Treballrealitzatper:ÁlvaroPridaGuillénDirigitper:ClimentMolinsBorrellPauTrubatCasalsGrauen:EnginyeriaCivilBarcelona,1dejunyde2017Departamentd’EnginyeriaCiviliAmbiental TR

EBAL

LFINAL

DEGR

AU

Designofthestructureofa100kWFloatable Offshore Wind Turbine(FOWT)

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ABSTRACTWindcrete isanewstructuraltechnologydevelopedattheUPCBarcelonaTech(Barcelona,Spain) that pretends to introduce concrete floating platforms for offshore wind energyproductioninthemarket.Usingthisconcept,inthisthesisitisdesignedthesparplatformofa Floatable Offshore Wind Turbine (FOWT) that is going to be located off the coast ofTarragona.Tocarryoutthestructuraldesign,twocriticalsituationsareconsidered.Thefirstonetakesplaceduring the stevedoringoperationswhenmoving the structure from thequay to thesea.ThesecondconsiderstheFOWTinoperation,assumingSevereSeaState(SSS)andwindspeed at rated (maximum production of energy). Hence, an analysis of stresses must bedone simultaneously for both situations, adjusting the design to satisfy the resistanceconditions. The pre-stressed concrete structure has been designed for Serviceability LimitState(SLS).ItalsohasbeencheckedtheresistanceofthestructureinUltimateLimitStress(ULS).Finally, a first estimation of the budget has been developed. It has permitted thedeterminationoftheitemsthathavemoreinfluenceintheprojectcosts.

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RESUMEN

Windcreteesunanueva tecnología encuadradaenel ámbitode las estructuras. EstaestádesarrolladaenlaUPCBarcelonaTech(Barcelona,España).Pretendeintroducirplataformasflotantes tipo spar en elmercado. A partir de este concepto, en esta tesis se diseña unaplataforma spar que forma parte de una estructura offshore flotante. Esta plataforma sesituaráenlacostadeTarragona.Para llevar a cabo el diseño de la estructura, se consideran dos situaciones críticas. Laprimera se produce durante las operaciones de estiba,mediante las que la estructura estransportada de un muelle al mar. La segunda contempla la estructura flotante enoperación,asumiendoEstadoSeverodelMarymáximaproducción.Eldiseñodebepoderresistir las tensiones para ambas situaciones. Por esta razón, el diseño se realizaconjuntamente. Laestructura,queserádehormigónpretensado,esdiseñadaparaEstadoLímitedeServicio (ELS).Además,secomprueba laresistenciade laestructuraparaEstadoLímiteÚltimo(ELU).Por último, se incluye una primera estimación del presupuesto, el cual ha permitidoreconoceraquellasunidadesdeobraqueincrementannotoriamenteelcostedelproyecto.

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RESUM

Windcreteésunanovatecnologiadedicadaal’àmbitdelesestructures.Estàdesenvolupadaa la UPC BarcelonaTech (Barcelona, Espanya). Pretén introduir plataformes flotants tipusspar almercat. A partir d’aquest concepte, en aquesta tesina es dissenya una plataformasparqueformaràpartd’unaestructuraoff-shoreflotant.LacitadaplataformasesituaràalacostadeTarragona.Per dur a terme el disseny de l’estructura, es consideren dues situacions critiques. Laprimera es produeix durant les operacions d’estiba, mitjançant les quals l’estructura éstransportadaalmar. La segona contempla l’estructura flotantenoperació, assumintEstatSeverdelaMarimàximaproducció.Eldissenyhadepoderresistirlestensionsperambduessituacions.Peraquestmotiu,eldissenyesrealitzaconjuntament.L’estructura,queseràdeformigó pretesat, està dissenyada per Estat Límit de Servei (ELS). Es comprova, també, laresistènciadel’estructuraperEstatLímitÚltim(ELU).Perúltim, s’inclouunaprimeraestimaciódel pressupost, el qual hapermès la localitzaciód’aquellesunitatsd’obraqueincrementennotablementelcostdelprojecte.

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Tableofcontents

1 Introduction................................................................................................................8

2 Motivationandobjectivesoftheproject..................................................................10

3 Locationoftheproject..............................................................................................11

4 Stateoftheart..........................................................................................................124.1 FloatingOffshoreWindTurbine(FOWT)platformstypologies..................................124.2 TheWindcreteplatform............................................................................................14

4.2.1 ComparisonamongWindcreteFOWT’sanditsmarketcompetitors..............................154.2.2 Conceptualdesign...........................................................................................................18

4.3 Motionsofafloatingstructure.................................................................................184.4 WindCretedesignprocess.........................................................................................194.5 Siteconditionsandloadcases(IEC61400–DNVOffshorewindturbines).................22

4.5.1 Siteconditions.................................................................................................................224.5.2 Loadcases........................................................................................................................25

4.6 HighPerformanceConcrete......................................................................................254.7 Pre-stressingsteel.....................................................................................................28

4.7.1 Typesofpre-stressingsteel.............................................................................................294.7.2 Stress-strainrelationship.................................................................................................314.7.3 Post-tensionedsteel........................................................................................................33

4.8 Steelducts................................................................................................................344.8.1 Grouting...........................................................................................................................344.8.2 Injectionprogram............................................................................................................35

4.9 Anchoragesystem.....................................................................................................354.10 Pre-stressingreinforcementdesign...........................................................................364.11 Transportationofthestructure.................................................................................384.12 Budget:previousconcepts........................................................................................38

5 Analysisof theServiceability Limit State (SLS)and theUltimate Limit State (ULS)ofthestructure....................................................................................................................40

5.1 ServiceabilityLimitState(SLS)..................................................................................405.1.1 Dataprovidedandcalculationofthedesignpre-stressingforce....................................405.1.2 Designofthesheaths......................................................................................................475.1.3 Anchors............................................................................................................................505.1.4 Calculationofthelosses..................................................................................................51

5.2 UltimateLimitState(ULS).........................................................................................59

6 Construction,transportandinstallation....................................................................65

7 Budget......................................................................................................................807.1 Measurements..........................................................................................................817.2 Feeschedule1..........................................................................................................907.3 Budget......................................................................................................................93

8 Conclusions...............................................................................................................988.1 Specificationsonthefinaldesign..............................................................................988.2 Finaloverview..........................................................................................................99

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9 References..............................................................................................................100

10 Appendix............................................................................................................10410.1 Appendix 1: Pre-stressing steel design. Operational state (Sea Severe State, windspeedatrated)........................................................................................................................104

10.1.1 Direct losses, time-dependent losses. Pre-stressing force after direct losses andpre-stressingforceatlongterm(SLS).........................................................................................10410.1.2 ResultsoftheULScheck.......................................................................................106

10.2 Appendix2:Pre-stressingsteeldesign.Stevedoringoperations.............................11010.2.1 Bendingmomentateachsectionofthestructure,fortheoptimalcombinationofm,n(m=3meters,n=20meters).................................................................................................11010.2.2 Checkofthestressesinthestructureatshortterm(SLS)....................................112

10.3 Appendix3:Matlabcodeforthecalculationofthepre-stressingdesign.................11410.4 Appendix3:Matlabcodeforthecalculationofthecrane’soptimalposition..........122

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Aknowledgements

Fromthat9thofSeptember2013–myfirstdayattheCivilEngineeringSchoolofBarcelona–IhavehadthelucktomeetgreatpeopleintheFaculty.NowthatIamabouttoconcludemyBSc,itistimetolookbackandrememberthosewhohaveaccompaniedmealongthis4-yeartrip.First, Iwould like to thankDr. ClimentMolins for givingme the possibility ofmeeting theWindcreteconcept,anewtechnologyinWindOffshoreEngineeringforthedevelopmentoffloating platforms. In the sameway, Iwould like to expressmy gratitude to theMSc PauTrubat, who has helped me unconditionally with my engineering hesitations along theproject.Idesireyoumajorsuccessesinthefuture.Second, Iwould like tomention thepermanent supportofmyparents, FernandoandEva,andmybrothers,FernandoandPelayo.IhopeIcandedicateyouallmanymoreprojectsinthe upcoming years. You must never forget that I have you always present, despite thekilometersthatseparateus.IdonotwanttoforgetmyfriendGonzaloforhisfrankadviceandfriendship.ThanksalsotomyfriendsandcolleaguesXaviandSergi,withwhomIhavegrownupatuniversity.Idesireyouallthebestinyourfuturecareers.Finally, Iwould like toexpressmygratitude toProf. JuanMiquelandProf.RosaEstela fortheirwillingnesstoadvisemewhenneeded.IencourageyoutokeepsharingyourknowledgeforthebenefitofthefuturecivilengineersfromourconsideredSchool.

Delft(NL),13thofJune2017

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1 Introduction

Thedevelopmentof floatingoffshoreplatformswaspioneeredby theOil&Gassector. Inthe late 1980s, the first oil well discoveries at very deep waters (1) put in question theconventional methods of extraction. The feasibility of the so far used bottom-fixedtechnology at that depths had been compromised. As a response, the offshore floatingplatformsroseasacompetitivealternativeintheoilextraction.On the other hand, the wind energy market needed more time to go offshore. The oilmarketwasverycompetitiveattheareasthathadlaunchedtheoffshorebusiness(e.g.GulfofMexico).OffshorewindtechnologystartedhispathintheNorthSea(Figure1.1),oncetheoffshoretechnologyhadbeenconsolidatedintheOilandGassector.First,newwindfarmsweresettleddowninshallowwaters.CountriessuchasDenmark,TheNetherlands,NorwayortheUKleadtheinnovativeoffshoreenergygreenproduction.ThepresenceofcontinentalshelfintheNorthSeamadethebottom-fixedmarketattractiveforinvestors.Beforelong,theoffshorewindtechnologyfacedanewchallenge.Manycountriescouldnotenjoytheadvantagesprovidedbytherecentdiscoveries.ResearchersintheUS,Japan,Spainand Portugal – amongst others – started to build a new dimension in the wind energyproduction.TakingtheOil&Gastechnologyasreference, theywantedto jumptodeeperwaters.Theideabehindtheconceptwaspowerful–togiveallthecoastalcountriesintheworldthecapabilityofproducingcleanenergy.However,therewerealsootherstrongreasonsthatsupportedthe investigation.Thewindenergy generation in deep waters permitted to increase the production. Generally,hinterland turbines cannot achieve their maximum throughput, since they exceed theallowedlevelsofnoise.Furthermore,usuallythewindflowismoreuniforminopensea.Thisfactisbeneficialforefficiencyandincreasesthelife-spanofthestructure.Windturbulenceisthusreducedand,consequently,fatiguedoesso.Asafinalremark,theoffshorelocationoftheturbinesavoidsvisualcontamination.

Figure 1.1. The proliferation of bottom-fixed platforms in the North Sea in the recent times is

clearlyexplainedinthispicture–thereisalargecontinentalshelfinthearea(71).

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Thewindoffshoretechnologyhasundergoneanoticeabledevelopmentinthelast15years.In 2002, the first commercial-scale offshorewindplantwas commissioned in the coast ofDenmark. It had a capacity of 160 MW. Since then, the increase on the yearly basisproductionhasbeenincreasingeveryyear.Bytheendof2015,theworld’sinstalledoffshorewind capacity exceeded12GW (2). The tendency followedby the installed andoperatingcapacityisverypositive(Figure1.2).The floating wind market is very young still. It is not competitive with bottom-fixedstructures for now. A low mature technology, the long steel mooring lines and theoperationalandmaintenancecostsincreasethecostsclearly,fornottotalkaboutthelargeamountofsteelcablerequiredtoconnectthestructurestothegrid.Nevertheless,countrieslikeJapanandtheUS,thathavelimitedareaswithcontinentalshelf,areexpectedtopushthemarketinthenextyears.Thismarketwillrarelybeopenuntil2020(2),butmaybeinaclosefutureithashisopportunity–theshallowwaterareainEuropeisexpectedtoreachitscapacityby2040.Furthermore,thespreadofthemarketwillmakeitmorefeasible,becausethe facilities will be shared. In the same line, the transmission networks are expected toreducetheircosts.

Figure1.2.Globalannualinstalledandoperatingcapacityforoffshorewindfarms,from2001to2015(2).

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2 Motivationandobjectivesoftheproject

Themotivation of the author is the exploration of a civil engineering disciplinewith highpotential. He never worked on the offshore engineering field and he is curious to get incontact. He considers the project a good opportunity to put in practice the knowledgegatheredalongthefouryearsofBSc–therewillbeusedconceptsfrommanybranchesofCivil Engineering. He desires to face the challenge that offshore conditions set on civilengineersandwantstogainexperienceinactualdesignprojects.Thespecialmotivationofthewriter lies in thepossibility towork ina realproject, thatwillbeprobablybuilt in thefuture.Theobjectivesoftheprojectcanbesummarisedin:

§ Gainingageneralinsightinthecurrentoffshoreengineeringmarket.§ StudyingthedifferentalternativesforFloatingOffshoreWindTurbines(FOWT).§ Understanding the differences between floating and bottom-fixed offshore wind

turbines.§ DiscoveringtheadvantagesofthenewtechnologyforFOWT’s:WindCrete.§ Studyingtheexternalactionsonthestructure.§ Designingthepre-stressingsteelofthestructure.§ Learning the construction procedures, designing the stevedoring operations, and

describingthetransportandinstallationofthestructure.§ Buildanideaontheitemsused,measurementsandprices inthecivilconstruction.

Quantificationofabudget.

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3 Locationoftheproject

ThelocationconsideredwasapositionofftheTarragonacoastattheZEFIRpilotparkzone.Therewere not toomany restrictions in terms of protected areas and the place had theadvantageof theproximityof thePortofTarragona.Furthermore, thereweresomemallsavailabletocarryoutthestevedoringoperations,incontrastwiththePortofBarcelona.ThesiteislocatedclosetothesouthdikeofTarragona(Figure3.1).ThePortofTarragonahasapproximatelyinallthespots20metersofwaterdepth.Sincethestructurethatiscarriedwillbetransportedandhorizontalandthemaximumheightinthispositionisaround5meters,problemsofexcessivedraughtwillnotturnup.Thewindconditionsareadequateforacontinuedproduction,becauseoftheuniformityandregularwindsinthearea.Ontheotherhand,thewaveswerelessdeterminingthaninotherplacesofCatalonia,suchasGulfofRoses.Consequently,itisnotexpectedthatheavyloadsregardingwavesoccur.ThedatasetincludingwaveandwindconditionsoftheareahasbeentakenfromathesisavailableatUPCommons(UPCBarcelonaTech).ThenameofthethesismentionedisEstudiicaracteritzaciódecondicionsextremes.Aplicacióal'onatgededissenydelparceòlicmarífase1delprojecteZEFIRTestStation.

Figure3.1.Theredrectanglespotsthelocationoftheproject(77).

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4 Stateoftheart

4.1 FloatingOffshoreWindTurbine(FOWT)platformstypologies

Remarkable institutions inthefield,suchastheEuropeanWindEnergyAssociation(EWEA(3)),haveclassifiedfloatingoffshoreplatformsinthreemaincategories(Figure4.2).

1. SparbuoysSparbuoysareveryslenderfloatingplatforms,withheightsofmorethan100m.Theyhavea cylindrical geometry. At the bottom of the cylinder, there is located a chamber that isfulfilled with ballast. Windcrete uses black slag, which has a specific weight of ! =25&'/)* (4). The objective of the ballast is to lower down the center of gravity of thestructure.Itwillbeassumedthatstabilityisachievedifthemetacenterislocatedatleast0.5metersabovethecenterofgravity(5).Ontheotherhand,ballastalso increases the inertia.Consequently,pitchandroll stiffnessincrease. Thus, oscillatory tilt movements created by external actions are reduced. As aresult,thelossesintheenergyproductionarereduced,sincetheyaremainlycausedbythedeviationofthebladesfromtheoriginalverticalplane.Thesefloatingstructuresaretetheredtothesoilbysteelcatenarymooringlines.Theyaretiedtosuctionpilesorembeddedanchor,thatareplacedintheseabed.Theworld's first large capacitywind turbineoperating indeepwaterswas inaugurated inSeptember 2009. It was called Hywind. It was located 10 km off Norway coast. It wassupportedbyasparbuoy.Thestructure,ownedbyStatoil,was120mtallandproduced2.3MW(6)(Figure4.1).

Figure4.1.HyWindsparbuoy,producedbyStatoil(7).

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2. TensionLegPlatforms(TLP)TLP’s are tethered by vertical mooring lines attached to the sea bottom through suctionpiles.Theverticalmooringlinestetherthestructurethoroughgroupsoftendons,locatedatevery corner of the platform. They get tensioned by the own buoyancy of the structure.Tethers have considerable axial stiffness, what mitigates the vertical motions of thestructureduetowaves,astheirelasticityisreduced.Nevertheless,thehorizontalrigidityisnot guaranteed and the horizontal motions generated by the external agents cancompromisetheresistanceofthetethers(8).TherearenorealTLPsatrealscalefunctioningnow.However,somemodelsatscalehavebeenundergone. In2008, an80-kilowatt turbinewasoperatedbyBlueHTechnologiesoftheNetherlands.Itwaslocatedat21kmoffthecoastofPuglia(Italy)inwaters113mdeep,togatherdataonwindandseaconditions(9).Itwasdecommissionedattheendofthedatacollection.

3. Bargesandsemi-submersiblestructures

Ontheonehand,bargesarebuoyancystabilizedplatformsthatuseconventionalcatenarymooringlines.Thefloatingplatformremainsinthesurface.On the other hand, the platform of semi-submersible structures is a reticulated hollowstructureformedbydifferentcolumns.Generally,thewindturbineisontopofoneofthem.It iscommonthatthereticulatedstructureformsatriangle.It isusedseawaterasballast,thatflowsinsidethehollowstructurecompensatingthemotionsofthestructure.Therearetwobenefitsderivedfromthementionedconnections.First,theymakeablethetransmissionof stressesamongst columns. Second, they facilitate themigrationofmarinewaterfromonecolumntoanotherbymeansofpipelines.Theymakepossibletheregulationofthehydrodynamicresponses.Asanoverall,bargesandsemi-submersiblestructureshaveahigh inertia inthehorizontalaxis. Consequently, they present a relative high resistance to the overturning momentgeneratedbytheexternalagents(10).As a representative example of semi-submersible platforms, the Windfloat design ismentioned. It was a real-scale prototype patented by Principle Power and installed inOctober2011offAguçadouracoast(Portugal).Thementionedwindturbinehadafinalcost24.9millioneuro(11).Anotherprototypeusingsemi-submersibleplatformistheMaineAquaVentusI(12),locatedatMaine(US). Ithas12MWcapacityand13spareMWthatcanbeusedinthefutureforgatheringdata.

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Figure4.2.TypesofFloatableOffshoreWindTurbines(FOWT)(13).

Experimental wind farms such as the Fukushima Floating Offshore Wind FarmDemonstrationProject(14)integratedifferenttypesofFOWT.Theprojectwasdividedintotwophases.Thefirst(2011-2013)consistedoftheoperationofafloatingsubstationandacompact semi-submersibleplatform (2MW).Subsequently, the secondphase (2014-2015)includedanadvancedspar(7MW)andaV-shapesemi-submersibleplatform(7MW).4.2 TheWindcreteplatform

Nowadays,theveryfewundergoneprototypesofFOWT'susesteelasmainmaterial,whatraisesnoticeablytheconstructioncosts.Withtheaimtocreateamorefeasibleproduct inthesector,agroupofresearchers fromtheDepartment of Civil and Environmental Engineering atUPC-BarcelonaTech (Barcelona,Spain)havedevelopedaconcretesparbuoybasedintheWindcreteconcept(15).InFigure4.3itisshownanexampleofWindcreteFOWT.Theprincipalcompetitors inthemarketarebottom-fixedwindturbinesandsteelFOWT’s.The basic improvements introduced by Windcrete with respect to the mentionedcompetitors are the reduction of Operational Expenditures (OPEX). Furthermore, the lifespanisincreased,whatgivesmorefeasibilitymargintotheprojects.Thesubstantialcostsoffloatingstructureslayontheplatformandthemooringsystems(especiallyforTLP).

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Figure4.3.WindcreteFOWTprototype(16).

4.2.1 ComparisonamongWindcreteFOWT’sanditsmarketcompetitors

On theonehand,Windcrete FOWT’s present several advantageswith respect to bottom-fixedstructures:

1. Foundationcosts.Bottom-fixedaredeeply foundedgenerallybydrivenmonopiles.This operation is carried out in the sea and at a certain depth, what increases itscomplexity. As a result, froma certain depth, the investment cost of bottom-fixedstructures is higher compared to the Windcrete FOWT’s, that use mooring linesconnectedtosmallsuctionpiles.

2. Maintenancecosts.Inthecaseofbottom-fixedstructures,scourprotectionmustbe

placedattheseabedwhensandysoilsarepresent.Sandsmigrateconstantlyduetowaves and currents. Therefore, a regular maintenance of this protection layer toerosionmustbe carriedout, increasing themaintenance costs. Scourprotection isnotaprobleminFOWT’s,asthepilesfloat.

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3. Market. Bottom-fixed structures are financially attractive at shallow waters. At acertaindepth,thefeasibilityoftheseprojects iscompromised.Thisfactrestricts itsmarket. The installation of bottom-fixed wind turbines is exclusive for thosecountrieswhichpresentcontinental shelf. Bycontrast,FOWT’sareaddressed toabroadermarket.Theycanbeinstalledregardlessofhavingornotcontinentalshelf.However, for the Windcrete case a certain depth must be guaranteed for theerection process of the tower. The table below (Table 4.1) summarizes thecomparisonbetweenbottom-fixedandWindcretetechnology.

BOTTOM-FIXED WINDCRETE

CAPEXdependonthedepth(heavymonopilefoundations)

CAPEXareveryhighduetomooringlinesandconnectiontothegrid(suctionpiles

andmooringlines)

HigherOPEX(scourprotection) LowerOPEX(reducedinsituinspections)

Implementationinshallowwaters Implementationindeepwaters

Table4.1.Comparisonbetweenbottom-fixedandWindcretewindturbines.

Ontheotherhand,therearesomeimprovementsintroducedbyWindcretewithrespecttosteelFOWT’s(4):

o Useofconcreteinsteadofsteel.Oil&Gasoffshoremarketrealizedoftheconcretegoodperformanceinmarineenvironmentsbackin1970s.However,itwasnotuntilsomeyearslaterthatitwasconfirmedthatconcretealsobehavesbetterthansteelin deep water extreme conditions. Based on the gathered data from offshorestructures in deep waters and the subsequent studies in the durability of theconcrete exposed to marine environments, the International Federation forStructuralConcrete(FIB)concludedinareportin1996(17):

§ The operational safety of concrete offshore platforms is completely

guaranteed.§ Theypresentanexcellentdurabilitybehavior.§ The operational expenditures (OPEX) are not expensive. The structure is

almostfreeofmaintenance.Reductionofinsituinspectionsthankstothelowpermeabilityandintegrityoftheconcrete.

§ Thelife-spanofthestructureshadbeenunderestimatedanditcanbemuchhigherthan20years(upto60years).

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After 20 years, concrete properties have been improved. In the concrete market,thereareavailablemixtureswithcompressiveresistanceofmorethan100MPa(highstrengthconcrete)andpermeabilitybelow10-12m/s(18).Also,therearetechniquesinthisfieldthatarecurrentlyunderinvestigation,suchasbacterialdegradationandpowerwashing(19).Theexplainedimprovementsleadtoanextensionofthelifespantoevenmorethan60 years. Furthermore, it is possible the reuse of the floating structure when itslifetimehasexpired.The high resistant low permeable concrete includes post-tensioned bars of steel(Y1860S7). They guarantee the resistance to tensile stresses in the tower andresistancetofatigue.

o Single member design. The sea water includes high concentrations of chlorides.

Joints between members are points of access of these ions to the structure.Chloridesgeneratecorrosionwhenenteringincontactwithsteel.Theconsequenceofcorrosionisthereductionoftheeffectivesteelsection,reducingtheresistancetodecompression and fatigue given by the pre-stressing steel. For this reason,Windcreteproposesanintegralstructuremadeofacontinuoussinglepiece,insteadofusing jointsbetweenmembers.Thismeasure reduces thechloridespenetration.Furthermore,ithasbeentestedthatjointsalsohaveabadinfluenceinthedurabilityandfatiguepropertiesoftheconcrete.

The table below (Table 4.2) summarizes the comparison between steel FOWT’s andWindcretetechnology.

STEELFOWT’S WINDCRETE

Joints(morepronenesstocorrosion) Monolithicstructureandlowpermeabilityoftheconcrete

20-yearlifespan 60-yearlifespan

HigherCAPEX(steelismoreexpensive) LowerCAPEX(concreteislessexpensive)

HigherOPEX(steelrequiresyearlyinsituinspections)

LowerOPEX(integrityoftheconcrete,lessinsituinspectionsrequired)

Table4.2.ComparisonbetweensteelFOWT’sandWindcretetechnology.

