Download - Different Construction for Storey Timber
ComparisonofDifferentConstructionMethodsforMulti‐StoreyTimberBuildings
LUCASBIENERT
SUPERVISORKatalinVertes
UniversityofAgder,2018FacultyofEngineeringandScienceDepartmentofEngineeringSciences
Abstract
MasterThesis‐LucasBienert I
AbstractInthismasterthesis,differenttimbermaterialsandconstructionmethodsareexaminedconcern‐ingtheapplicationinmulti‐storeytimberbuildings.
Althoughwoodasaconstructionmaterialhasmanyadvantages,itistodayonlyusedverylittleforlargerconstructions,concreteandsteeldominatethebuildingindustry.Plannersandengi‐neersareoftenlackingnecessaryexpertisetoutilisetimberinamodern,effectiveway.
Inordertopromotethedevelopmentofmodern,efficientmulti‐storeytimberbuildings,thegoalofthismasterthesisistocontributetoabetterunderstandingofthewood’scharacteristicprop‐ertiesandthebehaviouroftimberinlargerengineeringstructures.
For thispurpose, firsta literatureresearchhasbeenconductedtogather technicalknowledgeaboutmoderntimbermethods.Itcanbeconcludedthat,althoughwoodasanaturalmaterialhassome unfavourable properties,with an appropriate design, those problems can be overcome.Modernengineeredwoodproducts improvethebasicmaterial’spropertiesnoticeableandareimportantespeciallyformulti‐storeytimberbuildings.
Secondly,adesignhasbeencarriedoutforthreedifferentstructuralvariantsofthesameexistingmulti‐storeytimberbuilding.Bymeansof thisdesign,generalconclusionscouldbemadecon‐cerningthesuitabilityofthosedifferentconstructionmethods.Frameconstructionsareveryef‐fectiveforprovidingstabilityfortheoverallstructure.Prefabricatedmethodslikepanelconstruc‐tionshaveeconomicadvantages,should,however,onlybeusedincombinationwithothermeth‐odsforlargertimberstructures.Masstimbermethodsareverywellsuitedformulti‐storeytimberbuildingsandwillsupposedlyplayanimportantroleinthefuture.
Themainoutcomeofthismasterthesisisthattherearenolargehindrancesfortheuseofwoodinmulti‐storeybuildingstodayandthattimberstructuresstillhavemuchunusedpotential.
Declaration
MasterThesis‐LucasBienert II
Declaration
1. WiththisstatementIdeclarethatthismasterthesisismyownworkandthatIhavenotusedothersourcesorreceivedotherhelpthanwhatismarkedassuch.
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wasnotpreviouslysubmittedtoanotheracademicinstitutioninNor‐wayoranyothercountry.
doesnotrefertoexternalsourceswithoutthisbeingproperlymarked.
doesnotrefertoownearlierworkwithoutthisbeingproperlymarked.
includesabibliographywithallsources. isnocopyorduplicateofother’swork.
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3. IamawarethataviolationofthestatementsabovecancausenullificationoftheexaminationandexclusionfromuniversitiesinNorway,cf.Universitets‐oghøgskoleloven§§4‐7and4‐8andForskriftomeksamen§§31.
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6. Ihavestudiedtherulesandguidelinesconcerningtheuseofsourcesandref‐erencesonthelibrary’swebpages.
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LucasBienert,30.11.2018
PublishingAgreement
MasterThesis‐LucasBienert III
PublishingAgreement
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Theauthorhasthecopyrightforthework.Thisincludesamongstotherthingstheexclusiverighttomaketheworkavailableforthepublic(Åndsverkloven.§2).
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tomakethismasterthesisavailableforelectronicpublishing: ☒YES ☐NO
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LucasBienert,30.11.2018
Foreword
MasterThesis‐LucasBienert IV
ForewordDuringmystudiesofcivilengineeringattheLeibnizUniversitätHannover(LUH)inGermanyandtheUniversitetetiAgder(UiA)inNorway,therehadalwaysbeenonebuildingmaterialthatfasci‐natedmethemost,notonlybecauseofitsexcitingmechanicalproperties,butalsobecauseofitslonghistoryandtradition,itsarchitecturalvalueandlastbutnotleastbecauseofitsbeneficialenvironmentalproperties:wood.Thecoursesaboutwoodasaconstructionmaterial that Iat‐tendedwereinteresting,butIwantedtoworkmorewiththismaterial.Moreover,myexperiencesbothattheuniversityandworkingatanengineeringofficeatthesametimeshowedthatconcreteandsteelstilldominatethelargerengineeringstructurestoday.ThatwaswhyIdecidedtowritemymasterthesisaboutmulti‐storeytimberbuildings.
TheseconddecisionImadethenwastowritethemasterthesisinNorway,whichisknownforitsrichwoodenbuildingculture.IhadalreadybeenattheUiAinGrimstadduringbybachelor’sstud‐ies,thistimeIreturnedtofinishmymaster’studies.
Togetherwithmysupervisorat theUiA,KatalinVertes, Idevelopedthetaskandtheresearchquestionsforthemasterthesis.Theworkincludedanextensiveliteratureresearchtogetuptodateconcerningthemoderntimberengineering,aswellastheredesignofanexistingmulti‐storeytimberbuildingusingthreedifferentconstructionmethods.Thechoiceofthebuildingwasquitenatural–afterdoingsomeresearch,Idecidedtoworkwiththehighestwoodenbuildingoftoday,TreetinBergen,thesecondlargestcityinNorway(“Treet”istheNorwegianwordfor“thetree”).Especiallythedesignofthethreevariantsofthisbuildingwaschallenging,butithelpedmetomakesomeimportantexperiencesthatonedoesnotlearninanylecture,e.g.concerningthede‐velopmentofastructuralconcept.
Icouldnothavecompletedthisworkwithoutthehelpfromdifferentpeople.Mostofall,IwanttothankmysupervisorKatalinVertes.ShehadbeenthefirstpersontoteachmeaboutwoodwhenIhadbeenattheUiAforthefirsttimein2014and2015.Nowshewasthepersontoguidemewhileworkingatthismasterthesis.Inspiteofhavingtotravelalot,shewasalwaysreachableandassistedmewithhelpfuladviseorjustreassurancewhenIhaddoubts.
AnotherthankyouisalsomeantformyfriendsandmyfamilybothinNorwayandinGermany,fortheirsupportandforhelpingmetoclearmyheadwhenIneededit.
Finally,Ithankyou,thereader,forbeingopenmindedaboutthiswork,hopingtobeabletocon‐tributetoyourknowledgeabouttimberoratleasttogiveyouaninterestingreadingexperience.
LucasBienert
Grimstad,30.11.2018
TableofContents
MasterThesis‐LucasBienert V
TableofContentsAbstract...................................................................................................................................................................................I
Declaration...........................................................................................................................................................................II
PublishingAgreement....................................................................................................................................................III
Foreword.............................................................................................................................................................................IV
TableofContents..............................................................................................................................................................V
ListofFigures..................................................................................................................................................................VII
ListofTables......................................................................................................................................................................XI
AbbreviationsandSymbols.......................................................................................................................................XII
1. Introduction...........................................................................................................................................................1
2. SocietyPerspective.............................................................................................................................................3
2.1. HistoricalBackground..................................................................................................................................3
2.2. EvolutionofTimberTechnologies...........................................................................................................4
2.3. Today’sGlobalSituation..............................................................................................................................5
2.4. SummaryoftheSocietyPerspective......................................................................................................5
3. Theory......................................................................................................................................................................7
3.1. RulesandStandards......................................................................................................................................7
3.1.1. EuropeanStandards.............................................................................................................................7
3.1.2. NationalRulesandStandardsinNorwayandGermany.......................................................8
3.2. DesignBasis......................................................................................................................................................9
3.2.1. Parameters...............................................................................................................................................9
3.2.2. LoadCalculation.................................................................................................................................11
3.2.3. Software.................................................................................................................................................12
3.3. SummaryoftheTheory.............................................................................................................................12
4. ResearchQuestions.........................................................................................................................................13
5. Case/Materials...................................................................................................................................................14
5.1. TimberMaterials..........................................................................................................................................14
5.1.1. GeneralPropertiesofSolidWood...............................................................................................14
5.1.2. WoodinComparisontoOtherMaterials..................................................................................18
5.1.3. AspectsfromLifeCycleAssessment..........................................................................................20
5.1.4. EngineeredWoodProducts...........................................................................................................22
5.2. TimberConnections...................................................................................................................................25
5.3. TimberStructures.......................................................................................................................................31
5.3.1. TimberFraming..................................................................................................................................31
5.3.2. MassTimber.........................................................................................................................................34
5.4. NewDevelopments.....................................................................................................................................36
TableofContents
MasterThesis‐LucasBienert VI
5.5. SummaryoftheCase/Materials............................................................................................................38
6. Method..................................................................................................................................................................39
6.1. Procedure........................................................................................................................................................39
6.2. DesignVariants.............................................................................................................................................40
6.2.1. StructuralConcept.............................................................................................................................40
6.2.2. FrameConstruction..........................................................................................................................41
6.2.3. PanelConstruction............................................................................................................................43
6.2.4. CLTConstruction................................................................................................................................45
6.3. PreliminaryDesign.....................................................................................................................................46
6.4. EurocodeDesign..........................................................................................................................................49
6.5. FEMAnalysis.................................................................................................................................................50
6.5.1. GlobalFEMAnalysis..........................................................................................................................50
6.5.2. FEMConnectionAnalysis...............................................................................................................56
7. Results...................................................................................................................................................................60
7.1. ResultsfromtheDesignAnalysis..........................................................................................................60
7.2. Comparison....................................................................................................................................................66
8. Discussion............................................................................................................................................................69
9. Conclusions.........................................................................................................................................................71
10. Recommendations............................................................................................................................................72
Bibliography......................................................................................................................................................................73
Appendix.............................................................................................................................................................................75
A. Attachments........................................................................................................................................................75
B. SelectedRFEMResults...................................................................................................................................75
B.a) FrameConstruction...............................................................................................................................75
B.b) PanelConstruction.................................................................................................................................79
B.c) CLTConstruction....................................................................................................................................82
C. SelectedANSYSresults...................................................................................................................................87
ListofFigures
MasterThesis‐LucasBienert VII
ListofFiguresFigure5.1:Threeprincipalaxesofwoodwithrespecttograindirectionandgrowthrings
[16,5‐2]......................................................................................................................................................15
Figure5.2:Stress‐strain‐diagramforsolidwood[26,203]..........................................................................16
Figure5.3:Decreaseofthebendingstrengthoftimberdependingontheloadduration[26,135].....................................................................................................................................................17
Figure5.4:Meanmoisturecontentinwood(glulam90×100×600) versus time in a barn in Southern Sweden (Åsa)[26,155]......................................................................................................18
Figure5.5:Embodiedenergyandcarboncontentofdifferentbuildingmaterialsbasedon[24,415].....................................................................................................................................................21
Figure5.6:Comparisonofthefrequencydistributionofthestrengthofglulamandsolidwood[26,19].......................................................................................................................................................23
Figure5.7:Generalfailuremodesofatimberconnectionwitha)lowslenderness,b)mediumslendernessandc)highslenderness[17,68]............................................................................26
Figure5.8:ComparisonofexperimentallydeterminedstiffnessesofselectedtestswithcorrespondingdesignvaluesfromEC5forspecimenswithdifferentslenderness[17,77].......................................................................................................................................................27
Figure5.9:ComparisonofstrengthofselectedtestswithdesignvaluesfromEC5[17,77]..........27
Figure5.10:Examplesoftraditionaltimberjoints[21,58]..........................................................................28
Figure5.11:Examplesofnailedjoints[26,306]...............................................................................................28
Figure5.12:Steeldowelsandbolts[1,9.44].......................................................................................................29
Figure5.13:Examplesofjointsusingboltsordowels[26,308]................................................................29
Figure5.14:Examplesofapplicationsforfullythreadedscrews[1,9.55].............................................30
Figure5.15:Loadbearingbehaviourofareinforcedconnectionincomparisontoanon‐reinforcedconnection[26,324]......................................................................................................30
Figure5.16:Traditionalframeconstruction[21,56]......................................................................................32
Figure5.17:Panelconstruction(left)andballoonconstruction(right)[21,60‐61].........................32
Figure5.18:Exampleofamodernframeconstruction:schoolinWil,Switzerland[21,86]..........33
Figure5.19:Differentlogconstructionvariants[21,53]...............................................................................34
Figure5.20:Cornerdetailofastackedplankconstruction[21,122].......................................................35
Figure5.21:ExampleofaCLT‐construction:evangelicchurchinRegensburg,Germany[5]........36
Figure6.1:RFEMmodeloftheframeconstruction..........................................................................................41
Figure6.2:Sketchoftheconnectionbetweenthecolumnandthediagonal(nottoscale).............43
Figure6.3:RFEMmodelofthesecondstoreyofthepanelconstruction................................................43
Figure6.4:Sketchoftheconnectionbetweenthefloorandthewallinthepanelconstruction...44
Figure6.5:RFEMmodeloftheCLT‐construction.............................................................................................45
Figure6.6:SketchoftheconnectionbetweenwallandfloorintheCLT‐construction.....................46
ListofFigures
MasterThesis‐LucasBienert VIII
Figure6.7:Simplifiedsystemoftheframes.........................................................................................................47
Figure6.8:Convergenceanalysisoftheframeconstruction........................................................................51
Figure6.9:Convergenceanalysisofthepanelconstruction.........................................................................51
Figure6.10:ConvergenceanalysisoftheCLTconstruction.........................................................................52
Figure6.11:Conceptfordividingthepanelmodelintosub‐models........................................................53
Figure6.12:Sub‐modelinRFEMofthefirststoreyofthepanelconstructionwiththeloadsforLC1(self‐weight)....................................................................................................................................54
Figure6.13:Deformationuin[mm]oftheCLT‐constructionforLC3(windfromthefront),viewfromtheside............................................................................................................................................55
Figure6.14:Distributionoftheinternalnormalforcesin[kN/m]inwallx3forLC1(self‐weight).............................................................................................................................................56
Figure6.15:Distributionoftheinternalnormalforcesin[kN/m]inwallx21forLC3(windfromthefront)....................................................................................................................................................56
Figure6.16:GeometryoftheANSYSmodeloftheconnectionbetweendiagonalandcolumnintheframeconstruction.........................................................................................................................57
Figure7.1:InternalnormalforcesinthefrontframeoftheframeconstructionforLC4(windfromtheside)in[kN]...........................................................................................................................60
Figure7.2:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC4(windfromtheside)..................................................................................61
Figure7.3:Exampleoftheassumptionoftheloaddistributionintheloadbearingstudsinawallinthepanelconstructionforwindfromtherightsideaccordingtothepreliminarydesign..........................................................................................................................................................61
Figure7.4:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC4(windfromtheside)in[kN/m]................................................................................................................................62
Figure6.17:VonMisesstressσVMoftheconnectionin[N/mm2]...........................................................63
Figure6.18:Shearstressτxyoftheconnectionin[N/mm2].......................................................................64
Figure6.19:DefinitionoftheforcesandgeometricdimensionsforthecheckagainsttensionperpendiculartothegrainaccordingtoEC5[2,8.1.4]...........................................................65
Figure6.20:Totalstrainεoftheconnectionin[‐]............................................................................................65
FigureB.1:DeformationoftheframeconstructionforLC1(self‐weight)in[mm]............................75
FigureB.2:DeformationoftheframeconstructionforLC3(windfromthefront)in[mm]...........76
FigureB.3:DeformationoftheframeconstructionforLC4(windfromtheside)in[mm].............76
FigureB.4:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC1(self‐weight)in[kN].....................................................................................................................77
FigureB.5:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC2(snow)in[kN]................................................................................................................................77
ListofFigures
MasterThesis‐LucasBienert IX
FigureB.6:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC3(windfromthefront)in[kN]...................................................................................................77
FigureB.7:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC4(windfromtheside)in[kN].....................................................................................................78
FigureB.8:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC5(lifeload)in[kN]...........................................................................................................................78
FigureB.9:InternalnormalforcesinthefrontframeoftheframeconstructionforLC1(self‐weight)in[kN]........................................................................................................................................79
FigureB.10:DeformationofthefirstfloorofthepanelconstructionforLC1(self‐weight)in[mm]............................................................................................................................................................79
FigureB.11:DeformationofthefirstfloorofthepanelconstructionforLC2(snow)in[mm].....80
FigureB.12:DeformationofthefirstfloorofthepanelconstructionforLC3(windfromthefront)in[mm]..........................................................................................................................................80
FigureB.13:DeformationofthefirstfloorofthepanelconstructionforLC4(windfromtheside)in[mm].......................................................................................................................................................80
FigureB.14:DeformationofthefirstfloorofthepanelconstructionforLC5(lifeload)in[mm]81
FigureB.15:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC1(self‐weight)..................................................................................................81
FigureB.16:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC3(windfromthefront)................................................................................81
FigureB.17:DeformationoftheCLTconstructionforLC1(self‐weight)in[mm]..............................82
FigureB.18:DeformationoftheCLTconstructionforLC3(windfromthefront)in[mm]............82
FigureB.19:DeformationoftheCLTconstructionforLC4(windfromthefront)in[mm]............83
FigureB.20:InternalnormalforcesintheCLTconstructionforLC1(self‐weight)in[kN/m]......83
FigureB.21:InternalnormalforcesintheCLTconstructionforLC3(windfromthefront)in[kN/m]........................................................................................................................................................84
FigureB.22:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC1(self‐weight)in[kN/m]..................................................................................................................................84
FigureB.23:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC2(snow)in[kN/m]........................................................................................................................................................85
FigureB.24:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC3(windfromthefront)in[kN/m]..............................................................................................................................85
FigureB.25:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC5(lifeload)in[kN/m]...................................................................................................................................................85
FigureB.26:InternalshearforcesinthefirststoreyoftheCLTconstructionforLC3(windfromthefront)in[kN/m]..............................................................................................................................86
FigureB.27:InternalshearforcesinthefirststoreyoftheCLTconstructionforLC4(windfromtheside)in[kN/m]................................................................................................................................86
FigureB.28:Stressinglobalxdirectionσxoftheconnectionin[N/mm2]...........................................87
ListofFigures
MasterThesis‐LucasBienert X
FigureB.29:Stressinglobalydirectionσyoftheconnectionin[N/mm2]...........................................87
FigureB.30:Firstprinciplestressσ1oftheconnectionin[N/mm2].......................................................88
FigureB.31:Straininglobalxdirectionεxoftheconnectionin[‐]...........................................................88
FigureB.32:Straininglobalydirectionεyoftheconnectionin[‐]...........................................................89
ListofTables
MasterThesis‐LucasBienert XI
ListofTablesTable3.1:OverviewoverEuropeanstandardsforthedesignoftimberconstructions.......................7
Table3.2:Selectedmaterialsafetyfactors[3,NA.2.4.1]...................................................................................9
Table3.3:PartialsafetyfactorsaccordingtoECandtheNorwegiannationalannex[4,NA.A1.3.1]...........................................................................................................................................10
Table3.4:SelectedcombinationfactorsaccordingtoECandtheNorwegiannationalannex[4,NA.A1.2.2]...........................................................................................................................................10
Table3.5:Loadcases.....................................................................................................................................................11
Table3.6:Loadcombinations....................................................................................................................................11
Table5.1:Mechanicalpropertiesofsteel,concreteandwoodincomparison[1]..............................19
Table5.2:Pricesofsomeselectedengineeredwoodproductsincomparisontosolidwood[20,51].......................................................................................................................................................24
Table5.3:Advantagesanddisadvantagesofgluedconnections[26,334].............................................25
Table6.1:MaterialpropertiesfortheANSYSmodel[12,table5][16,5‐3]...........................................58
Table7.1:Evaluationmatrixforthecomparisonofthethreeconstructionvariantsframeconstruction,panelconstructionandCLTconstruction........................................................67
AbbreviationsandSymbols
MasterThesis‐LucasBienert XII
AbbreviationsandSymbolsAbbreviations3D three‐dimensional
CAD computer‐aideddesign
CLT cross‐laminatedtimber
CNC computerisednumericalcontrol
CO loadcombination(followedbythecorrespondingnumber)
DIN “DeutschesInstitutfürNormung”(GermanInstituteforStandardization)
EC Eurocode
EN EuropeanStandard
EQU equilibriumlimitstate
FE finiteelement
FEM finiteelementmethod
FSC ForestStewardshipCouncil
GEO geotechnicallimitstate
GHG greenhousegases
glulam gluedlaminatedtimber
LC loadcase(followedbythecorrespondingnumber)
LCA lifecycleassessment
LVL laminatedveneerlumber
MBO “Musterbauordnung”(Germanbuildingregulation)
M‐HFHHolzR “Muster‐RichtlinieüberbrandschutztechnischeAnforderungenanhochfeu‐erhemmendeBauteile inHolzbauweise” (Germanregulation for firesafetyrequirementsontimberelements)
OSB orientedstrandboard
PEFC ProgrammefortheEndorsementofForestCertification
PSL parallelstrandlumber
SLS serviceabilitylimitstate
STR structurallimitstate
TMT thermallymodifiedtimber
ULS ultimatelimitstate
VOC volatileorganiccompounds
AbbreviationsandSymbols
MasterThesis‐LucasBienert XIII
LatinSymbolsa years
c compression
CO2 carbondioxide
E Young’smodulus
f strength
f compressionstrength
f tensilestrength
G permanentloads
h hours
k modificationfactorforthestrengthofwood
Q variableloads
SL stresslevel
t tension
T time,loadduration
u ultimate
y yieldpoint
GreekSymbolsγ specificweight
γ partialsafetyfactorforpermanentloads
γ materialsafetyfactor
γ partialsafetyfactorforvariableloads
ε strain
λ heatconductivity
σ stress
σ reducedpreliminarydesignstrength
ψ combinationfactor
Introduction
MasterThesis‐LucasBienert 1
1. IntroductionAlthoughwoodisoneoftheoldestmaterialsthathavebeenusedforbuildings,todayithasmostlybeenreplacedbyconcreteandsteel.Thismasterthesisdealswithdifferentconstructionmethodsthatcanbeusedformulti‐storeytimberbuildings1toanalysethewood’spotentialinthisfield,alsoincomparisontoconcreteandsteel.
Oneofthemainmotivationstousewoodisthatitisrenewableandenvironmentallysuperiortothoseothermaterials.Globally,theconstructionindustryisresponsiblefor40%ofthetotalde‐pletionofnaturalresources,40%oftheconsumptionofthetotalprimaryenergy,15%oftheusageoffreshwater,25%ofallwasteand40to50%ofallgreenhousegasemissions[24,39].Usingwoodinsteadofconcreteandsteelhasthereforegreatpotentialtopromoteamoresustain‐ablesociety.
Itistodaynotechnicalchallengetobuildsmalltwo‐orthree‐storeyhousesfromwood.Buttheglobalpopulation increases,andaconsiderablepart ismoving to the largecities,where livingspacegetsscarce.Therefore,themajorityofnewbuildingswillbeerectedinthecitiesandwillprobablybemulti‐storeyconstructions.Fortimbertoreallymakeachange,thechallengesregard‐ingmulti‐storeytimberbuildingsmustbeaddressed.
Thegoalofthismasterthesisistocontributetothisdevelopmentbydiscussingthepropertiesofmodernwoodproducts and structures andby analysing the suitability of timbermethods formulti‐storeybuildings.Asamethodfortheanalysis,adesignwillbeperformedofthreedifferentalternativetimberstructuresforanexistingmulti‐storeytimberbuilding.
Firstofall,thesocietyperspectiveshallbedescribedinchapter2,alsolookingatthedifferentsituationsinNorwayandGermany.Thiswillstartwithasummaryofthehistoricaldevelopmentofwoodenbuildingsandconstructionmethods.Afterthat,thesituationoftodayispresented.Inchapter3,thetheoreticalbackgroundshallbeestablished.Hereitisimportanttotakealookattherulesandstandardsthatmustbefollowedinthedesign.Basedonthat,thebasisforthefol‐lowingdesigncanbecreated.Afterdefiningthecentralresearchquestionsforthefollowingworkinchapter4,thedifferenttimberstructures,materialsandconnectionsthatareavailabletodayorarebeingdevelopedwillbeexaminedinchapter5.
Finally, the above mentioned method, the design analysis is presented in chapter 6. Today’sworld’shighesttimberbuilding,Treet2inBergen(Norway)willberedesignedtoevaluatethreedifferentconstructionmethods.Thosethreevariantswillbeamodernframeconstructionfeatur‐ingalargegrid,apanelconstructionrelyingheavilyonprefabrication,andamasstimbercon‐structionusingcross‐laminatedtimber(CLT).Apreliminarydesignisconductedforallthreecon‐structions.Thisincludesshapingthestructuralideaanddeterminingdimensionsofcross‐sectionandconnections.Thispartofthedesignwillbegiventhemostattention,becausethisiswherethemost engineeringproblemsmustbe solvedand thegeneral structure is shaped.Basedon the
1 Inthecontextofthismasterthesis,amulti‐storeybuildingisconsideredtobeabuildingwithat leastthree,butalsomorethantenstoreys.Thetermtimberbuildingreferstoabuildingwiththeload‐bearingstructuremadefromtimberorengineeredwoodproducts.Whilethewordwoodisamoregeneraltermthatdescribesthebasicmaterialextractedfromtrees,timberisanykindofwoodproductusedforbuildingpurposes.2TheconstructionofTreetwasfinishedin2015anditisbytoday(2018)with14storeysandaheightofabout51mstillthehighesttimberbuildingintheworld[10].However,thereisanothertimberbuildingunderconstructioninNorwaythatwillbeevenhigher,MjøstårnetinBrumundal.Aftertheprojectedcom‐pletionoftheprojectin2019,itwillhave18storeyswithatotalheightof81m[22].
Introduction
MasterThesis‐LucasBienert 2
preliminarydesign,thefinaldesignaccordingtotheEurocodestandardsisperformed,includinga finiteelement(FE)analyses.The idea is todesignthreedifferentconstructions forthesamebuildingandtocomparethemafterwardsconsideringdifferentaspectssuchastheefficiencyoftheload‐bearingstructureorenvironmentalaspects,cf.chapter7.
Afteradiscussionoftheresultsinchapter8,thefinalconclusionsofthismasterthesisarepre‐sentedinchapter9,wheretheearlierstatedresearchquestionswillbeanswered.Basedonthoseconclusions, recommendations concerning the future of multi‐storey timber buildings can begiveninchapter10.
SocietyPerspective
MasterThesis‐LucasBienert 3
2. SocietyPerspective2.1. HistoricalBackground
Inearlyhistory,timberwasthemostimportantbuildingmaterialforresidentialbuildings.Oneofthemainreasonsforthatisthatitwasreadilyavailableinlargequantities,althoughthisdifferedfromregiontoregion.Accordingly,somecountrieshavearichhistoryofbuildingwithtimbertoday,whileothersrelymoreonothermaterials.Moreover,woodisrelativelyeasytoshape,incontrasttoe.g.stone.
Theworld’soldeststillstandingtimberbuildingistheHōryūtempleinJapan,whichwasbuiltinthe7.century[7].TheoldesttimberbuildinginNorwayistheBorgundchurchfromthe12.cen‐tury[26,1].Theseexamplesprovethattimberbuildingsareverydurableandcanpersistforapracticallyunlimitedamountoftimeifplannedandmaintainedcorrectly.Importantelementsofagooddesignconcerningthedurabilityarethatwaterandmoisturearenothinderedfromleavingthebuildingandthatdamagedcomponentscanbereplacedeasily[26,2].
InNorway,woodhasbeenthemostimportantmaterialforallkindsoftools,includingshipsandbuildings,sincethetimeoftheVikings.ThatisbecauseofNorway’swide‐spreadforests.WoodenhousesareanimportantpartoftheNorwegianculture,onlyinafewcountriesliketheUSAandCanadaistheshareoftimberbuildinginallexistingbuildingscomparablyhigh.Today,75to80%ofallnewlybuiltresidentialbuildingsinNorwayaretimberbuildings[18,7].
ThefirstwoodenhousesinNorwaywereprobablypalisadebuildingsmadefromlogsdrivenintotheearthvertically,butthiskindofstructuredidnotprevailbecauseofthedecayofthewoodintheground.Furtherdevelopment leadtostavebuildings likethewell‐knownNorwegianstavechurches.Adifferentmethodthatwasusedfromearlyinthehistoryisthelogconstruction,whichwaswidelyuseduntilthe19.century.Overthetime,moremethodsweredeveloped,leadingtomoreefficientbuildingconstructionsthatneededlessmaterialandweremoredurable.Anexam‐pleisthetraditionalframeconstructionwhichwasintroducedaround1700notonlyinNorway,butalsoinotherEuropeancountries.Inthebeginning,thespacein‐betweentheframeswasfilledwithe.g.brickworktosealthehouseagainsttheweather.Around1900,thebuildingsgotsheath‐ingbothontheinsideandtheoutsideandthespacesintheframeworkwereleftfree,whichsavedmuchmaterial,i.e.unnecessaryweightandcosts.Inthemiddleofthe19.century,thosecavitieswerethenfilledwithinsulation,whichimprovedtheindoorclimate.Today,thedevelopmentofnewmethodsisstillongoing.Prefabricationbecomesmoreandmoreimportantandnewtechnol‐ogiesase.g.compoundmaterialsareused[18,7‐10].
Intheearlyhistory,Germanywasalsocoveredwithrichforests.IncontrasttoNorway,however,deforestationandindustrialisationdevelopedfasterandstronger,possiblereasonsforthatarethe easier topography andGermany’s central position inEurope.During the industrialisation,woodwasmoreandmorereplacedbysteelandlateralsoreinforcedconcrete,becausethewoodworkingprocessesweretooslowandthereforemoreexpensive[20,6].Thiswasmainlyduetolabour‐intensiveconnectionssuchasdovetailconnections.Furthermore,thetimberindustrywasmorefocusedontraditions,alsobecauseofitslonghistory[25,5],andcouldthereforenotcom‐petewiththemodernsteelandconcreteindustry.
Duringthistime,thewaypeopleregardedthedifferentbuildingmaterialschanged.Onlybrickhouseswereregardedassufficientlydurable,woodenhouseswereespeciallyshort‐livedandthefireriskwashigher[25,6].Manyoftheseviewsoftimbersurviveduntiltoday,althoughthetim‐bertechnologychangedfundamentally.
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In thebeginningof the20.century,during the firstworldwar, the timber industrydevelopedstronglyagain.Manyconstructionswereneededforthewar,manyhousesweredestroyed,andsteelwasneededotherwise[25,6].Fastpanelconstructionswerepreferred[25,9].Afterthefirstandsecondworldwar,againmostlybrickworkandconcretestructureswereused,whichwerefasterandcheapertobuildthanwoodenstructures.
Today,about10%oftheexistingconstructionsfeaturewoodasmainbuildingmaterialinGer‐many,intheNordiccountriestheshareamountsto80to85%[24,408],whichisprobablymainlyduetothedifferenthistoricdevelopment.Thetechnologiesthatareusedtoday,however,donotdifferasmuchbetweenthecountriesbecauseofeasyexchangeoftechnicalknowledge.
2.2. EvolutionofTimberTechnologiesWhile thepreviouschapter focusedonthegeneraldevelopment inGermanyandNorway, thischapter dealswith the development of the timber technologies themselves. It is important toknowhowthetimbertechnologieschangedovertimetohaveabetterunderstandingoftoday’stechnologies.Furthermore,itcanhelptobetterunderstandthedoubtsthatexistamongstboththeclientsandthearchitects,plannersandengineers.
Theoldestwoodproductis,ofcourse,timbermadefromsolidwood,whichwasusedalmostex‐clusivelyuntilthe20.century.Nonetheless,thereweresomeearlyinventionsthatcombinedin‐dividualwoodmemberstoformbiggercomponentsthatcouldspanlargerdistances.Whenthoseearlyengineeredwoodproductsweredeveloped,theindividualmemberswereconnectedusingmechanicalfastenerssuchasnails,boltsordowels.Oneoftheearliestexamplesisanarchcom‐ponentmadefromtwotothreecurvedplanksthatstanduprightandarelinkedtogetherbycross‐members,developedbyaFrencharchitectasearlyas1561.Itallowedforlongerspans,withatthesametimelowerhorizontalshearforcesatthesupports,comparedtothetraditionalcoupleroof.In1830,anotherFrenchengineerdevelopedabeammadefromstackedhorizontalplanksholdtogetherbybolds,whichcanbeseenasthepredecessorofthemoderngluedlaminatedtim‐ber(glulam)[20,10].
Themechanicalfastenersusedfortheengineeredwoodproductswerewidelyreplacedbysyn‐theticgluesintheearlytwentiethcentury[26,7],thoseallowedasuperiorstressdistributionandbetterload‐slip‐behaviour.ThefounderofmoderngluedwoodproductssuchasglulamwasOttoHetzer(1846–1911),whoobtainedhispatentongluedtimberconstructions in1906[26,67].Someoftheearlierinventionsthatusedsyntheticglues,developedinthefirsthalfofthe20.cen‐tury,includeplywood,apanelmadefromthinlayersofveneer,andparticleboard,apanelmadefromfinewoodchipsandsawmillshavings[26,84].Later,glulambecamecommerciallyavailable.Someoftheoldestbuildingsstillinusethataremadefeaturingglulamasthemainbearingele‐mentare therailwaystations inMalmø(built in1922)andStockholm(1925),both located inSweden[26,67].Morerecentlydevelopedproductsincludeorientedstrandboardaswellasthesolidwood‐likeparallel strand lumberand laminatedstrand lumber,allmade fromstrandsofwood[26,84].Thosedevelopmentsmadeitpossibleforwoodtobeusedinlargeandcomplicatedengineeringstructures.
Overthetime,theplanningwasmoreandmoremovedfromtheconstructionsitetotheoffice.Morecomplexandefficienttechnologiesrequiredmorepre‐planning.
Inthe21.century,thedevelopmentwascharacterisedbynewtechnologieslikeCAD(computer‐aideddesign),CNC(computerisednumericalcontrol)andtheso‐calledindustry2.0.Thisallowedforthewoodproductstobemanufacturedveryefficiently,evencostumerspecificproductscouldbeproducedeconomically.Thisagainhelpedtheplannerstodesignmoreefficientbuildingswith
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speciallytailoredwoodproducts.Additionally,makinguseofthemanifoldpossibilitiestoshapetimberandengineeredwoodproductsopenedupgreatnewpossibilitiesforarchitectsandengi‐neers.
Today’sresearchfocusesamongstotherthingsonimprovementsofthewood’sproperties,sincehereinstillliethebiggestproblemsandchallenges.Thisconcernse.g.thedecayofwoodanditscomparably lowstiffness.Moreabout today’s researchanddevelopmentswillbedescribed inchapter5.4.
2.3. Today’sGlobalSituationWiththedevelopmentofnewtechnologiesthatmakewoodcompetitiveagain,thedemandforwoodproductsrises.Thereis,however,agapbetweendemandand(sustainable)supplyofwood,oneofthemostimportantissuesoftodayisthereforetheuseofwoodfromsensitiveecosystems,e.g.rainforests,inanon‐sustainableway.Theworld’stotalforestareadecreasedinthetimebe‐tween1990and2000by8,3millionha/aandfrom2000to2010by5,2millionha/a,mostlosseswereobservedinthetropicalregionsinSouthAmericaandAfrica[24,314].
Anotherissueistheconflictbetweentheindustrialuseofforeststoproducewoodproductsandthevalueofforestsforrecreationandforahealthyecosystem.Forestsarenotonlyveryimportantforthehealthofthelocalecosystems,butalsofortheglobalenvironmentandclimate.
Todissolvethoseconflicts,measuresmustbetakenatdifferentpoints.Ontheproductionside,sustainablemethodsmustbeestablishedworldwide,reforestationandforestplantationareim‐portantpartsofthismeasure.Thedevelopmentofnewtechnologiesforharvestingandmanufac‐turingleadstoahigherefficiencyandthusareducedwooddemand.Finally,newproductsthatusesmallerdiameterandlowerqualitywoodcanslowdowntherisingdemandforwood[26,81‐82],someexamplesforthisapproachareaddressedinchapter5.1.4aboutengineeredwoodprod‐ucts.
Topromotesustainableforestry,certificationisneeded.Onaglobalscale,therearetwodifferentsystemsforcertificationofforests,theForestStewardshipCouncil(FSC)andtheProgrammefortheEndorsementofForestCertification(PEFC).Thelatteristoday’sbiggestcertificationsystem[27,18‐19].Additionally, thereare alsonational certification systems like theNorwegian “Le‐vendeSkog”,thiswillbetakenupagaininchapter3.1.2.
Inspiteofalltheissuesdescribedabove,woodwilldefinitelyplayanimportantroleinthefuture.Withappropriatemanagement,thoseproblemscanbeovercome,becausewoodisstillsufficientlyavailable.InEurope,thewoodgrowthexceedsthefellingeachyear,andconsequently,theforestareaincreasedby0,7millionha/aduringtheperiodfrom2000to2010[24,314].InGermany,onethirdofthecurrentannualyieldofwoodwouldsufficetousewoodforallnewlybuiltcon‐structions[23,43]andinNorway,thenewgrowthofwoodperyearismorethantwiceashighastheusage[27,25].
2.4. SummaryoftheSocietyPerspectiveThepurposeofthischapterwastogiveanintroductionintobuildingwithtimberfromasocietypointofview.Itstartedwithasummaryofthehistoricaldevelopment,whichshowedthatwoodhasbeenused forbuildingpurposes forcenturies, longer thane.g.concreteandsteel,but thetechnologieshavechangedsignificantly.Large‐scalestructureshavebecomepossible.Moreover,formerproblemsconcerningthecombustibilityandthedecayofwoodhavelargelybeenover‐come.OldwoodenbuildingsliketheNorwegianstavechurchesprovethatwoodenbuildingscanbeverydurable,providedgoodplanningandmaintenance.Still,therearewide‐spreadreserva‐
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tionsagainsttimberamongstboththeclientsandtheplanners,andthetimberindustryisonlynowstartingtodevelop.
Today’sglobalsituationwasdescribed,pointingattheenvironmentalissuesconnectedtothepro‐ductionofwoodproductsconcerningunsustainableforestry.
Beforedealingindetailwiththedifferenttimbertechnologies,someofwhichhavealreadybeenmentionedinthischapter,itisnecessarytofirsttakealookatthetheoreticalbackgroundinthenextchapter.Thisincludestheinternationalandnationalrulesandstandardsthatformthebasisforanytimberdesign.OfcentralimportanceforallEuropeancountriesaretheEuropeanstand‐ardsincludingtheEurocodes(EC).Afterthat,adescriptionofselectednationalrulesandstand‐ardsinNorwayandGermanywillbegiven.
