287 

AdvancesinProductionEngineering&Management ISSN1854‐6250

Volume11|Number4|December2016|pp287–298 Journalhome:apem‐journal.org

http://dx.doi.org/10.14743/apem2016.4.227 Originalscientificpaper

  

Finite element method for optimum design selection of  carport structures under multiple load cases 

Özkal, F.M.a,*, Cakir, F.b,c, Arkun, A.K.d aErzincan University, Department of Civil Engineering, Erzincan, Turkey bYıldız Technical University, Department of Architecture, İstanbul, Turkey  cUniversity of California, Pacific Earthquake Engineering Research Center (PEER), Berkeley, California, USA dAmasya University, Department of Urban Design and Landscape Architecture, Amasya, Turkey   

A B S T R A C T   A R T I C L E   I N F O

Inthefieldofstructuralmodelling,itisobviousthatthenumberofapplicabledesigns foraparticularstructuralnecessity is limitless.Alongwith the inte‐grationofvariouskindsofavailablestructuralmaterialsintothiscomplexity,itgetshardertobeable todeterminethebestdesignbeforetheproductionstage.Inrecentyears,withtheimprovementofcomputationalandstructuraltechnology, there have beenmany studies on the optimal design selection.This study focusesoncarport structuresandpursuing theirbestproducibleshape.Forthisaim,aperformanceindexformulationwasdevelopedtoassistthe decision ofmaterial efficiency as well as structural rigidity. Thereafter,five conceptualmodelswere numericallymodelled and finite element anal‐yses (FEA) formultiple load caseswere carried out. Reviewing the FEA re‐sults, themostappropriatemodelwasdeterminedbytheapplicationofthisperformancequalificationmethod.Resultsoftheanalysesshowthatoptimumdesignofstructuresundermultipleloadcasescanbedeterminedusingfiniteelementmethod.

©2016PEI,UniversityofMaribor.Allrightsreserved.

  Keywords:StructuralproducibilityPerformancedecisionMultipleloadcasesManufacturingFiniteelementmethod

*Correspondingauthor:fmozkal@erzincan.edu.tr(Özkal,F.M.)

Articlehistory:Received26April2016Revised5October2016Accepted12October2016 

  

1. Introduction 

Structurescanbedesignedinmanydifferentwaystoprovidethestructuralrequirementssuchas performance, economy and appearance. The convenient design of structures is a very im‐portantfactorfortheirstructuralperformance.Shapeofthestructuresisaveryimportantfac‐tor for their structural behaviour. A poor designmight cause fault and quality problems in astructure.Itmayconducetodecreasequality,performanceandtoincreasecostandunnecessarymaterialusage.Therefore,structuraldesignisamajorconcerninengineeringstructures. Designobjectivesaregenerally imprecise real‐life situationsaswellas structuralproblemsandnaturalideaistodealdirectlywiththeseambiguousobjectives.Hence,businessexperienceshowsthatinmanycases,itisbeneficialtospecifythemcrispyandthensolvetheoptimizationproblem[1].Designofstructuresdependsonnotonlystructuralproblems,butalsoknowledgeand creativity of the designer. Therefore, design concepts can technically be discussed for astructureanddesignersseekthebestfeasibledesign.However,itisquitedifficulttodeterminewhichofthedesignsismoreefficientandbetterthantheotherones.Inrecentyears,withim‐provementsofcomputerandstructuraltechnology,oneofthewaystoachieveanefficientstruc‐turaldesignhasbeenmathematicaldesignoptimization.Maingoalofdesignoptimizationistodeterminethebestproducibledesignforastructureundervariousconstraints.Recently,design

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optimizationwith the finiteelementmethod(FEM)hasbecomemorepopularwithsignificantadvancesincomputertechnology.TodaymanydesignerandengineersappealtofiniteelementmethodandmanystructuralanalysissoftwarepackagesaresuitableforFEA.

Thedesignprocesscanbecategorizedinvariousways,butingeneral,itconsistsoffourmainphases[2].Thefirststageistodeterminethefunctionalityrequirementsandessentialparame‐ters;thesecondstageistodevelopconceptmodels;thethirdstageistoperformoptimizationonthedevelopedconceptmodelsandthelaststageistocomparetheoptimizationresultsandde‐cidethemostsuitabledesignbeforeproduction.Thegeneralflowdiagramofthestructuralde‐signprocess is shown inFig.1. In this study, thebestdesignof carport structureswasdeter‐minedbymeansofthesefoursteps.

