Moisture Induced Stresses in Glulam: Effect of Cross Section Geometry and Screw Reinforcement

Moisture Induced Stresses in Glulam

Effect of Cross Section Geometry and Screw Reinforcement

Thesis for the degree of Philosophiae Doctor Trondheim, February 2012

Norwegian University of Science and Technology

Faculty of Engineering Science and Technology

Department of Structural Engineering

Thesis for the degree of Philosophiae Doctor Faculty of Engineering Science and Technology Department of Structural Engineering

© Vanessa Angst-Nicollier

ISBN 978-82-471-3562-4 (printed ver.) ISBN 978-82-471-3563-1 (electronic ver.) ISSN 1503-8181

Doctoral theses at NTNU, 2012:139 Printed by NTNU-trykk

ThisdoctoralthesisissubmittedtotheNorwegianUniversityofScienceand Technology(NTNU)forthedegreePhilosophiaeDoctor(PhD).Theworkwas carriedoutattheDepartmentofStructuralEngineering,FacultyofEngineering ScienceandTechnologyatNTNUinTrondheim,Norway.

SupervisorhasbeenProfessorKjellArneMalo.

TheprojectstartedinJanuary2008andcompletedforsubmissioninFebruary 2012,including7monthsofmaternityleaveand7monthsofpartͲtimework (50%).

Theauthor,VanessaAngst,declaresthatthisthesisandtheworkpresentedinit areherownandhavebeengeneratedbyherastheresultoforiginalresearch whileincandidatureforthedegreeofPhilosophiaeDoctoratNTNU.Thethesis containsnomaterialthatwaspreviouslysubmittedforadegreeatthisuniversity oranyotherinstitution.

ThisworkhasbeenfundedbytheResearchCouncilofNorwaythroughtheKMB projectMoistureinducedeffectsonscrewsandthreadedbarconnectionsin timberstructures(Grantno186821/I10).Ithasmoreoverbeensupportedby industrialpartners,suchastheNorwegianorganizationTreindustrienandthe NorwegiancompanyChristianiaSpigerverkASaswellastheNorwegianPublic RoadAdministration.Theirfinancialcontributionsmakingtheprojectpossibleare kindlyacknowledged.

Iwouldliketothankmysupervisor,ProfessorKjellArneMalo,forencouragingme andgivingmetheopportunitytoworkonthisPhDproject,aswellasforvaluable discussions,criticalmanuscriptreadingsandfortakingcareofadministrative issues.

Iamalsogratefultoallthepeoplehelpingmeinmystruggletoobtainafully functionalclimatechamber,inparticularKjellOveSlutåsforhisinitiative,Ove LoraasandOleAunrønning(fromtheBuildingandMaterialTechnologygroup)for providingmeotherclimatechambersasinterimsolutions.Iwouldalsoliketo thanktheotherPhDstudentsattheDepartmentofStructuralEngineeringfora pleasantsocialenvironment.

Iwouldliketoexpressmydeepestgratitudetomyhusband,Ueli,forhissupport throughouttheproject,forhisinspiringinputstomyresearch,andforreadingmy manuscripts.Withouthisencouragementandhelp,thisthesiswouldnothave beenaccomplished.Finally,Iwouldliketothankmylovelydaughter,ElinHanna, for giving me so much joy and laughter, andalsomyunborn child,for unintentionallypushingmeonfinishingmythesis.

Itiswellknownthattimberstructuresareaffectedbytheclimatetowhichthey areexposed.Changesinrelativehumidityofthesurroundingsofastructural membersuchasaglulambeamleadtoaninhomogeneousmoisturedistribution inthecrosssection.Owingtohygroexpansionbeinginternallyrestrained,this resultsinmoistureinducedstressesperpendiculartograin.Acrosssection subjectedtooneͲdimensionalwettingexhibitscompressivestressesattheborder andtensilestressesinthecentre,whereasinadryingcase,theoppositeapplies.

Itwasintheliteraturereportedthatthestressesestablishedduringwettingare generallylargerthancorrespondingstressesduringdrying.Moreover,thetensile stresseswerefoundtoexceedthecharacteristictensilestrengthoftimber perpendiculartograin.Thisledtoanincreasinginterestinmoistureinduced stressesintimber,whichwasalsounderpinnedbytheoccurrenceofseveral failuresoftimberstructuresduringthelastyears,wheretensionperpendicularto grainwasoneofthemostcommonfailurecauses.

Thisthesispresentsastateoftheartonmoistureinducedstressesinglulam, complementedwithownfindings.Thesearecoveredindetailintheappended papers.Thefirstobjectivewastofindasuitablemodeltodescribemoisture inducedstresses,inparticularwithrespecttomechanosorption.Areviewof existingmodelsledtotheconclusionthattheselectionofcorrectmaterial parametersismorecriticaltoobtainreliableresultsthantheformulationofthe mechanosorptionmodel.Aseriesoflaboratorytestswasthusperformedinorder todeterminetheparametersrequiredforthemodelandtoexperimentally measuremoistureinducedstressesinglulamsubjectedtooneͲdimensional wetting/drying.Specialattentionwaspaidtousingglulamfromthesamebatch foralltheexperimentalmeasurementsinordertocalibratethenumericalmodel reliably.

Theresultsoftheexperimentsconfirmedthatmoistureinducedstressesare largerduringwettingthanduringdrying,andthatthetensilestressescould clearly exceed the characteristic tensile strength perpendicular to grain.

Nevertheless,experimentalapproachesareonlycapableofdeterminingaverage stresses(averageovercrosssectionheight).Thus,inasubsequentstep,a numericalmodelwasusedtocalculatelocalmoistureinducedstresses.Itwas shownthatthearisingstressesdependhighlyontheannualringconfigurationof theglulamcrosssection.Moreover,localstressescanbesignificantlylargerthan

withoutpiths.

Furthermore,theuseofselfͲtappingscrewsasameasuretoincreasetheload bearingcapacityofglulambeamssubjectedtoclimatevariationswasstudied.It wasshownthatthistimberreinforcementmethodwasabletosignificantly reducethelargetensilestressesarisingduringwettinginthecrosssectioncentre, whileduringdrying,itincreasedonlyslightlythetensilestressesattheborder.

Thenumericalmodelwasfurtherusedtostudytheeffectofthescrewdistance, crosssectionwidth,andpithlocationinthelaminatesduringwetting.Itwas foundthatallthreefactorsconsiderablyinfluencethestresses.Theresults indicated,however,thatasignificantreductionoftensilestressesispossiblewith practicalscrewdistances.

Preface...i

Acknowledgements...iii

Summary...v

Tableofcontents...vii

Listofpapers...ix

Symbols,indicesandabbreviations...xi

1 Introduction...1

1.1 Background...1

1.2 Objectives...2

1.3 Limitations...3

2 Glulamandsomeofitsproperties...4

2.1 Glulammanufacture...4

2.2 Moisturecontentanddimensionalchanges...5

2.3 Strengthandstiffness...7

2.4 Tensilestrengthperpendiculartograin...9

2.5 Fractureperpendiculartograin...14

3 Moistureinducedstresses...16

3.1 Introduction...16

3.2 Mechanosorption...17

3.3 Measurementofmoistureinducedstresses...18

3.4 Experimentalresults...20

3.5 Modellingofmoistureinducedstresses...22

3.6 Numericalresults...25

3.7 Summary...27

4 Superpositionofinternalandexternalstresses...29

4.1 Introduction...29

4.2 Superpositionofstressesinglulam...29

4.5 Summary...35

5 Dealingwithmoistureinducedstresses...36

5.1 Introduction...36

5.2 Moistureinducedstressesasanadditionalload...36

5.3 Coatingofglulambeams...38

5.4 Reinforcementperpendiculartograin...41

5.5 Summary...43

6 Conclusionsandfuturework...44

6.1 Summaryandconclusions...44

6.2 Futureresearchwork...46

7 References...47

8 AppendedpapersI,II,III,IV………..51 A AppendixA………A B AppendixB………B

Thethesisincludesthefollowingappendedpapers.Theyarereferredtobyname andyear.

1 Moistureinducedstressesperpendiculartothegraininglulam:

Reviewandevaluationoftherelativeimportanceofmodelsand parameters

VanessaAngstandKjellA.Malo Holzforschung64(2010)609–617

2 Theeffectofclimatevariationsonglulam–anexperimentalstudy VanessaAngstandKjellA.Malo

EuropeanJournalofWoodandWoodProducts(2012) DOI10.1007/s00107Ͳ012Ͳ0594Ͳy

3 Moistureinducedstressesinglulamcrosssectionsduringwetting exposures

VanessaAngstandKjellA.Malo

SubmittedtoWoodScienceandTechnology(2011)

4 EffectofselfͲtappingscrewsonmoistureinducedstressesinglulam VanessaAngstandKjellA.Malo

SubmittedtoEngineeringStructures(2012)

Declarationofauthorshipforpapers1Ͳ4

VanessaAngstplannedandconductedalltheexperiments,didthenumerical simulations,evaluatedtheresults,andwrotetheappendedpapers.ThecoͲauthor contributedwithconstructivecriticismthatincreasedthescientificqualityofthe publications.