Thedesignbasis,whichisbasedonthoserules,willcompletethetheoreticalbackgroundforthesubsequentexaminationsofthetimbertechnologiesandthedesignanalysis.
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3. Theory3.1. RulesandStandards
3.1.1. EuropeanStandardsManydifferentstandardsplayaroleinthedesignoftimberbuildings.ThedesignisconductedaccordingtotheEurocode5(EC5),i.e.EN1995‐1‐1.Additionalstandardsregulatethedifferentmaterials, give requirements for manufacturers and define material properties. Furthermore,therearesomeproductsthatarenotornotyetstandardised,wherethecharacteristicpropertiesarespecifiedbythemanufactureroratestinglaboratorycommissionedbythemanufacturer.Ta‐ble3.1givesanoverviewovertheEuropeanstandardsthatareimportantforthedesignoftimberconstructions.
Table3.1:OverviewoverEuropeanstandardsforthedesignoftimberconstructions
product mainstandard
productstandard
propertiesstandard
designstandard
solidwood EN14081‐1 EN14081‐1 EN338 EN1995‐1‐1glulam EN14080 EN14080 EN14080laminatedve‐neerlumber
EN13986 EN14374EN14279
manufacturer
plywood EN636 EN12369‐2orientedstrandboard
EN300 EN12369‐1
particleboard EN312hardfibreboard EN622‐2mediumhardfi‐breboard
EN622‐3
mediumdensefibreboard
EN622‐5
solidwoodpan‐els3
EN13353 EN12369‐3 ‐
cross‐laminatedtimber CLT
EN16351 EN16351 manufacturer ‐
Ascanbeseenfromthistable,forsomeproductslikelaminatedveneerlumber(LVL)andcross‐laminatedtimber(CLT),nopropertiesstandardshavebeenworkedoutyet,sothatcharacteristicpropertiesmustbetakenfromtechnicalapprovalsprovidedbythemanufacturer.Moreover,theEC5doesnotmentioneithersolidwoodpanelsorCLT.ThedesignrulesoftheEC5mustthereforebeadaptedforthosematerials,thatconcernsmainlythechoiceofadequatesafetyfactors.Thiswillplayarolelateroninthismasterthesis,whenitcomestothedesigntheCLTconstructionofTreet.Itcanberevealedatthispointthat,basedonresearchresults,itisrecommendedtousethesamedesignfactorsforCLTasforglulam[19,934].
Inadditiontothosetimberspecificstandards,Eurocode0(EC0)describesthegeneraldesigncon‐cept,andinthedifferentpartsofEurocode1(EC1),allthetypesof loadsaredefined.It isnot
3Solidwoodpanelsarepanelsmadefromoneorseveralpliesofwoodplanks; theycanhavethesamecompositionasCLTpanels,butincontrasttoCLTtheplankshavenotbeensortedintostrengthclassesandthegluehasnotbeentested.
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withinthescopeofthismasterthesistogointodetailconcerningthosebasicstandards.Atsomepoints,though,thestandardsallowe.g.theuseofdifferentformulae.Moreover,everycountrycanspecifytheirownsetofsafetyfactorsandcombinationfactorsandcanadaptthestandardswithinspecificboundariesinthecorrespondingnationalannexes.ToavoidmisunderstandingsandtohaveasolidfoundationfortheECdesign(cf.chapter6.4),designbasisisestablishedinchapter3.2.
Togivesomeexamplesofthedifferencesthatarisefromthedifferentnationalannexes,ashortcomparisonoftheNorwegianandtheGermannationaladjustmentsshallbepresented.
Quitenaturally,therearebigdifferencesconcerningthedeterminationoftheenvironmentalloadslikewindandsnowloads.Thisismostlyduetothefactthattheenvironmentalloadshighlyde‐pendonthegeographicalsituationinthedifferentcountries.TheNorwegiannationalannexestoEC1part1‐3(snowloads)andEC1part1‐4(windloads)featuredetailedtableswithfactorsforthecalculationoftheloadsatdifferentplaces.IntheGermannationalannextoEC1part1‐4,anaccidentalloadcase4forespeciallyhighwindloadsintheflatnorthernregionsisadded.
Concerningthetimberspecificstandard,EC5,theGermannationalannexfeaturesextensivead‐ditions,e.g.asimplifiedapproachforthedesignoftimberconnectionsusingγ 1,1aspartialsafetyfactorinsteadofγ 1,3.Furthermore,onecanfindadditionsfordifferentdetailsthatarenotcoveredbythemainstandard,e.g. forstrengtheningof transverseconnectionsusing fullythreadedscrewsandfortraditionalwoodworkingjoints.
3.1.2. NationalRulesandStandardsinNorwayandGermanyBesides the described standardswhich define the technical requirements, additional nationalrulesdefinefurtherrequirements,concerninge.g.thelayoutofthebuilding,firesafetymeasuresandtheexecutionofthebuildingproject.
InGermany,thatconcernsthe“Musterbauordnung”[9](MBO,Germanbuildingregulation)to‐getherwiththetimberspecific“Muster‐RichtlinieüberbrandschutztechnischeAnforderungenanhochfeuerhemmende Bauteile in Holzbauweise” [8] (M‐HFHHolzR, German regulation for firesafety requirementson timberelements).The fire safety requirements forwoodproductsarequitestrict,makingitnecessarytomakeadeviationrequestiftimberistobeusedvisiblyinbuild‐ingswithmorethanthreestoreys5.Thisleadstohighercostsfortimberconstructions.
InNorway,itisonlyallowedtousetimberinbuildingshigherthanthreestoreysatallsince1998.InaresearchdocumentcommissionedbytheNorwegiangovernmentin2013,itisfoundthat,asalong‐termeffectofthat,thetimberindustryisstillnotfullydevelopedandthatexpertiseismiss‐ing[13,4].Thismaysoundstrangeconsideringtherichhistoryofbuildingwithtimberwhichwasdescribedpreviously.Theproblem,however,isthatwoodisalmostexclusivelyusedforsmallerresidentialbuildings,butnot for largerstructures.Thestrategyof theNorwegiangovernmentaimsatusingmorewoodforpublicbuildings,therebysupportingthetimberindustry[13].ThismeasurecoulddefinitelyalsobetransferredtoGermany,wherethesituationofthetimberindus‐tryisapproximatelythesame,ifnotworse.Butacomparablestrategyhasnotyetbeenworkedout.
4ThedesignaccordingtotheECstandards isbasedontheanalysisofdifferent loadcaseswithspecificcombinationsof thedifferent loads.Accidental loadcasesarereserved forexceptional loads like fireorearthquakes.5Actually,therequirementsarelinkedtotheheightofthegroundfloorofthehighestinhabitedstoreyabovetheground.Thelimitissetto7m,whichcorrespondsapproximatelytoabuildingwiththreestoreys.
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Adifferentaspect, thathasalreadybeenmentionedearlier inthedescriptionoftoday’sglobalsituation,isforestcertification.Norwayhasitsownforestcertificationsystem“LevendeSkog”,whichfulfilstherequirementsforthePEFCcertification.Itwasfoundedin1998andaimsatthepromotionofamoresustainableuseoftheforests,balancingthethreecentralaspectsindustrialandeconomicalinterests,environmentalissuesandsocialinterests(cf.chapter2.3).Inthe“Le‐vendeSkog”system,theforestindustry,labourunions,recreationorganisationsandenvironmentorganisationsworktogether.Today,allNorwegianforestsarecertifiedafterthisstandard[27,19].
3.2. DesignBasis3.2.1. Parameters
Thepreliminarydesignwasperformedusingsimplifiedloads(seenextchapter)andreducedma‐terialpropertiestoaccountforthenecessarysafetymargins,e.g.σ 5N/mm forthestrength
ofwoodparalleltothegrain(bothbending,compressionandtension).Thisallowsforarelativelyquickpreliminarydesignwithresultsthatgenerallyareonthesafeside.Thepreliminarymaterialpropertiesaresummarisedintheprefaceofthepreliminarydesigndocumentation,whichisat‐tachedtothisdocument(seeappendixA).
For theECdesign, thematerial propertieswere taken from the relevantEuropean standards,whichweresummarisedinTable3.1.SincethedesignedbuildingislocatedinNorway,theNor‐wegiannationalannexesoftheECwereused.
AccordingtotheNorwegianrules,everystructuremustbeassignedareliabilityclass.Residentialbuildingsgenerallybelonginreliabilityclass2.ThismeansthatthebuildinghastobeassignedtotheplanningcontrolclassPKK2andtheexecutioncontrolclassUKK2,whichrequireadetailedqualitycontrol[4,NA.A1.3.1(901)‐(904)].
BecauseofdifferencesbetweentherecommendationsinthemainECstandardsandtheNorwe‐giannationalannexes,Table3.2toTable3.4summarisethesafetyandcombinationfactorsthathavebeenusedinthismasterthesis,whichcorrespondtotheNorwegiannationalannexes.
Table3.2:Selectedmaterialsafetyfactors[3,NA.2.4.1]
material materialsafetyfactorγsolidwood 1,25glulam,CLT 1,15plywood 1,15connections 1,3
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Table3.3:PartialsafetyfactorsaccordingtoECandtheNorwegiannationalannex[4,NA.A1.3.1]
load favourable/un‐favourable
partialsafetyfactor
EQU:basicloadcombinationforpermanentandtransientloadsG :permanentloads uf γ 1,20
f γ 0,90
Q :leadingvariableload i 1 uf γ , 1,50
f γ , 0
Q :furthervariableloads uf γ , 1,50
f γ , 0
STR,GEO:basicloadcombinationforpermanentandtransientloadsG :permanentloads uf γ 1,20
f γ 1,00
Q :leadingvariableload i 1 uf γ , 1,50
f γ , 0
Q :furthervariableloads uf γ , 1,50
f γ , 0
EQU equilibriumlimitstateSTR structurallimitstateGEO geotechnicallimitstate
Table3.4:SelectedcombinationfactorsaccordingtoECandtheNorwegiannationalannex[4,NA.A1.2.2]
load combinationfactorψ ψ ψ
liveloads A:residentialbuildings 0,7 0,5 0,3 H:roofs 0 0 0snowloads 0,7 0,5 0,2windloads 0,6 0,2 0
Itmustbenotedthat,sinceCLTisnotconsideredintheEC,assumptionshadtobemadefortheselectionofappropriatesafetyfactorsandotherparameters.Inaresearchprojectfrom2018,itisrecommendedtousethesamesafetyfactorsasforglulam(cf.Table3.2)[19,934].Accordingly,otherfactorslikethemodificationfactork toaccountforeffectsofmoistureandload‐dura‐tion,werealsotakenoverfromglulam.
Forthecalculationofthedeformations,EC5allowstwodifferentmethods,ageneralmethodandasimplifiedmethodforstructuresthatconsistofcomponentsthatallhavethesamecreepingbe‐haviour.Thethreedesignvariantsthatareanalysedinthismasterthesisfulfilthisrequirement(cf.chapter6.2.1),thereforethesimplifiedapproachisappliedfortheECdesign(see[3,2.2.3]).
AllotherparametersaredescribedinthedocumentationoftheECdesign,cf.appendixA.
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3.2.2. LoadCalculationForthepreliminarydesign,simplifiedloadswereusedtogetaquickideaofthegeneralmagnitudeoftheresultingforces.Theself‐weightofthefloors,forexample,wasassumedtobe2kN/m ,thelifeloadandthesnowloadontheroofwerebothsetto2kN/m ,too.Onlythewindloadswerecalculatedinmoredetail,becausetheyhaveastronginfluenceonthesystemofamulti‐storeybuildingandhighlydependonthelocationofthespecificproject.
FortheECdeign,adetailedloadcalculationwasperformedaccordingtoEC1,usingtheNorwegiannationalannexes.Thedocumentationoftheloadcalculationcanbefoundattachedtothisdocu‐ment,cf.appendixA.Differentloadcases(LC)hadtobedistinguished,thosearesummarisedinTable3.5.
Table3.5:Loadcases
LC description loadduration1 self‐weight permanent2 snow short‐term3 windfromthefront instantaneous4 windfromtheside instantaneous5 liveload categoryA medium‐term
Theindividualloadcaseswerecombinedindifferentloadcombinations(CO).Becausetheloadbearingbehaviourofwoodistimedepended(seechapter5.1.1),differentloadcaseswithdiffer‐entloaddurationshadtobeconsidered,cf.Table3.6.
Table3.6:Loadcombinations
CO self‐weight leadingvariableload
accompanyingvariableload
loadduration
1 self‐weight ‐ ‐ permanent2 self‐weight liveload ‐ medium‐term3 self‐weight snow liveload short‐term4 self‐weight liveload snow short‐term5 self‐weight windfromthefront snow,liveload instantaneous6 self‐weight windfromtheside snow,liveload instantaneous7 self‐weight liveload snow,windfrom
thefrontinstantaneous
8 self‐weight live load snow,windfromtheside
instantaneous
9 self‐weight snow windfromthefront,liveload
instantaneous
10 self‐weight snow windfromtheside,liveload
instantaneous
11 self‐weight windfromthefront ‐ instantaneous12 self‐weight windfromthe side ‐ instantaneous
CombinationsCO1toCO10aremeant for thecalculationof themaximumcompressive forces.Sinceforcompression,incontrasttotension,bucklingmustbeconsidered,thesecombinationswillbedecisiveforthedeterminationoftherequiredcross‐sections.
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CO11andCO12aremeantforthetensiondesign,whichise.g. importantforthedesignoftheanchorage6inthepanelandtheCLTconstruction.Thecorrespondinglowerpartialsafetyfactorfortheself‐weightwasused(γ 1,0insteadofγ 1,2).
3.2.3. SoftwareThepreliminarydesignwasmostlyperformedwithouttheuseofdesignsoftware.Stab2d,asim‐pleprogram for the analysis of two‐dimensional frameworks,wasused todetermine internalforcesanddeformations.MicrosoftEXCEL©wasusedforthestabilityanalysisofthepanelandtheCLT construction.The stability analysiswas conducted todetermine the shear forces andbendingmomentsintheindividualwallsduetotheglobalwindloads.
TheECdesignrequiredmoreaccuratecalculationmethods.TheFEMsoftwareRFEM©byDlubalSoftwareGmbHwasusedtomodelandanalysetheoverallstructureofallthreevariants.WithRFEM, both one‐dimensional members, two‐dimensional surfaces and three‐dimensional vol‐umescanbemodelled.OneofitsmajoradvantagesistheextensivelibraryofmaterialsandtheincorporationofmanystandardsincludingtheECanditsnationalannexes.RFEMcanautomati‐callycombineloadsaccordingtoloadcombinations.ThedetailsoftheFEManalysisusingRFEMareexplainedinchapter6.5.1.
Additionally,ananalysisofaselectedconnectiondetailwillbecarriedouttocomparewiththecalculationsaccordingtoEC.Thereasonsforthiswillbeexplainedinchapter5.2.Forthisanalysis,theFEMsoftwareANSYSwasused.ANSYS,incontrasttoRFEM,isaprogramthatfocusesmoreonin‐depthscientificcalculationsofdetailsinsteadofontheanalysisofwholeengineeringstruc‐tures.Italsoincludesanorthotropicmaterialmodelwhichisrequiredforwood.
3.3. SummaryoftheTheoryInthepreviouschapter,thetheoreticalbasisfortheexaminationsandthedesignanalysisthatwillfollowinthenextchaptershasbeenworkedout.Abriefoverviewoftherulesandstandardsthatdealwithtimberhasbeengiven.Somerulesarestillinfluencedbytheformerproblemsofwoodproducts like theGermanM‐HFHHolzRwhichdoes not allow visiblewoodmembers inbuildingswithmorethan3storeysduetofiresafetyreasons.InNorway,therewerecomparablerulesuntilrelativelyrecently,whichcanexplaintheweakpositionofthetimberindustrytoday.WiththenewstrategytosupportthetimberindustryinNorway,however,thesituationbeginstochange.
6Anchoragereferstotheconnectionsbetweenwallsaboveeachother,whichareresponsiblefortransfer‐ringtensileforces.Tensileforcesoccuratthebottomofthebuildingwheretheglobalbendingmomentduetothewindloadsissplitintocompressionandtensionforces.
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4. ResearchQuestionsThecentralresearchquestionforthefollowingexaminationsis:
1. Whichmaterialsandconstructionmethodsarebestusedforanefficientdesignofmulti‐storeytimberbuildingsfromastructuralpointofview?
Somesecondaryquestionshavealreadybeendealtwithinthepreviouswork:
2. Howdidthetimbertechnologydevelop,andwhichnewtechnologiesaredevelopedto‐day?
3. WhatarethemaindifferencesbetweenGermanyandNorwayconcerningthewaytocon‐structtimberbuildings?
4. Howdonationalrules influencethedevelopmentofthetimberbuildingindustryespe‐ciallyinGermanyandNorway?
Theanswerstothosequestionswillbesummarisedtogetherwiththeanswerstotheotherques‐tionsintheconclusionsinchapter9.
Furtherquestionsthatwillbediscussedinthefollowinginclude:
5. Whatarethemainadvantagesanddrawbacksoftimberincomparisontosteelandcon‐crete,alsoconsideringenvironmentalaspects?
6. Whichroledoconnectionplayinthedesignoftimberbuildings?7. Howcanfiniteelementsoftwarebeusedtoeffectivelydesigntimberconstructionsand
connections?8. Howwelldotheregulationsinthestandardsreflecttherealbearingbehaviouroftimber
constructionsandconnections?
Concerningthedesignanalysis,thismasterthesisfocusesonthestructuralaspectsofthetimbermaterials,whiletheconcreteandsteelmemberswillnotbetakenintoaccount.Fireprotectionandeconomicalaspectswillonlybediscussedbrieflyinthetext.
Inordertoanswerthosequestions,thenextchapterwilldealwiththepropertiesoftimbermate‐rialsandstructuresinmoredetail.Someoftheaspectsmentionedinthepreviouschapterswillbepickedupanddiscussed,liketheenvironmentalissuesandthenewdevelopmentsoftoday.
Themainmethodtofindanswerstothosequestion,however,isthedesignofthemulti‐storeytimberbuildingTreet,whichwillbepresentedinthefollowingchapter.
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5. Case/Materials5.1. TimberMaterials
5.1.1. GeneralPropertiesofSolidWoodAboveallelse,woodisanaturalmaterial.Thishassomegreatadvantagesbutalsoincludessomechallenges.Thischapterdealswithboth,describingimportantaspectstokeepinmindwhenplan‐ningatimberbuilding,andespeciallyoneaschallengingasamulti‐storeybuilding.Firstly,somegeneralpropertiesofwoodarepresented,followedbyanexaminationofitsmechanicalproper‐ties,whichareimportantforthelaterdesign.
Oneofthecharacteristicadvantagesofwoodisitsaestheticsurface,itdoesnotneedtobecoveredandisoftenusedforarchitecturalpurposes.Thisistrueforsolidwoodaswellasglulamandmostoftheengineeredwoodproducts.Moreover,withtoday’stechnologyitcanbeformedintoalmostanypossibleshape(agoodexampleforthatismasstimberlikeCLTwhichwillbedescribedlater).Besidesthat,woodstoresCO2,oneofthemaingreenhousegases(GHG).1m oftimbercontainsabout0,92tonnesCO2[27,26],therebyactivelycontributingtoslowingdowntheglobalwarming.Inadditiontothat,woodisarenewablematerialbecauseitalwaysregrows.
Acharacteristicdrawbackofwoodisthatitspropertiesvaryalot,dependingontheusedwoodspecies,butalsobetweensamplesofthesamespeciesbecauseofitsgeneralinhomogeneityanddefectslikeknotholes.Thismakesdesigningareliablestructuremoredifficult,largersafetyfac‐torsmustbeused.Ontheotherhand,differentspeciescanbeusedfordifferentpurposes,whichmakesdifferentstrengthclassesandeconomicadjustmentstothedesignpossible.Forstructuralelements, fastgrowingsoftwoods likespruceand firarepreferred. InNorway, theNorwegianspruceandpinearemainlyused.Hardwoodspecieslikeoakorbeechareusedforspecial,highlyloadedcomponentssuchaswooddowels[21,32].
Tocomebacktothegeneraldisadvantagesofwood,itisimportanttomentionthedecay.Thisismostofthetimeaconsequenceofmoistureinsidethewood.Measurestoenhancethewood’spropertiesconcerningdecaythereforefocusonsealingthewoodagainsttheinfiltrationwithwa‐ter.Today,manynaturalsubstancesandtechniquesareavailable,thereisnoneedforusingpoi‐sonous,environmentallydamagingchemicalwoodpreservatives.Oneoptionforthecoatingofthewoodarebiologicalsubstancesfromnaturalsources,examplesarechitosan,producedfromchitin,orpineoil[27,43].However,coatingisingeneralveryexpensive,smalldefectscandestroythepositiveeffectsandregularmaintenanceisnecessary[26,238].Acompletelydifferentpossi‐bilityisthebiological,chemicalorphysicalmodificationofthewood.Onerequirementforanysuchmethodisthatnopoisonisusedandnopoisonoussubstratesareemitted.Anexampleofchemicalwoodmodification is the furfurylation. Furfuryl alcohol is used, under heat it reactschemicallywiththewoodmolecules,thusrenderingthewoodsurfacemoreresistantagainstde‐cay.Furfurylalcoholisderivedfromfurfural,whichisproducedfrombiomasswaste,makingthefurfurylationarenewablemethod.Theprocessisstillquitecostlythough,sothatitisnotyeteco‐nomic inmostcases [24,319‐320].Anexampleofphysicalmodification is themanufactureofthermallymodifiedtimber(TMT)bymeansofaspecialheat treatment.All thosemodificationmethods,however,havethedrawbackthattheystillhaveanegativeinfluenceonthewood’sprop‐ertiesincludingtheloadbearingbehaviourandthetendencytocrack[20,26].
Anotherchallengefortimberstructuresisthecombustibilityofthewood.Buthereagain,withgoodplanning,anyproblemsconcerningthefiresafetycanberesolved.Whenexposedtofire,woodcreatesalayerofcoalonitssurface,whichprotectstheremainingpartofthecross‐section.Theratethatthethicknessofthecoallayerincreaseswithispracticallyconstantovertime,which
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makesitpossibletodeterminetheremainingcross‐sectionafteracertainamounttimeundertheinfluenceoffirequiteaccurately.EC5part1‐2forthefiredesignoftimberstructuresisbasedonthisprinciple.FromthoseexplanationsitalsofollowsthatmassivetimberelementslikeCLThaveadvantagescomparedtolighterframeworkstructureswhenitcomestofiresafety,becauseofthesmallersurfaceinrelationtothevolume.
Allthoseaspectsareimportanttokeepinmindwhendesigningbuildingsusingwoodproducts.Butofcourse,forthestructureitself,themechanicalpropertiesaremostimportant.
Firstofall,woodisanisotropic,morepreciselyorthotropic,thatmeansthatitsmechanicalprop‐ertiesaredifferentinthreeperpendiculardirections,paralleltothegrain,radialandtangential,cf.Figure5.1.Thisisduethewood’sinternalstructure,consistingoflonggrainsthatrunparalleltoeachotheralongthetrunkofatree.Additionally,thecross‐sectionofatreetrunkisbuiltupoutofrings,eachyearanewgrowthringisaddedtotheoutside,whichalltogetherleadstothethreedifferentdirections.
Figure5.1:Threeprincipalaxesofwoodwithrespecttograindirectionandgrowthrings[16,5‐2]
Indesignpractice,however,nodifferenceismadebetweentheradialandthetangentialdirection,onlyparallelandperpendiculartothegrainaredistinguished.Figure5.2showsthestress‐strain‐diagramofsolidwoodparalleltothegrain.Thetensionstrengthf ,thecompressionstrengthf andthestrainsεatthecorrespondingpointsarepointedout.
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Figure5.2:Stress‐strain‐diagramforsolidwood[26,203]
Thestrengthparalleltothegrainishighest,sincethisisthemaindirectionatreemustcarryloadsininthenature.Perpendiculartothegrain,woodhasalimitedbearingcapacityforcompression,but this can lead to large settlements.This is especially interesting formulti‐storeybuildings,whererathersmall settlementscanaddupoverall thestoreys toa considerabledeformationwhichcanendangerthestabilityoftheoverallstructure.Compressionperpendiculartothegrainshouldthereforegenerallybeavoidedinmulti‐storeybuildings.Thetensionstrengthperpendic‐ulartothegrainisevensmaller,about30to50timessmallerthanparalleltothegrain[26,19‐20].Asidefromthat,itisinterestingtonotethatahigherstrengthclassofwooddoesnotleadtoaconsiderablyhighertensilestrengthperpendiculartothegrain.Knotsinthewood,however,which leadtoagrading ina lesserstrengthclass,seemtohaveapositiveeffectonthetensilestrengthperpendiculartothegrain[26,112‐113].
Incompliancewiththosefindings,failureoftimberstructuresinpracticeisinmostcasesaresultoftensionperpendiculartothegrain.Thisoccurse.g.atconnectionswithmetalfasteners,atholesandnotchesandattheapexofgableroofbeams.Changesinmoisturecontentcanalsoleadtoeigenstressesandcrackswhich increasethedangerof fractureperpendiculartothegrain[26,153].Thebehaviourofwoodunderstressesperpendiculartothegrainisnotyetfullyunderstood.Empiricalmethodsarecommonlyused, likeminimumdistancesofmetal fasteners,orstressesperpendiculartothegrainareavoidedcompletely,e.g.byapplyingadditionalstrengtheninglikefullythreadedscrewsintheapexofgableroofbeams[26,19‐20].Thefailureitselfischaracterisedbyaratherbrittlebehaviour[20,15].
Anotherimportantfactorthatinfluencesthewood’spropertiesistime.Woodlosesitsstrengthandstiffnessunderlong‐termloads.Unlikemostothermaterials, thisbehaviourcannotbene‐glected,forsolidwoodthestrengthaftertenyearsofloadingcanbereducedbyupto40%[26,21].Thelong‐termbehaviourofwoodisstillapartoftheresearch.Testresultsshowalogarithmicrelationshipbetweentheloadingdurationandthestrengthforbending,cf.Figure5.3.
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Figure5.3:Decreaseofthebendingstrengthoftimberdependingontheloadduration[26,135]
Fortheteststhattheabovediagramisbasedon,specimenswereloadedwithaconstantbendingloadatdifferentstresslevelsandthetimeuntilfailurewasmeasured.Thelongertheloaddura‐tion,thelowertheacceptablestresslevel.Forotherfailuremodesthanpurebending,onlyverylittlestudiesexist.Thesesuggest,however,thatforanykindofloadingparalleltothegrain,thebehaviourfollowsapproximatelythecurvefromabove,whileloadingperpendiculartothegrainleadstoastrongerdecreaseinstrength[26,141].IntheEC5,theinfluenceoftheloaddurationisconsideredviathemodificationfactorforthewood’sstrengthk .
Moistureinwoodhasalreadybeenmentionedinconnectionwiththedecay.Italsoshortensthetimeto failure formemberssubjectedto long‐termloads[26,141].Moreover,with increasingmoisturecontent,boththestrengthandtheYoung’smodulusoftimberdecrease.Themoisturecontentinthewoodwilladapttothehumidityofthesurroundingair.Thatmeansthatdifferentclimaticconditionsleadtodifferentmoisturecontentinthewoodandthushaveadirecteffectonthebearingbehaviour.ThiseffectisincludedintheEC5viethesamemodificationfactorasfortheloadduration,k .
Besidesthestaticmoisturecontentinthewood,thechangesofthiscontentalsohaveanimpactonsomethewood’sproperties.Astheairhumiditygenerallychangesoverthetimeofayear(de‐pendingontheregion),atimbermemberthatisnotinaprotectedindoorclimate,willgothroughmanycyclesofmoisturechanges,cf.Figure5.4.
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Figure5.4:Meanmoisturecontentinwood(glulam90×100×600) versus time in a barn in Southern Sweden (Åsa)[26,155]
Those changes of moisture content will amongst other things lead to increased creep defor‐mations[26,141].
Avoidinghighmoisturecontentsandmoisturechanges is importanttoensurethatthewood’spropertiesdonotchangefortheworse.Furthermore,decayeffectsmustbeexcludedtoguaranteedurabilityandalonglifetimeofatimberstructure.Toachievethis,somemeasureshavealreadybeenmentionedinthebeginningofthischapter.Ageneraldesignruleistokeepwoodmembersindrysurroundingsorat least toallowwatercoming incontactwiththewoodtorunoffandevaporatewithouthindrances.Itisalsorecommendedtokeepdistancesbetweenwoodmembersandcomponentsmadefromdifferentmaterialstopreventmoisturefromgatheringinthegroovethatcandamagethewood.Averyeffectivemeasuretoprotectwoodencomponentsfromwaterisapplyingalayeronthecomponent(e.g.woodencladding)thatcaneasilybereplaced.
5.1.2. WoodinComparisontoOtherMaterialsNowthatageneralbasisiscreatedconcerningthecharacteristicpropertiesofwood,thisbasisshallbeextendedbycomparingwoodtoothermaterials,namelyreinforcedconcreteandsteel,whichareitsmostimportantcompetitors.
Oneaspectthathasalreadybeenmentionedisthewood’svariabilityandinhomogeneity,whichleads tohigheruncertaintiesconcerning itsmechanical (andother)properties.Both steel andconcretehavemuch lowerorpracticallynosuchvariabilityand inhomogeneity,althoughcon‐crete,becauseitisoftenproduceddirectlyonsite,alsohassomeuncertainties.ThisisdirectlyreflectedinthematerialsafetyfactorsthataredefinedinthedifferentEurocodesforthosethreematerials:γ 1,3forsolidwood7,γ 1,5forconcreteandγ 1,0forsteel.
7Someengineeredwoodproducts,becausetheyhavealowerinhomogeneity,havelowersafetyfactors,e.g.γ 1,2forlaminatedveneerlumber.
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Furthermore,theorthotropyofwoodhasbeenexplained.Whilesteelispurelyisotropic,i.e.itsmechanicalpropertiesarethesameinanydirection,reinforcedconcretefeaturesadifferentkindofanisotropy.Althoughbothitsbasicmaterials,concreteandsteel,areisotropic,thefinalproducthasadistinctiveanisotropydependingonthelayoutofthereinforcement.
Anotherimportantaspectisthefailurebehaviour.Whereaswoodhasaratherbrittlefailurebe‐haviour,concreteandespeciallysteelcandeveloplargeplasticdeformationsbeforefailure.Ontheotherhand,woodhasgoodstressdistributionproperties,whichareadvantageousforcom‐binedloadslikecompressionandbending.
Togiveanideaoftheoverallperformanceandcapacityofthethreematerials,someinterestingpropertiesaresummarisedinTable5.1.
Table5.1:Mechanicalpropertiesofsteel,concreteandwoodincomparison[1]
property steelS355 concreteC30/37 glulamGL24hyieldstrengthf 355N/mm 30 N/mm 24N/mm specificweightγ 78,5kN/m 25 kN/m 3,7kN/m heatconductivityλ 50W/ m ⋅ K 2,3 W/ m ⋅ K 0,12W/ m ⋅ K Young’smodulusE 210000N/mm 33000 N/mm 11600N/mm
Asonecouldalreadyguessfromthepreviousdescriptions,steelissuperiortowoodinmostme‐chanical properties. This canbepartly compensated, however, by thewood’s low self‐weight,whichmakesmore light‐weight,efficientstructurespossible.Thesmallweightcombinedwithgoodelasticityisalsoadvantageousforloadsfromearth‐quakes.Whatstillisachallengeespe‐ciallyinstructureswithlargespans,isthewood’slowYoung’smodulus,whichleadstolargede‐formations(evenifthematerialwouldnotfail).Insuchcases,specialstructuresareneededlikearchedbeamsorlatticegirders.Vibrationsandaninferiorsoundprotectionarefurtherproblemsconnectedtothewood’slowYoung’smodulusandweight.Steelbeams,ontheotherhand,canbeusedforlargerspanswithoutspecialmeasures,despitethesteel’slargeweight.
Oneinterestingpropertybesidesthemechanicalbehaviouristheinsulationcapability.Theheatconductivityofwoodisabout20timessmallerthanthatofconcreteandmorethan400timessmallerthanthatofsteel.Moreover,woodregulatestheclimateinsideabuildingbyadaptingitsmoisturecontent.Consequently,woodcanfulfilmultiplefunctionsinabuilding,notonlyload‐bearingbutalsobuildingphysicalones(and,additionally,architecturalones,asdescribedbefore).
Concerningthedecay,steelandconcretehaveadvantages.But,asexplainedearlier,ifdesignedproperly,decaycanbeprevented,andsteelandconcreterequirespecialmeasuresaswelltoavoidcorrosion,whichcanbeseenasthe“decay”ofsteel.Inreinforcedconcrete,theconcretecoverisnormallydimensionedtoprotectthesteelbarsfromcorrosionfor50years.Steelrequiresexpen‐sivecoatingorgalvanisingwhenexposedtotheweather.
Whenitcomestologisticsandtheerectionofabuilding,thewood’slowself‐weightisagainad‐vantageous.Thisalsomakesahighdegreeofprefabricationpossible,allowingforveryeconomicstructures.Inadditiontothat,woodproductscanrelativelyeasilybeadjustedontheconstructionsite.Here,steelhassomedisadvantages,while(non‐prefabricated)concreteallowsforthehighestdegreeofadaption.
Lookingatecologicalaspects,woodrevealsitsgreatestadvantages.Becauseofthelowweight,lessenergyisneededfortransportanderection.Woodisinfinitelyavailableanddoesnotdamagetheenvironmentifsustainableforestryisapplied.Incontrasttothat,whiletherawmaterialsfor
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steelandconcreteareabundantaswell,theirexploitationisoftenconnectedtoenvironmentaldamages.Whenmanufacturingtimber,thewastewoodcanbeusedtopowerthefactory.Noad‐ditionalenergyisneededwhenusingmodern,efficientpowerproductionwithheatrecovery.Andwhenitcomestotheproductionofthefinalbuildingproduct,timberusesingenerallessenergythanconcreteorsteel[27,26].
Recyclingattheendofthelifetimeofabuildingcaneffectivelyreducethedemandfortherawmaterialsandistodaypossibleforallthreematerials.Therecyclingofsteelismosteffective,whileconcretecanonlybecrushedandusedasaggregatefornewconcreteagain.Itis,however,alsopossibletouseby‐productsfromsteelandpowerproductionlikeslagandflyashfornewconcrete[24,412].Woodcanbereusedforengineeredwoodproductsor,asalastpossibility,burnedandusedasanenergysource.
Sinceecologicalaspectsplayamoreandmoreimportantroleinoursocietyandareoneofthecentralfactorswhenplannersdecidetousewoodforacertainproject,thoseaspectswillbead‐dressedinmoredetailinthenextchapter,focusingagainmoreonthewooditself.Asameanstoanalysetheecologicalaspects,lifecycleassessment(LCA)willbeused.
5.1.3. AspectsfromLifeCycleAssessmentBeforestartingtoanalyseaspectsfromLCA,aquickexplanationofLCAmethodsshallbegiven.“LCAisamethodologyusedtoanalysecomplexprocesseswhichfocusondealingwiththeinputandoutputflowsofmaterials,energyandpollutantstoandfromtheenvironmentfromalifecycleperspective”[24,49].Itsobjectivesare,ontheoneside,toquantifytheenvironmentalpropertiesofaproductorprocess,andontheotherside,toassesspotentialsforimprovingtheproductorprocess[24,49].WithoutknowingmuchmoreaboutLCA,itcanbeguessedthattoquantifyalltheenvironmentalinfluencesofaproductinonenumberoreveninseveralnumbersispracticallyimpossible.TheresultsofanLCAanalysisareneverexactlycorrectbecauseofthehighcomplexityoftheprocessesandbecauseitisnotpossibletopredictthefutureaccurately.ThismustbekeptinmindwheninterpretingLCAresults.Hence,LCAisespeciallysuitedtocomparedifferentalter‐nativesbymeansofrelativeresults,notsomuchtoobtainabsoluteresultsforoneproductorprocess.Lookingattherelativeresults,LCAgivescorrectresultsalmosteverytime[24,417‐418].
Astrongtoolfortheinterpretationoftheresultsisanevaluationmatrix,whichbalancesenviron‐mental,economicandsocialfactorse.g.fortheselectionofamaterialforaspecificproject[24,44].(Asimilarmatrixwillbeusedattheendofthismasterthesisinchapter7.2tocomparethethreedifferentconstructionmethodsthatwillbedesignedandanalysed,extendingthetoolbytechnicalaspects.)
ImportantaspectsinanLCAstudyforbuildingproductsare
resourceefficiency, energyefficiency, GHGemissions, pollutionpreventionand wastemanagementaftertheendofthelifetime[24,421].
Theresourceefficiencyincludestheexploitationoftherawmaterialsaswellasreuseandrecy‐cling.
Theenergyefficiencyisabigfactorwhichincludesalltherequiredenergyfromdepletingtherawmaterials,tomanufacturing,transportingandmaintainingtheproduct,alsocalledembodieden‐ergy. Influencing factors are amongst others the lifetime of a product and the amount of
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maintenancethatisrequired.Toensurealonglifetime,measuresmustbetakentopreservethewood,ashasalreadybeenexplained.Theembodiedenergyrepresentsnormallyaround10to60%ofthetotalenergyusedduringthewholelifetimeofabuilding,whichincludestheenergyforheatingandusingthebuilding.Asbuildingsbecomemoreenergy‐efficientconcerningheatingandtheuseofelectricity,theembodiedenergyinthematerialsbecomesproportionallymoreim‐portant[24,421].
GHGemissionsisanothercentralaspectforthewholelifetimeofabuilding.Woodasaconstruc‐tionmaterialcanbecarbonneutralorevencarbonnegativewithgoodrecycling[24,418],be‐causecarbonisstoredinthewood.However,takingintoconsiderationaspectsfromafullLCA,studiesshowedthatthetotalamountofavoidedcarbonisactually2,1timeshigherthanthecar‐bonstoredinthewooditself.Thisisduetolesscarbonemissionsintheindustrialprocessescom‐paredtoothermaterialsandusageofby‐productsfromthemanufacturingofwoodproductsasbiofueltoreplacefossilfuels[24,326].Concerningtheforestry,somestudiesfoundthatintensiveforestryhaslessCO2emissionsthantraditionalforestry.Thisisbecausetheproductivityismuchhigher,thereforemoreCO2canbestored.Nonetheless,itmustbekeptinmindthatCO2isnottheonlyfactorforLCAandanintensiveforestrycanproduceconflictswithotheraspects,e.g. thebiodiversity[27,27].
Figure5.5showsthecarboncontentandtheembodiedenergyofsomeselectedbuildingmateri‐als.Itmustbenotedthatthecarbonstoredinsidethewoodisnotconsideredinthepresentedvalues.Moreover,thevaluesaregivenrelatedto1kgofthecorrespondingmaterial,butdifferentamountsareneededfordifferentmaterialsinthesamestructure.Theratioofthetotalrequiredweightofmaterialbetweenawoodenstructureandacomparableconcretestructurecanbeupto1:5[24,413].
