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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN , ISBN CAMBbRING lf TIMBbR ClMPlSITb BbAMS BY MbANS lf SCRbW FASTbNbRS Ivan Giongo N, Maurizio Piazza O, Roberto Tomasi P ABSTRACT qheaimofthispaperistoinvestigatethepossibilityofcamberingatimberbeambysimplyputting anotherbeamonthetopofitandinsertingscrewsinclinedat45 relativetothebeamaxis.qothis purposeithreeexperimentaltestshavebeenperformedattheiaboratoryoftheaepartmentof jechanicalandptructuralbngineeringeafjpfoftherniversityofqrento.afterthecalibration ofanumericalmodelthathelpedinunderstandingthe camberingphenomenon Iananalytical formulationhasbeenproposed.qheresultingformulafordeterminingtheupwardcamberegiventhe mechanicalpropertiesofthebeamsandofthefastenersfhasshownthecapabilityofreproducingthe experimentalbehaviourwithpromisingaccuracy.eoweverifurthertestingisrecommendedsoasto validatethemethodfeasibilitytoexistingbeams. Keywords: Timber camber beam, Wood camber by screws, Reinforced wooden floors N. INTRlaUCTIlN thenrehabilitatinghistoricalmasonrybuildingsitiscertainlynotraretocometodealwithsagged timberfloorswhichcannotbebuttressedduetoheritageissues.asimilarproblemoccurswhen historicalbuildingsarereadaptedtoanewbuildingusagewhichprovidesforanincreaseinfloor loads.fnthiscasethetimberfloorsioriginallydesignedtobearlowloadsiwillinevitablyshowan excessivemidspandeflectioneserviceabilitylimitstatef.qhereforethedevelopmentofaprocedure whichenablesto lift abeambyjustsuperposinga dryreinforcementelement Icouldproveof someinterest. af bf cf m q kn jn j ko jo df ef m kn jn ko jo Fig. N Camberingprinciplesforacompositebeam N fvandiongoiaepartmentofmechanicalandstructuralbngineeringirniversityofqrentoiviajesianotti f-punopqrentoiftalyiivan.giongo]ing.unitn.it O jauriziomiazzaiaepartmentofmechanicalandstructuralbngineeringirniversityofqrentoiviajesianotti f-punopqrentoiftalyimaurizio.piazza]ing.unitn.it P oobertoqomasiiaepartmentofmechanicalandstructuralbngineeringirniversityofqrentoiviajesianotti f-punopqrentoiftalyiroberto.tomasi]ing.unitn.it OMOV
2 ffoneconsidersacompositebeamiasincig.naiwherethefastenersformsavm anglewiththebeam axisiitcanbeseenthatwithoutanyotherexternalloadallthecompressionforcesduetothepressure generatedbythescrewsareinequilibriumandthereforethebeamremainsundeformed.assoonas aloadisappliedcig.nbithebeambeginstosagandthetwocomponentelementsexchangeasystem offorcessimilartothatincig.nc.lntheotherhandiifthescrewsarepositionedasincig.ndiin ordertoreachtheequilibriumithetwocontactsurfaceshavetoexchangeashearactionecig.nefthat isoppositetothatincig.ncandconsequentlythebeamrises. O. Teb bxpbrimbntai TbSTS qheaimofthispaperistoinvestigatethepossibilityofcamberingatimberbeambysimplyputting anotherbeamonthetopofitandinsertingscrewsinclinedat4r relativetothebeamaxis.poasto discoveritithreetestshavebeencarriedoutattheiaboratoryoftheaepartmentofjechanicaland ptructuralbngineeringeafjpfoftherniversityofqrento.bachspecimeniscomposedbytwo MIN MINm O glulambeams4mlongiconnectedbydoublethreadedscrewsecig.nf.qhefastener spacingenmmmmfiisrelatedtotheneedofobtainingaclearcamberemorethannmmmfthroughthe connectorsatdisposal.ftisutterlyacknowledgedthattheflexuralstiffnessofacompositebeamis directlyrelatedtothefastenerscapabilityofhinderingthetwocontactsurfacesfromslippingeach other.pincetheinterfaceslipismaximumattheendsofthecompositebeamandminimuminthe centralparticamberingisexpectedtobemoredifficultwhenthescrewassemblystartsfromtheouter partsofthebeamratherthanwhenitstartsfromtheinnerpart.consequentlytestsko.nandphave beenperformedinsertingthescrewsfromthemiddletotheendsefnt-to-bxtfandtestko.ohasbeen carriedoutfromtheendstothemiddleebxt-to-fntf.beforeinsertinganymechanicalconnectori