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4.2.2 Conceptualdesign

TheWindcreteconceptconsidersthefollowingaspectsforthedesignoftheFOWT’s:

§ Shapeofthestructure.Thestructureisformedbyacylindricalfloaterandaconical-shaped tower. They are matched by a conical-shaped transition member. Thedimensionsofthediameterofthecylinderwilldependonthepowerproduced.

§ Marine hydrodynamics. The most hazardous degrees of freedom in open sea for

floatingstructuresarepitching,rollingandheaving.Toguaranteestabilityandavoidresonance,thenaturalfrequencyofoscillationofthestructuremustbeoutsidetheregions1Pand3Poftherotor.Furthermore,thenaturalfrequencyofoscillationofthemovementduetoexternalactionsmustbeoutsidetheseawavesfrequency.Forthewaveperiod,itisassumedavaluebelow15seconds(20).Thus,thestructuremustbestiffenoughatpitching, rollingandheavingtoachieveperiods larger thanthepreviouslyspecified.

§ Operationofthewindturbine.Forminimizingtheenergylossesofthewindturbine,

the rotor plane must be as vertical as possible. The resistance to hydrodynamicmotionsdependsonthestiffnessoftheplatform.Thehigherthestiffness,thehigherthepitchandrollEigenperiod.Asaresult,theadjustedvalueofthestiffnessrestrictstheAnnualEnergyProduction(AEP)lossestoa1%whensubjectedtothemeanrotorthrustforce(21).ThatcorrespondstoatiltangleoftheFOWTof5°withrespecttotheverticalaxis.

4.3 Motionsofafloatingstructure

The FOWT in operation has six modes of freedom of motion: three lateral and threerotational (22). Consequently, the spar platform can respond to external forces (waves,wind,currents)insixdifferentmodes,oracombinationofthem.Ontheonehand,thethreelateralmotionsareswaying,surgingandheaving.Ontheotherhand,thethreerotationaldegreesoffreedomrespondtoyawing,pitchingandrolling.Allsixdegreesoffreedomareshowngraphicallyinthefigurebelow(Figure4.4).

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Figure4.4.HydrodynamicresponsesoftheFOWT(16).

4.4 WindCretedesignprocess

From 2014, a consortium formed by Gas Natural Fenosa, Universitat Politècnica deCatalunya and University of Stuttgart presented the AFOSP (Alternative Platform FloatingDesign) project (23). It consists of the construction in one piece of the platform and thetowerusingbasicallypost-tensionedconcrete.TheWindcretedevelopersdesigntheFOWT’susingthemethodthatisexplainedinthenextparagraphs(21)(Figure4.6):

1. ConceptselectionTheWindcrete technology works with spar floating platforms. This step is implicit in thedesignconceptused.Spar floating platforms are considered the most suitable option amongst the type ofplatforms described before for two reasons. First, they are less affected bywind, as theypresenta largerdraft.Second,theyare lesssensitiveto loadchanges,astheyhaveahighmomentofinertia,duetotheballastincludedatthebottomofthefloater.

2. HydrostaticselectionThereareestablishedrangesofvaluesforseveraldimensionsofthestructure(e.g.radius,thicknessofthestructure,heightofthestructure).UsingMatlab,alargenumberofdesignsareobtainedbycombiningdimensionsof thementioneddomainsofvalues.Asa result,astiffnessmatrixisobtainedforeachdesignofthestructure.

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Thestiffnessmatrixincludesthestiffnessofthesixdegreesoffreedomofthestructure.Tomakeafirstselection,afirstboundaryconditionisapplied.Itisimposedthatthestructurecannotachievetiltangleshigherthan5°.ThereasonispreviouslyexplainedinChapter4.2.1.Thisinclinationoftheplatformdeterminesaminimumpitchingstiffness.Finally,thedesignswhosepitchingstiffness(C55)islowerthantheminimumpitchingstiffnessarerejected.

3. NaturalfrequencyofoscillationandRAOThenextstepintheprocessisthecalculationofthenaturalfrequencyofoscillationofthestructure.Itiscomputedthankstothesetofpitchingstiffnessobtainedforeverydesigninthehydrostaticselection.Thesparplatformhashisownnatural frequencyofoscillationforeachofhis6degreesoffreedom.Ifwavespresentafrequencyclosetonaturaloscillationfrequencyoftheplatform,resonance canoccur.Whilepitchingandheavingaregenerallydampedmotions, rolling isquiteresonancesensitive.Indeepwaters,thenaturalrollandpitchperiodoftheplatformrunsfrom25to30seconds.Thecommonwaveperiod forwind-generatedwaves isbetween6and10seconds, thusapriorithesewavesdonotrepresentarealproblemofresonance.Nevertheless,thenaturalfrequencyofthewavesshouldbecheckedthoroughlywhendesigningtheFOWT,asmanyscenarioscanoccur.Theengineermustmakesurethattheprobabilityofresonanceis lowenough.Every turbine has a minimum and maximum rotor velocity, generally given in themanufacturerbrochureofthemodel.Thisspeedisgiveninrpm.Convertingit intoradiansper second, the angular velocity is obtained. The 1P-frequency of the rotor can be easilycomputed by using the mentioned angular velocity. The 3P maximum and minimumfrequencies are three times the 1P limit frequencies. As explained before, the naturaloscillationfrequencyofthestructurecannotbeinthe1Pand3Pregionsdelimited.To calculate the motions of the FOWT, Response Amplitude Factors can be used. Theresponse of the ship is calculated for many distinctive wave periods. The ResponseAmplitude Factor is defined as the ratio between the motion amplitude and the waveamplitudeforacertainfrequency.Considering all the wave frequencies that are registered in the wave spectrum (all theResponseAmplitudeFactors), it isobtaineda transfer functioncalledResponseAmplitudeOperator (RAO).Obviously, it isdifferent forevery floatingstructure,as itdependsonthegeometry. Once the RAO for a structure is obtained, the six degrees of freedom can beobtainedbymeansofthewavespectrum.Anexampleofthespectrumsofthewavesandashipisshownbelow(Figure4.5).ThecaseisanalogousforaFOWT.

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Figure4.5.Frequencyvsenergydensityspectrumofthewavesandtheverticalshipmotions(23).

InFigure4.5,resonanceoccursatT=17s.Theenergydensityoftheshipmotionreachesapeak for this value. The shipmotion is obtained bymultiplying thewave spectrum times(RAO)2. Therefore, the peak of the ship motion is not necessarily achieved for the wavespectrumpeakorthehighestvalueofRAO.The RAO analysis constitutes, then, another sieve for the design. Those models that arepronetocauseresonancearerejected.Inthisproject,RAOhasonlybeenappliedtocheckthatthedisplacementsaresmall.

4. LoadsandstabilitycheckAtthisstep,theenvironmentalloadsareappliedtothestructure.Theobjectiveofthisstageisverifying the resistanceof thecandidatedesigns.Toquantify them,a3DFiniteElementMethodModeldevelopedbyresearchersfromtheUniversitatPolitècnicadeCatalunya(24)has been implemented. Themodel considers the aerodynamic loads, the hydrostatic andhydrodynamic (Morison forces) loads, the elasticity of the structure and his mooringresponse.

5. MinimizationofmaterialcostsAfinalselectionismadeaccordingtodimensionsofthestructure.Thus,toreducethecostsofconstructionasmuchaspossible,itischosenthestructurethathasthelowestmass.

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Figure4.6.DesignprocessoftheFOWT(20).

4.5 Siteconditionsandloadcases(IEC61400–DNVOffshorewindturbines)

DetNorskeVeritas isaglobaland independentclassificationsocietydedicatedtoprovidesservicestomanyindustrialsectors.Ithasaveryimportantpresenceintheenergeticsector,including the offshore engineering division. In relation to offshore wind turbines, it hascreated a document that includes rules tomanage risks. Their documents include servicespecifications (procedural requirements), standards (technical requirements) andrecommendedpractices(guidance)(25).4.5.1 Siteconditions

Assaid inthestandard(26),siteconditionsconsistofallsite-specificconditionswhichmayinfluencethedesignofawindturbinestructurebygoverningitsloading,itscapacityorboth.Site conditions attend all the environmental conditions on the site. Meteorologicalconditionsandoceanographicconditionsplayabigroleonthem,andtheycanbemutually

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dependent.Otherattendedsiteconditionsaresoilconditions,seismicity,biologyandotherhumanactivities. Inthenextparagraphs,abriefexplanationonthevarioussiteconditionswillbemade,accordingto(26).Therewillbeoutlinedtheaspectsconsideredmorerelevantforthepresentprojectthesis.

WindclimateThere are presented twowind states: normal and extremewind conditions.Normalwindconditions are used to determine the fatigue loads and the extreme loads. Extremeconditionsare foundbyextrapolationof theprevious,according toprobabilities.TheyarefoundusingaWeibulldistribution,thatfitsadequatelythedatasetofwindspeeds.Normally it is given the 3-hours exceedance of the different return periods for windvelocities.ThereferenceinDNVstandardsarethe10-minutesofexceedanceofthedifferentreturnperiodvalues.Therefore,thewindvaluesfortherespectivereturnperiodsmustbeconvertedtothereference.On the other hand, the wind data normally provides data at 10 m height, which is thegeneral height at which themeteorological stations are located. Thus, to attend the realwindload,itmustbetransformedtothehubheightbymeansofalogarithmicprofile.Todeterminethedirectionofthewindspeed,windrosesarecreatedfordifferentrangesofwindspeed.Theyconsiderthenumberofoccurrenceforeachcase.

WaveclimateThesignificantwave(Hs)isdefinedasfourtimesthestandarddeviationoftheseaelevationprocess.Itcanalsobedefinedasthemeanofthe1/3highestwavesofthesample.Intheoffshoresector,thewaveclimateisgenerallydescribedbya2Dscatterdiagramthatestablishes the number of occurrences of each combination of significant wave Hs andspectralpeakperiodTP.Athirddimensionisaddedforwindturbinedesign,to includethewindvelocityVW.

Theextremevaluesaredefinedasthemaximumwaveheightthatoccursforacertainreturnperiod.Empiricalformulasrelatethesignificantwaveheightwiththemaximumwaveheightforacertainreturnperiod.Other aspect considered is the wind direction. It is represented by wave roses. Anotherscatter plot is created. On it there are represented the number of occurrences for eachdirection.

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CurrentThe surface and sub-surface currents are described according to any of the proposedempiricalformulae(27).Thecurrentvelocitiesarefunctionofthedepthz.WaterconditionsThere has been assumed the density, the salinity and the temperature of the seawater.AccordingtoPuertosdelEstado(28),itisalsoobtainedthebathymetryoftheareaofstudy.Moreover,thewaterlevelsmustbedetermined.Thisincludestheeffectofthetidesinthewater level, the positive and negative storm surges and the mean sea level (MSL). AschematizationofthemisshowninFigure4.7.

Furthermeteorological–oceanographicalparametersAs mentioned before, it is considered the temperature of the water, but also thetemperatureof the air. The temperatureof the emplacement is stable above0 along theyear.Forthisreason,icescenariosarenotconsidered.SoilInvestigationsandgeotechnicaldataItischeckedthatthesoilhasresistanceenoughtoplacethesuctionpilesthatwillholdthecatenarymooringlines.Scourprotectioncanbeincludedinthefoundations.

Figure 4.7.Water levels to be determined. HSWL: Highest SeaWaterLevel; HAT: Highest Astronomical Tide; MSL: Mean Sea Level; LAT:LowestAstronomicalTide; CD: ChartDatum;LSWL:LowestSeaWaterLevel. HSWL and LSWL include a positive and negative storm surge,respectively(70).

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4.5.2 Loadcases

TheloadcaseconsideredisspecifiedinDNVGL-ST-0437(29).Thedesignsituationisinpowerproduction (it is the case 1.6 of the standard). It is considered power production inwindspeedatrated,whatmeansthattherotorisinmaximumproductionand,consequently,theforce inthehub isalsomaximum. It is importanttonoticethat incasetheforce ishigherthanthedesigned,thestructurepitchestoavoidtheburningoftheengine.Thisloadcasehasseveralfeatures:

§ TheNormalTurbulenceModelisconsidered(NTM).Thismodelincludestheincreaseoftheroughnessoftheseasurfacewiththewindspeed.Thevelocityoftheairinthehubisbetweenthevelocityofthewindenteringthebladesandthevelocityofthewindflowingout.

§ It is consideredSevereSeaState (SSS). It isdefinedbya significantwaveheight, a

peak period and a wave direction. The wind velocity also plays his role. ThesignificantwaveforSSS,Hs,sss, isdefinedbyextrapolationoftheavailablesitedata.ThemagnitudeofthewaveissuchthattheresultantloadofthecombinationofHs,sssand the 10-min wind speed at the hub Vhub generates a wave of 50-year returnperiod.Agoodestimation forHs,sss is thesignificantwaveheight for50-year returnperiodHs,50-yr.

§ Thewindcanblowco-directionally(COD)oruni-directionally(UNI).

§ It is followed the Normal Current Model (NCM). This model combines wind

generatedcurrentsandtidalcurrents.Tidalcurrentsaretakenasthemeanoftidalcurrentspeeds.Itdoesnotincludestorm-generatedandsubsurfacecurrents.

Accordingtothesecharacteristicsandforthisscenario,thedimensionsofthestructurearecomputed.4.6 HighPerformanceConcrete

ToconstructtheFOWT’s,theWindcretetechnologyusesHighPerformanceConcrete(HPC).This typeof concrete ismadeof carefully selectedhigh-quality ingredients andoptimizedmixture design; these are batched, mixed, placed, compacted and cured to the highestindustrystandards(30).Theprocessingoftheconcreteanditscomponentswilldependontherequirementsofthefinalproduct.WindcreteFOWT’saredesignedforextremeenvironmentalconditions.Thus,itisdesiredtouse thematerial thatguaranteesbetteroutputs.For this reason, it isusedHPC insteadofnormalconcrete.Inthenextparagraphs,thefeaturesoftheHPCthatapplytoFOWT’swillbeexplained,accordingto(30).

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Whilefornormalconcretethecompressivestrengthat28daysgenerallyrunsfrom28to35MPa, the design strength for High Strength Concrete (HSC) reaches at least 70 MPa.Furthermore, improved performance can be achieved by slowing down the constructionprocess.Inthiscase,aslowerprocessofhydrationleadstoabettercuring.InthetablebelowthereareshowntheprincipalpropertiesofthetypicalHPCmixturesusedforstructures(Table4.3).

Table4.3.MixtureproportionsandpropertiesofcommerciallyavailableHigh-StrengthConcrete(36).

TheconcretemixusedforHSCpresentsahighstiffnessandareducedslump.Thematerialisconsolidated by prolonged vibration or shock methods. It is common the use ofsuperplasticizerstoimprovetheworkabilityoftheHSC.

§ Cementandadditives.HSCpresentsalowwatertocementratio(0.2-0.4).Thelowerthew-cratio,thehigherthedesignresistance.Nevertheless,problemsofworkabilitymightappearforveryloww-cratios.To achieve high levels of concrete durability and resistance, supplementarycementingmaterialsmustbeadded.Thesematerialsare,forinstance,flyashes,silica

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fume or slags. The optimal dosage should be found by carrying out trial batches.Generally, the dosage rate is between 5% and 20% by mass of cement mix. Theoptimalquantityofcementingmaterialisdeterminedbalancingresistance,durabilityandvolumestability.AttheendofthischapterthereareshownthematerialsusedinHigh-StrengthConcrete(Table4.4).

§ Aggregates.Experimentaldatahasshownthatcrashed-stonesaggregatespresenta

highercompressionstrengthresistancethangravelaggregate,giventhesamesizeofaggregate and the same cementing material content. On the other hand, manystudieshavedeterminedthattheoptimumstrengthisachievedfor9.5mmto12.5mmnominalmaximum-sizeaggregates.

Furthermore, cleanness in coarse aggregates is fundamental for reducing the w-cratio.Fines (dustandclay)mustbeavoidedas they increase thewaterneeded fortheconcretemix(theyhaveaveryhighspecificsurface).Itisalsoimportanttohaveawell-gradedaggregate,sincethevariabilityinstrengthsalongthemixturewouldbelower.

§ Placing,consolidation,curingandqualitycontrol.Incasetheprocessofdeliveryand

placingistooslow,batchsizesmustbereduced.Itshouldbeavoidedtheadditionofwaterduetohighwaitingtimes.Workabilitymustonlybeimprovedbytheadditionofasuperplasticizer.

Once the concrete is placed in the slip-form, it is vibrated. The vibrationmust becontrolled.Otherwise,segregationorlossofentrainedaircanhappen.Theentrainedairchambersprovideadditionalspacetorelieveinternalpressureprovokedbywater.

The finishingoperationsmustbe reducedasmuchaspossible,asgreatpartof theconcretegetssticktothefinishingmachinery.Subsequently,thecuringprocessmustbe developed under adequate temperature conditions during a prolonged period.Fogcuringandevaporationretardersaresuitabletoavoidcrackingduetoshrinkageandcrusting.

To control the quality of thematerial, periodic testingmust be done to check theuniformityoftheconcrete.Toavoidinaccuracies,thestiffnessofthequalitycontrolmachinerymustbeveryhigh.Theparametertakentocontroltheconcretestrengthisusuallythecoefficientofvariation.

§ Permeability,diffusion, carbonationandtemperature.While thepermeabilityofa

conventionalconcreterunsaround10-10m/s, thepermeabilityofHSCcanbe lowerthan10-13m/s.Thus,itisfarbetterprotectedtothepenetrationofchlorides,waterandair.Thelowpermeabilityalsoensuresalowrateofcarbonation.Furthermore,incaseaggressiveionssucceedinenteringthestructure,theirspreadwillbelow.Thisisduetotheloww-cratio,thatreducedthediffusivebehavior.

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Hightemperaturesintheconcretemustbeavoided.Averyfasthydrationcanleadtomicroandmacro-cracking in the concrete.Applying iceor chilledwater to themixcanbeasolutiontohightemperatures.Analternativetothatisthereductionofthecementcontent.

§ Chemicalattackandalkali-silica reactivity.Thehighdensity, the loww-c ratioand

thelowpermeabilityprotecttheconcretefromexternalchemicalagents.

Alkali-silica reaction can be mitigated by reducing the relative humidity of theconcrete, this is, the w-c ratio. The alternative solution is the application of greatamountsofsupplementarycementingmaterials.

As it can be seen, there are some properties that cannot be achieved at maximumperformance simultaneously. In these cases, a trade-off must be made according to theproperties desired. In Table 4.4, the contribution and properties of a list of materials isexposed.

Table4.4.MaterialsusedinHigh-StrengthConcrete(36).

4.7 Pre-stressingsteel

Thepre-stressingofconcretestructureisatechniqueusedtotransmitthestressesfrompre-stressing steel members to the concrete structure. The objective of the pre-stressingtechniqueistheimprovementofthetensilebehaviouroftheconcrete.Thetensilestressesin the steel members are transmitted by bound to the concrete, compressing it. Thisadditionalcompressionincreasesthemarginoftheconcretetoresisttensions.

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4.7.1 Typesofpre-stressingsteel

Thepre-stressingsteelcanhavedifferentforms(31):

1. BarsTheyhaveadiameterfrom15to50mm.ThesteeltyperangesfromY1030HtoY1230.Thenumber indicates the nominal tensile strength in N/mm2. The last letter, refers to themanufacturing process. In this case, H means hot rolled. The bars can be subjected tosubsequentprocessing toacquire thedesiredproperties (e.g. tempering,coldstretching).Thebarscanbeplain(P)orribbed(R)(Figure4.8).

Figure4.8.Ribbed(left)andplain(right)steelpre-stressingbars

Ribbedbarscanbecutandanchoredatanypositionorextendedbycoupling.Furthermore,theypresentbetterbondbehaviorthanplainbars.Dependingontheprocessing,theYoungmoduluswilldiffer.

o For only rolled bars, or rolled stretched and tempered bars the Youngmodulusis205GPa.

o ForrolledstretchedbarstheYoungmodulusisaround165GPa.Inthetablebelow,thepropertiesofpre-stressingbarsareshownaccordingtoEN10138-4(Table4.5).

Table4.5.Propertiesofstressingbars(EN10138-4).

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2. WiresThediameterofthewiresrunsfrom3to10mm.TheyrangefromY1570CtoY1860C.TheletterCreferstocold-drawn.Moreover,theyareheat-treated.Theycanalsoberibbedandplain.TheYoungmodulusisabout205GPa.ThetypesofwiresareshowninFigure4.9.

Figure4.9.Ribbedandplainpre-stressingwires.

ThepropertiesofthewiresspecifiedinEN10138-2are(Table4.6):

Table4.6.Propertiesofcolddeformedpre-stressingwires(EN10138-2).

3. Strands

Strandsaresteelmembersformedbywrappedwires.ThesteeltyperangesfromY1670toY2160.Thenumberofwiresperstrandisspecifiedinthecodeused.Forinstance,thesteelY1860S7 uses 7wires per strand that have a tensile strength of 1860N/mm2. The Youngmodulusofthestrandsis195GPa.

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Thereareconsideredstrandsof3or7wires(Figure4.10).Thediameterofthewiresrangesfrom2to5mm.Thecentralwiremusthaveadiameter,atleast,2%greaterthantheouterwires.Thelaylengthisbetween14and18timesthenominalstranddiameter.

Figure4.10.Sevenwirestrand.

Thepropertiesofthestrandsarepresented,accordingtoEN10138-3(Table4.7).

Table4.7.Propertiesof3and7wirepre-stressingstrands(EN10138-3).

4.7.2 Stress-strainrelationship

In the figurebelow (Figure4.11), it is shown the strain-stress relationshipofpre-stressingandreinforcingsteelobtainedexperimentally.TocalculatethebendingmomentresistanceinULS,aschematizationoftheexperimentalstrain-stressrelationshiphasbeencarriedout(Figure4.12).

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Figure4.11.Strain-stressrelationshipsofreinforcingconcreteandpre-stressingconcrete.

Figure4.12.Schematizationofthestrain-stressrelationshipforpre-stressingsteel(EN1992-1-1).Safety factors are applied to the idealized curved to determine the design strains andstresses.Theparametersoftheidealizedgraphare:./0:(maximum)characteristicyieldstressofthepre-stressingsteel./1.30: stress at the pre-stressing steel that, after unloading, causes a permanentdeformationof0.1%./4:designyieldstressofthepre-stressingsteel!5:pre-stressingsteelsafetyfactor(= 1.1)784:designultimatelimitstrainofthepre-stressingsteel780:characteristicultimatelimitstrainofthepre-stressingsteel

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In this project, it is used the design branch in which the stress remains constant afteryieldingofthesteel(after./4 isreached).ThesteelY1860S7isbroadlyusedforpre-stressedconcrete.Thediameterofthestrandscanbe13mmor15.2mmdependingonthetype,andtherespectiveareasare100mm2and140mm2,respectively.AccordingtoEHE-08,theinitialstressforsteelY1860S7is:

9/:1 = min 0.75./0, 0.85./1.30 = min 1395,1423 = 1395'/))Dandthemaximumstressduringstressing:

9/,:EF = min 0.8./0, 0.9./1.30 = min 1488,1507 = 1488'/))D4.7.3 Post-tensionedsteel

Therearemainlytwomethodstopre-stresstheconcrete:

§ Useofpre-tensionedsteel.Theconcreteiscastaroundtensionedtendonsofhigh-qualitysteel.

§ Use of post-tensioned steel. The steel is tensioned once after the concrete has

hardened.

For this project, it has been used post-tensioned steel, as the stressing of the tendons isdoneinsitu.Nevertheless,theywillrequireanchoragesthatincreasethematerialcosts.Thepost-tensionedsteelcanalsobedividedintotwotypes(31):

§ Post-tensioningwithbondedtendonsSpecial profiled ducts are installed in the mold before the concrete is cast. Tendons areinstalledintheductsbeforeoraftercastingoftheconcrete.Aftercastingandhardeningoftheconcrete,theendfacesoftheconcreteelementareusedassupportsforthejacksandanchoragesareusedtostressthetendons.Sincethetendonsareplacedinducts,theycandeformrelativetotheconcrete.Aftertensioning,thetendonsareanchored.Thepre-stressingforceisnowtransferredfromtheanchorageplatestotheconcrete.Theducts(orsheaths)aretheninjectedwithaspecialgrout. The grout bonds the tendons to the duct, enabling the transfer of forces from thetendonstotheconcrete.Moreover,thetendonisprotectedagainstcorrosion.

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§ Post-tensioningwithun-bondedtendons

Tendonsarefirstcoatedwithgreaseorabituminousmaterialandthencoveredbyasmoothplastic sheeting.Thispreventscorrosionof the tendon.The tendon is thenput inpositionbeforetheconcreteiscast.After the concrete has sufficient strength, the tendons are stressed to a pre-determinedforceandanchored.Becausethetendoncanslipinitssheetingandthesheeting–concreteinterface is relatively smooth, there ishardlyany force transferbybond fromconcrete tosteel(Figure4.13).