Inpreviousstudies,manyresearchershaveinvestigatedthedesignprocessanddesignopti‐mizationofmanydifferent structures [3‐8]. In almostallof thepast studies,urbanstructureshavenotbeencompletely investigated.Therefore, thisstudy focusesonthecarportstructuresandtheirbestproducibledesign,sincetheyareoneofthemostcommonurbanstructures.Thestudy contributes to thebest designof carport structuresundermultiple load cases in that itdevelopsaperformanceindexformulation,revealstheimpactofmaterialefficiencyandstruc‐turalrigidityonthebestdesign.Moreover,thisstudyhelpstodeviseimplementstrategiesanddevelop actions to improve best design. It is also indicated that the effective optimumdesignselectioncontributestoimproveefficientstructuraldesign.

Fig.1Flowdiagramofthestructuraldesignprocess

2. Carport structures 

Carportstructures,whicharealsoknownascarshelters,parkingshadesandparkingstructures,areopensidedstructuresthatusuallyconsistofaroofandloadbearingparts.Carportsarepop‐ular all around the world and they are widely used at houses, office buildings, public areas,shoppingmalls,retailoperationsandshoppingmalls.Carportsbringmanygreatbenefits,suchas preventing damage from hailstones, snow and rain, minimizing sun damage, protectingagainst poorer weather, moisture and corrosion. Carports, which can be freestanding or at‐tachedtoabuilding,mayhavearoofedorcanopiedformandsidesofcarportsareleftwhollyorpartiallyopen. Inotherwords, carportscanbedefinedasa semi‐openspace in thecontextofarchitectureorspacedesign. Theentranceofacarportisincontrasttoagenerallyopengarage.Acommonvariantoftheroofingisacorrugatedsheet,trapezoidalortheirtransparentformscorrugatedlightpanelsortrapezoidalplates.Opencarportswithoutaroofareusuallyusedasanopticalsettingofoutdoorspaces to emphasize this by surrounding open spaces. Increasingly, free areas of the roof arealsoused forsolarsystemsandasanextensivegreenroof.Agreenroofcancontribute tode‐creasetemperaturesandreducetheheatislandeffectintheurbanenvironment. Furthermore,usingcarports, lessmaterialsareneededandtheconstructiontimeisshorterthangarageconstruction.Carportsareassumedtobegreener.Moore[9]liststheadvantagesofcarportsasservingasacoveredmainentranceandaplacetoentertainanddooutdooractivi‐

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ties,inadditiontotheprovidingprotectionandstorageforthecars.Healsomentionsthatcar‐ports reduce complexity providing more than sufficient shelter, necessitate less constructionmaterials, and accommodate as aesthetically architectural design. Conclusively, he states thatpeopleconsidertheenvironmentalimpactofgaragescomparedtocarportsandchoosethecosteffectivecarportsduetotherisingenvironmentalconcerns.Theseseveraladvantagescontrib‐ute to widespread use of carports. On the other hand, carports offer no privacy, protectionagainsttheftorvandalism.Agarageismoresecurethanacarport.

2.1 Historical background of carport structures 

Carownershiphasincreasedveryquicklyoverthepastfortyyears.Thisincreasecreatespark‐ing spaceneed.Besidesopen spaceparking areas, carportswhichare semiopen spaceswereemerged especially in a single‐detacheddwelling setting.Gebhardproposes theolder formoftheportecochèreasthepredecessorforthecarportssinceitservessimilarlytocarportintermsofshelteringpassengersastheyexitedcarriagesorautomobiles.Gebhard[10]alsostatedthatthearchitectWalterBurleyGriffinusedcarportsintheSloanHouseinElmhurst,Illinoisintheearly1900s.By1913,severalPrairieSchoolarchitectssuchastheMinneapolisfirmofPurcell,Feick&ElmsliealsousedcarportsinahomeatLockwoodLake,Wisconsin.AccordingtoFoxandJeffery[11],theexpression“carport”wasproposedbyDavidGebhard,anarchitecturalhistorian,forthewaythatthetermwasbegunfromthecomponent'sutilizationin1930sstreamlinepre‐sentdaystructures.Robinson[12]notesthatcarportswereusedbyAmericanfamousarchitectFrankLloydWrightinUsonianHousesdesigninthe1940s.Thesecarportstructuresaredemon‐stratedinFig.2.