Figure5.5:Embodiedenergyandcarboncontentofdifferentbuildingmaterialsbasedon[24,415]
Pollutionpreventionconcernsthereleaseofpollutinggasesduringboththemanufacturingpro‐cessandtheuseofaproduct[24,45‐46].
Withthewastemanagement,potentiallyincludingrecycling,thecycleclosesagain.
Buildingsareverycomplexstructuressincematerialsandmembersgenerallyfulfilseveralfunc‐tions.Becauseofthatandbecausedifferentmaterialsrequiredifferentquantitiestofulfilaspecific
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function,thematerialscannotbedirectlycompared.Moreover,allthecomponentsinsideabuild‐inginfluenceeachotherinsomewayoranother.ThebestwaytoperformanLCAanalysisisthere‐foretocomparewholebuildingsthathavethesamefunctionality.Conclusionsfromvarioussuchstudiesshowthatwoodenconstructionshaveingenerallowerenvironmentalimpactthanequiv‐alentstructuresusingnon‐woodmaterials[24,321].
Besidesthechoiceofmaterial,structuresthatcaneasilybedisassembledareadvantageousfromanLCApointofview,becauseit improvesrecyclingcapabilities. Inwoodbuildingsthiscanbeachievedbypreferablyusingbolts insteadofadhesives.Monolithicconcretestructures,ontheotherhand,havetobedemolishedforrecycling[24,418].
Acontroversialpointconcerningmodernwoodproducts istherollofprefabrication.Prefabri‐catedproductshavealowerenvironmentalimpactduringthemanufacturing,theconstructionandattheendoftheirlife,butthetransportationhasamuchhigherimpact[24,438].Thedistancebetweenthebuildingsiteandthefactoryiscritical[24,452].Thedistancesaregenerallymuchlarger for specially manufactured products than for individual standard components. This ishighlydependentonthespecificproject.
Tosumup,anexampleofafullLCAstudyconductedin2000byBörjessonandGustavssonshallbegiven.ItcomparedthenetCO2emissionsoftwosimilarfour‐storeyapartmentbuildings,oneinSwedenfeaturingawoodframestructure,theotherinHelsinkimadefromaconcreteframestructure.Theresultsshowedthatthewoodconstructionreleased30to133kg/m²lessCO2intotheatmosphere.Lateradditionalresearchconfirmedthegeneralresultsandfoundthatconcretestructuresneed16to17%moretotalenergythanwoodenstructures.Thoseresultsare,however,onlytruefornorthernEurope,wherewoodisavailablelocally[24,414‐416].
Lookingintothefuture,woodstillhasunusedpotentials.Onepotentialistoincreaserecyclingandtousemorewastestoreplacefossilfuelsforenergyorheatproduction.E.g.inNorway,onlyabout5%ofthewoodfrombuildingsisrecycled,70%isusedforenergyproduction,9%issendtolandfills,2%iscompostedand17%isusedforunknownintentions[27,44].Toachieveim‐provements,differentindustriesliketheforestry,energy,buildingandthewasteindustrymustworktogether[27,26].Wastes,hithertolittleusedspeciesandrecycledmaterialcanwellbeusedfornewengineeredwoodproducts,whichisthetopicofthenextchapter.
5.1.4. EngineeredWoodProductsEngineeredwoodproductsare todayalreadyan importantpartof thesupportingstructure inmostbuildings.Theiradvantagesareobvious:Whereassolidwoodisonlyavailableintheformoflinearmembersandthecross‐sectionareaislimitedbythesizeofthetreetrunk,engineeredwoodproductsallowarbitrarycross‐sectionsandalsotwo‐dimensionalmemberslikeplates.Moreover,thepropertiesofthewoodcanbeimprovedpurposefully.
Engineeredwoodproductsareingeneralmadefromboards,veneers,strandsandflakesofwoodthatarejoinedtogetherwiththeuseofadhesives.Thefinalproductscanbeofvariableform,e.g.boardsortimber‐likebeams.Thefinalproductsaremuchmorehomogeneousthantheinitialsolidwood,knotsandotherdefectscanbeeliminatedoratleastevenlyarrangedoverthewholecom‐ponent[26,82‐83].
Themanufacturingofengineeredwoodproductsrisestheefficiencyofthetimberproductionbe‐causeitalsoallowstheuseofpartsfromtheinitiallogsthatcannotbeusedforsolidwoodbeams,likethebranchesandthewastefromtheproductionofsolidwood.Thisallowsforamoreefficientuseofthewood,comparedtothemanufacturingoftraditionalsolid‐woodmembers,whichhasarelativelyhighdegreeofwastebecauserectangularcross‐sectionsarecutfromaroundlog.
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Therearemanydifferentengineeredwoodproductsavailabletoday,andmorearebeingdevel‐oped.
Oneofthemostwidelyusedengineeredwoodproductsisgluedlaminatedtimber(glulam).Glu‐lamismadeofseveralplanksthataregluedtogetherontopofeachother,formingacross‐sectionthatcanbeashighas2m[26,7].Withglulamitispossibletoovercomeoneofthesolidwood’slimitingfactors,whichisthesize.Thebiggestpossibledimensionforsolidwoodisabout300mm,thusthemaximumpossiblespanofatimberbeaminpracticeisabout5to7m[26,7].Glulamallowspracticallyarbitrarycross‐sectionsforspansofupto100m[26,8].Usingfinger joints,beamsoftheoreticallyanylengthcanbeproduced.Duetotransportationlimitations,however,themaximum length in practice is limited to 16 to 20m [26, 68]. It can beproduced in bothstraightandcurvedforms,sothate.g.wholearchescanbeproducedasonesolidwoodcompo‐nent.
Aswithotherengineeredwoodproducts,glulamhasenhancedmaterialpropertiesincomparisontosolidwood,thestrengthandstiffnessareincreased,whilethevariabilityissmaller[26,69],thisisdepictedinFigure5.6.
Figure5.6:Comparisonofthefrequencydistributionofthestrengthofglulamandsolidwood[26,19]
Sincetheheightofthecross‐sectionisnormallymuchhigherthanitsthickness,stabilityfailuremodessuchaslateraltorsionalbucklingareofhigherimportanceforglulamthanforsolidwood.
Adifferentengineeredwoodproductisparallelstrandlumber(PSL),whichwasdevelopedwiththeideatoutiliseforestwastessuchasbranches.Itismadefromlong,thinstrandsofwoodwithalengthofupto2,4mandcanbemanufacturedwithcross‐sectionsofupto280×480mm,whichliesinthesamerangeasthepossiblecross‐sectionswithsolidwood.Itisthereforemainlyusedasasubstituteforsolidwood,withthebenefitsthatitmakestheforestrymoreefficientandhasahigherbendingstrengthaswellaslessshrinkageandsplittingcomparedtosolidwood[26,88‐91].
Laminatedveneerlumber(LVL)ismadefromlayersofwoodveneerthataregluedtogether,allwith the orientation of the grain along the long axis of the member. Cross‐sections of up to90×1200mmarepossible,thelengthcanbe25m.Itcanbeusedforbeamsinsmallandbigcon‐structionsandisalsocommonlyusedforflangesofI‐joists[26,93‐95].
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I‐joistsarebendingmemberswithamoreefficientstructuralshape,becausethematerialiscon‐centratedintheouterregionsofthecross‐section,theflanges.ThosearecommonlymadefromsolidwoodorLVL.Thewebistypicallymadefromorientedstrandboard(OSB)orplywoodpan‐els,i.e.woodenpanelswithahighshearcapacity[26,97].OnedrawbackofI‐joistsistheirvul‐nerabilitytofirebecauseofthethinweb.
Forplywood,layersofwoodveneeraregluedtogether,butunlikeforLVL,thoselayersarerotatedby90°toeachother,formingaboardthathasgoodbearingcapacityinbothdirectionsandamoreisotropicbehaviour.Orientedstrandboard (OSB) ismade fromsmall strandsofunderutilisedwoodspecies.Bothproductscanbeusedassheathingforwallsandfloors,wheretheyprovidestiffeningofthecomponentandactascoveratthesametime.OSB,however,hasthehighestemis‐sionsofvolatileorganiccompounds(VOC)ofallengineeredwoodproducts[27,35]andshouldthereforebeusedwithcareinresidentialbuildings.
Amorerecentlydevelopedengineeredwoodproductiscross‐laminatedtimber(CLT),whichisamasstimberproduct.Itconsistsoflayersofparallelboards,10to35mmthick,whicharethengluedtogetherat90°toeachothertoformbothmassiveplatesandmassivememberswithlargecross‐sections.Wherethebreadthofglulamcross‐sectionsislimitedbythebreadthoftheindi‐vidualboards,membersmadeofcross‐laminatedboardscanhavearbitrarydimensionsinbothdirections.Thecross‐laminationleadstoamorehomogenousbehaviourcomparedtosolidwood.Italsoreducestheshrinkageandswellingtoaninsignificantamount[20,52‐55].Furthermore,CLTpanelsareingeneralairtight(dependingonthespecificproduct)[21,115].Theyarethere‐foremainlyusedforfloorsandwalls,wheretheycanfulfilthefunctionofanairtightmembraneinadditiontotheloadbearingandthestiffening.CLTistodayreadilyavailableinpracticallyallpossibledimensions.
Besidesthemechanicalproperties,therearealsonoticeablepricedifferences.Althougheconomicaspectsarenotwithinthescopeofthismasterthesis,Table5.2givesanideaofthepricediffer‐ences,whichwillofcourseplayaroleintheplanningofatimberbuilding.
Table5.2:Pricesofsomeselectedengineeredwoodproductsincomparisontosolidwood[20,51]
material pricesolidwood 300–400 €/m³glulam 1000 €/m³parallelstrandlumber 1500 €/m³
Acentraldrawbackofalltheengineeredwoodproductsisthattheyusesyntheticaladhesives.Thosearetypicallyurea‐orphenol‐formaldehydewhicharemadefromnon‐renewablemineraloil.Moreover,theyemitformaldehydeduringtheirlifetime(indifferentamounts,dependingontheproduct).Newdevelopmentsaimatreducingtheuseofadhesivesorusingnaturalalternativessuchaslignin‐basedadhesives[24,317].
Inthefuture,whenenvironmentalrestrictionsmayleadtolessavailablelarge‐sizesolidwood,engineeredwoodproductswillbecomemore important[26,83].Today,solidwoodisalreadymeetingits limitswhenitcomestostructureslikemulti‐storeytimberbuildings.ProductslikeglulamandCLTopenupacompletelynewwayoftimberdesign.Itwillbeseeninchapter6.2thatnoneoftheanalysedstructuresusessolidwoodasacentralstructuralmaterialbecauselargercross‐sectionsarerequiredthanwhatispossiblewithsolidwood.Ithasalsobeenexplainedhowdeformationsduetocompressionperpendiculartothegrainormoisturechangescanbedecisive
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formulti‐storeybuildings.Inthisregard,thedescribedengineeredwoodproductsaresuperiortosolidwood,too.
5.2. TimberConnectionsThemissing linkbeforemovingon todiscussingentire timberstructuresare theconnections.Connections are ofmajor importance for timber constructions and especially formulti‐storeybuildingsbecauseofthehighloads.Evaluationofdamagedtimberbuildingsafterextremewindshowedthatconnectionsareoneofthemajorweakpoints[28,81].
Thereare,ingeneral,twopossibilitiestoformconnections:
gluedconnectionsor connectionswithdowel‐typefasteners(nails,bolts,screws,dowels,commonlymadeof
steel)[26,303].
Whilegluedconnectionsaremainlyappliedonprefabricatedcomponents,e.g.forfingerjointsinglulamelements,dowel‐typefastenersarewellsuitedforanyon‐siteassembly.Sincetheproper‐tiesofgluedconnectionsaremostofthetimealreadyincludedinthedescriptionofthepropertiesofthecorrespondingengineeredwoodproduct,thefollowingdiscussionswillfocusmoreoncon‐nectionsusingfasteners.Nonetheless,itshallbenotedthatnewtechniquesarebeingdevelopedthatalsoallowtheeconomicmanufactureofgluedjointson‐site.Table5.3summarisesthemainadvantagesanddisadvantagesofgluedconnections.
Table5.3:Advantagesanddisadvantagesofgluedconnections[26,334]
advantages disadvantages/problems higherrigidity canbehighlyautomated makesspecialconnectionspossible,
e.g.fingerjoints thecross‐sectionisonlyminimally
damaged,ornotatall
moresensitivetounskilledmanufac‐ture
lowerinherentredundancy ingeneral,noon‐sitemanufacture
possible oftenverybrittlebehaviour emissionofVOC complexmechanicalbehaviour,stress
peaks
Focusingonconnectionswithdowel‐typefastenersfromnowon,firstsomegeneralaspectswillbeexplainedbeforelookingatthedifferenttypesofconnectionsinmoredetail.
Resultsofexperimentsshowcorrelationsbetweenseveralparametersandthecapacityorfailurebehaviouroftheconnection.
Oneimportantparameteristheslenderness,i.e.therationbetweenthesidewidthofthewoodmemberandthedoweldiameter,whichleadstodifferentfailuremodesandthusverydifferentloadbearingcapacities,seeFigure5.7.Alowslendernessgenerallymeansthattherearenoplasticdeformationsinthedowel,onlyinthewood.Amediumslendernessleadstooneplastichingeinthedowel,whileforahighslendernesssecondaryplastichingesdevelop[17,68‐69].Largerwoodthicknessesgenerallyleadtoahighermaximumload,ahigherstiffnessandlargerdeformations.
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Figure5.7:Generalfailuremodesofatimberconnectionwitha)lowslenderness,b)mediumslendernessandc)highslenderness[17,68]
Moreover,thereisalinearcorrelationbetweenthedensityofthewoodandthemaximumloadandstiffnessoftheconnection.Aconnectionwithhighdensitywoodischaracterisedbyahighercapacity,lessdeformationsinthedirectionofthegrainandamorebrittlefailurebehaviourwithsplittingperpendiculartothegrain(aswasexplainedinchapter5.1.1,thetensilestrengthper‐pendiculartothegraindoesnotchangemuchevenforstrongwoodandthusbecomesdecisiveinanotherwisehighstrengthconnection).Thespacingbetweenthefasteners inamulti‐fastenerconnectionandtheirenddistancesalsohaveastronginfluenceonthecapacityofthewoodsincetoosmalldistancesprovoketheriskofsplitting[17,70‐74].
Johansendevelopedayieldtheorythatcanbeusedtodeterminethefailuremodeandtocalculatetheresistanceofawoodconnection,althoughitisnotsuitedtodeterminetheload‐slipbehaviour.Accordingtothistheory,therearethreemainaspectsthateffectthestrengthofaconnection:thebendingcapacityofthedowel,theembeddingcapacityofthewoodorengineeredwoodproductandthewithdrawalresistanceofthedowel.Theembeddingstrengthdependsmainlyontheden‐sityofthewood[26,316‐322]
Today’sdesignrulesforconnectionsine.g.theEC5standardaremainlybasedonempiricalin‐vestigationsandtheJohansen‐theory.ComparingthefindingsoftheexperimentswithcalculatedvaluesaccordingtoEC5revealsagoodaccordanceforthestiffnessandconservativevaluesforthestrengthformediumslendernessconnections.Forsmallslenderness,EC5overestimatesthestiffnessandthestrength,whileforhighslenderness,EC5underestimatesthestiffnessbutover‐estimatesthestrengthagain[17,76‐79],cf.Figure5.8andFigure5.9.
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Figure5.8:Comparisonofexperimentallydeterminedstiffnessesofselectedtestswithcorre‐spondingdesignvaluesfromEC5forspecimenswithdifferentslenderness[17,77]
Figure5.9:ComparisonofstrengthofselectedtestswithdesignvaluesfromEC5[17,77]
Becauseofthosediscrepancies,theapplicabilityoftheEC5rulesforconnectionsislimitedandanoptimiseddesignisdifficult[17,67].Sinceconnectionsareacentralpartofanytimberstructure,especiallyofmulti‐storeybuildings,onesectioninchapter6willbededicatedtoanalysingase‐lectedconnectioninoneoftheinvestigatedstructuresusingFEMtogainabetterunderstandingofitsbehaviour.
Therestofthischapterwillfocusonthecharacteristicsofthedifferentconnectionmethodsusingdowel‐typefasteners.
Thefirsttypeofconnectionthatwillbediscussedaretraditionaltimberjoints,someexamplesareshowninFigure5.10.
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Figure5.10:Examplesoftraditionaltimberjoints[21,58]
Theirmaincharacteristicisthattheydonotusemuchsteel,fastenersareonlyrequiredtosecurethe individual componentsagainstunwantedmovements.Those connections thereforehaveagoodfireresistance.Ontheotherhand,theycanhaveacomplicatedgeometry,especiallyiften‐sionforcesmustbetransferred.Withtoday’smodernCNCwood‐workingmachines,however,itispossibleagaintomanufacturesuchjointseconomically[26,304‐305].
Rightafterthetraditionaltimberjoints,nailshavebeenusedforalongwhileintimberbuildings.Todaytheyarerelativelycheap,oftennopre‐drillingisneeded,andmanydifferentconnectionsarepossible [26,306‐307],cf.Figure5.11.Onedisadvantage is that theyhavearelatively lowloadbearingcapacity,whichlimitstheirapplicabilityespeciallyinmulti‐storeytimberbuildings.
Figure5.11:Examplesofnailedjoints[26,306]
Thisiswhereboltsanddowelscomein,theycanbeusedforhigh‐strengthconnectionsinbigandcomplexstructures.Bothfastenersarenormallymadefrommetal,withmuchlargerdiametersthannails(acommonboltise.g.anM20‐boltwith20mmdiameter).Boltsarethreadedandhaveacounternutandwashers,whiledowelshaveasmoothsurfaceandarecompletelyhiddeninsidethewoodmember,cf.Figure5.12.
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Figure5.12:Steeldowelsandbolts[1,9.44]
Thelargediametersrequiresthewoodtobepre‐drilledwhichmakessuchconnectionsmorela‐bour‐intensive[26,307].Ontheotherhand,whenprefabricationisused,theholescanalreadybeproducedinthefactory.Thechoiceofdiametereffectstheloadbearingcapacityandbehaviour,largerdiametersleadtohigheracceptableloadsbutalsoabrittlebehaviourduetosplitting(cf.explanationsconcerningtheslendernessofaconnectionabove).ExamplesoftypicalapplicationsfordowelsorboltsareillustratedinFigure5.13.
Figure5.13:Examplesofjointsusingboltsordowels[26,308]
Arathernewdevelopmentarescrewjoints,withthescrewsbeingsubjectedtotensileloads.Thisisabigdifferencetoallothermethodsdescribedsofar,whichrelyontheshearcapacityofthefasteners.Modernhand‐heldtoolstoeasilydrivescrewsintothewoodhaveledtoscrewsmoreandmorereplacingnails.Atthesametime,theycanbedisassembledmoreeasily[26,307‐308].Moreover,modernfullythreaded,self‐tappingscrewsdonotrequirepre‐drilling[26,328].Theself‐tappingscrewsmakenew,effectiveconnectionspossible,someexamplesareshowninFigure5.14.
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Figure5.14:Examplesofapplicationsforfullythreadedscrews[1,9.55]
Adifferentpossibleapplicationoffullythreadedscrewsisthereinforcementofwoodenmembersperpendiculartothegrain.Thisensuresaductilebehaviouroftheconnectionandincreasestheloadbearingcapacity, sincea failureperpendicular to thegrain, i.e. splitting, isprevented [26,311‐313][26,317].ThepositiveeffectsofthisreinforcementarenotcoveredbytheJohansen‐theory,though,andarethereforenotconsideredintheEC5yet[17,79].
AnotherdrawbackoftheJohansen‐theoryandtheregulationsintheEC5isthatthetheoryhasbeendevelopedonlyforsinglefasteners.Thedesignofconnectionswithseveralfastenersisbasedonthepropertiesoftheconnectionwithonefastener,consideringaneffectivenumberoffasten‐ers,whichrespectsamongstotherthingsthespacingbetweenthefasteners.Formulti‐fastenerconnections,reinforcementperpendiculartothegrainisespeciallyinteresting.Withreinforce‐ment,groupeffectscanbeexcluded,sothattheload‐carryingcapacityoftheconnectioncanbeassumedtobethesumofthecapacitiesofallfasteners[26,322‐324].ProofforthevastlydifferentloadbearingbehaviourisdepictedinFigure5.15.Notonlyistheacceptableloadoftheconnectionhigher,buttheductilityisincreasedstrongly,too,whichcanbeseenfromthelargedeformationsthatoccurbeforetheconnectionfails.
Figure5.15:Loadbearingbehaviourofareinforcedconnectionincomparisontoanon‐reinforcedconnection[26,324]
Whenusing connectionswith several fasteners, it is important to allow formoisture inducedmovements.Connectionswherethewoodisrigidlyfixedatmorethanoneconnectorshouldbe
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avoidedbecausethiscanleadtocrackswhenshrinkageoccursduetochangesinthemoisturecontent[26,160].
Withthedescriptionofthebehaviourofmulti‐fastenerconnections,thechapteraboutconnec‐tionsiscompleted.Whilethedescriptionsanddiscussionssofardealtwithwoodingeneral,orspecificproductsandindividualcomponentsandconnections,thenextstepistolookatentiretimberstructuresthatconsistofthosecomponents.Inthenextchapter,thedifferencesbetweenthedifferentstructuralmethodsandtheirvariantsaredescribed,givinganideaofwhichmethodsarebestused inwhichcases.Basedonthose findings, thedesignanalysis inchapter6willbeplannedandconducted.
5.3. TimberStructures5.3.1. TimberFraming
Ingeneral,twomainconstructionmethodsaredistinguished.Timberframingstructures,featur‐ingone‐dimensionalelementsinthemainloadbearingstructure,willbeexaminedinthischapter.Masstimberstructures,whichusemasstimbermaterialslikeCLT,willbethetopicofthefollow‐ingchapter.
Structuresthatuseatimberframingmethodaregenerallycharacterisedbyanopenloadbearingstructure,aclearforcedistributionandacleardistinctionbetweentheloadbearingfunction,thestiffeningfunctionandtheroomseparation.Theloadsareconcentratedintheindividualmem‐bers,whichthuscanbeadaptedaccordingly,concerninge.g.thecross‐section.Connectionsaremorechallengingthanformasstimberstructuresbecauseofthehighconcentratedloadsandbe‐comethereforeoftendecisiveforthedimensioningofacomponent.
Thefollowingvariantswillbediscussedinthischapter:
traditionalframeconstruction, panelconstruction, balloonconstructionand modernframeconstruction.
ThetraditionalframeconstructionspreadinEuropearoundtheyear1700(cf.chapter2.1)andistodayoftenassociatedwithmedievaltimberhouses.Theframeworkconsistsofhorizontalandverticalbeamsaswellasdiagonalsforthestabilityandstiffening,seeFigure5.16.Theframeworkisoftenvisiblefromtheoutsidewiththecavitiesfilledwithe.g.brickwork.Thismethodismainlyusedforsmallone‐ortwo‐storeybuildings,theerectionoflargerbuildingsbecomesverycostly[21,55].
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Figure5.16:Traditionalframeconstruction[21,56]
ThepanelconstructionisanenhancementofthismethodandisillustratedinFigure5.17(left).
Figure5.17:Panelconstruction(left)andballoonconstruction(right)[21,60‐61]
ItreplacesthediagonalswithwoodenpanelsmadeofplywoodorOSBassheathing.Thisallowsinsulationtobeplaced in thesame layeras the loadbearingstructure, in‐betweenthecloselyspacedverticalmembers,thestuds.Thebigadvantageofthiskindofstructureisthebeneficialwaytheindividualelementsworktogether,becausethesheathingpreventsthestudsfrombuck‐linginthedirectionoftheirweakaxis.Thismakesveryslenderconstructionpossible,thepanelconstructionisthereforeprobablythemoststructurallyefficientsystem.
Thewallstudsareashighasonestorey,whichmakesthismethodhighlysuitableforprefabrica‐tion.Wallsandfloorsorevenentireroomsormodulescanbeprefabricated.Thisalsoleadstoasimpleerection,nospecialequipmentisrequired.Fromastructuralpointofview,prefabricatedwallpanelswithnailedsheathingarehighlyredundant.Arelativelylowgradeoftimbercanbeused[26,386].
Thepanel construction is commonlyused for smallerbuildingswithone to threestoreys.Formulti‐storeybuildings,thewallsneedhighershearresistanceandverticalloadbearingcapacitytowithstandthehighwindloadsandverticalloadsfromtheself‐weightaswellastheliveload.
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Newdevelopments to increase the shear capacityofwalls includebrace systemsbetween thestudsoradditionalsheathing[26,404].
Theballoonconstructionissimilartothepanelconstruction,withthemaindifferencethatthewallstudsgooverthewholeheightofthebuildingoratleastoverseveralstoreys(cf.Figure5.17(right)).Verticallycontinuousmembersarealwaysadvantageous inmulti‐storeybuildingsbe‐causetheyleadtolessdeformationsduetoshrinkageandgravityloads.Ontheotherhand,pre‐fabricationisnolongerpossibleinthesamedegreeasforthepanelconstruction[26,238][21,60‐61].
Finally,themodernframeconstructionisalsobasedonthetraditionalframeconstruction,buttakesthetimberframingtothenextlevel.AnexampleofamodernframeconstructionisdepictedinFigure5.18.
Figure5.18:Exampleofamodernframeconstruction:schoolinWil,Switzerland[21,86]
In contrast to the previously describedmethods, themodern frame construction features bigspans,withtheloadbearingcomponentsbeingwidelyspreadonalarge,regulargrid.Theload‐bearingstructureconsistsofasystemofcolumns,mainandsecondarybeams.Thewallsdonotcarryanyloads,thehorizontalloadsarerathertransferredbytheverticalmembersviabendingorvialarge‐spandiagonals.Thisopensupnewarchitecturalpossibilitieslikebigwindows.Italsooffersmaximumfreedomwhenitcomestosubdividingtheinteriorintorooms,changesarepos‐siblewithoutaffectingthestructure.Besides,theenclosingenvelopeformedbythewallscanbearrangedoutsideoftheloadcarryingstructure.Thishasthreemainadvantages:Firstly,theloadcarryingstructureandenclosingenvelopearecompletelyindependent,whichallowsforeasycon‐nections.Secondly,thewallsactasprotectionoftheloadcarryingstructurefromtheweather,andthirdly,theloadcarryingstructurestaysvisiblefromtheinside.
Forthemodernframeconstruction, largercross‐sectionsarerequired,therefore,glulamisthepreferredmaterial.Animportantpartoftheconstructionaretheconnectionsbetweenthecol‐umnsandthemainbeams.Therearedifferentpossibilities,thedecisionwilldependonproject‐specificstructuralrequirementsandarchitecturalaspects.Onecanusecontinuouscolumnswithtwo‐partcontinuousbeamsattachedtothesidesofthecolumns,orwithsimplysupportedbeamsin‐betweenthecolumns,attachedtothemwiththeirfrontends.Anotherpossibilityistousetwo‐
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partcolumnsorforkedcolumnswiththebeamsin‐between[21,86‐94].Tosumup,themodernframeconstructionishighlysuitedformulti‐storeybuildings.
5.3.2. MassTimberMasstimberconstructionsconsistoftwo‐dimensionalcomponents,i.e.wallsthatcarrytheverti‐calloadsandtheshear,andfloorswhichaccountforthehorizontalloaddistribution.Incompari‐sontoframeconstructions,masstimberconstructionshaveamorecomplexbehaviour.Thisisbecausethecomponentsperformdifferentfunctionsatonce,liketheloadbearing,thestiffeningandtheroomseparation.The loadsaremoredistributedandthereforegenerally lower.Asidefromthepurelystructuralproperties,masstimberisalsocharacterisedbyahigherweightwhichleadstoabettersoundprotection.Thefiresafety is increased,too,sincetwo‐dimensionalele‐mentsareonlyaffectedbythefireononeside,insteadofonuptoallfoursidesforone‐dimen‐sionalelements.
Thedifferentconstructionmethodsusingmasstimberthatwillbeexaminedinthischapterare
logconstructions, stackedplankconstructionsand CLT‐constructions.
Thelogconstructionhasalreadybeenmentionedinchapter2.1concerningthehistoricaldevel‐opmentinNorway.Itisoneoftheoldestmethodsandisstillinuse,althoughinmodifiedform.Anoverviewoverdifferentvariantsof the logconstructionareshowninFigure5.19,withtheoldestonesontheleftandmorerecentdevelopmentstotheright.Anyofthoselogconstructionsconsistsoflogsthatarehorizontallystackedontopofeachother.Thethirdonefromtherightshowsaprefabricatedsandwichelement.Thenexttwoarethermallyinsulatedlogwallswhichareassembledonsite.
Figure5.19:Differentlogconstructionvariants[21,53]
Thebiggestproblemwiththelogconstructionisthatlargecompressivestressesoccurperpen‐diculartothegrain.Asexplainedearlier,thisleadstohighsettling,about25mmperstorey,whichiswhylogconstructionarenotsuitedformulti‐storeybuildings[21,50‐53].
Adifferentmasstimbervariantisthestackedplankconstruction,whereplankswiththicknessesbetween20and50mmarestackedverticallynexttoeachothertoformwallsorhorizontallynexttoeachotherforfloors,cf.Figure5.20.Theplanksareconnectedwitheachotherontheflatsideswitheitheradhesivesorwithmetalfastenerssuchasnailsordowels.Woodenhardwooddowelscanalsobeused.Whiletheplanksthemselvesprovidethecompressionorbendingstrength,theconnection(eithertheglueorthefasteners)mustbedesignedfortheshear.Bothprefabrication
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or fabricationonsitearepossible.Thethicknessof thewallor floorequalsthebreadthof theplanksandiscommonlybetween80and240mm[21,122].
Figure5.20:Cornerdetailofastackedplankconstruction[21,122]
Inasimilarfashion,glulambeamscanbeusedtoformmassivewallsandfloors.Theindividualbeamsarethenjoinedusingatongueandgrooveconnection[21,176].
Finally,today’smostimportantmassivetimbermethodistheCLTconstruction.ThepropertiesofCLTanditsadvantagescomparedtosolidwoodhavealreadybeendiscussedinchapter5.1.4.Incontrasttotheothermassivetimbermethods,theCLTelementstakeonallnecessarystructuralfunctions inonesingleelement.As floorelements theyalsoallowbiaxial loadcarrying,whichmakesmoreeffectivestructurespossible.CLTelementsareexclusivelyprefabricatedandoftenadaptedtothespecificprojectconcerningopeningsforwindowsortechnicalinstallations.Theassemblyonsiteisthereforeverysimple,onlyaminimumofconnectionsisrequired.AnexampleofaCLT‐constructionisshowninFigure5.21.
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Figure5.21:ExampleofaCLT‐construction:evangelicchurchinRegensburg,Germany[5]
5.4. NewDevelopmentsInthepreviouschaptersaboutthetimberdesignbasics,boththebasictimbermaterialsandprod‐ucts,theconnectionstojointhoseproductsandfinallywholetimberstructureshavebeendis‐cussed.Tocompletethischapter,asmalloutlookintothefutureofthetimberdesignshallbegivenbyexaminingtoday’sresearchandnewdevelopments.
Inaccordancewiththestructureofthepreviouschapters,firstsomenewwoodenmaterialsorproductsshallbedescribed,followedbynewconnectiontechnologiesandnewlydevelopedstruc‐turalmethods.
Onenewmaterialismouldedwood,whichismadefromsolidwoodthatiscompressedbyabout30%,thencutintopoles,whichcanfinallybegluedtogetheragaintoformmanydifferentshapes.Withthistechnique,e.g.circularhollowtubecross‐sectionsbecomepossible.Thegoalistoman‐ufacturehighlyefficientshapesinthestyleofsteelcross‐sections[20,28].
Anothernewmaterialcanbemanufacturedbypressuretreatmentofsolidwoodand iscalledpressedwood.Thebasicsolidwoodisheatedto130°Candcompressedat5MPa.Thus,thecross‐sectionisreducedbyabout50%byeliminatingmostofthepores.Thetensileandcompressivestrengthsparallelwiththegrainaredoubled,thebendingstrengthincreasesbyafactorof2,5andtheshearstrengthbya factorof1,7.Someof thedisadvantagesthatarestillbeingworkedonincludeahigherriskofsplittingandlessbeneficialpropertiesconcerninggluedjoints[20,26‐28].
Connectionsaremaybethefieldoftimberdesignwheremostinnovationsaredevelopedtoday.Differentmanufacturersbringmanynewproductsontothemarket,aselectionshallbepresentedhere.Thewaysthatalreadyestablishedtimberconnectionsaredesignedandusedalsochange.
Diagonalscrewshavealreadybeenmentionedandareagoodexampleofhowalreadyestablishedconnectorsareusedinnewways.Sincetheyaresubjectedtotensioninsteadofshear,theload‐bearingismuchmoreeffective.Theycanevenbeusedtoconnecttwomembersthatdonottoucheachother,e.g.becausethereisathinlayerofinsulationbetweenthem[20,16].
Theenvironmentalproblemswithsyntheticadhesiveshavealsobeendiscussed.Theresearchfo‐cuses not only on usingmore natural substances but also on optimising the time it takes to
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manufacturesuchaconnection.Today’sstandardgluesneedabout20minutesopentime(thetimebetweentheapplicationoftheadhesiveandthejoiningofthetwocomponents),15minutespresstime(whenthecrampingpressureisapplied),andonlyaveryshortrestingtimeafterwards.Newpolyurethaneadhesivesonlyneed5minutesopentimeand2minutespresstime,whichal‐lowsforamoreproductivemanufacturingandmakesthemanufacturingofgluedjointsonsitepossible[20,17].Anexampleofaproductthatisalreadyavailableistheon‐sitefingerjointde‐velopedbyHESS[6].
Stillunderdevelopmentaregluedconnectionsthatdonotuseartificialadhesivesatall,butrathermakeuseofthewood’sownglue,thelignin.Thismethodiscalledwoodwelding.Applyingfric‐tionalheat,thelignininsidethewoodliquifiesattemperaturesabove200°Candcanthenbeusedtogluecomponentstogether.Ithardensinjustafewseconds[20,24‐25].
Glued‐insteeltubesandsteelplatesareconnectorsthatcanbeusedfornewkindsofjoints.Thesteeltubesarearound50mmindiameterand125mmlongandaregluedintothewoodparalleltothegrain,whichallowsforanoptimalloadtransferadaptedtothewoodscharacteristicstruc‐ture.Steelplatesworkliketongueandgroovejointsandcanbeassembledonsite,securedwithbolts[20,21].
Anothernewdevelopmentthatalsoconsidersenvironmentalaspectsaredowelsmadefromhard‐wood,tryingtominimisetheuseofenvironmentallyquestionablesteel.Hardwooddowelscanbeusedassubstitutes forsteeldowels,e.g. toconnectsecondarybeamstomainbeamsor inthestackedplankconstruction,asmentionedearlier.Hardwooddowelshavealreadybeenusedsuc‐cessfully,buttheyarenotyetincludedintheEC5.Itispossibletoreachthesameload‐carryingcapacityaswithsteeldowels,althoughthefailureisgenerallymorebrittle[20,22].
Whenitcomestowholetimberstructures,newdevelopmentsincludecompositestructuresthatfeaturebothwoodandanothermaterialasmainstructuralmaterials.Timberandconcretecanbecombinedtoformtimber‐concretecompositefloors,wherethewoodismainlyresponsibleforthetensilestresseswhiletheconcretetakesonthecompressionstresses.Incomparisontofloorsthatarepurelymadefromwood,thecompositefloorshavemuchbettersoundprotectionandahigherstiffness.Thehigherweightcancontributeto improvetheeigenfrequencyof thewholebuilding.That isparticularly interesting formulti‐storeybuildings,wherewind‐inducedvibra‐tionscanleadtodangerousresonanceeffects.Accordingtothebasicequationfortheeigenfre‐
quencyofastructure,f K/M,whereKisthestiffnessandMthemassofthesystem,ahighermasscanbeuseddirectlytodecreasetheeigenfrequencyandgetitoutoftherangeoftheexcita‐tionduetowindturbulences.Inadditiontothoseadvantages,theconcretealsoprovidesaverygoodfireprotection.
Concretecanbeusedfordifferentkindsoftimberfloors,e.g.joistfloorsorstackedplankfloors,hollow‐boxfloorswherethecavitiesarepartiallyfilledwithconcretearepossible,too[21,180‐181].
Thedisadvantagesofsuchhybridsystemsmostlycomefromthedifferentpropertiesandthedif‐ferentbehaviouroftheusedmaterials,e.g.concerningtemperaturedeformations,creepingandshrinkage.Thestructuremustbedesignedinawaythatallowsforrelativemovementsbetweencomponentswithdifferentmaterialstoavoidrestraintstresses.Ingeneral,hybridsystemsarealsomoreexpensivebecausedifferenttradesarerequiredontheconstructionsite.
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5.5. SummaryoftheCase/MaterialsThebasicpropertiesofwoodasa constructionalmaterialhavebeenexplained,mostof thosepropertiesareeitherdirectlyorindirectlylinkedtothefactthatwoodisanaturalmaterial.Incomparisontoconcreteandsteel,woodhasalowerstrength,whichcan,however,becompen‐satedbyitslowself‐weight,whichallowsforefficient,light‐weightstructures.AchallengewithtimberisitslowYoung’smodulusconcerningdeformationsandvibrations.IntermsofadesignbasedonEC5,theserviceabilitylimitstate,whichdealswiththoseaspects,oftenbecomesdeci‐sive.Thiswillbepickedupagaininthenextpart.
Furthercharacteristicsofwoodincludethatitsstrengthdependsontheloaddurationandmois‐turecontentinsidethewoodandthatitcandecay.Durabilityisthereforeimportanttoconsiderinthedesignfromanearlypointonwards.Thebiggestadvantagesoftimberbuildingsincompar‐isontothosemadefromsteelorconcreteareenvironmentalones,thishasbeendiscussedindetailconsideringaspectsfromLCA.
Modernstructuresandnewdevelopmentscarrythetimbertechnologiesfurtherandmakethemcompetitiveagain.Differentsolutionshavebeenpresented.Engineeredwoodproductslikeglu‐lam,plywoodorCLTplayacentralroleintoday’stimberconstructions.Concerningthedesignoftheoverallstructure,itcanbeconcludedthatmoderntimberframingstructures,CLTmasstimberconstructionsandpanelconstructionsarebestsuitedformulti‐storeybuildings.Ingeneral,andespeciallyforbuildingswithmanystoreys,clearloadpathsarehelpfulandallowforamoreeffi‐cientdesign.