Figure4.13.Exampleofapre-stressedconcretebeam(31).

4.8 Steelducts

Before the casting of the concrete, steel ducts – also called sheaths – are put in theformwork.Thetendonswillbeintroducedonthemoncetheconcretehasbeencastedandhardened.Then,thegroutisspilledintothesheaths,fulfillingthefreespace.4.8.1 Grouting

To ensure the protection of the active reinforcement against corrosion, the sheaths arefulfilled using a grouting product. In this case, it is used adherent grouting. Thematerialsthat compound the grouting cannot include substances that could compromise theresistance of the steel, such as corrosive substances. The grouting material presents thefollowingfeatures:

o ItwillbeusedcementCEMI.o Thewaterusedcannotcontainneithermorethan300mg/lofchloridesnor200mg/l

ofsulphates.o Theaggregateusedwillcontainsiliceousandcalcareousgrains,thatneithercontain

acidionsnorlaminatedparticles(e.g.micaorslate).o Theadditivescannotcontaindangeroussubstances,speciallynitrates,sulphides,and

nitrates.Theircontentmustbelimitedto0.1%,thechloridesarelimitedto1g/lofliquidadditive,thepHmustbeintherangedefinedbythemanufacturerandthedryextractmustbe±5%theonedefinedbythemanufacturer.

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Thegroutingmustsatisfy:

o Limitationofthechloridesto0.1%ofthemassofcement.o Limitationofthesulphatesto3.5%ofthemassofcement.o Limitationofthesulphidestothe0.01%ofthemassofcemento Thefluiditymustbeunder25secondsatanytime.Itmustbecalculatedwiththe100

mm diameter cone of Marsh, at the range of temperatures specified by themanufacturer.

o Themaximumwaterexudedafter3hoursmustbelowerthan2%inthetestofthetubeofexudation,attherangeoftemperaturesspecifiedbythemanufacturer.

o Reductionofvolumelowerthan1%andvolumetricexpansionunder5%.o Relationwater/cementequalorunder0.44.o Compressiveresistancehigherthan30N/mm2at28days.o Thecuringoftheconcretecannotstartbefore3hoursattherangeoftemperatures

specifiedbythemanufacturer.Thecuringcannotexceedthe24hours.o Thecapillaryabsorptionat28daysmustbelowerthan1g/cm2.

4.8.2 Injectionprogram

The planning of the procedure followed to introduce the grouting in the sheaths mustincludethefollowingpoints:

o Features of the grouting material, including the time of using and the time ofhardening.

o Featuresoftheinjectionequipment,suchaspressuresandinjectionspeed.o Cleaninglaboursofthetubes.o Sequenceofthe injectionoperationsandtheteststhatmustbecarriedoutonthe

freshgrouting(fluidity,segregation,etc).o Productionoftesttubes(exudation,retraction,resistance,etc).o Volumeofgroutingthatmustbeprepared.o Performance plan in case of incidents, like during the injection, or adverse

environmentalconditions(lowtemperatures).

4.9 Anchoragesystem

Anchorsareusedtofastentheendsofthepre-stressedtendons.Theymustbecapableoftransmittingtheloadintroducedbythetendonstotheconcrete.InFigure4.14,thepartsoftheanchoringsystemareshown.

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Figure4.14.Partsoftheanchor(32).

4.10 Pre-stressingreinforcementdesign

The FOWT structure is formed by three parts: a cylinder as a floater – that includes asemispherichollowtapatthebottomtoclosethestructure–,atransitionpartthatconsistsofatruncatedconeandatoweralsoconsistingofatruncatedcone.Onthetopof it, it isplacedthesteelturbineequipment,consistingofthenacelleandtheblades.TheFOWT is fullypre-stressed– tensile stressesarenot allowed tooccur in the concreteunderServiceability Limit State (SLS) loadand thecompressive forcesare limited toavoidfatigue failure (this feature is discussed in Chapter 5). Additionally, it is assumed that thestructurewillremainun-crackedforSLSloads.Theexternal loadsacton the structure,generating internal stresses.Togain resistance tothe bendingmoment, the concrete structure is pre-stressedwith longitudinal tendons ofsteel.Thesewill transfercompressionstresses to theconcrete, increasing its resistance totensilestresses.Inthiscase,therehavebeenusedpost-tensionedstraightsteeltendons,sothe steel and the concrete act together in resisting forces once the grout injected in theductsishardened.Thepre-stressingprocesswillbeexplainedinChapter6.Once thedimensionsof the structure aredetermined and the loadson it are known, thediagramofstresses isobtained.Theenvelopofstressesshowsthemostcritical sectionofthestructure,whichwillbethereferencefortheprototypepre-stressingsteeldesign.Thetwomorecriticalsituationsintermsofsolicitationare:

1. Liftingof thestructurebycranes.Thestructure is liftedby twocranesandmovedfromthemalltotheseawater.

2. FOWTinoperationatSeaSevereState.Thestructureissubjectedtoexternalloads.

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It has been already done a previous analysis of the transport operation and it has beendeliveredthatthecaseisnotascriticalasthetwo-exposedabove.In the figure below (Figure 4.15) it is shown a general case of pre-stressed statisticallydeterminatestructure inhorizontalposition. It isalwaystriedtosimplifytheproblemtoabeamcase.Thiswouldbethesamecasethanforthefirstcriticalsituationexposedabove.Todotheanalysisofstresses, the fictitioustendonmethod isapplied.All thetendonsarereduced toone tendon, thatpasses through thecenterofgravityof the tendonsofeverysection.Thepre-stressingforceintroducedbythesteeltendonsgenerateaxialcompressivestressesand in case there is an eccentricity, they also induce stresses via bending moment. Thedirectionofthesestressesdependsonthepositionoftheexternalforcewithrespecttothecentroidal axis – it is considered the center of gravity of the section of study. Sometimescurved tendons are introduced, what generate also a drape. This drape includes anadditionalbendingmoment,translatedinmorestresses.

Figure4.15.Stressesatthemid-spanofageneralcaseofapre-stressedconcretestructure(28).

However, in the current case of study only straight tendons are used – it would not bepossibletoplacecurvedtendons inthisstructure,forgeometricalreasons.Thus,nodrapeappears.Furthermore,thelongitudinalpost-tensionedsteelisuniformlydistributedineverycircular cross section, yet it will be reduced with the reduction of radius of the cross-sections. Consequently, the fictitious tendon coincides with the centroidal axis in everysection of the structure, avoiding eccentricities. As a result, the pre-stressing steel onlyinducesaxialstressesofcompression.Thepre-stressingforcethatisintroducedatthebeginningoftheprocessdecreasesduetodirect losses (friction, wedge set and elastic losses) and due to time-dependent losses(creep, shrinkage and relaxation of the concrete). For this reason, the initial pre-stressingforcemustbehigherifthisinitialincreasedoesnotgeneratetensilestressesonanysection.

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4.11 TransportationofthestructureCommonly, structures in offshore engineering are transported by heavy lifting vessels.Nevertheless, this kind of boats are very expensive. With the aim of reducing costs,WindCrete suggests transportation of the structure to the final location bymeans of tugboats.Inthetablebelowacomparisonbetweenbothmethodsoftransportisshown(Table4.8):

METHOD ADVANTAGES DISADVANTAGES

Heavyliftingvessels

Fast and economic forlongdistancesPossibilityofchanging therouteThe structure is notdamagedinthetransport

Not feasible for shortdistancesInfluence of the center ofgravityoftheload

Tugboattowing Feasible for shortdistances

It can cause problems ofloadstabilityandfloatationPossible damage of thestructure

Table4.8.Comparisonbetweenthetransportationmethodstocarrythestructuretothefinallocation(33).

4.12 Budget:previousconceptsToevaluatethecostofaproject,itisdevelopedabudget.Themannertodiscouralongthisitemwill be according to the Ley de Contratos del Sector Público (LCSP) (33). This is theSpanish legislationthatregulatesthemannertoproceed intheelaborationofbudgets forpublicworks.Note that the initialsused to refer to somebudget concepts in this chaptercorrespondtotherespectiveSpanishterms.First, the Direct Costs (CD) are computed. They include items such as the materials, themachinery,thelabor,thefacilitiesandthesubcontracts.Theyresultfromtwodocuments–themeasurementsandthefeeschedules.

§ Measurements.Thisdocumentincludesalltheitemsusedintheconstruction.Theyalso include lump sums, this is, itemswhose payment ismade at once. There arespecifiedthequantitiesandtheunitsofeachitem.

§ Feeschedules.Thefeeschedule1includestheunitcostofeachitemspecifiedinthe

measurements.The feeschedule2 isabreakdownof the feeschedule1. It isonlyusedwhen theremustbepaid incompleteworks,becauseof rescissionoranotherreason. It helps to determine the quantities thatmust be paid to the determinedpartsifitwerethecase.

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TheCDareobtainedbymultiplying themeasurementofeach itemby the respectiveunitcost.

HI = JKLMNOK)KPQR · TPUQVOUWKRR

Atthispoint,therearenewcoststhatmustbeaddedtoarriveatthefinalbudget:

§ SiteOverhead(CI).Itincludesalltheexpensesthatarerequiredfortheexecutionofthecivilworkbutthatarenotgatheredinthedirectcosts(CD),sincetheycannotbeassigned clearly to a specific item. In this type of costs are included the non-permanentfacilities,andtheadministrationstaff,astheyarenottakingpart inthefinal construction. In Spain, the sum of CD and CI is known asMaterial ExecutionBudget(PEM).

XYJ = HI + H[

§ HomeOverhead(CG).Itincludesalltheexpensesoftheconstructioncompanythat

cannotbeassignedtoaspecificwork.Asanexample,itincludestheexpensesofthedifferentdepartments,likethestaffandthebuildings.

§ Industrial Benefit (BI). It is the expected benefit of the contractor. He expects to

obtainanincomefromtheworkdone.AccordingtotheLeydeContratosdelSectorPúblico(LCSP)(33),thepercentagesfortheSiteOverhead(CI),theHomeOverhead(CG)andtheIndustrialBenefit(BI)mustbedeterminedbeforehand.Usually,inSpain,thevalueofthispercentagesisgenerally:

§ H[ = 3%HI§ H] = 13%XYJ§ ^[ = 6%XYJ

However,itseemsthatinrecenttimestheCIhaveincreasednoticeably.Somesourcesstatethat theCI is nowadays between the 5%and the 12%of the PEM. For this reason, to beconservative in theestimationof thebudget itwillbe takenan8% (34).Asanote, in theSpanishcivilengineeringfieldthesumofCGandBI ispopularlyknownasStructureCosts.On theotherhand, it is important to remark that theCI percentage is applied to theCD.Thus,beforeincludingtaxes,thecostis:

H`MQabcdebfEFb5 = HI + H[ + H] + ^[Finally, the taxesareapplied toarriveat the finalbudgetof theproject. In Spain, the taximposedistheIVA,andconstitutesa18%ofthecostbeforetaxes.Thus:

Hghgij = HI + H[ + H] + ^[ + [kl

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5 Analysis of the Serviceability Limit State (SLS) and the Ultimate

LimitState(ULS)ofthestructure

5.1 ServiceabilityLimitState(SLS)

Theconcretestructure issubjectedtostressesconstantlyrightafter itsconstruction.First,duringthestevedoringoperations,thestructureisliftedbycranesandputinthesea.Duringthe lifting,stressesareproducedduetothetensionforceofthecables.This isconsideredone of the two critical situations. The position fromwhich the cranes lift the structure iscalculatedindetailinChapter6.Sincetheoperationlastsforashorttime,itischeckedthatat time t=0 no tensile stresses are produced in any section of the structure and thecompressionsarelimited.The other attended situation to determine the design is the operational state of thestructureatopensea.Itissubjectedtothecyclicloadsofwavesandwind,thatcanproducetensile stresses and fatigue. The design must resist them. Excessive tensile stresses orexcessive compressions canoriginate transversal cracks – in the case of tensile stresses –and longitudinalmicro-cracksand reductionof the fatigue resistance– in thecaseofhighcompressions.Theobjectiveof theanalysiscarriedoutbelow is toobtaina rangeofpre-stressing forcesthatsatisfythefourconditionsimposed,explainedbelow.Thereareobtainedfourforces–onefromeachcondition.Twoforcesareupperboundsandtheothertwoarelowerbounds.Themaximumofthetwolowerboundsistheactuallowerbound,sinceitismorerestrictivethantheotherone.Inthecaseoftheupperbounds,theminimumofthetwoupperboundsobtainedistheactualupperboundofthepre-stressingforce.5.1.1 Dataprovidedandcalculationofthedesignpre-stressingforce

Thebendingmomentstowhichthestructureissubjectedhavebeenobtainedbymeansofanumerical model based on the Finite Element Method (FEM) (24), developed at UPCBarcelona-Tech.Thedatacollectedhasbeencheckedthroughscaledtestsonthestructureinaflume,toobtainthehydrodynamiccoefficients.TheaerodynamicforcesareobtainedbymeansoftheindependentsoftwareFASTcoupledtothecode.Themooringlineforcesarealsocomputeddynamically.Thedataset includes the internal forces acting along the structure, that is divided into72sections.Thevalueofthemomenthasbeenobtainedfirstcalculatingthenormofthetwogivencomponentsof it (componentsyyandzz) for thepositiveand thenegativemomentdistribution,andthentakingthemaximumofthetwomomentsobtainedforeachsection.Thelongitudinalaxisofthestructureisthex-axis.Thedistributionofbendingmomentsalongthestructureduetowindandwavesaction isshown(Figure5.1):

41

Figure5.1.Diagramofbendingmomentsofthestructure,duetoactionofwindandwaves

ThedesignoftheFOWTiscarriedoutaccordingtotheEHE-08(Spanishcodeforconcretestructures)(35).ThewindturbineusedisthemodelnED100fromNorvento(36).Themodelestablishesthehubheightat24.5,26or29.5meters–ithasbeenchosenahubheightof24.5meters.Thus, if thedistancefromthehubtothetopof theconcretestructure is0.6meters,theheightoftheconcretetoweroftheFOWTis23.9meters.Inafirstestimationofthedesign,therestofthedimensionsofthestructurehavebeenassumed(Figure5.2).Theheightof the floater seizes33.75metersand the transitionpiece7meters, constitutingatotaldraftof40.75meters.Theexternalradiusofthefloateris2.43metersandtheexternalradiusatthetopsectionofthetransitionpieceis1.2meters.Theexternalradiusatthetopofthetoweris0.424meters.Thesemi-sphericaltapatthebottomissolid.At the beginning of the design, the floater and transition piece wall thickness were 0.3meters, while the initial tower wall thickness was 0.2 meters. Nevertheless, the finalthicknessof thewhole structurewall resulted in0.272meters, since the geometryof thedesignhadtobeadjustedtosatisfytheboundaryconditionsandthestandards–theyarespecifiedsomeparagraphsbelow.Theexceptioninthisthicknessisastretchthatrunsfromthe bottom of the tower to a section located 11.42 meters above. This stretch has anincreasing thickness. The reason of this additional thickness is the creation of space toanchor some tendons that finish at this section. This aspect will be explained in Chapter5.1.2.

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

8000000

9000000

10000000

1 3 5 7 9 11131517192123252729313335373941434547495153555759616365676971

Bend

ingmom

ent[Nm]

x[m]

BendingMoments[Nm]

42

Figure5.2.MaindimensionsoftheFOWT.

43

Thetypeofsteelusedis,asmentionedinChapter4.6,theY1860S7.Regardingtheconcrete,initially it was taken a 70 MPa-compression-resistant. This value has been adjustedeventually to satisfy the conditions imposedby the standards.The final.m0 resulted in95MPa,thusitisnecessarytheuseofHigh-PerformanceConcrete(HPC)(Chapter4.6).IthasbeenpreparedacodeinMatlabfortheimplementationofthedatamentioned(seeAppendix10.1).AccordingtotheEHE-08,thesafetyfactorstoapplyare(Table5.1):

ServiceabilityLimitState(SLS) UltimateLimitState(ULS)

Favourableeffect Unfavourableeffect

Favourableeffect

Unfavourableeffect

Permanentactions !n,c,ojo = 1.0 !n,8pc,ojo = 1.0 !n,c,qjo = 1.0 !n,8pc,qjo = 1.35Pre-stressingforce !r,c,ojo = 0.9 !r,8pc,ojo = 1.1 !r,c,qjo = 1.0 !r,8pc,qjo = 1.0

Table5.1.SafetyfactorsimposedbytheEHE-08

Apartfromthesafetyfactorsexposed,thevariablesconsideredinthecalculationsare:9[JXL]:stressinthestructure.9 > 0istension,while9 < 0iscompression.X1[']:pre-stressingsteelforce' ' :axialforceonthestructureJ[')]:bendingmomentlm[)D]:areaoftheconcretesectionx[)*]:sectionmodulusEveryoneof thesevariables takeavalue foreachsection.Thesestructureswill remain inoperationforalongtime.As said above, it is considered that the compressive stresses are negative and the tensilestresses,positive.Theexternalactionsthatinfluencethestressesonthestructureare:

§ Pre-stressing force (yz). Thepre-stressing steel introduces compressive stresses inthe structure in all the cases. Then the sign of this force is negative for all thescenarios.

§ Axialforce({).Duetotheself-weightofthestructure,anaxialforceisactinginthestructure. Italso introducescompressivestresses inall thecases.Consequently, itssignisalwaysalsonegative.

§ Bendingmoment(|).Theactionsonthestructureduetowindandwaves,andthe

tensionforceofthemooringlinesgeneratebendingmoments.Sincethedirectionsinwhichtheyareactingarerandom,it isconsideredthesignofthebendingmomentthatcouldcompromiseinagreatermannerthelimitsinthestressesimposed.Thus,thesigncanbepositiveornegative.

44

Thecheckofthestressesatshortandlongtermexposedbelowisappliedtoallthesectionsofthestructure:

1. } = zThe tensileandcompressivestressesmustbecontrolled.For this reason, themostunfavourable situation is studied. The safety factors are applied according to thefavourableorunfavourablenatureoftheexternalaction.In this case, the most unfavourable situation occurs when the external bendingmoment creates tensile stresses, that must be compensated by the compressionsinduced by the pre-stressing force and the axial force. This situation is studied toensure resistance to fatigue, which is notoriously reduced when the structure issubjectedtoexcessivecompressions.

9 = −!r,c,ojoX1

lm−!n,c,ojo'

lm+!n,8pc,ojoJ

x≤ 0

Thenextcondition imposesthatthecompressionsmustbe limited.Theworstcaseoccurs when the bending creates compression stresses in the section, as the pre-stressing and the axial force do. It is established a limit on compressions becausethese structures are subjected to cyclic loads,what can end in fatigue failure. Thestandardestablishesthatthecompressionstressescannotexceed0.6.m0.However,sincethesestructuresaresubjectedtolargecyclicloadsithasbeenputthelimiton0.45.m0tobemoreconservative.

9 = −!r,8pc,ojoX1

lm−!n,8pc,ojo'

lm−!n,8pc,ojoJ

x≥ −0.45.m0

2. } → ∞Forlongtermstates,therearealsotwoconditionstoimpose.Theyareanalogoustothementionedabove.Itisassumedthattimedependentlossesascendto18%.

9 = −!r,c,ojoXÉ

lm−!n,c,ojo'

lm+!n,8pc,ojoJ

x=

= −0.82!r,c,ojoX1

lm−!n,c,ojo'

lm+!n,8pc,ojoJ

x≤ 0

9 = −!r,8pc,ojoXÉ

lm−!n,8pc,ojo'

lm−!n,8pc,ojoJ

x=

45

= −0.82!r,8pc,ojoX1

lm−!n,8pc,ojo'

lm−!n,8pc,ojoJ

x≥ −0.45.m0

Derivingtheseequations,itisobtained:

X1 ≥

!n,8pc,ojoJlmx − !n,c,ojo'

!r,c,ojo(1)

X1 ≤0.45.m0 − !n,8pc,ojo' −

!n,8pc,ojoJlmx

!r,8pc,ojo(2)

X1 ≥

!n,8pc,ojoJlmx − !n,c,ojo'

0.82!r,c,ojo(3)

X1 ≤0.45.m0 − !n,8pc,ojo' −

!n,8pc,ojoJlmx

0.82!r,8pc,ojo(4)

Theresultingvaluesare:

X1 1 ≥ 12860&'X1 2 ≤ 19842&'X1 3 ≥ 12831&'X1 4 ≤ 31314&'

Thefinaldomainofthepre-stressingforceX1takesthemorerestrictiveconditionsimposedbythe4resultsabove.

X1,ÑdÖbe = 12860&' ≤ X1 ≤ 19842&' = X1,8//be Subsequently, it is taken theminimumpre-stressing force thatmeet the requirements tocarryoutthedesignofthestructure,sinceitisthemosteconomicaloptionpossible.Then:

X1 = 12860&'Thechecksonstressesaremadeforthesectionatwhichtheminimumpre-stressingforceneeded to satisfy the conditions ismaximum.This critical section is locatedataheightof41.248meters,slightlyovertheconnectionbetweenthetransitionpieceandthetower(0.5metersupfromthesectionwherethetowerandthetransitionpartmeet).ThemaximumstressgivenbyX1totheactivereinforcementcanbe,asmentionedinEHE-08:

9/1 ≥ min 0.75./:EF,0, 0.85./0 = 1395'/))D

46

where:./:EF0 '/))D :maximumcharacteristicunitaryload(=1860'/))D).

./0 '/))D :characteristicelasticlimit(cÜáàâä

ãå= 1691'/))D,where!5 = 1.1isthesteel

safetyfactor).Then,theminimumareaofpre-stressingsteelis:

l/ ≥X19/:1

= 9219))D

Thetotalareal/isdividedintendons,formedinturn,bystrands.Thestrandsareformedby7wireseach,asthetypeofsteeluseddenotes(Y1860S7).Theareaofthestrandsis140))Deach–thediameterofthestrandsis15.2mm.First, it has been tried to use theminimum steel area required, in order to carry out themosteconomicdesignpossible.However,thereweresomesectionsthatdidnotsatisfythestress conditions previously mentioned, since the direct losses reduced the pre-stressingforceundertheminimumforcerequired.Taking theminimum area, the steel can be divided in 67.34 strands. In the firstmomentthere were considered 13 strands per tendon, resulting in 5.18 tendons – hence, it wasroundedto6tendons.However,sincethestressconditionswerenotsatisfied,thesteelareawas increased, to reduce the excessive stress in the tendons. Instead of 13 strands pertendons,therearefinallyplaced15tendonspertendon.Therefore,thetotalarearesultsin:

l/ = l/,fbp4dpPfbp4dp5 = 12600))DTheobjectiveistostressthesteelasmuchaspossible,toimprovetheresistancetotensilestresses of the concrete as much as possible. Thus, it is desired an initial steel stress of9/:1 = 1395'/))D.Duetotheincrementofsteelarea,toachievethis levelofstress itmust be increased the pre-stressing force on the steel. Then, themaximum pre-stressingforceinthesteelafterlossescanbe:

X:EF1 = 9/1l/ = 17577&'It canbechecked that thisvalueof thepre-stressing force is in thedomainof forces thatsatisfytheconditionsoncompressionandtensionabove(12860&' ≤ X:1 ≤ 19842&').Tocompensatethelosses,theinitialpre-stressingforceonthesteel(whenanchoring)mustbehigher,inordertoachievethecomputedmaximumforceafterlosses.Tocompensatethe

47

directlosses,thetendonsmustbeoverstressedwhenanchoring,untilamaximumstressof1488N/mm2.ThisaspectwillbeexplainedinChapter5.1.4.5.1.2 Designofthesheaths

Theconcreteusedforthissystemisadherent.AccordingtotheEHE-08,theconcretecoverofthestructureis:

Wpd: = W:Rp + ∆Wwhere:Wpd:[))]:nominalthicknessoftheconcretecoverW:Rp[))]:minimumthicknessoftheconcretecoverthatmustbeguaranteedinthewholestructure∆W[))]:marginoftheconcretecover,dependingofthelevelofcontrolintheexecutionThemarginoftheconcretecoverrangesfrom0to10mm,dependingonthelevelofcontrolof execution. To be on the safe side, it is considered that the margin concrete covermeasures10mm.Thejustificationliesinthefactthatthestructureisconstructedinsituandissubjectedtomarineenvironments.Therearesomerestrictionsintheminimumthicknessoftheconcretecover(Figure5.3):

• Itmustbehigherthanthemaximumofthefollowingvalues:- Theminordimensionofthesheaths- Halfofthemajordimensionofthesheathsorhalfofthemajordimensionofthe

sheathsincontact• Itcanbemaximum80mmthick.

Figure5.3.LimitationsintheconcretecoverincludedintheEHE-08.

