4 Hull Structure 4.1 Main frame and general arrangement 4.1.1 Frame spacing Usuallyshipswithlengthover120mareconsideredlongships,anditisdesirabletoadoptlongitudinalframingsystem.Thesystemisdesignedtowithstandlongitudinalbendingmoments,whicharedominantinlongvessels.Althoughicebreakersaredifferentcasebecauseofhighiceloadsandicebreakerstendtohaveamixedframingstructure.[14]It'sgoodforshipthatneedsgoodstrengthaspect.Becauseoftheiceloadsheneedstransverseframingsystemonbottomplateandsidesbecausewhenthereisahugestressforcenotjustoneframebecomesoverstrained.Angledortshapedstiffenersshouldbeutilized.Ingeneral,stiffenersshouldbearrangedsothattheyareperpendiculartotheicestresses.Onthespoonlikebow,theframingshouldbehoweverlongitudinal,andicerammingmustbetakenaccountinthestrengthcalculations.Useofhighstrengthsteelsshouldbeconsideredincriticalplaces.[15]Thespacingbetweenframesissetto600mmwithawebframeoneverythirdframe,resultinginwebframespacingof1800mm.ThisrelativelysmalltransversalspacingischosenbecauseofhighiceloadswhenoperatinginKaraSea.Theinitialspacingbetweenlongitudinalswillbethesame600mmbutthespacinginlongitudinalgirdersiseverysixth,so3600mm.[16]4.1.2 Main frame ThemainframeofValerianAlbanovischosentobebetweenframes152and153.Theinitialmainframeisshownonappendix1Mainframebytheengineroom.Theseframesareonthebowsideofwatertightbulkheadonframe150.Themainframeislocatedontheframethatcutstheshipatthemainengineroom.Avesselhasamixedframing.Thisisdonebecauseofhighiceloadsonshell.Anotherframedrawingwillbetakenbetweentheframes125and126andshownintheappendix2Mainframebythemoonpool.Thisistheareawheretheshipsmoonpoolislocatedwhichmakesitacriticalpointindesign.Therearespacereservationsmadearoundthemoonpoolinthegeneralarrangementphase.Thisallowstoreinforcethestructuresaroundthepool.AccordingtoShipConceptualDesigncourseourdoublebottomheightiskepttobe1350mmanddoublesides1200mm.Pillarsarechosentobeoneverysecondwebframeandattheintersectionofwebframeandlongitudinalgirder.[17]Asmentionedearlier,longitudinalgirdersareoneverysecondsidekeelwhichmeansspacing3600mm.[16]Alllighteningholesareveryinitial.4.2 Loads 4.2.1 Definition of load types Ourdefinitionofloadtypesandtheirfrequenciesarepresentedintable4.1.Themostsignificantmagnitudeofloadsarealsopresentedintable4.1andtheircalculationsareshownlater.MPVValerianAlbanovwillbedesignedfor20years.Itsratherlowdesignlife,butconditionsaresoharshinKaraSeasoontheotherhanditwillbebettertomakeshipnottooheavy.Table4.1:DefinitionofLoadsDefinitionofload Typeofload Frequency Magnitude1 Levelice Impact Typicaljourneytime 9,16MPa2 Crane Constant Whenused 250t3 Shipownweight Constant Nonperiodic 18850t4 Dockingperiod Dockingperiod Dockingperiod 5 HydrostaticpressureJourney Typicaljourneytime 61,76kPa6 Thermalloads Journey Constant 7 Waveloads Wave Wavelengthperiod,shipspeed8 Mainengines Constant/vibrations Nonperiodic 9 Tankpressures Constant Random 85kPa10 Anchoring Impact/constant Whileanchored 11 VibrationsinstructureVibrations Eigenfrequencyofthestructure12 Pods Journey Typicaljourneytime 13 StillwaterBendingMomentConstant Nonperiodic 546414kNm4.2.2 Pressures on decks TheValerianAlbanovhasfivedecksabovethemaindeck,asshownintheappendix1MainFrame.Accordingtogeneralarrangementthepressuresondecksabovemaindeckwillbemorelikeinpassengership.AccordingtoDNVandlecturenotesweassumepressuresondecksinlivingareatobe5kPa.Pressureonweatherdeckiscalculatedtobe27kPa.(RMRS:2.6.3.1)Asintable4.1ismentioned,cranewillcreatesignificantlocalloadtoweatherdeckonstarboardsideandapproximatelytoframe83.Ondeck0theheaviestmassisestimatedtobeTEU.WhenTEUisfullyloadeditsweightis30,5t.