Moreover, Fox and Jeffery [11]points out that carportswere accepted as an alternative togaragesbecauseoftheircostandeasyconstructionafterSecondWorldWar.AccordingtoMoore[9], inthe19thcenturycarportsbecametypicaldesignelementofsingle‐familyresidencesandhotels.Todayavastrangeofsizesanddesignsofcarportsareavailable.

Fig.2PorteCochère(a),SloanHouse(b),Usonian(c)[13‐15]

   

(a) (b)

(c)

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2.2 Structural failures of carport structures 

Carportstructuresareexposedtomanydifferentexternalandinternaleffectsthroughouttheirlives.Therefore,acarportstructureshouldbedesignedtowithstandstructuralloadingscenari‐os.Hence,theaccurateestimationoftheloadsandtheircombinationsonacarportmightbethemostimportantandthemostdifficulttaskfordesigners.Loadsoncarportstructuresarebasedondifferenttypesandforces,whicharedeadloads, live loadsandlateral loads.Carportstruc‐turesaddressthecarryingproblemsoftheseloads. Althoughcarportstructuresarehighlydurable,someofthemintheworldunfortunatelyaredeteriorated,damaged, collapsedor faileddue todifferenteffects. Ingeneral, thesestructuresaredestroyedandlosttheirqualitiesduetomanyreasonssuchasenvironmentalconditionsandnatural disasters. Therefore, it causes irreversible negative effects on the structure. Observedstructural failures occurs generally due to thematerial degradations and poor design. In thepast, severalcarportproblemsarosebecauseofpoordesign. Ifacarport isnotwelldesigned,successfully analysed and well‐constructed; it may face some problems like collapse, defor‐mation,fracture,fatigue,crackingorfailureoffixtures,fittingsorpartitionsanddiscomfortforoccupants.Manycarportstructuresareexposedtodestructiveverticalloadssuchasdeadloadandsnow loads,and these loadingscenarioscancausedamages to thecarports (Figs.3a,3b).Thistypeofdamageisverydangeroussinceitmaycausefatalanddestructivecrashesandfrac‐tures,alsocausesdiversifieddisplacementof thecarport components.Therefore,damageriskshouldbeconsideredandsomeprecautionsshouldbetakenagainstit.

Inadditiontoverticalloads,lateralloadssuchasearthquakeandwindloadsmayalsoaffectthecarports.Lateralloadsgenerallycausetothelateraldisplacementandirrevocabledamage.Windloadsleadtofailureofthecarportroofandaffectthestructuralstability(Fig.3c).Moreo‐ver, many carport structures are exposed to destructive earthquakes and these earthquakescausesomedamagestothestructure.Earthquakebaseddamagesoccurespeciallyontheverticalbearingcomponentsofthecarportsuchascrackinganddisintegrationofthestructure(Fig.3d).

Fig.3Structuralfailureofcarportstructuresduetosnowload–(a)and(b),windload(c),earthquake(d)[16‐19]

(a) (b)

(c) (d)

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3. Concept designs 

Thesecondpartof thedesignprocess is todevelopconceptualmodels. In thisstage,designerselectstheinitialforms,typeofstructuresandmaterialsintermsofrequiredstructuralfunction.Successatthisstagedependsontheability,creativityandengineeringapproachofdesigners.

3.1 Material properties 

Structural performance and behaviour of a structure technically depend on the constructionmaterials. Moreover, the cost, quality, and design of a structure vary by selected materials.Therefore,selectionoftheappropriatematerialtypeisacrucialandvitalprocessforengineer‐ingstructures.Today,thousandsofmaterialscanbeusedforthealltypesofstructures.Howev‐er,noteverymaterialmaybeacorrectchoiceforastructure;therefore,itisveryimportanttoselectsuitablematerials. Carportstructuresaregenerallymadeofsteel,wood,plasticandcomposites.Becauseofprov‐en properties and significant advantages, steel has been the dominatingmaterial for the loadbearingpartsofstructures.Moreover,polymersarewidelyusedfornon‐bearingpartsofstruc‐turesduetotheirlightweight,availability,easyusabilityandcorrosionresistance.Inthisstudy,load‐bearingpartsofthecarportsweredesignedasstructuralsteelandroofsaspolyethylene.MaterialspropertiescanbeobtainedfromANSYSlibrary[20],whicharesummarizedinTable1.