Basedonthefindingsandconclusionsfromthischapter,thenextchapterwillbededicatedtothedesignandanalysisofthreedifferentvariantsofthetimberbuildingTreet.
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6. Method6.1. Procedure
Whilethepurposeofthepreviousworkwastocreateanobjective,up‐to‐datesummaryoftimbertechnologies,pointingoutaspectsthatareespeciallyinterestingformulti‐storeybuildings,thefurtherworkwillbemoreexperimental.Bymeansofthedesign,newinsightsintothedescribedconstructionmethodsshallbederived.Thegoalistomakesomesmallcontributionstotakethebuildingwithtimberintothenextstage.
Beforebeginningwiththedesign,firsttheprocedurethatwasfollowedduringthedesignshallbepresented.
Thefirstdecisionthathadtobemadewaswhichkindofstructuresshouldbeanalysed.Inthesummaryofthecase/materials(cf.chapter5.5),threestructureshavealreadybeenpointedout.Consequently,thefollowingthreedesignvariantsweredefined:
a) frameconstruction8b) panelconstructionc) CLTconstruction
Anotherdecision,whichiscloselyrelatedtothefirstone,wastoonlyanalysepurevariants,i.e.structuresthatuseonlyonesinglestructuralmethod.Attheendof thedesignof thedifferentvariants,oneofthemainconclusionswillbethatalltheconstructionmethodshaveadvantagesanddisadvantagesandthatthebestsolutionwillbeacombinationoftheabovethatmakesuseofeachmethod’scharacteristicadvantages.However,howthefinalresultwilllooklikeheavilyde‐pendsonthespecificproject,buttheintentistofindconclusionsandgiverecommendationsthatareasgeneralandapplyforasmanydifferentprojectsaspossible.Besides,analysingonlythepurevariantsmakesitmucheasiertocarveouteachmethod’sowncharacteristics.
Thesubsequentdesignfollowedthreemainsteps:
1. draftdesign2. preliminarydesign3. ECdesign
Thedraftdesignstartedoncethedesignvariantsweredefined,firstdraftsweremadetogetanideaoftheoverallstructuralsystem.Someimportantdetailswerealsoalreadyplannedtocheckthegeneralfeasibilityofthegeneralsystem.Thestructuralconceptsforthethreevariantswillbelaidoutinthenextchapter6.2.
Thepurposeofthepreliminarydesignistocalculatefirstestimatesofthedimensionsofthecom‐ponentsandchoosewhichmaterialsandconnectionsshallbeused.Thedocumentationofprelim‐inarydesigncanbefoundattachedtothisdocument,cf.appendixA,andisdiscussedinchapter6.3.
TheECdesign is required toprove the feasibilityof thewholeconstructionbasedon theEC5standard.ThedocumentationoftheECdesignisalsoattached(cf.appendixA).Somecommentsonthisphaseofthedesignaredescribedinchapter6.4.
Forthismasterthesis,moreemphasisisputonthegeneraldesign,i.e.designphases1and2,andlessonthefinaldetaileddesign.Thegoalisnottodesignabuildinginalldetails,butratherto
8Inaccordancewiththetermsusedbefore,varianta)isamodernframeconstruction.Forreasonsofbetterreadability,thisvariantwillinthefollowingchapterssimplybereferredtoasframeconstruction.
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checkiftheconstructionisfeasibleandtoanalysetheoverallcharacteristics.Forthosepurposes,averydetaileddesignisnotnecessaryandcouldevendistractfromthemoreimportantaspects.
Sinceamulti‐storeybuildingisacomplexstructure,FEMwasusedforboththedesignandthegeneralanalysisofthestructure.Moreover,asmentionedbefore,sinceconnectionsaresuchanimportantpartofany timberconstruction,aselectedconnectionshallbeexaminedalsousingFEM.TheFEMcalculationswillbedescribedinchapter6.5.
6.2. DesignVariants6.2.1. StructuralConcept
Treet,themulti‐storeytimberbuildingthatistheobjectofthisanalysis,hasalreadybeenpre‐sented in the introduction (cf. chapter 1). Here, first the original building shall be describedquicklytocreatethebasisforthedraftdesignofthethreevariants.
Treet has 14 storey and an underground car park, its ground dimensions are a/b20,65/22,34m,thehighestpointlies47,48mabovetheground(withoutthecarpark).Thebuild‐ingisexclusivelyusedforresidentialpurposes.Eachstoreyconsistsoffourtofiveapartmentsthatareconnectedbyacorridor.Abigstaircaseandaliftinthemiddleofthebuildingconnectthestoreysvertically.Asecondarystaircase isaddedat thesideof thecorridor.Thearchitecturalplansofthebuildingcanbefoundintheattachment(cf.appendixA).
Treetconsistsofrectangularmoduleswhichareplacednexttoandontopofeachother.Thosemodulesareprefabricatedandarefullyequippedincludingakitchenandabathroom.Aframe‐workmadeofglulamontheoutsideandin‐betweenthemodulesisresponsiblefortheoverallstability.Thefifthandthetenthstoreyareaso‐calledpowerstoreys,featuringadditionalglulambracingstoachieveahighstiffnesssothatthosestoreyscanactasaplatformonwhichthenextmodulesareplaced.Prefabricatedconcreteslabsontopofthepowerstoreysprovideextraweighttocontrolthewind‐inducedvibrationsbyadaptingtheeigenfrequencyofthebuilding.ThestairsaremadefromCLT[14].
Tobeabletoconcentratemoreonthegeneralstructurethanproject‐specificdetails,somesim‐plificationsofthelayoutofthebuildingwereaccepted(cf.architecturalplans):
The15.storeyisconsideredtobeafullstorey,onlytheareaofthecorridor,theliftsandthestaircasesprotrudesonestoreyhigher.
Thebalconiesareneglected. Thedoorsandwindows,alsothoseintheoutsidewalls,areconsideredtobeofthesame
heightasonestorey,thepartsofthewallsaboveandbelowthoseopeningsareneglected.ThisisespeciallyimportantfortheanalysisofthewallsforthepanelandtheCLTcon‐struction(thelengthofeachwalliscalculatedasthedistancebetweentwoopenings).
Thestaircasesandtheliftareneglectedandconsideredasfloorareawiththecorrespond‐ingliveload.
Aconstantheightforallstoreysisassumed.Itiscalculatedastheaverageheightpersto‐reyoftheoriginalbuilding.
Theroomfortheliftandstairwaysisleftopenfromtheside,sothattheliftcaneasilybeaddedattheend,afterthemainstructureisfinished.
Withthosesimplifications,thestructuralconceptsofthethreevariantswereworkedout.Generalimportantcriteriaforagooddesign,thatshouldbeconsideredfromthefirststageon,are(innospecialorder):
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intendedusage structuralsafety architecturalvalue economicalaspects environmentalaspects firesafety thermalprotection noiseprotection possibilityofprefabrication suitabilityforextensions layingofserviceinstallations requiredmaintenance erectionmethods deconstruction
Concerningthechoiceofmaterials,thesamebasicmaterialswereusedfortheframeandpanelvariants(glulamforthemainstructuralcomponentsandplywoodforthestructuralsheathing)tomakeadirectcomparisonmorevalid.PlywoodisusedinsteadofOSBbecauseoftheratherhighVOCemissionsofOSB(cf.chapter5.1.4).Themassivetimberconstructionusesadifferentmate‐rial(CLT),sincethematerialisinthiscaseoneoftheaspectsthatshallbecompared.
6.2.2. FrameConstruction
Figure6.1:RFEMmodeloftheframeconstruction
AsdepictedinFigure6.1,theframe’sload‐bearingstructureconsistsofcolumnsthatgocontinu‐ously throughall storeys, two‐partbeams thatareattached to thecolumnsoneithersideand
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diagonalsintheoutsidewallsin‐betweenthecolumns.Thus,largeframesarecreatedonallfoursidesofthebuildingthatcarrytheglobalbendingmomentduetothewindloads.
Inanearlierstageofthedesign,itwasfirstplannedtohavethediagonalsontheoutsideoftheload‐bearingstructure.Thiswouldhavehadahigherarchitecturalvaluebecausethediagonalswouldhavebeenvisiblefromtheoutside.However,duringthedesign,itbecameobviousthattherequiredconnectionbetweentheouterdiagonalandthecolumnwasnotpossible,mostlybecauseofthehighforcescombinedwiththeeccentricityofthediagonal.Thefirstdesignwasthereforechangedtohavethediagonalsinthesamelayerasthecolumns,whichisadvantageousfortheloadtransfer.
Thecolumnsareplacedonasixbysixgridwithanaveragedistanceofabout4,3m.Thecontinu‐ouscolumnswiththecompoundbeamsonthesidesmakeanoptimalload‐bearingbehaviourpos‐sible,becausenoholesarenecessaryforthebeams,whichwouldweakenthecross‐section.An‐otheradvantageofarrangingthebeamsonthesidesisthatthestressesperpendiculartothegrainareminimised.Asexplainedbefore,thisisofgreatimportanceformulti‐storeytimberbuildings.
Thebeamsrunparalleltothefrontofthebuilding,wherethegridlineshavesimilardistances.Continuousbeamswithequalspansarestaticallymoreeconomicthansingle‐spanbeamsorcon‐tinuousbeamswithvaryingspans.
Thefloorjoistsareplacedonthebeamsandgoperpendiculartothefront.Becauseofthevaryingdistancesinthisdirection,thejoistsaredesignedassingle‐spanbeams,whichcanbeadaptedtothecorrespondingspans.Thisalsoimprovesthenoiseprotectionbecausethefloorscanbedi‐videdbetweenapartments.
Attachedtothetopofthefloorjoists,astructuralsheathingmadeofplywoodaccountsfortheshearstiffnessofthefloorsanddistributestheliveloadsandtheself‐weightoftheflooroverthejoists.Thefloorsactashorizontalbeamsthattransferthewindloadsintotheframesonthesides.
Oneimportantfactorforthedesignwastohaveassimpleconnectionsaspossible.Formulti‐sto‐reybuildingswithaverylargenumberofconnections,costlyconnectionscanleadtoeconomicproblems.
Theconnectionofthebeamstothecolumnsisrealisedbyusingsteelbolts.Theboltsareloadedindoubleshearwhichmakesthemmoreefficient.Theholesfortheboltscanbepre‐drilledinthefactory,allowingforaquickassemblyonsite.Theconnectionofthediagonalstothecolumnswasmorecomplexdueto theexpected large forces.Theconnection isrealisedusing internalsteelplatesinsidethewoodmembersandsteeldowels,seeFigure6.2.Thebigadvantageoftheinternalsteelplatesisthatmultipleplatescanbeused,creatingtwoshearplaneseach,whichincreasesthecapacityper fastener.Toavoidconflictswithotherconnections (especially in the corners,where two diagonals from perpendicular directionsmeet at the same column), some specialmeasureshadtobetaken.Ontheonehand,thecross‐sectionofthecolumnmustbelargeenoughfortheconnectionstobenexttoeachother.Ontheotherhand,completelyhiddensteeldowelsarerequired,sothatthebeamscancontinuealongthesideoftheconnection.Atthemiddlecol‐umns,thesteelplatessimplygothroughthecolumn,directlyconnectingthetwodiagonalswitheachother.
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Figure6.2:Sketchoftheconnectionbetweenthecolumnandthediagonal(nottoscale)
Onechallengewasthattheforcefromthediagonalactsonthecolumnunderanangletothegrain.Topreventthewoodfromsplitting,fully‐threadedscrewsaredrivenintothecolumnperpendic‐ulartothegrainasreinforcement.
6.2.3. PanelConstruction
Figure6.3:RFEMmodelofthesecondstoreyofthepanelconstruction
ThecentralconceptofthepanelconstructionisinspiredbytheoriginalstructureofTreetusingmodules.Eachstoreyconsistsof12modulesthatarepremanufactured,transportedtothecon‐structionsiteandthenconnected.Themodulesconsistofthewallsandthegroundfloor,cf.Figure6.3,andcanthusbefullyequippedincludingserviceinstallations,thebathroomandthekitchen.Theuppersideisclosedwhenthenextmodulesareplacedontop.
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Theindividualelementsofthepanelconstructionincludethestuds,theblockingin‐betweenthestuds,thestructuralsheathingnailedtotheoutsideandinsideofthewalls,thefloorbeams,thefloorjoists,andthestructuralsheathingofthefloors,cf.Figure6.4.Thestudscarrytheverticalloads,at theouterwalls, theyarealsosubjectedtobending fromthewindpressure.The floorjoistscarry the load fromthe floorsand transfer themvia the floorbeams into thestuds.Theblockingstabilisesthewallsinthedirectionperpendiculartothestuds.Themainfunctionofthesheathingistocarrytheshearstressesinthewalls.Thefloorsactasdiaphragms,transferringhorizontalloadsasshearforcesintothewalls.Allmembersaresinglespanbeamsduetothena‐tureoftheindividualmodules.
Figure6.4:Sketchoftheconnectionbetweenthefloorandthewallinthepanelconstruction
Incontrast tothe frameconstruction,where loadsareconcentrated inthemainmembers, theforcesaremoredistributedwithinthepanelwalls.Thismakesitpossibletoachievesmallerdi‐mensions.Ontheotherhand,however,italsomakestheloadtransferlessclearandthedesignmuchmorecomplex.
Toensureloadtransferbetweenthemodules,theconnectionsbetweenadjoiningmodulesplayacrucialrole.Toachieveaclearloadtransfer,itwasdistinguishedbetweenshearstressesandnor‐malstresses.
Theshearstressesaretransferredbythestructuralsheathing.Toachievetheloadtransfer,theedgesofthemodulesareleftwithoutsheathingwhenmanufacturedinthefactory,themissingsheathingisaddedonthesite,thuseffectivelyconnectingadjoiningmodules.
Thecompressionstressesaretransferredviadirectcontactbetweentheendgrainsofthestuds,thusstressesperpendicular to thegrainareavoided.Theblocking isarranged in‐between thestudsandthefloorbeamisattachedtotheinsideofthewall,sothatthecross‐sectionofthestudsisnotweakened.
Totransfertensileforcesbetweenmodulesaboveeachother,specialhold‐downdevicesarenec‐essary,e.g.boltsthatconnectthemodulewalls.Whileforsmallerstructureswithlowerloads,itispossibletoonlyusethenailsofthesheathingtotransferallforces,forhightensileforces,astheynaturallyoccurinmulti‐storeybuildings,thisisnotrecommended.Aclearseparationbe‐tweenthetransferofshearandtensionisimportant.
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Thefourlargerapartmentsineachstoreyconsistoftwomodules.Attheopensidesofthosemod‐ules,beamsandcolumnsareaddedtocarrytheloadsfromthefloors.Thecolumnsofthetwomodulesareconnectedaftertheyhavebeenbroughtinplacetoreachahigherbucklingresistance.
Ascanalreadybeguessedfromthosedescriptions,thepanelconstructionturnedouttobethecostliestvariantconcerningtheload‐bearingstructure.Manydifferentcomponentsandconnec‐tionswerenecessaryandmultiple iterationstepswereneededto findastructure that isbothcapableofbearingtheloadsandaseconomicaspossibleatthesametime.However,themajorpartofworkcanbedoneinthefactory,whichmakesthisstructureeconomicagainconcerningtheexecutionoftheconstruction.
6.2.4. CLTConstruction
Figure6.5:RFEMmodeloftheCLT‐construction
Inthisdesign,CLTwasusedinformofplatesforboththewallsandthefloorslabs,themodelisshowninFigure6.5.Again, toavoidstressesperpendiculartothegrain, insteadofplacingtheslabsin‐betweenthewallsofthetwostoreysaboveandbeneath,asisnormallydoneinthedesignofsmallerbuildings,theslabsareattachedtothewallslaterally.Agrooveiscutintothewallele‐mentsinwhichtheslabsareplaced,cf.Figure6.6.
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Figure6.6:SketchoftheconnectionbetweenwallandfloorintheCLT‐construction
Similartotheloadbearingbehaviourofthepanelconstruction,theCLTwallscarrytheverticalloadsandtheshear,whilethefloorsactasdiaphragmsthattransferthehorizontalloadsintothewalls.
OneadvantageoftheCLTconstructionisitssimplicity,itonlyconsistsofCLTelementsandonekindofconnection.Thisconnectionisrequiredtotransferthetensileloadsbetweenwallsaboveeachother.
6.3. PreliminaryDesignThegoalof thepreliminarydesign is to findastructure that fulfils therequirements fromtheintendedusage,isabletobeartheactingloads,ispossibletobuildandaseconomicaspossible.Sincethedesignofacomplexstructurelikeamulti‐storeybuildingtakesseveraliterationsteps,thepreliminarydesigncanbeunderstoodasthefirststepinthisiteration(althoughtheprelimi‐narydesignitselfalreadytakesmorethanonestep,too).Aftereverystep,thestructuralelementsareadapted,thecorrespondingloadschanged,andtheloadtransferrecalculated.
Thefirststepinanyiterationalwaysusessomeassumptionsandestimates,thesameistrueforthepreliminarydesign.Someexampleshavealreadybeengiven inchapter3.2concerningthematerialpropertiesandthe loads.Anothersimplification is the formulaethatareused,e.g. toquicklycalculatethecapacityofaconnection,sincetheECformulaecanbeverycomplex(theformulaethathavebeenusedforthedesigninthismasterthesisaredescribedintheprefaceofthepreliminarydesigndocumentation,seeappendixA).Themotivationistofindafeasiblestruc‐tureasefficientlyaspossible.
Duringthepreliminarydesignphase,themostengineeringcompetenceisrequired.Concerningthetopicofthismasterthesis,themostimportantfindingsweremadeduringthisphase.Thosefindingsshallbedescribedinthefollowing.
Thepreliminarydesignoftheframeconstructionwasrelativelystraightforward,moststructuralelementscouldbedesignedindependently.Oneexceptionweretheframesintheouterwallsthatcarrytheglobalbendingmomentduetothewind.Sincetheframesarestaticallyindeterminate,thecross‐sectionsdirectlyaffecttheloaddistribution.Therefore,theforcesmustbeestimatedasafirstsub‐step.Asimplifiedsystemwasusedtodeterminethosefirstestimates,cf.Figure6.7.Thewholeframewasdividedintotwohalfframes,whichwereconsideredtoactlikeBernoulli‐beams.Thisallowedforthesimplecalculationofthereactionforcesinthecolumns,whichfunctionedasthe tension and compression chords of the beams. Based on the forces in the columns,
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approximate forces in thediagonalscouldbedetermined.Withthoseestimated forces, there‐quiredcross‐sectionswerecalculated,whichcouldthenbeusedtomodeltheframewiththecor‐rectstiffnesses.
Figure6.7:Simplifiedsystemoftheframes
Abigpartofthepreliminarydesignoftheframeconstructionweretheconnections.Thebeamsareconnectedtothecolumnswithbolts.Theconnectionbetweenthediagonalandthecolumnsfeaturesinternalsteelplatesanddowels.Tocarrythewindsuctionloadsthatactonthefaçade,fullythreadedscrewswereused.Thesheathing,thejoistsandthebeamswereconnectedtoeachothervianails.However,althoughtherearemanydifferentconnections,allofthemcouldbede‐signedrelativelyeasilyusingthesimplifiedpreliminarydesignformulae.
ForboththepanelconstructionandtheCLT‐construction,thestabilisationofthebuildingwasanimportantandnottrivialpartofthepreliminarydesign.Thefunctionoftheframesintheframeconstructionisheretakenoverbyaninteractionofthewalls.Inthestabilityanalysis,theshareofeverywallintheglobalhorizontalshearloadandtheglobalbendingmomentiscalculated.Bothhavetheirmaximumintheloweststorey.
Inthecontextofthepreliminarydesign,someassumptionsweremadeforthestabilityanalysis:
Thebuildingisidealisedasaverticalcantileverbeam. Thefloordiaphragmsareperfectlyrigid. Thestiffnessofeachwallisproportionaltoitslength,i.e.allwallshavethesameheight,
thicknessandshearmodulus.
Basedonthoseassumptions,theshearforceisdistributedoverallwallsaccordingtotheirbend‐ingstiffnesses,cf.formula(4.1).Iftheshearforceactsatadistancetotheshearcentre(whichitdoesforwindfromtheside),anadditionaltorsionalmomentmustbeconsideredaccordingtoformula(4.2).
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V V ⋅EI∑ EI
(4.1)
V M ⋅EI ⋅ e∑ EI ⋅ e
(4.2)
where V =shearforceofthecurrentwallk
V =globalactingshearforce
EI =stiffnessofawall
M = torsionalmoment due to eccentricity of the global actingshearforce
e =distanceofawalltotheshearcentre
Tocarrytheglobalbendingmoment,eachwallcarriesashareofthisbendingmomentdependingonitsbendingstiffness(cf.formula(4.3))andanormalforcedependingonitsextensionalstiff‐nessanddistancetothecentreofgravity(cf.formula(4.4)).
M M ⋅EIEI
(4.3)
N M ⋅EA ⋅ eEI
(4.4)
where M =bendingmomentofthecurrentwallk
M =globalactingbendingmoment
EI = total stiffness of all walls according to Steiner’s theoremwithrespecttothecentreofgravity
N =normalforceofthecurrentwallk
EA =extensionalstiffnessofawall
e =distanceofawalltothecentreofgravity
Finally,theverticalloadsduetotheself‐weightofthestructureandthelifeloadcouldbeaddedtoobtainthetotalloadsforwhichtodesignthewalls.
Concerningthepanelconstruction,duringthedesignofthewalls,somechallengeshadtobeover‐come.Ascouldbeexpected,theloadsinthewallswereveryhigh,buttheyalsovariedsignificantlybetweentheindividualwalls,whichwasduetotheirdifferentpositionsandlengths.Thosevari‐ationsmadeanefficientandeconomicdesigndifficult.Dimensioningallstudsaccordingtothehighestoccurringloadswouldhavebeenhighlyuneconomic,whileadaptingeverysinglestudtoitsindividualloadisnotpractical.Finally,asolutionin‐betweenthosetwoextremeswaschosen.Onlyaselectednumberofstudswasconsideredtobeloadbearingineverywallandthusgivenarespectivelargercross‐section(upto28/28cm),whilethenon‐loadbearingstudscouldhaveamuchsmallercross‐section(e.g.8/28cm).Thenumberandarrangementof loadbearingstudscouldbeadaptedaccordingtotheloaddistributionineachindividualwall.
Thismethodprovedtobemosteffective,becauseithelpedtoconvertthevastlydifferentloadsonthewallstomoreequalloadsonthestuds.Shortwallswithrelativelylowloadscoulde.g.only
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havetwoloadbearingstuds,oneateachend,whileinthewallswithveryhighloads,almosteverystudwasloadbearing(thespacingofthestudsis61cm).
Becausethisstillledtoconsiderableloaddifferencesbetweenthestuds,themethodwastakenonestepfurther,introducingtwodifferentwallthicknesses.Inthefirstfloor,theouterwallsrun‐ningparalleltothebearingdirectionofthefloorshaveathicknessof20cm(withthecross‐sectionoftheloadbearingstudsbeing20/20cmandtheoneofthenon‐loadbearingstuds8/20cm)whileallotherwallshaveathicknessof28cm(heretheloadbearingstudsare28/28cmandthenon‐loadbearingstuds8/28cm).
Anotherchallenge for thepaneldesignwas theanchorage.Theproblemwere thecomparablysmallcross‐sectionsofthestuds,whichdidnotallowmuchspacefortheconnections.Finally,thisproblemwassolvedbyusinginternalsteelplatesinthestudsinquestionwhich,togetherwithsteelbolts,formatensionresistantconnectionbetweenthestuds.Thesteelplatescanbepre‐attachedtothelowerstuds,includingthebolts.Whenthenextmoduleisplacedontop,there‐mainingboltsareadded.Theboltsarelocatedabovethefloor,sothatthisworkcanbedonein‐dependentlyfromtheassemblyoftheadditionalsheathing,whichislocatedunderneaththefloor.
TheanchoragewasalsoachallengefortheCLTdesign.Forthisconstruction,longsteelplatesareused,thatareplacedingrooveswhicharecutintothelongtopedgesofthewallelements.Equallyspaceddowelsensureacontinuousloadtransferalongthewholelengthofthewalls.Usingglueinsteadofdowelswouldalsohavebeenpossible(cf.chapter5.4),butEC5doesnotyetincluderulesforthedesignofthiskindofconnection.
Theshearinthewallsduetowindloadswasnotdecisiveincomparisontothenormalforces.
6.4. EurocodeDesignInthischapter,firstsomegeneralfindingsfromtheECdesignshallbepresented,afterthat,againtheexperienceswiththethreedifferentconstructionvariantsaredescribed.
Ifthepreliminarydesignwasthefirstiterationstep,onetotwomorestepswererequiredintheECdesign.
ThesecondstepincludedadetailedloadcalculationandthebuildingoftheFEMmodelsaccordingtothedimensionsthathadbeenfoundinthepreliminarydesign.Withthehelpofthosemodels,moreaccurateinternalforcescouldbecalculated.ThenecessaryECcheckswereperformedforallrelevantstructuralcomponents.Theevaluationoftheresultsshowedthatsomecomponentsdidnotfulfiltherequirements,whileothercomponentswereonlyusedtoasmallpartoftheircapacity.
Theadaptionofthosecomponentswasthethirditerationstep.Thecross‐sectionsandconnec‐tionswerechangedsothatallchecksweresatisfied.Butbecausethe internal forcesagainareinfluencedbythesechanges, themodelshadtobechanged, the loadsrecalculated,andtheECchecksrepeated.Thistime,allcomponentsstillfulfilledtherequirementsandthedesigncouldbefinished.
Duringtheevaluationof theresultsof thechecks, itcouldbeconfirmedthattheserviceabilitylimitstate,i.e.thedeformations,becamedecisiveinsomecases.Concerningtheserviceability,itisimportanttoclearlydefinethecriterionfortheECverification.Forthefloorsinallthreecon‐structionvariants,thedeformationsaremainlyconnectedtothecomfortoftheresidents.Thereisalsoariskofdamageofothercomponentslikenon‐loadbearingwallsinsidetheapartments.IncompliancewiththeNorwegiannationalannextoEC5,thelimitvaluesforthedeformationswere
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definedasl/300fortheinstantaneousdeformationandl/150forthefinaldeformation(includingcreepandothertime‐dependenteffects),cf.[3,NA.7.2].
Asindicatedbefore,onlythemostrelevantelementsfromeachconstructionwerecheckedintheECdesign,somedetailsareonlyconsideredinthepreliminarydesign.Anexampleistheconnec‐tionofthesheathingofthefloorstothejoistsintheframeconstruction.Becauseofthelowloads,thisconnectionisclearlynotdecisiveandhasthereforealsonoinfluenceontheremainingstruc‐ture.
Thedesignoftheframeconstructioncouldbeperformedwithoutthehelpoffiniteelementpro‐grams,merelythesimpletwo‐dimensionalframeworkanalysisprogramStab2dwasusedtosolvestaticallyindeterminedsub‐systemsliketheframesonthesides.Asidefromthat,thechecksdur‐ingthesecond iterationsteprevealedthat thepreliminarydesignhadalreadyproducedquiteaccurateresults.Bothfactsdemonstratewelltheclearload‐transferviamainlyone‐dimensionalmembers,whichmakesiteasiertointerpretthestructureandallowsforaflexibledesign.Onlyforsomecomponents(e.g.thecolumns),thedimensionscouldbedecreasedinordertoachieveahigherdegreeofefficiency.
Inthepanelconstruction,theconnectionofthefloorjoiststothefloorbeamhadtobechanged.Thefullythreadedscrews,whichwerechoseninthepreliminarydesign,werenotabletotransfertheloadsbecauseofthelargerequireddistancetotheendgrain.Instead,joisthangerswereusedthatcouldtransfertheloadswithoutproblems.Adisadvantageofthissolutionistheprice,be‐causeitcanbeexpectedthatsuchmanufacturer‐specificproductsaremoreexpensivethanstand‐ardwoodscrews.Moreover,thedimensionsofsomecomponentsthatallhadthesamedimen‐sionsbefore,werechangedtodifferentdimensionstomakethedesignmoreeconomic.E.g.thejoistswiththesmallestspanwereadaptedtohaveasmallercross‐sectionthantheotherjoists.Thesolutionwiththedifferentiationbetweenloadbearingandnon‐loadbearingstudswasveryeffectivealsowiththemoreaccuratecalculations,sothatthecross‐sectionsofthestudsdidnothavetobechanged.
FortheCLTconstruction,becauseofthemorecomplicatedloaddistribution,anFEManalysiswasinevitable.Thisanalysisshowed,however,thattheestimationoftheforcesactingonthewallsinthepreliminarydesignhadbeenfaulty(thedetailswillbediscussedinchapter6.5.1).Therefore,thedimensionsofthewallshadtobeincreased.ThiscanbeseenasanindicationforthemorecomplexbehaviourofmassivetimberconstructionsandespeciallytheCLTmaterial.
6.5. FEMAnalysis6.5.1. GlobalFEMAnalysis
FEManalyseshavealreadybeenmentionedseveraltimes,mostmodernstructurescannotbede‐signedanymorewithoutthehelpofFEM.Italsowasanimportantpartofthedesignperformedinthecontextofthismasterthesis.Therefore,oneentirechapterisdedicatedtothistopictobeabletolookatsomeimportantaspectsoftheFEManalysisinmoredetail.
Besideshelpingtoverifytheloadbearingcapabilityoftheoverallstructures,thecreationofthedifferentmodelsalsoalreadygaveanideaofhowcomplexandcostlyconcerningtherealerectionthestructuresare.
Beforesolvingthemodels,aconvergenceanalysiswasconductedforeachmodeltofindasuitablesizeforthefiniteelements.Thisisofcentralimportancesinceanelementsizethatistoolargecanleadtoconsiderabledeviationsofthesolution,whiletoosmallelementsleadtoahighcomputa‐tiontime.InFigure6.8toFigure6.10,theresultsoftheconvergenceanalysisofallthreestructures
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arevisualised.Theselectedelementsizeforthesubsequentmainanalysisismarkedineachdia‐gram.Fortheconvergenceanalysis,asforallsubsequentcalculations,alinearfirstordertheorywasused.
Figure6.8:Convergenceanalysisoftheframeconstruction
Figure6.9:Convergenceanalysisofthepanelconstruction
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Figure6.10:ConvergenceanalysisoftheCLTconstruction
FortheCLTconstruction,thenumberoffiniteelementshadasignificanteffect,whereasfortheframeconstruction,theinfluenceofthenumberofelementsontheresultwasneglectable.Apos‐sibleexplanationforthisisthattheframeconstruction’smainload‐bearingstructureconsistsofone‐dimensionalmembers,theinfluenceofthesheathingofthefloorsisonlysecondary.Thecal‐culationoftheinternalforcesforthisframeworkiscomparablesimpleanddoesnotdependonthenumberoffiniteelements.Indeed,thisstructurecouldalsobesolvedasathree‐dimensionalframeworkwithouttheneedforFEM.TheCLTconstructionontheotherhandconsistssolelyoftwo‐dimensionalsurfaceelements,whichcanonlybesolvedusingFEM.
Asmentionedbefore,theFEMmodelwasnotstrictlynecessaryforthedesignoftheframecon‐struction, theECcheckscouldalsobeperformedusingsimplersub‐models.But the3Dmodelallowstotakeacloserlookattheglobalbehaviourandgivesanimpressionoftheoverallstruc‐ture.AcomparisonoftheresultsfromthedesignwiththosefromtheFEM‐modelshowedthatthedesigngenerallywasonthesafeside.
WhiletheframeandtheCLTconstructionscouldbemodelledinonepiece,thepanelconstructionconsistedoftoomanystructuralelementssothatthewholemodelcouldnotbesolvedinaprac‐ticalmanner.Somesmallerchangesweremadetoavoidnodesthatlieclosetoeachother,result‐inginanunnecessaryfinemeshatthosepoints.Still,thenumberoffiniteelementsexceededthenumberthatcouldbesolvedinareasonabletime.Tobeabletosolvethemodel,ithadtobedi‐videdintosmallersub‐models.Thebestsizeforthesub‐modelswasthatofonestorey,thecon‐sistentnumberingofthemodelnodesallowedforastraight‐forwardloadtransferbetweentheindividualsub‐models.Theconvergenceanalysiscouldbeconductedforthehigheststorey(cf.Figure6.9).
Sincethemodulesconsistofthewallsandthefloor(cf.chapter6.2.3),thesamecompositionwastakenfortheindividualsub‐models.Especiallyforthehorizontalwindloads,however,theupperfloorwasneededfortheloadtransfer.Becauseofthat,theupperfloorwasaddedtoeachsub‐model(withoutaddingthecorrespondingloadsagain).TheconceptforsubdivisionofthepanelmodelisillustratedinFigure6.11.
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Figure6.11:Conceptfordividingthepanelmodelintosub‐models
Someadditionalconsiderationwasnecessarytodeterminethecorrectconditionsatthetransi‐tionsofthesub‐models.Thebuildingasawholewasidealisedasacantileverbeam.Performingcutsthroughthisbeam,equivalenttodividingthemodelintosub‐models,willreleasebothmo‐ments,shearforcesandnormalforces.Sincethestudsareconsideredtobeconnectedtoeachotherbetweenstoreysviahinges(i.e.withouttransferringbendingmoments),eachsub‐modelissupportedatitslowerend,i.e.thelowercut,withhingedsupports.Thesupportreactions(whichareequaltotheinternalforcesinthestuds)couldthenbetransferredtothesub‐modelofthenextstoreyassingleloads.Becausetheupperfloorhadbeenaddedtothesub‐models,theuppercutwent throughthestudsthemselves(insteadof throughtheconnectionbetweenthestuds).Toassurecorrectboundaryconditions,supportswereneededattheupperendsoftheelementsofeachsub‐modelthatpreventrotationperpendiculartotheirverticalaxis,butallowingfor freedisplacementinalldirections.Asanexample,Figure6.12showsthemodelofthefirststoreywiththe loads forLC1(self‐weight) includingthesingle forces thatare transferred fromthestoreyabove.
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Figure6.12:Sub‐modelinRFEMofthefirststoreyofthepanelconstructionwiththeloadsforLC1(self‐weight)
Withthismethod,itwasfinallypossibletocalculatereliableresults.
FortheCLTconstruction,itwaspossibleinRFEMtodefinethecompositionoftheCLTelementsusingtheadd‐onRF‐LAMINATEandthedatafromthetechnicalapprovaloftheselectedmanu‐facturer(see[11]).Theadd‐onallowedforadetaileddefinitionofthecompositionoftheCLT‐elements,itcoulde.g.alsobespecifiedthattheindividualplanksarenotgluedtogetheralongthenarrowedges.
ToavoidFEM‐relatedsingularitiesduetosurfacesthatintersecteachother,themodelhadtobeadaptedtoleavesmallgapsbetweenthewallsinordertoassurethattheoverallloadbearingbe‐haviourcorrelatedwiththerealbehaviouraswellaspossible.
ConcerningtheresultsoftheCLTmodel,ithasalreadybeenmentionedthatthoseresultsdifferedsignificantlyfromtheresultsofthepreliminarydesign.Someoftheassumptionsforthestabilityanalysishadnotbeencorrect.Firstly,thebuildingdoesnotbehavelikeabeambasedontheBer‐noulli‐theory.Sheardeformationhasalargeinfluence,whichisprobablyalsobeaneffectoftheCLT‐material.ThiscanbeseenfromthedeformationinFigure6.13,whichisnotcurvedasonewouldexpectforthewindloads(foraBernoulli‐beam,constantdistributedloadsleadtoadefor‐mationintheshapeofathirdorderpolynomialfunction).Thefloordiaphragmsarealsonotrigid,especiallybecauseeachdiaphragmconsistsofseveralCLT‐slabswhichhavehingedsupports.
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Figure6.13:Deformationuin[mm]oftheCLT‐constructionforLC3(windfromthefront),viewfromtheside
WhenevaluatingtheresultsoftheFEManalysis,precautionshadtobetakenbecauseofunrealis‐ticstressconcentrations,whichoccurredespeciallyatthefoundationwherethesupportsatthebottomlinesofthesurfacescreatedrigidboundaryconditions.Theresultshadtobecorrectedtoexcludesuchstressconcentrations.
Ingeneral,theminimuminternalforceperwallwasselectedforthedesign(i.e.thehighestcom‐pression force).Todetect stressconcentrations, thedifferencebetween theminimumand themaximuminternalforce,themiddlein‐betweenthetwo,themedianandthestandarddeviationwerecalculatedforeachwall.Ahighstandarddeviationmeansthattheindividualvaluesononewalldeviatefromeachother,thisismainlythecaseatwallsthatcarryapartofthebendingmo‐mentfromthewindloads.Themiddlebetweenthetwoextremevaluesis,togetherwiththeme‐dian,bestsuitedtodetectthestressconcentrations.Iftherearestressconcentrationsinawall,onlyafewvalueswilldifferfromtherest,sothatthemedianisonlyslightlyaffected,whilethemiddle valuewill changeproportionally. Assuming negative values for compression, amiddlevaluethatismuchhigherthanthemedianwillmeanthattherearetensilestressconcentrations.
Asanexample,wallx3hadforLC1(self‐weight)amedianverticalinternalforceof 87,8kN/m,withtheextremevaluesbeing32,9and 121,1kN/m,whichmeansthemiddlevaluewas 44,1kN/m9.Thelargedifferencebetweenmedianandmiddlevaluesuggeststhattherearetensilestressconcentrations.AlookatthediagraminFigure6.14provesthishypothesis,thereasonforthestressconcentrationsisprobablythesupportwhichdoesnotallowanydeformationsalongthebottomline.Inthiscase,theminimumvalue( 121,1kN/m)wasselectedforthedesign.
9Theevaluationof the internal forceswasconductedatspecificgridpointsonthesurface,whichwereevenlydistributed.Sincethepositionsofthosepointswerestatic,theresultsdonotnecessarilycoverthewholerangeofinternalforcesandslightdeviationscanoccurincomparisontothediagrams.Thisisbene‐ficial,becauseitalreadyhelpstobalancestressconcentrations.
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Figure6.14:Distributionoftheinternalnormalforcesin[kN/m]inwallx3forLC1(self‐weight)
Adifferentexample iswallx21forLC3(windfromthefront).Here, thetheminimumandthemaximumvalueare 98,1and 33,7kN/mrespectively,themedianwas 41,7kN/mandandthemiddlevalue 65,9kN/m,whichshowedthepossibilityofcompressionstressconcentrations.ThiscanagainbeprovedbylookingatFigure6.15.Consequently,forthiswallthevalueofthedesign force had to be reduced to exclude the unrealistic concentrations. A factor of 0,5waschosentointerpolatebetweentheextremevalues, leadingtothefinaldesignvalueof 33,70,5 ⋅ 98,1 33,7 65,9kN/m.