[18]Thisgivesapproximatelypressureof21kPa.FromRMRS(2.6.3.2)wegetforplatformsintheengineroomtheminimumthatthedesignpressureis18kPa.Butontheotherhand,basedonRMRS(1.3.4.2.1)theoilgatheringtankscreatespressureof85kPa,whichissignificantlyhigherthaninengineroomarea.Thus,basedonsameformulas,thepressureontanktopis105kPa.Alsoreferringtolecturewecansupposethatmaterialthicknessrequirementforenginebedis45mm.Underthecircumstances,wehaveshowninthemainframesketchmaximumpressuresfromdifferentframes.4.2.3 Pressures on hull StillwaterbendingmomentcanbecalculatedaccordingtoDNVforthehoggingandsaggingsituationsamidshipswithformulas[33]:ItgiveswithourvaluesthatourstillwaterbendingmomentofMSO=406802kNm(hogging)andMSO=546414kNm(sagging).ThedesignpressureactingontheshipshullexposedtoweatherisdeterminedaccordingtoRMRS:1.3.2.1[19]:p = pst+ pw(4.2.1)wherethepressureactingontheshipshullisdividedtostaticanddynamicpressure.Staticpressureorhydrostaticpressureiswellknownformula:gh pst = (4.2.2)anddynamicpressureinwaterlinecanbepresentedas:c a a pwo = 5 wv x(4.2.3)where isthewavefactoranditis: cw0,5 for90 00m cw = 1 7 ( )100300L 3/2< L < 3 (4.3.4)andaccelerationterms and : avax , ( ,) , av = 0 8v0LL103 + 0 4 + 1 5 (4.3.5)(1 )0,67wherek isequalto0,inaftand0,infore ax = kx L2x2x8 5 (4.3.6)Thedynamicloadgetsthemaximumvalueattheshipswaterline.Pressuresbelowandabovewaterlineareconsideredseparately.Thestaticpressureisaddedtothedynamicloadtocalculatethetotalexternalpressure.Figure4.1DistributionofloadpWoverthehull.[21]Infigure4.1isshowndistributionofdynamicpressurepWonsideshell.ValuesforthoseaccordingtoValerianAlbanovarepresentedintables4.1and4.2wherez[m]isthedistancefromwaterline.Table4.1Pressuredistributionbelowwaterline.z[m] 0 1,5 3,0 4,5 6,0 7,5 9,0 9,5pw[kPa] 61,7659,72 57,67 55,62 53,58 51,53 49,78 48,80Table4.2Pressuredistributionabovethewaterline.z[m] 0 1,0 2,0 3,0 4,0 5,0pw[kPa] 61.77 55.85 49.94 44.03 38.12 32.21Forthetotalexternalpressure,thestaticpressureisaddedtothedynamicpressurebelowthewaterlineandpresentedinthetable4.3.Thetotalloadabovethewaterlineisthedynamicpressureabovewaterline.Table4.3.Totalpressuredistributionbelowwaterline.z[m] 0 1,5 3,0 4,5 6,0 7,5 9,0 9,5ptot[kPa] 61.7774.43 87.10 99.77 112.44 125.10 137.77 141.99IcepressuresaccordingtoRMRSiceclassARC7(RMRS:3.10.3.2.1)[21]aredividedintofourregionsforthesideshellaspresentedinfigure4.2.Pressuredistributionduetoiceloadsonshellarecalculatedandisshownintable4.4.Figure4.2Regionsoficestrengthening.[19]Table3.4.Pressuredistributionduetoiceloadsonshell.pA1[kPa] pA1I[kPa] pB1[kPa] pC1[kPa]9156 5711 3763 37634.2.4 Other determined loads Periodofthermalloadissupposedtobeconstant.Itoccurswhenoutsidetemperatureisverycold,asitisinKaraSea,andforinsteadHFOtanksareheated.Thereareotherveryhotspotsinsidetheshipaswell.Alsothermalloadpeakmightarisewhenoutsidetemperaturegetshigher.Thevesselsoneimportantmissionisseabeddrillingandduringthisoperation,vesselshouldbestationary.Thereforeshiphasbiganchorsandthosecreateshighlocalloadstoforeship.ValerianAlbanovhastwoAzipodelectricpodpropulsors.Thosearedoingveryseriouspressuresandvibrationsinaftpartoftheship.Podplantshavetobethoroughlyutilizedsothatshipcanhandleallpodsandvibrationsarekeepedintheminimum. 4.3 Load analysis 4.3.1 Wave spectrum AsweknowthatthevesselisforverymultipurposeoperationitisreasonabletouseNorthAtlanticasadesignarea.MostrecommendedwavespectrumforNorthAtlanticisPiersonMoskowitz.[22]PiersonMoskowitzcanbedefinedwithmanydifferentformulas.Wetrieddifferentonesandtwoofthosearepresentedasformula3.3.1[22]andformula3.3.2[22].() ,795/ XP( ,4 g//U) ) S = 0 75*E 0 7 *(4 (4.3.1)() ( ) exp( ( ) ) S = 4Hs2Tz2 4 51Tz2 4 4(4.3.2)where isangularwavefrequency,H_sisthesignificantwaveheightandT_zistheaverage zeroupcrossingwaveperiod.InfirstformulaisalsoUwhichiswindspeedbutwedidntfoundanyaccuratewinddatasowechoseformula3.3.2.FormulasfrombookDynamicsofaRigidShip[24]werealsotriedbutwhenwechoseIACSdata,wealsousedequationgiventhere.Theprobabilityofoccurrenceisassumedtobe0,2accordingtoBMTsGlobalWaveStatisticsgiveninlecture.