48

According to the Table 8.2.2 from the EHE-08, the specific class of exposition relative tocorrosionoftheactivereinforcementisIIIc.Thestructureisexposedtochemicalattackduetothecontactoftheconcretewiththeseawater.Theminimumconcretecoverchosenis80mm (the maximum allowed), due to the permanent contact of the concrete with theMediterraneansaltywaters.Therefore,thenominalthicknessoftheconcretecoveris90mm.Atthispoint,theremustbefoundthesheathswherethetendonswillbelocated.AccordingtotheEHE-08,thefreedistancesamongstsheathsmustbeatleastequaltothemaximumofthefollowingvalues:Inverticaldirection:

o Thediameterofthesheath.o Theverticaldimensionofthesheathorgroupofsheaths.o 5centimeters.

Inhorizontaldirection:

o Thediameterofthesheath.o Thehorizontaldimensionofthesheath.o 4centimeters.o 1.6 times the highest dimension of the individual sheaths that form a group of

sheaths.As recommended in the catalogue VSL – Post-Tensioning Solutions (32), the externaldiameterof thesteelductsorsheaths includingtendonsofupto15strandsshouldbe92mm.Inafirstmoment,itwasconsideredtoputthe6tendonsrunningthewholestructure.Theystartedatthetopsectionofthetower,theyranuntilthebottomtapwheretheymadea180°turnandtheywentuptoarriveattheoppositesideofthestaringsection,atthetopofthetower.However, theminimumdistance conditions between ductswere not satisfied – the smallsectionatthetopofthetowerwastoobusy,with12ductsectionsonit(6tendons=12ductsections inevery transversal sectionof the structure).On topof that, theamountofpre-stressedsteelrequiredatthetopofthetowerwasfarlessthantheamountneededatthecriticalsection.Thus,thereweretechnicalandeconomicreasonstoreducetheamountofpre-stressingsteelatthetoppartofthetower.To solve this issue, the amount of pre-stressing steel has been reduced from a sectionlocated at 11.42meters up from the bottomof the tower to the top. It has beenput anadditional thickness inthe innerpartofthewall, fromthesectionofcontactbetweenthetransitionpieceandthetowerto11.42metersup.Thisadditionalthicknessgrowsinternallytowardsthelongitudinalaxisofthestructureuntilitreaches27.2cm.

49

Always attending the EHE-08, the thickness of the walls (Q) results from the sum of theinternal and external concrete covers (Wpd:,R + Wpd:,é = 2Wpd:) plus the diameter of thesheath(∅5êbEfê).Thissumresultsin:

2Wpd: + ∅5êbEfê = 2 · 90 + 92 = 272))The condition exposed above about minimum vertical distance between sheaths (ducts)does not apply in this case, since there is only one duct in this direction. Regarding theminimum horizontal distance between ducts, the governing condition is the last oneexposed–theminimumhorizontaldistancebetweensheathswillbe1.6timesthediameterofthesheath.AsitcanbeseeninFigure6.5,thehorizontaldistancebetweentwosheathsinthesectionwheresheathsarecloser,which is thetopofthetower, is288 − 2 · ëD

D= 196)) > 1.6 ·

92 = 147.2)).Thus,theconditionissatisfied.Aplanview(Figure5.4),afrontview(nextpage)andadetailofthesectionwherethepre-stressingsteelisreduced(Figure5.5)areshownbelow.Intheplanview,thedarkbluelinesrepresent the floater section, the green lines represent the top section of the transitionpiece–thisis,thebottomsectionofthetower–,theturquoisebluelinesshowthesectionatwhichthepre-stressingsteelisreducedandtheredlinesshowthetoptowersection.Inthe frontview, it is shownthepositionof thepre-stressingsteel tendons ina longitudinalsection.

Figure5.4.Planviewofthestructure.Distancesinmeters.

2.430

31.320

7.001

11.449

12.451

0.2720.6801.090

50

Figure5.5.Sectionatwhichthenumberoftendonsisreduced.

5.1.3 Anchors

Thetendonsusedhaveadiameterof15.2mm(approximately0.6inchesofdiameter).Eachtendonincludes15strands.Therefore,accordingtoVSL–Post-TensioningSolutions(32),thetypeofanchorsusedis6-15.Theanchorspresentthefollowingdimensions(32)(Figure5.6,Table5.2).

Figure5.6.Geometryoftheanchor(32).

51

Unit A B ØC ØD E F ØH J ØK L6-15 260 240 113 190 85 240 113 316 M16 145

Table5.2.Dimensionsoftheanchor(39).

Alltheanchorstakepartofasteelouterringof260mmheight,asspecifiedinTable5.2–slightlysmallerthanthewallthickness(272mm).Thissystemisusedinthesectionwherethepre-stressingsteel is reducedandat topsectionof the tower.Additionally, in this lastsectionthereareincludedtheboltedjointsthatconnectthetowerwiththewindturbine.5.1.4 Calculationofthelosses

Thereareconsideredtwotypesoflossesinthesystem:

• Direct losses. There are included in this type the friction losses, the wedge set(anchorage)lossesandtheelastic losses.Theyareproducedjustafterthesteelhasbeenpre-stressedandanchored.

• Time-dependent losses. These are the ones caused by creep, shrinkage andrelaxation. After a significant period of time since the pre-stressing steel wasanchored,theycanbecomeimportant.

Inthenextparagraphstheprocedurefollowedtocalculateeverytypeof loss isexplained.AllthecalculationsrelatedtothelosseshavebeendevelopedwithMatlab.ThecodeusedisshowninAppendix10.3.ThetablewiththeresultsbysectionscanbefoundattheAppendix10.1.1. For these calculations, it is considered that the origin of the x-axis is at the topsectionofthestructureandincreaseswhengoingdown.5.1.4.1 Directlosses

• Frictionlosses

During thepre-stressingof thesteel, lossesareproduceddue to thecontactbetweenthetendonsandthesheaths–orducts.Theselossesdependonthepositionwithrespectwhichthesteelisbeingstressedbythejacks(í),theanglerotatedfromsinceuntilthesectionofstudy (ì), a friction coefficient (î) that depends on the type of steel and the unintendedcurvaturesofthepre-stressingduct(Wobbleeffect,representedby&).Frictionlossesfollowtheexpression:

∆Xï í = X:EF,1 1 − Kñï∆óñ0F where:î = 0.18:the tendons are composed of various elements thatmeet at the same sheath,withoutsuperficialtreatment.

52

& = 0.0018)ñ3:Wobble-effectisnotaffectingthatmuchtotendons.Itmustberemarkedthattheanglerotatedfromthetowertothetransitionpieceis∆ì3 =8.1° and the angle rotated from the tower to the floater is∆ìD = ∆ì3 + 9.7 = 18.1°. Agraphshowingthelossesalongthestructureisexposedbelow(Figure5.7).

ThetableincludingthelossesduetofrictionpersectionisshowninAppendix10.1.1.

• WedgesetlossesThistypeoflossesoccursduringanchoringoperations.Ifwedgesareused,somesliphappenwhenreleasingthejack.Thisleadstoalossinthepre-stressingforce(Figure5.8).Theslipofstrandsisgenerallybetween5and15mm.

Figure5.7.Lossesdue to frictionalongthestructure.Therecanbeseenseveralchangesofslope.The firstoneoccurs atx=11.42m,sincetheamountofsteelof thesection is reduced tothehalf.Thesecondoneisproducedatthesectionoftransitionbetweenthetowerandthetransitionpiece.Thethirdonehappensatthesectionoftransitionbetweenthetransitionpieceandthefloater.Thelasttwoareverysteepbecausethereoccursuddenincrementsofangleinthesteel.

53

Figure5.8.Lossofpre-stressduetowedgeslipoftheanchoratthetensionedside(31).

Tocalculatethelosses,firstitmustbefoundtheinfluencelengthofthewedgeset.Itcanbecomputedbysolvinganimplicitequationbyiteration:

ôÖ =öl/Y/

X:EF,1 1 − Kñï∆óñ0Ñõ

Thevariablesthathavenotbeenpresentedbeforemean:ö[))]:slipofthestrands(assumed5)))Y/[

ú

::ù]:Youngmodulusofthesteel(195000 ú

::ù)ThewedgesetlossesaresubsequentlyfoundbyaderivationfromtheEHE-08expression:

∆XÖ5 = 2∆Xï ôÖ = 2X:EF,1 1 − Kñï∆óñ0Ñõ ThetableincludingthelossesduetowedgesetpersectionisshowninAppendix10.1.Theplot belowexposes the losses due towedge set in the different sections of the structure(Figure5.9):

54

• Elasticlosses

When compressed, the concrete undergoes an elastic shortening that reduces the pre-stressingforceintroducedbythecompressionofthesteel.Thelossesduetothisshorteningareexpressedby:

∆XbÑ =P − 12

l/Y/lmYm

X:EF,1

The table presenting the elastic losses per section is exposed in Appendix 10.1.1. Thefollowinggraphshowsthelossesalongthestructure(Figure5.10).

Figure5.9. The changeof tendencyof thewedge set losses is also clearly influencedby the changeofincrementofrotationangle.So,changesintendencyareobservedinthebottomofthetowerandatthebottomofthetransitionpiece.

55

Toachievethemaximumpre-stressing force in theconcrete, it is tried tocompensate thedirectlossesthatoccurinthestructure.Thisisachievedbyoverstressingthetendonsatthebeginningof theprocess.However,neither themaximumstressallowedbyEHE-08 in theconcrete nor the upper boundof the pre-stressing force can be exceeded. Themaximumstresswhenanchoringallowedinthesteelis:

9/:EF,1 = min 0.8./:EF,0, 0.9./0 = 1488'/))D

Ontheonehand,theincrementofpre-stressingforceiscalculated.Thelossesofdifferentnatureareadded:

∆X = ∆Xï + ∆XÖ5 + ∆XbÑ

Consequently,thepre-stressingforcetobeintroducedinthesteelwhenanchoringtoobtainastressof1395'/))D afterlossesshouldbe,persections:

X1,ojo = X:EF,1 + ∆X

Theforcerequiredtocompensatethedirectlossesofallthesectionsis:

Figure5.10.Lossesduetotheelasticityof theconcrete. Itcanbeseenasuddenreductionof loss inthesectionwherethesteelisreducedtothehalf.Furthermore,atthetopof thetower,theareaoftheconcretesection is smaller– thisaspect leadstohigh lossesduetotheelasticbehaviourof theconcrete.Inthefloater,thelossesareconstant,duetotheconstantsectionofsteelandconcrete.

56

X1,ojo = X:EF,1 + max ∆X = 24590&'

Nevertheless,itmustbecheckedthatthisforceisequalorlowerthantheupperboundoftherangeofpre-stressingforcespreviouslycomputedandthemaximumpre-stressingforcewhenanchoring.Thesetwoconditionsare:

X1,ojo ≤ X:1,8//be = 19842&'

X1,ojo ≤ 9/:EF,1l/ = 18748&'Thus,itcannotbeachievedthemaximumstressafterlossesof1395'/))D.Consequently,theactualpre-stressingforceappliedduringanchoringisthemorerestrictive:

X1,ojo = 9/:EF,1l/ = 18748&'that corresponds to a stress after losses introduced in the concrete – that is different ateverysection–of:

X1 = X1,ojo − ∆XThe pre-stressing force on each section of the structure after losses is presented in theAppendix 10.1.1. A plot showing the remaining pre-stressing force in each section of thestructureisshownbelow(Figure5.11).

Figure5.11.Pre-stressingforceremainingafterdirectlosses(blackline)andupperandlower limit of it foreachsection. It is important tonote that notalways thesectionthatneedsthehighestminimumpre-stressingforceafterlosses isthecriticalsection.Itcanhappenthatanothersectionthathashigherdirectlossesturnsuptobecritical.

57

5.1.4.2 Time-dependentlosses

Threetypesoflossesareconsideredtoaffectthepre-stressingatlongterm:

• CreepItistheincreaseofdeformationwithtimeunderasustainedconstantload.Concretecreepsduetothedeformationofthegelstructureandthecapillarystressofthechemicallynon-bondedwater. Itdepends in factors like thehumidityand the temperature, thedegreeofhydrationoftheconcrete,thestrengthclassoftheconcrete,thedurationoftheloadingorthedimensionsofthecrosssection(37).

• ShrinkageWhen concrete dries, concrete contracts and shortens. It is a phenomenon that occurswithout the application of any load. Factors that influence shrinkage are the relativehumidity, the strength classof the concrete, thedimensionsof the cross-section, and theageoftheconcrete.

• RelaxationIn this case, the deformation of the material remains constant, while the initial stressesdecreasewithtime.Thebehaviorofthethreephenomenaisshowninthefigurebelow(Figure5.12):

Figure5.12.Creep,shrinkageanddeformation,inthisorder,fromthetoptothebottomfigure(37).

58

TheEHE-08proposesaformulathatintegratesthethreephenomena.Thisis:

∆Xfñ4 =P† Q, Q1 9m/ + Y/7m5 Q, Q1 + 0.8∆9/e l/

1 + Pl/lm

1 +lm°/D

[m1 + ¢†(Q, Q1)

°/[))]: distance from the center of gravity of the pre-stressing steel to the centre ofgravityofthesection(itisequalto0astheycoincide)P[−]:equivalencecoefficient(

£Ü£§= 5.42)

† Q, Q1 [−]:creepcoefficient(0.9–ageoftheconcrete:28days;.m0 = 95JXL)9m/[

ú

::ù]:stressproducedbytheforceX = X1 − ∆Xï − ∆XÖ5atthecenterofgravityofthe

pre-stressingsteel7m5 Q, Q1 [−]:strainproducedbytheshrinkageoftheconcrete(assumed0.2/1000)∆9/e[

ú

::ù]:lossesproducedbyrelaxationatconstantlength(=

p(•§ÜiÜñ∆r¶ß)

iÜ)

[m[))®]:inertiaoftheconcretesection¢[−]:agecoefficient.Itisassumed0.8,accordingtoEHE-08.Consequently,thevalueofthepre-stressingforceatlongterm(Q → ∞)is,ateverysection:

XÉ = X1 − ∆Xfñ4 In Appendix 10.1.1, a table with the time-dependent losses of each section and the pre-stressingforceatlongtermXÉispresented.Graphsshowingthetime-dependentlossespersection (Figure5.13)and thecomparisonamongst thepre-stressing forcewhenanchoring(X1,ojo), the pre-stressing force after direct losses (X1) and the pre-stressing force at longterm(XÉ)(Figure5.14)areexposedbelow.

Figure5.13.Thetime-dependentlossesaresubjectedtoasweepincreasefrom

thesectionatwhichthesteelisdoubledinquantity.

59

Themaximumpre-stressingforceatlongtermoccursatthesectionlocatedat12.45metersfromthetopofthetower.Theforceatthissectionis:

max(XÉ,R) = 15376&'Theyieldingforceofthepre-stressingsteelis:

X©,/ = ./4l/ = 18341&'Sincemax(XÉ,R) ≤ X©,/,thesteelremainsinelasticbehavioratlongterm.5.2 UltimateLimitState(ULS)

TheUltimateLimitState(ULS)ofthestructureoccurswhenconcretecracks. It isassumedthatthestructurearrivesfirstatULSduetobendingmoment.Thus,itmustbecheckedthattheresistancetobendingofthestructureishigherthanthesolicitation:

J£4 ≤ J™4

Figure 5.14. Comparison of the pre-stressing force when anchoring (X1,ojo), the pre-stressingforceafterdirectlosses(X1)andthepre-stressingforceatlongterm(XÉ).

60

First,thesolicitationiscomputed.ItwillbeusedthesafetyfactorforunfavorableconditionsinULSexposedinTable5.1.

J£4,R = JR!n,8pc,qjoThereareobtaineddifferentsolicitationsforeachsection,astheyaresubjectedtodifferentactions.Thesearegiven,asmentionedinChapter5.1.1.Themomentresistance iscomputedbyequilibriumofmomentumatanarbitrarypointofthe section. It is computed for each of the 72 sections that are studied. Afterwards, it iscomparedtothesolicitationinbending,J£4.ItalsomustbecheckedthatthestrainofthesteelatULS(7/8)islowerthantheultimatestraininthesteel(780).Incasethisconditionissatisfied,whenconcretecracks(ULS)thesteelstillcanresiststressesbeforecollapsing.Thiskind of rupture helps to identify the resistance problem in the structure with someanticipationandavoidssuddencollapseofthestructure(brittlefailure).The Eurocode 2 EN 1992-1-1 (38) considers two possible branches for the strain-stressrelationship after yielding. For this case, it is considered that the stress remains constantonce theyield stressof thesteel (./4) is reached (Figure5.15).Thus, the lowerBcurve isconsidered:

Figure5.15.Simplifiedstress-strainrelationship,accordingtoEurocode2(38).

Itisrememberedthatinthisgraph784 isthestraininthesteelatULS(concretecrack)and780istheultimatestraininthesteel(780 = 0.035).Forthelowerdesignbranch,theyieldstressofthesteel(./4)andthestressofthesteelatULS(./8)havethesamevalue(./4 = 1455.7'/))D).

61

All the transversal sectionsof the structure, inexceptionof the corresponding sectionsofthe bottom tap, are circular hollow sections. Thus, for the calculation of the concretecompressive height (°) (° is required to calculate the concrete compressive force) it isneededtheparametrizationofthesection.Dependingonthecompressiveheight,theanglecomprising the compressive area variates. This leads to the variation of the area (Figure5.16).

Figure5.16.Theanglevarieswiththevariationofy.Consequently,thecompressiveareaalsochanges.

First,theangleìisexpressedas:

ìR = ìR °R = arcsinÆR − °RÆR − QR

whereÆR representstheradiusoftherespectivesectionsalongthestructure,°Rrepresentsthe compressive height for each section and QR is the thickness of the concretewalls, foreach section. Then, for each section, ìR depends on the parameter °, that is initiallyunknown.To determine the transformed length of the outer ring of the compressive area, it isconsidered the intermediate section of the outer ring. Then, the area of the compressivezoneineverysectionis:

lmd:/,m,R = lmd:/,m,R °R = 2ìR °R QR ÆR −QR2

Theresultingcompressiveforceoftheconcreteis:

'm,R = lmd:/,m,R.m4

62

where.m4 is the design resistance of the concrete in compression (.m4 =

c§äã§= 63.33'/

))D).Ontheotherhand,theforceinthesteelatULSis:

Xqjo,/ = X©,/ = 18341&'Atthispoint,itiscomputedtheequilibriumofverticalforcesinthesection:

Ø∞,R = 0 =R

Xqjo,/ + 'R − 'm,R

where'R istheaxialexternalforceateachsection(given,assaidinChapter5.1.1).By means of the implementation of the function fsolve in Matlab, it can be solved theproblem of zeros of functions coming from the equilibrium of vertical forces, for eachsection.Thecompressiveheights°foreachsectionare,then,obtained.Oncethecompressiveheightofeachsectionisknown,itcanbecomputedtheresistancetobendingofeachsection.Todothat,itisconsideredanarbitrarypointateverysectionanditismadethesumofmomentumsatthementionedpoint.Inthiscase,ithasbeentakenthepointatwhich'm,R isapplied.Thecenterofgravityoftheouterringisobtainedtofindthepointofapplicationof'm,R.Theouterringgeneratedbythecompressiveheightcanbesimplifiedasthemid-sectionoftheouterring,whichisanarcofcircunference.Thecenterofgravityofthisarcofcircumferenceforeachsectionisatadistancefromthecenterofthecircumferenceof(39):

°m,R =ÆRMUPìRìR

AsexplainedinChapter4.10,thetheoryofthefictitioustendonisapplied.Thus,thecenterofgravityofthetendonsislocatedatthecenterofthecircumferenceforallthesections,asthe tendonsaredistributed symmetrically tobothaxis in theplaneof the section.As'm,R andXqjo,/areappliedatthecenterofthecircumference,°m,R coincideswiththelevelarmoftheseforces.Finally,fromtheequilibriumofmomentumsitresults:

J™4,R = ('m,R + Xqjo,/)°m,R Aschematizationofageneralsectionisexposedbelow(Figure5.17):

63

Figure5.17.Schematisationofageneralsectionofthestructure.

Atthispoint,itischeckedthatthesolicitation(J£4,R)islowerthantheresistancetobending(J™4,R). In the graph below (Figure 5.18), it is shown that all the sections have sufficientresistance:

Figure5.18.Checkof theresistancetobendingmomentin thestructure.Theredlinereferstotheresistanceandtheblacklinetothesolicitation.

64

InAppendix10.1.2.1itisshownatablewiththeresultsobtained.Atthispoint, it isalsocheckedthattherupture isductile.Asexplainedbefore,thismeansthatwhen theconcretecracks, the steel cancarry the loadandkeepson sufferingplasticdeformation.Thisaspectisverycrucialbecausebymeansofthedeformation,thestructurewarnsthatthecollapseofthesteelisclose.Thisconditionissatisfiedif,atULS,thestrainofthesteelislowerthanitsultimatestrain(780 = 0.035).UsingthediagramofstrainsshowedatthetopofFigure5.17,thestrainonthesteelatULSisforeachsectionis:

7/R = 7m8ÆR − °R°R

ThischeckisshownbymeansofatableinAppendix10.1.2.2.Itisprecisethatthedeformationcheckisnotdoneatthesectionsrunningfromthetopofthetowerto18.42metersdown.ThereasonisthatforthissectionthedeformationofthesteelinULSisinelasticregime.Therefore,thematerialrecoversitsinitialgeometryandnowarning can be observed. From this section to the bottom, the deformation exceeds theyieldstrain.Thus,itispermanentandthedeformationcheckcanbecarriedout.

65

6 Construction,transportandinstallation

TheconstructionoftheoftheFOWTismadeinsitu.ItisusedanavailablemallinthePortofTarragona.Fromthere,thestructurewillbetuggedtotheoffshoreactualemplacementofoperation.Oncethestructurearrivestothesite,thefloaterisfilledwithseawateruntilthetop of the tower is reachable by the catamaran that brings the turbine. At thismoment,there are installed the nacelle and the blades. The next paragraphs explain moreexhaustivelythisprocess:

§ Firststage:constructionoftheconcretestructureTheconstructionoftheFOWTwillbemadeinhorizontalposition,astheirvastdimensionsmakestheverticalconstructionatthedockverycomplex.Ontopofthat,thereisnospotintheportwherethedraftwouldbesufficienttobuilditinvertical.Theconstructionmethodfollowsthenextsteps:

1. Provide(formwork)supportsandputtheformworkready.2. Positionthereinforcement.3. Installbarchairstosetthetendonprofilesinthecorrectposition.4. Installationoftheductsforposttensioning.5. Completeendofformworkatbothendsofthestructure.6. Push strands into the ducts and install anchor plates with spiral

reinforcement.7. Completetheinstallationofeverytendon.8. Casttheconcreteuntiltheformworkisfulfilled.9. Installtheanchorheadsandwedges.10. Withthehelpofhydraulicjacks,thetendonsarestressed.11. Cuttingtheendofthestrands.Consequently,theconcreteiscompressedby

thestrengthtransmittedbythesteeltendons.12. Installanchorgroutcaps.13. Groutoftheducttubestopreventthetendonsfrombeingexposedtoairor

water – that would cause corrosion, which would greatly reduce thecompressivestrengthofthetendons.

14. Removegroutcaps.15. Covertheanchorswithe.g.concretetoavoidcorrosion.

§ Secondstage:constructionsiteandstevedoring

Normally,structuresofhighdimensions–e.g.caissons–arebuiltinadryconstructionsitenexttothesea,bymeansoftheconstructionofanartificialdike,orusinganexistingone.Inthe case a new one is constructed, operations of dewatering are carried out in the areathroughwaterpumpstoreducethegroundwaterleveltoapproximate0.5metersundertheflooroftheconstructionsite.Intheseconditions,thestructureisfabricatedinsitu.Oncethestructure has hardened, the dry dock is removed and the construction site is, hence,

66

flooded.Thebuiltstructurestartsfloating.Finally,itistuggedtothefinallocationbymeansoftugboats.Nevertheless,thedimensionsoftheFOWTarenotveryvast,comparedtoFOWTdestinedtoproducehigherratesofenergy(theheightofa5MWFOWTcanbearound250meters).Forthis reason, the structure can be built in one of the available apron areas of the port ofTarragona.Thus,theconstructionofadrydockisnotnecessaryinthiscase.Thestructureisbuiltclosetothewater,formaneuverabilityreasons.Thestevedoringoperationswillbecarriedoutby twoheavy liftingcranesonrubber tires.Theyare steerable,whatmakes thecranesmore flexibleandeasilymoved to thedesiredposition. The cranemodel has been determined according to theweight that each cranemustlift.ThemechanismusedtograbthestructureisshowninFigure6.1.

Figure6.1.Pictureofthehook,supportedbyropes(40).