Symbol Meaning Dimension

ɲ Hygroexpansioncoefficient Ͳ

D Diffusioncoefficient m²/s

E Modulusofelasticity MPa

ɸc Creepstrain Ͳ

ɸe Elasticstrain Ͳ

ɸms MechanoͲsorptivecreepstrain Ͳ

ɸs LinearshrinkageͲswellingstrain Ͳ

ɸmean Meanreleasedstrain Ͳ

H Crosssectionheight mm

kDOL Stresslevelatfailure(ratiooffailureload

totheshortͲtermstrength) Ͳ

kmod ModificationfactorforDOLandMC Ͳ

L Specimenlength(inlongitudinaldirection) mm

Ɏ Loadcombinationfactor Ͳ

ʍ Stress MPa

S Surfaceemissioncoefficient m/s

tF Timetofailure days

u Moisturecontent %

ueq Equilibriummoisturecontent %

usurf Surfacemoisturecontent %

W Crosssectionwidth mm

mean meanvalue

R radialdirection

T tangentialdirection

Abbreviation Meaning

d Days

DOL Durationofload

EMC Equilibriummoisturecontent

FSP Fibresaturationpoint

GEV Generalisedextremevaluedistribution

MC Moisturecontent

MiS Moistureinducedstresses

MOE Modulusofelasticity

RH Relativehumidity

ͳ

1.1 Background

Timberistheoldestbuildingmaterial.Ithasbeenusedsinceancienttimefor structuralpurposessuchasboatconstructions,housingsandbridges.Timberhas beenextensivelyused,duetoitsworkability,itstraditionandparticularlydueto itsavailabilityalmosteverywhere.JapanandScandinaviaareregionswithalong traditionoftimberconstruction,whereeventimberstructuresfromtheseventh andtwelfthcentury,respectively,arestillexisting(Thelandersson2003).Before modernstructuralmaterialsbecameavailable,timberwasthepredominant materialusedinbridgeconstruction.Oneoftheoldeststillexistingtimberbridges istheChapelBridgeinLucerne,Switzerland,builtin1333.Theseexamplesshow thatiftimberstructuresareproperlydesigned andmaintained,theyhave excellentdurability(Thelandersson2003).

Today,timberasastructuralmaterialisusedinawidevarietyofapplications, suchassinglefamilyhouses,largescaleresidentialandindustrialbuildings,as wellasbridges.Timberhasseveraladvantagescomparedtootherbuilding materials:Itisenvironmentallyfriendly,easilyrecyclableandexhibitsverylow energyconsumptionduringproduction(Thelandersson2003).Moreover,timber hasahighstrengthͲtoͲweightratio,whichfacilitatesproduction,transportand erectionandwhichcontributestoagoodperformanceoftimberbuildingsduring earthquakes(KaracabeyliandPopovski2003).Inaddition,timberisaesthetically pleasing,thusofferinggreatpossibilitiesinarchitecturaldesign.

Duetothefactthatthemaximumdimensionofsolidtimberisnaturallylimited, engineeredwoodproductsweredevelopedtoextendthespansfortimber structures.Gluedlaminatedtimber(glulam)wasoneofthefirstengineeredwood products,whichisproducedbygluingtogethertimberlaminatestoformlarger members.Glulamisstillhighlycompetitiveinmodern,largeͲscaleconstructions, asitcanbeproducedinalmostanyshapeandsize(Thelandersson2003;Glulam handbook2003).

Theincreasingenvironmentalawarenessandthetrendtowardsusingecologically soundmaterialsinconstructionleadtoagrowingpopularityoftimber.However, severalfailuresofwoodenroofstructuresthatoccurredincentralandnorthern Europeinthelastyearsnegativelyaffectedtheimageoftimberasaconstruction

material.Inthecases,wherethesefailuresledtofatalitiesandaccordingly receivedlargemediaattention,weaknessesrelatedtothematerialtimberitself werebelievedtobethecause(Frühwaldetal.2007).Thetruthisthoughthat almostwithoutexception,structuralfailureswereduetohumanerrors.Failure analyses showed that a majority of mistakes were related to incorrect assumptionsorinsufficientconsiderationofloadsandactions.Inmanycases,the inadequateconsiderationofclimaticeffectsledtointolerableeffectsfortimber structures.Themostcommonproblemiscracksperpendiculartograinasarising frommoistureinducedstresses(Frühwaldetal.2007;FreseandBlass2007).

Inthepastyears,studieswereperformedtoinvestigatetheeffectofclimate variationsonglulammembers,e.g.(AicherandDillͲLanger1997;Jönsson2005b).

Thesehaveshownthatsignificantmoistureinducedstressesperpendicularto graindevelop,whichincreasetheriskforcracking.Thereisaneedforincreasing theknowledgeaboutmoistureeffects,inordertoproperlytaketheminto accountindesignstandardsandthusinthedesignofsafetimberstructures.

1.2 Objectives

Theobjectiveofthethesiswastoapproachtheproblemofmoistureinduced stressesperpendiculartograininglulambymeansofthefollowingtasks:

1. Numericalmodelformoistureinducedstresses

Reviewtheliteratureandfindasuitablemodeltodescribemoisture inducedstresses,inparticularwithrespecttomechanosorption 2. Experimentstocalibratethenumericalmodel

Experimentallymeasuremoistureinducedstressesinglulamspecimens;

measurethematerialparametersrequiredforthenumericalmodel 3. Mainparametersandlocalstresses

Usetheexperimentalresultsandthemodeltoidentifythemain parametersthatdeterminemoistureinducedstresses;focusinparticular onlocalstressesinadditiontostressesaveragedoverthecrosssection height

4. Reinforcementscrews

AssessthesuitabilityofselfͲtappingscrewsasmeanstomitigatecracking perpendiculartograinowingtomoistureinducedstresses

1.3 Limitations

IntheexperimentsandnumericalsimulationsonlyglulammadeofNorwayspruce (PiceaAbies)isconsidered.Thestudiedspecimensareonamacroscalelevel,thus includingvariousdefectssuchasknots,fibreinclination,reactionwoodandresin pockets.The propertyandtheimpactofthesedefectsas wellasofthe microstructureofthewoodarenottreated.Effectsfromvaryingmoisture contentsresultingfromvaryingRHlevelsarestudied,whilethe effectof fluctuatingtemperatureisdisregarded,aswellaspossiblehysteresiseffects.

Othereffects,suchassizeanddurationofloadeffectsareaddressedinthe theoreticalandreviewpart,butareneglectedintheexperimentsandsimulations performedbytheauthor.Similarly,timeͲdependentcreepisignored.

ʹ

2.1 Glulammanufacture

Thedimensionofstructuraltimbersawnfromlogsisnaturallylimited.To overcometheselimitationstimberbeamsaregluedtogethertoformlarger members,commonlyreferredtoasgluedlaminatedtimberorsimplyglulam.

Inprinciple,anywoodspeciescanbeusedforglulamproduction,butinpractice mainlysoftwoods(spruce)areused,ashardwoodsareoftenassociatedwith difficultiesingluing.Laminatesofacertainthicknessaresawnfromthelogand driedtouniformmoisturecontent,beforebeingstrengthgraded.Thestrength gradingallowsaglulamcrosssectiontobebuiltupoflaminateswiththesame strength(homogeneousglulam),orwithhigherqualityintheouterlaminates, wherestressesnormallyarehighest(combinedglulam).Thelaminatesarejoined lengthwisebymeansoffingerͲjointsandcuttotherequiredlength.Thelaminates arethenplacedontopofeachother,withtheirgraininthelongitudinaldirection ofthemember,andgluedtogethertoformthedesiredcrosssection.Toreduce internalstressesthelaminatesareplacedinsuchawaythatthecoresidesare identicallyorientedthroughoutthecrosssection,whiletheoutermostlaminates arealwaysturnedwiththecoresideoutwards(Fig.1).

Fig.1Orientationoflaminatesinaglulambeam

Thelaminatepackageorglulammemberisthenliftedovertobencheswherethe necessarypressureisapplied.Whenpressureisapplied,thelaminatesmaybe bentto produce camberedor curved forms.Theoretically,glulamcan be manufacturedinalmostanydesiredshapeandsize.Inpractice,however,thesize islimitedforreasonsrelatedtotransportation,sizeoftheproductionareaand opentimeoftheadhesive.Glulamissuitableforawidevarietyofuses,butowing toitshighstrengthͲtoͲweightratioitisespeciallyappropriatefortheconstruction ofhallswithlargespans.Furtherinformationaboutglulamcanbefounda.o.in theGlulamhandbook(2003).

2.2 Moisturecontentanddimensionalchanges

Themoisturecontent(MC)isdefinedastheweightofwatercontainedinthe woodrelativetotheweightofdrywood.Watercontainedinwoodmaybe presentintwoforms,asfreewater(inthecelllumen)orasboundwater(bound incellwalls).Whenwoodisdried,freewaterisfirstlost.Themoisturecontent, whenthecellwallsaresaturatedwithwaterbutnofreewaterispresentinthe celllumen,iscalledfibresaturationpoint(FSP).Generally,thefibresaturation pointrangesfrom25Ͳ35%,where30%isareasonableaverageformostpractical purposes(GlassandZelinka2010).

Thelaminationsusedinglulamcomponentsaredriedindividuallytoawood moisturecontentofabout12%beforegluing.Underdifferentclimaticconditions themoisturecontentoftheglulammemberwillintimeadjustitselftothe surroundingrelativehumidity(RH)andtothetemperature.Themoisturecontent whichisinequilibriumwiththerelativehumidityandthetemperature,istermed theequilibriummoisturecontent(EMC)anddependsonwhetheritisreachedas aresultofdesorptionoradsorption.Thisphenomenonisknownashysteresis.As aconsequenceofseasonalchangesintheclimate,themoisturecontentina structurewillvarycontinuously.