Table1Mechanicalpropertiesofthecarportmaterials

Structuralmaterials

Young’smodulus(MPa)

Bulkmodulus(MPa)

Shearmodulus(MPa)

Poisson’sratio

Density(kg/m3)

Structuralsteel 2E+5 1.67E+5 0.77E+5 0.30 7,850

Polyethylene 1,100 2,291 387 0.42 950

3.2 Conceptual models 

Conceptualmodelsmean topreparealternativemodels fora structure. In thispart, designersdevelop variousmodels such as simple and complex shapes. This step is themost interactivesectionforthedesignandmainaimofdevelopingconceptualmodelsistoconsiderallpossibleoptions.Developedconceptualmodelsdependtotallyontheimagination,skillsandexperienceofthedesigners. Inthisstudy,fivedifferentconceptualmodelsweredevelopedanditwasconsideredtocovertheequalareaforallof them.Althoughthereis infinitenumberofotherpotentialmodelsandsomeofthemsurelyfitthepurposeevenbetter,thefactaboutoptimizationapproachesisthatitisneverpossible toachieve theglobaloptimum,but just the localoptimumresult.Sincemaingoalofthisstudyistoinvestigatethesuccessoffiniteelementmethodwhileconsideringspeci‐fiedstructuralcriteria,itispossibletoapplythecurrentdesignapproachoneverysortofdiffer‐entmodels.Moreover,severalsystems,whicharethemostpopularstylesofthecarportstruc‐tures,wereusedinthisstudy.Formodel‐1andmodel‐2,aslopingflatrooftypewasused.Ontheotherhand,aconcaverooftypewaspreferredformodel‐3,model‐4andmodel‐5.Thesetypesofroofsweredesigned in order to providemaximumvehicle coverage and aesthetic.DevelopedconceptualmodelsinthisstudyareshowninFig.4.

4. Numerical models 

Numericalmodelsaremathematicalexpressionofastructuralmemberorsystemandtheyareused to determine the structural behaviour that might be subjected to multiple load cases.Therefore,numericalmodellingisabeneficiarymethodintermsofthemathematicalmodellingof thestructures.Numericalmodellingofstructuresgetseasierowingto the improvements incomputertechnologiesdaybyday.Inthescopeofthisstudy,conceptualmodelswerenumeri‐callymodelled using ANSYSWorkbench [20] software. Finite elementmodelwas constituted

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withSOLID186elements,whichhavequadratic20‐nodedhexahedrons/10‐nodedtetrahedrons,andthreedegreesoffreedompernode.Meshingwasgeneratedaccordingtothecomplexityofthe designs and adequate refinementwas applied on some of the regions,whichwere deter‐minedsubsequenttothepre‐andpost‐analysischecking.Thisiswhythenumberofnodesandelementsforsomeofthedesignsvary.Fig.5showsthenumericalmodelpropertiesofthecar‐portstructureswiththeillustrationofthemesheddesigns.

