel was designedbased on the wave-induced bending momentrequired by the ABS Rules, which is345,8oo meter-tons , and an allowablestill-water bendina moment of 207.800meter-tons. The d=signed section’ modul”,sis 333,9oo cm2-meters for mild steel,leading to a bending stress at midshipsection of 1.658 tons/cm’ which is theDeOmissible stress sDecified in the CUI.-rent ABS Rules (see ilso equation (lb)of this paper) Other information of thesample ship i~ shown in Table IV. InFigure 3, a sketch is presented showingthe p~ofile and cargo tank arrangement ofthe sample ship, where indication of theextent of the structural model used inthe stress analysis is also given.m,, lag,, k,.,,” .er,.ndimla.sB, t.,,.,,, mO.ld6dD, depth mu!...,, ,,.,, fun, ,0.,4.b, blockcoefficient for . ..ign draft“, .,1, s,eed ,,.1,..,the head sea with an interval of 30 de–grees, where the probability of encounteringthe dlffe~ent heading angle isassumed to be the same . The responsespectra are calculated based on the H-family wave spectra and the transferfunction of vertical bendlnE moment bythe program ABS/SHIPMOTION, -wherein theship speed is taken as 75 percent ofdesign speed. ABS/SHIPMOTION program incomputing the transfer function followsthe stFiD method and the linearized shiDmotion theory. The mathematical deriva:tion and the computational procedure ofthe program are discussed in the worksof Raff [14], Kaplan [15], Kaplan, Sargentand Silbei-t [16] , and Stiansen andChen [12].In the calculation of mean squareresuonse value for detez-mininz the conditionalprobability by equat;on (5) ,the cosine-square spreading function isemployed to simulate the short-crestednessof the seaway . The spreading functionused in the computation is given asf(llu)=; cost(llu) (18)where v is the heading angle of theship witi+ respect to the wave Furthe~more,the ship ,s response in a seaway isconsidered as a random process which isnot necessarily narrow band. For thiscase, the mean square value of the Fesponsespectrum is obtained by multiplyingthe mea” square value of a narrowband process by a factor of (1-s2/2) asOchi and Bolton [61 suf?!zested. Here Estands for the b~o’idne;; ok responsesgectrum.Table IV - Principal particulars of the The conditional probability funcsampleship tions based on the H-family wave spectraare substituted into equation (4) forResults of Long-term Exceedance Prob -calculating the total probability, whereability Predictionthe Der’centage of ‘acc”I’renceof eachWhen Lewis 8 long-term response predictionis used for computing the dynamicvertical bendin!z moment . the H-familvwave spectra di&ussed in the previo; ssection aye applied. The conditionalprobability for each wave group is evaluatedaccording to equation (5) at 12heading angles from the following sea to255wave height group given in Table I Isemployed. Since the total probabilityis equal to the Reciprocal of the numberof response cycles, a cu.ve can be obtainedto represent the response of exceedanceversus the number of resnonsecycles (hence the probability lev~i) .Shown in Figure 4 is such a curve forthe dynamic vertical bending mome?.:‘~-

amidships of the sample ship in the fullyloaded condition.6.W05r“’’’’’””’..,,,.,.,, ,.,..,““ibending moment to be exceeded at probabilitylevels of 10-7 .“ and 10-’.’1are respectively 3.68x105 and 4.54x10’meter-tons Comparing these resultswith those based an the H-family, it is-”lnterestinE to notice that lon~-termprediction-values of the two differentfamilies are very close .Results of Ochiv s Extreme Values,.,., ,,~ab, ,,, ., ,...=,...,Fig. 4 - Long-term vertical dynamicbending moment at midship sectionof the sample ship in fullYloaded condition, based on theH-family wave spectraAssuming two-thirds of 20-year servicetime that the ship is exposed to thesea. the total number of vertical bendinxmom~nt cycles of the sample ship, n, i;calculated by equation (11) . It shouldbe noted that, for a non-narPow band responsespectrum, the average number ofresponse per unit time of short-term response,‘3, ‘n ‘qUatiOn (11), should bemodified as suggested by Ochi and Bolton.The number of ~esponse cycles, n, calculatedfor the sample ship in this manneris 10-7.’