Glulam,likeothertimbermaterials,exhibitsdimensionalchangesasaresultof moisturevariations(belowfibresaturation):Glulamshrinkswhenthemoisture contentdecreasesandswellswhenitincreases.Thesedimensionalchangesor movementsarenotequalinalldirections.Oftentangentialchangesareabout twicetheradialchanges,whereaslongitudinalchangesarenegligible(Glassand Zelinka2010).Toquantifythesemovements,dimensionalchangesarerecorded overarangeofrelativehumiditiesormoisturecontents.Thelinearrelationship

betweenchangeinlengthȴlandchangeinmoisturecontentȴucanbeexpressed withthefollowingequation:

' ˜ 'l D u,whereɲisthehygroexpansioncoefficient. (1) Thepresentauthorhasperformedmeasurementsandcalculationsconcerningthe hygroexpansioncoefficientintangentialandradialdirection,reportedinAngst andMalo(2012a)andAppendixA.Inthefirstreference,glulamspecimens(Fig.1) wereseasonedineitherdry(40%RH)orwetclimate(90%RH)beforebeingcut intoslicesalongtheheight.Thesliceswereexposedtowettingordrying, respectively,while the change inlengthsandthemoisturecontentswere measured.Therelationbetweenchangeinlengthsandchangeinmoisture contentsresultedineffectivehygroexpansioncoefficientsalongtheheightofthe slices.Bymeansofanumericalmodel,theeffectivehygroexpansioncoefficients couldbedividedinatangentialandaradialhygroexpansioncoefficient.In contrasttotheliterature,thepresentauthorfounddifferentcoefficientsforthe case of wetting and drying. Additional measurements and calculations of hygroexpansioncoefficientsreportedinAppendixArevealedthesame:Different coefficientswereobtainedforwettinganddrying.Moreover,theindividual coefficients were similar in both studies (Table 1), although these were determinedondifferentspecimenssubjectedtodifferentclimatevariations.The resultswereintherangeofliteraturevaluesforthesametypeofglulam,or glulamlaminationbeingNorwayspruce(Piceaabies),respectively.Table1shows thatthecoefficientsobtainedbydifferentauthorsvaryconsiderablyalthough theywererecordedonthesamematerial.Therelationbetweentangentialand radialcoefficient,however,isverysimilar,beingapproximately2:1.

Table1HygroexpansioncoefficientsforNorwayspruce(Piceaabies)

Tangentialdirection Radialdirection

Presentauthor (AngstandMalo2012a)

0.32/0.26 wetting/drying

0.15/0.14 wetting/drying

Presentauthor (AppendixA)

0.34/0.28 wetting/drying

0.17/0.14 wetting/drying

Jönsson(2005b) 0.22 0.11

Ormarsson(1999) 0.35 0.19

Dinwoodie(2000) 0.15 0.07

Inordertominimizedimensionalchangesofglulammembersinservice,the membersaredriedtoamoisturecontentclosetotheequilibriummoisture contentlikelytobeencounteredinservicebeforeassembly.Otherwise,hindered shrinkagedeformationscan occurwhich may, for example, cause tension perpendiculartograinandleadtoaprematurefailure.

2.3 Strengthandstiffness

Glulamcomponentsachieveingeneralgreaterstrengthandstiffnessproperties than corresponding dimensions of ordinary structural timber, because the variabilityinstrengthwithinthememberissmaller.Strengthreducingdefectsof solidwoodareeitherremovedduringmanufactureormoreuniformlydistributed inthefinishedglulammembersothateachdefecthaslessimportancecompared tosolidwood.ThiscanbeexplainedbythesoͲcalled“laminationeffect”,which meansthattheloadsharingbetweenlaminationsallowslocallyweakzonesto redistributestresstoadjacentstrongerregions(Glulamhandbook2003).The strengthofordinarystructuraltimber,ontheotherhand,correspondstothe strengthoftheweakestcrosssection,usuallyatthelocationofaknotorsimilar weaknesses.

Strengthandstiffnesspropertiesvaryconsiderablywithrespecttothematerial direction.Duetotheorientationofthewoodfibres,strengthandstiffnessare muchhigherinthelongitudinaldirectionthaninthetransversedirection.The propertiesdifferalsointhetransversedirection,betweenradialandtangential direction. In engineeringdesign, however,nodistinction is madebetween tangential and radial direction, and thus only parameters parallel and perpendiculartothegrainareprovided.Aglulambeamiscomposedofseveral laminates,eachwithadifferentannualringpattern,andthusdifferentmaterial orientations(Fig.1).Thereby,theoriginofthematerialorientationsislocatedin thepith ofeachlaminate,i.e.thecentre of the annualrings. This nonͲ homogeneityofglulamresultsinirregularstressdistributionswithinthecross sectionuponloading.Astandardglulamcrosssectionwhichissubjectedto uniformlydistributedtensileloadingof0.2MPainverticaldirectionrevealstwo issues (Aicher andDillͲLanger1997): Thehorizontal distribution of vertical stressesattheloweredgeofoneboardlocatedinthecentreofthecrosssection exhibitsapronouncedstresspeaknearmidͲwidth(Fig.2).Thispeakisbelievedto resultfromthedifferencesbetweentangentialandradialstiffnessandalsofroma soͲcalledshearcouplingeffect.TheverticalstressdistributionalongthecentreͲ line(midͲwidth)showsanincreaseofthestresstowardsthegluelines(Fig.2),due

tothebreakingofthepolarmaterialsymmetryattheinterfacesoftheglued laminations.Themaximumstressesareapproximately2.5timestheapplied uniformtensilestressonthecrosssection.Asimilarstudyinvolvingglulamcross sectionswithdifferentannualringpatternsobtainedmaximumstresseswhich werebetween2.5and4.4timestheapplieduniformtensilestress,dependingon thegeometricalconfigurationofthecrosssection(AicherandDillͲLanger2005).

Ananalogousinfluenceofthecrosssectionconfigurationwasalsofoundin curvedglulambeamswhichweresubjectedtoanopeningbendingmoment.

Fig.2Stressdistributionsinaglulamcrosssectionduetouniaxialtensileloadinginvertical direction(AicherandDillͲLanger1997)

Inaddition,themechanicalpropertiesarealsoinfluencedbyothereffects,suchas moisturecontent,durationofloading(DOL),andcrosssectionsize.Thelatteris commonlyreferredtoas“sizeeffect”or“volumeeffect”andmeansthatlarge beamstendtohavelowerstrengththansmallbeams.Generally,thisisexplained by“Weibull’sweakestlinktheory”,astochasticphenomenon,whichstates,that theprobabilityofencounteringadefectabletocausefailureinabeamincreases withanincreaseinthevolumeofthebeam.However,thissizeorvolumeeffectis believedtoalsobecausedbyadeterministicphenomenon,namelybystress

concentrations(Astrupetal.2007).Thesestressconcentrations,whichcause lowerstrength,arisefromthecylindricalorthotropicstructureofglulam.

2.4 Tensilestrengthperpendiculartograin

Glulamhasaverylowtensilestrengthperpendiculartograin,whichisalso influencedbythedifferent effectsmentionedabove.Inthefollowing,the differenteffectswillbediscussedspecificallywithregardtotensilestrength perpendiculartograin,asthispropertyisrelevantforthepresentresearch.The mainobservationsandresultsfromliteratureconcerningtensilestrengthof glulamperpendiculartograinwillbepresented.

EffectofMClevel:TensilestrengthincreaseswithdecreasinglevelofMC Tensiletestsperformedonglulamspecimens,whichhavebeenseasonedin differentclimates,showacleareffectoftheMClevel.ThehighertheMCinthe glulamis,theloweristhecorrespondingtensilestrength.Note,thatinthe presentsectiononlyspecimenswithconstantMCoverthecrosssectionsare regarded.

ThefollowingresultsarefromJönssonandThelandersson(2003).Theyperformed tensile tests perpendicular to grain on thin glulam specimens (W*H*L = 90*270*16mm³),whichwereseasonedin40%,in60%,orin80%RHpriorto testing.Figure3showsthemeanultimatetensilestrengthofspecimensseasoned in40%,60%and80%RHthatcorrespondtoequilibriumMCofapprox.9,11,and 16%,respectively.Itcanbenoticedthatthestrengthinadrystage(40%RH)is 60%higherthaninawetstage(80%RH).

Fig.3Effectofmoisturecontentontensilestrengthperpendiculartograin(basedon valuesfromJönssonandThelandersson(2003))

Durationofloadeffect:Tensilestrengthdecreasesunderlongtermloading Timberorglulamexperiencesasignificantlossofstrengthandstiffnessunder longtermloading,whichiscommonlyreferredtoasdurationofload(DOL)effect.

DOLisgenerallyquantifiedbycomparingthestrengthofspecimensunderlongͲ termloadingandstandardshortͲtermtests.Thereby,differentspecimenshaveto beusedforthesetwotests,asthesamespecimencannotbebrokentwice.To minimizethiseffect,matchedsamplesareusuallycompared(Hoffmeyer2003).

ThelongͲtermtestsareperformedunderconstantorramploadsuntilfailure occurs.Thestresslevelatfailure,whichistherelationbetweenthelongͲtermand shortͲtermstress,denotestheDOLeffect:

Stresslevelatfailure: V

V

long term

F DOL

short term

SL t k (2)

DOLtestsperformedontensionspecimens(90and140mmwidth)andcurved glulambeams(90and140mmwidth,4Ͳpointbendingtests)inconstantclimates (65%and85%RH)showed,thatthetensilestrengthisreducedunderlongterm loading(Aicheretal.1998;Gowdaetal.1998):Stresslevelsatfailure(kDOL)of tensionspecimens(90and140mm)were0.70and0.75,whereastheywere0.77 and0.87inthecaseofcurvedbeams.Thus,thedurationofloadeffectappearsto beslightlylesssevereincurvedbeams.Theassociatedtimestofailurewere22Ͳ24 daysinthecaseoftensionspecimensand4Ͳ14dayswithcurvedbeams.