[22]Thismeansperiodof12,5sandsignificantwaveheight16,5mwhichisthebiggestwaveheightfromtableandwithhighestprobability.WedontknowyetouractualRAOandtherearentavailableinformationaboutthoseforourreferenceshipsornotevenforsimilarships.WedecidedtochooseRAOforMVArcticfromlecturenoteswhichtransferfunctionisshowninfigure4.3.Itisntsimilarforourshipbutitisbetterguessthannothing.WemakedasimilarapproximationcurvetoExcelandusedvaluesfromthat.Withthosevalueswecancalculateourapproximationresponseinwaveswithwellknownrelation(fromlecturenotes):AO Syy = Sxx *R (4.3.3)Figure4.3:TransferfunctionforMVArcticWhenwehavecalculatedresponse,wecancalculatespectralmomentmwithformula:S()d mk = 0k (4.3.4)whereweusedSimpsonsrulefornumericalintegration.Inappendix3WaveSpectrumisshownourcalculationtable.Therecanbealsoseendiagramforwavespectra,transferfunction,RAOandforresponse.4.3.2 Three hour maximum for the bending moment TheextremevalueforGaussianprocesscanbecalculatedwithformula[25]:) 2 n( (60)*lT22m0m2 m0 (4.3.5)wherespectralmomentsm0andm2arefromappendix3Wavespectrum.SpectralmomentsarecalculatedwithwavespectrumandRAO.ThreehourmaximumforValerianAlbanovisthen357364,0kNm.4.3.3 Ship response based on Bonjean curves Inappendix4BonjeancurvesisshownspreadsheettoolforcalculatingBonjeancurves,stillwaterbendingmomentandstillwatershearforce.ToolusesSimpsonRulefornumericalintegrationwhereoneframeisdividedtofiveparts.Theniscalculatedadisplacementwhichobviouslyleadstoforce.Prohaskamethodisusedforestimateinitialweightdistribution.[26]TheinputdatatospreadsheetistakenfromDelftShip.Wegothalfbreadthinformationonlybelowwaterlineandthatiswhytooldoesnotcalculateframeareaabovewaterline.Thuswehavecalculatedforcesonlyinstillwater(T=9,5m).Thetoolislatereasilyexpandedtotakeintoaccountalsovolumeabovewaterline.ThismakesitpossibletoputBonjeancurveswithrespecttowaveandcalculateforexampleasimplesaggingsituation.Toolwouldbemuchbetterifvesselcouldhavebeendividedintotwentysectionswhichisrecommended.[27]NeverthelessitseemsthatatleastdisplacementbasedonBonjeancurvesveryclosetoourdesigndisplacement,asshownintable4.5.Inthatcasewecankeepthistoolreliable.Table4.5.ComparisonofdisplacementsDesigndisplacement 23747m^3Bonjeancurvesdisplacement 24219m^3However,whencomparingstillwaterbendingmomentsbasedonBonjeancurvesandDNVestimates,somewhatbigerrorsoccur.Seetable4.6.EarliertheSWBMiscalculatedwithDNVrulesforstillwaterbendingmomentinhoggingandsaggingamidships.Thisformulamakesitestimationbasedonlength,breadthandblockcoefficient.[28]Table4.6.ComparisonofstillwaterbendingmomentsSWBMBonjeancurves 350780tonmSWBMDNV(hogging) 61419.4tonmThiserrorintable4.6seemstobesobigthatbeforetrusttheseresultsfurthercalculationisneeded.4.3.5 Problems of defining design loads with RAO DefiningResponseAmplitudeOperator(RAO)isextremelydifficulttocalculateintheearlyphaseofdesign.DefiningRAOrequiresaquitecompletemodeloftheshiporsignificantamountoftimedomainsimulations.SecondproblemconcerningtheloaddefinitionwiththeRAOisinthelongtermresponseanalysis.FindingtheworstcasewavespectrumcorrespondingtoshipsRAOinlongtermanalysismightbechallenging. 4.4 Plates and stiffeners 4.4.1 Beam and plate bending response ThebeamandstiffenerbendingresponseiscalculatedthroughanapplicationofEulerBernoullibeamtheory.Thetheorycombinestheinternalresponseofthebeamandtheexternalloadonasmallbeamelement.Theequilibriumbetweenthesetwogivesthedifferentialequationforthelineloadasfunctionofdisplacement.Theclassificationsocietyrulebooksapplythesametheoryresultinginaformulathatdefinestheminimumsectionmodulusofplateandstiffenertogether[29].(4.4.1)Wherethemaximumallowablestress=160f1=160MPa.Therulebookdefinesminimumplatethicknessfordifferentstructuralpartsincludingdeckplatinginbottomstructure,tanktop,machinerydeckandweatherdeck.Theminimumplatethicknessfordecks[29]:(4.4.2)Butnottobebelow[29]:(4.4.3)Table4.7.Thecorrosionadditiontk.[DNV:RulesforShips,July2012Pt.3Ch.1Sec.2Page23]Forthesidestructurestheiceloadsarethesignificantfactordefiningthescantlingsfordifferentstructuralmembers.TheshellplatingandstiffenersizewillbecalculatedaccordingtoicerulesofRMRSforshipwithiceclassArc7.