. Consequently, as can beseen from Figure 4, the dynamic verticalbending moment of exceedance in 20-yearservice time is 3.61x10S mete~-tons atthe probability level of 10-7. s .The concept of applying a risk parameter,a, in Ochits design extremevalue can also be incorporated in thelong-term exceedance probability prediction.Karst showed in Appendix A ofReference [17] that, with (1-a) percentassurance, the expected response to beexceeded should be read from the longtermresponse curve as the one in Figure4 at a probability level of an-’ , prclvldedCl1. This Is equiva–lent to the exceedance to be expectedonce in the service time of (l/a) similarships. Taking a=O.01, the expected verticalbending moment of the sample shipto be exceeded in the sea way representedby the H-family wave spectra is given atthe probability level of 10-8. G, which is4 .6x10’ meter-tons ,Similar to the H-family wave data,the six-parameter wave spectra generatedby equation (17) based on the characteristicsin Table III, are also employed inLewis 1 long-term response prediction forthe sample ship. The number of verticalbending moment cycles in 20-year servicetime is 107.”. The expected “erticalThe short-term probable extremevalue and the short-term design extremevalue of vertical bending moment of thesample ship, are calculated by equations(8) and (9)”. In the calculation, onlythe six-parameter wave spectral familyis employed. Assuming two-thirds of the20-year service time that the ship isexposed to the sea, the total time ofthe most severe sea state of 17 meterssignificant wave height that the shipwill encounter is 10.37 hours. If theaverage duration of this sea state is7.3 hours . the number of encounters withibis sea ;Ondition is about 3 times .For the sample ship, the calculationsshow that the vessel in head sea conditionsgive rise to the maximum verticalbending moment , which is 3. 42x10’ metertonso? the probable extreme value, andis 4.65x10’ meter-tons of the design extremevalue with a risk parameter a=O. 01.Since Ochi !s long-term extreme valuesshould be the same as the short-term extremevalues, aB discussed by Ochi [7] ,the long-term extreme vertical bendingmoments for the sample ship In the presentwork are not presented. In orderto compare the results of the two statistical/probabilistic approaches andthat required by ABS Rules, Table V isprepared, from which it can be seen (a)There is practically no difference In thelong-term exceedance predictions usingthe H-family wave data and the six-parameterspectra, (b) Comparing probable anddesibzn extreme values with lonx-ter’m exceed~ncepredictions at probab~listic levelsof 10- 7.’ and 10-9.’, ~espectively,calculation shows that the results ofthese two different statistical/Drobabilisticmethods are comparable, and (c)The nominal vertical wave-induced bendingmoment requi~ed in ABS Rules is about 4percent less than the exceedance predictionat a DrObabilit!J level of 10-7. ‘.and about ihe same w~th the short -terkprobable extreme value.r,ong-,.rm .E,..ed..ce OChi . ,.,,..,Am ml.. 10-7.6 ~o., .,,robable .e. im,,,58,,0, 3,6,,,0, 4.6.10> 3.,2.1,, 4.65.,0,Table V - Comparison of vertical wavebending moments amidships ofthe sample shipNote: Bending moment in meter-tons.256

STRUCTURAL RESPONSE ANALYSISThe structural response analysis isperformed for the sample ship by usingthe program SHIPOPT developed by Hughes,Mistree and Zanic [18]. This program wasdeveloped for analyzing the st~ucturalresponse (stress, deflection, etc ), pi-edictingthe critical OF failure values ofthe structural response, and optimizingthe scant llngs of all girders, frames andstiffened panels in segments of the hullgirder. To achieve the functions justmentioned, the ship structure is representedby a finite-element structuralmodel which consists of a number of compartmentswith the transverse bulkheadsas the boundaries. The basic type ofelements to represent the hull structureare:(a) Multiribbed plane stress elementfor modeling the panels of stiffenedplating. The element is rloncont’orming,and has constant shear stressand linearily varying direct stresses.(b) Composite beam element for nmdelingof bracketed beams attached toplating.(c) Strut element for modeling ofpillars, screen bulkheads, passageway s.,and other portions of structure whichaFe not primarily structural membersbut , because of their inplane rigidity,do contribute to the stiffness of theoverall structure.