To calculate theweight that every cranemust lift, it has been developed aMatlab code(Appendix10.4).Toavoidslidingofthecableswhenliftingthestructure,itcanbegrabbedfromasectionthatislessthan3metersseparatedfromeveryedge.Anyway,ithasbeenrunall the possible combinations of distances from the floater extreme (m) and the towerextreme(n)from1to20meters.Incasetheoptimumcasedoesnotrespecttheminimumsafetydistance,thatcasewouldbedisregarded.AsmentionedinChapter4.10,theFOWTcanbesimplifiedasastaticallydeterminedbeam,withtwopinnedsupports.Assaidintheparagraphbefore,thesimplysupportsarelocatedatintermediatesections,forsafetyreasons.Thetwocriteriatodeterminethecranemodelusedare:

67

1. Loadcarriedbyeachcrane.Thisconditionpretendstousetwocranesofthesamemodel–amodelthatsuitstherequiredmasstolift–,asitisassumedthatiseconomicallymorefeasiblethanusingcranesofdifferentmodels.Forthisreason,theoptimalcombinationoftensionsinthecablesistheonethatminimizesthedifferencebetweenthetensionforceofthecables.

2. Bendingmomentsolicitation.Itmustbecheckedthatallthesectionsofthe

structure can assume the stresses produced during the stevedoringoperation. These are produced by the self-weight of the structure and thetensionsinthecables.

Inthesystemofstudy,onlythreeforcesareacting–thetwoverticalreactionsandtheself-weight of the structure, acting as a uniformly distributed load. The conditions of stabilityappliedtofindthetensionoftheropeshavebeen:

1. Ø∞± = 0≤

2. Jh± = 0≤ The first equation indicates that the sum of vertical reactionsmust be equal to the self-weightofthestructure.Thesecondequationensuresthatthesumofmomentumsactingateverypointof the structuremustbe0. Ithasbeenconsidered the floaterextremeof thestructureasturningpointtostablishthemomentumequilibrium.The position of the lifting cables is not determined yet. The distance from the floaterextremetothefirstsupportisassignedtothevariable)andthedistancefromthetowerextremetothesecondsupportisassignedtothevariableP(Figure6.2).Ithasbeenrunallthepossiblecombinationsof)andPfrom1to20meters(400combinations).

Figure 6.2. Stevedoring system of forces. The self-weight is a distributed load that changes depending on the section. Itequilibratestheverticalforcesintroducedbythetensionofthecables.Distancesinmeters.

68

Consequently,theinitialsystemof2equationsand4variables(k3, kD,), P)isreducedtoadetermined systemof 2 equations and 2 variables (k3, kD). The vertical reactions (tensionforceofthecables)are:

k3 =xm(ô − í≥nm − P)

ô − ) − P

kD = xm − k3

where,followingtheSI:k3[']:tensioninthecablethatholdthestructurefromthefloater.kD[']:tensioninthecablethatholdthestructurefromthetower.xm[']:self-weightofthestructure.í≥nm[)]:centerofgravityofthestructure.P[)]: distance from the tower extreme to the the cable that holds the structure by thetowerpart.)[)]:distancefromthefloaterextremetothecablethatholdsthestructurebythefloaterpart.Subsequently,tosatisfythefirstcriterionalreadyexposed,therehavebeencomputedtheabsolute value of the differences betweenk3andkD. At this stage, it has been created amatrix of 400x5, including all the possible combinations of) and P (columns 1,2), thetension forces (columns 3,4) and the absolute difference between them (column 5), inascendantorderaccordingtocolumn5.Followingthisprocedure,thecandidatestooptimalcaseareexposedinorderofpreference,beingtherow1thefirstcandidate.Then,thediagramofbendingmomentsiscomputedforeachcase.Thestructurehasbeendivided into66 transversal sections respectivelyseparatedby1meter– the lastsection isseparated0.65metersfromtheonebehindit,tocompletethelengthof64.65m.Inafirstmoment,thebendingmomentdiagramswerecalculatedwithExcel.However, itcouldnotcopewiththenumerousconditionsthathadtobeapplied.Atsomepointofthecalculation,Excelcouldnotmanagetoapplyseveralconditions.Thus, ithasbeendecidedtoswitchtoMatlabwhichhasmadethecalculationsmorestraightforward.The400x66matrix containing thebendingmoments law for the 400 combinationsofm’sandn’s is created.Afterwards, it is annexed to the400x5matrix that ithadbeencreatedbefore,generatinga400x71matrix(matrixB).Once thebendingmoment lawsarecomputed, thesecondcriterionofdesignapplies.Forevery section, it is checked at t=0 – the operation last for a short time – that no tensilestressesareproducedandthecompressionstressesdonotexceedthelimit.Asusedforthedesignofthepre-stressingsteel,theEHE-08codeisfollowed.Thisis:

69

1. 9 = −ã¥,µ,∂∑∂rá∏

i§+

ãπ,∫ªµ,∂∑∂ºµ

Ω≤ 0 : No tensile stresses allowed in the

structure.

2. 9 = −ã¥,∫ªµ,∂∑∂rá∏

i§+

ãπ,∫ªµ,∂∑∂ºµ

Ω≥ −0.45.m0: Limited compressions in the

structure.where,consideringtheSI:9['/))D]:stressinthestructure.9 > 0istension,while9 < 0iscompressionX:1[']:pre-stressingforceintroducedbythesteellm[)D]:areaoftheconcreteJc[')]:bendingmomentoneachsectionx[)*]:sectionmodulusofeachsection.m0[JXL]:characteristicresistanceoftheconcrete!r,c,ojo[-]:safetyfactorforthepre-stressingsteel,infavourableconditions(SLS)!r,8pc,ojo[-]:safetyfactorforthepre-stressingsteel,inunfavourableconditions(SLS)!n,ojo[-]:safetyfactorfortheexternalloads,forfavourableorunfavourableconditions(SLS)Anewvectoriscreated,havinga1asoutputifbothstressconditionsabovearesatisfiedora0ifoneornoneofthemaresatisfied.AftertheannexofthisvectortothematrixB,therows that satisfy both stress conditions are extracted. These are directly in order ofpreference,sincetheywerealreadyorderedwhenitwasappliedtheconditionofminimumdifferencebetweentensionsinthecables.Thus,therow1ofthematrixwillbetheoptimalcase.ThebendingmomentdiagramofitisshowninFigure6.3.

Figure6.3.Diagramofbendingmomentsoftheoptimalcase.

70

Inthegraph,itcanbeseenaninflectionpointatí = 44).Tounderstandthereasonwhyitappears,itmustberememberedthatthestructureisdividedinsectionsof1meter.Atí =45), the mass of the section stops the decreasing tendency and starts increasing withrespect to the last section. The mass decreases during the transition piece due to thetruncated-conical shape of this part. When increasing x at this part, the section areadecreases. However, from the bottom of the tower, the additional thickness of the wallstarts acting. The loss of mass due to the truncated-conical shape of the tower iscompensatedbytheincreaseofmassduetotheadditionalthicknessofthewall.Atsectioní = 45), the increase of mass due to the additional thickness exceeds the decrease ofmassdue to thedecreaseof the sectionarea.Consequently, themassof the sectioní =45)ishigherthanthemassofthesectioní = 44).ThebendingmomentpersectionscanbefoundinAppendix10.2.1.Inrelationtothelimitationofcompressionstressesandtheavoidanceoftensilestressesinthewholestructure,thestressesateachanysectionmustsatisfy:

−42.75'/))D ≤ 9 ≤ 0'/))DInthefollowinggraph(Figure6.4),itisshownthattheconditionaboveissatisfied:

Figure6.4.Theregionbetweenthetworedlinesrespondstotheallowedstressesinthestructure.Theblacklineisthestressateverysection.Theplotshowsthatthestressconditionsaresatisfied.

71

ThetableincludingthestressateverysectioncanbecheckedintheAppendix10.2.2.Thedataoftheoptimalcaseis(Table6.3):m[m] n[m] æø[kN] æ¿[kN] |¡¬√[kNm] x(|¡¬√)[m] |¡≤ƒ[kNm] x(|¡≤ƒ)[m]

3 20 2390.29 2393.73 17675.24 24 –4545.63 46

Table6.1.Dataoftheoptimalcase.

Oncetheweightstobecarriedbyeachcraneareknown,itcanbedeterminedthetypeofcranesthatarerequiredtodothestevedoringoperations.Themassthatneedstobecarriedbyeachcraneis:

J3 =k3≈= 243.66Q`PKM

JD =kD≈= 244.01Q`PKM

whereJ3andJDarethemassthatthecraneatthefloaterandthecraneatthetowermustlift,respectively.TheprovidercompanyofthecraneswillbeLiebherr.Theyhavemodelsofmobilecranesforportsupto308tonesofcapacity(LHM800).Themaximumradiumalloweddependsonthecapacity that must be lifted. Theminimum radium is also a limiting factor. Several frontviewsandaplantviewofthecranesareshowninFigure6.5.

Figure6.5.Frontview

sandplantviewoftheLiebherrLHM

800.

ThefirststabilitycheckhasbeendonefortheLHM800.Inthefigurebelow(Figure6.6)therelationcapacity-outreachofthismodelisshown:

Figure6.6.Relationshipcapacity-outreachofthemodelLHM800.

Lookingatthegraph, for!"and!# themaximumoutreach isapproximately21.5metersforbothcranes.

74

Consideringthattheminimumradius is12metersandthatthesideofthecrane–squareshaped in top view–measures 15meters, it has beenusedAutoCad to find thepossibleregions where the center of gravity of the crane can be placed (Figure 6.8). It has beenconsideredthatthecenterofgravityislocatedatthecenterofthecrane.Theminimumdistancebetweentheexternalradiusofthefloateratthemallandtheedgeofthemallis1.5meters.Thesamedistancemustbeguaranteedfromtheedgeofthemalltothestructurewhenitisloweredattheseasidebythecranes(Figure6.6).Rubbertiresof0.5metersbroadand1meterdiameterareputinthequaywalltomitigatedamagebyimpact.

To find the regionswhere thecranescanbeplacedwithoutcompromising the stability, ithasbeenproposedagraphicalsolution.Theremustbesatisfiedallthelimitationsexposedabove.Todoit,ithasbeenusedAutoCad.Thepossibleregionsareshownbelow,withthestabilityareashadowed(magentaandblue).Onthenexttwopages,thesolutionchosenisexposed(Figure6.8andFigure6.9).The main features of the crane LHM800 are exposed in the brochure given by themanufacturerandare(Figure6.7):

Figure6.7.MainfeaturesoftheLiebherrLHM800crane.

Therefore,asanoverview,forthestevedoringprocessthereareusedtwocranesLHM800,fromLiebherr.Thecraneholdingthefloaterwillbelocatedat3meters’distancefromthebottom of the structure and the crane holding the tower will be located at 20 meters’distancefromthetopofthetower.A3Dviewofthesituationatthemall,previouslytothestevedoring, is presented in Figure 6.10.

Figure6.8.Thestableregionsareshadowedinm

agenta(floater)andblue(tower).Distancesinm

eters.

76

Figure6.9.Finalpositionofthecranes.Distancesinmeters.

77

Figure6.10.3Dviewofthesituationatthem

all,previouslytothestevedoringofthestructure.

As exposed in Chapter 3, it has been checked that the draft in the port is sufficient to

guaranteethetransportationofthestructurewithoutdamagingit.Thewaterdepthinthe

PortofTarragonaisaroundthe20metersinthewholearea(41),sothewaterdepthdoes

notcausemajorinconvenienceinthetransport.

§ Fourthstage:transportofthestructuretothefinallocationTheWindcrete concept proposes to tow the concrete structure with tug boats from the

shore to the final location. This isonlypossible if theenvironmental and sea conditions–

waves,windvelocity–aresuitableforthetransport,anddonotrepresentahazardforthe

structure. Otherwise, the structure can only be transported on the deck of heavy lifting

vessels,whatrepresentshighercosts.

Thestructureissubjectedtoaresistanceforcewhenistowed,actinginoppositedirection

tothemovement.Thequantificationofthisforcedeterminesthetypeoftugboatneededto

transport the structure. This resistance force is the sum of the resistance due to water

viscosity, the still air and the waves created by the movement of the structure. The

resistanceforceisproportionaltothesquareofthevelocity.Thefollowingfigureshowsthe

relationbetweenthesetwoparameters(Figure6.11):

Figure6.11.Relationvelocity-resistanceforce(42).

Ithasbeendemonstratedthatforlowvelocitiesthetotalresistanceiscarriedmainlybythe

water viscosity. As shown in the graph above, low velocities imply low resistances. Low

transportspeedsalso leadtobettercontrolofthestructure.Theresistanceduetostillair

onlyappearathighspeeds,thus itcouldbeneglectedforthiscaseofstudy.Ontheother

hand,theresistanceduetowavesgeneratedbytheownvesselcanbeskippedincasethe

Froudenumber is lowenough.Thevelocityof transportwillbe lowenough tohavesmall

79

resistancesandhighcontrolofthestructure.Oncetheresistanceiscomputed,thetugboat

canbechosen.

Tochoose themost feasible tugboat theremustbeattendedthecostofeverycandidate

vesselperunittime,theoperationalcostsandthecruisevelocity.Bycombiningtheseterms,

itcanbedeterminedthemostfeasibleoptiontocarryoutthetransportofthestructureto

thedestination.

§ Fifthstage:erectionofthestructureandinstallationoftheturbine

Once the concrete structure arrives at the final location, the steps explained below are

followed:

1. Floodingof the structurewith seawater. Thebottomof the floater starts to sink

whenaddingseawater,thatactsasballast.Tocontroltherotationofthestructure

generatedbytheweightoftheballast,thefloateristiedtothetugboatbymeansof

a cable. It also avoids the jump produced when the structure achieves theequilibriumintheverticalposition,thisis,whentheweightofthestructureandthe

ballastequalsthebuoyancyforce.Theobjectiveofthisoperationisthesubmersion

ofthestructureuntilthetopofitisreachabletoplacetheturbine.

2. InstallationofthenacelleandthebladesoftheFOWT.Atthispoint,thetopofthestructureisplacedatareachablepositionfortheinstallationofthenacelleandthe

bladesbymeansofacatamaran.Itisavoidedtheuseoffloatingcranes,thatwould

increasenoticeablythecostofthisoperation.

3. Replacementoftheseawaterballastbypermanenthighdensityballast.Theballastusedinthiscaseisblackslagfromelectricalfurnaces,whichhasaspecificweightof

25kN/m3.Thislowersthecenterofgravityofthestructure,increasingthedistance

from it to the metacentric height. The larger this distance is, the higher righting

momentisgeneratedincaseoftiltofthestructureduetoexternalforces(43).This

leadstohigherstabilityofthestructure.

Ontheotherhand,italsoinduceslargermomentofinertia,whatincreasesthepitch

androllstiffness.Thisfactpermitsthelimitationofthetiltangleand,consequently,

thereductionoftheenergyproductionlosses.

4. Installation of the catenarymooring lines. They avoid themigration of the FOWT

due to the external forces. These steel cables are anchored to the sea bottom by

meansofsuctionpilesorembeddedanchors.

80

7 Budget

Theobjectiveof this chapter is theestimationof the costsof constructionof the100kW

FOWT.ThepricesoftheitemsusedhavebeentakenmainlyfromtheInstitutdeTecnologia

delaConstrucció(iTeC)(44).Theitemsthatcouldnotbefoundinthisdatabaseweretaken

fromtheprojectdevelopedbytheresearcherfromUPCAlexisCampos,calledProjectebasicd’estructuraflotantSPARdeformigóallitoralMediterraniperalsupportd’unaerogeneradorde5MW(45).

Ontheotherhand,themeasurementsaretakenasaroughestimation.Theobjectiveofthis

budget is to get a first idea of the costs. Furthermore, since it is a first estimationof the

project,therehavebeentakensomelumpsums:

§ It has been assumed a lump sum equal to the 1% of the budget for thematerial

executionoftheworksfortheexpensesinqualitycontroloftheconstruction.Inthe

material execution of the works it has not been included neither the health and

safetymeasuresnorthewastemanagementexpenses.

§ It has been assumed a lump sum equal to the 3% of the budget for thematerial

executionoftheworksfortheexpenses inhealthandsafetyequipment.Thevalue

taken as material execution of the works skips the waste management and the

qualitycontrolexpenses.

In the next pages, the measurements of the items used and the fee of schedules 1 are

exposed. The fee of schedules 2 is not included in this budget, since in this first

approximationofcostsitisnotgoingtotakeaspossiblerescissionsofthecontractorother

similar incidences. Asmentionedbefore, the unit prices are taken directly from the iTeC

and,consequently, theyarenotexplicitly justified.Theunitprices integrate the labor, the

machinery, the materials and other expenses.

7.1 Measurem

ents

CHAPTER

1

Floatin

gstru

cture

SUBCH

APTER

1

Concre

ting

NUMBER

CO

DE

UA

DESCR

IPTION

1G4531LH

4m3

Concretefor

beams,

HP-95/B

/20/IIIa,soft

consistencyand

granularmaxim

um

sizeof

20mm,spilledw

ithpump

Num

berText

Type[C]

Total

1

Floater

135.5047451

135.50

2

Transitio

n

19.01501313

19.02

3

Tower

21.38394155

21.38

4

Cap

19.62578063

19.63

TOTA

L195.53

2G7811100

m2

Painttheconcretewithverticalw

allcoveringmade

with2kg/m

2ofcationicbituminousem

ulsionofECR-1

Num

berText

Type[C]

Total

1

Paint1

mwidth

111.5871446

111.59

TOTA

L111.59

3G4D

DAD12

m2

Assem

blyand

dismantling

ofthe

formworkw

ithsteeldropceiling,forrightdirective

Num

berText

Type[C]

[D]

Total

C

Units

m2

1

Floater

2

622.18

1,244.35

82

2

Tower

2

122.00

244.00

3

Cap

2

74.20

148.41

TOTA

L1,636.76

4G4D

E1900m3

Assem

blyand

dismatling

ofscaffold

with

metal

reinforcing,maxim

um10m

height

Num

berText

Type[C]

[D]

[E]

Total

1

Totalvo

lume

64.65

4.86

4.86

1,527.01

TOTA

L1,527.01

CHAPTER

1

Floatin

gstru

cture

SUBCH

APTER

2

Reinforce

ment

NUMBER

CO

DE

UA

DESCR

IPTION

1G4A

71171u

Steelsheet

activeanchorage,

formaxim

um

3000kNstressedtendons,placed

Num

berText

Type[C]

Total

1

Sheeta

nchorages

12

12.00

TOTA

L12.00

83

2G4A

81B11

m

Sheathsof

corrugatedsteel

tubes,of

100mm

ofdiameterand0.3m

m

Num

berText

Type[C]

[D]

Total

1

Tendons0

.6''

1

3

128.37

385.10

2

Tendons0

.6''

2

1

103.41

103.41

3

Tendons0

.6''

3

2

55.24

110.48

TOTA

L598.98

3G4A

A1220

kgTendon

formed

bycord

foractive

reinforcement

Y1860S7,until

19cords

ofnom

inaldiam

eter15.2m

m,introducedw

ithsheathsofmorethan70m

Num

berText

Type[C]

[D]

[E]

Total

C

Kg/m

Le

ngth

Numbe

r

1

Tendons0

.6''

1

8.19

128.37

3

3,153.98

2

Tendons0

.6''

2

8.19

103.41

1

846.90

3

Tendons0

.6''

3

8.19

55.24

2

904.79

TOTA

L4,905.68

4G4A

C1400t

3000kNsteeltendonstressing,w

ithhydraulicjack

Num

berText

Type[C]

Total

C

Number

Load

1

Tendons0

.6''

6

276.0611621

1,656.37

84

TOTA

L1,656.37

5G4G

E1100t

Injectionof

sheathsfor

activereinforcem

ent,withcem

entgrouting

Num

berText

Type[C]

C

l/m

Length

Total

1

Tendons0

.6''

1.97

128.3669908

252.88

2

Tendons0

.6''

1.97

103.4069908

203.71

3

Tendons0

.6''

1.97

55.23778714

108.82

TOTA

L565.41

CHAPTER

1

Floatin

gstru

cture

SUBCH

APTER

3

Internalstru

cture

NUMBER

CO

DE

UA

DESCR

IPTION

1G4R

11025kg

Austenitic

stainlesssteel

AISI

304for

structures,L

laminated

profiles,circular,

squared,rectangular,

hexagonal,sheet,manufacturedatfactoryandw

eldedatplace

Num

berText

Type[C]

[D]

Total

C

kg

Number

1

Piecefo

rtheca

ble

entra

nceto

thestru

cture

3780

1

3,780.00

2

Elevatorp

latfo

rms(x3

)

7139.67

3.00

455.00

3

Indoor-o

utdoor

connecto

rs

455

1

455.00

4

Acce

ssdoorfra

me

1926

1

1,926.00

TOTA

L6,616.00

85

2PA

00GP

uPum

pingsystem

for

theextraction

ofthe

waters

filteredinsidethestructure

TOTA

L1.00

3PA

00AS

uLum

psum

for

theinstallation

of1

elevator.It

includesalltheelementstoputitinoperation

TOTA

L1.00

4PA

00PEu

Lump

sumfor

theconstruction

ofa

boatgate

type,with

fastensystem

by

indoor-outdoortireofm

aximum

2x1.5msize

TOTA

L1.00

5G9N

00Tm2

Metalic

gridform

edby

gussetgrill

made

ofgrey

steel(TRAMEX20x3m

m),form

inga30x30mm

gridand

steelfram

ewith

electrowelded

joints,placedonm

etalstructure

Num

berText

Type[C]

Total

1

Floaterp

latfo

rms

62.83185307

62.83

2

Towerp

latfo

rms

10.05309649

10.05

3

Acce

ssplatfo

rm

43.10265121

43.10

TOTA

L115.99

86

6GB122CA

M

m

Galvanizedsteelhandrail,w

ithbanister,lowerstock,

postsevery

100cm

,thick

barsevery

15cm

of

100cm

height,

mecanically

fastenedto

thestructurebysteelpeg,m

illstoneandbolt

Num

berText

Type[C]

Total

1

Floater

42.85371429

42.85

2

Tower

116.8449796

116.84

TOTA

L159.70

CHAPTER

1

Floatin

gstru

cture

SUBCH

APTER

4

Windtu

rbine

NUMBER

CO

DE

UA

DESCR

IPTION

1PA

AER

O05

MW

100kW

offshore

wind

turbinesupply,

includingall

theneccessary

elements

foroperation.

Itincludes

advisoryand

iniciationof

operationonce

ithas

beeninstalled.

Itdoes

notinclude

connectiontothehinterlandgridnorassembly

Num

berText

Type[C]

Total

1

Offsh

oreW

ind

Turbine100kW

1

1.00

TOTA

L1.00

2PA

00001u

Assem

blyof

thewind

turbineon

topof

thestructure,

includingthe

craneoperations

andpositioning

TO

TAL

1.00

87

CHAPTER

2

FOWTtra

nsporta

tion

andfo

undatio

ns

NUMBER

CO

DE

UA

DESCR

IPTION

1PA

00002RE

uLum

psum

accounting

forthe

towing

ofthe

structurefrom

the

portmall

tothe

finallocation(m

ax.40milesofdistanceand12h/day)

TOTA

L2.00

2B033R

J00m3

Supplyofballastofdensityhigherthan25kN/m

3

TO

TAL

78.09

3PA

00003FO

u

Lump

sumaccounting

forthe

additionof

ballastin

thestructure.