[31:Formulas(3.10.4.3.4and(3.10.4.5.1)]4.4.2 Dimensions for plates and stiffeners Table4.8.Platethicknessfordifferentdecksaccordingtoformulas12.1.2and12.1.3. kas[m] p[kPa] [MPa] tk[mm] tplate,rule[mm]tselected[mm]Flatbottom 1 0,6 142 235 3,36 17,63 18,0Deck2Tanktop 1 0,6 105 160 3 10,68 11,0Deck1Engineroom1 0,6 85 160 2 8,91 9,0Deck0Storage 1 0,6 21 160 1 7,38 8,0Deck1Maindeck 1 0,6 27 160 0,5 7,88 8,0Deck2Laboratory 1 0,6 5 160 0,5 6,88 7,0Deck3Gym/Sauna1 0,6 5 160 0,5 6,88 7,0Deck4Cabins 1 0,6 5 160 0,5 6,88 7,0Deck5Cabins 1 0,6 5 160 0,5 6,88 7,0Deck6Bridge 1 0,6 5 160 0,5 6,88 7,0Afterselectingtheplatethicknessesfordifferentdecks,westarttochoosestiffenersfromRuukki[30]andcheckthesectionmodulusaccordingtorulebook(formula3.4.1).Accordingtolecture,HPprofileisveryefficientprofileforstiffenersandisveryoftenusedinships.Whenprofilewasselected,wecomparedourcalculatedsectionmodulusvaluestoDNVsrulesandafterthattoRuukkistablewherestiffenerprofileisselectedaccordingtosectionmodulus.Thesecalculationsarepresentedinthetable4.9.Thewebframespanl=1,8mlongitudinalspacings=0,6mdesignstress=160MPaarethesameforallthedeckandthereforenotpresentedinthetable.Intable4.8thethicknessforflatbottomiscalculatedbyRMRS2.2.1.Table4.9.Stiffenerselectionandsectionmoduluscalculation. Zrule[cm3] ProfileselectedZtop,selected[cm3] Zbottom,selected[cm3]Flatbottom 143,2 HP180x9 210,8 1324,0Deck2Tanktop 105,9 HP160x8 138,3 788,6Deck1Engineroom 85,7 HP160x7 129,0 688,3Deck0Storage 21,2 HP100x5 38,9 314,8Deck1Maindeck 27,2 HP100x5 38,9 314,8Deck2Laboratory 15,0 HP100x5 38,4 293.7Deck3Gym/Sauna 15,0 HP100x5 38,4 293.7Deck4Cabins 15,0 HP100x5 38,4 293.7Deck5Cabins 15,0 HP100x5 38,4 293.7Relativelyshortwebframespan(l=1,80m)resultsinquitelowsectionmodulusrequirementfromtherulebook.ThisagainresultsinspecificminimumsectionmodulusrequirementfortheupperdeckswhichisZ=15cm3.Platethicknessforshellplatinginthefouricebeltregions:A1Fore,A1lForeshoulder,B1MidBodyandC1Aftisdeterminedinthetable4.10.ItischosenthatValerianAlbanovhasadditionaliceframesinicebeltarea.Thisleadstoframespan0,3minicebeltandreducessectionmodulusrequirementssignificantly.Preliminaryischosenthatordinaryframeisthesameprofilethaticeframethroughthevessel.Stiffenerselectionisshownintable4.11.Formidandaftpartoficebelt,HPprofileischosenbutforforeicebeltischosenLprofilebecauseofgivensectionmodulus,allRuukkisHPprofilesaretoosmall.Table4.10.Icebeltshellthickness. p[kPA] u(corrosionreduction)[mm]trule[mm] tselected[mm]A1Fore 9156 0,50 51,88 52A1lForeShoulder 5711 0,50 42,55 43B1MidBody 3763 0,35 33,70 34C1Aft 3763 0,35 33,70 34Table4.11.Stiffenerprofilesforsideshell. Zrule[cm3]Profileselected Ztop,selected[cm3] Zbottom,selected[cm3]A1Fore 2529,36 Lprofile350x40x100x402680.31 4870.69A1lForeShoulder1577,67 Lprofile250x40x100x401646.22 2948.59B1MidBody 1039,53 HP370x13 1566.58 3559.08C1Aft 1039,53 HP370x13 1566.58 3559.08PlatethicknessesonsideshellbelowandabovetheicebeltiscalculatedbyRMRS2.2.1and1.6.4.4areshownintable4.12.Pressuresarethesameonesthatwerecalculatedearlier.RMRScalculatesthecorrosionadditionaccordingtooperationalyearswhichisconsideredtobeRMRSdefault24years.Table4.12.Platethicknessbelowandaboveicebelt p[kPA] u(corrosionreduction)[mm]trule[mm] tselected[mm]Aboveicebelt 61,78 3,4 12,8 13,0Belowicebelt 112,4 3,4 16,0 16,0Initiallyitischosenthatabovetheicebeltis13,0mmplateandbelow16,0mm,untiltheflatbottomplate.BottomshellischosentostartbeforebilgeradiusatpointZ=5,5mandthethicknessissupposedtobeconstant.4.5 Web frame and girder bending 4.5.1 Design principles Forthewebframeandgirderbending,thesameEulerBernoullibeambendingtheoryisappliedaswiththeplatesandstiffenerswhichistakenintoaccountinDNVformula[32]: Z = 83l spw2k(4.5.1)Afterknowingthesectionmodulusrequirementandtheplatethicknesswecantryoutdifferentsizedbeamsandcalculatetheactualsectionmodulusfortheseplateandbeamcombinations.Thefinalselectionwillbeabeamthatfulfillstherulebookrequirementandhassmallreservecomparedtotherequirement.Withthewebframesandgirderstheshearlageffectneedstobetakenintoaccountwhichmeanscalculatingtheeffectivebreadthbeforallthebeams.Forexampleforgirderswhicharesupportedbypillarlines,usingpillarlinespacingasbwouldresultintoohighsectionmodulus.Withtheeffectivebreadthconceptwecanevaluatetheeffectiveflangeofthegirder.Theeffectivebreadth,be,isdeterminedbysimplifiedapproachoftherulebook[32].Withthismethodthewebframespacing,loadandtheboundaryconditionsdefinethebe.