Sizeorvolumeeffect:Tensilestrengthincreaseswithdecreasingvolume NumerousshortͲtermtensiletestsperformedonglulamspecimensandoncurved glulambeams(testedunder4Ͳpointbending)inconstantclimatesreportedinthe literatureshowaclearsizeorvolumeeffect:Withincreasingspecimensize(or volume)themeanultimatetensilestrengthdecreases.

Figure4showsthevolume(a)andtheheight(b)oftensionspecimensversusthe meanultimatetensilestrengthfromthreedifferentliteraturesources(Aicheret al.1998;BlassandSchmid2001;Astrupetal. 2007).Inprismaticglulam specimensunderuniaxialtensileloadingtheheightappearstobethedominant factorforthesizeeffect.

Fig.4Sizeeffectinglulamspecimensundertensileloading

Figure5ashowsthevolume(ofconstantmomentarea)ofcurvedglulambeams versusthemeanshortͲtermtensilestrengthunder4Ͳpointbendingfromtwo differentliteraturesources(EhlbeckandKürth1992;Aicheretal.1998).Plotting thestrengthversusthebeamheight(Fig.5b)revealsthatincurvedbeamsunder bendingtheheightisnottheonlyfactorcontrollingthesizeeffect.Inparticular thedatafromAicheretal.(1998)showsthatthewidthandthelengthratherthan theheightaffectthemeasuredstrength.

Fig.5Sizeeffectincurvedglulambeamsunder4Ͳpointbending

Thevolumeeffectcanbedescribedasfollows(adaptedfromtheexpressiongiven inEurocode5(2004)):

0 , 0 ,

n

t V t V

V f f

V

§ · ˜

¨ ¸

© ¹ , (3)

whereV0isareferencevolume(m³)havingstrength ft,V0.

Inthefollowing,theexponentnforthevolumeeffectwascalculatedbasedon themeantensilestrengthsfromtheglulamspecimensdisplayedinFig.4a.The referencevolumewassetto0.01m³,assuggestedinEurocode5(2004).The resultingexponentwasfoundtobe0.37(Fig.6a).Similarly,aheighteffect exponentcanbecalculated.Inthepresentcase,theexponentwasfoundtobe 0.4forareferenceheightof400mm.Thevolumeeffectexponentcalculated basedonmeanvaluesfromcurvedglulambeamsisabout0.28.Thisrelationship isdisplayedinFig.6b.Thus,thisvolumeeffectisofaslightlylowersizeincurved glulambeamsthanintensionspecimens.

Fig.6Fittedexponentforthevolumeeffect

Effectofgeometricalconfiguration:

Tensiletestsperformedonglulamlaminatesoronthinslicesofsolidwood (spruce,W*H*L=45*180*70mm³),respectively,revealedthattheresultsare stronglyinfluencedbythemainannualringpattern(BlassandSchmid2001).The largesttensilestrengthwasobtainedwhentheannualringswereorientedmainly inradialdirection.Whentheringswereorientedunder45degree,themean strengthwas20%lower,andintangentialdirection,themeanstrengthwas30%

lowerthaninradialdirection.However,whenapithwaspresentwithinthe testedwoodslice,themeanstrengthwaseven60%lowerthantheoneinradial direction,independentoftheannualringorientationinthisslice.

Thegeometricalconfigurationalsoinfluencesthefailurebehaviour.Whenthe pithispresentwithinthefailedlaminate,thecrackgenerallystartsatthepithand evolvesradiallytotheedges.ThiswasobservedbothbyBlassandSchmid(2001) inthecaseoftensiletestsonwoodslices,andbyJönsson(2005b)inthecaseof tensiletestsonglulamspecimens.Whenthepithisabsent,failurestartsin locationsofstressconcentrations.Jönssonobservedthatfailureoccurredinthe vicinityoftheglueline,wherestressconcentrationsarepresentduetodifferences intheannualringpatternbetweenthelaminates(compareFig.2).Similarly,in thecaseoftheglulambeamstestedin4ͲpointbendingbyEhlbeckandKürth (1992),failurestartedatthelocationwiththehighesttensilestressandcontinued alongthelaminate.Mostofthecracksappearedinorinthevicinityoftheglued joint.Butastheseshowedwoodfibresonthesurface,itwasassumedthatnot thegluewasthecauseforfailurebutthechangeinwoodstructurebetweenthe laminates.

2.5 Fractureperpendiculartograin

Asmentionedabove,glulamorwoodingeneralhasaverylowtensilestrength perpendiculartograin, butalsoalowresistancetocrackpropagation.In structuraldesign,effortsaremadetoavoidtensionperpendiculartograin,asit mayleadtocracking,whenthecorrespondingstrengthisexceeded.However, suchstressescannotalwaysbeavoided,andseveraltimberfailuresdueto fractureperpendiculartograinhaveoccurred.Infact,accordingtodifferent failureanalysesoftimberstructures,tensionfailureperpendiculartograinisone ofthemostcommonfailuremodes(FreseandBlass2007;Frühwaldetal.2007).

Avarietyofcausescanleadtotensilestressesperpendiculartograin(Gustafsson 2003).Firstly,certaingeometricalshapesofthestructuralmembercanimply tensionperpendiculartograinuponloadingofthestructure(Fig.7).Curved glulambeams,forexample,whicharesubjectedtoamomentexhibitradial stresses.Ifthemomenttriesto“flatten”thebeamtheradialstresseswillbe tensilestresses(perpendiculartograin).Similarly,curvedglulambeamsunder vertical,downwardloadingexhibittensilestressesperpendiculartothegrain withinthecurvedpart.Largeholesinglulamorstructuraltimberbeamsi.e.

suddenchangesinthecrosssection,impedetheflowofforces.Thisleadstolocal tensilestressesneartheholesuponloading.Notchesinbeamendscause concentratedtensilestresses,whichmayleadtocrackingevenatlowexternal loading.

Fig.7Structuralmembersexhibitingtensilestressesperpendiculartograin

(Gustafsson2003)

Eigenstressesarefurthercausesfortensionandthusfractureperpendicularto grain.Adecreaseinmoisturecontentmaygiveeigenstressesduetothedifferent shrinkageinthetangentialandtheradialdirections.ThenonͲuniformmoisture contentinastructuralmember,asaresultofseasonalclimatechanges,canlead tohighcompressiveandtensilestressesperpendiculartograin,andthusproduce crackingevenwithoutexternalload.Thiskindofeigenstresseswillbediscussedin detailinthenextchapter.

Also the nonͲhomogeneity of wood may induce high tensile stresses perpendiculartograin(Fig.8).Theannualringpatterninaglulamcrosssection, forexample,whichisresponsibleforthelocalvariationsofmaterialorientation, mayresultin crackingwhenaglulamspecimenis loadedin compression perpendiculartograin.

Fig.8NonͲhomogeneityofwoodleadingtotensilestressesperpendiculartograin (Gustafsson2003)

Thereareofcoursealsofurthercasesofperpendiculartograinfracture,suchas inmechanicalandadhesivejoints,butasthesearenotrelevantinthepresent context,theyareomitted.

͵

3.1 Introduction

Themoisturecontentofglulammembersinservicevarieswithvaryingclimate conditionsofthesurroundings.Asmoisturetransportintimberorglulamis relativelyslow,largermembersgenerallyexhibitnonuniformmoisturecontent distributionsacrossthecrosssection.Thesemoisturegradientsleadtointernal stresses,whichareoftenreferredtoasmoistureinducedstresses:Thetimberin thecrosssectioncannotexpandorshrinkaccordingtoitsactualmoisture content,asitisrestrainedbyadjacenttimberexhibitingdifferentmoisture contents.Inawettingcase,forinstance,themoisturecontentincreasesinthe outerpartsofthecrosssection,givingrisetoexpansion.However,theexpansion movementisrestrainedbytheinnerpartsofthecrosssection(havinglower moisturecontents).Inconsequenceoftherestraint,compressivestressesarisein theouterparts,whereastensilestressesariseinthecentreofthecrosssection.In adryingcase,theoppositeeffecttakesplace:Theouterpartsexhibitdecreasing moisturecontents,givingrisetoshrinkage.Owingtotheinternalrestraint,tensile stressesarecreatedintheouterparts,andcompressivestressesinthecentre.

Duetothefact,thatnoexternalstressesarepresent,thecompressiveandtensile stresseswithinthecrosssectionareselfͲbalancing.Themoistureinducedstresses canbetensilestressesinaperpendiculartograindirectionandthusmaycause cracksintheglulammember.Duetothelowcrackresistanceinthisdirection, thesecracksmayevolveandcausefailureofthewholemember.Accordingtothe correspondingstressdistributioninawettingcase,thesecrackswouldstartinthe centreofthebeam,whiletheywouldstartonthesurfaceinthedryingcase.

Moistureinducedstressescanbeevaluatedbymeansofexperimentsorwith numericalsimulations.Atypicalcaseinpracticeisalongglulambeam(withL>>

WandH)thatiscoveredonthetopside.Asclimatechangesareprimarilyinduced fromthelateralfaces(e.g.rain,sun),moistureinducedstressesareinthiscase generally assumed to result from a oneͲdimensional moisture transport perpendiculartograin.