aseriesofelasticbendingtestshasbeenperformedinordertodeterminethejoboftheconsidered elementseqablenf. -screwsinsertedat4r -tworows -spacingnmmmm Fig. O qestsetup Table N joboftestedelements CompositeBeam CN CO CP blement jn jo jp j4 jr js bxjpaz TPOT NOMO4 NNUSP UTNO NNPRU VO4R Table O bxperimentalupwardcamber w L/2 xmmz pcrewingpattern CN NP.PV fnt-to-bxt CO S.V4 bxt-to-fnt CP N4.VO fnt-to-bxt qableoshowstheresultsofthecamberingprocedure.asexpecteditestko.oebxt-to-fntfexhibits afinalvaluesignificantlylowerthantheothertests. qhecamberamounteithasbeenobservedanupwarddeflectionofaboutonethree-hundredthofthe totalbeamlengthfcouldpossiblybeincreasedbyreducingthescrewspacingorbyusingfasteners abletogenerateagreaterpressure.fndoingsoikeenattentionshouldbepaidtothemagnitudeofthe internalstressstateimposedbythecamberingprocedure.ftisalsoquiteevidentthatfurthertestingis OMPM
3 neededsoastofullyunderstandthebehaviourofsuchacompositebeaminthelong-termperiod.cor thetimebeingithethreeassembledspecimenshavebeenmonitoredfor4uhoursiduringwhichno camberlosshasbeendetected. Fig. P CompositebeamCNafterfastenerinsertionEstartingfromthebeamcentreF P. Teb NUMbRICAi Mlabi AnumericalmodelhasbeendevelopedthroughthefiniteelementsoftwarepAmOMMM.fnparticularIas toreproducetheactofinsertingthescrewsoneaftertheotherithenonlinearstaged-construction functionhasbeenemployedxnz.qhechoiceofnotutilizingthestructuresymmetryisduetothe impossibilityiduring real assemblyiofinsertingthefastenersonsymmetricpositions simultaneously.eoweverinthatcaseiaslightlylowervalueofthefinalcamberwouldhavebeen reachedsinceattheapplicationofthescrewpressureitheconnectorstiffnessisalreadyinplaceeother solutionshavebeentestedbuthaveledtoexcessivevaluesofupwardcamberf.boththefastenersand thewoodelementshavebeenmodelledaslinearelasticmaterials.qhestiffnessofthescrewcouplek c hasbeendeterminedinaccordancewithxozek c OSPMPkLmmFandhasbeenreproducedbymeansof twocrossedrodseinclinedat4r FwhoseaxialstiffnessisequaltoK c itself.qhescrewpressurehas beenintroducedasasystemoftwoinclinedforcesactingatthescrewnodes.fnadditioniinextensible rodshavebeenusedtokeeplockedthedistancebetweenthebarycentrelinesofthewoodelements. Fig. 4qhec.b.model aoubleqhreadedpcrew eeadblement ORkkioadCell qipblement Fig. R pcrewpressuretestsetup OMPN
4 poastodeterminewhatsortofpressureistobeassignedtothescrewcoupleisometestshavebeen performedirelyingonthesetupshowedincig.r.janyparametershavebeenpriedee.g.screwangle withrespecttothegraindirectioniinitialpressureiheadpenetrationlengthithreadedpartlengthi connectortypologyiwooddensityitime-dependencefandfurthertestinghasalreadybeenstarted. Aresultantpressurevalueof4.4kkforthesinglescrewhasbeendeemedasacceptable. qheresultsobtainedfromthenumericalmodelaregiveninqablepoegardingspecimenscnandcpi itcouldbeseenthatthenumericalmodelreproducestheexperimentalbehaviourwithsufficient precisionforboththetestedscrewingpatternsefnt-to-bxtandbxt-to-fntf.anunderestimationofthe cambervaluehasbeenobservedforspecimencp. Table P bxperimentaldatass.kumericalvaluesxmmz bxperimental kumerical brr.b CN NP.PV NP.TU O.VN CO S.V4 T.4M S.SP CP N4.VO NO.RO NS.MV 4. Teb ANAiYTICAi FlRMUiA ptartingfromequilibriumconsiderationsxpzandtakingintoaccountthestaticschemeofcig.siifone assumestheabsenceoftheexternalbendingmomentiitispossibletoobtainbq.enfandconsequently bq.eofw 2 N 1,i'' ExF- α N1,i ExF 0, with N 1,i'' E0F 0, N1,i EsiF T ENF TsinhEaxF N1,i ExF sinheasif EOF wherew N 1,i istheaxialforceintheupperelementofthecompositestructureethebeamlengthisequaltosif; N 1,i ''isthesecondderivativeofn 1,i ; iisthenumberofthescrewcoupleelabellingstartsfromtheinternalsidef; Tisthehorizontalcomponentoftheresultantpressureyieldedbyonecoupleofinclinedscrews; k c