Itincludes

theoperations

oftransport

ofthe

ballastuntil

thedestination,

witham

aximum

distanceof40miles

TOTA

L1.00

4PA

00004PIu

Lumpsum

fortheexecutionofseabedsuctionpiles

TO

TAL

3.00

CHAPTER

3

Waste

Management

NUMBER

CO

DE

UA

DESCR

IPTION

1G2R

35039m3

Classificationof

theconstruction

ordem

olitionwaste

materials

atthe

constructionsite

bymanualm

eans,accordingtoREA

LDECR

ETO105/2008

Num

berText

Type[C]

Total

1

Steelandiro

n

0.934126531

0.93

88

2

Plastic

0.084440816

0.08

3

Specia

lenvelops

1.546322449

1.55

4

Wood

0.369428571

0.37

TOTA

L2.93

2G2R

64239m3

Loadingandtransportationofconstructioninertand/ornon-special

waste

toautorized

installationsfor

thewastetreatm

ent,with7ttruckandw

aitingtimefor

theloadingbymechanicm

eans,andfrom10km

to15km

todestination

Num

berText

Type[C]

Total

1

Steelandiro

n

4760.35102

4,760.35

2

Plastic

50.13673469

50.14

3

Specia

lenvelops

184.7142857

184.71

4

Wood

4945.065306

4,945.07

TOTA

L9,940.27

3G23A

61H0

m3

Controleddisposal

ata

reclamation

emplacem

entofinertconcretew

astematerialofdensity1.45t/m

3,com

ingfromconstructionordem

olition,with170101

codeaccording

tothe

EuropeanList

ofWaste

(MAM/304/2002)

Num

berText

Type[C]

Total

1

Steelandiro

n

4760.35102

4,760.35

2

Plastic

50.13673469

50.14

3

Specia

lenvelops

184.7142857

184.71

4

Wood

4945.065306

4,945.07

TOTA

L9,940.27

89

CHAPTER

4

Others

4CO

DE

UA

DESCR

IPTION

1PA

00SSu

Lumpsum

accountingthehealthandsafetyoftheconstructionsite

TOTA

L1.00

2PA

00CQ

uLum

psumaccountingfortheQ

ualityControloftheconstruction

TOTA

L1.00

90

7.2 Feeschedule1

NUMBER

CO

DE

UA

DESCR

IPTION

PRICE

1

B033RJ00

m3

Supplyo

fballasto

fdensityh

igherth

an25kN

/m3

10.75€

2

G23A61H0

m3

Contro

leddisp

osalata

recla

matio

nemplacemento

finert

concre

tewaste

materia

lofdensity

1.45t/m

3,coming

fromconstru

ctionor

demolitio

n,with

170101code

acco

rdingto

theEuropeanListo

fWaste

(MAM/304/2002)

1.45€

3

G2R35039

m3

Classifica

tion

of

the

constru

ction

or

demolitio

n

waste

materia

lsat

the

constru

ction

site

by

manualm

eans,a

ccordingto

REALD

ECRETO105/2008

18.44€

4

G2R64239

m3

Loading

and

transporta

tion

of

constru

ction

inert

and/or

non-sp

ecia

lwaste

toautorize

dinsta

llatio

ns

forthewaste

tre

atm

ent,

with

7ttru

ckandwaitin

g

timefortheloadingby

mechanic

means,

andfro

m

10km

to15km

todestin

atio

n

1.40€

5

G4531LH

4

m3

Concre

te

for

beams,

HP-95/B/20/IIIa

,soft

consiste

ncy

and

granular

maxim

um

size

of

20m

m,sp

illedwith

pump

600.00€

6

G4A71171

u

Steel

sheet

active

anchorage,

for

maxim

um

3000kN

stresse

dte

ndons,p

laced

157.09€

7

G4A81B11

m

Sheaths

of

corru

gatedste

el

tubes,

of

100mm

ofd

iametera

nd0.3m

m

5.03€

8

G4AA1220

kg

Tendonform

edby

cordfor

active

reinforce

ment

Y1860S7,

until

19

cords

of

nominal

diameter

15.2m

m,in

troducedwith

sheathso

fmoreth

an70m

1.32€

91

9

G4AC1400

t3000kN

steelte

ndonstre

ssing,w

ithhydraulicja

ck1.22€

10

G4DDAD12

m2

Asse

mbly

and

dism

antlin

g

of

the

form

workw

ithste

eldropce

iling,fo

rrightd

irective

72.22€

11

G4DE1900

m3

Asse

mbly

anddism

antlin

gof

scaffo

ldwith

metal

reinforcin

g,m

axim

um10m

height

11.67€

12

G4GE1100

tInjectio

n

of

sheaths

for

active

reinforce

ment,

with

cementg

routin

g

1.34€

13

G4R11025

kg

Auste

nitic

stainless

steel

AISI

304for

structu

res,

Llaminatedprofile

s,circu

lar,

squared,

recta

ngular,

hexagonal,

sheet,

manufactu

red

at

facto

ryand

weldedatp

lace

4.09€

14

G7811100

m2

Painttheconcre

tewith

vertica

lwall

coverin

gmade

with

2kg/m

2ofca

tionicb

ituminouse

mulsio

nofE

CR-1

5.11€

15

G9N00T

m2

Metalic

grid

form

edby

gusse

tgrill

madeof

grey

steel(TRAMEX20x

3mm),

form

inga30x

30mm

grid

and

steel

frame

with

electro

welded

joints,

placedonm

etalstru

cture

50.27€

16

GB122CAM

m

Galva

nize

dste

elh

andrail,w

ithbaniste

r,lowersto

ck,posts

every1

00cm

,thickb

arse

very1

5cm

of1

00cm

height,

mecanica

llyfaste

nedtothestru

ctureby

steelpeg,

millsto

neandbolt

136.82€

17

PA00001

u

Asse

mbly

of

the

wind

turbine

on

top

of

the

structu

re,

inclu

ding

the

crane

operatio

ns

andpositio

ning

35,000.00€

18

PA00002RE

u

Lump

sum

acco

untin

g

for

the

towing

of

the

structu

re

from

the

port

mall

to

the

final

locatio

n(m

ax.4

0m

ileso

fdista

nceand12h/day)

30,000.00€

92

19

PA00003FO

u

Lumpsumacco

untin

gfor

theadditio

nof

ballast

in

the

structu

re.

Itinclu

des

the

operatio

ns

of

transport

of

the

ballast

until

destin

atio

n,

with

am

axim

umdista

nceof4

0m

iles

5,000.00€

20

PA00004PI

u

Lumpsu

mfo

rtheexecutio

nofse

abedsu

ctionpiles

130,000.00€

21

PA00AS

u

Lumpsumfor

theinsta

llatio

nof

1elevator.

It

inclu

desa

lltheelementsto

putitin

operatio

n

75,000.00€

22

PA00CQ

u

Lumpsumacco

untin

gfortheQuality

Contro

lofthe

constru

ction

5,854.45€

23

PA00GP

u

Pumpingsyste

mfor

theextra

ctionof

thewaters

filteredinsid

eth

estru

cture

18,471.43€

24

PA00PE

u

Lumpsumfor

theconstru

ctionof

aboat

gate

type,

with

faste

n

system

by

indoor-o

utdoor

tireofm

axim

um2x1

.5m

size

50,000.00€

25

PA00SS

u

Lumpsumacco

untin

gthehealth

andsafety

ofthe

constru

ctionsite

17,563.34€

26

PAAERO05

MW

100

kW

offsh

ore

wind

turbine

supply,

inclu

ding

all

the

necce

ssary

elements

for

operatio

n.

It

inclu

des

adviso

ryand

inicia

tion

of

operatio

n

onceit

has

beeninsta

lled.

Itdoes

not

inclu

de

connectio

nto

thehinterla

ndgrid

nora

ssembly

200,000.00€

93

7.3 Budget

CHAPTER

1

Floatin

g

structu

re

SUBCH

APTER

1

Concre

ting

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

G4531LH

4

m3

Concre

te

for

beams,

HP-95/B/20/IIIa

,soft

consiste

ncy

and

granular

maxim

um

size

of

20m

m,sp

illedwith

pump

600.00€

195.53

117,317.69€

2

G7811100

m2

Painttheconcre

tewith

vertica

lwallcoverin

gmade

with

2kg/m

2ofca

tionicb

ituminouse

mulsio

nofE

CR-1

5.11€

111.59

570.21€

3

G4DDAD12

m2

Asse

mbly

and

dism

antlin

g

of

the

form

workw

ithste

eldropce

iling,fo

rrightd

irective

18.44€

1,636.76

30,181.88€

4

G4DE1900

m3

Asse

mbly

anddism

atlin

gof

scaffo

ldwith

metal

reinforcin

g,m

axim

um10m

height

11.67€

1,527.01

17,820.17€

CHAPTER

1

Floatin

g

structu

re

SUBCH

APTER

2

Reinforce

ment

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

G4A71171

u

Steel

sheet

active

anchorage,

for

maxim

um

3000kN

stresse

dte

ndons,p

laced

157.09€

12.00

1,885.08€

2

G4A81B11

m

Sheaths

of

corru

gatedste

el

tubes,

of

100mm

ofd

iametera

nd0.3m

m

5.03€

598.98

3,012.89€

3

G4AA1220

kg

Tendonform

edby

cordfor

active

reinforce

ment

Y1860S7,

until

19

cords

of

nominal

diameter

15.2m

m,in

troducedwith

sheathso

fmoreth

an70m

1.32€

4,905.68

6,475.49€

4

G4AC1400

t3000kN

steelte

ndonstre

ssing,w

ithhydraulicja

ck1.22€

1,656.37

2,020.77€

5

G4GE1100

tInjectio

n

of

sheaths

for

active

reinforce

ment,

with

cementg

routin

g

1.34€

565.41

757.65€

94

CHAPTER

1

Floatin

g

structu

re

SUBCH

APTER

3

Internal

structu

re

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

G4R11025

kg

Auste

nitic

stainless

steelAISI

304for

structu

res,

Llaminatedprofile

s,circu

lar,

squared,recta

ngular,

hexagonal,

sheet,

manufactu

redat

facto

ryand

weldedatp

lace

4.09€

6,616.00

27,059.44€

2

PA00GP

u

Pumpingsyste

mfor

theextra

ctionofthewaters

filteredinsid

eth

estru

cture

18,471.43€

1.00

18,471.43€

3

PA00AS

u

Lumpsumfor

theinsta

llatio

nof

1elevator.

It

inclu

desa

lltheelementsto

putitin

operatio

n

75,000.00€

1.00

75,000.00€

4

PA00PE

u

Lumpsumfor

theconstru

ctionof

aboat

gate

type,

with

faste

n

system

by

indoor-o

utdoor

tireofm

axim

um2x1

.5m

size

50,000.00€

1.00

50,000.00€

5

G9N00T

m2

Metalic

grid

form

edby

gusse

tgrill

madeofgrey

steel(TRAMEX20x3mm),

form

inga30x30mm

grid

andste

el

framewith

electro

weldedjoints,

placedonm

etalstru

cture

50.27€

115.99

5,830.70€

6

GB122CAM

m

Galva

nize

dste

elhandrail,

with

baniste

r,lowersto

ck,

posts

every

100cm

,thick

bars

every

15cm

of

100

cm

height,

mecanica

llyfaste

ned

to

the

structu

rebyste

elpeg,m

illstoneandbolt

136.82€

159.70

21,849.98€

95

CHAPTER

1

Floatin

g

structu

re

SUBCH

APTER

4

Windtu

rbine

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

PAAERO05

MW

100kW

offsh

orewindturbinesupply,

inclu

ding

all

the

necce

ssary

elements

for

operatio

n.

It

inclu

des

adviso

ryand

inicia

tion

of

operatio

n

onceit

has

beeninsta

lled.

Itdoes

not

inclu

de

connectio

nto

thehinterla

ndgrid

nora

ssembly

200,000.00€

1.00

200,000.00€

2

PA00001

u

Asse

mbly

of

thewindturbineontopof

the

structu

re,

inclu

ding

the

crane

operatio

ns

andpositio

ning

35,000.00€

1.00

35,000.00€

CHAPTER

2

Transporta

nd

foundatio

ns

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

PA00002RE

u

Lumpsumacco

untin

gfor

thetowingof

the

structu

re

from

the

port

mall

to

the

final

locatio

n(m

ax.4

0m

ileso

fdista

nceand12h/day)

30,000.00€

2.00

60,000.00€

2

B033RJ00

m3

Supplyo

fballasto

fdensityh

igherth

an25kN

/m3

10.75€

78.09

839.47€

3

PA00003FO

u

Lumpsumacco

untin

gfor

theadditio

nofballast

inthestru

cture.

Itinclu

des

theoperatio

ns

of

transport

of

theballast

until

thedestin

atio

n,

with

am

axim

umdista

nceof4

0m

iles

5,000.00€

1.00

5,000.00€

4

PA00004PI

u

Lumpsu

mfo

rtheexecutio

nofse

abedsu

ctionpiles

130,000.00€

3.00

390,000.00€

96

CHAPTER

3

Waste

Management

NUM.

CODE

UA

DESCR

IPTION

PRICE

MEA

SUREM

ENT

COST

1

G2R35039

m3

Classifica

tionof

theconstru

ctionor

demolitio

n

waste

materia

lsat

the

constru

ction

site

by

manualm

eans,a

ccordingto

REALD

ECRETO105/2008

18.44€

2.93

54.11€

2

G2R64239

m3

Loadingandtra

nsporta

tionof

constru

ctioninert

and/ornon-sp

ecia

lwaste

toautorize

dinsta

llatio

ns

forth

ew

aste

treatm

ent,w

ith7ttru

ckandw

aitin

g

timefortheloadingbymechanic

means,

andfro

m

10km

to15km

tofin

aldestin

atio

n

1.40€

9,940.27

13,916.37€

3

G23A61H0

m3

Contro

leddisp

osala

tare

clamatio

nemplacemento

f

inert

concre

tewaste

materia

lofdensity

1.45t/m

3,

comingfro

mco

nstru

ctionord

emolitio

n,w

ith170101

codeacco

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SUMMARYOFTHEBUDGET

CHAPTER COST

1FLOATINGSTRUCTURE 578,253.37€

2TRANSPORTANDFOUNDATIONS 490,839.47€

3WASTEMANAGEMENT 28,383.87€

5OTHERS 24,530.13€

CD 1,122,006.84€

CI(6%CD) 67,320.41€

PEM 1,189,327.25€

CG(13%PEM) 154,612.54€

BI(6%PEM) 71,359.64€

SUBTOTAL 1,415,299.43€

18%IVA 254,753.90€

TOTAL 1,670,053.33€

8 Conclusions8.1 SpecificationsonthefinaldesignInthepresentthesis,ithasbeendesignedaFloatableOffshoreWindTurbineof100kW.Thestructurehasbeendesignedconsideringtwocriticalsituations–thestevedoringprocesstomove the structure from a mall to the sea water and the FOWT in operational state(assumedSea Severe State andwind speedat rated). The reference standard followed toarrivetothefinaldesignhasbeentheEHE-08code(Spanishconcretestandard).To increase the resistanceof the structure, ithasbeendecided to introducepre-stressingsteelintheconcretestructure.Fortheoperationalstate,thestructurehasbeendesignedtoresisttheloadsinServiceabilityLimitState(SLS).Ithasbeenassumedthatforthisstatenotensile stresses can occur at any section of the structure and that compressionsmust belimitedto0.45fck,atshortandlongterm(t=0andtà¥),duetothereductionofthefatigueresistancecausedbycyclicloads.It has been concluded that High-Performance Concrete (HPC) is required to resist thestressestowhichthestructureissubjected.Theconcreteusedforthepresentdesignhasacharacteristicresistanceof!"# = 95()*(compression).Ontheotherhand,thegeometryof the structure has also beenmodified to obtain a pre-stressing force that is inside theboundariesimposedbytheabovementionedconditions.Furthermore, it hasbeenobserved that the concrete cannotbe stressedat themaximumvalueallowedby the standards (afterdirect lossesapplication),which is 1395N/mm2.Thereasonisthatnotallthelossesduetofriction,wedgesetandelasticityoftheconcretecanbecompensated,astherequiredstressofthetendonstoachievecompletecompensationexceeds the values allowed by the standards. Consequently, the tendons have beenoverstressedduringanchoringuntilthemaximumpermittedbyEHE-08(1488N/mm2).The final pre-stressed system consists of 6 tendons of 15 strands each. Three of thementionedtendonsrunalongthewholestructure.Theybeginatthetopofthetower,theyturnatthetapatthebottomofthefloaterandtheygettothetopofthetoweragain.Theotherthreetendonsstartatthesectionatwhichthepre-stressingforceafterdirectlossesisreduced to thehalf in the tower. This criterionhasbeen followed forbotheconomicandtechnicalreasons–first,becausetherewasa largeamountofpre-stressingsteelthatwasnot actually needed due to the lower solicitation and second, because the minimumdistancesbetweenductsstablishedbytheEHE-08werenotsatisfied.In order to anchor the shorter tendons, an additional thickness is introduced in the innerpartof thewall thicknessof thestructure,startingat thebeginningof thetoweruntil thementioned intermediate section of it. The anchorages take part of a steel ring, throughwhichthestressesaretransmittedtotheconcrete.Thismechanismisalsousedinthetopsectionofthetower,wherethereareadditionallyplacedboltedconnectionstoimplementtheturbine.For thedesignof thestructure, sufficient resistancemustbeguaranteedtocopewith thetwo critical situations. For this reason, in parallel to the operational state, it has beenchecked that there is sufficient resistance toassume thebendingdue to the liftingof the

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cranes during the stevedoring operations. For this second critical situation, the resistancehas alsobeen checked for SLS, but at short term (t=0), since theoperationdoesnot takelongtime.ThestevedoringoperationsarecarriedoutbytwoLiebherrLHM800cranes–oneholdsthefloaterandtheother,thetower.Therehavebeendeterminedthepositionswheretheymustbelocatedtoguaranteestability.Thefinalconsiderationsatisfiestheconditionsimposed: minimum difference of weight lifted by each crane and stress limitations (notensilestressesinthestructureandcompressionsnotexceeding0.45fck.Ithasbeenpossibletheuseofthesamecranemodelforbothcranes.Accordingtothebudget,itisremarkabletheimportantinfluencethatthesubmarinecablesof connection to the hinterland grid has in the total expenses. The price per meter ofsubmarine cable can reach 1000 euros. This means that if the FOWT is supposed to beinstalledat40kmoffthecoastofTarragona,justthecostofthesubmarinecablesrisesto4millioneuros.Thisamountdemonstratesthe longpath in termsof reductionofcosts thatthe sector must go over in the future. The other units that increment noticeably theexpensesare the catenarymooring linesand the suctionpiles.However, theyare far lesstranscendentthanthesubmarinecables.Sinceitisapreliminarydesignandtheobjectiveoftheprojectistocheckifthestructurecanresist the external loads, the cables of connection to the grid are not considered in theproject.Verylowlevelsofproductionareachieved,asthecapacityoftheturbineisjust100kW.No feasibility canbeobtainedat thementioned lowpower.Alternatively, therehavebeenusedresistancestogiveofftheenergyproducedinformofhead,inordertoavoidthelargeexpensescarriedbytheinstallationofsubmarinecables.8.2 FinaloverviewThe complexityof theprojecthas lied first in themodelingof theproblemand second insatisfyingseveralboundaryconditionssimultaneously. InSLS, ithasbeenobservedthattodetermine the design pre-stressing force, the critical section is not necessary the oneaffected by the highest external action. It can occur that due to the direct losses that asection suffers, the minimum force after losses required to satisfy the conditions is notachieved.InULS,ithasbeennoticedthatnotonlyisfundamentaltodesignastructurethatresiststhesolicitations,but it isalso importanttoobtainaductileruptureincaseULSisreached.Forthisreason,ithasbeencheckedateverysectionthatthestrainofthesteelinULSislowerthantheultimatestrain.For the success in the realization of the project it has been fundamental the use of theknowledge acquired during the Bachelor in Civil Engineering. The tools needed to solveeveryproblemthatappearsintheprojectmustbedominated.Particularlyforthisprojectithasbeencheckedthatstructuraltheoryis importanttodoaproperdesign,butalsobeingfamiliarwith powerful computational software – i. e.Matlab in this case – facilitates thecalculationprocedurestogettothesolution.

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9 References1. National Commission on the BP Deepwater Horizon Oil Spill and Offshore Drilling. ABrief History of Offshore Oil Drilling. [Online] September 2010.http://web.cs.ucdavis.edu/~rogaway/classes/188/materials/bp.pdf.2. IInternational Renewable EnergyAgency. InnovationOutlook -OffshoreWind. IRENA .AbuDhabi:s.n.,2016.3. Google Maps. Google Maps. [Online]https://www.google.nl/maps/@40.7875473,2.0802352,8.61z.4.EuropeanWienEnergyAssociation.Deepwater-Thenextstepforoffshorewindenergy.s.l.:EuropeanWindEnergyAssociation,2013.5.Campos, A., et al. Spar concretemonolithic design for offshorewind turbines. s.l.: ICEpublishing,2014.6.MolenaarW.andVoorendtM.HydraulicStructures.s.l.:TUDelft,2017.7.Neville, A. Top Plants: Hywind FloatingWind Turbine, North Sea, Norway. Powermag.[Online] 12 January 2009. http://www.powermag.com/top-plants-hywind-floating-wind-turbine-north-sea-norway/.8. Statoil. Statoil. HyWind installation. [Online] April 2017.https://www.statoil.com/en/what-we-do/new-energy-solutions.html.9. Maritime Research Institute Netherlands. Ships & Structures: TLP. MARIN. [Online]http://www.marin.nl/web/Ships-Structures/Offshore-structures/TLP.htm.10.VanderZee,T.Floatingwindturbines:apromisingstart.TijdoVanderZee.[Online]May2016.https://tijdovanderzee.com/2016/05/16/floating-wind-turbines-a-promising-start/.11.Matzat, G.. AdvancedOffshoreWind Tech: Accelerating NewOpportunities for CleanEnergy.Energy.[Online]May2014.semi-submersiblewindturbinestriangular.12.Macguire,E.Floatingoffshorewindturbinespotential.CNN.June2012.13.Offshore4C.NewEnglandAquaVentusIOffshoreWindFarm.Maine:4COffshore.14. Principle Power, Inc. Principle Power. [Online] 2017.http://www.principlepowerinc.com.15.Ishihara,T.FukushimaFloatingOffshoreWindFarmDemonstrationProject.DepartmentofCivilEngineering.UniversityofTokyo,FukushimaOffshoreWindConsortium.Tokyo:s.n.,2015.16.Molins,C.andGironella,X.Windcrete.US20150308068A12009.17. International WindTech. A Monolithic Concrete Platform for Floating Offshore WindTurbines. Windcrete. [Online] January 2016. https://www.windtech-international.com/editorial-features/windcrete.18.(FIB)InternationalFederationforStructuralConcrete.DurabilityofConcreteStructuresintheNorthSea.s.l.:FIB.19.Holand, I., Gudmestad, O. and Jersin, E.Design of Offshore Concrete Structures. s.l.:Taylor&Francis,2003.20.Hughes,P.ProceedingsoftheInstitutionofCivilEngineers-MaritimeEngineering.s.l.:ICEpublishing,2013.21.Chakrabarti,S.HandbookofOffshoreEngineering.s.l.:Elsevier,2005.22.ClimentMolins,etal.EfficientPreliminaryFloatingOffshoreWindTurbineDesignandTesting Methodologies and Application to a Concrete Spar Design. s.l.: PhilosophicalTransactionsoftheRoyalSocietyA,2015.23.Ligteringen,H.PortsandTerminals.Delft:TUDelft,2012.

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24. Gas Natural Fenosa. AFOSP. Gas Natural Fenosa. [Online]http://www.gasnaturalfenosa.com/en/activities/innovation/projects/1297281184076/afosp.html.25.Molins,C.etal.A3DFEMmodelforwindturbinesupportstructures.EscoladeCamins,UPCBarcelonaTech.2017.26.DetNorskeVeritas.DesignofOffshoreWindTurbineStructures.DNV.Oslo:s.n.,2014.27. DNV-RP-C205, Recommended Practice. Environmental Conditions and EnvironmentalLoads. Recommended Practice DNV-RP-C205. [Online] April 2007.https://rules.dnvgl.com/docs/pdf/DNV/codes/docs/2007-10/RP-C205.pdf.28.DesignBasis(K13ShallowWaterSite)–UpWindWP4.29.MinisteriodeFomentodelGobiernodeEspaña.PuertosdelEstado.PuertosdelEstado.[Online]http://www.puertos.es/es-es.30. (GL-COWT) Germanischer Lloyd. Guideline for the Certification of Offshore WindTurbines,RulesandGuidelines, IV- IndustrialServices,Part2GuidelinefortheCertificationofOffshoreWindTurbines.2005.Vol.2.31.GLAS,DNV.DNVGL-ST-0437Loadsandsiteconditionsforwindturbines(2016).s.l.:DNV,2016.32. Department of Civil Engineering of The University of Memphis. High-PerformanceConcrete.Memphis:s.n.33.JCWalravenandCRBraam.PrestressedConcrete.Delft:TUDelft,2015.34.VSL.VSL–Post-TensioningSolutions.VSL.2015.35.MinisteriodeEconomíayHacienda.Textorefundidode laLeydeContratosdelSectorPúblico.GobiernodeEspaña,BoletínOficialdelEstado(BOE).2015.36.RIBSpain.Costesindirectosycostesgenerales.Madrid:s.n.,2016.37.Ministeriode FomentodelGobiernode España. InstruccióndelHormigónEstructuralEHE-08.MinisteriodeFomento,GobiernodeEspaña.38. Norvento. Norvento nED100 Wind Turbine. Renewables First. [Online] 2015.http://www.renewablesfirst.co.uk/windpower/wind-turbines/norvento-ned100-100-kw-wind-turbine/.39.Walraven,JC.andBraam,CR.PrestressedConcrete.Delft:TUDelft,2015.40. Walraven, JC. Eurocode 2: Design of concrete structures EN1992-1-1. SymposiumEurocodes: Backgrounds and applications. [Online] February 2008.http://eurocodes.jrc.ec.europa.eu/doc/WS2008/EN1992_1_Walraven.pdf.41. Terrel, W. Física: teoría y práctica. SlideShare. [Online] February 2015.https://es.slideshare.net/aritmetica2000/fsica-teora-y-prctica-walter-prez-terrel.42. LHM, Liebherr LHM 800. Mobile Harbour Crane. Mobile Harbour Crane LHM 800.Liebherr. [Online] 2012. https://www.liebherr.com/external/products/products-assets/258831/liebherr-lhm-800-mobile-harbour-crane-datasheet-english.pdf.43.PuertodeTarragona.PuertodeTarragona.ThemifyWordPressThemes.[Online]2017.http://www.porttarragona.es/puerto-comercial/.44.Trubat,P.Procedimentsconstructius imaterialsperaestructuresoff-shore.Aplicacióaaerogeneradors. Enginyeria de la Construcció, Universitat Politècnica de Catalunya.Barcelona:s.n.,2012.45.Molenaar,WF.andVoorendt,M.ManualHydraulicStructures.Delft:TUDelft.pp.186-190.46. iTeC. Metabase iTeC. Banc BEDEC. [Online] 2017. https://itec.cat/banc-preus-bedec/partides-obra-enginyeria-civil/index-a7.html.