3.2 Mechanosorption

Timberorglulamwhichissubjectedtobothstressesandvarying climate conditionsexhibitadditionaldeformations–aneffectcalledmechanosorption.

Thereby,thesestressescanbecausedbyanexternalloadorbyinternalstresses, suchasinthecaseofmoistureinducedstresses.Thus,wherevermoisture induced stresses are present, mechanosorption takes place. Since mechanosorptionissimilartopurecreep,itisalsoreferredtoasmechanoͲ sorptivecreep.Thedifferenceisthatpurecreepisaneffectoftime,while mechanosorptionisaneffectofvaryingmoisturecontents.

Theconsequencesofmechanosorptiondifferdependingonwhethertheeffectis aresultoflongitudinalstressesortransversestresses(suchasmoistureinduced stresses).Extensiveworkhasbeenperformedbydifferentresearcherstostudy thephenomenonofmechanosorption,e.g.(Grossman1976;Hoffmeyerand Davidson 1989;RantaͲMaunus 1975; Mårtensson and Thelandersson 1990;

Mårtensson1994a,b).Thesestudiesweredealingmainlywithlongitudinal bendingstressesduetoexternalload.Typically,thedeflectionofabeam subjectedtoconstantloadandsimultaneousmoisturevariationsismonitored.

Initially,anelasticdeflectiontakesplace,which,ifmoisturecontentandloadare constant,isfollowedbyapurecreepdeflection.Ifthemoisturecontentisvaried instead,anincreaseddeflectionoccurs,asaresultofmechanosorption.Thismay leadtoserviceabilityproblems.However,inthecaseoftransversestressesdueto swelling and shrinkage, which is relevant for the present research, mechanosorptionisbeneficial,astheadditionaldeformationsenablerelaxation of internal stresses. Anexperimental study performed by Mårtensson and Svensson(1997)concluded,thatunderrestrainedconditionsmechanosorption significantlyreducesthestresslevel.Thisconclusioncanbeconfirmedbythe presentauthor,whofoundconsiderablemechanoͲsorptivecreepeffectsinglulam specimensundermoistureinducedstresses(AngstandMalo2012a).Further experimentalstudiesregardingmechanosorptionperpendiculartograinfound a.o.thatthemechanoͲsorptivestrainrateislargerduringdryingthanduring wetting(MårtenssonandSvensson1997),andthatmechanosorptionisvery similarincompressionandtension(SvenssonandToratti2002;RantaͲMaunus 1993).Generally,itwasnoticed,thatmechanosorptionismoresignificantin directionsperpendiculartothegrainthaninlongitudinaldirection(RantaͲMaunus 1993).

Basedonexperimentalresultsregardingmechanosorption,constitutivemodels havebeenformulatedtodescribetheresponseoftimberunderstressandvarying moisturecontents(seesection3.5).Suchmodelsareindispensableforthe simulationofmoistureinducedstresses.

3.3 Measurementofmoistureinducedstresses

Forthemeasurementofmoistureinducedstressestheslicingtechniqueis commonlyused(AngstandMalo2012a;Jönsson2004;SvenssonandToratti 2002).Aspecimenwhichisunderaninternalstressstateiscutintoslicesto releasetheinternalstresses.Thelengthofeachsliceismeasuredbeforeandafter cutting.Anincreaseinlengthaftercuttingindicatescompressionstresses,anda decreaseindicatestensilestresses.

ThemeasurementprocedureindetailisvisualisedinFig.9(forthecaseof wetting)andexplainedinthefollowing.Generally,theprocedureisverysimilar amongdifferentexperimentalstudiesintheliteratureregardingmoistureinduced stresses.Thetimberorglulamspecimensarepreparedbyseasoningthemina certainclimateuntilahomogeneousmoisturecontentisobtainedthroughoutthe crosssection.Then,top,bottom,frontandbackfacesofthespecimenaresealed, beforebeingexposedtoaclimatechange(Fig.9a).Thesealingmakesitpossible toobtainaoneͲdimensionalmoisturetransportperpendiculartothegrain(only thelateralfacesareexposed).Afteracertaintimeofclimateexposure,the specimenexhibitsdifferentialdimensionalchanges(Fig.9b).Thespecimenisthen cutintoslicesalongtheheight(Fig.9c),whilethereleaseddeformationsalongthe height are measured. For the measurement of the releaseddeformations differentequipmentscanbeused.Thedeformationscan,forexample,be measuredbytransducerspositionedagainsttheendofthespecimens(Svensson andToratti2002)orbyacontactfreetechniqueusingeitheradigitalcamera (JönssonandSvensson2004)oravideoextensometer(AngstandMalo2012a).

Thecontactfreetechniqueworksasfollows:Eachsliceinthespecimenismarked withadotalongtheupperandlowerside.Beforeandaftercuttingthespecimen intoslices,thecameraorthevideoextensometerrecordsthelocationofthedots.

Thelengthbetweenthesedotsisevaluatedinbothrecordings,L0andL1.The meanreleasedstrainoverthemeasuredlengthcanthenbecalculatedaccording to:

1 0

0

H_mean ^{L L}

L (4)

Fig.9Experimentalprocedureforevaluationofmoistureinducedstresses(wettingcase)

Oncethereleaseddeformationsareknown,themoistureinducedstressescanbe calculated.Themeanmoistureinducedstressescorrespondtothemeanreleased deformationsmultipliedbythemodulusofelasticity,accordingto:

V_mean E_mean˜H_mean (5) Thus,withexperiments,onlymeanmoistureinducedstressescanbeobtained, i.e.oneaveragevalueovertheheightforeachslice.Thisgivesanaveragestress distributionacrossthecrosssection.Theprocedureexplainedabovedoesnot permitthedeterminationoflocalstressesindifferentpointsinthecrosssection.

Theaccuracyofmoistureinducedstressesdeterminedbymeansofexperiments dependsondifferentfactors.Ontheonehand,theaccuracyofthemeasurement ofthereleaseddeformations,whichdependsonthetechniqueused,playsan importantrole.Ontheotherhand,asapparentfromEq.(5),theselectionofa correctmodulusofelasticity(MOE),usedforthecalculationofstresses,is essential.ThevaluefortheMOEcaneitherbeselectedfromtheliteratureor measured directly on the studied specimen. As literature values scatter considerablyforthesametypeoftimberorglulam(compareTable4inAngstand Malo(2010)),itispreferabletomeasurethemodulusofelasticityoneachsliceof thespecimen.Thenagain,theaccuracydependsontheselectedprocedurefor measuringtheMOE.Furthermore,materialparameterssuchastheMOEare highlyinfluencedbythegeometricalconfigurationofthespecimen,onwhichthe parametersaremeasured(AngstandMalo2012a).Thismeansthattwodifferent

specimens can give different MOE distributions and thus different stress distributions.

3.4 Experimentalresults

Intheliterature,experimentalresultsconcerningmoistureinducedstressesin glulamarescarce.Themostknownandoftencitedstudyistheoneperformedby Jönsson(2004).JönssonmeasuredtheMCdistribution,thereleasedstrainsand modulusofelasticityinglulamspecimens(W*H*L=90*270*16mm³)subjected tosingleandcyclicclimatechanges.Withtheobtainedresults,Jönssoncalculated theaveragemoistureinducedstresses.Theclimatevariationscomprehended wettingfrom40%to80%RH,dryingfrom80%to40%RHandmoisturecycling between40%and80%RH,startingat60%RH.Asimilarstudywasperformedby thepresentauthor(AngstandMalo2012a),investigatingtheaveragemoisture inducedstressesinglulamspecimens(W*H*L=90*270*90mm³)subjectedto wettingfrom50%to90%RHanddryingfrom90%to50%RH.Theaverage stresses after 12 and 21 days of climate exposure are displayed in Fig.10,there“average”meansstressesaveragedoverspecimenheight.

Fig.10Averagemoistureinducedstressesafter12and21daysofa)wettingandb)drying andcharacteristictensilestrength(0.5MPa)accordingtoprEN14080(2011).Thisfigureis

amodificationofFig.8inAngstandMalo(2012a)

Theconclusionsfrombothstudiesconcerningaveragestressesalongsliceswere similar.Duringwetting(Fig.10a),thetensilestressesarisinginthecentreofthe specimenmayclearlyexceed0.5MPa,whichisthecharacteristictensilestrength limit for glulam perpendicular to grain according to prEN 14080 (2011).

Furthermore,thetensileandcompressivestressesarealwayslargerduring wettingexposurescomparedtodryingexposures(Fig.10).Figure11showsthe

absolutevalueofthestressesinthecentreandattheborderofthespecimens duringwettinganddrying(averageoverspecimenheight).Thefigureincludes resultsfromJönsson(2004),whicharethestressesafter3,11,and38dofclimate exposure,andtheresultsfromAngstandMalo(2012a),whicharethestresses after5,12,21,and38dofexposure.Thefigureclearlyrevealsthatstressesare largerduringwettingthancorrespondingstressesduringdrying.

TheresultsconcerningcyclicclimatechangesperformedbyJönsson(2004)andby thepresentauthor(AppendixB)showthesameeffect:Afterawettingperiodthe stressesaresignificantlylargerthanafteradryingperiod.Thereby,nocumulative effectofrepeatedmoisturecyclingwasobserved.