(dJ Basic plane stress element(triangular and quadrilateral element) .In the present work, the midshipportion containing three compartments asindicated in Figure 3 is modeled by finiteelements . The midship portion ofthe ship is chosen, as it usually issubjected to the largest bending moment.Figure 5 illustrates a typical structuralsection where the st~ake number andnode point number assigned in the finiteelementstructural model are also shown.Figure 6 shows one-half of the finiteelementmodel with the centerline planeas the plane of structural symmetry.Figures 7 and 8 show the transversebulkhead at model Frame O and the webframe at model Frame g. For tbe arlalysis,the bending moments and shear forcesare applied at the two end bulkheadsof the structural model The bendingmoments and shear forces on the boun~ariesof the structural model are computedby setting the ship on a simple wave witha length approximately the same as theship, s length. The wave height is chosensuch that the total “ertical bending momentis equal to the sum of the dynamicbending moment and the still-water bendingmoment of the ship in the loadingcondition under consideration. Bendingmoments and shear forces at the two endboundaries of the structural model ayeobtained from the qua5i-static condition.Pressure exerted an the side and bottomshell structure is directly calculatedbased on the local draft of the ship inthe simple wave.In view of the long-term exceedanceresults, which are “cry close to thoseby Ochi’s extreme value approach, asshown in Table V, structural analysisis performed for two cases where the dynamicvertical bending moment amidshipsare 3 .61x105 and U .6xIo’ meter-tons .These cases correspond to Lewist ~esultsat ~o-7.6 probability level (correspondingto Ochi 1s probable extreme value)and 10–’ .‘ (corresponding to Ochi’s de–sign extreme value ), respectively . Thelongitudinal inplane plating stressesfor these two cases are shown in Figure9, which indicates that fop the case of10–7 ‘ probability level, the maximumstress is 2,10 tons/cm2 in the deck and2.16 tOns/cm2 in the bottom plating.For the case of 10–9 ‘ probability levelthe maximum stress is 2.43 tons/cm2 inthe deck and 2.32 tons/cm2 in the bottomplating. It should be noted that theinplane stress consists of the primaryst~ess and the secondary stress Itshould also be noted that, as indicatedin Figure 5, the bottom and deck plating,and other parts of the structure are ofhigh-tensile steel. For these structuralmembers the allowable stress value ishigher than in mild steel by the ratio ofNode ,.,,., Nu,rb,rT s,,.,. Numbsr>Fig. 5 - Typical section of structure,to~ether with strake and nodepoint number used in finite -element structural modelIi —II257

1/0.78 or 1.28. Applying this factor to Pequired nominal permissible stress ofthe stresses obtained from the finlte-1.658 tons/cm2. In the case of a 1O–’.’element analysis, it can be seen that the probability level, the maximum Inplanestress level for the case of a 10- 7.’ stress exceeds the nominal permissibleprobability level is close to the ABS re- stress by about 14 percenta w ,, m ,0, ,2, ,“0 ,,0 ,80 *O1,,1,,,,71,0Model Frame,,,IFig. 6 - Finite-element structural modelII115000 500!99 Is la=..“..5000 5000Snnn5000.,.5000 55 17s50‘Fig. 7 - Finite-element structural modelof transverse hulkhead at modelFrame O258Fig. 8 - Finite-element structural modelof web frame at model FFame 9j1- t

. .Fig. 9 - Stress values of midship sectionstructureCONCLUDINGREMARKSThe clynamlc bending moment of thesample ship has been computed usingdifferent methods. Corresponding structuralanalysis is performed by using astructural finlt e-element program. Basedon the results of the present study onthe sample ship, the following conclusionscan be drawn:1. The H-family wave data and Ochi’ssix-parameter wave spectral family of themean North Atlantic are comparable inpredicting the long-term response prediction.This may not be totally surprising,because of the fact that the twofamilies of wave spectra aPe generatedfrom similar wave data in the North Atlantic.2. Numerical comparison shows thatusing Ochils pz’obable extreme “alue approachis equivalent to using the longtermexceedance approach, predicted at aprobability level corresponding to 20-Z5years service time. In the present studyfoF the sample ship, the probabilitylevel is 10-, .s for the ve~tical bentiingmoment. The “designtr extreme value witha risk parameter of 0.01 coIv’esponds tothe long-term exceedance p~edictlon at acomparable probability level of 10–9 .6.3. The dynamic vertical wave bendingmoment required by ABS Rules agrees verywell with the probable extreme value byOchi’s method and is about 4 percent lessthan the exceedance prediction at 10-7.6probability level for the sample ship.This indicates that the nominal wave load259predicted theoretically is in good as:ee -ment with ABS Rules .4. For the case where the long-t err.dynamic bending moment at 10-7. ‘ probabilitylevel is considered, the maximumin-plane stress calculated for the sampleship is comparable to the nominalpermissible stress specified by ABSRules This indicates that the long-termexceedance predictions