Plan Elevation 3DModel

Model–1

Steel Beams

Polyethylene Roof

Steel Beams

Steel Column

Steel Beam

Steel Tie Bar

Steel Column

Model–2

Steel Beams

Polyethylene Roof

Steel Beams

Polyethylene Roof

Steel Beams

Model–3

Steel Beams

Polyethylene Roof

Steel Beams

Steel Column

Polyethylene Roof

Steel Beams

Steel Column

Model–4

Polyethylene Roof

Steel Beams

Steel Column

Steel Beams

Model–5

Polyethylene Roof

Steel Column

Steel Column

Polyethylene Roof

Fig.4Conceptualcarportmodels

Model‐1 Model‐2 Model‐3 Model‐4 Model‐5

Elements 20016 21584 3724 7286 1684

Nodes 110963 58192 26332 21765 12943

NumericalModel

Fig.5Finiteelementparametersoftheconceptualmodels

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5. Finite element analysis 

Material typeswereassigned to the structural componentsof the carport structures from theANSYSmaterial library.Thesematerialsarepolyethyleneandstructuralsteel for theroofandloadcarrierparts,respectively.Threetypesofanalyseswereperformedforeachofthemodels.One of them is themodal analysis that examines the structural behaviour for the firstmode,whiletheothersarestaticstructuralanalysesforsnowandwindloadings.Accordingtotheas‐sumptionsbasedoninternationalbuildingcodes,asnowloadof750Pawasappliedverticallyontheroof.Windloadwasappliedonlytotheroofbecauselateralloadingtothecarrierpartscouldbeneglectedowingtotheirinconsiderablesurfaceareas.Additionally,simplificationandroundingoffbutstillbasedontheinternationalcodeswerepreferredforthecalculationofwindloaddistributioninordertogeneralizetheloadingeffectforallofthestructuraldesigns.There‐fore,apositivepressureof400Patothebottomfacetandasuctionpressureof200Patothetopfacetoftheroofwereappliedinthenormaldirectionofsurfaceelements. With respect to thedeterminationof theoptimumdesignof conceptual carport structures,volumesoftheloadcarrierpartsandtotaldisplacementvaluesofthewholestructurewererec‐ordedandusedintheperformanceindexformulation.Moreover,itisdifficultandcomplicatedto provide analysis results for each node and element. Therefore, contour pictures and scaletableswereusedtopresenttheresults(Figs.6,7).Inthisstudy,multipleloadcaseswerecon‐sideredandtheFEAresultsarediscussedwithintheresultsanddiscussionssection.

Modal Snow Wind

Model–1

Model–2

Model–3

Model–4

Model–5

max min

Fig.6Totaldisplacementdistributionofthesteelbearingcomponents

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Modal Snow WindModel–1

     

Model–2

     

Model–3

     

Model–4

     

Model–5

     

max min

Fig.7Totaldisplacementdistributionoftheallstructuralcomponents

6. Determination of the optimum design 

Astructuraldesignershouldconsider theeffectiveuseofmaterialsalongwith thesafety limitandestheticalsemblanceobjectives.Althoughthispointhasbeeninvestigatedindetailbysev‐eralresearchersoverthelastfewdecades,manufacturersgenerallyputthesemblanceforwardfor thepurposeof commercial concernsandpush the structuralperformanceof theirdesignsintobackground. Ifa technique issought inorder toanswerthequestion“Whichone is thebest?”,aperfor‐mancequalificationmethod isneeded tobeconstitutedsubsequent to thedefinitionofall thedesigncriterions[21]. Inthisstudy, fivetypesofpopularcarportdesignscoveringequalareaswereevaluated.Becauseexpectedconsumerbenefitequality isprovided forallof themodels,thereisnoneedtoconsiderthisfactor.Furthermore, itshouldbenotedthateachproduct, in‐cludingcarportstructures,mustbeoptimizednotonlybasedonmaterialconcernsorstructuralbehaviour,butalsobyconsideringtheeasy‐for‐manufactureandeasy‐for‐assemblyparadigms.Themost suitabledesign is usually a compromise among the abovementioned requirements.Becausecurrentstudydealswiththeroughdesignatthepre‐productionstage,ithasalsobeenneglectedfortheaimofobtainingoptimumresult.Forinstance,astabilityanalysisincorporat‐ingstructuralassemblydetailsthatwasstudiedbyManifold[22]orageotechnicalinvestigationthatwasstudiedbyHrestaketal.[23]couldbeintegratedasapost‐verificationstagetothede‐signprocessinordertomakesureeveryconstraintissatisfiedbeforetheproduction.

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Designobjectiveforacarportstructurecouldbesummarizedassatisfyingmaterialefficiencyobjectivewhilemaintainingarigidbehaviouragainstvariouspossibleloadcases.Althoughuni‐formstresslevelsforthewholestructurewillassistmaterialefficiency,sizeandshapedissimi‐larity of finite elements prevent an accurate calculation. Hence, a newmodified performanceindexformulation,basedgenerallyonthenodaldisplacement levels,shouldbebuiltaccordingtothefollowingproblemdefinition:

minimize ∑

subjectto ∗ ⇒ ∗

1

∗ ⇒ ∗ 1

where istheweightofthestructure, isthematerialdensity, isthevolumeoftheethele‐ment, isthetotalnumberofelements, istheabsolutevalueofthemaximumnodaldis‐placement, istheabsolutevalueoftheaveragenodaldisplacementvaluewhile ∗ and∗ aretheupperandlowerboundlimitsofthedisplacementconstraints,respectively. Forthedeterminationoftheoptimalityofcarportdesigns,aperformanceindex,whichcouldbeappliedinageneralscopeandconsidersalltheloadcases,shouldbedevelopedstepbystep.Inordertoconstitutearigidstructure,structuralperformancelevelbasedonthemaximumdis‐placementvalueoftheithmodelforthejthloadcaseisfirstlydefined.