Fig.11Absolutemoistureinducedstressesduringwettinganddryingina)thecentreand

b)attheborderofthespecimens(squares=wetting,circles=drying,black=Jönsson, white=AngstandMalo)

Afurtherstudyinvestigatedmoistureinducedstressesinaglulamlaminateorina boardofNorwayspruce(W*H*L=120*40*20mm³)(SvenssonandToratti2002).

Incontrasttothepreviouslymentionedstudies,theoneͲdimensionalmoisture transportoccurrednotalongthewidth,butinthedirectionoftheheight.

Accordingly,thespecimenswerecutalongthewidthandnotalongtheheight.

Thus,themoistureinducedstresseswereinvestigatedmainlyintangential directionafterwettingfrom40%to90%RHordryingfrom90%to40%RHduring 1,14,and43days.After1dthemaximumaveragestressesweresignificantly largerduringwetting(1MPa)thanduringdrying(0.5MPa),whichconformswell withtheresultsfromthepreviouslymentionedstudies.Inthepresentcase,the specimenswererelativelysmall,especiallyindirectionoftheoneͲdimensional moisturetransport(40mm).Asaresult,thestressesduringwettinganddrying

werereversedalreadyafter14d.Interestingly,thereversedstresseswerelarger duringdryingthanduringwetting.

3.5 Modellingofmoistureinducedstresses

Thecalculationofmoistureinducedstressesbymeansofnumericalsimulationsis wellestablished.Thecommonlyappliedbasicmaterialmodelisbasedonastrain rateformulation.Generally,thisformulationtakesonthefollowingform:

İ İ _e İ_s İ_ms İ_c (6)

Thetotalstrainrateisthesumoftheelasticstrainrate,İ_e,thelinearshrinkageͲ swellingstrainrate, İ_s,themechanoͲsorptivecreepstrainrate,İ_ms,andthe creepstrainrate,İ_c.Thedotdenotesderivativewithrespecttotime.Themodel ismostoftenoneͲdimensional,butinrecentyearsseveralthreeͲdimensional modelshavebeenapplied,e.g.(Fortinoetal.2009;GerekeandNiemz2010;

Ormarssonetal.1998).

Elasticstrain:

Thestrainrateiscommonlywrittenas:

İ_e Cı Cı (7)

HereıisthestressvectorandCthecompliancematrix,which,inmatrix notation,isasfollows:

1 0 0 0

1 0 0 0

1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

Q Q

Q Q

Q Q

ª º

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

« »

¬ ¼

LR LT

L R T

RL RT

L R T

TL TR

L R T

LR

LT

RT

E E E

E E E

E E E

C

G G

G

(8)

Thecharacters,E,G,andQ,denotemoduliofelasticity,shearmoduliand Poisson’sratios,respectively.Theindices,L,R,andTdenotelongitudinal,radial andtangentialdirection,respectively.

ThelastterminEq.(7)impliesthatthematerialparameters,whicharethemoduli ofelasticityE,theshearmoduliGandPoisson’sratiosQ,arefunctionsofmoisture content,andthus,time.Thus,therateofthecompliancematrixisneeded.

However,measurementsofmoduliofelasticityEinglulamspecimenshaveshown thatintherangeofclimatevariationsoccurringinpractice,theeffectofMCis negligible(AngstandMalo2012a).Inthepresentwork,thesameassumptionis madefortheeffectofMConshearmoduliGandonPoisson’sratiosQ.Inthis case,thelasttermofEq.(7)canbeomittedandthusİ_ebecomestheelastic strainrate.Forratherextremeclimatevariations,though,aneffectofMCon modulusofelasticitycouldbeobserved,namelythatthemodulusofelasticity increaseswithdecreasingMC(AppendixA).

LinearshrinkageͲswellingstrain:

ThelinearshrinkageͲswellingstrainrateisderivedfromthehygroexpansion coefficientvectorĮandtherateofchangeofmoisturecontentutobe

˜

İ_s Į u (9)

ThevectorĮisdefinedas

>

@

Į _{L R T} ^T (10)

MechanoͲsorptivecreep:

Intheliterature,variousmodelshavebeenproposedformechanoͲsorptivecreep.

AreviewofthesemodelsisgiveninHanhijärvi(2000).Theproposedmodels includemainlyMaxwelltypeandKelvintypemodels,wherebythelatterare usuallymoreadvancedcomprisingmoremodelparameters.However,ithasbeen shownthatforthepresentapplication,whichismodellingofmoistureinduced stressesintimberwithoutexternalload,thetypeofselectedmodelhasa relativelysmalleffect,whiletheselectionofcorrectmaterialparametersismuch moreimportant(AngstandMalo2010).Forthepresentresearch,themechanoͲ sorptivecreepstrainmodel,proposeda.o.byOrmarsson(1999)isused:

˜ ˜

İ_ms m ı u (11)

Thematrixmisamechanosorptionpropertymatrixdefinedas:

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

P P

P P

P P

ª º

« »

« »

« »

« »

« »

« »

¬ ¼

m

L RL R TL T

LR L R TR T

LT L RT R T

LR LT

RT

m m m

m m m

m m m

m m

m

(12)

wheremaremechanosorptioncoefficientsintheorthotropicdirectionsand planesandʅarecouplingcoefficients.

TimeͲdependentcreep:

Intheliterature,differentmodelscanbefoundtomodeltimeͲdependentcreep.

Averysimplewaytoincludecreepeffectsistoreducetheelasticmodulus (MårtenssonandSvensson1997).However,theeffectoftimeͲdependentcreep atlowmoisturecontentsandtemperaturesisconsideredtobesmallcompared withmechanoͲsorptive creep (Mårtenssonand Svensson 1997; Toratti and Svensson2000;Virtaetal.2006).Asaresult,thistermisoftenneglectedinthe strainrateformulationpresentedinEq.(6)(Ormarssonetal.1998;Svenssonand Toratti2002;Häglund2008;GerekeandNiemz2010).

Moisturetransport:

Thestrainrateformulation(Eq.6)withitstermsisafunctionofthemoisture contentchangewithinthetimbercrosssection.Generally,amoisturetransport modelbasedonFick’ssecondlawofmassdiffusionisusedforthecalculationof themoisturecontent,which,forthecaseofoneͲdimensionaldiffusion,canbe writteninthefollowingform:

w w§ w ·

¨ ¸

w w © w ¹

u u

t x D x (13)

Forsimplicityreasons,thediffusioncoefficientDcanbeassumedtobeequalin radialandtangentialdirection(Koponen1983;RosenkildeandArfvidsson1997), thusresultinginonevalueforthecrossgraindirection.Themoistureflow throughthetimbersurfaceisexpressedwiththefollowingequation:

§ w ·

¨ w ¸

© ¹ ^{eq surf} D u S u u t

x (14)

ThesurfaceemissioncoefficientStakesintoaccountthemoisturetransfer resistanceatthesurface,wherethemoistureflowisdrivenbythedifference betweentheactualsurfacemoisturecontent u_surf t andtheequilibrium moisturecontentu_eq,i.e.themoisturecontentreachedatt=ьunderexposure toacertainRH.

3.6 Numericalresults

Thebasicmaterialmodel(Eq.6)presentedabovehasbeenusedinawiderange ofapplicationsbydifferentresearchers.Ithas,amongothers,beenusedto predictcheckingduringtimberdrying(Salin1992),tostudytheshapestabilityof timber(Ormarssonetal.1998),ortomodeltangentialswellingstressesinspruce (Virtaetal.2006).

Inthefollowing,resultsfromtheliteratureconcerningmoistureinducedstresses inglulam,obtainedbymeansofnumericalsimulations,arepresented.Although themodelformulationandtheprocedureareverysimilaramongthedifferent studies, the objectives differ. In some studies absolute stress values are prospected,whereastheinfluenceofvariousparametersisinvestigatedinother studies.Inthefollowing,theresultswillbegroupedaccordingtotheirspecific objectives.Pleasenotethatonlyresultsconcerningmoistureinducedstressesin glulamwithoutexternalloadareconsidered.Thepresenceofanadditional externalloadisdiscussedinalaterchapter.

Effectofnaturalclimatevariations:

Astudydealingwithglulambeams(W*H=90*270mm²),hasshownthat calculatedmoistureinducedstressesusingnaturallyvaryingindoorRH(calculated frommeasuredoutdoorRH)atdifferentlocationsinSwedenduringseveralyears arealmostindependentofthelocation(Häglund2008).Themoisturevariationsat thedifferentlocationsinducedsimilarstresslevels.Furthermore,asexpected,the stressvariabilityintimewasfoundtobelargernearthesurfaceofthebeamthan inthecentreofthebeam.Inthecentreofthebeamlargetensilestressesdid arise,whichwerearound1MPa,thussignificantlyabove0.5MPa(beingthe characteristictensilestrengthaccordingtoprEN14080(2011)).Thesetensile stressesdidariseduringsummer.Theclimatevariationsoveralltheseasons correspondedtoavariationoftherelativehumiditybetween40%and90%RH.

NeglectingthesmallRHfrequenciesintime,themainRHvariationexhibitedlong

moisturecyclesofhalfayearbetween90%and40%RHandhalfayearbetween 40%and90%RH.

Effectofmaterialandmodelparameters:

Variationofdifferentinputparameterssignificantlyaffectstheresultingmoisture inducedstressesperpendiculartograin.Thecalculationofinternalstressesby meansofanumericalmodel,therebyvaryingthelevelofindividualinput parametersprovidesinformationabouttherelativeeffectofasingleparameter.