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47.Campos,A.Projectebàsicd’estructura flotant”SPAR”de formigóal litoralMediterraniper al suport d’un aerogenerador de 5MW. Departament d'Enginyeria Civil i Ambiental,UniversitatPolitècnicadeCatalunya.s.l.:UPC,2012.48. Aissaoui, A. Research Gate. Spar Floating Platforms. [Online]https://www.researchgate.net/profile/Adel_Adelbatna/publication/310870167_new_design_aspar_platform/links/583aad8c08ae3a74b49ee929.pdf?origin=publication_list.49. Aqua Ventus. Tapping into Maine’s maritime heritage and natural wind resource toadvance clean, domestic energy while strengthening coastal economies. Aqua Ventus -Maine.[Online]2017.http://maineaquaventus.com.50.Molins, C. et al.Windcrete: concrete floating platforms forwind turbines.Windcrete.[Online]2009.http://www.windcrete.com.51.Campos,A.,etal.ExperimentalRAO’sAnalysisofaMonolithicConcreteSPARStructureforOffshoreFloatingWindTurbines.ASME201534th InternationalConferenceonOcean,OffshoreandArcticEngineering.s.l.:ASME,2015.52.SematH.andKatz,R.Physics:Hydrodynamics(FluidsinMotion).s.l.:DigitalCommons,1958.53. Graham Wallis, B. Added mass. Thermopedia. [Online] February 2011.http://thermopedia.com/content/289/.54.Kato,N.andTullis,T.RadiationDampingasApproximationtoInertialTermforDynamicSlip. Radiation Damping. [Online] July 2000.http://www.geo.brown.edu/faculty/ttullis/Radiation_Damping.htm.55. Campos, A. et al. Analysis of Strutural Second Order Effects on a Floating ConcretePlatformforFOWT's.s.l.:Elsevier,2016.56. Maritime Research Institute Netherlands. Green Water Loads. MARIN. [Online]http://www.marin.nl/web/Research-Topics/Loads-responses/Green-water-loads.htm.57. MARIN. Seakeeping. [Online] http://www.marin.nl/web/Organisation/Business-Units/Ships/Seakeeping.htm.58.Williamson,C.H.K. andGovardhan,R.Vortex-InducedVibrations. s.l.: AnnualReviews,January2004,AnnualreviewofFluidMechanics.59.Bailey,H.,Brookes,L.andThompson,P.AssessingEnvironmental ImpactsofOffshoreWind Farms: Lessons Learned and Recommendations for the Future. s.l.: Research Gate,2014.60. Thanh-Toan, T. and Dong-Hyun, K. The platform pitchingmotion of floating offshorewindturbine:Apreliminaryunsteadyaerodynamicanalysis.s.l.:Elsevier,2015.61. Härer, A. et al. Optimisation of Offshore Wind Turbine Components in Multi-BodySimulations for Cost and Load Reduction. Proceedings of the EWEA Offshore. Brussels:EuropeanWindEnergyAssociation,2013.62.ANSYSAQWA.ANSYS.[Online]http://www.ansys.com/products/structures/ansys-aqwa.63.Sandner,F.etal.ReducedNonlinearModelofaSpar-MountedFloatingWindTurbine.Proceedings of the GermanWind Energy Conference (DEWEK 2012). Bremen: DeutschesWindenergie-Institut,2012.64. Grupen, R. Newton-Euler Equations. Robotics. [Online] 2007. http://www-robotics.cs.umass.edu/~grupen/603/slides/DynamicsII.pdf.65. DNVGL-RP-C104, Recommended Practice. Self-Elevating Units. DNVGL. [Online] July2015.https://rules.dnvgl.com/docs/pdf/dnvgl/RP/2015-07/DNVGL-RP-C104.pdf.66. BMT Fluid Mechanics. Wave Period Data. Global Wave Statistics. [Online] 2011.http://www.globalwavestatisticsonline.com/Help/period_data.htm.

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67.Trubat,P.ProcedimentsConstructius iMaterialsperaEstructuresOffshore.AplicacióaAerogeneradors.Barcelona:s.n.,2012.68.Sandner,F.etal.Integratedoptimizationoffloatingwindturbinesystems.ProceedingsoftheASME201433rdInternationalConferenceonOcean,OffshoreandArcticEngineering(OMAE2014).NewYork:s.n.,2014.69.Molenaar,W.andVoorendt,M.ManualHydraulicStructures.Delft:TUDelft,2017.p.282.70.Burg,RG.andOst,BW.EngineeringPropertiesofCommerciallyAvailableHigh-StrengthConcretes.PortlandCementAssociation.s.l.:ResearchandDevelopmentBulletin,1994.p.62.RD104.71. Wijdeven, B. Planning and design of port water areas. Department of HydraulicEngineering,TUDelft.2016.72.Arquimedes.PrincipleofArquimedes.Buoyancyforce.73. Campos, A. Projecte bàsic d’estructura flotant ”SPAR” de formigó Annex 8 Estudid’impacte ambiental al litoral Mediterrani per al suport d’un aerogenerador de 5MW.Departament d'enginyeria Civil i Ambiental, Unuversitat Politècnica de Catalunya.Barcelona:s.n.,2012.74.Buzzle.ContinentalShelf:ALabeledDiagramandSomeInterestingFacts.Buzzle.[Online]2016.http://www.buzzle.com/articles/facts-about-the-continental-shelf-with-diagram.html.75.Liebherr.MobileHarbourCraneLiebherrLHM600.Liebherr.2017.76.VSL.Multi-strandtendonpropertiesforpost-tensionedsteel.VSL.2017.77.VSL.VSL-Post-tensioningsolutions.VSL.2017.78.Inc,PrinciplePower.[Online]April2017.http://www.principlepowerinc.com.79.VSL.StrandandTendonProperties.VSLMultistrandSystems.2017.80. WBR. Sheaths for Prestressed Concrete. WBR. [Online] http://wbr-rohre.de/en/products-construction/sheaths-for-prestressed-concrete/accessories/.

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10 Appendix10.1 Appendix1:Pre-stressingsteeldesign.Operationalstate(SeaSevereState,wind

speedatrated)10.1.1 Direct losses, time-dependent losses.Pre-stressing forceafterdirect lossesandpre-

stressingforceatlongterm(SLS)

x[m] ∆,-[kN]∆,./[kN]

∆,01[kN] ∆,232[kN] ,4[kN]

∆,256[kN] ,7[kN]

0.498 7.9 1235.8 5769.4 7013.1 11736.0 358.6 11377.41.494 23.6 1235.8 5215.0 6474.4 12274.0 359.3 11914.72.49 39.3 1235.8 4757.8 6032.9 12716.0 360.0 12356.03.485 55.0 1235.8 4374.4 5665.2 13084.0 360.5 12723.54.481 70.6 1235.8 4048.1 5354.5 13394.0 360.9 13033.15.477 86.2 1235.8 3767.1 5089.1 13660.0 361.3 13298.76.473 101.8 1235.8 3522.6 4860.2 13889.0 361.7 13527.37.469 117.4 1235.8 3307.9 4661.1 14088.0 362.0 13726.08.465 132.9 1235.8 3117.9 4486.6 14262.0 362.2 13899.89.46 148.4 1235.8 2948.5 4332.7 14416.0 362.5 14053.510.456 163.9 1235.8 2796.6 4196.3 14553.0 362.7 14190.311.452 179.3 1235.8 2659.5 4074.6 14674.0 362.9 14311.112.448 194.7 1235.8 1577.6 3008.1 15741.0 364.4 15376.613.444 225.9 1235.8 1566.0 3027.7 15721.0 724.4 14996.614.44 256.9 1235.8 1570.8 3063.5 15685.0 724.4 14960.615.435 288.0 1235.8 1587.5 3111.3 15638.0 724.3 14913.716.431 318.9 1235.8 1612.2 3166.9 15582.0 724.2 14857.817.427 349.8 1235.8 1641.1 3226.7 15522.0 724.0 14798.018.423 380.7 1235.8 1670.3 3286.8 15462.0 723.8 14738.219.419 411.5 1235.8 1695.3 3342.6 15406.0 723.7 14682.320.415 442.2 1235.8 1711.8 3389.8 15359.0 723.6 14635.421.41 472.9 1235.8 1715.6 3424.3 15325.0 723.6 14601.422.406 503.5 1235.8 1703.0 3442.3 15306.0 723.7 14582.323.402 534.1 1235.8 1672.0 3441.9 15307.0 723.8 14583.224.4 992.5 1742.7 1523.5 4258.7 14490.0 724.7 13765.325.4 1022.3 1742.7 1321.8 4086.8 14662.0 725.8 13936.226.4 1052.1 1742.7 1167.3 3962.1 14787.0 726.7 14060.327.4 1081.8 1742.7 1045.2 3869.7 14879.0 727.4 14151.628.4 1111.4 1742.7 946.2 3800.3 14948.0 727.9 14220.129.4 1141.1 1742.7 864.3 3748.1 15001.0 728.4 14272.630.4 1170.6 1742.7 795.4 3708.7 15040.0 728.8 14311.231.307 1197.4 2518.5 765.0 4480.9 14268.0 728.9 13539.132.121 1221.4 2518.5 765.0 4504.9 14244.0 728.9 13515.1

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32.934 1245.3 2518.5 765.0 4528.8 14220.0 728.9 13491.133.748 1269.2 2518.5 765.0 4552.7 14196.0 728.9 13467.134.562 1293.1 2518.5 765.0 4576.6 14172.0 728.9 13443.135.376 1316.9 2518.5 765.0 4600.4 14148.0 728.9 13419.136.189 2236.8 2518.5 765.0 5520.3 13229.0 728.9 12500.137.003 2259.3 2518.5 765.0 5542.8 13206.0 728.9 12477.137.817 2281.7 2518.5 765.0 5565.2 13184.0 728.9 12455.138.631 2304.1 2518.5 765.0 5587.6 13161.0 728.9 12432.139.444 2326.5 2518.5 765.0 5610.0 13139.0 728.9 12410.140.258 2348.8 2518.5 765.0 5632.3 13117.0 728.9 12388.141.072 2371.1 2518.5 765.0 5654.6 13094.0 728.9 12365.141.886 2393.3 2518.5 765.0 5676.8 13072.0 728.9 12343.142.699 2415.6 2518.5 765.0 5699.1 13050.0 728.9 12321.143.513 2437.7 2518.5 765.0 5721.2 13028.0 728.9 12299.144.327 2459.9 2518.5 765.0 5743.4 13005.0 728.9 12276.145.141 2482.0 2518.5 765.0 5765.5 12983.0 728.9 12254.145.954 2504.1 2518.5 765.0 5787.6 12961.0 728.9 12232.146.768 2526.2 2518.5 765.0 5809.7 12939.0 728.9 12210.147.582 2548.2 2518.5 765.0 5831.7 12917.0 728.9 12188.148.396 2570.2 2518.5 765.0 5853.7 12895.0 728.9 12166.149.209 2592.2 2518.5 765.0 5875.7 12873.0 728.9 12144.150.023 2614.1 2518.5 765.0 5897.6 12851.0 728.9 12122.150.837 2636.0 2518.5 765.0 5919.5 12829.0 728.9 12100.151.651 2657.9 2518.5 765.0 5941.4 12807.0 728.9 12078.152.464 2679.7 2518.5 765.0 5963.2 12786.0 728.9 12057.153.278 2701.5 2518.5 765.0 5985.0 12764.0 728.9 12035.154.092 2723.3 2518.5 765.0 6006.8 12742.0 728.9 12013.154.906 2745.0 2518.5 765.0 6028.5 12720.0 728.9 11991.155.719 2766.7 2518.5 765.0 6050.2 12699.0 728.9 11970.156.533 2788.4 2518.5 765.0 6071.9 12677.0 728.9 11948.157.347 2810.1 2518.5 765.0 6093.6 12655.0 728.9 11926.158.161 2831.7 2518.5 765.0 6115.2 12634.0 728.9 11905.158.974 2853.3 2518.5 765.0 6136.8 12612.0 728.9 11883.159.788 2874.8 2518.5 765.0 6158.3 12591.0 728.9 11862.160.602 2896.3 2518.5 765.0 6179.8 12569.0 728.9 11840.161.416 2917.8 2518.5 765.0 6201.3 12548.0 728.9 11819.162.229 2939.3 2518.5 765.0 6222.8 12526.0 728.9 11797.163.043 2960.7 2518.5 765.0 6244.2 12505.0 728.9 11776.164.05 2987.2 2518.5 161.7 5667.4 13082.0 732.4 12349.6

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10.1.2 ResultsoftheULScheck10.1.2.1 CheckoftheresistancetobendingofthestructureinULS

x[m] 896[kNm] 8:6[kNm] 8:6 ≥ 8960.498 6.00E+04 5.55E+06 TRUE1.494 1.34E+05 6.14E+06 TRUE2.49 2.24E+05 6.73E+06 TRUE3.485 3.31E+05 7.33E+06 TRUE4.481 4.57E+05 7.93E+06 TRUE5.477 6.03E+05 8.52E+06 TRUE6.473 7.70E+05 9.12E+06 TRUE7.469 9.59E+05 9.72E+06 TRUE8.465 1.17E+06 1.03E+07 TRUE9.46 1.41E+06 1.09E+07 TRUE10.456 1.67E+06 1.15E+07 TRUE11.452 1.95E+06 1.21E+07 TRUE12.448 2.27E+06 1.03E+07 TRUE13.444 2.61E+06 1.13E+07 TRUE14.44 2.98E+06 1.23E+07 TRUE15.435 3.38E+06 1.32E+07 TRUE16.431 3.81E+06 1.42E+07 TRUE17.427 4.27E+06 1.50E+07 TRUE18.423 4.76E+06 1.59E+07 TRUE19.419 5.28E+06 1.67E+07 TRUE20.415 5.84E+06 1.75E+07 TRUE21.41 6.43E+06 1.82E+07 TRUE22.406 7.06E+06 1.90E+07 TRUE23.402 7.72E+06 1.96E+07 TRUE24.4 8.40E+06 2.16E+07 TRUE25.4 8.99E+06 2.50E+07 TRUE26.4 9.54E+06 2.84E+07 TRUE27.4 1.00E+07 3.18E+07 TRUE28.4 1.05E+07 3.54E+07 TRUE29.4 1.09E+07 3.88E+07 TRUE30.4 1.13E+07 4.26E+07 TRUE31.307 1.16E+07 4.46E+07 TRUE32.121 1.17E+07 4.47E+07 TRUE32.934 1.18E+07 4.49E+07 TRUE33.748 1.19E+07 4.50E+07 TRUE34.562 1.19E+07 4.52E+07 TRUE35.376 1.19E+07 4.53E+07 TRUE

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36.189 1.18E+07 4.55E+07 TRUE37.003 1.17E+07 4.57E+07 TRUE37.817 1.16E+07 4.58E+07 TRUE38.631 1.14E+07 4.60E+07 TRUE39.444 1.12E+07 4.62E+07 TRUE40.258 1.10E+07 4.71E+07 TRUE41.072 1.08E+07 4.73E+07 TRUE41.886 1.05E+07 4.75E+07 TRUE42.699 1.02E+07 4.76E+07 TRUE43.513 1.00E+07 4.78E+07 TRUE44.327 9.68E+06 4.87E+07 TRUE45.141 9.50E+06 4.89E+07 TRUE45.954 9.30E+06 4.91E+07 TRUE46.768 9.07E+06 4.93E+07 TRUE47.582 8.81E+06 4.95E+07 TRUE48.396 8.53E+06 4.96E+07 TRUE49.209 8.22E+06 4.98E+07 TRUE50.023 7.88E+06 5.00E+07 TRUE50.837 7.52E+06 5.05E+07 TRUE51.651 7.14E+06 5.06E+07 TRUE52.464 6.73E+06 5.08E+07 TRUE53.278 6.29E+06 5.10E+07 TRUE54.092 5.82E+06 5.12E+07 TRUE54.906 5.33E+06 5.14E+07 TRUE55.719 4.81E+06 5.16E+07 TRUE56.533 4.26E+06 5.18E+07 TRUE57.347 3.69E+06 5.19E+07 TRUE58.161 3.08E+06 5.21E+07 TRUE58.974 2.45E+06 5.26E+07 TRUE59.788 1.83E+06 5.33E+07 TRUE60.602 1.30E+06 5.42E+07 TRUE61.416 8.61E+05 5.50E+07 TRUE62.229 5.15E+05 5.58E+07 TRUE63.043 2.58E+05 5.67E+07 TRUE64.05 9.10E+04 2.63E+07 TRUE

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10.1.2.2 CheckofthestraininthesteelatULS(ductilefracture)

x[m] <=>[N/mm2] <=> ≤ <>@ = 4. 4BC0.498 0.0021 TRUE1.494 0.0025 TRUE2.49 0.0029 TRUE3.485 0.0033 TRUE4.481 0.0036 TRUE5.477 0.004 TRUE6.473 0.0044 TRUE7.469 0.0048 TRUE8.465 0.0052 TRUE9.46 0.0055 TRUE10.456 0.0059 TRUE11.452 0.0063 TRUE12.448 0.0018 TRUE13.444 0.0024 TRUE14.44 0.0032 TRUE15.435 0.004 TRUE16.431 0.0048 TRUE17.427 0.0058 TRUE18.423 0.0067 TRUE19.419 0.0076 TRUE20.415 0.0085 TRUE21.41 0.0093 TRUE22.406 0.01 TRUE23.402 0.0106 TRUE24.4 0.0117 TRUE25.4 0.0135 TRUE26.4 0.0153 TRUE27.4 0.017 TRUE28.4 0.0187 TRUE29.4 0.0203 TRUE30.4 0.0219 TRUE31.307 0.0227 TRUE32.121 0.0227 TRUE32.934 0.0227 TRUE33.748 0.0227 TRUE34.562 0.0227 TRUE35.376 0.0227 TRUE36.189 0.0227 TRUE37.003 0.0227 TRUE

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37.817 0.0227 TRUE38.631 0.0227 TRUE39.444 0.0227 TRUE40.258 0.0227 TRUE41.072 0.0227 TRUE41.886 0.0227 TRUE42.699 0.0227 TRUE43.513 0.0227 TRUE44.327 0.0227 TRUE45.141 0.0227 TRUE45.954 0.0227 TRUE46.768 0.0227 TRUE47.582 0.0227 TRUE48.396 0.0227 TRUE49.209 0.0227 TRUE50.023 0.0227 TRUE50.837 0.0227 TRUE51.651 0.0227 TRUE52.464 0.0227 TRUE53.278 0.0227 TRUE54.092 0.0227 TRUE54.906 0.0227 TRUE55.719 0.0227 TRUE56.533 0.0227 TRUE57.347 0.0227 TRUE58.161 0.0227 TRUE58.974 0.0227 TRUE59.788 0.0227 TRUE60.602 0.0227 TRUE61.416 0.0227 TRUE62.229 0.0227 TRUE63.043 0.0227 TRUE64.05 0 TRUE

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10.2 Appendix2:Pre-stressingsteeldesign.Stevedoringoperations10.2.1 Bendingmomentateachsectionofthestructure,fortheoptimalcombinationofm,n

(m=3meters,n=20meters)

x[m] M[kNm]0 01 -2322 -5623 -9904 8755 26416 43097 58808 73529 872610 1000311 1118112 1226113 1324314 1412815 1491416 1560217 1619218 1668419 1707920 1737521 1757322 1767323 1767524 1757925 1738526 1709427 1670428 1621629 1563030 1494631 1416432 1328433 1230634 1123035 10058

111

36 879737 745538 603939 455840 301841 142642 -21043 -189144 -361545 -454646 -396447 -342848 -293849 -249450 -209851 -175052 -145053 -119854 -97555 -77956 -60857 -46258 -33959 -23760 -15561 -9262 -4763 -1764 -3

64.65 0

112

10.2.2 Checkofthestressesinthestructureatshortterm(SLS)

D[N/mm2] D ≥ −FG. HC D ≤ 4-1.112 TRUE TRUE-5.315 TRUE TRUE-5.392 TRUE TRUE-5.493 TRUE TRUE-5.055 TRUE TRUE-4.641 TRUE TRUE-4.249 TRUE TRUE-3.88 TRUE TRUE-3.535 TRUE TRUE-3.212 TRUE TRUE-2.912 TRUE TRUE-2.636 TRUE TRUE-2.382 TRUE TRUE-2.152 TRUE TRUE-1.944 TRUE TRUE-1.76 TRUE TRUE-1.598 TRUE TRUE-1.46 TRUE TRUE-1.344 TRUE TRUE-1.251 TRUE TRUE-1.182 TRUE TRUE-1.135 TRUE TRUE-1.112 TRUE TRUE-1.111 TRUE TRUE-1.134 TRUE TRUE-1.179 TRUE TRUE-1.248 TRUE TRUE-1.339 TRUE TRUE-1.454 TRUE TRUE-1.592 TRUE TRUE-1.752 TRUE TRUE-1.936 TRUE TRUE-2.142 TRUE TRUE-2.372 TRUE TRUE-2.621 TRUE TRUE-2.915 TRUE TRUE-3.311 TRUE TRUE-3.853 TRUE TRUE-4.612 TRUE TRUE

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-5.712 TRUE TRUE-7.376 TRUE TRUE-9.762 TRUE TRUE-11.928 TRUE TRUE-14.289 TRUE TRUE-16.915 TRUE TRUE-18.613 TRUE TRUE-18.014 TRUE TRUE-17.371 TRUE TRUE-16.719 TRUE TRUE-16.092 TRUE TRUE-15.525 TRUE TRUE-15.054 TRUE TRUE-14.722 TRUE TRUE-21.763 TRUE TRUE-22.337 TRUE TRUE-23.008 TRUE TRUE-23.791 TRUE TRUE-24.711 TRUE TRUE-25.795 TRUE TRUE-27.08 TRUE TRUE-28.617 TRUE TRUE-30.471 TRUE TRUE-32.736 TRUE TRUE-35.541 TRUE TRUE-39.079 TRUE TRUE-41.901 TRUE TRUE

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10.3 Appendix3:Matlabcodeforthecalculationofthepre-stressingdesignclc; close all; clear all; %------------------ Prestressing design ----------------- %% Main characteristics of the section % We work in Newtons (N) and millimeters (mm) l_f = 33.75*1000; % Length of the floater (mm) l_trans = 7*1000; % Length of the transition piece (mm) l_draft = l_f + l_trans; % Draft of the FOWT (mm) l_t = 23.9*1000; % Length of the tower (mm) l = l_f + l_trans + l_t; % Total length of the FOWT (mm) R_f = 2.43*1000; % External radius of the floater (mm) t_f = 0.272*1000;% Thickness of the floater walls (mm) R_tb = 1.2*1000; % External radius of the bottom of the tower (mm) R_tt = 0.424*1000; % Thickness of the tower walls (mm) t_t = 0.272*1000; % Thickness of the tower walls (mm) % Concrete properties gamma_c = 25/(10^6); % Specific weight of the concrete (N/mm3) f_ck = 95; % Characteristic resistance of the concrete (N/mm2) CHANGED sf_c_SLS = 1.0; % Safety factor of the concrete in SLS(-) sf_c_ULS = 1.5; % Safety factor of the concrete in ULS(-) f_cd = f_ck/sf_c_ULS; % design resistance of the concrete (N/mm2) E_c = 36000; % Young modulus of the concrete (N/mm2) eps_cu = 3.5/1000; % Strain of the concrete at ULS (-) % Pre-stressing steel properties f_p_max = 1860; % Characteristic resistance of the steel (N/mm2) sf_s_SLS = 1.0; % Safety factor of the steel in SLS (-) sf_s_ULS = 1.15; % Safety factor of the steel in ULS (-) f_pu = f_p_max/sf_s_ULS; % Design stress (real branch) (N/mm2) f_pk1 = 1674; % 0.1% fractile (N/mm2) f_pd = f_pk1/sf_s_ULS; % Design stress of the steel (N/mm2) sigma_p0max = min(0.75*f_p_max,0.85*f_pk1); % Maximum pre-stressing force after tensioning (N/mm2) sigma_pmax = min(0.8*f_p_max,0.9*f_pk1); % Maximum pre-stressing force during tensioning (N/mm2) E_p = 195000; % Young Modulus of the steel (N/mm2) eps_uk = 35/1000; % Characteristic strain of the steel at ULS A_strand = 140; % Area of a strand (mm2) for Y1860S7 % Safety factors in SLS (according to EHE 08) sf_E_sls = 1.0; % Safety factor for the permanent loads in SLS (favourable or unfavourable) (-) sf_p_fav_sls = 0.9; % Safety factor for the favourable action of prestressing steel in SLS (-) sf_p_unfav_sls = 1.1; % Safety factor for the unfavourable action of prestressing steel in SLS (-) % Safety factors in ULS (according to EHE 08)