Figure6.15:Distributionoftheinternalnormalforcesin[kN/m]inwallx21forLC3(windfromthefront)
Thisprocedurewasusedforallwalls,adaptingthecorrectionfactoraccordingtohowstrongtheconcentrationswere(measuredbymeansofcomparingthemedianandmiddlevalue).
ThemainresultsoftheglobalFEManalysiswillbepresentedinchapter7.1.
6.5.2. FEMConnectionAnalysisInadditiontotheanalysisoftheoverallstructure,oneselectedconnectionwasexaminedtoim‐prove theunderstandingof the loaddistribution inconnectiondetails. Ithasalreadybeenex‐
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plainedthatconnectionsplayanimportantroleintimberstructures,andthattherulesintheEC5areonlybasedonsingle‐fastenerconnections,usinganeffectivenumberoffastenerstoaccountforgroupeffects.Inlargemulti‐storeytimberbuildings,though,connectionsgenerallyconsistofmultiplefastenersbecauseofthecomparablyhighloads.Inordertoaddressthisaspect,thecon‐nectionbetweenthediagonalandthecolumnintheframeconstructionwasselectedtobeana‐lysedusingFEM. Itconsistsof the twowoodenmembersaswellas three internalsteelplatestogetherwithtensteeldowelsinboththecolumnandthediagonal(cf.chapter6.2.2).TheFEM‐softwareANSYSwasusedforthispurpose.
ThegeometryofthemodelisshowninFigure6.16,incomparisontotheoriginalconnection,thegeometrywassimplifiedtomakeamoreefficientFE‐solutionpossible,makinguseofthesym‐metryoftheconnection.Togetaclearviewofthedistributionoftheinternalstresses,oneofthemiddlelayersofthewoodcomponentsbetweentwosteelplateswasmodelled.
Figure6.16:GeometryoftheANSYSmodeloftheconnectionbetweendiagonalandcolumnintheframeconstruction
Thewood and steel partsweremodelled using the solid 8‐node brick element SOLID185. Tomodelthedowels,springelementsoftypeCOMBIN14wereapplied.
Sincewoodisanorthotropicmaterial,thecorrespondingorthotropicmaterialmodelhadtobeused.ThevaluesfortheelasticitymoduliweretakenfromEN14080forglulamGL24h.Thepois‐son’sratiosfordifferentwoodspeciescanbefoundintheliterature.Forthisapplication,theprop‐ertiesoftheDouglasfirwereused,whichisalsocultivatedinEurope.Thelongitudinaldirection
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ofthegrainwasassumedtocoincidewiththex‐axis,theradialdirectionwiththey‐axisandthetransversaldirectionwiththez‐axis.AllmaterialpropertiesaresummarisedinTable6.1.
Table6.1:MaterialpropertiesfortheANSYSmodel[12,table5][16,5‐3]
woodE 11500 N/mmE 300 N/mm
E 300 N/mmG ,G ,G 650 N/mm
ν 0,292
ν 0,449 ν 0,390
ρ 420 kg/msteelE 210000 N/mmν 0,3
Toobtainthecorrectstiffnessforthesprings,theslipmodulusofthedowelswascalculatedac‐cordingtoEC5[2,7.1],seeequation(6.1).
Kρ , ⋅ d
23⋅ 2 (6.1)
where ρ =meandensityofthewoodin[kg/m ]
d =diameterofthedowelin[mm]
Thefactor2inequation(6.1)isduetothesteelplatesthatareusedintheconnection.ForM20dowels(cf.preliminarydesign,seeappendixA)theslipmodulusperfastenerandpershearplaneresultsin:
K420 , ⋅ 20
23⋅ 2 14969N/mm
SinceonespringintheANSYSmodelrepresentstheactionofonedowelinoneshearplane,thisvaluecouldbeuseddirectlyasthespringstiffnessofthoseelements.
The tensile load in the diagonal was determined in the preliminary design and amounts to530,9kN.Distributedoverthecross‐sectionofthediagonalofb/h 40/40cm,theresultantten‐silestressis:
p530900400
3,318N/mm
Becausethewoodmembersforthemodelwerecutoutofthewholestructure,boundarycondi‐tionshadtobeappliedatthecuts.Forthecolumn,whichtransfersbothnormalandshearforcesaswellasbendingmoments,arigidsupportwasmodelled.Thediagonal,ontheotherhand,trans‐fersmostlynormalforces,shearforcesandbendingmomentcanbeneglected,thereforeonlythenormalpressurepisappliedtorepresenttheactionoftheinternalnormalforce.Additionally,tosupportthemodelagainstlateralmovement,supportsinthelateraldirections, i.e. inglobalz‐directionandperpendiculartothediagonal,hadtobeapplied.Thiswasnecessarybecausethe
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springelementsonlytransferforcesinthedirectionoftheirlocalx‐axis,whichmeansthatmove‐mentsperpendiculartothisaxisarenotconstraint.Withoutadditionalsupport,thiscausesthecalculationofthemodeltofailbecauseofrigidbodymovements.
Basedonthoseconsiderations,themodelcouldfinallybesolved.Butitisimportanttokeepthementionedassumptionsinmind,becausethemodeldoesnotrepresenttheconnectionaccuratelyenoughtoe.g.replacetheECcheckbythisFEanalysis.Theintentionisrathertogainabetterunderstandingofthedistributionoftheinternalstressesofarealisticconnectiondetail.
Theresultswillbepresentedinthenextchapter.
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7. Results7.1. ResultsfromtheDesignAnalysis
Theresultofthedesignshowedthatitistechnicallypossibletouseallthreeanalysedstructuralmethodsfortheconstructionofmulti‐storeybuildings.Thedesigndocumentationsandthetech‐nicalplansthatshowthefinaloutcomeofthedesignareattachedtothismasterthesis,cf.appen‐dixA. There are, however, important differences between the three variants concerning bothstructural,othertechnical,architecturalandenvironmentalaspects.Adetaileddiscussionofthoseresultswillfollowinchapter8.Inthischapter,theresultsfromtheFEManalyseswillbepresentedinrelationtothedesign.
TheglobalFEManalysishelpedtoverifytheoverallstabilityandloadbearingbehaviourofthethreestructures.Asanexample,theinternalnormalforcesinthefrontframeoftheframecon‐structionareshowninFigure7.1.Thisresultprovestheclearloaddistributionofthisconstruc‐tionwhichmakesitaveryefficientmethod.Theoverallstabilityisachievedrelativelyeasilywhichallowsforaflexibleinteriordesign.
Figure7.1:InternalnormalforcesinthefrontframeoftheframeconstructionforLC4(windfromtheside)in[kN]
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ThedistributionoftheinternalforcesforthepanelconstructionisdepictedinFigure7.2forthefirststorey.Althoughitisnotpossibletoreadindividualvalues,thefigurestillgivesagoodim‐pressionoftheloaddistribution.
Figure7.2:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC4(windfromtheside)
Thefigureshowsthatforpurewindloads(withoutself‐weightorliveload),thenormalforcesaremostlyconcentratedintheendstudsofeachwall.Incontrasttothat,forthepreliminarydesign,thewindloadsweredistributedoverthestudswiththewallmodelledasabeamsupportedtheloadbearingstuds,cf.Figure7.3,whichresultedinmoreevenlydistributedloads,orratherhigherloadsinthemiddlestuds.Whilethismethodismorevalidfortheconstantverticalloadsfromtheself‐weightandtheliveload,itisapparentlynotacorrectassumptionforthewindloads.
Figure7.3:Exampleoftheassumptionoftheloaddistributionintheloadbearingstudsinawallinthepanelconstructionforwindfromtherightsideaccordingtothepreliminarydesign
Thedesignofthepanelconstructionwasnonethelesssuccessfulbecausethestudsthatwerecon‐siderednon‐loadbearingprovideadditionalloadcarryingcapacity.Thismakesthedesignmoreredundant.Nevertheless,theeffectoftheconcentratedwindloadsshouldbeconsideredforthedesignofpanelconstructionsinmulti‐storeybuildingswithhighwindloads.
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TogiveanexampleoftheloaddistributionintheCLTconstruction,Figure7.4depictsthenormalforcesinthewallsofthefirststoreyforwindfromtheside.
Figure7.4:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC4(windfromtheside)in[kN/m]
Itcanbeseenclearlythatallthewallsparalleltothedirectionofthewindcarryapartoftheglobalbendingmoment.Theloaddistributionineachwall is linearaccordingtotheequationforthenormalstressesσ M/I ⋅ z,whereσisthenormalstresses(or,inthiscase,thedistributednormalforces),Mistheactingmoment,Ithesecondmomentofinertiaandzthecoordinatethroughthecross‐section(inthiscasealongthewall).However,unliketheassumptionsthathadbeenmadeinthepreliminarydesign,thewallsperpendiculartothewinddirectioncarrypracticallynoloads.Theloadsintheparallelwallsareaccordinglyhigher.ThisisprobablyanotherreasonwhytheECdesignhadtobereworkedratherextensivelyfortheCLTconstructioninrelationtotheprelimi‐narydesign.
FurtherresultsforallthreeconstructionvariantscanbefoundinappendixB.TheelectronicfilesoftheRFEM‐analysisarealsoattached,seeappendixA.
Anotherpartofthedesignanalysiswastheexaminationoftheconnectiondetailasdescribedinchapter6.5.2.Togetafirstimpressionofthestressdistribution,theequivalentvonMisesstressisshowninFigure7.510.
10ThedeformationinallfigureswithANSYSresultsisscaledbyafactorof100.Thesteelplatesarenotshown.
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Figure7.5:VonMisesstressσVMoftheconnectionin[N/mm2]
Itcanbeseenthatthestressintheupperpartofthediagonalismainlyinfluencedbythetensileload,thevonMisesstressthereamountsapproximatelyto3,318N/mm .Goingdownthediago‐nal,thestressesgraduallydecreaseastheloadsaretransferredviathedowelstothesteelplatesandthenintothecolumn.However,stressconcentrationsoccurintheupperrangeoftheconnec‐tion,themaximumstressthereisaround1,5timeshigherthanthetensileload.Thisismostprob‐ablyduetothefactthatthedowelsaredistributedlaterallyalongverticallinesinsteadofperpen‐diculartothegrainofthediagonal.Thatleadstothefirstdowelintheupperrightcorneroftheconnectiontakingovermostoftheloads,whilethedowelsinthelowerregionscarrymuchlessloads.Thestressesinthewooddevelopaccordingly.
ThedistributionoftheshearstressesdepictedinFigure7.6yieldsthesamegeneralresult.Theshearstressesarealsoconcentratedaroundtheupperdowels.
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Figure7.6:Shearstressτxyoftheconnectionin[N/mm2]
Inadditiontothat,however,shearstressesalsodevelopinthediagonalinsomedistancefromtheconnection,wherethelocaleffectsofthedowelshavenoinfluenceanymore.This isprobablyagainduetothearrangementofthedowels,sincethediagonal,asapartoftheframeintheframeconstruction,isapuretensionmember.Onepossibleexplanationistheasymmetricalloadtrans‐ferfromthewoodintothedowels.Becausehigherloadsaretransferredintheupperregionoftheconnectioncomparedtothelowerregion,theinternalforcesareunbalanced.Tosatisfytheequi‐libriumofforces,additionalshearforcesarerequired.
Shearstressesalongthegrainarepotentiallydangerousbecausetheycanleadtocracks.IntheEC,thecheckagainstcracks,i.e.thecheckfortensionperpendiculartothegrain,isbasedontheshearforceinthememberinquestion.Thecapacityagainsttensionperpendiculartothegrainiscalculatedusingformula(6.2)withthegeometricdimensionsaccordingtoFigure7.7.
F , 14 ⋅ b ⋅ w ⋅h
1 h /h (6.2)
where w =modificationfactor,w 1forallconnectionsexceptfornailplates
b,h ,h =geometricdimension,seeFigure7.7
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Figure7.7:Definitionoftheforcesandgeometricdimensionsforthecheckagainsttensionperpen‐diculartothegrainaccordingtoEC5[2,8.1.4]
Sincethischeckisonlynecessaryforaforcethatactsatanangletothegrain,itisonlyrequiredforthecolumnandnotthediagonal(seeEurocodedesignfortheexecutionofthischeck,cf.ap‐pendixA).TheFEresultsontheotherhandsuggestthattheshearforcesarelargerinthediagonal,duetotheasymmetricarrangementofthedowels.Thisaspectis,however,notconsideredintheEC.
Lastly,Figure7.8showsthetotalstraininsidethewoodmembers.Theresultsreinforcethesug‐gestionsthathavebeenmadesofar.SincethestrainandthestressaredirectlylinkedviaHooke’slawσ E ⋅ ε,withthestressesσ,thestrainsεandtheYoung’smodulusE,theplaceswiththehigheststressesalsoshowthehigheststrains.Thesheardeformationinthediagonalcanalsobeseenrelativelyclearlywhenlookingatthedeformedshapeofthemodel.
Figure7.8:Totalstrainεoftheconnectionin[‐]
FurtherfigurescanbefoundinappendixC,whichshowthesameoverallresults.TheelectronicfiecontainingtheANSYSmodelisalsoattached,seeappendixA.
Tosumup,themostimportantinsightfromtheANSYSanalysisisthatthearrangementofthefasteners in amulti‐fastener connection has a significant influence on the distribution of thestressesandthustheloadbearingbehaviourandpotentiallyalsothecapacityoftheconnection.It
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appearstobedisadvantageoustoarrangethefastenerswithanoffsetparalleltothegrain.Asaresultofthat,theloadtransferisunbalancedandadditionalshearstressesdevelop.Theshearstressesraisetheriskforsplitting,thestressconcentrationsaroundthefrontdowelscanalsoleadtocracks.Butitisimportanttorememberthatthisanalysiswascarriedoutwithoutconsideringthesplittingitselforrelatedeffects.
TheEurocodedoesconsiderthedistancesbetweenthefastenerstodetermineaneffectivenum‐beroffasteners,buttheoffsetalongthegrainisnotincluded.AccordingtoEC,theeffectivenum‐beroffastenersforthecolumnn 6,74islowerthanforthediagonalwithn 7,93(seeEu‐rocodedesign,cf.appendixA),whiletheaboveresultssuggestalessbeneficialstressdistributionforthediagonal. InadditiontothechecksfromtheEC,thedescribedeffectsshouldbekept inmindforthedesignofmulti‐storeytimberbuildingsandthelayoutofsuchconnectionsadjustedaccordingly.
7.2. ComparisonToelaboratethecentralresultsfromallpreviouschapters,ashortcomparisonofthethreevari‐antsshallbemadeinthischapter.Asatoolforthecomparison,anevaluationmatrixshallbeused,aswasdescribedinthecontextoftheLCAinchapter5.1.3.Forthiscomparisonhowever,amoregeneralevaluationmatrixisestablished,consideringalltheabovementionedaspects.TheresultispresentedinTable7.1.
First,allcriteriawereweightedtoaccountfortheirimportance.Inthenextstep,allthreevariantswereassignedvaluesbetween1and5foreachcriterion,were1istheworstratingand5thebestrating,thatmeansthate.g.alowdifficultyoftheconstructionwouldberatedwithahighvalue.Thescalefrom1to5isfineenoughtoclearlybringoutthedifferencesbetweenthethreecon‐structions,butnottoofine,forwhichthereisnosufficientbasis.Theresultswerecalculatedbymultiplyingthevaluewiththeweightingofthecorrespondingcriterion.
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Table7.1:Evaluationmatrixforthecomparisonofthethreeconstructionvariantsframeconstruction,panelconstructionandCLTconstruction
criteria weighting frameconstruction panelconstruction CLTconstructionvalue result value result value result
complexityofthestructure
10% 3 30 1 10 5 50
difficultyoftheerection
20% 2 40 5 100 4 80
difficultyofthetransport
10% 5 50 1 10 3 30
deconstructionandreuse
5% 5 25 1 5 2 10
suitabilityforprefabrication
10% 2 20 5 50 3 30
firesafety
15% 2 30 3 45 5 75
noiseprotec‐tion
5% 1 5 2 10 5 25
environmentalaspectsofthematerials
15% 4 60 4 60 2 30
difficultyofad‐justmentsoftheinterior
5% 5 25 1 5 3 15
architecturalvalue
5% 4 20 1 5 5 25
sum 100 % 305 300 370
TheresultsrevealthattheCLTconstructionisbestsuitedfromthisall‐integratingpointofview.Itdidnotgetthelowestvalue1foranycriterion,theworstratingswereattainedfordeconstruc‐tionandreuse,sincetheCLTelementsareengineeredwoodproductsthatarehighlyadjustedtothespecificproject,andenvironmentalaspects,becausemostsyntheticadhesivesarerequiredforthemanufacturing.Theframeconstructionandthepanelconstructionhavealmostthesameresult,althoughthescoringat the individualcriteria isoftenopposite.For thedifficultyof thetransport,forexample,theframeconstructionscoreshighbecausethebasiccomponentsarerel‐ativelyeasilyavailableandcanbetransportedefficiently.Thepanelelements,however,prefabri‐catedwallsandfloorsorevenwholeprefabricatedmodules,aremoredifficulttotransportandthedistancebetweenthefactoryandtheconstructionsiteispresumablymuchbigger.Forthedifficultyoftheerectionontheotherhand,thepanelconstructiongetsahighvaluebecausetheprefabricatedelementsonlyhavetobeconnectedonsite,whiletheerectionoftheframeismorecostly.
Itisimportanttoremindthatthisevaluationwillnotvalidforeverycase,itisonlyintendedtogiveageneralideaofthedifferences,theadvantagesanddrawbacksofthethreestructuralmeth‐ods.Thedecisionforoneoranotherofthemethodswillinadditiontothoseresultshighlydependonproject‐specificaspects,whichcannotbeconsideredhere.Moreover,theabovevalueswereonlydeterminedqualitativelybasedonthefindingsofthismasterthesis.Foramorethorough
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evaluation,especiallywhenappliedtoarealbuildingproject,inputfromexpertsfromdifferentfieldsshouldbeconsidered.
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8. DiscussionApartfromtheaspectsofthepreviouschapter,somemoredetailedresultsconcerningtheout‐comeofthedesignandtheexperienceswiththethreevariantswillbediscussedinthischapter.
Theframeconstruction isveryeffectiveto transferthewind loadswhichcreatea largeglobalbendingmomentatthefootofbuilding.Thisisnaturallyabigchallengeforallmulti‐storeybuild‐ings.Lookingatexistingmulti‐storeytimberbuildingstoday,liketheoriginalTreetconstructionortheMjøstårnet(cf.chapter1),mostofthemfeaturesomekindofframeconstructionontheoutsideofthebuilding.
Lookingattheconnectiondetailintheframeconstruction,onecanconcludethatitwouldhavebeenmoreappropriatetoseparatetheconnectionofthetwodiagonalsthatmeetatthecornercolumn.Thisconnectionisquitecomplex,ascouldbeillustratedintheFEManalysisofthecon‐nectioninchapter6.5.2.Muchspaceisneededtosecurelytransfertheveryhighloads.Thetwo‐dimensionalconnectionmakesthistaskevenmorecomplicated.Basedonthoseexperiences,itcanberecommendedtoalwayspreferone‐dimensionalconnections,althoughagain,thecondi‐tionscanbedifferentinaspecificproject.
Ofallthreevariants,thepanelconstructionisleastsuitableformulti‐storeybuildings.Thepanelconstructionisanefficientandlightweightconstructionmethodforsmallerbuildings,whichhasmanyadvantageslikethegoodsuitabilityforprefabricationanditssmallweight.Itis,however,notefficientforbuildingswithmanystoreysbecauseoftheveryhighloadsthatoccurinmulti‐storeybuildings.Theextensivepreliminarydesignandthe issueswithcreatinganFEMmodelillustratethecomplexityoftheconstruction.Theloaddistributionisnotclear,whichmakesanoptimisationofthedesigndifficult.
Incontrasttothat,themainadvantageofthemasstimbervariantisitssimpleconstruction.Es‐peciallycomparedtothepanelconstruction,butalsotheframeconstruction,lessdifferentstruc‐turalelementsandthereforealsolessconnectionsarenecessary.Themasstimberelementscom‐binethedifferentstructuralfunctionsinaneffectiveway.
However,thepreliminarydesignhadtobereworkedcomparablystronglyfortheCLTconstruc‐tion.Thisisobviouslyduetoinadequateassumptionsforthepreliminarydesign,e.g.concerningthestrengthortheYoung’smodulus.Inthepreliminarydesign,itwasnotaccountedforthedif‐ferentmaterialparametersinthedifferentdirectionsoftheplates,althoughthoseactuallydiffersignificantly.
Onereasonforthoseproblemsisthelackofexperiencewiththismaterial.Adequateassumptions(whicharealwaysbasedonexperience)arenotavailableyetasextensivelyasfortheothercon‐structionmethods.AnotherissueforthedesignoftheCLTconstructionisthatstandardisedrulesforthedesignofCLTarestillmissing.IntheEC,CLTisnotmentionedatall.Assumptionshadtobemade,butbecauseoftheadvantagesofCLTthatwerepointedoutearlier(aboveallthesupe‐riorhomogeneity),thereispotential fore.g.highermodificationfactorsk whichwouldin‐creasetheefficiencyofthismaterial(seealso[19]).
Ontheotherhand,however,itwascomparativelyeasytoadjustthedimensionsofthemembersinquestion.Inspiteoftheconsiderablechangesthathadtobemade,theloaddistributiononlychangedrelativelylittle.Thisprovesagainthesimplicityofthestructure.Thestructuralelementsarequiteindependentofeachotherconcerningtheloadtransfer.Thesimplicityoftheconnec‐tionswasalsobeneficial,becauseconnectionsoftenrepresentfixedpointsforthedesign,formingboundaryconditionsthatlimitthefreedomofthedesignperceptibly.
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Tocomebacktothereasonforthosenecessaryadjustments,thereisstillsomeworkandresearchtobedonetogainmoreexpertiseaboutthismaterial.ExtensionstothestandardsarenecessarytoincludeCLT,especiallybecauseitisusedmoreandmoreandwillverylikelyplayanimportantroleinthefutureofmulti‐storeytimberbuildings,aswasdiscussedearlier.TheFEM‐softwareRFEMalreadyincludedanadd‐ontomodelCLT‐materialsrealistically.Thiscanbeseenasasignthattheindustryhasalreadyunderstoodtheimportanceofthismaterialandisusingit,whiletheresearchandstandardisationstillhavetocatchup.CLThasalsobeenusedindifferentextendforthemulti‐storeytimberbuildingsTreetandMjøstårnet.
Itcanbeseenfromtheoutcomeofthismasterthesis,thatallthreevariantshaveadvantagesanddrawbacks.Thisisnotsurprisingandhadalreadybeenindicatedinchapter6.1.Torounduptheconclusionsofthedesignanalysis,ashortlookwillbetakenathowtocombinethedifferentvar‐iantseffectively.
Sincetheframeisverywellsuitedtotakeoverthewindloads,itmakessensetousethisstructureontheoutsideofthebuildingfortheglobalstability.Ontheinside,modulesinpanelconstructioncanbeused.Tominimisetheloadsonthepanelwalls,itispossibletoconnectthemodulestotheframestotransfertheverticalforcesthere.Thiscaneitherbedonewitheverystoreyorwithsev‐eralstoreys,creatingplatformsatequalintervals,verymuchliketheoriginalstructureofTreetwascarriedout.Thismakesitpossibletomakeuseofthepanelconstruction’sadvantages.None‐theless,higherloadswillprobablyoccurinthepanelwallscomparedtosmallerbuildings.Con‐cerningthis,thesolutionwithadistinctionbetweenloadbearingandnon‐loadbearingstudshasprovedtobeveryeffective.
ACLTconstructionisverywellsuitedformulti‐storeytimberbuildingswithoutadditionalstruc‐tures. For even bigger buildings, constructions in the style of traditionalmonolithic concretestructurescanbeimagined,withaninternalmassivecore,providingthestability.Inthisway,CLTcanalsobecombinedwithothermaterials,e.g.alightweightpanelconstructiontoformtheouterwalls.Furthermore,floorslabsmadefromCLTarewellsuitedtobeusedindifferentconstruc‐tions,oneoftheiradvantagescomparedtoe.g.joistfloorsiftheircapabilityofbearingloadsinbothdirections,whichmakesthemmuchmoreefficient.Becauseoftheirmassivestructureandhighweight,theyalsoaddagoodfireandnoiseprotection.
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9. ConclusionsInthismasterthesis,anextensivebasisformoderntimberdesignwasestablishedandcouldsuc‐cessfullybeusedtoperformadesignanalysisofthreevariantsofthemulti‐storeytimberbuildingTreet.Onevariantwasaframeconstruction,oneapanelconstructionandoneaCLTconstruction.Fromtheexperiencesduringthedesignandfromthefinaloutcome,conclusionscouldbemadeconcerning thesuitabilityof those threevariants, thusgivingaversatileanswer to thecentralresearchquestion(questionnumber1)thatwasformulatedinchapter4.Someofthemostim‐portantfindingsare:
Aframeconstructioniswellsuitedtoprovidestabilityinmulti‐storeytimberbuildings. Apanelconstructionshouldonlybeusedincombinationwithotherconstructionmeth‐
ods,butthenithassomegreatadvantages,aboveallthegoodsuitabilityforprefabrica‐tion.
CLTcanbeusedforvariouspurposesinmulti‐storeytimberbuildings,eitheronitsownorincombinationwithothermaterialsandstructuralmethods.
Aclearloadtransferisbeneficial,especiallyfortheoptimisationofthedesign. EngineeredwoodproductslikeglulamandCLTarepracticallyinevitableformulti‐storey
timberbuildings. Stressesperpendiculartothegrainshouldbeavoided.
Togiveanswerstothesecondaryquestions,herearethefurtherimportantpoints,gatheredfromallchaptersofthemasterthesis:
2. Woodistheoldestmaterialusedforbuildingpurposes.Muchexperienceexistsfortimberconstructions,buttoday’stechnologiesdifferconsiderablyfromthoseusedearlierinhis‐tory.Therearestillmanyreservationsamongstbothclientsandplannersinthebuildingindustry, which are connected to the disadvantages of the traditional technologies,althoughthenewtechnologiessolvedmostofthosedisadvantages.
3. Inspiteofthedifferenthistoricaldevelopments,inbothNorwayandGermany,asinmanyothercountries,thetimberindustrylacksexpertiseforthosenewtechnologies.
4. SupportedbyprogramsliketheNorwegianstrategytopromotetheuseofwoodinpublicbuildings,however,thetimberindustryisdeveloping.
5. Woodisanaturalmaterialwithalltheadvantagesanddrawbacksthatareconnectedtothisfact.Itsgreatestadvantagecomparedtosteelandconcreteisprobablyitsenviron‐mentalproperties.Butwoodhasstructuraladvantages,too,likethelowself‐weight.
6. Theroleconnectionsplayinthedesignoftimberbuildingsdependsontheconstructionmethod.Fortheframeandthepanelconstruction,theconnectionsplayanimportantrole,a largepartofthedesigndocumentationisdedicatedtotheconnections.TheCLTcon‐structionontheotherhandonlyrequiresaminimumofconnections.
7. ThedesignofthepanelandtheCLTconstruction,likemostmodernengineeringconstruc‐tions,requiredtheuseofFEM‐software.Specialcautionisrequiredwhenevaluatingtheresultsbecauseofmodel‐relatedeffectsthatcaninfluencetheresultsunrealistically.Theframeconstructioncouldbedesignedonlymakinguseofasimple frameworkanalysisprogram.
8. TheFEM‐analysisoftheconnectionsshowedthatthelayoutofthefastenersinmulti‐fas‐tenerconnectionshasanimportanteffectonthestressdistributionandisnotcompletelyconsideredintheEC.Generally, itcanberecommendedtoarrangethefastenersonanorthogonalgridparallelandperpendiculartothegraintoachieveanevenloadtransfer.
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10. RecommendationsAsdescribedintheintroductioninchapter1,today’shighesttimberbuilding,Treet,hasaheightof51m,whentheMjøstårnetwillbefinishedin2019,itwillhaveaheightof81m.Thinkingfur‐ther into the future, it canwellbe imagined that there soonwillbewoodenskyscraperswithheightsfarabove100m.Theaspectsdiscussedinthismasterthesiswillstillbeabletobeusedinageneralsenseforsuchbuildings,butthestructuresmustofcoursebeadapted.Toobtainthenecessarycross‐sections,CLTwilldefinitelyplayanimportantrole.Newproductslikemouldedwoodimprovethewood’spropertiesandwillmakesuchnewstructurespossible.Tomakethosenewproductsapplicable,furtherresearchisneeded.
Toeconomicallydesignnewconstructions,improvementsmustbemadetothecurrentstandards,e.g.toincludeCLTintheEC.
Apartfromthat,withthismasterthesisitcouldbedemonstratedthattherearetodaynotechnicalhindrancestoconstructmulti‐storeybuildingsusingtimber.Itisnowthetaskofthelegislativeorgantoprovidemodern,contemporaryrulesthatsupporttimberstructures,especiallyconsid‐eringthebigenvironmentaladvantagesthathavebeendiscussed.Atthesametime,theresponsi‐bleplannersinthebuildingindustryshouldbemoreawareofthetechnicalpossibilitiesthathavebeenpresented,andridthemselvesofthereservationsconnectedtoearlierweaknessesoftimber.
Allinall,thismasterthesisshowedthattimberconstructionsstillhavemuchunusedpotential,alsofortomorrow’sbuildings.
Bibliography
MasterThesis‐LucasBienert 73
Bibliography[1] BautabellenfürIngenieure.20.ed.,editor:AlfonsGoris.2012:WernerVerlag.[2] DINDeutschesInstitutfürNormunge.V.:DINEN1995‐1‐1:2004+AC:2006+A1:2008,
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[7] Hōryūji:ABriefHistory.Availablefrom:http://horyuji.or.jp/en/garan/,lastaccessdate:29.11.2018.
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[9] GermanMinisterialConferenceforBuilding:Musterbauordnung.2012.[10] Slikbyggesverdenshøyestetrehus.Availablefrom:
https://byggmesteren.as/2014/03/11/slik‐bygges‐verdens‐hoyeste‐trehus/,lastaccessdate:29.11.2018.
[11] SINTEFByggforsk:TekniskGodkjenningMartinsonsKL‐trä.2013,Oslo.[12] Europeancommitteeforstandardization:EN14080,Timberstructures–Gluedlaminated
timberandgluedsolidtimber–Requirements.2013.[13] Treforbyggogbyggitre:kunnskapsgrunnlagforøktbrukavtreioffentligebygg.2013,
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byggeplassen/,lastaccessdate:29.11.2018.[15] Norskearkitekterslandsforbund:Verdenshøyestetrehus.Availablefrom:
https://www.arkitektur.no/treet,lastaccessdate:28.11.2018.[16] Bergman,Richardetal.:WoodHandbook,WoodasanEngineeringMaterial.2010,
Madison,Wisconsin:ForestProductsLaboratory,UnitedStatesDepartmentofAgricultureForestService.
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[23] Möller,Eberhard:TendenzenimHolzbau.In:Bautechnik,2013.Vol.90(1):p.42‐46.[24] Pacheco‐Torgal,Fernando;Pacheco‐Torgal,F.:Eco‐efficientconstructionandbuilding
materials:lifecycleassessment(LCA),eco‐labellingandcasestudies.2014,WoodheadPub.[25] Rug,Wolfgang;Held,Heidrun:LebensdauervonHolzhäusern.1.ed.2001.[26] Thelandersson,Sven;Larsen,H.J.:Timberengineering.2003,Chichester:Wiley.[27] Wærp,Silje;Flæte,PerOtto;Svanæs,Jarle:Mikado:miljøegenskaperfortre‐ogtrebaserte
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Animproveddesignprocedure.In:ConstructionandBuildingMaterials,2014.Vol.60:p.81‐90.
Appendix
MasterThesis‐LucasBienert 75
AppendixA. Attachments architecturalplansoftheoriginalbuildingTreetP01–P06(PDF)[15] loadcalculation(PDF) preliminarydesign(PDF) Eurocodedesign(PDF) technicalplans(PDF) EXCELdesignfiles(XLSX) RFEMmodels(RF5) ANSYSmodel(DB)
B. SelectedRFEMResultsB.a) FrameConstruction
FigureB.1:DeformationoftheframeconstructionforLC1(self‐weight)in[mm]
Appendix
MasterThesis‐LucasBienert 76
FigureB.2:DeformationoftheframeconstructionforLC3(windfromthefront)in[mm]
FigureB.3:DeformationoftheframeconstructionforLC4(windfromtheside)in[mm]
Appendix
MasterThesis‐LucasBienert 77
FigureB.4:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC1(self‐weight)in[kN]
FigureB.5:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC2(snow)in[kN]
FigureB.6:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC3(windfromthefront)in[kN]
Appendix
MasterThesis‐LucasBienert 78
FigureB.7:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC4(windfromtheside)in[kN]
FigureB.8:InternalnormalforcesinthecolumnsoftheframeconstructioninthefirststoreyforLC5(lifeload)in[kN]
Appendix
MasterThesis‐LucasBienert 79
FigureB.9:InternalnormalforcesinthefrontframeoftheframeconstructionforLC1(self‐weight)in[kN]
B.b) PanelConstruction
FigureB.10:DeformationofthefirstfloorofthepanelconstructionforLC1(self‐weight)in[mm]
Appendix
MasterThesis‐LucasBienert 80
FigureB.11:DeformationofthefirstfloorofthepanelconstructionforLC2(snow)in[mm]
FigureB.12:DeformationofthefirstfloorofthepanelconstructionforLC3(windfromthefront)in[mm]
FigureB.13:DeformationofthefirstfloorofthepanelconstructionforLC4(windfromtheside)in[mm]
Appendix
MasterThesis‐LucasBienert 81
FigureB.14:DeformationofthefirstfloorofthepanelconstructionforLC5(lifeload)in[mm]
FigureB.15:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC1(self‐weight)
FigureB.16:DistributionoftheinternalnormalforcesinthestudsofthefirststoreyofthepanelconstructionforLC3(windfromthefront)
Appendix
MasterThesis‐LucasBienert 82
B.c) CLTConstruction
FigureB.17:DeformationoftheCLTconstructionforLC1(self‐weight)in[mm]
FigureB.18:DeformationoftheCLTconstructionforLC3(windfromthefront)in[mm]
Appendix
MasterThesis‐LucasBienert 83
FigureB.19:DeformationoftheCLTconstructionforLC4(windfromthefront)in[mm]
FigureB.20:InternalnormalforcesintheCLTconstructionforLC1(self‐weight)in[kN/m]
Appendix
MasterThesis‐LucasBienert 84
FigureB.21:InternalnormalforcesintheCLTconstructionforLC3(windfromthefront)in[kN/m]
FigureB.22:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC1(self‐weight)in[kN/m]
Appendix
MasterThesis‐LucasBienert 85
FigureB.23:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC2(snow)in[kN/m]
FigureB.24:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC3(windfromthefront)in[kN/m]
FigureB.25:InternalnormalforcesinthefirststoreyoftheCLTconstructionforLC5(lifeload)in[kN/m]
Appendix
MasterThesis‐LucasBienert 86
FigureB.26:InternalshearforcesinthefirststoreyoftheCLTconstructionforLC3(windfromthefront)in[kN/m]
FigureB.27:InternalshearforcesinthefirststoreyoftheCLTconstructionforLC4(windfromtheside)in[kN/m]
Appendix
MasterThesis‐LucasBienert 87
C. SelectedANSYSresults
FigureB.28:Stressinglobalxdirectionσxoftheconnectionin[N/mm2]
FigureB.29:Stressinglobalydirectionσyoftheconnectionin[N/mm2]
Appendix
MasterThesis‐LucasBienert 88
FigureB.30:Firstprinciplestressσ1oftheconnectionin[N/mm2]
FigureB.31:Straininglobalxdirectionεxoftheconnectionin[‐]
Appendix
MasterThesis‐LucasBienert 89
FigureB.32:Straininglobalydirectionεyoftheconnectionin[‐]
LoadCalculation
TableofContents
LoadCalculation‐LucasBienert 2
TableofContentsTableofContents...............................................................................................................................................................2
Self‐weight............................................................................................................................................................................3
Liveloads............................................................................................................................................................................10
Snowloads.........................................................................................................................................................................10
WindLoads........................................................................................................................................................................12
Appendix.............................................................................................................................................................................18
Self‐weight
LoadCalculation‐LucasBienert 3
Self‐weightTechnicaldrawingsofthewall,floorandroofconstructionscanbefoundintheappendix.