∗

(1)

Secondly, theaveragenodaldisplacementvalueshouldbeaddedto the formulation for thepurposeofassistingmaterialefficiencyqualification.

∗

∗ (2)

Themathematicaldefinitionofstructuralperformancelevelisfinalizedbyimplementingtheweightvalueasfollows.

1 ∗

∗ (3)

However, there is a need to define a reference performance level in order to compare thedesignswitheachother.Consideringacertainnumberofmodelsareevaluatedinthisstudy,thisreferencelevelcouldbeformulatedasthemeanperformancelevelofallmodels.

1 1 ∗

∗ (4)

Finally, a performance index formulation is generatedby theproportionof the ithmodel’sandreferenceperformancelevelvalues.Itisnamedas becauseoftheaimtoattainarigiddesignwhileminimizingthematerialweightofthestructure;inotherwords,whilemaximizingthematerialefficiency.

1 ∑

1 ∑ 1 ∑

(5)

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Thisperformanceindexissuitabletobeusedforanytypeofdesignoptimizationorcompari‐sonprobleminordertodeterminetheoptimumstructurethatachievesarigidstructuralbehav‐iourwiththeefficientmaterialuseundermultiple loadcases.Optimumdesignselectioncouldbepracticedsimplybychoosingthemodelthathasthegreatestperformanceindex.

7. Results and discussions

Fiveconceptualmodelsofcarportstructureswereanalysedandinvestigatedinthisstudy.Ex‐pectedconsumerbenefitequalityisprovidedforallofthemodelsbecausetheyhaveequalcoverarea.Modal analysis and static analyses of snow andwind loadings have been performed foreachofthemodels.Weightsofthemodelswerecalculatedaccordingtothesolidvolumeofgeo‐metricaldesignsandmaterialdensityofthestructuralparts.Subsequenttotheanalyses,maxi‐mumdisplacementandaveragedisplacementvaluesofthestructuralnodeswererecordedforthe calculation of performance index ( ). However, an important decision is needed to bemadeforthecalculationof .Becausecarportstructuresconsistofaroofand loadbearingparts,whicharemadeofdifferentkindsofmaterial,itwouldnotbecompletelyappropriatetocalculate forthewholemodel.Itshouldbenotedthatthemaximumdisplacementwascon‐firmedtooccurontheroofpartforallofthemodelsandanalyses.Itispossibletodecreasethedisplacementvalueofroofpartswiththeaidof littledesignmodificationsthatwouldnotsub‐stantiallyaffectthestructuralperformanceineitherapositivenornegativeway.Sincethestruc‐turalbehaviourof loadbearingpartsismoreimportantinordertodesignarigidmodel; ,whichiscalculatedjustfortheloadbearingparts,shouldbeconsideredfortheoptimumdesignselection.Performanceindexvaluesofthewholestructureforallofthemodelsarealsogiveninthisstudyforthepurposeofprovidinginsightintotheperformancedecisionconcept.Geometricalproperties (volume and weight) of the models, average‐maximum displacement values for themultipleloadcases(modal,snowandwindloadings)andperformanceindexvaluesarepresentedinTable2.

Table2Structuralanalysisresultsoftheconceptualmodels

Structuralparts

Volume(m3)

Weight(kg)

Modal Snow Wind

(mm)

(mm) (mm)

(mm)

(mm)

(mm)