(m) Cb be= (4.5.2)whereb=sumofplateflangewidthoneachsideofgirderandCfromtable4.13.Table4.13.Cvalues[29]Asthedesignloadsforthisshiparedefinedaspressuresthenumberofpointloadswillbeconsideredr6forallthesituations.Distancebetweenpointsofzeromomentsisaanddependsontheboundaryconditions,whetherthebeamhasclampedsupportintheendsorfreelysupportedoramixofthese.Forthethreecasesmomentequationsareshowninthefigure4.4.Withtheseequationswecancalculatetheadistances(betweenpointsofzeromoment):af ree = l(7.1.3) aclamped = l3(7.1.4) amixed = 43l(7.1.5)Figure4.4.The3differentmomentequations.Wecanconsiderthegirdersandwebframestobeclampedduetocontinuityofthestructureseverywhereexceptinthesideshellsanddoublebottomwherethebeamsareweldedtothesideorbottomplate.4.5.2 Web frame and girder selection SelectionwillbecarriedoutbycalculatingtheDNVsectionmodulusrequirement.Thedeckpressuresvaryandareevaluatedearlier.Thedifferentspansneedtobetakenintoaccount,forwebframespacing1,6mandgirderspan3,2m.Oncewehavetherequirementweselectabeamthatgivesapproximately10%highersectionmodulusthantherequirement.MaterialthatwillbeusedisnormalstrengthsteelwithupperyieldstressREH=235MPa.Calculationsareshownintheappendix6.2and6.4Structuralcalculations.Becausethesideconditionsforthemiddledeckpartsgivehigherrequirementsforsectionmodulus(shorterspan),thewebframesforthewholedeckbreadthareselectedaccordingtothemiddlepart.Thisresultsinsamesizedwebframeforthewholeshipbreadth.Thesamemethodwillalsobeappliedforthelongitudinalgirders.Thegirderswillalsobechosenwiththesameheightasthewebframestocreatesameheightintersectionsforpillars.InthedoublebottomtherewillbenoTbeamsbutplatesalongthewholedoublebottomheight.Thicknessofthesefloorplates(transversals)andgirderplates(longitudinals)willbecalculatedaccordingtoseparateDNVrules.Bothfloorsandgirdershavethesamespanof1,6m.Inthedoublebottomthecorrosionfactorwillbe3duetothefactthatareawillbeusedasballastwatertank.Thefinalresultsareshownintheappendix6.1Structuralcalculations.ForthedoublesidetheicepressuresdeterminetheIbeamsusedintheicebeltarea.Thebeamsselectedareshownintheappendix6.3Structuralcalculations.4.6 Hull girder response 4.6.1 Normal stress response in bending Thehullgirderbendingresponseisevaluatedbycalculatingthesectionmodulusforthemidshipstructure.Therulebookgivestwominimumrequirementsforsectionmoduluswherefirstoneisnotdependingonwaterbendingmoment:(4.6.1)wherethevalueforCWOistakenfromrulebooktable.Forashipwith130>L>140theCWO=8.53.Thesecondrequirement:(4.6.2)where1=175f1=175MPawithournormalstrengthsteelandwithin0.4Lamidships.Thecalculationsfortheactualmidshipsectionmodulusandneuralaxisarepresentedinappendix7Sectionmodulus.Therehavebeenmadesomesimplificationwhencalculatingthesectionmodulus.ForexampleHPprofileistakenasaflatbarandneutralaxisforHPprofilesaresimplified.4.6.2 Vertical distribution of normal stresses Theverticaldistributionofnormalstressisobtainedforthemidshipsectionbyusingthemaximumbendingmomentcalculatedearlier.Thebendingmomentwasobtainedwithbonjeancurves,prohaskaweightestimationmethodandwithawaveconditionappliedonthecurves.MSW=436209kNmMW=37196kNmFigure4.5:Verticalnormalstressdistribution.Aboveonfigure4.5isshownthenormalstressdistributioninhoggingsituation.4.6.3 Shear stress distribution ShearstressesmightcauseadditionalandsignificantdeflectionsinbeamswithL/hratiolowerthan10.