a)FrameConstruction
roof characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 2 cm 0,047 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2 1,458 kN/m2roofjoists,glulamGL24h 3,7 kN/m3 14 cm 24 cm 65 cm 0,19 kN/m2
1,65 kN/m2
floor characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 4 cm 0,10 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2 1,15 kN/m2floorjoists,glulamGL24h 3,7 kN/m3 14 cm 24 cm 65 cm 0,19 kN/m2
1,34 kN/m2
outerwall,facade characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 1 cm 0,06 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2verticalcarriers,C24 4,2 kN/m3 6 cm 16 cm 60 cm 0,07 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 1 cm 0,06 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
0,44 kN/m2
b)PanelConstruction
roof1,2 characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 2 cm 0,0468 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2roofjoists,glulamGL24h 3,7 kN/m3 16 cm 24 cm 60 cm 0,24 kN/m2
1,69 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 4
roof3 characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 2 cm 0,0468 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2roofjoists,glulamGL24h 3,7 kN/m3 8 cm 24 cm 60 cm 0,12 kN/m2
1,58 kN/m2
floor1,2 characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 4 cm 0,10 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2floorjoists,glulamGL24h 3,7 kN/m3 16 cm 20 cm 60 cm 0,20 kN/m2
1,35 kN/m2
floor3 characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 4 cm 0,10 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2floorjoists,glulamGL24h 3,7 kN/m3 8 cm 20 cm 60 cm 0,10 kN/m2
1,25 kN/m2
outermodulewall28/28studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 28 cm 28 cm 60 cm 0,48 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 28 cm 0,05 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 28 cm 0,05 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
1,04 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 5
outermodulewall24/24studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 24 cm 24 cm 60 cm 0,36 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 24 cm 0,04 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 24 cm 0,04 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
0,90 kN/m2
outermodulewall20/20studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 20 cm 20 cm 60 cm 0,25 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 20 cm 0,04 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 20 cm 0,04 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
0,78 kN/m2
outermodulewall16/16studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 16 cm 16 cm 60 cm 0,16 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 16 cm 0,03 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 16 cm 0,03 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
0,67 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 6
outermodulewall8/16studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 8 cm 16 cm 60 cm 0,08 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 16 cm 0,03 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 16 cm 0,03 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 2 cm 0,04 kN/m2ventilation+battens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 3 cm 0,13 kN/m2
0,59 kN/m2
innermodulewall28/28studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 28 cm 28 cm 60 cm 0,48 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 28 cm 0,05 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 28 cm 0,05 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2
0,88 kN/m2
innermodulewall24/24studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 24 cm 24 cm 60 cm 0,36 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 24 cm 0,04 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 24 cm 0,04 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2
0,73 kN/m2
innermodulewall20/20studs characteristicweight dimensions spacing load h=3,195m γ b t a g innerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2studs,glulamGL24h 3,7 kN/m3 20 cm 20 cm 60 cm 0,25 kN/m2bottomblocking,glulamGL24h 3,7 kN/m3 16 cm 20 cm 0,04 kN/m2bottomplate,glulamGL24h 3,7 kN/m3 10 cm 24 cm 0,03 kN/m2topblocking,glulamGL24h 3,7 kN/m3 16 cm 20 cm 0,04 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 2 cm 0,09 kN/m2
0,61 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 7
c)CLTConstruction
roof1 characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 1,8 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 1,8 cm 0,0468 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2CLT 4 kN/m3 14,5 cm 0,58 kN/m2
1,95 kN/m2
roof2,3 characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 1,8 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 1,8 cm 0,0468 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2CLT 4 kN/m3 20,9 cm 0,84 kN/m2
2,20 kN/m2
roof4 characteristicweight dimensions spacing load γ b h a g gravel,protectivelayer 0,2 kN/m2/cm 5 cm 1 kN/m2plywoodsheathing,spruce 0,05 kN/m2/cm 1,8 cm 0,09 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 30 cm 0,02 kN/m2airtightinsulation,wood‐fibre 0,026 kN/m2/cm 1,8 cm 0,0468 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2horizontalcarriers,C24 4,2 kN/m3 6 cm 16 cm 30 cm 0,13 kN/m2CLT 4 kN/m3 9,5 cm 0,38 kN/m2
1,75 kN/m2
floor1 characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 3,6 cm 0,10 kN/m2CLT 4 kN/m3 14,5 cm 0,58 kN/m2
1,64 kN/m2
floor2,3 characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 3,6 cm 0,10 kN/m2CLT 4 kN/m3 20,9 cm 0,84 kN/m2
1,90 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 8
floor4 characteristicweight dimensions spacing load γ b h a g floortilesincl.mortar 0,3 kN/m2/cm 1 cm 0,30 kN/m2cementscreed 0,22 kN/m2/cm 3 cm 0,66 kN/m2footfallsoundinsulation,woodfibre 0,028 kN/m2/cm 3,6 cm 0,10 kN/m2CLT 4 kN/m3 9,5 cm 0,38 kN/m2
1,44 kN/m2
outerwallt=170mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 17,0 cm 0,68 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2verticalcarriers,C24 4,2 kN/m3 6 cm 16 cm 60 cm 0,07 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 1,2 cm 0,06 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 1,5 cm 0,04 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 2,5 cm 0,13 kN/m2
1,06 kN/m2
outerwallt=145mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 14,5 cm 0,58 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2verticalcarriers,C24 4,2 kN/m3 6 cm 16 cm 60 cm 0,07 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 1,2 cm 0,06 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 1,5 cm 0,04 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 2,5 cm 0,13 kN/m2
0,96 kN/m2
outerwallt=120mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 12,0 cm 0,48 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2verticalcarriers,C24 4,2 kN/m3 6 cm 16 cm 60 cm 0,07 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 1,2 cm 0,06 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 1,5 cm 0,04 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 2,5 cm 0,13 kN/m2
0,86 kN/m2
outerwallt=95mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 9,5 cm 0,38 kN/m2heatinsulation,woodfibre 0,005 kN/m2/cm 16 cm 0,08 kN/m2verticalcarriers,C24 4,2 kN/m3 6 cm 16 cm 60 cm 0,07 kN/m2outerplywoodsheathing,spruce 0,05 kN/m2/cm 1,2 cm 0,06 kN/m2airtightinsulation,wood‐fibre 0,0235 kN/m2/cm 1,5 cm 0,04 kN/m2ventilation+counterbattens,C24 4,2 kN/m3 4 cm 3 cm 60 cm 0,01 kN/m2cladding,wood 5 kN/m3 2,5 cm 0,13 kN/m2
0,76 kN/m2
Self‐weight
LoadCalculation‐LucasBienert 9
halfinnerdividingwallt=170mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 17 cm 0,68 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 8 cm 0,04 kN/m2
0,72 kN/m2
halfinnerdividingwallt=145mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 14,5 cm 0,58 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 8 cm 0,04 kN/m2
0,62 kN/m2
halfinnerdividingwallt=120mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 12 cm 0,48 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 8 cm 0,04 kN/m2
0,52 kN/m2
halfinnerdividingwallt=95mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 9,5 cm 0,38 kN/m2soundinsulation,woodfibre 0,005 kN/m2/cm 8 cm 0,04 kN/m2
0,42 kN/m2
innerwallt=246mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 24,6 cm 0,98 kN/m2
0,98 kN/m2
innerwallt=170mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 17 cm 0,68 kN/m2
0,68 kN/m2
innerwallt=95mm characteristicweight dimensions spacing load h=3,195m γ b t a g CLT 4 kN/m3 9,5 cm 0,38 kN/m2
0,38 kN/m2
Liveloads
LoadCalculation‐LucasBienert 10
LiveloadsVerticalLifeLoads
category description q kN/m Q kNA residential buildings, kitchen, bathroom, living and
sleepingrooms,e.g.inhospitals,hotels
floor 2,5* 2,0H roofs,notwalkable,onlymaintenance slopeα 0° 20° 0,75 1,5* including0,5kN/m additionalloadfornon‐loadbearingwalls
reductionfactorforverticaldistributedliveloadsq inmultiplestoreys
α2 n 2 ψ
n
α2 14 2 ⋅ 0,7
140,74
n 14
loadcategory A(ψ 0,7)
SnowloadssnowloadonthegroundforBergen,Hordaland,South‐Norway
s , 2,0kN/m
H 150m
H 2m. o. h.
s 2,0kN/m
snowloadontheroof
s μ ⋅ C ⋅ C ⋅ s exposurefactorC 1,0(normalexposure)
thermalfactorC 1,0
s μ ⋅ s
Snowloads
LoadCalculation‐LucasBienert 11
Figure1:Roofreference
Roof1
α 0° 15°
μ 0
b 2,10m
b 9,275m
h 52,92 49,92 3,0m
μb b2 ⋅ h
2,10 9,2752 ⋅ 3,0
1,90 2 ⋅ 3,67/2 3,67
s 1,90 ⋅ 2,0 3,80kN/m
Onthesafeside,thehighersnowloadisconsideredtobeconstantalongthelengthoftheroofofthelift,until4,08mbeforetheendoftheroof,andthendecreaselinearly.
l 2 ⋅ 3,0 6,0m 4,08m
μ 0,81,90 0,8
6,06,0 4,08 1,15
s 1,15 ⋅ 2,0 2,30kN/m
Roof2
α 0°
WindLoads
LoadCalculation‐LucasBienert 12
μ 0,8
s 0,8 ⋅ 2,0 1,6kN/m
Roof3
α 0° 15°
μ 0
b2,10 7,295
24,70m
b 9,275m
h 52,92 49,92 3,0m
μ4,70 9,275
2 ⋅ 3,02,33 2 ⋅ 3,00/2 3,00
s 2,33 ⋅ 2,0 4,66kN/m
l 2 ⋅ 3,0 6,0m b 9,275m
Figure2:Summaryofthesnowloadsontheroof
WindLoadsreferencewindspeedforterraincategoryII(openterrainwithindividualhousesortrees)
v , 26m/s v 30m/s
basicwindspeedwithdirectionfactorc 1,0,seasonfactorc 1,0andprobabilityfactorc 1,0.
H 2m. o. h.
H 900m
H 1500m
WindLoads
LoadCalculation‐LucasBienert 13
c 1,030 26 2 90026 1500 900
0,77 1,0
c 1,0
v 1,0 ⋅ 26 26m/s
10minutesaveragewindspeedovertheheightzforterraincategoryIV
roughnessfactor:k 0,24
roughnesslength:z 1,0m
z 16m
z 200m
c z 0,24 ⋅ lnz
1,0 m z z z
c z c z z
terrainformfactor: 1,0
0,24 ⋅1,0
⋅ 26 /
turbulenceintensity(ratiobetweenthestandardderivationfortheinstantaneouswindspeed(1second)andthe10minutesaveragewindspeed)
turbulencefactor: 1,0
1,0
1,0 ⋅ 1,0
10minutesaveragewindspeedpressure
airdensity 1,25 /
0,5 ⋅ 1,25 / ⋅
gustwindspeedpressure
peakfactor 3,5
1 2 ⋅ 3,5 ⋅ ⋅
generalgeometry
52,92 2,0 50,92
20,65
22,34
WindLoads
LoadCalculation‐LucasBienert 14
2
windfromthefront/back
20,65
0
20,65 16
50,92 20,65 30,27
50,92 200
i
3 50,92 24,52 0,254 375,8 1044,02 30,27 21,28 0,293 283,0 863,41 20,65 18,17 0,330 206,3 683,0
windfromthesides
22,34
0
22,34 16
50,92 22,34 28,58
50,92 200
i
3 50,92 24,52 0,254 375,8 1044,02 28,58 20,92 0,298 273,5 844,01 22,34 19,38 0,322 234,7 763,7
WindLoads
LoadCalculation‐LucasBienert 15
Figure3:Summaryofthegustwindspeedpressure
windpressure
⋅
windpressureonthewalls
windfromthefront/back
22,34
20,65
22,3420,65
5 5 ⋅ 20,65 103,25
/ 50,92/20,65 2,47
WindLoads
LoadCalculation‐LucasBienert 16
A B D E
, ‐1,2 ‐0,8 0,8 ‐0,57
, ‐1,4 ‐1,1 1,0 ‐0,57
windfromthesides
20,65
22,34
20,65 22,34
/ 50,92/22,34 2,28
areaCisneglected
A B D E
, ‐1,2 ‐0,8 0,8 ‐0,56
c , ‐1,4 ‐1,1 1,0 ‐0,56
WindLoads
LoadCalculation‐LucasBienert 17
windpressureontheroof
windfromthefront/back
F G Hc , ‐1,8 ‐1,2 ‐0,7
c , ‐2,5 ‐2,0 ‐1,2
windfromthesides
F G H Ic , ‐1,8 ‐1,2 ‐0,7 /‐0,2
c , ‐2,5 ‐2,0 ‐1,2 /‐0,2
Appendix
LoadCalculation‐LucasBienert 18
Appendix
a)FrameConstruction
Figure4:Verticalsectionthroughthewallandtheflooroftheframeconstruction
Appendix
LoadCalculation‐LucasBienert 19
Figure5:Verticalsectionthroughthewallandtheroofoftheframeconstruction
Appendix
LoadCalculation‐LucasBienert 20
b)PanelConstruction
Figure6:Verticalsectionthroughthewallandthefloorofthepanelconstruction
Appendix
LoadCalculation‐LucasBienert 21
Figure7:Verticalsectionthroughthewallandtheroofofthepanelconstruction
Appendix
LoadCalculation‐LucasBienert 22
c)CLTConstruction
Figure8:VerticalsectionthroughthewallandtheflooroftheCLTconstruction
Appendix
LoadCalculation‐LucasBienert 23
Figure9:VerticalsectionthroughthewallandtheroofoftheCLTconstruction
PreliminaryDesign
TableofContents
PreliminaryDesign‐LucasBienert 2
TableofContentsTableofContents...............................................................................................................................................................2
General...................................................................................................................................................................................4
Remarks............................................................................................................................................................................4
DescriptionoftheBuilding.......................................................................................................................................4
LoadbearingConcept...................................................................................................................................................4
Assumptions....................................................................................................................................................................6
Materials...........................................................................................................................................................................6
Software............................................................................................................................................................................7
Literature..........................................................................................................................................................................7
PreliminaryDesignFormulae..................................................................................................................................7
Loads..................................................................................................................................................................................8
a)FrameConstruction..................................................................................................................................................11
3.1Joists.........................................................................................................................................................................12
3.2Joists.........................................................................................................................................................................13
2.2Beam.........................................................................................................................................................................14
2.1Beam.........................................................................................................................................................................16
2.3Beam.........................................................................................................................................................................18
7Diaphragm.................................................................................................................................................................20
8Frame...........................................................................................................................................................................21
2.4Beam(Front)........................................................................................................................................................22
2.4Beam(Side)...........................................................................................................................................................24
1Columns......................................................................................................................................................................27
4Diagonal......................................................................................................................................................................31
5StructuralSheathingoftheFloors...................................................................................................................33
6VerticalFaçadeCarriers......................................................................................................................................35
ConnectionsOverview.............................................................................................................................................36
ConnectionBeam2.2toColumn1.1..................................................................................................................37
ConnectionOuterBeam2.4ontheSidetoColumn1.3..............................................................................38
ConnectionDiagonal4toColumn1.2................................................................................................................40
ConnectionSheathing5toJoists3......................................................................................................................42
ConnectionJoists3toBeams2............................................................................................................................43
b)PanelConstruction....................................................................................................................................................44
1.1FloorJoists.............................................................................................................................................................45
1.2FloorJoists.............................................................................................................................................................46
TableofContents
PreliminaryDesign‐LucasBienert 3
1.3FloorJoists.............................................................................................................................................................47
3Walls/Studs...............................................................................................................................................................48
3.y8StudsinWally3.................................................................................................................................................50
3.y1StudsinWally1.................................................................................................................................................54
4Sheathing...................................................................................................................................................................57
2FloorBeam................................................................................................................................................................59
6Beam............................................................................................................................................................................60
5Columns......................................................................................................................................................................62
ConnectionsOverview.............................................................................................................................................63
Anchoring......................................................................................................................................................................64
ConnectionFloorJoists1toFloorBeam2......................................................................................................66
ConnectionFloorBeam2toStuds3..................................................................................................................67
c)CLTConstruction.......................................................................................................................................................69
1FloorSlab...................................................................................................................................................................70
2,3FloorSlab..............................................................................................................................................................71
4FloorSlab...................................................................................................................................................................72
5Walls............................................................................................................................................................................73
5.y5OuterWall...........................................................................................................................................................75
Anchoring......................................................................................................................................................................78
Appendix.............................................................................................................................................................................79
Attachments.................................................................................................................................................................79
b)PanelConstruction...............................................................................................................................................80
c)CLTConstruction...................................................................................................................................................88
General
PreliminaryDesign‐LucasBienert 4
General
Remarks
This documentation summarises the results of the preliminary design. The relevant files areattachedforfurtherreference.Technicalreferenceplansarealsoattached(cf.appendix).
DescriptionoftheBuilding
ThesubjectofthisdesignisthebuildingTreet,locatedinBergen,Norway.Theexactaddressis:
Damsgårdsveien995058BergenHordaland,South‐Norway
Three different structures will be designed for this building, using three different timberconstructionmethods:
a) frameconstruction
b) panelconstruction
c) CLTconstruction
Thedimensionsofthebuildingarea/b/h 22,34/20,65/47,925m.Itconsistsofasinglelevelundergroundcarparkplus14normalstoreys,eachhavingaheightof3,195m.Theusageofthebuildingispurelyresidential.Eachstoreyconsistsof5units,4ofthemareapartmentsandoneiseitherastorageroomoranother,smallerapartment.
Eachstoreyhasacentralcorridorandallstoreysareconnectedviaalargestaircaseandaliftinthemiddleandsecondarystairwayononesideofthecorridor.
Thebuildinghasflatroofs,withtheareaofthecorridor,thestaircasesandtheliftsprotrudingonestorey higher than the apartments (which gives a height of 47,925 3,195 51,12m at thehighestpoint).Therefore,snowdriftsmustbeconsideredonthelowerroofs.
LoadbearingConcept
a)FrameConstruction
Theverticalloadsfromthefloorsarecarriedbythefloorjoists(elementreferencenumber3,cf.elementreferenceplanPa1.1)whichrunalongtheverticalaxes.Thejoistsaresingle‐spanbeamsandaresupportedbythebeams(2)whichrunperpendiculartothejoists,alongthehorizontalaxes.
Thebeamsarecompoundbeamsconsistingoftwoidenticalcross‐sectionsthatareattachedtothecolumns(1)onbothsides.TwoadditionalbeamsareattachedtotheoutsideofthecolumnsintheverticalaxesAandF.
Tostabilisethestructureagainstwind,diagonals(4)areaddedinbetweentheoutercolumns,formingtwoframesineachdirection.
Thewindpressureactsonthefaçade,inwhichverticalcarriers(6)carrythebendingmoment.Theverticalcarriersspanonestoreyandtransferthewindloadstotheouterbeams(2.4)andintothe floors.The floors act asdiaphragmswith the structural sheathing (5)providing the shearstiffnesstopasstheloadsontotheframesoneachside.
General
PreliminaryDesign‐LucasBienert 5
Thediaphragmsbehavelikesimplysupportedbeams.Theframesarethesupports,thebeams2.4theflanges,takingcompressionandtensionforces,andthesheathingthechord,takingtheshear.
Wind suctionon the roofwasnot considered, it canbe carriedby thebattens andhorizontalcarriersintheroofstructure,butisnotdecisiveincomparisontothesnowloadandself‐weight.
b)PanelConstruction
Thepanelconstructionfeaturestwelveprefabricatedmodulesperstoreythatconsistofwallsandthefloor(theuppersideisclosedwhenthenextmoduleisplacedontop).
Thevertical loadsarecarriedbythefloorjoists(1,cf.elementreferenceplanPb4.1).Theyaresupportedbythefloorbeams(2)whichareattachedtotheinsideofthewallsandtransfertheloadsintothewalls.Thewallsconsistofverticalstuds(3)whichcarrytheloads,thestructuralsheathing(4)whichprovidestheshearstiffnessandhorizontalblockinginbetweenthestuds.
Themodules1,2,6and7(cf.modulereferenceplanPb3)areopenononeofthefoursides.There,thefloorissupportedbyabeam(6)onfourcolumns(5).
Tocarrythehorizontalwindloads,thefloorsactasdiaphragmsandthewallsasshearwallswiththesheathingprovidingthenecessaryshearstiffness.Tocalculatetheloadsontheshearwallsfromthewind,astabilityanalysismustbeconducted.
Thenon‐loadbearingwallsinsidetheapartmentsarenotconsideredforstabilitytomakelaterchangestotheinteriorlayoutpossible.Thedoublewallswheretwomodulesmeetareconsideredastwoseparatewalls.
Forthestabilityanalysis,thebuildingisidealisedasaverticalcantileverbeamwiththemaximumverticalloads,horizontalshearandglobalbendingmomentatthesupportatthefoundation.Theshareofeverywallinshearandinbendingiscalculatedandtheverticalloadsfromtheself‐weightandthelifeloadareadded.Tocarrytheglobalbendingmoment,eachwallcarriesashareofthisbendingmomentdependingonitsstiffnessandanormalforcedependingonitsdistancetothecentreofgravity.
The studs carry the vertical forces in the walls. The studs in the outer walls also carry thehorizontalloadfromthewindandtransfertheseloadsintothediaphragms.
Onlyselectedstudsareconsideredtobeloadbearingandhaveanaccordinglylargercross‐sectioncomparedtothenon‐loadbearingstuds.Allstudsarearrangedonaregulargridwhichisfittedtothesizesoftheplywoodpanelsthatformthesheathingofthewalls.
Fortensilestresses,specialhold‐downdevicesfunctionasanchoring.Thelargesttensilestresseswill also occur at the support since the global bending moment, which causes the tension,increasesquadraticallywhiletheself‐weight,whichcancelsoutpartofthetension,onlyincreaseslinearlyovertheheight.
c)CLTConstruction
TheCLT‐constructionconsistssolelyofmasstimberpanelsmadefromCLT.Panelswithdifferentthicknessesareusedforthedifferentwalls(5,cf.elementreferenceplanPc3.1)andfloorslabs(1–4).Betweendifferentapartments,doublewallsareusedtoincreasethesoundprotection
Tocarrythehorizontalwindloads,thefloorsactasdiaphragmsandthewallsasshearwalls.Tocalculatetheloadsontheshearwallsfromthewind,astabilityanalysismustbeconducted.
Thenon‐loadbearingwallsinsidetheapartmentsarenotconsideredforstabilitytomakelaterchangestotheinteriorlayoutpossible.Thedoublewallsareconsideredastwoseparatewalls.
General
PreliminaryDesign‐LucasBienert 6
Toavoid large compression stressesperpendicular to thegrain, the floor slabs arenotput inbetweenthewallelements,butsetintoagroovecutintothelowerwall.
Toaccount for firesafety,onlyCLT‐panelswithat least5 layersareused. If theouter layer isdestroyedduringafire,thenextlayer,whichisorientedperpendiculartotheouterlayer,isalsorenderedineffectiveforthebearingoftheloadsandthreelayersremain,twoinloaddirectionandoneperpendiculartothat.Thus,theelementisstillabletocarryareducedamountofloads.
Assumptions
For the preliminary design, all checks are made with characteristic values and reducedpreliminarydesignstrengths.Theusedmaterialpropertiesaresummarisedintable…
material property preliminarydesignvaluesolid wood,glulam
strengthparalleltothegrain σ 5 N/mm
compressionstrengthperpendiculartothegrain σ , 1,5N/mm
Young’smodulus E 10000N/mm
plywood shearstrength σ , 1,5N/mm
out‐of‐planebendingstrength σ 8 N/mm
Young’smodulus E 4 000N/mm CLT strengthinthestrongdirection σ 5 N/mm
strengthintheweakdirection σ 4 N/mm
in‐planebendingaroundthestrongaxis σ , 4N/mm
compressionstrengthperpendiculartothegrain σ , 1,5N/mm
in‐planeshearstrength σ , 0,6N/mm
Young’smodulus E 4 000N/mm
steel strength σ 140N/mm
FortheCLT,thevaluesarederivedfromthetechnicalapproval[1].Thisdocumentalsoincludesrecommendationsconcerningthespanlengthofslabelements,whichareusedforthepreliminarydesign.
The loads in multi‐storey buildings change strongly over the height. In this design, only therequired cross‐sections in the lowest storey, where the loads are highest, are determined.Assumingtheforcesresultingfromtheverticalloadstochangelinearlyandtheforcesfromthebendingduetothewindloadstochangequadraticallyovertheheight,reducedcross‐sectionsortheupperstoreysareestimated.
Materials
Forthepreliminarydesign,noconcretestrengthclassesaredefinedyet,insteadthepreliminarydesignstrengthsareused(seetableabove).OnlyfortheCLTaspecificmaterialischosen,becausethepropertiesofthismaterialarenotdefinedinstandardsbutbythemanufacturerdirectly.
woodenmembers(beams,studs,floorjoists,…):glulam structuralsheathing:plywood CLTbyMartinsons(distributedinNorwaybySplitkonAS)
General
PreliminaryDesign‐LucasBienert 7
Software
Stab2d(simpleanalysisprogramfortwo‐dimensionalframeworks) MicrosoftEXCEL©
Extracts from the calculations with EXCEL can be found in the appendix. The EXCEL‐filesthemselvesarealsoattachedformoredetailedinformation.
Literature
[1] TekniskGodkjenningMartinsonsKL‐trä[2] BautabellenfürIngenieure,20thedition2012
Thetechnicalapproval[1]containstableswithrecommendedthicknessesforfloorslabsthathavebeenusedforthepreliminarydesign.
PreliminaryDesignFormulae
Thesimplifieddesignformulaeusedforthispreliminarydesignaretakenfrom[2].
element property formulafloorjoist height h l/20steelbolts,dowels capacity per fastener single
shearF 2,0 ⋅ d
capacityperfastener doubleshear
F 4,4 ⋅ d
requiredspaceperfastener req A 30 ⋅ d capacity at an angle to thegrain
F 1α360
⋅ F
capacitywithsteelplate F 1,25 ⋅ Ffullythreadedscrews capacity per screw axial
tensionF 5 ⋅ d
requiredspaceperscrew req A 60 ⋅ d nails capacitypernail shear F 3,5 ⋅ d din cm Ain cm Fin kN
Forcontinuousbeams,thereactionforcesarehigherthanforrowswithsimplysupportedbeams.Toaccountforthiscontinuityeffect,afactorof1,15isaddedincaseswhereit ispossiblethatbeamsactascontinuousbeams.
Toaccountforbuckling,generallyonly70%ofthestrengthareconsidered(factor0,7).Forthestudsinthepanelconstruction,afactorof0,8isused,becausethesheathingpreventsthestudsfrombucklingaroundintheirweakdirection.
General
PreliminaryDesign‐LucasBienert 8
Loads
Simplifiedloadsareusedforthepreliminarydesign.
verticalloads
liveload q 2,0 kN/mself‐weightfloors g 2,0 kN/mself‐weightwalls g 1,0 kN/msnowload s 2,0 kN/m
reductionfactorforlifeloadoverseveralstoreys
α 0,74
windloads
General
PreliminaryDesign‐LucasBienert 9
windfromthefront
c , A ‐1,2B ‐0,8D +0,8E ‐0,57
horizontalwindforce
q , 1,044 ⋅ 20,650,8634 0,6830
2⋅ 9,62 0,6830 ⋅ 20,65 43,1kN/m
Q , 43,1 ⋅ 22,34 962,9kN
c D E 0,8 0,57 1,37
W 1,37 ⋅ 962,9 1319kN
bendingmomentofthecantileverbeam
m , 1,044 ⋅ 20,65 ⋅ 50,9220,652
0,683 ⋅ 9,62 ⋅ 20,659,622
12⋅ 0,8643 0,683 ⋅ 9,62 ⋅ 20,65
23⋅ 9,62
0,683 ⋅ 20,65 ⋅20,652
1212kNm/m
M , 1212 ⋅ 22,34 27076kNm
c D E 0,8 0,57 1,37
M 1,37 ⋅ 27076 37094kNm
General
PreliminaryDesign‐LucasBienert 10
windfromthesides
c , A ‐1,2B ‐0,8D +0,8E ‐0,57
totalhorizontalwindforce
q , 1,044 ⋅ 22,340,844 0,7637
2⋅ 6,24 0,7637 ⋅ 22,34 45,4kN/m
Q , 45,4 ⋅ 20,65 937,5kN
c D E 0,8 0,56 1,36
W 1,36 ⋅ 937,5 1275kN
bendingmomentofthecantileverbeam
m , 1,044 ⋅ 22,34 ⋅ 50,9222,342
0,7637 ⋅ 6,24 ⋅ 22,346,242
12⋅ 0,844 0,7637 ⋅ 6,24 ⋅ 22,34
23⋅ 6,24
0,7637 ⋅ 22,34 ⋅22,342
1246kNm/m
M , 1246 ⋅ 20,65 25722kNm
c D E 0,8 0,56 1,36
M 1,36 ⋅ 25722 34982kNm
a)FrameConstruction
PreliminaryDesign‐LucasBienert 11
a)FrameConstructionElementReferenceOverview
referenceno element page
1 columns
1.1 innercolumns 27
1.2 cornercolumns 27
1.3 sidecolumns 27
1.4 sidecolumns 27
2 beams
2.1 beam 16
2.2 beam 14
2.3 beam 18
2.4 beam 22
3 joists
3.1 joists 12
3.2 joists 13
4 diagonal 31
5 structuralsheathingofthefloors 33
6 verticalfaçadecarriers 35
7 diaphragm 20
8 frame 21
connectionsoverview 36
a)FrameConstruction
PreliminaryDesign‐LucasBienert 12
3.1Joists
system
l9,2752
4,64m
hl20
46420
23,2cm
selectedspacing:e 65cm
loads
q 2,0kN/m
g 2,0kN/m
loadsononejoist
q 2,0 ⋅ 0,65 1,3kN/m
g 1,3kN/m
internalforces
maxM 2 ⋅ 0,125 ⋅ 1,3 ⋅ 4,64 7,0 kNm
reqW 700/0,5 1400cm
selecteddimensions
b/h 14/24e 65cm
I 16128 cm
W 1344 cm
deformation
maxδ2 ⋅ 1,3/100 ⋅ 46476,8 ⋅ 1000 ⋅ 16128
0,973cm
l/250 464/250 1,86cm
maxreactionforces
A 0,5 ⋅ 1,3 ⋅ 4,64 3,02kN
A 0,5 ⋅ 1,3 ⋅ 4,64 3,02kN
A 6,03kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 13
3.2Joists
system
l 2,10m
loads
q 2,0kN/m
g 2,0kN/m
loadsononejoist
q 2,0 ⋅ 0,65 1,3kN/m
g 1,3kN/m
selectedspacing:e 65cm
selecteddimensions
b/h 14/24e 65cm
I 16128cm
W 1344cm
joist3.2isnotdecisive,thesamedimensionsareselectedasforjoist3.1
maxreactionforces
A 0,5 ⋅ 1,3 ⋅ 2,1 1,37kN
A 0,5 ⋅ 1,3 ⋅ 2,1 1,37kN
A 2,73kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 14
2.2Beam
system
l 4,47m forsimplicity,anaveragespaniscalculated
loads
g3,020,65
4,65kN/m
q 4,65kN/m
[email protected] 0,65misthespacingofthefloorjoists,
thereactionforcesareconvertedtodistributedloads
internalforces
maxmomentinthefirstfield
maxM 0,078 0,100 ⋅ 4,65 ⋅ 4,47 16,54kNm
reqW 1654/0,5 3308cm
correspondingmomentatthesupportB
M 0,105 0,053 ⋅ 4,65 ⋅ 4,47 14,7kNm
maxmomentatthesupport
maxM 0,105 0,12 ⋅ 4,65 ⋅ 4,47 20,9kNm
reqW 2090/0,5 4181cm
selecteddimensions
b/h 16/42I 98784 cm
W 4704 cm
a)FrameConstruction
PreliminaryDesign‐LucasBienert 15
deformation
maxδ2 ⋅ 4,65/100 ⋅ 44776,8 ⋅ 1000 ⋅ 98784
147016 ⋅ 1000 ⋅ 98784
⋅ 447
0,489 0,186 0,30cm
l/250 447/250 1,79cm
substitutesystem:
maxreactionforces
A 0,395 ⋅ 4,65 ⋅ 4,47 8,2kN
A 0,447 ⋅ 4,65 ⋅ 4,47 9,3kN
A 17,5kN
B 1,132 ⋅ 4,65 ⋅ 4,47 23,5kN
B 1,218 ⋅ 4,65 ⋅ 4,47 25,3kN
B 48,8kN
C 0,974 ⋅ 4,65 ⋅ 4,47 20,2kN
C 1,167 ⋅ 4,65 ⋅ 4,47 24,3kN
C 44,5kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 16
2.1Beam
system
l 4,47m averagespan
loads
g3,020,65
4,65kN/m
q 4,65kN/m
dimensions
b/h 16/42I 98784cm
W 4704cm
beam2.1isnotdecisive,thesamedimensionsareselectedasforbeam2.2
a)FrameConstruction
PreliminaryDesign‐LucasBienert 17
maxreactionforces
A 0,395 ⋅ 4,65 ⋅ 4,47 8,2kN
A 0,447 ⋅ 4,65 ⋅ 4,47 9,3kN
A 17,5kN
B 1,132 ⋅ 4,65 ⋅ 4,47 23,5kN
B 1,218 ⋅ 4,65 ⋅ 4,47 25,3kN
B 48,8kN
C 0,974 ⋅ 4,65 ⋅ 4,47 20,2kN
C 1,167 ⋅ 4,65 ⋅ 4,47 24,3kN
C 44,5kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 18
2.3Beam
system
l 4,47m averagespan
loads
g1,370,65
2,1kN/m
q 2,1kN/m
dimensions
b/h 16/42I 98784cm
W 4704cm
beam2.3isnotdecisive,thesamedimensionsareselectedasforbeam2.2
a)FrameConstruction
PreliminaryDesign‐LucasBienert 19
maxreactionforces
A 0,395 ⋅ 2,1 ⋅ 4,47 3,7kN
A 0,447 ⋅ 2,1 ⋅ 4,47 4,2kN
A 7,9kN
B 1,132 ⋅ 2,1 ⋅ 4,47 10,6kN
B 1,218 ⋅ 2,1 ⋅ 4,47 11,4kN
B 22,1kN
C 0,974 ⋅ 2,1 ⋅ 4,47 9,1kN
C 1,167 ⋅ 2,1 ⋅ 4,47 11,0kN
C 20,1kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 20
7Diaphragm
system
windload windfromthefrontbecomesdecisive
maxw D E 1,044 ⋅ 0,8 0,571,43kN/m
w 1,15 ⋅ 1,43 ⋅ 3,195 5,25kN/m
h 3,195 mistheheightofonestorey theverticalcarriersinthefaçade(6)in
betweenthebeams2.4aresingle‐spanbeams;toaccountforcontinuityeffects,afactorof1,15isadded
internalforces
|P | |P |5,25 ⋅ 22,34
8/20,65 15,9kN
V5,25 ⋅ 22,34
258,6 kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 21
8Frame
system
windload windfromthefrontbecomesdecisive
maxw D E 1,044 ⋅ 0,8 0,571,43kN/m
internalforces
normalforces[kN]
a)FrameConstruction
PreliminaryDesign‐LucasBienert 22
2.4Beam(Front)
Thebeam2.4onthefrontofthebuildingissubjectedmultipleloads:
horizontalbendingfromthewind verticalbendingfromtheself‐weightofthefaçade compressionortensionaspartofthediaphragm
Windfromthefrontbecomesdecisive.
system
loads
self‐weightofthefaçade(vertical)
g 1kN/m
g 1,15 ⋅ 1 ⋅ 3,195 3,67kN/m
windload(windfromthefront,windareaD,horizontal)
w D 1,044 ⋅ 0,8 0,84kN/m
w 1,15 ⋅ 0,84 ⋅ 3,195 3,09kN/m
compressionfromthediaphragm
|P | 15,9kN
factor1,15toaccountforcontinuityeffects
dimensions
b/h 16/42A 672cm W 4704cm
W 1792cm
thesamedimensionsareselectedasforbeam2.2
a)FrameConstruction
PreliminaryDesign‐LucasBienert 23
internalforces
windload
maxM 4,41kNm
self‐weightofthefaçade
maxM 5,24kNm
σ4411792
5244704
15,9672
0,38kN/cm
0,5kN/cm
Forthewindload,thebeamisbentarounditsweakaxis(z)andfortheself‐weightofthefaçadearounditsstrongaxis(y).
maxreactionforces
windload
A 5,46kN
B 14,55kN
C 14,5kN
self‐weightofthefaçade
A 6,49kN
B 17,3kN
C 17,2kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 24
2.4Beam(Side)
Thebeam2.4onthesideofthebuildingissubjectedmultipleloads:
horizontalbendingfromthewind verticalbendingfromtheself‐weightofthefaçade compressionor tensionaspartof the frame(togetherwith theoutercolumnsand the
diagonals)
Windfromthefrontbecomesdecisive.
system
globalsystem(frame)
localsystem
loads
self‐weightofthefaçade(vertical)
g 1kN/m
g 1,15 ⋅ 1 ⋅ 3,195 3,67kN/m
factor1,15toaccountforcontinuityeffects
a)FrameConstruction
PreliminaryDesign‐LucasBienert 25
windload(windfromthefront,windareaAandB,horizontal)
w A 1,2 ⋅ 1,044 1,25kN/m
w 1,15 ⋅ 1,25 ⋅ 3,195 4,59kN/m
w B 0,8 ⋅ 1,044 0,84kN/m
w 1,15 ⋅ 0,84 ⋅ 3,195 3,09kN/m
dimensions
b/h 16/42A 672cm W 4704cm
W 1792cm
thesamedimensionsareselectedasforbeam2.2
internalforces
windload
maxM 7,94kNm
self‐weightofthefaçade
maxM 5,87kNm
normalcompressionforcefromtheframe
N 243kN
check
σ7941792
5874704
243672
0,93kNcm
0,5kN/cm
woodhasgoodstressredistributionproperties,whicharenotconsideredhere,theresultisthereforeacceptedforthepreliminarydesign
forthewindload,thebeamisbentarounditsweakaxis(z)andfortheself‐weightofthefaçadearounditsstrongaxis(y)
a)FrameConstruction
PreliminaryDesign‐LucasBienert 26
maxreactionforces
windload
A 8,55kN
B 21,5kN
C 9,94kN
self‐weightofthefaçade
A 6,59kN
B 20,1kN
C 11,3kN
a)FrameConstruction
PreliminaryDesign‐LucasBienert 27
1Columns
loads
self‐weightandliveload
reactionforcesofthebeams
windload(windfromthefront,windareaD+E)
horizontalwindforce
W 1319kN
W 1319/2 659,5kN oneframetakeshalfthetotalwindforce
bendingmomentofthecantileverbeam
M 1,37 ⋅ 27076 37094kNm
M 37094/2 18547kNm oneshearframetakeshalfthetotalmoment
internalforces
self‐weightandliveload theloadperstoreyN isaddedupfortheroofandthe14storeyswithareductionfactorα 0,74fortheliveload
a)FrameConstruction
PreliminaryDesign‐LucasBienert 28
column load 1.1 N , 2 ⋅ 23,5 47,0kN
N , 2 ⋅ 25,3 50,6kNN 47,0 ⋅ 15 50,6⋅ 1 14 ⋅ 0,74 1600 kN
[email protected](eachcolumncarriestheloadfromtwobeams)
1.2 N , 8,2 6,49 6,59 21,3 kNN , 9,3kNN 21,3 ⋅ 15 9,3⋅ 1 14 ⋅ 0,74 425,1 kN
[email protected] [email protected](front) [email protected](side)
1.3 N , 2 ⋅ 8,2 20,1 36,5 kNN , 2 ⋅ 9,3 18,6kNN 36,5 ⋅ 15 18,6⋅ 1 14 ⋅ 0,74 758,8 kN
[email protected] [email protected](side)
1.4 N , 8,2 3,7 11,3 23,2 kNN , 9,3 4,2 13,5kNN 23,2 ⋅ 15 13,5⋅ 1 14 ⋅ 0,74 501,4 kN
[email protected][email protected] [email protected](side)
windload
Theframesconsistoftwohalfframeswithdiagonalsthatareconnectedviathebeams2.4.
columns1.2,1.4
N18547/29,275
1000kN
column1.3
N 1000/2 500 kN
thenormalforcesinthecolumnsareestimated:themomentisdistributedoverthetwohalfframes,whereapairofforcescreatesthereactionmoment
a)FrameConstruction
PreliminaryDesign‐LucasBienert 29
This table sums up the results for all columns. The required cross‐sections are calculatedconsideringafactorof0,7forthecompressioncapacitytoaccountforbuckling.
column self‐weight andliveload[kN]
windload[kN] totalload[kN] A [cm
1.1 1600 0 1600 45711.2 425,1 1000 1425,1 40721.3 758,8 500 1258,8 35971.4 501,4 1000 1501,4 4290
selecteddimensions
b/h 40/120A 4800cm
inthefirststep,allcolumnshavethesamedimensions
Withthoseestimateddimensionsandtheestimateddimensionsofthediagonals(seebelow),asimpletwo‐dimensionalframeworkanalysisisconductedtoobtainmoreaccurateresultsfortheforces due to the wind. The results are shown in the following table. The dimensions of thecolumnsareadjusted.