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sf_p_uls = 1.0; % Safety factor for the action of prestressing steel in ULS (favourable or unfavourable) (-) sf_E_fav_uls = 1.0; % Safety factor for the permanent favourable loads in ULS(-) sf_E_unfav_uls = 1.35; % Safety factor for the permanent unfavourable loads in ULS (-) % We import the Excel where the bending moments are provided ext1 = xlsread('Norvento_Internal_Forces.xlsx'); % We read the first column, that corresponds to the length coordinates (mm) % We will work in rows --> we transpose the column x = (ext1(:,1)*1000)'; N = (ext1(:,2))'; % Axial force due to selfweight (N) M = (ext1(:,11)*1000)'; % Norm of My and Mz (Nmm) % Radius and wall thickness of each section R = zeros(1,72); t = zeros(1,72); for i = 1:72 if x(i) <= l_f R(i) = R_f; t(i) = t_f; elseif l_f < x(i) && x(i) <= l_draft R(i) = R_f-(R_f-R_tb)/l_trans*(x(i)-l_f); t(i)=t_f; else R(i) = R_tb-(R_tb-R_tt)/l_t*(x(i)-l_draft); if l_f < x(i) && x(i) <= x(60) % Extension function: y = 20.91*sqrt(x) slope_tower_vert = l_t/(R_tb-R_tt); add_t = 0.272*1000; % (x(60)-l_draft)/slope_tower_vert; % Additional thickness to put the anchor plate ? intermediate section tower (mm) ctt = (x(60)-l_draft)/sqrt(add_t); t(i) = t_f + ((x(i)-l_draft)/ctt)^2; else t(i)=t_t; end end end t(1) = R_f; % The bottom tap is completely solid A_conc_comp = zeros(1,72); % Area of concrete for each section (mm2) for i = 1:72 A_conc_comp(i) = pi*(R(i)^2-(R(i)-t(i))^2); end I = zeros(1,72); % Second moment of area (mm4) for i = 1:72 I(i) = pi*(R(i)^4-(R(i)-t(i))^4)/4; end W = I./R; % Section modulus (mm3) %% Prestressing forces: upper and lower bounds (SLS) [flotador y torre] % t = 0 --> -Pm0/A_c+M/W-N/A_c = sigma_tens <= 0 Pm0 = zeros(1,72); for i = 1:72

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Pm0(i) = (sf_E_sls*M(i)*A_conc_comp(i)/W(i)-sf_E_sls*N(i))/sf_p_fav_sls; % Possible lower bound of the prestressing force end % ------------------------------------------------------------------ % t = 0 --> -Pm0fat/A_c-M/W-N/A_c = sigma_comp => -0.45*f_ck Pm0fat = zeros(1,72); for i = 1:72 Pm0fat(i) = (0.45*f_ck*A_conc_comp(i)-sf_E_sls*N(i)-sf_E_sls*M(i)*A_conc_comp(i)/W(i))/sf_p_unfav_sls; % Possible upper bound of the prestressing force (N) end % ------------------------------------------------------------------ % t->inf --> -Pinf/A_c-M/W-N/A_c = sigma_comp => -0.45*f_ck Pinf_comp = zeros(1,72); for i = 1:72 Pinf_comp(i) = (0.45*f_ck*A_conc_comp(i)-sf_E_sls*M(i)*A_conc_comp(i)/W(i)-sf_E_sls*N(i))/(0.82*sf_p_fav_sls); % Possible upper bound of the prestressing force (N) end % ------------------------------------------------------------------ % t->inf --> -Pinf/A_c+M/W-N/A_c = sigma_tens <= 0 (TENSION) % Pinf_tens = zeros(1,72); for i = 1:72 Pinf_tens(i) = (sf_E_sls*M(i)*A_conc_comp(i)/W(i)-sf_E_sls*N(i))/(0.82*sf_p_unfav_sls); % Possible lower bound of the prestressing force (N) end % ------------------------------------------------------------------- % The structure is divided into 2 parts: % --> Floater % --> Tower % The design of the prestressing steel will be different for both. The % steel of the tower will go through all the structure (except on the bottom tap), while the steel of % the floater will start at the bottom of the transition and will go round % the tap. %% % Domain of the prestressing force Pmin0_tower = max(max(Pm0,Pinf_tens)); % Lower bound (N) Pmin0_tower_sect = max(Pm0,Pinf_tens); Pmax0_tower = min(min(Pm0fat,Pinf_comp)); % Upper bound (N) Pmax0_tower_sect = min(Pm0fat,Pinf_comp); for i = 1:72 Pmin0_tower_sect(i) = Pmin0_tower_sect(73-i); Pmax0_tower_sect(i) = Pmax0_tower_sect(73-i); end

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pos_Pmin0_tower = find(max(Pm0,Pinf_tens) == Pmin0_tower); % Pmin0_tower is the maximum force that can remain on the steel after % anchoring (after direct losses) A_p_min = Pmin0_tower/sigma_p0max; % Minimum area of steel required (mm2) n_strands = A_p_min/A_strand; % Number of strands needed n_strands_per_tendon = 15; % Number of strands per tendon % n_tendons = ceil(n_strands/n_strands_per_tendon); % Number of tendons n_tendons = 6; D_duct = 92; % Diameter of the duct (mm) A_tendon = n_strands_per_tendon*A_strand; % Area per tendon according to VSL (mm2) A_duct = pi*D_duct^2/4 ; % Area of the ducts (mm2) A_p = A_tendon*n_tendons; % Area of the prestressing steel (mm2) P_0design = sigma_p0max*A_p; % Maximum stress on the steel after losses(N/mm2) A_p_sect = zeros(1,72); % Area of steel per sections (mm2) for i = 1:72 if i <= 13 A_p_sect(i) = A_p/2; else A_p_sect(i) = A_p; end end P_max_stressing = A_p*sigma_pmax; % Maximum force that can be applied during stressing (N) %% Losses %%%%%%%%%%%%%%% Direct losses %%%%%%%%%%%%%%%%% x_inv = zeros(1,length(x)); for i = 1:length(x) x_inv(i) = l-x(length(x)+1-i); % We generate a vector with the same global positions than x_tw_loc1 to compare the losses in the same sections end A_c_inv = zeros(1,length(A_conc_comp)); for i = 1:length(A_conc_comp) A_c_inv(i) = A_conc_comp(length(A_conc_comp)+1-i); end R_inv = zeros(1,length(R)); for i = 1:length(R) R_inv(i) = R(length(R)+1-i); end % Angles slope_tw = (R_tb-R_tt)/l_t; % Slope of the tower with respect to the vertical (-) angle_tw = atan(slope_tw); % Angle of the tower with respect to the vertical (rad) slope_trans = (R_f-R_tb)/l_trans; % Slope of the transition with respect to the vertical (-) angle_trans = atan(slope_trans); % Angle of the transition with respect to the vertical (rad) alpha_1 = angle_trans-angle_tw; % Variation of angle from the tower to the trans (rad) alpha_2 = alpha_1+angle_trans; % Variation of angle from the transition to the floater (rad)

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mu = 0.18; % Angular coefficient friction (sheds with various elements and slight lubrication) (-) k = 0.0018/1000; % Unintentional angular rotation due to the Wobble effect (rad/m) deltaPm0_fr = zeros(1,72); for i = 1:72 if x_inv(i) <= l_t if i <= 13 deltaPm0_fr(i) = P_0design/2*(1-exp(-k*x_inv(i))); % Losses due to friction from left side (N) else deltaPm0_fr(i) = P_0design/2*(1-exp(-k*x_inv(i)))+P_0design/2*(1-exp(-k*(x_inv(i)-x_inv(13)))); end elseif x_inv(i) > l_t && x(i) <= l_t+l_trans deltaPm0_fr(i) = P_0design/2*(1-exp(-mu*alpha_1-k*x_inv(i)))+P_0design/2*(1-exp(-mu*alpha_1-k*(x_inv(i)-x_inv(13)))); else deltaPm0_fr(i) = P_0design/2*(1-exp(-mu*(alpha_1+alpha_2)-k*x_inv(i)))+P_0design/2*(1-exp(-mu*(alpha_1+alpha_2)-k*(x_inv(i)-x_inv(13)))); end end % plot(x_inv/1000,deltaPm0_fr/1000,'black'); % xlabel('x [m]'); % ylabel('\DeltaP_\mu [kN]'); P_fr = P_0design-deltaPm0_fr; % -------------Wedge set--------------- a = 5; % Wedge set (mm) deltaPm0_ws = zeros(1,72); for j = 1:72 if x_inv(j) <= l_t alpha = 0; % The design section is at the tower l_a = 50000; % Affected length by the wedge set (mm) for i = 1:10000 l_a = a*E_p*A_p/2/(P_0design/2*(1-exp(-alpha*mu-k*l_a))); % Implicit equation end deltaPm0_fr_ws = P_0design*(1-exp(-mu*alpha-k*l_a)); % deltaPmo_fr(l_a) (N) deltaPm0_ws(j) = 2*deltaPm0_fr_ws; % Wedge set losses (N) elseif x_inv(j) >= l_t && x_inv(j) <= l_t+l_trans alpha = alpha_1; l_a = 50000; for i = 1:10000 l_a = a*E_p*A_p/(P_0design*(1-exp(-alpha_1*mu-k*l_a))); end deltaPm0_fr_ws = P_0design*(1-exp(-mu*alpha-k*l_a)); deltaPm0_ws(j) = 2*deltaPm0_fr_ws; elseif x_inv(j) >= l_t+l_trans alpha = alpha_2; l_a = 50000; for i = 1:10000 l_a = a*E_p*A_p/(P_0design*(1-exp(-alpha_2*mu-k*l_a)));

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end deltaPm0_fr_ws = P_0design*(1-exp(-mu*alpha-k*l_a)); deltaPm0_ws(j) = 2*deltaPm0_fr_ws; end end % plot(x_inv/1000,smooth(deltaPm0_ws/1000),'black') % xlabel('x [m]') % ylabel('\DeltaP_w_s [kN]') % -------------Elastic losses-------------- n = n_tendons; % pre-stressing operations when introducing the cables(they can be two by two) for i = 1:72 if x_inv(i) <= x_inv(13) deltaPm0_el = (n-1)/2*E_p*A_p/2/E_c./A_c_inv*P_0design/2; else deltaPm0_el = (n-1)/2*E_p*A_p/E_c./A_c_inv*P_0design; % Average loss per tendon, according to Eurocode (kN) end end % plot(x_inv/1000,deltaPm0_el/1000,'black') % xlabel('x [m]') % ylabel('\DeltaP_e_l [kN]') % Total direct losses pos_inv_P_0design = find(x_inv == l-x(pos_Pmin0_tower)); deltaPm_tot_initial = deltaPm0_fr+deltaPm0_ws+deltaPm0_el; % delta_initial_stresses = deltaPm_tot_initial/A_p_sect; % initial_prestress_steel = delta_initial_stresses(pos_inv_P_0design)+sigma_p0max; if max(deltaPm_tot_initial)+P_0design <= P_max_stressing && max(deltaPm_tot_initial)+P_0design <= Pmax0_tower Pm0_SLS = max(deltaPm_tot_initial)+P_0design; else if P_max_stressing >= Pmax0_tower Pm0_SLS = Pmax0_tower; else Pm0_SLS = P_max_stressing; end end P_after_dir_los = Pm0_SLS-deltaPm_tot_initial; check_Pm0_SLS = zeros(1,72); for i = 1:72 if P_after_dir_los(i) >= Pmin0_tower_sect(i) && P_after_dir_los(i) <= Pmax0_tower_sect(i) check_Pm0_SLS(i) = 1; else check_Pm0_SLS(i) = 0; end end % Upper_bound_force = Pmax0_tower_sect/1000; % Lower_bound_force = Pmin0_tower_sect/1000;

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% plot(x_inv/1000,P_after_dir_los/1000,'black') % hold on % plot(x_inv/1000,Upper_bound_force,'r') % hold on % plot(x_inv/1000,Lower_bound_force,'r') % xlabel('x [m]') % ylabel('P_m_0 [kN]') Matrix_direct_losses = [x_inv;deltaPm0_fr;deltaPm0_ws;deltaPm0_el]'/1000; TOTAL_direct_losses = Matrix_direct_losses(:,2)+Matrix_direct_losses(:,3)+Matrix_direct_losses(:,4); %%%%%%%%%%% Time dependent losses %%%%%%%%%%%%%%% % Creep + Shrinkage + Relaxation rho_e = E_p/E_c; % Young modulus ratio (-) fi = 0.9; % Creep coefficient according to age (Eurocode) (-) sigma_cp = (Pm0_SLS-deltaPm0_fr-deltaPm0_ws)/A_p_sect; %stress provoked by the prestressing steel minus the friction and wedge set losses (N/mm2) eps_cs = 0.2/1000; % Deformation caused by shrinkage (-) y_p = 0; % Distance from the CoG of the section to the CoG of the prestressing steel in every section (mm) rho_1 = 0.11; % Value of the relaxation for constant length and at t-->inf (-) deltasigma_pr = rho_1*(sigma_cp*A_p_sect-deltaPm0_el)/A_p_sect; % Losses due to relaxation for constant length and t-->inf (N/mm2) deltaP_time = (rho_e*fi*+E_p*eps_cs+0.8*deltasigma_pr)*A_p_sect./(a+rho_e*A_p_sect./A_c_inv*(1+0.8*fi)); % Total losses due to creep, shrinkage and relaxation (N) % plot(x_inv/1000,deltaP_time/1000,'black') % xlabel('x [m]') % ylabel('\DeltaP_t_-_d [kN]') Pinf = P_after_dir_los-deltaP_time; % Pm0_SLS_sect = Pm0_SLS*ones(1,72); % plot(x_inv/1000,Pm0_SLS_sect/1000,'g') % hold on % plot(x_inv/1000,P_after_dir_los/1000,'black') % hold on % plot(x_inv/1000,Pinf/1000,'r') % xlabel('x [m]') % ylabel('P [kN]') % legend('P_0_,_S_L_S','P_0','P_\infty') %% Checking the resistance for ULS M_Ed = zeros(1,72); for i =1:72 M_Ed(i) = sf_E_unfav_uls*M(73-i); % Bending moment acting in every section in ULS (solicitation) (Nmm); N end % It is assumed that once the stress arrives at yielding it remains % constant (design graph of the EC) N_inv = zeros(1,72);

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for i = 1:72 N_inv(i) = N(73-i); end t_inv = zeros(1,72); for i = 1:72 t_inv(i) = t(73-i); end t = t_inv; alpha = @(y) acos((R_inv - y)/(R_inv - t)); A_conc_comp = @(y) t*2*alpha(y).*(R_inv - t/2); N_c = @(y) A_conc_comp(y)*f_cd; P_p_ULS = A_p*f_pd; Sum_Ext_Forces = @(y) P_p_ULS + N_inv - N_c(y); yf = real(fsolve(Sum_Ext_Forces,R_inv)); z = (R_inv - t/2).*sin(alpha(yf))/alpha(yf); M_Rd = (P_p_ULS+N_inv).*z; check_resist_moment = zeros(1,72); % Check of the bending moment resistance for i = 1:72 if abs(M_Rd(i)) >= abs(M_Ed(i)) check_resist_moment(i) = 1; else check_resist_moment(i) = 0; end end eps_p = eps_cu*(R_inv - yf)./yf; check_ductility = zeros(1,72); for i = 1:72 if eps_p(i) <= eps_uk check_ductility(i) = 1; else check_ductility(i) = 0; end end plot(x_inv/1000,abs(M_Ed)/10^6,'black'); hold on plot(x_inv/1000,abs(M_Rd)/10^6,'r'); xlabel('x [m]'); ylabel('Bending Moment [Nm]');

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10.4 Appendix3:Matlabcodeforthecalculationofthecrane’soptimalposition % Analyisis of the pre-stressed concrete clc; close all; clear all; % ---------------------------------------------------------- % Dimensions of the tower l_f = 33.75; % Length of the floater (m) l_trans = 7; % Length of the transition piece (m) l_draft = l_f + l_trans; % Draft of the FOWT (m) l_t = 23.9; % Length of the tower (m) l = l_f + l_trans + l_t; % Total length of the FOWT (m) R_f = 2.43; % External radius of the floater (m) t_f = 0.272;% Thickness of the floater walls (m) R_tb = 1.2; % External radius of the bottom of the tower (m) R_tt = 0.424; % tThickness of the tower walls (m) t_t = 0.272; % Thickness of the tower walls (m) g = 9.81; % Acceleration of gravity (m/s2) % --------------------------------------------------------- % Concrete properties gamma_c = 25; % Specific weight of the concrete (kN/m3) f_ck = 95; % Characteristic resistance of the concrete (N/mm2) sf_c = 1.1; % Safety factor of the concrete (-) f_cd = f_ck/sf_c; % design resistance of the concrete (N/mm2) E_c = 36000; % Young modulus of the concrete (N/mm2) eps_cu = 3.5/1000; % Strain of the concrete at ULS (-) %-------------------------------------------------------------------------- % Pre-stressing steel properties f_pk = 1860; % Characteristic resistance of the steel (N/mm2) sf_s = 1.1; % Safety factor of the steel (-) f_pkr = f_pk/sf_s; % Design stress (real branch) (N/mm2) f_pk1 = 1674; % 0.1% fractile (N/mm2) f_pd = f_pk1/sf_s; % Design stress of the steel (N/mm2) sigma_pm0 = 0.75*f_pk; % Maximum pre-stressing force after tensioning (N/mm2) sigma_pmax = 0.8*f_pk; % Maximum pre-stressing force during tensioning (N/mm2) E_p = 195000; % Young Modulus of the steel (N/mm2) epsilon_uk = 35/1000; % Characteristic strain of the steel at ULS %% Weight sf_p_f_sls = 0.9; sf_p_unf_sls = 1.1; sf_E_sls = 1.0; x = (0:65)'; x(end)=l; long=zeros(length(x),1); long(1:end-1)=(x(2:end)-x(1:end-1))/2; long(2:end)=long(2:end)+(x(2:end)-x(1:end-1))/2;

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t = zeros(66,1); R = zeros(66,1); for i = 1:66 if x(i) <= l_f R(i) = R_f; t(i)=t_f; elseif l_f < x(i) && x(i) <= l_draft R(i) = R_f-(R_f-R_tb)/l_trans*(x(i)-l_f); t(i)=t_f; else R(i) = R_tb-(R_tb-R_tt)/l_t*(x(i)-l_draft); if l_f < x(i) && x(i) <= x(53) % Extension function: y = 20.91*sqrt(x) slope_tower_vert = l_t/(R_tb-R_tt); add_t = 0.272; % +(x(60)-l_draft)/slope_tower_vert; % Additional thickness to put the anchor plate ? intermediate section tower (mm) ctt = (x(53)-l_draft)/sqrt(add_t); t(i) = t_f + ((x(i)-l_draft)/ctt)^2; else t(i)=t_t; end end end t(1)=R_f; Area = zeros(66,1); for i = 1:66 Area(i) = pi*(R(i)^2-(R(i)-t(i))^2); end Mass = zeros(66,1); % Mass of the structure (tones) for i = 1:66 Mass(i) = Area(i)*gamma_c/g*long(i); end Weight = sum(Mass)*g; % Weight of the structure (kN) %% Second moment of inertia I = zeros(66,1); % Second moment of area (m4) for i = 1:66 I(i) = pi*(R(i)^4-(R(i)-t_f)^4)/4; end W = zeros(66,1); % Section modulus (m3) for i = 1:66 W(i) = I(i)/R(i); end %% Vertical forces % All the possible combinations of m, n that range from 1 to 20. In total % there are 400 combinations of pairs (m,n) vect_m_n = zeros(400,2); c = 1:1:20; for k=1:20 vect_m_n(20*k-19:20*k,1)=k; vect_m_n(20*k-19:20*k,2)=c; end m = vect_m_n(:,1); % Distance from the extreme floater side ('left') of the structure until the supports provided by the crane (m)

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n = vect_m_n(:,2); % Distance from the extreme tower side ('right') of the structure until the supports provided by the crane (m) M_sw = zeros(66,1); % Moment due to selfweight (kN) for i = 1:66 M_sw(i) = sum(Mass(1:i-1).*(x(i)-x(1:i-1))*g); end V1 = zeros(66,1); % Tension of the cable of the crane that sustains the structure by the floater side. It can be considered a simple support (kN) for i = 1:400 V1(i) = (M_sw(66)-Weight*n(i))/(l-m(i)-n(i)); end V2 = zeros(66,1); for i = 1:400 V2(i) = Weight - V1(i); end diff_V = zeros(length(V1),1); % Minimum difference to satisfy the first criterion exposed in the Chapter 5 for i = 1:length(V1) diff_V(i) = abs(V1(i)-V2(i)); end ord_min_diff_V = sort(diff_V); pos_min_diff_V = zeros(400,1); for i = 1:400 pos_min_diff_V(i) = find(ord_min_diff_V == diff_V(i)); end %% Diagram of bending moments M = zeros(400,66); for j = 1:400 for i = 1:66 if 0 <= x(i) && x(i) <= m(j) M(j,i) = -M_sw(i); elseif m(j) < x(i) && x(i) <= l-n(j) M(j,i) = V1(j)*(x(i)-m(j))-M_sw(i); elseif l-n(j) < x(i) M(j,i) = V1(j)*(x(i)-m(j))+V2(j)*(x(i)-(l-n(j)))-M_sw(i); end end end %% Check of fully prestressed conditions A = [m,n,V1,V2,diff_V,M]; B = sortrows(A,5); M_ord = B(:,6:end); load 'Pm0_SLS.mat'; % For t-->0, -Pm0/A_c-M/W = sigma_compression => -0.45*f_ck check_comp = zeros(400,66); for j = 1:400

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for i = 1:66 if -sf_p_unf_sls*Pm0_SLS/1000/Area(i)+sf_E_sls*M_ord(j,i)/W(i) >= -0.45*f_ck*1000 check_comp(j,i) = 1; else check_comp(j,i) = 0; end end end % For t-->0, -Pm0/A_c+M/W = sigma_tension <= 0 check_tens = zeros(400,66); for j = 1:400 for i = 1:66 if -sf_p_f_sls*Pm0_SLS/1000/Area(i)+sf_E_sls*M_ord(j,i)/W(i) <= 0 check_tens(j,i) = 1; else check_tens(j,i) = 0; end end end check_comp_tens = zeros(400,66); for j = 1:400 for i = 1:66 if check_comp(j,i) == 1 && check_tens(j,i) == 1 check_comp_tens(j,i) = 1; else check_comp_tens(j,i) = 0; end end end check_compatibility = zeros(400,1); for i = 1:400 if check_comp_tens(i,:) == ones(66) check_compatibility(i) = 1; else check_compatibility(i) = 0; end end Matrix_checks = [B,check_compatibility]; u = find(check_compatibility == 1); C = Matrix_checks(u,:); %% Optimus case All_data_opt = C(1,:); M_opt = C(1,6:(end-1)); M_max = max(M_opt); M_min = min(M_opt); [x_max] = find(M_opt == M_max); [x_min] = find(M_opt == M_min); data_opt = [All_data_opt(1:4),M_max,x_max,M_min,x_min]; m_opt = All_data_opt(1); n_opt = All_data_opt(2); V1_opt = All_data_opt(3); V2_opt = All_data_opt(4);

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mass_V1_opt = V1_opt/g; % tones mass_V2_opt = V2_opt/g; % tones sigma = zeros(1,66); for i = 1:66 sigma(i) = (-sf_p_unf_sls*Pm0_SLS/1000/Area(i)+sf_E_sls*M_opt(i)/W(i))/1000; end x_sigma = zeros(1,66); y_sigma = ones(1,66)*(-0.45*f_ck); plot(x_sigma,'r') hold on plot(y_sigma,'r') hold on plot(sigma,'black') xlabel('x [m]') ylabel('\sigma [N/mm^2]')