(4.6.3)whereshearforceQcausedbytheexternalloadonstructureinducesshearstress onthesheararea.Therulebookgivesagainasimplifiedapproachwherethedistributionoftheshearforceisgivenfordifferentcrosssectionsofthemidship.Thetable4.14indicatesvaluesforshearforcedistributionsdependingontheshipslongitudinalbulkheads.ForValerianAlbanov,shearstressdistributioniscalculatedwithusingBonjeanCurvestableandisshowninappendix4BonjeanCurve.Table4.14.ShearforcedistributionfactoraccordingtoDNV[33].WhileknowinghowmuchbulkheadtakesofshearforceQbyusingwecanevaluatethestresswiththeformula: = AQ=h b*(Q +Q )SW W(4.6.4)4.6.4 Stress levels Werealizethatthenormalstressestimationfortheshipcannotbeexactlycorrectduetofactthatthesuperstructureisneglected.Howeverinthiscaseitdoesnotproduceproblembecausethesuperstructureonlystiffenstheforeship.Normalstressesforthehullareconsiderablylowerthanallowablestresslevel.Materialusedforthesuperstructurewillbenormalstrengthsteelbutwithhigherbrittlestrength.Thenormalstresslevelsarerelativelysmallwiththeestimatedloads.Itmeansthattheshiphashighsafetyfactorsinrelationtothenormalstresses.Perhapsthisissomethingtoconsiderintheoptimizationphaseofthedesign.TheshearstresseswillnotproduceanysignificantproblemsfortheshipduetothefactsthatshipcanconsideredasclosedcrosssectionandshipbeamshavehighL/hratio(>10). 4.6.5 Torsion Torsionisverycriticalwhenstructureisopen.Forexample,whenthereareopeningslikehatchopeninginbulkcarriers.Wedonthavehatchopeningsonthemaindeckandourstructureismoreorlessclosed.Butwehavemoonpoolwhichcanbeverycriticalduetothetorsion.TorsionisbecomingmorecriticalwhenshipislongerthanValerianAlbanov.Inourcase,shipcanbeenhandledmoreorlesslikethinwallclosedsection.Thenthereisrelation,knownasBredtsformula,thatangleoftwistisgivenwithformula[34]:ds = 12GAC0xs(4.6.5)whereGistheYoungsmodulus,Aisareawithinthecenterlineand isshearstress.When xswallthicknesstisaconstant,Eq.(15.5.1)canbeshowninmucheasierform(Parnes12.10.15b): = TS4A Gt2(4.6.6)whereSistheperimeteralongthecenterline.Nowwecanseethatifwehaveatorqueaffectingonship,theangleoftwistissmallerifwehavehighYoungsmodulusandthestructuralarrangementareaisbigandthick.Startingpointisobviouslythatthestructuralarrangementiscontinuousthroughthewholeshipandthestructureisclosed.MaterialwhichisusedisveryimportantandincriticalplacesshouldconsidertoutilizematerialswithhigherYoungsmodulus.Inmoonpoolareashouldbeenmadeverycarefulstructuralarrangementandthinkingalsostrengtheningmaterialsaroundmoonpoolhole.Theinternaltorsionmomentisalsoinequilibriumwiththeexternalmoment.[35].Accordingtothat,weatherandseaconditionshasthebiggestimpactintotorsion.Torsionstrengthshouldbeencalculatedaccordingtorequiredweatherconditionsandalsosimulatetorsionswith3Dmodel.4.7 Vibratory response 4.7.1 Measures to control vibratory levels InValerianAlbanovvibratorysourcesare:mainengine(WrtsilGenset38,600rpm)podsandthepropeller(4blades,D=5,5m)waveslammingloadsduetotheinefficientbowshape(whipping)iceloads(whipping)springingismorecriticalonshipswithlargeL/Bratio(cruiseships)anditisnotcriticalinValerianAlbanov.Thesesourceswillinducevibratorywakeswithdifferentfrequencies.Weneedtoidentifythemostcriticaloneswiththehighestenergy.Oncewehaveidentifiedthecriticalones,wewilldecidethecriticalfrequencyvalue.Thisvaluedefinestheminimumvaluefortheeigenfrequenciesoftheplates,stiffenersandgirders,otherwisetheriskofresonancewiththecriticalvibrationsissevere.Itisimpossibletoestimateallthepossiblewakesinducedbytheshiporitoperations.Thisiswhythecriticalfrequenciesareidentifiedandtheriskofresonanceexcludedbysettingtheminimumeigenfrequencyforstructuralparts.Figure4.7.Responsespectrum.Ascalculatedintheearlierassignmentandalsoshowninthefigure4.7,thecriticalwavefrequenciesarelessthan1Hz.Forthepropellerinducedwakewecandoaroughestimate[37]fromknowingthebladenumberandrevolutions.Inourcasethebladenumberis4andpropellerrevolution110rpm.Thisresultsin:n/60 10/60 7,3Hz = Z = 4*1 = 3 (4.7.1)Themainengineinduceswakeoffrequencyaround10Hz.FortheiceinducedwakeswerefertoBelovsstudiesontheicebreakersSanktPetersburgandArktika[36].Thestudiesshowthatmostcriticalvibrationsaregeneratedatthefrequencyrangeof012Hz.Bytakingaccountallthemajorwakesourceswedefinethattheminimumfrequencyvalueforthestructuralmembersissetfcr=15Hz.Itmeansthatallstructuralmembersneedtobedesignedtohavehighereigenfrequencythanfcr.Thehigherfrequenciesthanthecriticalonewillbedampedbyutilizingtheconventionalmethodsinships:insulationfoamorothermaterialondecks,sidesandbulkheadsdampingelementsformainenginevibrationsthereisdifferentcorrectiveactions,forinsteadbalancingflywheel.