Oneofthestrongesteffectsarisesfromthemasstransfercoefficient,which governsthemoisturetransferatthesurfaceoftheglulam.Byloweringthis coefficientthrough,forexample,surfacecoatingofthebeam,stressescan significantlybereduced(Häglund2010).Otherconsiderableeffectsarisefromthe material parameters, whereby the influence of different hygroexpansion coefficientsisstrongerthanthatofdifferentMOE’s(Häglund2010;Angstand Malo2010).Theselectionofacertainmechanosorptionmodelaswellasthe magnitudeofthemechanosorptioncoefficients,however,werefoundtobeless importantwithregardtomoistureinducedstressesperpendicularto grain withoutexternalload(Häglund2010;AngstandMalo2010).

Thesefindingssuggestthatwhencalculatingmoistureinducedstressesbymeans ofanumericalmodeltheemphasisshouldbeputonselectingcorrectmaterial parameters,duetotheirstrongeffectontheresults.Asthematerialparameters proposedintheliteraturescatterwidelyforthesamematerial,measurementof allrelevantparametersonthesamebatchofmaterialisrecommendedinorderto obtainreliableresults.Moreover,themechanosorptionmodelparameters,which cannotorcanonlyhardlybemeasured,mayonlybeproperlycalibrated,when thematerialparametersareknownfortheactualcase.Forperformingsensitivity analyses,however,literaturedataareuseful.

Effectofgeometricalconfiguration:

Thegeometricalconfigurationofaglulamspecimen,whichisthedistributionof thepithlocationsamongthelaminates,significantlyinfluencesthestresses.Ithas astrongeffectparticularlyonthelocalmoistureinducedstressesinthecross section,butalsoontheaveragestresses.Inthevicinityofapith,largelocal stressesarise,andwhenapithispresentwithinalaminate,alsolargeaverage stressesareinduced(AngstandMalo2010,2011;Gowdaetal.1998).Anumerical studybythepresentauthorinvestigatedtheeffectof24differentgeometrical configurations(manuallyrecordedonglulamspecimens)onmoistureinduced

stresses(AngstandMalo2011).Theratiooflocalandaveragestresseswasfound tobeintherange2Ͳ7,dependingonthegeometricalconfiguration,inparticular thepresenceorabsenceofpithswithinthelaminates,butalsothelocationof pithswithinthecrosssection.Thestudiedwettingexposure(wettingfrom50to 90%RH)resultedinlocaltensilestresses,whichexceededthetensilestrengthof thematerial,andconsequentlycouldleadtosmallcracksinthecrosssection.It wasconcluded,thatconfigurationscontainingpithsweremorevulnerableto crackformationcomparedtopithͲfreecrosssections.

Effectofcrosssectionwidth:

Anumericalstudyperformedbythepresentauthor(AngstandMalo2011) investigatedtheeffectofdifferentglulamcrosssectionwidths(W=90,140, 215mm)onmoistureinducedstresses.Theaveragestresseswerecalculatedfor 5,12,21,and38dofwettingfrom50to90%RH.Inaddition,alsothe developmentovertimeofaveragestresses(overcrosssectionheight)andlocal stresses(inselectedpointswhereduetothegeometricalconfigurationhighlocal stressesarise)werecomputed.Theresultsshowedthatthewideracrosssection was,thelongerittookuntillargestressesarose,duetothefactsthatthearising tensileforceisdistributedoveralargerinternalpartofthecrosssectionandthat moretimeisneededuntilthecrosssectioncentreisaffectedbyamoisture contentchange.Ontheotherhand,however,thelargestresseswerepresentfor alongerperiodoftimecomparedtosmallercrosssections(becauselarge moisturegradientsaremaintainedlonger).Thehighestaverageandlocalstresses wereattainedinthe140mmwidecrosssection,followedbythe90mm(8Ͳ12%

lower),andthe215mmwidecrosssection(14Ͳ15%lower).Itwasconcluded,that widercrosssectionsareonlypronetocrackingwhenlongwettingcycles(>20 days)occur.

3.7 Summary

Moistureinducedstressescanbedeterminedwithexperimentsandnumerical simulations.Whileonlyaveragestresses(averageovercrosssectionheight)can beobtainedbymeansofexperiments,numericalsimulations,ontheotherhand, makeitpossibletoalsoevaluatelocalstresseswithinthecrosssection.Inthecase ofexperiments,theaccuracyoftheobtainedstressesdependsontheaccuracyof themeasured parameters. In the case of numerical simulations, different parameterstudieshaveshownthatcalculatedresultsarestronglyaffectedbythe selectedmaterialparametersandbytheusedgeometricalconfigurationofthe

specimen.Thus,theaccuracyofnumericalresultsdependsontheselectionof correct parameters and configurations. Different investigations regarding moistureinducedstressesinglulamunderrealisticclimaticconditionshave shownthatsignificanttensilestressesdevelop,whichmayclearlyexceedthe characteristictensilestrengthofglulam.Thus,cracksmightbeinducedeven withoutexternalloading.Furthermore,itwasfoundthatlargerstressesdevelop duringwettingthanduringdrying.

Ͷ

4.1 Introduction

Often,internalstresses,suchasmoistureinducedstresses,occurincombination withstressesfromexternalloads.Thisis,forexample,thecaseinstructurally loadedmemberswhichexhibittensionperpendiculartograinduetotheir geometricalshapeandwhichareatthesametimesubjectedtoclimatechanges.

Aspreviouslypresented(section2.5),suchmembersincludecurvedglulam beams, beamswith largeholes andendͲnotchedbeams.Superpositionof different stresses may lead to very nonͲuniform stress distributions with unfavourablestressconcentrations.Itcanalsoresultinlargetensilestresses perpendiculartograin,whichmightexceedthelowtensilestrengthofglulamin thisdirectionandleadtocracking.Whenthesecracksevolveinthelongitudinal direction,failureofthebeammightoccurandinextremecasesevenleadto failureofthewholestructure.

4.2 Superpositionofstressesinglulam

Thestressdistributioninaglulambeamorspecimenexhibitinginternaland externalstressesisacombinationofthenonͲuniforminternalstressV_i x and thenonͲuniformstressV_e x imposedbytheexternalloading.ThelatterisnonͲ uniform,becausethemodulusofelasticityinloadingdirectionvariesoverthe crosssectionwidth(x)oftheglulambeamorspecimen.Themodulusofelasticity isabouttwotothreetimeslargerinthecentralpartofthecrosssectionthanin theouterpartsduetotheannualringorientationofthelaminates,with predominantradialdirectionsinthecentralpart.Thecombinedstresscanbe expressedasfollows(JönssonandThelandersson2003):

Combinedstress:V_c V_e V_i F^u E x V_i

x x x x

A E , (15)

whereFuistheexternalload,E x thevaryingmodulusofelasticityoverthe crosssectionwidth,and Etheaveragemodulusofelasticityoverthecross section.

Wetting:

Inawettingcase,thesuperpositionofinternalmoistureinducedstressesand external stresses from tensile loading results in an unfavourable stress distributionwithlargetensilestressesinthecrosssectioncentre:Asdiscussedin chapter3,theinternalstressesexhibit tensilestressesinthecentre and compressivestressesattheborder.Thedistributionoftheexternalstresses dependsdirectlyonthevariationofthemodulusofelasticity(compareEq.15) andasthelatterincreasestowardsthecrosssectioncentre,thedistribution exhibitsasimilarshapeastheinternalstresses.Asaresult,thecombinedstress takesonadistributionasschematicallyshowninFig.12a.Thefindingsfromthe experimentalstudyperformedbythepresentauthor(AngstandMalo2012a)and Eq.(15)weretakenasabasisfordrawingFig.12.

Fig.12Superpositionofstressesoverthecrosssectionwidth,schematicallyshown

fora)wettingandb)drying

Drying:

Inadryingcase,thesuperpositionofstressesleadstoamoreuniformstress distribution.Asshowninchapter3,theinternalmoistureinducedstressesexhibit compressivestressesinthecentreandtensilestressesattheborderofthecross section.Theexternalstressesresultingfromtensileloadingexhibitinprinciplethe samedistributionasinthewettingcase:Thestressdistributionisdirectlyrelated tothevariationoftheMOEacrossthecrosssectionwidthandexhibitsthusthe oppositeshapeastheinternalstresses.Whenbothstressesarecombined,a distributionasschematicallyshowninFig.12bisobtained.

Parametersaffectingthecombinedstressdistribution:

Thedistributionsfromthesuperpositionofstressespresentedabove(Fig.12)are especiallytrueforglulamspecimens,exhibitingtypicalcrosssectionswithannual ringpatternsasshowninFig.1.Incrosssections,builtupwithlaminateshaving flatannualrings,forexample,theMOEvariationacrossthecrosssectionwidth wouldbemoreuniform.Thiswouldresultinmoreuniformexternalstress distributions and consequently in a more favourable superposed stress distributioninthewettingcase.

4.3 Experimentalresults

Tensilestrengthperpendiculartograin:

Theinternalstressstateinaglulambeamoraspecimen,asforinstancearising frommoistureinducedstresses,willaffectthetensilestrengthperpendicularto grainthatremainstotakeupexternallycausedstresses.Incases,wheremoisture inducedstressesareverylarge,theresidualtensilestrengthoftheglulammay accordinglybeverylow.Theinternalstresseswillnotonlyaffectthestrengthbut alsothefailurebehaviourofthebeam.