1.step
column self‐weight andliveload[kN]
windload[kN] totalload[kN] A [cm selecteddimensions
1.1 1600 0 1600 4571 40/1201.2 425,1 636,6 1062 3034 40/801.3 758,8 232,3 991 2831 40/801.4 501,4 815,1 1317 3763 40/120
2.step
Theanalysisisrepeatedwiththenewdimensionswhichleadstothefollowingfinalresults(cf.8Frame).
column self‐weight andliveload[kN]
windload[kN] totalload[kN] A [cm selecteddimensions
1.1 1600 0 1600 4571 40/1201.2 425,1 613,7 1039 2968 40/801.3 758,8 185,5 944 2698 40/801.4 501,4 839,1 1341 3830 40/120
The cross‐section of the column can decrease over the height of the building because of thedecreasing loads. Assuming the loads due to the self‐weight and the life load (N) to decreaselinearlyandtheloadsduetothewind(M)todecreasequadratically,thefollowingcross‐sectionsarecalculated:
a)FrameConstruction
PreliminaryDesign‐LucasBienert 30
column1.1 column1.2 column1.3 column1.4storeyno M N b/h b/h b/h b/h‐ [%] [%] [cm/cm] [cm/cm] [cm/cm] [cm/cm]
0 100,00 100,00 40/120 40/80 40/80 40/1201 87,11 93,33 40/120 40/80 40/80 40/1202 75,11 86,67 40/120 40/80 40/80 40/1203 64,00 80,00 40/120 40/80 40/80 40/1204 53,78 73,33 40/100 40/60 40/60 40/805 44,44 66,67 40/100 40/60 40/60 40/806 36,00 60,00 40/100 40/60 40/60 40/807 28,44 53,33 40/100 40/60 40/60 40/808 21,78 46,67 40/60 40/40 40/40 40/609 16,00 40,00 40/60 40/40 40/40 40/6010 11,11 33,33 40/60 40/40 40/40 40/6011 7,11 26,67 40/60 40/40 40/40 40/6012 4,00 20,00 40/40 40/40 40/40 40/4013 1,78 13,33 40/40 40/40 40/40 40/4014 0,44 6,67 40/40 40/40 40/40 40/4015 0,00 0,00 40/40 40/40 40/40 40/40
Note that thecolumns1.2,1.3and1.4onthesidescannotbesmaller than40/60becausethebeamsareattachedtothem.
a)FrameConstruction
PreliminaryDesign‐LucasBienert 31
4Diagonal
Thediagonalsarepartoftheframesandthusresponsibleforthetransferofthewindloads.
system
angleofthediagonals
α arctan4 ⋅ 3,1959,275
54°
h 3,195 mistheheightofonestorey
loads
bendingmomentatthesupport
M 18547kNm
calculationofthewindloadsseeabove
simplifiedconstantwindpressure
w 2 ⋅ 18547/50,92 14,3kN/m
bendingmomentatthetopendofthediagonal
M12⋅ 14,3 ⋅
34⋅ 50,92 10428 kNm
forsimplicity,thewindpressureisconvertedintoanequivalentconstantload
internalforces
normalforceinthecolumnatthebottomendofthediagonal(seeabove)
N18547/29,275
1000kN
normalforceinthecolumnatthetopendofthediagonal
N10428/29,275
562 kN
tocalculatetheforceinthediagonal,thenormalforcesinthecolumnsatitsbottomend(atthesupport)andatitstopendareestimated
a)FrameConstruction
PreliminaryDesign‐LucasBienert 32
forceinthediagonal
F1000 562cos 54
745kN
A745
0,7 ⋅ 0,52129cm
factor0,7toaccountforbuckling
selecteddimensions
b/h 48/48
Thesimpletwo‐dimensionalframeworkanalysisleadstomoreaccurateresults(cf.above).
(…)
finalresults
F 512,2kN
A 1463cm
b/h 40/40
a)FrameConstruction
PreliminaryDesign‐LucasBienert 33
5StructuralSheathingoftheFloors
Thesheathingofthefloorshastwomainfunctions:
provide shear stiffness for the floor diaphragm (shear in the vertical sections, i.e.perpendiculartothesurfaceofthesheathing)
carrytheliveloadfromthefloor,spanningbetweenthefloorjoists
system
loads
windload(windfromthefront)
w 5,25kN/m
liveload
q 2,0kN/m
cf.diaphragm
internalforces
shear
V5,25 ⋅ 22,34
258,6kN
l 20,65 6 ⋅ 0,4 18,25m
v58,618,25
3,21kN/m
theshearforceVisdistributedoverthelengthofthefloor(columnsmustbesubtracted)
reqt3,21/1000,15
0,21cm preliminarydesignshearstrength
σ , 1,5 N/mm
a)FrameConstruction
PreliminaryDesign‐LucasBienert 34
bending
l 0,65m
M2 ⋅ 0,65
80,106kNm/m
thespanofthesheathingequalsthespacingofthesecondarybeams
reqW0,106 ⋅ 100
0,813,3cm /m
reqt13,3 ⋅ 6100
0,90cm
deformation
limitation:δ l/250
δ2/100 ⋅ 6576,8 ⋅ 400 ⋅ I
65/250
reqI 44,7cm /m
reqt44,7 ⋅ 12100
1,75cm
preliminarydesignbendingstrength
σ , 8
selecteddimension
t 18mm
indirectcomparison,thebendingisclearlydecisiveandtheshearalmostneglectable
a)FrameConstruction
PreliminaryDesign‐LucasBienert 35
6VerticalFaçadeCarriers
system
h 3,195m
carriersspacing
e 60cm
loads
q 1,044kN/m
c A 1,2
w 1,2 ⋅ 1,044 1,25kN/m
loadsononecarrier
w 0,6 ⋅ 1,25 2,0kN/m
internalforces
maxM2,0 ⋅ 3,195
82,55kNm
reqW 255/0,5 510cm
reqb510 ⋅ 616
12,0 cm
selecteddimensions
b/h 12/16e 60cm
W 512cm
theheightofthecarrierequalsthethicknessofthefaçade,whichagainequalsthebreadthoftheouterprimarybeams(cf.e.g.2.4),i.e.16cm
a)FrameConstruction
PreliminaryDesign‐LucasBienert 36
ConnectionsOverview
Thisisanoverviewofallconnections.Someconnectionsareshownindetailinthenextsections(markedinboldfont),theotherconnectionsfollowthesameprinciples.
connection b/hconnection loads typeoffastener
capacityperfastener *
numberoffasteners
beam/column2.2/1.1middle
120/42 2 ⋅ 48,897,6 kN
M20bolt 13,2kN 11M20
2.2/1.3side 40/42 2 ⋅ 17,535,0 kN
M20bolt 13,2kN 4M20
2.1 2.3/1.4side
80/42 17,5 7,925,4 kN
M20bolt 13,2kN 2M20
2.1 2.4/1.2front
40/42 18,5 6,4925 kN
M20bolt 13,2kN 2M20
2.1 2.4/1.4front
120/42 44,5 17,261,7 kN
M20bolt 13,2kN 5M20
2.1 2.4/1.3front
80/42 48,8 17,366,1 kN
M20bolt 13,2kN 5M20
2.4/1.2side 40/42 6,59 kN v8,55 kN h
Ø8screw 3,2kN 3up 2down
2.4/1.3side 40/42 20,1 kN v21,5 kN h
Ø8screw 3,2kN 9up 5down
2.4/1.4side 40/42 11,3 kN v9,94 kN h
Ø8screw 3,2kN 5up 3down
diagonal/column4/1.2 ‐ 530,9 kN M20dowel 17,6kN 2x10M20
3steelplates
4/1.4 ‐ 454,0 kN M20dowel 17,6kN 2x10M203steel
platessheathing/joists5/3 ‐ 0,19 kN/m Ø3nails 0,32kN 1nail/mjoists/beam3/2 ‐ 3,92 kN Ø3,4nails 0,4kN 2x5nails
steelangle
* per2shearplanesforboltsanddowels
a)FrameConstruction
PreliminaryDesign‐LucasBienert 37
ConnectionBeam2.2toColumn1.1
Fortheconnectionsbetweenthebeamsandthecolumns,M20boltsareused.
system
availablespace
A 120 ⋅ 42 5040cm
requiredspaceperboltM20
A 30 ⋅ d 30 ⋅ 2,0 120cm
maxn5040120
42
loads
F 2 ⋅ 48,8 97,6kN [email protected]
check
capacityperbolt(doubleshear)
F 4,4 ⋅ d 4,4 ⋅ 2,0 17,6kN
capacityat90°tothegrain
F 190360
⋅ 17,6 13,2kN
reqn97,613,2
7,4
selectedconnectors
11 M20
a)FrameConstruction
PreliminaryDesign‐LucasBienert 38
ConnectionOuterBeam2.4ontheSidetoColumn1.3
Fortheconnectionsoftheouterbeamsonthesidetothecolumns,fullythreadedscrewsØ8mmareused.Thescrewscarryloadsinaxialdirection.Boththeverticalloadsfromtheself‐weightofthefaçadeandthehorizontalloadsfromthewindsuctionmustbeconsidered.Thescrewsthatgoat45°upwardscarrytheverticalloads,whileanequalamountofupwardanddownwardscrewscarrythehorizontalloads.
system
availablespace
A 40 ⋅ 42 1680cm
requiredspaceperscrew
A 60 ⋅ d 60 ⋅ 0,8
38,4cm
maxn168038,4
43
principleoftheforcedistributionintheconnection
loads
self‐weightofthefaçade(vertical)
F 20,1kN
inthedirectionofthescrew
F20,1sin 45
28,4kN
[email protected]‐weightofthefaçade
windloads(horizontal)
F 21,5kN
inthedirectionofthescrew
F21,5sin 45
30,4kN
check
a)FrameConstruction
PreliminaryDesign‐LucasBienert 39
capacityperscrew
F 5 ⋅ d 5 ⋅ 0,8 3,2kN
reqn28,43,2
9
reqn30,43,2
10 5 5
selectedconnectors
9up 5 down∅8
a)FrameConstruction
PreliminaryDesign‐LucasBienert 40
ConnectionDiagonal4toColumn1.2
Thediagonalsareinthesamelayerasthecolumnsandareconnectedtothemdirectlyviasteelplatesinsidethewood.Asfasteners,M20steeldowelsareused.
system
requiredspaceperdowel
A 30 ⋅ d 30 ⋅ 2,0 120cm
loads
maxtensionsforceinthediagonal
F 530,9kN
check
capacityperdowel(2shearplanes)
F 4,4 ⋅ 2 17,6kN
capacityfor6shearplanes
F 3 ⋅ 17,6 52,8 kN
3steelplatesareusedinsidethewood,giving6shearplanesintotal
thewidthofthesinglewoodlayersisb 40/4 10cmandshouldnotbesmallerthanmin b 5 ⋅ d 5 ⋅ 210 cm
capacityatanangle theangleofthediagonalsisα 54°(cf.4diagonal)
a)FrameConstruction
PreliminaryDesign‐LucasBienert 41
F 136360
⋅ 52,8 47,5kN
25%highercapacitywithsteelplates
F 1,25 ⋅ 47,5 59,4kN
reqn530,959,4
9 → 10
seln 10
reqA 10 ⋅ 30 ⋅ 2 1200cm
withsteelplatesthecapacityisapproximately25%higher
checkofthesteelplates:
F530,93
177kN
b 35,2 3 ⋅ 2 29cm
reqt 177/29/14 0,44cm
selectedthicknessofthesteelplate
t 6mm
preliminary design strength of steelσ 14 kN/cm
a)FrameConstruction
PreliminaryDesign‐LucasBienert 42
ConnectionSheathing5toJoists3
Thesheathingisconnectedtothejoistswithnails.
system
loads
windload(windfromthefront)
w 5,25kN/m
cf.diaphragm7 windfromthesidesisnotdecisive
internalforces
forceinone“row”ofjoists
F 5,25 ⋅ 0,65 ⋅ 1,15 3,92kN
v3,9220,65
0,19kN/m
capacitypernailØ3,0mm
F 3,5 ⋅ 0,3 0,32kN
reqn0,190,32
1/m
spacingofthesecondarybeamse 65 cm
factor1,15toaccountforcontinuityeffects
a)FrameConstruction
PreliminaryDesign‐LucasBienert 43
ConnectionJoists3toBeams2
Thejoistsareconnectedtothebeamswithsteelanglesandnails.
system
loads
windload(windfromthefront)
w 5,25kN/m
cf.diaphragm7 windfromthesidesisnotdecisive
internalforces
forceinone“row”ofjoists
F 5,25 ⋅ 0,65 ⋅ 1,15 3,92kN
spacingofthesecondarybeamse65 cm
continuityfactor1,15
Thisforcemustbetransferredfromtheouterbeam2.1toeachjoist3.
capacitypernailØ3,4mm
F 3,5 ⋅ 0,34 0,4kN
reqn3,920,4
10 5 5
Thisappliestoallconnectionsofallsecondarybeams3withtheouterprimarybeam2.1.
Atallinnerconnection,withthebeams2.2and2.3,noloadtransferisnecessary,onlyareducedamountofnailsisselectedtoavoidlargedeformationdifferencesbetweenthedifferentbeams.
n 6 3 3
b)PanelConstruction
PreliminaryDesign‐LucasBienert 44
b)PanelConstructionElementReferenceOverview
referenceno element page
1 floorjoists
1.1 floorjoistsmodules3,4 45
1.2 floorjoistsmodules1,2,6,7 46
1.3 floorjoistsmodules5 47
2 floorbeam 59
3 walls/studs 48
4 wallsheathing 57
5 columns 62
6 beam 60
connectionsoverview 63
b)PanelConstruction
PreliminaryDesign‐LucasBienert 45
1.1FloorJoists
system
l 5,15m
hl20
51520
25,8cm
loads
q 2,0kN/m
g 2,0kN/m
loadsononejoist
q 2,0 ⋅ 0,6 1,2kN/m
g 1,2kN/m
selectedspacing:e 60cm
internalforces
maxM2 ⋅ 1,2 ⋅ 5,15
87,96kNm
reqW 796/0,5 1592cm
selecteddimensions
b/h 16/24e 60cm
I 18432 cm
W 1536 cm
deformation
maxδ2 ⋅ 1,2/100 ⋅ 51576,8 ⋅ 1000 ⋅ 18432
1,19cm
l/250 515/250 2,06cm
maxreactionforces
A 1,2 ⋅ 5,15/2 3,1 kN
A 1,2 ⋅ 5,15/2 3,1kN
A 6,2kN
b)PanelConstruction
PreliminaryDesign‐LucasBienert 46
1.2FloorJoists
system
l 4,215m
loads
q 2,0kN/m
g 2,0kN/m
loadsononebeam
q 2,0 ⋅ 0,6 1,2kN/m
g 1,2kN/m
selectedspacing:e 60cm
selecteddimensions
b/h 16/24e 60cm
I 18432cm
W 1536cm
joists1.2arenotdecisive,thesamedimensionsareselectedasforjoist1.1
maxreactionforces
A 1,2 ⋅ 4,215/2 2,5kN
A 1,2 ⋅ 4,215/2 2,5kN
A 5,0kN
b)PanelConstruction
PreliminaryDesign‐LucasBienert 47
1.3FloorJoists
system
l 2,1m
loads
q 2,0kN/m
g 2,0kN/m
loadsononebeam
q 2,0 ⋅ 0,6 1,2kN/m
g 1,2kN/m
selectedspacing:e 60cm
selecteddimensions
b/h 16/24e 60cm
I 18432cm
W 1536cm
joists1.3arenotdecisive,thesamedimensionsareselectedasforjoist1.1
maxreactionforces
A 1,2 ⋅ 2,1/2 1,3 kN
A 1,2 ⋅ 2,1/2 1,3kN
A 2,6kN
b)PanelConstruction
PreliminaryDesign‐LucasBienert 48
3Walls/Studs
ThefullstabilityanalysiswasperformedusingExcel(seeappendix).Here,onlythewallsWy1andWy8areshown.Wy8hasthehighestvertical load,whileWy1hasthehighesthorizontalwindload.
Basedontheloadsonthewalls,theloadsontheindividualstudswerecalculatedasthereactionforcesofacontinuousbeam(seesystemsketchbelow).
system
h 3,195m
loads
windloads(windfromthefront)
W 1319
M 37094kNm
windloads(windfromtheside,windareaD+E)
totalhorizontalwindforce
W 1275kN
bendingmomentofthecantileverbeam
M 34982kNm
internalforces
wallWy8forwindfromthefront
shearforce
v 20,39kN/m
normalforce(compression)
n 394,3kN/m
horizontalwindload
w 0
fordetailedcalculations,seeExcelanalysis
b)PanelConstruction
PreliminaryDesign‐LucasBienert 49
wallWy1forwindfromtheback
shearforce
v 6,22kN/m
normalforce(compression)
n 237,5kN/m
horizontalwindload
w 0,98kN/m
In the endof thepreliminarydesign, twodifferent thicknessesof thewallsweredetermined:20cm(withtheloadbearingstudsbeingb/h 20/20cm)and28cm(withtheloadbearingstudsbeingb/h 28/28cm).Becauseofthedecreasingloadswiththeheightofthebuilding,thecross‐sectionsofthestudscouldbeadaptedinthehigherstoreys.Assumingtheloadsduetotheself‐weightandthelifeload(N)todecreaselinearlyandtheloadsduetothewind(M)todecreasequadratically,thefollowingcross‐sectionsarecalculated:
storeyno M N b/h b/h
‐ [%] [%] [cm/cm] [cm/cm]
0 100,00 100,00 20/20 28/281 87,11 93,33 20/20 28/282 75,11 86,67 20/20 28/283 64,00 80,00 20/20 28/284 53,78 73,33 20/20 28/285 44,44 66,67 16/16 24/246 36,00 60,00 16/16 24/247 28,44 53,33 16/16 24/248 21,78 46,67 16/16 24/249 16,00 40,00 16/16 24/2410 11,11 33,33 16/8 20/2011 7,11 26,67 16/8 20/2012 4,00 20,00 16/8 20/2013 1,78 13,33 16/8 20/2014 0,44 6,67 16/8 20/2015 0,00 0,00 16/8 20/20
b)PanelConstruction
PreliminaryDesign‐LucasBienert 50
3.y8StudsinWally3
system
loads
self‐weightofthewall
g 1,0kN/m
over14storeys
g 1 ⋅ 14 ⋅ 3,195 44,7kN/m
floorload
p3,20,6
⋅ 153,20,6
⋅ 1 14 ⋅ 0,74
136kN/m
totalverticalload(constant)
n 44,7 136 181kN/m
[email protected] theloadperstoreyisaddedupforthe
roofandthe14storeyswithareductionfactorα 0,74fortheliveload
b)PanelConstruction
PreliminaryDesign‐LucasBienert 51
windloads(linear)
windfromthefront
maxn 178kN/m
minn 213kN/m
windfromtheback
maxn 213kN/m
minn 178kN/m
windfromtheleftside
maxn minn 9,2kN/m
windfromtherightside
maxn minn 9,2kN/m
cf.Excelanalysis
b)PanelConstruction
PreliminaryDesign‐LucasBienert 52
internalforces
windfromthefront
windfromtheback
windfromtheleftside
windfromtherightside
For each loadbearing studs (each support), the required cross‐section is calculated using thepreliminarydesignstrengthoftimberof5 N/mm witha factorof0,8toaccountforbuckling.Sincethesheathingpreventsthestudsfrombucklinginonedirectionandalsomakesbucklingintheotherdirectionmoredifficultbyeffectivelyconnectingtheindividualstuds,ahigherbucklingfactorischosen.
selecteddimensions
b/t 28/28A 784 cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 53
studno 1 2 3 4 5 6 7 8 9 10 11 12maxforce[kN]
116 295 111 275 281 230 311 292 150 222 232 78
reqb[cm] 10 26 10 25 25 21 28 26 13 20 21 7selectedb[cm]
28 28 28 28 28 28 28 28 28 28 28 28
b)PanelConstruction
PreliminaryDesign‐LucasBienert 54
3.y1StudsinWally1
system
loads
self‐weightofthewall
g 1,0kN/m
over14storeys
g 1 ⋅ 14 ⋅ 3,195 44,7kN/m
floorload
p2,50,6
⋅ 152,50,6
⋅ 1 14 ⋅ 0,74
109,8kN/m
totalverticalload(constant)
n 44,7 109,8 154,5kN/m
[email protected] theloadperstoreyisaddedupforthe
roofandthe14storeyswithareductionfactorα 0,74fortheliveload
windloads(linear)
windfromthefront
maxn 83kN/m
minn 133kN/m
windfromtheback
maxn 133kN/m
minn 83kN/m
cf.Excelanalysis
b)PanelConstruction
PreliminaryDesign‐LucasBienert 55
windfromtheleftside
maxn minn 40kN/m
windfromtherightside
maxn minn 40kN/m
horizontalwindpressure(windfromtheback)
c B 1,2
q 1,044kN/m
|w| 1,2 ⋅ 1,044 1,25kN/m
windpressureperstud
|w| 1,15 ⋅ 1,25 ⋅ 0,61 0,88kN/m
spacingofthestudse 0,61cm continuityfactor1,15
internalforces
windfromthefront
windfromtheback
windfromtheleftside
windformtherightside
b)PanelConstruction
PreliminaryDesign‐LucasBienert 56
bendingmomentfromwindpressure
M 0,88 ⋅ 3,195 /8 1,12kNm
selecteddimensions
b/t 28/28A 784cm W 3659 cm
studno 1 2 3 4 5 6maxforce[kN]
139 295 145 182 258 129
reqb[cm] 12 26 13 16 23 12selectedb[cm]
28 28 28 28 28 28
stresscheck
σ295784
1123659
0,38 0,03 0,41kN/cm
0,8 ⋅ 0,5 0,40kN/cm
thewindpressurehasalmostnoeffectcomparedtothehighnormalforces
b)PanelConstruction
PreliminaryDesign‐LucasBienert 57
4Sheathing
Thesheathingisconnectedtothestudsandtheblockingvianails.
WallWx15becomesdecisiveforthesheathingforwindfromtheleftside.
system
loads
v 21,4kN/m
cf.Excelanalysis
nails
selected:Ø5mm
shearcapacitypernail
F 3,5 ⋅ d 3,5 ⋅ 0,5 0,88kN
reqn 20,4/0,88 23,3/m
selectednails
Ø5mml 100 mme 8 cm in2rows
minimumdistances(α 0°)
betweennailsin1row a 12 ⋅ 0,5 6 cm 8 cm
betweentherows a 5 ⋅ 0,5 2,5cm
tothesideedges a 5 ⋅ 0,5 2,5cm
requiredbreadthofthewoodenmembers(studsandblocking)
reqb 3 ⋅ 2,5 7,5 cm
selectedblocking
b 16cmhacc.tothewidthofthewall
attheseamsofthesheathingpanels,theblockingmustbeb 2 ⋅ 7,5 15cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 58
selectedsheathing
reqt21,4/1000,15
1,43cm
t 18mm
preliminarydesignshearstrengthσ , 1,5 N/mm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 59
2FloorBeam
The floor beams are only connected to the load‐bearing studs. The floor beam in axis 1–3/Abecomesdecisive.
system
loads
g2,50,6
4,2kN/m
q 4,2kN/m
thesingleforcesfromthefloorjoistsareconvertedtoaconstantcontinuousload
internalforces
maxmomentatsupportD
maxM 2,38kNm
reqW2380,5
476 cm
selecteddimensions
b/h 10/24I 11520cm
W 960 cm
A 240 cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 60
6Beam
system
l 9,275/4 2,32m
loads
g2,50,6
4,17kN/m
q2,50,6
4,17kN/m
[email protected] spacingofthefloorjoists=0,6m
internalforces
maxmomentinthefirstfield
maxM 0,08 0,101 ⋅ 4,17 ⋅ 2,32 4,06kNm
reqW4060,5
812cm
correspondingmomentatthesupport:
M 0,1 0,05 ⋅ 4,17 ⋅ 2,32 3,37kNm
maxmomentatthesupportB
maxM 0,10 0,117 ⋅ 4,17 ⋅ 2,32 4,87kNm
reqW4870,5
974 cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 61
selecteddimensions
b/h 10/24W 960 cm
I 11520 cm
deformation
maxδ2 ⋅ 4,17/100 ⋅ 23276,8 ⋅ 1000 ⋅ 11520
33716 ⋅ 1000 ⋅ 11520
⋅ 232
0,273 0,098 0,18cm
l/250 232/250 0,93cm
substitutesystem:
b)PanelConstruction
PreliminaryDesign‐LucasBienert 62
5Columns
system
loads
g2,50,6
⋅ 15 62,5kN/m
q2,50,6
⋅ 1 14 ⋅ 0,74 47,3kN/m
[email protected] spacingofthefloorjoists=0,6m theloadsareaddedupoverall15
storeys
internalforces
columnsA,D
N 0,400 ⋅ 62,5 ⋅ 2,32 0,45 ⋅ 47,3 ⋅ 2,32 107,4kN
reqA107,40,7 ⋅ 0,5
306,9cm
columnsB,C
N 1,100 ⋅ 62,5 ⋅ 2,32 1,2 ⋅ 47,3 ⋅ 2,32 291,2kN
reqA291,20,7 ⋅ 0,5
832 cm
selecteddimensions
columnsA,D
2 b/h 16/28A 2 ⋅ 448cm
columnsB,C
2 b/h 28/28A 2 ⋅ 784 cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 63
ConnectionsOverview
connection b/hoverlap loads typeoffastener
capacityperfastener
numberoffasteners
anchoring3/3 ‐ 134,7kN M20
dowels22,0kN * 2 7M20
steelplatefloorjoists/floorbeam1/2 16/24 6,2kN v screwsØ8 3,2kN 3Ø8floorbeam/studs2/3 24/28 26,6kN M20
dowels8,0kN ** 5M20
* doubleshear** singleshear
b)PanelConstruction
PreliminaryDesign‐LucasBienert 64
Anchoring
Fortension,wallWx7becomesdecisiveforwindfromtheleftside.
Thehold‐downdeviceconsistsofasteelplateinsideeachload‐bearingstudandsteeldowels.
system
globalsystem
localsystem
b)PanelConstruction
PreliminaryDesign‐LucasBienert 65
loads
self‐weightofthewall
g 1,0kN/m
over14storeys
g 1 ⋅ 14 ⋅ 3,195 44,7kN/m
liveload
p 0
totalverticalload(constant)
n 0,5 ⋅ 44,7 22,4kN/m tobeonthesafeside,only50%oftheself‐weightandliveloadsareconsidered
windloads(linear)
windfromtheleftside
maxn 140,1kN/m
minn 78,3kN/m
cf.Excelanalysis
internalforces
windfromtheleftside
maxF 134,7kN
steeldowels
capacityperdowelM20(doubleshearwithinnersteelplate)
F 4,4 ⋅ 2 17,6kN
25%highercapacitywithsteelplates
F 1,25 ⋅ 17,6 22,0kN
req n134,722
7
b)PanelConstruction
PreliminaryDesign‐LucasBienert 66
ConnectionFloorJoists1toFloorBeam2
ThisconnectionusesscrewsØ8mmthataresubjectedtotension.
system
loads
F 6,2kN [email protected]
internalforces
forceinthescrewsatanangleof45°
S6,2sin 45
8,77kN
check
capacityperscrew
F 5 ⋅ d 5 ⋅ 0,8 3,2kN
reqn8,773,2
3
requiredspace
reqA 3 ⋅ 60 ⋅ 0,8 115,2cm
availablespace
A 16 ⋅ 24 384cm
theavailablespaceequalsthecross‐sectionofthefloorjoist16/24
b)PanelConstruction
PreliminaryDesign‐LucasBienert 67
ConnectionFloorBeam2toStuds3
Forthisconnection,steeldowelsM20areused,thatdon’tinterferewiththehold‐downdevice(cf.anchoring).Thefloorbeaminaxis1–3/Aisdecisive.
system
loads
F 15,5kN
check
capacityperdowel(singleshear)
F 2 ⋅ d 2 ⋅ 2 8kN
at90°tothegrainforthefloorbeam
F 190360
⋅ 8 6kN
req n15,56
3
requiredspace
reqA 3 ⋅ 30 ⋅ 2 360cm
b)PanelConstruction
PreliminaryDesign‐LucasBienert 68
availablespace
A 24 ⋅ 20 480cm
floorbeam:14/24 stud: 20/20 (in the upper storeys, the
cross‐section28/28isreducedto20/20)
c)CLTConstruction
PreliminaryDesign‐LucasBienert 69
c)CLTConstructionElementReferenceOverview
referenceno element page
1 floorslab 70
2,3 floorslab 71
4 floorslab 72
5 Walls 73
anchoring 78
Remarks
Thefloorslabsaredesignedassumingtheyonlyspaninonedirection.Thisisonthesafeside,astheyactuallyspaninbothdirectionssothatamulti‐axialstateofstresscanbedevelopedandloadscanbebetterdistributed.
The load transfer from the floor slabs to the walls is calculated in a simplified manner bydeterminingalengthofinfluenceforeverywallandtransferringtheloadsfromtheslabwithintheresultingareaofinfluencetothewall.
Tocalculatetheshearforcesandbendingmomentsinthewallsfromthewindloads,astabilityanalysiswasperformedusingExcel.Onlyselectedwallsarepresentedinthisreport.
c)CLTConstruction
PreliminaryDesign‐LucasBienert 70
1FloorSlab
Itcouldbeseenfromthesheathingofthediaphragmintheframeconstructionthatshearfromhorizontalwindforcescanbeneglectedforthepreliminarydesign.
system
l8,5952
4,30m
themiddlesupportisthebeam6
loads
g 2,0kN/m
q 2,0kN/m
selecteddimensions
t 145mm19 44 19 44 19
maxreactionforces
A 0,375 ⋅ 2,0 ⋅ 4,30 3,2kN/m
A 0,438 ⋅ 2,0 ⋅ 4,30 3,8kN/m
A 7,0kN/m
B 1,25 ⋅ 2,0 ⋅ 4,3 10,75kN/m
B 1,25 ⋅ 2,0 ⋅ 4,3 10,75kN/m
B 21,5kN/m
pressureperpendiculartothegrain
endwallsupports
reqt6,99/1000,15
0,47cm
middlewallsupport
reqt21,5/1000,15
1,43cm
preliminarydesigncompressionstrengthperpendiculartothegrainσ , 1,5N/mm
c)CLTConstruction
PreliminaryDesign‐LucasBienert 71
2,3FloorSlab
system
l 5,15m
loads
g 2,0kN/m
q 2,0kN/m
selecteddimensions
t 170 mm19 31,5 19 31,5 19 31,5 19
maxreactionforces
A 2,0 ⋅ 4,30/2 4,3 kN/m
A 2,0 ⋅ 4,30/2 4,3kN/m
A 8,6kN/m
pressureperpendiculartothegrain
wallsupports
reqt8,6/1000,15
0,57cm
preliminarydesigncompressionstrengthperpendiculartothegrainσ , 1,5N/mm
c)CLTConstruction
PreliminaryDesign‐LucasBienert 72
4FloorSlab
system
l 2,10m
loads
g 2,0kN/m
q 2,0kN/m
selecteddimensions
t 95mm19 19 19 19 19
forfiresafetyreasons,aslabwithatleast5layersisselected
maxreactionforces
A 2,0 ⋅ 2,1/2 2,1kN/m
A 2,0 ⋅ 2,1/2 2,1kN/m
A 4,2kN/m
pressureperpendiculartothegrain
wallsupports
reqt4,2/1000,15
0,28cm
preliminarydesigncompressionstrengthperpendiculartothegrainσ , 1,5N/mm
c)CLTConstruction
PreliminaryDesign‐LucasBienert 73
5Walls
The full stabilityanalysiswasperformedusingExcel (seeappendix).Here,only thewally5 isshown.
system
globalloads
windloads(windfromthefront)
W 1319
M 37094kNm
windloads(windfromtheside)
W 1275kN
M 34982kNm
Intheendofthepreliminarydesign,wallswiththreedifferentthicknesseswereused:95mm,120mmand259mm.Toachieveamoreeconomicdesign,thethicknessesweredecreasedinthehigherfloors,makinguseofthedecreasingloads.Assumingtheloadsduetotheself‐weightandthelifeload(N)todecreaselinearlyandtheloadsduetothewind(M)todecreasequadratically,thefollowingthicknessesarecalculated:
c)CLTConstruction
PreliminaryDesign‐LucasBienert 74
storeyno M N t t t‐ [%] [%] [mm] [mm] [mm]
0 100,00 100,00 95 120 2591 87,11 93,33 95 120 2592 75,11 86,67 95 120 2593 64,00 80,00 95 120 2594 53,78 73,33 95 120 2595 44,44 66,67 95 95 1706 36,00 60,00 95 95 1707 28,44 53,33 95 95 1708 21,78 46,67 95 95 1709 16,00 40,00 95 95 17010 11,11 33,33 95 95 9511 7,11 26,67 95 95 9512 4,00 20,00 95 95 9513 1,78 13,33 95 95 9514 0,44 6,67 95 95 9515 0,00 0,00 95 95 95
c)CLTConstruction
PreliminaryDesign‐LucasBienert 75
5.y5OuterWall
system
loads
self‐weightofthewall
g 1,0kN/m
over15storeys
g 1 ⋅ 15 ⋅ 3,195 47,9kN/m
floorload
g 2,0kN/m
q 2,0kN/m
c)CLTConstruction
PreliminaryDesign‐LucasBienert 76
loadfactortoaccountfortheopenings
k20,65
5,125 1,1 2,6 1,1 5,1251,37
lengthofinfluence
l4,382
2,19m
g 1,37 ⋅ 2 ⋅ 2,19 6,01kN/m
q 1,37 ⋅ 2 ⋅ 2,19 6,01kN/m
over15storeys
g 15 ⋅ 6,01 90,15kN/m
q 15 ⋅ 0,74 ⋅ 6,01 66,71kN/m
totalverticalload(constant)
n 47,9 90,15 66,71 204,8 kN/m
fromfloorslab1 theloadperstoreyisaddedupforthe
roofandthe14storeyswithareductionfactorα 0,74fortheliveload
windload(linear)
windfromtheback
maxn 76,5kN/m
minn 133,4kN/m
v 9,2kN/m
cf.Excelanalysis
windpressure
c 0,8
q 1,044kN/m
w 0,8 ⋅ 1,044 0,835kN/m
internalforces
totalnormalforce
n 204,8 133,4 338,2kN/m
reqt338,2/1000,7 ⋅ 0,5
9,66cm factor0,7toaccountforbuckling
bendingmomentduetowind
M 0,835 ⋅ 3,195 /8 1,07kNm/m
selecteddimensions
t 95mmA 100 ⋅ 9,5 950cm /m
W 100 ⋅ 9,5 /6 1504cm /m
c)CLTConstruction
PreliminaryDesign‐LucasBienert 77
check
normalforce
σ338,2950
1071504
0,36 0,07
0,43kN/cm
0,8 ⋅ 0,5 0,40kN/m
thewindpressurehasalmostnoinfluencecomparedwiththehighverticalloads
0,8isusedasafactortoaccountforbucklingbecauseitisassumedthatmassiveelementsarelesspronetobuckling
shearforces
τ9,2
100 ⋅ 9,50,01kN/cm
0,06kN/cm
c)CLTConstruction
PreliminaryDesign‐LucasBienert 78
Anchoring
Fortensilestresses,wally7becomesdecisiveforwindfromthefront.Toconnecttwowallsontopofeachother,aninternalsteelplate isput intoagroovecut intothewallsoverthewholelengthusingsteeldowelsM20.
system
loads
n 132,4kN/m
tobeonthesafeside,only50%oftheself‐weightandliveloadsareconsidered
steeldowels
capacity per dowel M20 (double shear withsteelplate)
F 1,25 ⋅ 4,4 ⋅ 2 22kN
reqn 132,4/22 7/m
7M20/m
Appendix
PreliminaryDesign‐LucasBienert 79
Appendix
Attachments
stabilityanalysisforthepanelconstruction(XLSX) calculationofthepanelstuds(XLSX) stabilityanalysisfortheCLTconstruction(XLSX) technicalplansfortheframeconstructionPa1.1,Pa2(PDF) technicalplansforthepanelconstructionPb1–Pb3,Pa4.1(PDF) technicalplansfortheCLTconstructionPc1–Pc2,Pc3.1(PDF)
Appendix
PreliminaryDesign‐LucasBienert 80
b)PanelConstruction
SummaryoftheStabilityAnalysis
Appendix
PreliminaryDesign‐LucasBienert 81
Appendix
PreliminaryDesign‐LucasBienert 82
Appendix
PreliminaryDesign‐LucasBienert 83
Appendix
PreliminaryDesign‐LucasBienert 84
Appendix
PreliminaryDesign‐LucasBienert 85
LoadsandSelectedCross‐SectionsoftheStuds
Utilisingthesymmetryofthebuilding,onlyonehalfofthewallsisconsidered.