isthedistributedstiffnessoffasteners; aisthedistancebetweenthecentrelineofthetwoelements; αxek c EJ FLE EJ 0 EA 0 Fz M.R ; EJ 0 istheflexuralstiffnessofthecompositebeamwithnomechanicalconnections; EJ istheflexuralstiffnessoftheidealcompositebeam; EA 0 ( 1/EA j ) -1 ; EA j isthe axialstiffnessofthej-thelement; sisthefastenerspacing. AfterdeterminingN 1,i Ithecalculationofthei-thbeamdeflectioncanbeattainedasfollowsW N1,i Ex F a w'' i Ex F -, with wie0f 0,w' ie0f 0 EJ 0 EPF Ta é sinheaxfù wiex F x EJ0 sinhe sif ê - a a ë a ú û E4F eenceitiseasytocharacterizethecontributionofthei-th screwcoupletothebeamcamberw æ L ö D wi,l/2 wiesif+ w' i Esi F ç - si 2 è ø ERF OMPO
5 cinallytheevaluationofthebeamcamberispresentedw n n ïì1 Ta écoshea F( ) ùïü D ë si 2si - L + Lû nta wl/2 å w i,l/2 åí ý- 2 i1 i1 ï sinhea F a ï a î 2 si EJ0 þ EJ 0 ESF wheren isthetotalnumberecig.tfoffastenercouples. x wl/2 L L/2 wl/2 q q Kc w1,l/2 Kc K c w2,l/2 s 2s Fig. S ptaticschemeadoptedfortheanalyticalformulation Table 4 bxperimentaldatass.analyticalvaluesxmmz bxperimental Analytical brr.b CN NP.PV NP.OU M.UO CO S.V4 - - CP N4.VO NO.UU NP.SU qable4providesacomparisonbetweenexperimentaldataandanalyticalvaluesobtainedthrough eq.esf.qheproposedformulaseemsabletoreproducetheexperimentalcamberofcnspecimenwith quitegoodprecisioniwhileacertainerrorenpbfhasbeenobservedforcpspecimen.ftshouldbe notedthatforcompositebeamcpthenumericalmodelgaveaverysimilarpredictionenvberr.f. Fig. T afcoupleeffectivenesstotheupwardcamber;bfcamberevolution Asoutlinedincig.TaItheeffectivenessofani-th screwcoupledependsonhowmanycoupleshave alreadybeeninsertedandonthefastenerspacing.althoughithasbeenobservedthatecig.ufthe OMPP
6 greaterthespacingthegreatertheeffectivenessiifonefocusesontheglobalresultitisclearthat increasingthespacingreducestheamountofscrewsandconsequentlythefinalcamberecig.tbf. Fig. U pcrewcoupleeffectivenessss.ftspositionalongthebeam R. ClNCiUSIlNS qheexposedcamberingprocedurehasprovedtobeeffectiveandpermitstoobtainsignificantvalues ofupwarddeflection.lbviouslyithecamberhastobeconsistentwithwhatisconnectedtobeam.fn additioniitoughttobeunderlinedthattheexperimentaltestspresentedinthepaperihaveinvolved newtimberbeamswithclearlydefinedboundaryconditions.qoassesstherealeffectivenessofthis methoderegardingtherefurbishmentofoldfloorsfianexperimentalcampaignonexistingsagged beamsishouldthereforebeundertaken.marticularattentionwillhavetobepaidtotheinternalforces thatthisproceduregeneratesintoanallegedlydeterioratedbeam. Boththeexperimentaltestsandthenumericalmodelhaveshownthatthebestwaytoobtainan upwarddeflectionistostarttheassemblyfromthecentreandalternativelyproceedtowardstheends ofthebeam. qheproposedanalyticalformulaseemstobeabletoreproducetheexperimentalbehaviourand presentsthebenefitofbeing easilymanageable.qhisismainlyduetothechoiceofconsidering aconstantfastenerspacingalongthebeamaxis.ltherwiseiitwouldhavebeennecessarytointroduce couriertransformsx4zthatwouldhavepreventedtheanalyticalmodelfrombeinghandledwithout aspecificsoftwareforsymboliccalculation. RbFbRbNCbS xnz CpfxComputersandptructuresfnc.zEOMM4FCpfAnalysisoeferencejanualcorpAmOMMM I bqabp IandpAcb.CSI, Berkeley. xoz qomasio.icrosattia.imiazzaj.eomnmfqheoreticalandexperimentalanalysisoftimber-to-timber jointsconnectedwithinclinedscrews. Construction and Building Materials O4WNRSM-NRTN. xpz kewmarkk.j.ipiessc.m.isiestf.j.envrnfqestsandanalysesofcompositebeamswith fncompletefnteraction.proceedings, Society for Experimental Stress AnalysisIsol.VIko.NITR-VO. x4z diongof.imiazzaj.iqomasio.eomnoflutofplanerefurbishmenttechniquesofexistingtimber floorsbymeansoftimbertotimbercompositestructures.wcte 2012 World Conference on Timber EngineeringEfnmressF. OMP4
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