An experimental study performed by Jönsson and Thelandersson (2003) investigatedthe(residual)tensilestrengthperpendiculartograinofglulam specimens, having internal stresses. Thin glulam specimens (W*H*L = 90*270*16mm³)weresubjectedtodifferentclimatehistories,tocreateinternal moistureinducedstresses,beforeperformingtensiletestsperpendiculartograin.

Theclimatehistoriesinvolvedalongwettingcyclefrom40%to80%RH,along dryingcyclefrom80%to40%RH,andshortwettingͲdryingcycles(7daysinterval) between80%and40%RH,startingat60%RH.

Theresultsshowed,that,inthewettingcase,thetensilestrengthperpendicular tograinwassignificantlylowerthanthestrengthofcorrespondingspecimens seasonedinhighhumidity.After5daysofwettingthemeanultimatestrength startedtobelowerthanthestrengthofspecimensseasonedin80%RH.After24 daysofwettingthestrengthwaslowest,being30%lowerthanthestrengthin 80%RH.

However,forthedryingcase,theresultsshowedthatthetensilestrength perpendiculartograinwasbarelyaffected,i.e.itwasofasimilarmagnitudeas thestrengthofspecimensseasonedinlowhumidity.

Theresultsfromspecimenssubjectedtomoisturecycling,revealedthefollowing:

Ifthespecimenwasinawettingphaseattesttime,itbehavedsimilartothe wettingcase,andifthespecimenwasinadryingphaseattesttime,itbehaved similartothedryingcase.Thereby,thenumberofthecycleswasnotsignificant.

Thestrengthofcyclingspecimensinawettingphaseattesttimewas11%lower thanspecimensseasonedin60%RH,whereasspecimensinadryingphaseattest timeexhibited11%higherstrengththanspecimensseasonedin60%RH.

Thefailurebehaviouroftheglulamspecimensduringtesting,observedby JönssonandThelandersson(2003),isinaccordancewiththecombinedstress distributionatfailure,showninFig.13:Inthewettingcase,crackingstartedinthe centre(duetothelargecombinedtensilestressofaround2MPathere)andgrew untilfinalfailure(nonbrittle).Inthedryingcase,theultimatefailurestartedwith acrackattheborderofthespecimenleadingtobrittlefailure.Thereasonforthe crackstartingattheborderwasbelievedtobeduetotheannualringorientation oftheglulam.Attheborderofthecrosssectionglulamconsistsmainlyof tangentialwood,whichhaslowerstrengthpropertiesthanradialwood(inthe crosssectioncentre)(Dahl2009).

Fig.13Superpositionofstressesatfailureafter5daysofa)wettingandb)drying(Jönsson

andThelandersson2003)

Anotherexperimentalstudyinvolvedcurvedglulambeams(W=140mm),which weresubjectedtocyclichumidity(between55%and90%RH),beforetestingthe shortͲtermtensionstrengthperpendiculartograinbya4Ͳpointbendingtest (Gowdaetal.1998).Thestudyshowedsimilarresultsastheonespresented above:Themaximumtensilestrengthofbeamsinawettingphasewas12%lower thanthetensilestrengthofbeamsseasonedinhighhumidity(85%RH).

Bendingstrength:

Thebendingstrengthofcurvedglulambeamsappearstobesimilarlyaffectedby internalmoisturegradients.Jönsson(2005a)performedbendingtestsoncurved glulambeams(W*H=90*280mm²),whichhadpreviouslybeensubjectedto wettingfrom40%to80%RHordryingfrom80%to40%RH.Inthewettingcase, thebendingstrengthwasreducedascomparedwithbeamsexhibitingconstant moisturecontents,i.e.beingfreefrominternalstresses:After11daysofwetting exposurethebendingstrengthwasfoundtobelowest,being40%lowerthanthe bendingstrengthofcorrespondingbeamsseasonedin80%RH.Inthedryingcase, thebendingstrengthwasfoundtobeslightlyhigherthanthebendingstrengthof correspondingbeamsseasonedin40%RH.

Another study investigated thebendingstrength of curvedglulam beams (W=140mm),whichhadbeensubjectedtocyclichumidity(between55%and 90%RH)beforebeingtestedinawettingphase(Gowdaetal.1998).Thestudy showedsimilarresults,althoughlesspronounced.Thebendingstrengthwas foundtobe10%lowerthantheoneofbeamsseasonedinhighhumidity (85%RH).

Durationofload:

Generally,durationofloadeffectisacceleratedundersimultaneousmoisture changesandmechanicalloading.

ExperimentalstudieshavebeenperformedtoinvestigatetheDOLeffectsof glulamundervaryingclimatechanges(Gowdaetal.1998;Aicheretal.1998).DOL effectsin tension perpendicularto grain were investigated with prismatic specimens and curved beams. The prismatic glulam specimens (W*H*L = 90*400*275mm³andW*H*L=140*528*405mm³)weresubjectedtoanaxial tensileforceperpendiculartograinduringDOLtest,whereasthecurvedglulam beams(W=90and140mm)wereloadedin4Ͳpointbending,bothwithstepwise increasingloads.Duringtesting,theclimatewasvariedbetween55%and90%RH withcyclelengthsof28days.Theresultsshowedthatthestresslevelsatfailure wereconsiderablylowerundercyclicexposurethaninconstantclimate(85%RH), namelybyca.35%intheaxiallyloadedtensionspecimensandbyca.30%

(W=90mm)and13%(W=140mm)inthetestswithcurvedbeams,respectively.

Themeanstresslevelsatfailure(kDOL)were0.45and0.50inthecaseofsmalland largetensionspecimens,and0.60and0.66inthecaseofcurvedbeams.The associatedmeantimestofailurerangedfrom15to28days.AsthemajorDOL

effectresultsfromtheclimatevariations,thewidercrosssections(140mm), whicharelessaffectedbyclimatechanges,showed10%lesssevereDOLeffect comparedtothesmallercrosssections(90mm).Thefailureofthebeams occurredalmostalwayswhentheclimatewasatahighRHͲlevel(75%and 90%RH).Tensilestressesperpendiculartograinwerefoundtobehighestinthe centreofthecrosssection(comparesection4.2),andasaresult,failureofthe beamstookplacewiththeappearanceofasinglemajorcrackinthecentreofthe beams.

Otherspecimensweresubjectedtonaturallyvaryingclimateinshelteredoutdoor conditionsinsteadofthecyclicclimatechangesmentionedabove.Inthiscase,it couldbeobservedthatthemajorityofthesamplesalsofailedduringmoist weatherconditions.ThestudiesconcludedthattheincreasedDOLeffectin variableclimateresultsfromthesuperͲimposedeigenstressescausedbythe transientmoisturegradients.

4.4 Numericalresults

Different numerical studies have investigated how the tensile stresses perpendiculartograininglulamareaffectedbysimultaneousexternaland internalloading.Theinternalstresses,whichresultfromvaryingclimatechanges, haveshowntocausesignificantadditionaltensilestresses.

Zhouetal.(2009)investigatedasimplysupportedglulambeam(W=90mm) undernormalserviceloadandclimaticvariations.Whilethestressperpendicular tograininducedbytheserviceloadalonewas0.3MPa,thestressinducedbyload anddailyMCvariationsbetween11and13%MCwas2.2MPa.Thesestresses correspondedtomaximumlocalstressesonthesurfaceofthebeam.Thismeans that,inthiscase,themaincontributiontothestressesperpendiculartograin resultedfromtheclimatechangesofthesurroundings.Duetothelargetensile stresses,thereisahighriskfortheglulambeamtocrack.Itshouldbenoted, however,thatonlyveryshortmoisturecycleswereappliedandthusthemoisture contentvariedonlyatthesurfaceofthebeam,wherebythelargetensilestresses aroseduringdrying.

Anotherstudyinvestigatedaglulamcrosssection(W*H=90*396mm²)subjected toanexternallyappliedtensilestressperpendiculartograinof0.2MPaand climatevariationsbetween50and90%RH(AicherandDillͲLanger1997).The cycleswhichlasted4weeksyieldedconsiderablyhigherstressesthancycles

lasting only 2 weeks. Generally, the stresses after wetting periods were significantlylargerthanafterdryingperiods,whichconformswellwithother studies(AngstandMalo2012a;Jönsson2004).Themaximumstressesinthecross sectioncentreresultingfromclimatevariationsandexternalloadingwereabout 1MPa,whiletheywereabout0.7MPaattheborder.Thecalculationofafictive constantstress(Weibullstress)actingonthewholecrosssectionwidthyielded stressesvaryingbetween0.2and0.65MPa,wherebythelargerstressesoccurred afterwettingperiods.

4.5 Summary

Thesuperpositionofinternalandexternalstressestakesonaverydifferentform dependingoniftheinternalstressesaretheresultofwettingordryingexposure.

Inthecaseofwetting,thecombinationofstressesleadstohightensilestresses perpendiculartograininthecrosssectioncentre.Inthedryingcase,however,the combinationofstressesresultsinamoreuniformstressdistributionoverthe crosssection.Asaconsequence,theremainingtensilestrengthisreduced,ifthe glulambeamorspecimenisinawettingphase,whereasitisbarelyaffected,if theglulambeamorspecimenisinadryingphase.Thereby,itappearsnottobe importantifthewettingordryingphaseresultsfromasingleoracyclicclimate change.Itcanthusbeconcluded,thatwettingisworsethandryingwithrespect tothesuperpositionofstressesandtheremainingstrengthofthebeam.

Inasimilarmanner,theDOLeffectofglulamspecimensandcurvedbeamsis affectedinavaryingclimate.Thestresslevelsatfailureareupto35%lower comparedtotheonesinconstantclimates.