for 20-25 yearsservice time (similarly Ochi’s probableextreme values) are in line with thosespecified by ciassific”ation societies.On the other hand, if the dynamic bendingmoment at 10-9. K probability level (also,Ochils “desiRn” extreme value) is used inevaluating siiipgirder strength, it isadvisable to cansidey using a higherstress limit which is based on extremeload considerations .5. The H-family and the six-parameterwave spectral data which representthe general sea conditions of the NorthAtlantic may not be adequate for the dynamicload calculation for shipe in otherareas OF specific ship Toutes, such ascoastal water regions , the North Pacific,etc. . For ships in a particular oceanarea other than the North Atlantic, representativewave data of the particularlocation similar to the two spect?alfamilies are needed.6. The dynamic load, in particularthe vertical bending moment of the sampleship presented in this paper, is calculatedbased on linear theory of shipmotion. For ships where the effects ofnonlinear motion. such as slamminx. flareimpact, green waier, etc ., are si~iificant,further study is needed in order to,aPPIY the Probabilistic lstatl$tical methodsin the determination of hull Elrderstrength.ACKNOWLEDGEMENTgratitude toward the staff ;embers of theR & D Department of the American BuFeauof Shipping for their assistance and suggestionsduring the course of this study .In particular, the author’s appreciateMI-. S. G. Stiansen, Vice President of ABSfor his encoui.agement of this I’eseaFchwork, and Dr. H. Y. Jan, Dr. M. K. Ochiand Pro fessoF E. V. Lewis for their reviewand invaluable comments during thepreparation of this paper.REFERENCES1. St. Denis, M. , and Pierson, W.J., 7,0”the Motions of Ships in confusedSea, ” =. SNAME, 1953.2. Jasper, N. H., !’Statistical Distr f-2-:-tion Patterns of Ocean Waves 2:?Wave-Induced Ship Stmes$es ax? H:-tions, with Engineering ApP:::2-tions, ” Trans, SNAME, 19:E-—

3.4.5.6.7.8.9.10.11.12.13.Nordenstrom, N. , “On Estimation of 14Long-Term Distributions of Wave-Induced Midship Bending Momentsin Ships ,11Chalmers Tekniska Hogskola,1963.15Band, E. G. U., “Analysis of ShipData to Predict Long-Term Trendsof Hull Bending Moments ,‘,AmericanBureau of shipping, November 1966.Lewis, E. V., “Predicting Long- Temn 16Distribution of Wave-Induced Bend_ing Moments on Ship Hu116, 17SNAMESPring Neeting, Montreal, 1967.Ochi, M. K. and Bolt On, W. E. , “Statisticsfor Pvedictlon of ShipPerformance in a Seaway, 1,InternationalShipbuilding Progress,February, April and September 1973.Ochi, M. K., “Wave Statistics for theDesign of Ships and Ocean Structures,” -. SNAME, 1978.Little, R. S. and Lewis E. V., llA 18Statistical Study of Wave-InducedBending Moments on Large OceangoingTankers and Bulk Carrier s,” -SNAME, 1971.PierSon, W. J., Moskowitz, L., andMehr, E., ‘tWave Spectra Estimatedfrom Wave Records obtained by theOWS Weather Explorer and OWS WeatherReport er, ,, New York Uni Ver–sitv Research Di”ision Reoort .Pari I, November 1962, P~rt Ii,March 1963, Part III, June 196s.American Bureau of Shipping Rules forBuilding and Classing Steel Vessels1981Hoffman, D. , and Karst , 0. J. , “TheTheory of the Rayleigh Distributionand Some of Its Applications, rqJournal of Ship Research, Vol. 19,September 1975.Stiansen, S. G.,I!AppliCa~io~ Ofand Chen, H. H.,Probabilistic De–sign Methods to Wave Loads PI’edic–tion for Ship Structure Analysis ,91Report for Panel HS-4 (Design PPocedureand Philosophy) of the HullStructure Committee, SNAME, April1981.Ochi, M. K. and Motter, L. I. , ‘TPr.e.diction of ExtFeme Ship Responsein Rough Seas of the North Atlantic,“ International Symposium onthe Dynamics of Marine Vehiclesand Structures in Waves, UniversityCollege London, ApFil 1974.17Raff, P.., !fProgram SCORES -ShipStructural Response in Wanes ,1,Ship Structures Committee ReportSSC-230, 1972.Kaplan, P., “Modifications to ProgramSCORES - Ship Structural Responsein Wa”e S,,!oceanics, Inc. , RePOrtsubmitted to the American Bureau ofShipping, April 1974.Kaplan, P ., Sargent, T. P. and Silbert,M. N., ,1ACorrelation Studyof SL-7 Load.! and Notions - ModelTests and Computer Simulation,,!Oceanics, Inc. , Report 76-133 forProject SR-130 of the Ship StructureCommittee, September 1976.Hoffman. D. and Lewis . E. V. . ‘,Arialysis”andInterpretation o; Full-Scale Data on Midship BendingStresses of DFy Car&o Ships, rtReport SSC-196, The Ship Structurecommittee, June 1969.Hughes, O. F. , Mistree, F. and Zanic,V. . llAPractical Method for theRa~ional Design of Ship Structure, ”Journal of Ship Research, Vol. 24,No. 2, June 1980260!---