[38]4.7.2 Eigenfrequencies for plates, stiffeners and girders Theeigenfrequencyforsimplysupportedbeamsiscalculatedby: = 2EI/m (3.7.2)wheremass,misareamassofthebeamand=/Lforthesimplysupportedbeam.Weareonlyconsideringmode1waveforthebeamwhichcorrespondsinthehighestfrequency(worstcasescenario).Eigenfrequenciesforthebeamsarepresentedinthetable4.15.Theeigenfrequencyfortheplatesiscalculatedby: = a2Eh312m(1 )2(4.7.3)Thefortheplatecasedependsonthesupporttypeandwavemodebutalsoonthea/bratiooftheplate.Eigenfrequenciesfortheplatesarepresentedinthetable4.16.Thewidthoftheplatesisassumedtobethespacingbetweenstiffeners.Table4.15.Eigenfrequenciesofstiffeners.STIFFENERS L[m]lamda[1/m] Area[m^2] I[m^4] Eigenfrequency[Hz]Bottom 1,8 1,75 0,01365750,0000536 157,97Deck1 1,8 1,75 0,008364 0,0000296 150,01Deck0 1,8 1,75 0,007004 0,0000271 156,85Deck1 1,8 1,75 0,00552940,00000526 77,77Deck2 1,8 1,75 0,00552940,00000526 77,77Deck3 1,8 1,75 0,00492940,00000512 81,27Deck4 1,8 1,75 0,00492940,00000512 81,27Deck5 1,8 1,75 0,00492940,00000512 81,27Deck6 1,8 1,75 0,00492940,00000512 81,27Deck7 1,8 1,75 0,00492940,00000512 81,27Table4.16.Eigenfrequenciesofplates.PLATES t[m] Eigenfrequency[Hz]Bottom 0,018 12021,42Deck1 0,011 2743,57Deck0 0,009 1502,68Deck1 0,008 1055,38Deck2 0,008 1055,38Deck3 0,007 707,02Deck4 0,007 707,02Deck5 0,007 707,02Deck6 0,007 707,02Deck7 0,007 707,02Fromtheeigenfrequencytableswecanseethatallthestructuralmembershavehighereigenfrequencythanthecriticalone.4.8 Buckling and Ultimate Strength 4.8.1 Buckling Thecriticalbucklingstressforplates,stiffeners,pillarsandgirderswillbeevaluatedwiththeEulerstheoryforelasticbuckling.ForthememberswithlowslendernesstheJohnsonsparabolaistakenintoaccount.Thetheoryisthesameasgivenintherulebook[39]:Fortheidealcompressivebucklingstresselthestiffeners,pillarsandgirderswillbeconsideredasbeamsandtheplateswillbetreateddifferently.Forthebeams:andfortheplates:wherethefactorkwillbesimplifiedtok=4duetofactthatourshipislongitudinallystiffenedandcompressiveloadsareconsideredtobeevenlydistributedalongtheplatesides.Withtheseformulasthecriticalbucklingstressesarecalculatedandshownintheappendix8Buckling.Figure4.8.NormalstressdistributionInthefigure4.8thestressesarecalculatedwiththemaximumsaggingmomentwhichcanbeconsideredtobethemostcriticalsituation.Whencomparingtheactingstressesonthecriticalbucklingstresseswenoticethatalthoughalltheactingstressesarebelowthebucklingcorrespondents,theorderofbucklingisnotwhatitshouldbe.Theplatesarethefirststructurestobucklebutafterthatthestiffenerandgirderhavequitethesamebucklingstress.Theorderofstabilitylossshouldbeplate,stiffenerandafterthatthegirder.Thismeansthatwemustconsiderifthegirdersizeinthedeck1shouldbeincreasedorifthematerialshouldbehighstrengthsteel.4.8.2 Ultimate strength Whenestimatingtheultimatestrengthofthehullgirder,theprocedureisdoneinawaythattheactingmomentisincreasedlinearlytolocatethecriticalpositionswheretheyieldingofthestructurestarts.Iftheshipstructuresfollowthecorrectbucklinghierarchy,thesequenceoffailuresshouldbefirstthebucklingofanunstiffenedplate,nextthebucklingofthestiffenerandforthelastthebucklingofthewholepanel.Theultimatestrengththatthestructurecancarryisdeterminedatthepointwherethewholecrosssectionofpanelisplastic.Itmeansthatstructuralmemberdoesnothaveanyloadcarryingcapacityleftandthestructurefails.Toestimatetheultimatestrengthinthisshipfirstweneedtocheckthatthefailinghierarchyofstructuresiscorrect.Afterthatwecandeterminethesequenceoffailuresandtheactingmomentsthatcausethesefailurestohappen.Table4.17.Orderoffailureinstructures. Moments[MNm] Descriptionoffailure1 1900 Bucklingofplateindeck12 3150 Bucklingofstiffenerindeck13 3200 Bucklingofgirderindeck14 3450 Firstfiberyieldofplateindeck15 4100 Bucklingofplateindeck06 5500 Bucklingofgirderindeck17 6200 