Model‐1

Bearing 0.550 4,318 15.09 26.99 1.56 3.03 1.29 2.50 0.31

Total 0.909 4,659 15.28 49.97 1.86 27.77 1.53 22.13 0.18

Model‐2

Bearing 0.037 291 41.20 103.27 28.96 69.97 24.90 58.93 3.55

Total 0.075 326 44.56 160.13 40.54 358.99 34.27 290.77 2.94

Model‐3

Bearing 0.516 4,053 9.84 28.76 1.56 5.13 1.28 4.18 0.20

Total 1.000 4,512 12.43 29.30 2.05 5.64 1.69 4.59 0.48

Model‐4

Bearing 0.179 1,408 14.13 45.77 3.51 11.78 5.01 15.19 0.56

Total 0.611 1,818 17.62 45.84 6.89 47.26 8.34 42.63 0.75

Model‐5

Bearing 0.312 2,445 6.28 15.09 6.32 17.35 4.80 13.70 0.39

Total 0.801 2,910 27.75 92.90 29.36 82.93 22.57 63.07 0.65

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Accordingtotheperformanceindexvaluesoftheirloadbearingparts,thebestcarportstructurethroughoutthefiveconceptualmodelsismodel‐2.ItisseeninTable2that valueofmodel‐2is thehighestonebyawidemargin incomparison to theothermodels’. Its value is3.55while thesecondbestmodel’s is0.56and the lastmodel’s is0.20.Even though themaximumdisplacementof therespectivemodel ismuchhigheraswell, theclosenessof theaveragedis‐placementvaluestothemaximumandparticularlythelowestmaterialweight,suggeststhatthismodeltohavethebeststructuralperformance. When thedifferencesof values,whichwerecalculated for thewholeofanystructuralmodels,areinvestigated,structuralperformancesoftheroofpartsshouldbeevaluatedcarefully.

values forthewholestructureofmodels‐1and‐2are lowerthanthe values forthebearingparts,whilethisrelationisinversefortheothermodels.Becausethematerialamountisequalforallthemodels,onecanassumethatmaximumdisplacementvaluesoftheroofpartsofthese twomodelsareexcessivelyhigher than thevaluesatbearingparts. It is true thatmaxi‐mumdisplacementvaluesarehigherbutthereasonwhy valueishigherformodels‐3,‐4and ‐5 is thataveragedisplacementvalue increased, asdid themaximumdisplacementvalue.Therefore,whenthestructuralbehaviourof thesefivecarportstructuresareevaluatedbytheperformance indexconcept, thismethod indicates thatmodel‐2has thebeststructuralperfor‐mance,regardlessofhavinghigherdisplacementvalues.However,thismodelcanbeimprovedin order to decrease themaximum displacement value by littlemodifications at lower levels.Magnification of cross‐sections or supplementation of newbearingmembers especially at themoststressedregionswillverifythisobjectivewithoutincreasingthematerialweighttoomuch.Thesemodellingmodificationsshoulddependondesigner’schoiceorconsumer’snecessity,alsoanyappropriategeometricaloptimizationmethodcouldbeemployedasanalternativeway.

8. Conclusion 

Astructuraldesignproblempriortotheproductionstagecomeswithmanyquestions.Thesearerevisionofprevioussimilarsolutions,selectionofthematerialstobeused,geometricalmodel‐lingmethodtobeperformedanddeterminationofthebestdesignthroughoutthepossiblede‐signs,respectively.Incasethereisaneedtoconsidermultipleloadcases,thecomplexityoftheproblemgetsbigger.Thisstudyseekstheanswertothelastquestionandevaluatesfiveconcep‐tualcarportstructuresdependingonastructuralperformancequalificationapproach.Themaincontributionof thisresearch is todevelopaperformance index formulation inorder todeter‐mine thebestdesignbefore theproduction stage.The study intended to investigate effectsofmaterialefficiencyandstructuralrigidityonthedesignofcarportstructuresbyusingfiniteele‐mentanalysis.Forthisaim,aperformanceindexformulationwasdevelopedtoassistthedeci‐sionofmaterialefficiencyaswellasstructuralrigidity,thatiscalledas .Formulationstepsconsidertheinfluenceofthegeometricalpropertiesandfiniteelementanalysisresultsthatex‐hibitthestructuralbehaviourcollectively. Subsequent to the finiteelementanalysesof theconceptualmodels,whicharesubjectedtomultipleloadcases,their valueshavebeencalculatedandcommentedwithrespecttotheanalysisresults.Actually,thebestmodelcouldhavebeenevaluatedasinadequatewithoutanyqualificationmethodbuttheperformanceindexconceptleadsthewaybynumericalresultsandfacilitatesoneofthemostimportantstepsofastructuraldesignproblem. Additionally,theproductionprocessofanytypeofstructureinvolvesnotonlymaterialsfromwhich theproduct ismadeof, but also themanufacturingprocesses,machine tools, tools, fix‐tures, assembly process, environment requirements etc. Integrating also esthetical semblancewill make the optimum design problemmore complex, however, conducting a questionnairethroughoutthesectoralexpertstoattainasensitivitydegreeispossible. Inordertoovercomemanufacturingrelatedconcerns,modificationofperformanceindexformulationusingthatsen‐sitivitydegreeorconsultingsomeotheroptimizationmethodssuchasfuzzylogiccouldbecon‐sideredinfuturestudies.

Özkal, Cakir, Arkun

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