Bucklingofstiffenerindeck0Fromtable4.17andfigure4.8itcanbeobservedthatthehierarchyofbucklingisasitshouldbe.Deck1seemstobethemostcriticaldecktobeobservedinpointofultimatestrength.Withthemomentof5500MNmthegirdersatthedeck1willstartbuckle,whichwillmeanfailureofthewholedeck.Thetopmostpointofourultimatestrengthcurveisreachedatthepointwheredeck1istotallyplasticandfromthereonwardsthestructuresabilitytocarryhigherloadswillonlydecrease.Itisalsoknownthatshippanelscancarryhigherloadsthanthebucklingstressofsimpleplateandastiffenerduetoeffectivewidthconcept.Inthatcasethestresswillbeconcentratedclosetoareawherethestiffenerisattached.Byapplyingthisconceptwecouldachievemorerealisticvaluesforplatebuckling.Buteffectivewidthisneglectedinthiscase.Withtheconservativeapproachweknowthatsomesafetymarginisleftintheultimatestrengthestimation.Figure4.9.Thesketchoftheultimatestrengthcurve.4.9 Fatigue and Fracture Strength 4.9.1 Fatigue InDNVsclassificationnotesno.30.7ispresentedsimplifiedfatiguecalculationmethod.Fatiguestrengthcalculationisstartedwithcalculatingtheloads.Inappendix9Fatigueisshownourcalculationtablewhereiscalculatedstresslevelsforeachdeckandstructuralmemberbyapplyingthedifferenceofwaveinducedhullgirderbendingmoments.Waveinducedhullgirderbendingmomentsarecalculatedasisshowninsection6.2.1.[40]Afterthatwecalculatedwaveinducedverticalhullgirderstressas:Stressconcentrationfactorshouldbecheckedfordifferentcasesandchoosethemostcriticalone.Weused1,6asagoodaveragevalue.Itvariesalittlebitfordifferentcaseslikeforthepointwherewebframeisconnectedtodeck,bulkheadtodeckandforweldedjointsetc.Wetriedalsodifferentonesbutitdoesntchangetheresultssomuch.Formoreaccurateresultsitwouldbeofcourseveryimportant.Combinedglobalandlocalstressrangeiscalculatedasshowninsection2.3.4andnowwehavecalculatedloadsandresponsessowecanuseDNVsdamagecalculation.ThemethodcombinesWeibulldistributionoflongtermstressrangeandaoneslopeSNcurveandispresentedas:(4.9.1)ForValerianAlbanov, isjustonebecauseofsimplification, issomethingbetween Nloadpn0,85and1,so0,9isagoodguess.Designlife forValerianAlbanovis20yearsand Tdweibullstressrangeshapedistributionparameter iscalculatedfordecklongitudinalswhen hn= and : hnh0h0 (4.9.2)ShapeparametervalueforValerianAlbanovisthen1,05.Formoreaccurateresultsweshouldcalculatealsoshapeparameterforshipsideabove,belowandatthewaterlineandforbottomlongitudinalsandforbulkheads.Becauseofsimplification,methodisenoughaccurate.TheWeibullscaleparametercanbedefinedfromthestressrangelevel, ,withformula: 0(4.9.3)where isthenumberofcyclesoverthetimeperiodforwhichthestressrangelevel is 0 0defined.Withhighcyclefatigueweused0,7*10^8.Wehavetodosomesimplificationsforfatiguecalculations,sowecanusethezerocrossingfrequencyas:(4.9.4)whereListheshipRulelengthinmeters.ForValerianAlbanov =0,117. Gammafunctionisdescribedwith:(4.9.5)wheremisSNfatigueparameter.WhenwearecalculatingSN1forweldedjointswecanuseaccordingtolecturenotesthatmis3,0andnowwegetfromtableG1[40]thatourgammafunctionvalueis5,029.Nowwecancalculatefatiguedamagevaluefordifferentcase.Ourcalculationtableisshowninappendix9Fatigue.Therehavebeenmadesimplificationsasmentionedearliersothemostreliableresultisfordeck1anditsstiffenerswhichgivesdamagefactor0,014forthedeckand0,019forthestiffeners.Reliableiscomingfromthefactthatwewerecalculatingdecklongitudinalswithproperstressconcentrationfactor.Resultsseemstobereasonablealsoanditisalotlessthan .[41] = 1 4.9.2 Material grades Astheshipisdesignedtoworkinextremelycoldconditions(upto40C)theriskofbrittlefractureishigh.Inthefirstchapterthematerialgradesfortheshipswerechosenaccordingtorulebook[42].Allsteelsusedwillbenormalstrengthsteelwithminimumyieldstrengthof235MPa.ThiswasalreadychosenearlierandutilizedinallowablestresscalculationforNVNS:f1=1,0.Tokeepthemanufacturingefficiencyonagoodlevel,theselectionofmaterialgradesshouldcontainasfewdifferentmaterialsaspossible.Thissimplifiestheselectionasthecoldtemperaturesetsrequirementsforthematerialsused.ForalltheexteriormembersofstructurethesteelgradeEwillbeusedduetocoldambientairtemperature.FortheinteriorstructuresthegradeAwillsufficientaccordingtotherulebook(interiorplatethicknesses