Appendix
PreliminaryDesign‐LucasBienert 86
Appendix
PreliminaryDesign‐LucasBienert 87
Appendix
PreliminaryDesign‐LucasBienert 88
c)CLTConstruction
SummaryoftheStabilityAnalysis
Appendix
PreliminaryDesign‐LucasBienert 89
Appendix
PreliminaryDesign‐LucasBienert 90
Appendix
PreliminaryDesign‐LucasBienert 91
EurocodeDesign
TableofContents
EurocodeDesign‐LucasBienert 2
TableofContentsTableofContents...............................................................................................................................................................2
General...................................................................................................................................................................................4
Remarks............................................................................................................................................................................4
Materials...........................................................................................................................................................................4
Software............................................................................................................................................................................4
Literature..........................................................................................................................................................................4
Loadcasesandcombinations...................................................................................................................................4
DesignFactors................................................................................................................................................................5
a)FrameConstruction.....................................................................................................................................................6
3.1RoofJoists.................................................................................................................................................................7
3.1FloorJoists................................................................................................................................................................9
3.2Joists.........................................................................................................................................................................11
2.2RoofBeam..............................................................................................................................................................12
2.2FloorBeam............................................................................................................................................................17
2.1RoofBeam..............................................................................................................................................................20
2.1FloorBeam............................................................................................................................................................21
2.3Beams......................................................................................................................................................................22
7Diaphragm.................................................................................................................................................................23
8Frame...........................................................................................................................................................................24
2.4Beam(front).........................................................................................................................................................25
2.4Beam(side)...........................................................................................................................................................29
1.1Column....................................................................................................................................................................36
1.4Column....................................................................................................................................................................38
4Diagonal......................................................................................................................................................................40
5StructuralSheathingoftheFloors...................................................................................................................42
6VerticalFaçadeCarriers......................................................................................................................................45
ConnectionBeam2.2toColumn1.1..................................................................................................................47
ConnectionOuterBeam2.4ontheSidetoColumn1.3..............................................................................50
ConnectionDiagonal4toColumn1.2or1.4...................................................................................................53
b)PanelConstruction....................................................................................................................................................56
1.1RoofJoists..............................................................................................................................................................57
1.1FloorJoists.............................................................................................................................................................59
1.2RoofJoists..............................................................................................................................................................61
1.2FloorJoists.............................................................................................................................................................62
TableofContents
EurocodeDesign‐LucasBienert 3
1.3RoofJoists..............................................................................................................................................................63
1.3FloorJoists.............................................................................................................................................................64
2RoofBeam..................................................................................................................................................................65
2FloorBeam................................................................................................................................................................70
3Studs............................................................................................................................................................................75
6Beam(Roof)..............................................................................................................................................................77
6Beam(Floor)............................................................................................................................................................82
5Columns......................................................................................................................................................................87
Anchoring......................................................................................................................................................................90
ConnectionRoofJoists1toRoofBeam2.........................................................................................................92
ConnectionFloorJoists1toFloorBeam2......................................................................................................94
ConnectionFloorBeam2toStuds3..................................................................................................................95
ConnectionRoofBeam2toStuds3....................................................................................................................98
c)CLTConstruction.......................................................................................................................................................99
1RoofSlab..................................................................................................................................................................100
1FloorSlab................................................................................................................................................................104
5.x9OuterWall.........................................................................................................................................................106
AnchoringWall5.y3...............................................................................................................................................108
Appendix..........................................................................................................................................................................110
Attachments..............................................................................................................................................................110
a)FrameConstruction..........................................................................................................................................110
b)PanelConstruction............................................................................................................................................116
c)CLTConstruction................................................................................................................................................121
General
EurocodeDesign‐LucasBienert 4
General
Remarks
TheintentionoftheECdesignistoprovethefeasibilityofthestructures.Adescriptionofthebuildingandtheloadbearingconceptofthethreestructuresisincludedinthedocumentationofthepreliminarydesign.
Onlythedecisiveloadcombinationsareshowninthisdocument,acompletesummaryofallthecheckswasdoneinExcel.AnextractoftheExceldocumentcanbefoundintheappendix,thefilesthemselvesareattachedelectronically.Technicalreferenceplansarealsoattached(cf.appendix).
Materials
woodenmembers(beams,studs,floorjoists,…):glulamGL24ho propertiesaccordingtoEN14080
structuralsheathing:plywoodFinnforestSprucekonstruksjonskryssfiner(distributedunderthename“GranIII/III”byFritzøeEngrosAS)
o typeEN636‐1(plywoodforuseindryclimate)o propertiesaccordingtothetechnicalapproval[3]
masstimber:CLTKL‐träbyMartinsons(distributedbySplitkonAS)o propertiesaccordingtothetechnicalapproval[1]
Software
Stab2d(simpleanalysisprogramfortwo‐dimensionalframeworks) MicrosoftEXCEL© DlubalRFEM©
Extracts from the calculationswith EXCEL andRFEM can be found in the appendix. The filesthemselvesareattachedelectronically.
Literature
[1] TekniskGodkjenningMartinsonsKL‐trä[2] BautabellenfürIngenieure,20thedition2012[3] TekniskGodkjenningFinnforestSprucekonstruksjonskryssfiner[4] EN1990[5] EN1991‐1‐1[6] EN1995‐1‐1[7] TechnicalDataSheetSimpsonStrongtieBT4Bjelkebærere
Loadcasesandcombinations
ForconsistentnumberingbetweenthisdesignandtheRFEM‐models,alwaystwonumbersarereservedforloadcasesandcombinationsthatincludewindloads,oneforwindfromthefront(orback)andoneforwindfromtheside.IntheFEM‐analysiswithRFEM,onlywindfromthefrontandfromtheleftsidewasexamined,makinguseofthesymmetryofthebuilding.
General
EurocodeDesign‐LucasBienert 5
loadcase description symbol durationLC1 self‐weight G permanentLC2 snow S short‐termLC3/4 wind W instantaneousLC5 liveload Q medium‐term
loadcom‐binationno
combinationrule duration
CO1 E 1,2 ⋅ G permanentCO2 E 1,2 ⋅ G 1,5 ⋅ Q medium‐termCO3 E 1,2 ⋅ G 1,5 ⋅ S 1,5 ⋅ 0,7 ⋅ Q short‐termCO4 E 1,2 ⋅ G 1,5 ⋅ Q 1,5 ⋅ 0,7 ⋅ S short‐termCO5/6 E 1,2 ⋅ G 1,5 ⋅ W 1,5 ⋅ 0,7 ⋅ S 1,5 ⋅ 0,7 ⋅ Q instantaneousCO7/8 E 1,2 ⋅ G 1,5 ⋅ Q 1,5 ⋅ 0,7 ⋅ S 1,5 ⋅ 0,6 ⋅ W instantaneousCO9/10 E 1,2 ⋅ G 1,5 ⋅ S 1,5 ⋅ 0,6 ⋅ W 1,5 ⋅ 0,7 ⋅ Q instantaneousCO11/12 E 1,0 ⋅ G 1,5 ⋅ W instantaneous
DesignFactors
SinceCLTisnotconsideredintheEC,thesamedesignfactorsareappliedasforglulam.
materialsafetyfactors
material γglulam 1,25CLT 1,25plywood 1,2connections 1,3
modificationfactors
material loadduration climateclass1 2 3
glulam,CLT,plywood permanent 0,6 0,6 0,5medium‐term 0,8 0,8 0,65short‐term 0,9 0,9 0,7instantaneous 1,1 1,1 0,9
deformationfactors
material climateclass1 2 3
glulam,CLT 0,6 0,8 2,0plywood 0,8 ‐ ‐
a)FrameConstruction
EurocodeDesign‐LucasBienert 6
a)FrameConstructionElementReferenceOverview
referenceno element page
1 columns
1.1 innercolumns 36
1.2 cornercolumns ‐
1.3 sidecolumns ‐
1.4 sidecolumns 38
2 beams
2.1 beam 20
2.2 beam 12
2.3 beam 22
2.4 beam 25
3 joists
3.1 joists 7
3.2 joists 11
4 diagonal 40
5 structuralsheathingofthefloors 42
6 verticalfaçadecarriers 45
7 diaphragm 23
8 frame 24
connections 47
Remarks
In comparison to the preliminarydesign, the cross‐sections of the columnswere reduced.Allcolumnsarenowb/h 40/40cm,exceptforthoseatthesides.Becausethebeamsareattachedtothem,theyneedalargercross‐section:b/h 40/60cm.Becausetheconnectionstothebeamsrequirethisspace,thecross‐sectionsarenotdecreasedovertheheightofthebuilding.
a)FrameConstruction
EurocodeDesign‐LucasBienert 7
3.1RoofJoists
system
l9,2752
4,64m
cross‐section
b/h 14/24
e 65cm
A 336cm
I 16128cm
W 1344cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g 1,65kN/m
s 3,8kN/m
q 1044N/m
c I 0,2
g 1,65 ⋅ 0,65 1,07 kN/m
s 3,8 ⋅ 0,65 2,47 kN/m
w 0,2 ⋅ 1,044 0,21 kN/m
q H 0,75kN/m
w 0,21 ⋅ 0,65 0,14 kN/m
q 0,75 ⋅ 0,65 0,49 kN/m
Q 1,5 kN
ULSCO3
k 0,9
p 1,20 ⋅ 1,07 1,50 ⋅ 2,47 4,99kN/m
Q 1,50 ⋅ 0,70 ⋅ 1,5 1,58kN
M 0,125 ⋅ 4,99 ⋅ 4,64 0,250 ⋅ 1,58 ⋅ 4,6415,26kNm
σ15261344
1,14kN/cm
f 0,9 ⋅2,41,15
1,88 kN/cm
thesingleloadQbecomesdecisive
a)FrameConstruction
EurocodeDesign‐LucasBienert 8
η1,141,88
0,60 1,0
V 0,500 ⋅ 4,99 ⋅ 4,64 1,58 13,16 kN
nolateraltorsionalbuckling,becausethesheathingsecuresthecompressionflangeofthejoists
τ 1,5 ⋅13,16
0,67 ⋅ 3360,088kN/cm
f 0,9 ⋅0,351,15
0,27kN/cm
η0,0880,27
0,32 1,0
τ 1,5 ⋅V
k ⋅ A
(forrectangularcross‐sections)
SLSCO9/10
w ,
1,07100 ⋅ 464
76,8 ⋅ 1150 ⋅ 161280,349 cm
w , 0,804cm
w , 0,044cm
w ,1,5 ⋅ 464
48 ⋅ 1150 ⋅ 161280,168cm
wp ⋅ l
76,8 ⋅ EI
(forsinglespanbeams)
instantaneousdeformation
w0,349 0,804 0,6 ⋅ 0,044 0,7 ⋅ 0,1681,30cm
maxw464300
1,55cm
η1,301,55
0,84 1,0
characteristiccombinationacc.toEC5‐1‐12.2.3(2):
w w w , ψ , w ,
finaldeformation
w0,349 ⋅ 1 0,6 0,804 ⋅ 1 0,2 ⋅ 0,60,044 ⋅ 0,6 0 ⋅ 0,6 0,168
⋅ 0,7 0,3 ⋅ 0,6 1,63cm
maxw464150
3,09cm
η1,633,09
0,53 1,0
simplifiedapproachacc.toEC5‐1‐12.2.3(5):
w w , w , , w , ,
w , w , 1 k
w , , w , , 1 ψ , k
w , , w , , ψ , ψ , k
maxreactionforces
A 0,500 ⋅ 1,07 ⋅ 4,64 2,49kN
A 0,500 ⋅ 2,47 ⋅ 4,64 5,73kN
A 0,500 ⋅ 0,14 ⋅ 4,64 0,31kN
A 0,500 ⋅ 0,49 ⋅ 4,64 1,13kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 9
3.1FloorJoists
system
l9,2752
4,64m
cross‐section
b/h 14/24
e 65cm
A 336cm
I 16128cm
W 1344cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g 1,34kN/m
s 0
q 0
g 1,34 ⋅ 0,65 0,87 kN/m
q A 2,5kN/m
q 2,5 ⋅ 0,65 1,63 kN/m
Q 2 kN
ULSCO2
k 0,8
p 1,20 ⋅ 0,87 1,05kN/m
q 1,5 ⋅ 1,63 2,44kN/m
M 0,125 ⋅ 1,05 2,44 ⋅ 4,64 9,37kNm
σ9371344
0,70kN/cm
f 0,8 ⋅2,41,15
1,67 kN/cm
η0,701,67
0,42 1,0
V 0,500 ⋅ 1,05 2,44 ⋅ 4,64 8,08 kN
nolateraltorsionalbuckling,becausethesheathingsecuresthecompressionflangeofthejoists
a)FrameConstruction
EurocodeDesign‐LucasBienert 10
τ 1,5 ⋅8,08
0,67 ⋅ 3360,054kN/cm
f 0,8 ⋅0,351,15
0,24kN/cm
η0,0540,24
0,22 1,0
SLSCO7/8
w ,
0,87100 ⋅ 464
76,8 ⋅ 1150 ⋅ 161280,283cm
w , 0
w , 0
w , 0,529cm
instantaneousdeformation
w 0,283 0,529 0 0 0,81cm
maxw464300
1,55cm
η0,811,55
0,53 1,0
finaldeformation
w 0,283 ⋅ 1 0,6 0,529 ⋅ 1 0,3 ⋅ 0,6 0 0 1,08cm
maxw464150
3,09cm
η1,083,09
0,35 1,0
maxreactionforces
A 0,500 ⋅ 0,87 ⋅ 4,64 2,02kN
A 0
A 0
A 0,500 ⋅ 1,63 ⋅ 4,64 3,77kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 11
3.2Joists
Thejoists3.2havethesamedimensionsandloadsasthecorrespondingjoists3.1,buttheirspanisonly2,10m.Acheckisthereforenotnecessary.
a)FrameConstruction
EurocodeDesign‐LucasBienert 12
2.2RoofBeam
system
maxl 5,15m
cross‐section
b/h 16/42
A 672cm
I 98784cm
W 4704cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g2,490,65
3,7 ⋅ 0,16 ⋅ 0,42 4,08kN/m
s5,730,65
8,82kN/m
w0,310,65
0,48kN/m
q1,130,65
1,74kN/m
[email protected] thesingleforcesfromthejoistsare
convertedintoaconstantdistributedload
reactionforces,internalforcesanddeformations
thereactionforces,internalforcesanddeformationsarecalculatedbymeansofdimensionless“1”‐loads
theactualinternalforcesarethencalculatedbymultiplyingtherealloadwiththecorrespondingresultfromthe“1”‐loads
a)FrameConstruction
EurocodeDesign‐LucasBienert 13
constantload
loadingandreactionforces
bendingmoment
shearforce
deformations
a)FrameConstruction
EurocodeDesign‐LucasBienert 14
unfavourableloads
loadingandreactionforces
bendingmoment
shearforce
loadingandreactionforces
a)FrameConstruction
EurocodeDesign‐LucasBienert 15
loadingandreactionforces
deformations
ULSCO3
k 0,9
p 1,20 ⋅ 4,08 1,50 ⋅ 8,82 18,12kN/m
q 1,5 ⋅ 0,7 ⋅ 1,74 1,83kN/m
M 1,884 ⋅ 18,12 2,457 ⋅ 1,83 38,66 kNm
σ38664704
0,82kN/cm
f 0,9 ⋅2,41,15
1,88 kN/cm
η0,821,88
0,44 1,0
V 2,572 ⋅ 18,12 2,871 ⋅ 1,83 51,86kN
τ 1,5 ⋅51,86
0,67 ⋅ 6720,17kN/cm
f 0,9 ⋅0,351,15
0,27kN/cm
η0,170,27
0,64 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
SLSCO9/10
w , 4,08 ⋅ 0,0254 0,104cm
w , 8,82 ⋅ 0,0254 0,224cm
w , 0,48 ⋅ 0,0254 0,012cm
a)FrameConstruction
EurocodeDesign‐LucasBienert 16
w , 1,74 ⋅ 0,0435 0,076cm
instantaneousdeformation
w0,104 0,224 0,6 ⋅ 0,012 0,7 ⋅ 0,0760,39cm
maxw515300
1,72cm
η0,391,72
0,23 1,0
finaldeformation
w0,104 ⋅ 1 0,6 0,224 ⋅ 1 0,2 ⋅ 0,60,012 ⋅ 0,6 0 ⋅ 0,6 0,076 ⋅ 0,7 0,3
⋅ 0,6 0,49cm
maxw515150
3,43cm
η0,493,43
0,14 1,0
maxreactionforces
A 4,08 ⋅ 1,768 7,21kN
A 8,82 ⋅ 1,768 15,59kN
A 0,48 ⋅ 1,768 0,86kN
A 1,74 ⋅ 1,892 3,29kN
B 4,08 ⋅ 4,714 19,22kN
B 8,82 ⋅ 4,714 41,56kN
B 0,48 ⋅ 4,714 2,28kN
B 1,74 ⋅ 5,268 9,17kN
C 4,08 ⋅ 4,691 19,12kN
C 8,82 ⋅ 4,691 41,36kN
C 0,48 ⋅ 4,691 2,27kN
C 1,74 ⋅ 5,446 9,48kN
maxinternalforces
V , 2,612 ⋅ 4,08 10,65kN
V , 2,612 ⋅ 8,82 23,03kN
V , 2,612 ⋅ 0,48 1,27kN
V , 2,701 ⋅ 1,74 4,70kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 17
2.2FloorBeam
system
maxl 5,15m
cross‐section
b/h 16/42
A 672cm
I 98784cm
W 4704cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g2,020,65
3,7 ⋅ 0,16 ⋅ 0,42 3,36kN/m
s 0
w 0
q3,770,65
5,8kN/m
internalforces
cf.2.2RoofBeam
ULSCO2
k 0,8
p 1,20 ⋅ 3,36 4,03 kN/m
a)FrameConstruction
EurocodeDesign‐LucasBienert 18
q 1,5 ⋅ 5,8 8,7kN/m
M 1,884 ⋅ 4,03 2,457 ⋅ 8,7 29,0 kNm
σ29004704
0,62kN/cm
f 0,8 ⋅2,41,15
1,67 kN/cm
η0,621,67
0,37 1,0
V 2,572 ⋅ 4,03 2,871 ⋅ 8,7 35,34kN
τ 1,5 ⋅35,34
0,67 ⋅ 6720,12kN/cm
f 0,8 ⋅0,351,15
0,24kN/cm
η0,120,24
0,49 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
SLSCO7/8
w , 3,36 ⋅ 0,0254 0,085cm
w , 0
w , 0
w , 5,8 ⋅ 0,0435 0,252cm
instantaneousdeformation
w 0,085 0,252 0 0 0,34cm
maxw515300
1,72cm
η0,341,72
0,20 1,0
finaldeformation
w0,085 ⋅ 1 0,6 0,252 ⋅ 1 0,3 ⋅ 0,60 0 0,434cm
maxw515150
3,43cm
η0,433,43
0,13 1,0
maxreactionforces
A 3,36 ⋅ 1,768 5,94kN
A 0
A 0
a)FrameConstruction
EurocodeDesign‐LucasBienert 19
A 5,8 ⋅ 1,892 10,97kN
B 3,36 ⋅ 4,714 15,83kN
B 0
B 0
B 5,8 ⋅ 5,268 30,55kN
C 3,36 ⋅ 4,691 15,75kN
C 0
C 0
C 5,8 ⋅ 5,446 31,59kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 20
2.1RoofBeam
cf.2.2RoofBeam
a)FrameConstruction
EurocodeDesign‐LucasBienert 21
2.1FloorBeam
cf.2.2FloorBeam
a)FrameConstruction
EurocodeDesign‐LucasBienert 22
2.3Beams
Thebeams2.3havethesamedimensionsandspansasthecorrespondingbeams2.2,buttheirloadissmallerbecausetheygettheloadsfromthejoists3.2whichhaveasmallerspan.Acheckisthereforenotnecessary.
a)FrameConstruction
EurocodeDesign‐LucasBienert 23
7Diaphragm
system
windload windfromthefrontbecomesdecisive
maxw D E 1,044 ⋅ 0,8 0,571,43kN/m
w 1,15 ⋅ 1,43 ⋅ 3,195 5,25kN/m
h 3,195 mistheheightofonestorey theverticalcarriersinthefaçade(6)in
betweenthebeams2.4aresingle‐spanbeams;toaccountforcontinuityeffects,afactorof1,15isadded
internalforces
|P | |P |5,25 ⋅ 22,34
8/20,65 15,9kN
V5,25 ⋅ 22,34
258,6 kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 24
8Frame
system
windload windfromthefrontbecomesdecisive
maxw D E 1,044 ⋅ 0,8 0,571,43kN/m
internalforces
normalforcesN[kN]
a)FrameConstruction
EurocodeDesign‐LucasBienert 25
2.4Beam(front)
system
maxl 5,15m
cross‐section
b/h 16/42
A 672cm
I 98784cm
W 4704cm
i42
√1212,1cm
I 14336cm
W 1792cm
i16
√124,6cm
ih
√12
I 0,140 ⋅ 42 ⋅ 16 24084cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
E , 9600N/mm
G , 540N/mm
k 0,6
I 0,140 ⋅ h ⋅ b
(forrectangularcross‐sections)
a)FrameConstruction
EurocodeDesign‐LucasBienert 26
loads
g 0,5kN/m g 1,15 ⋅ 3,195 ⋅ 0,5 3,7 ⋅ 0,16 ⋅ 0,422,09 kN/m
s 0
q 1044N/m
c D 0,8
windfromthefront
w 0,8 ⋅ 1,044 0,84 kN/m
N , 15,9kN
q 0
w 1,15 ⋅ 3,195 ⋅ 0,84 3,07kN/m
reactionforces,internalforcesanddeformations
cf.2.2RoofBeamforverticalloads becauseofthesmallermomentofinertiaforhorizontalloads(I ),thedeformationsdue
tohorizontalloadsmustbecalculatedseparately
constantload
loadingandreactionforces
deformation
ULSCO5/6
k 1,1
p 1,20 ⋅ 2,09 0 2,50kN/m
w 1,50 ⋅ 3,07 4,60kN/m
N 1,50 ⋅ 15,9 23,85kN
q 0
M 1,884 ⋅ 2,50 0 4,72kNm
a)FrameConstruction
EurocodeDesign‐LucasBienert 27
σ472474
0,10kN/cm
M 1,884 ⋅ 4,60 8,68kNm
σ8681792
0,48kN/cm
σ23,85672
0,035kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
lateraltorsionalbuckling
l 5,15m
σ ,π ⋅ √960 ⋅ 14336 ⋅ 54 ⋅ 24084
515 ⋅ 47045,49kN/cm
λ ,2,45,49
0,66 0,75
k 1,0
flexuralbuckling
λ51512,1
42,6
λ ,42,6π
⋅249600
0,677
k 0,5 ⋅ 1 0,1 ⋅ 0,677 0,3 0,677
0,748
k ,1
0,748 0,748 0,6770,938
λ5154,6
112,0
λ ,112π
⋅249600
1,78
k 0,5 ⋅ 1 0,1 ⋅ 1,78 0,3 1,782,16
k ,1
2,16 2,16 1,780,296
a)FrameConstruction
EurocodeDesign‐LucasBienert 28
η0,035
0,938 ⋅ 2,300,10
1,0 ⋅ 2,300,482,30
0,10
1,0
η0,035
0,296 ⋅ 2,300,10
1,0 ⋅ 2,300,482,30
0,27
1,0
V 2,572 ⋅ 2,50 0 6,54kN
τ 1,5 ⋅6,54
0,67 ⋅ 6720,022kN/cm
V 2,572 ⋅ 4,60 12,02kN
τ 1,5 ⋅12,02
0,67 ⋅ 6720,040kN/cm
f 1,1 ⋅0,351,15
0,33kN/cm
η0,022 0,040
0,330,14 1,0
σk , ⋅ f
σ
k ⋅ fσf
1
and
σk , ⋅ f
σ
k ⋅ fσf
1
cf.[2,9.33]
SLSCO9/10
w , , 2,09 ⋅ 0,0254 0,053cm
w , , 0
w , , 3,07 ⋅ 0,1751 0,537cm
w , , 0
instantaneousdeformation
w , 0,053 0 0 0,053cm
w . 0,537cm
w 0,053 0,537 0,54cm
maxw515300
1,72cm
η0,541,72
0,31 1,0
finaldeformation
w , 0,053 ⋅ 1 0,6 0 0 0,085cm
w , 0,537 ⋅ 1 0 0,537cm
w 0,085 0,537 0,54cm
maxw515150
3,43cm
η0,543,43
0,16 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 29
2.4Beam(side)
system
maxl 5,15m
cross‐section
b/h 16/42
A 672cm
I 98784cm
W 4704cm
i42
√1212,1cm
I 14336cm
W 1792cm
i16
√124,6cm
I 0,140 ⋅ 42 ⋅ 16 24084cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
E , 9600N/mm
G , 540N/mm
k 0,6
a)FrameConstruction
EurocodeDesign‐LucasBienert 30
loads
g 0,5kN/m g 1,15 ⋅ 3,195 ⋅ 0,5 3,7 ⋅ 0,16 ⋅ 0,422,09 kN/m
s 0
q 1044N/m
c A 1,2
c B 0,8
windfromthefront
w A 1,2 ⋅ 1,044 1,25kN/m
w B 0,8 ⋅ 1,044 0,84kN/m
N , 243,2kN
q 0
w A 1,15 ⋅ 3,195 ⋅ 1,25 4,60kN/m
w B 1,15 ⋅ 3,195 ⋅ 0,84 3,07kN/m
reactionforces,internalforcesanddeformations
verticalconstantload
loadingandreactionforces
bendingmoment
a)FrameConstruction
EurocodeDesign‐LucasBienert 31
shearforce
deformations
horizontalwindload becausethewindloadisnotconstant,itmustbecalculatedseparately
loading
bendingmoment
a)FrameConstruction
EurocodeDesign‐LucasBienert 32
shearforce
deformation
ULSCO5/6
k 1,1
p 1,20 ⋅ 2,09 0 2,50kN/m
w A 1,50 ⋅ 4,60 6,90kN/m
w B 1,50 ⋅ 3,07 4,60kN/m
N 1,50 ⋅ 243,2 364,8kN
q 0
M 2,442 ⋅ 2,50 0 6,11kNm
σ611474
0,13kN/cm
M 14,59kNm
σ14591792
0,81kN/cm
σ364,8672
0,54kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
lateraltorsionalbuckling
l 4,64m
a)FrameConstruction
EurocodeDesign‐LucasBienert 33
σ ,π ⋅ √960 ⋅ 14336 ⋅ 54 ⋅ 24084
464 ⋅ 47046,09kN/cm
λ ,2,46,09
0,63 0,75
k 1,0
flexuralbuckling
λ46412,1
38,3
λ ,38,3π
⋅249600
0,61
k 0,5 ⋅ 1 0,1 ⋅ 0,61 0,3 0,61
0,702
k ,1
0,702 0,702 0,610,953
λ4644,6
100,9
λ ,100,9π
⋅249600
1,61
k 0,5 ⋅ 1 0,1 ⋅ 1,61 0,3 1,611,86
k ,1
1,86 1,86 1,610,358
η0,54
0,953 ⋅ 2,300,13
1,0 ⋅ 2,300,812,30
0,43
1,0
η0,54
0,358 ⋅ 2,300,13
1,0 ⋅ 2,300,812,30
1,01
1,0
V 2,727 ⋅ 2,50 0 6,82kN
τ 1,5 ⋅6,82
0,67 ⋅ 6720,024kN/cm
V 19,16kN
τ 1,5 ⋅19,16
0,67 ⋅ 6720,065kN/cm
f 1,1 ⋅0,351,15
0,33 kN/cm
a)FrameConstruction
EurocodeDesign‐LucasBienert 34
η0,024 0,065
0,330,21 1,0
SLSCO5/6
w , , 2,09 ⋅ 0,02488 0,053cm
w , , 0
w , , 1,353cm
w , , 0
instantaneousdeformation
w , 0,053 0 0 0,053cm
w . 1,353cm
w 0,053 1,353 1,35cm
maxw464300
1,55cm
η1,351,55
0,88 1,0
finaldeformation
w , 0,053 ⋅ 1 0,6 0 0 0,085cm
w , 1,353 ⋅ 1 0 0,537cm
w 0,085 1,353 1,36cm
maxw464150
3,09cm
η1,363,09
0,44 1,0
maxreactionforces
vertical
B 2,09 ⋅ 5,48 11,43kN
B 0
B 0
B 0
C 2,09 ⋅ 3,442 7,18kN
C 0
C 0
C 0
horizontal
a)FrameConstruction
EurocodeDesign‐LucasBienert 35
B 20,88kN
a)FrameConstruction
EurocodeDesign‐LucasBienert 36
1.1Column
Thecolumn1.1carriesonlytheverticalself‐weightandlifeload,butdoesnottakepartincarryingtheglobalbendingmomentfromthewindloads.ThecolumninaxisBbecomesdecisive.
system
cross‐section
b/h 40/40
A 1600cm
I I 213333cm
i i40
√1211,5cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
loads
g 3,7 ⋅ 0,4 ⋅ 0,4 0,592kN/m self‐weightofthecolumn
N 2 ⋅ 19,22 14 ⋅ 2 ⋅ 15,83 481,6 kN
s 0
N 2 ⋅ 41,56 83,12kN
w 0
N 2 ⋅ 2,28 4,57kN
q 0
N 2 ⋅ 9,17 14 ⋅ 0,74 ⋅ 2 ⋅ 30,55 651,4 kN
[email protected] 2beamsareattachedto1column theloadsareaddedupfortheroofand
14floors
ULSCO2
k 0,8
g 1,2 ⋅ 0,592 0,71 kN/m
N1,2 ⋅ 481,6 0,71 ⋅ 16 ⋅ 3,195 1,5 ⋅ 651,41591,4kN
σ1591,41600
0,99kN/cm
f 0,8 ⋅2,41,15
1,67kN/cm
flexuralbuckling
λ319,511,5
27,8
onthesafeside,theself‐weightofthecolumnisaddedupover16storeys
a)FrameConstruction
EurocodeDesign‐LucasBienert 37
λ27,8π
⋅249600
0,44
k 0,5 ⋅ 1 0,1 ⋅ 0,44 0,3 0,440,604
k1
0,604 0,604 0,440,983
η0,99
0,983 ⋅ 1,670,61 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 38
1.4Column
Thecolumn1.4ispartoftheframethatcarriestheglobalbendingmomentfromthewindloads.
system
cross‐section
b/h 40/40
A 1600cm
I I 213333cm
i i40
√1211,5cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm
loads
g 3,7 ⋅ 0,4 ⋅ 0,4 0,592kN/m
N 19,12 7,18 14 ⋅ 15,75 7,18
347,3kN
s 0
N 41,36kN
w 0
N 839,1kN
q 0
N 9,48 14 ⋅ 0,74 ⋅ 31,59 336,7 kN
[email protected](side) 1beam2.1and1beam2.4areattached
tothecolumn
ULSCO5/6
k 1,1
g 1,2 ⋅ 0,592 0,71kN/m
N1,2 ⋅ 347,3 0,71 ⋅ 16 ⋅ 3,195 1,5 ⋅ 839,11,5 ⋅ 0,7 ⋅ 41,36 1,5 ⋅ 0,7 ⋅ 336,72108,7kN
σ2108,71600
1,32kN/cm
f 1,1 ⋅2,41,15
2,30 kN/cm
a)FrameConstruction
EurocodeDesign‐LucasBienert 39
flexuralbuckling
λ319,511,5
27,8
λ27,8π
⋅249600
0,44
k 0,5 ⋅ 1 0,1 ⋅ 0,44 0,3 0,440,604
k1
0,604 0,604 0,440,983
η1,32
0,983 ⋅ 2,300,58 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 40
4Diagonal
Thediagonalispartoftheframethatcarriestheglobalbendingmomentfromthewindloads.Although the tensile forces in thediagonalsareslightlyhigher, compressionbecomesdecisivebecauseoftheflexuralbuckling.
system
maxl15,792
7,90m
cross‐section
b/h 40/40
A 1600cm
I I 213333cm
i i40
√1211,5cm
material
glulamGL24h
γ 3,7kN/m
f 24N/mm eachdiagonalconsistsoftwoindividualmemberswhichspantwostoreys
loads
g 0
s 0
w 0
N 512,2kN
q 0
see8Frame
ULSCO5/6
k 1,1
N 1,5 ⋅ 512,2 768,3kN
σ768,31600
0,48kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
flexuralbuckling
λ79011,5
68,7
λ68,7π
⋅249600
1,09
a)FrameConstruction
EurocodeDesign‐LucasBienert 41
k 0,5 ⋅ 1 0,1 ⋅ 1,09 0,3 1,091,14
k1
1,14 1,14 1,090,678
η0,48
0,678 ⋅ 2,300,31 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 42
5StructuralSheathingoftheFloors
Intheroof,theverticalloadsarecarriesbythehorizontalcarriersandthejoists,thesheathingdoesnotcarryanyloads.Thehorizontalcarriersrunperpendiculartotheroofjoists,sothattheloadsfromtheroofdonotlieonthesheathing.Onlyinthefloorsthesheathingmustcarrytheverticalloads,self‐weightandlifeload,betweenthejoists.Additionally,italsoisresponsiblefortheshearstiffnessofthediaphragm.
system
globalsystem(diaphragm)
localsystem
l 0,65m
t 18mm
A 180cm/m
I 48,6cm /m
W 54cm /m
a)FrameConstruction
EurocodeDesign‐LucasBienert 43
material
plywood
m 1200Nmm/mm
k 1,0
EI 4320kNmm /mm
k 0,8
the material properties are taken fromthetechnicalapproval[3]
loads
g 1,34kN/m
s 0
w 0
shearfromthediaphragm
l 20,65 6 ⋅ 0,4 18,25m
v58,618,25
3,21kN/m
q A 2,5kN/m
the shear force is distributed over thewholelengthofthebuilding,thecolumnsmust be subtracted because they gothroughthesheathing
ULSCO2
k 0,8
g 1,20 ⋅ 1,34 1,61kN/m
q 1,5 ⋅ 2,5 3,75kN/m
M 0,125 ⋅ 1,61 3,75 ⋅ 0,650,28kNm/m
M 0,8 ⋅1200/1000
1,150,83kNm/m
η0,280,83
0,34 1,0
Theshearloadsfromthediaphragmarenotdecisive,cf.preliminarydesign.
SLSCO7/8
w ,
1,34100 ⋅ 65
76,8 ⋅ 4320/100,072cm
w , 0
w , 0
w ,
2,5100 ⋅ 65
76,8 ⋅ 4320/100,135cm
instantaneousdeformation
w 0,072 0,135 0 0 0,21cm
a)FrameConstruction
EurocodeDesign‐LucasBienert 44
maxw65300
0,22 cm
η0,210,22
0,95 1,0
finaldeformation
w0,072 ⋅ 1 0,8 0,135 ⋅ 1 0,3 ⋅ 0,80 0 0,30cm
maxw65150
0,43cm
η0,300,43
0,68 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 45
6VerticalFaçadeCarriers
system
h 3,195m
cross‐section
b/h 6/16
e 60cm
A 96cm
I 2048cm
W 256cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm E , 11500N/mm k 0,6
loads
g 0
q 1044N/m
c A 1,2
w 1,2 ⋅ 1,044 1,25 kN/m w 1,25 ⋅ 0,6 0,75 kN/m
ULSCO5/6
k 1,1
w 1,50 ⋅ 0,75 1,13kN/m
M 0,125 ⋅ 1,13 ⋅ 3,195 1,44kNm
σ144256
0,56kN/cm
f 1,1 ⋅2,41,15
2,30 kN/cm
η0,562,30
0,24 1,0
V 0,500 ⋅ 1,13 ⋅ 3,195 1,80kN
τ 1,5 ⋅1,80
0,67 ⋅ 960,042kN/cm
f 1,1 ⋅0,351,15
0,33 kN/cm
nolateraltorsionalbuckling,becausethesheathingofthewallssecuresthecarriersfrombothsides
a)FrameConstruction
EurocodeDesign‐LucasBienert 46
η0,420,33
0,13 1,0
SLSCO5/6
w , 0
w , 0
w ,
0,75100 ⋅ 319,5
76,8 ⋅ 1150 ⋅ 20480,433cm
w , 0
instantaneousdeformation
w 0,433cm
maxw319,5300
1,07cm
η0,4331,07
0,41 1,0
finaldeformation
w 0,433 ⋅ 1 0 ⋅ 0,6 0,433cm
maxw319,5150
2,13cm
η0,4332,13
0,20 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 47
ConnectionBeam2.2toColumn1.1
Theconnectionundertheroofbecomesdecisive.
system
angleoftheforcetothegrain
beam:α 90°
column:α 0°
fasteners
11M20bolts
f 240N/mm
f 400N/mm
material
glulamGL24h
ρ 385kg/m
strengthclass4.6
minimumdistances
beam
a 4 cos 90 ⋅ 2,0 8cm
a 4 ⋅ 2,0 8cm
a max 2 2 sin 90 ⋅ 2,0 8; 3 ⋅ 2,0 68cm
a 3 ⋅ 2,0 6cm
column
a 4 cos 0 ⋅ 2,0 10cm
a 4 ⋅ 2,0 8cm
a 3 ⋅ 2,0 6cm
capacityperfastenerpershearplane
a)FrameConstruction
EurocodeDesign‐LucasBienert 48
M , 0,3 ⋅ 400 ⋅ 20 , /1000 289,6 Nm
beam(member1)
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
k 1,35 0,015 ⋅ 20 1,65
f , ,25,26
1,65 ⋅ sin 90 cos 9015,3N/mm
column(member2)
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
β25,2615,3
1,65
F ,
1,15 ⋅2 ⋅ 1,651 1,65
⋅ 2 ⋅ 289,6 ⋅ 1000 ⋅ 15,3 ⋅ 20/100017,1kN
failuremodekbecomesdecisive the axial capacity of the fasteners is
neglected
loads
F 2 ⋅ 19,22 38,4 kN
F 2 ⋅ 41,56 83,1kN
F 2 ⋅ 2,28 4,6kN
F 2 ⋅ 9,17 18,3kN
shearforcesinthebeamattheconnection
V 2 ⋅ 10,65 21,3kN
V 2 ⋅ 23,03 46,1kN
V 2 ⋅ 1,27 2,53kN
V 2 ⋅ 4,70 9,4kN
ULSCO3
k 0,9
F 1,2 ⋅ 38,4 1,5 ⋅ 83,1 1,5 ⋅ 0,7 ⋅ 18,3190,0kN
F . 17,1 ⋅ 11 ⋅ 2 376,0
F , 0,9 ⋅376,01,3
260,3kN
η190,0260,3
0,73 1,0
11boltsand2shearplanes
a)FrameConstruction
EurocodeDesign‐LucasBienert 49
checkfortensionperpendiculartothegraininthebeam
V 1,2 ⋅ 21,3 1,5 ⋅ 46,1 1,5 ⋅ 0,7 ⋅ 9,4104,5kN
F 14 ⋅ 2 ⋅ 160 ⋅ 1 ⋅330
13346
/1000
153,1kN
F 0,9 ⋅153,11,3
106,0kN
η104,5106,0
0,99 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 50
ConnectionOuterBeam2.4ontheSidetoColumn1.3
system
angleofthescrews
α 45°
principleoftheforcedistributionintheconnection
angleoftheforcetothegrain
beam:α 90°
column:α 0°
fasteners
forverticalloads
9screwsØ8mm
n 9 , 7,22
forhorizontalloads
10screwsØ8mm
n 10 , 7,94
the9screwsatthebottomthatgoupwardscarrytheverticalloads,the5upperscrewstogetherwith5ofthelowerscrewscarrythehorizontalloads
f 240N/mm
f 400N/mm
material
glulamGL24h
strengthclass4.6
a)FrameConstruction
EurocodeDesign‐LucasBienert 51
ρ 385kg/m
minimumdistances
a 7 ⋅ 0,8 5,6cm
a 5 ⋅ 0,8 4cm
a 4 ⋅ 0,8 3,2cm
capacityofthescrews
pull‐outoftheshaft
(notdecisive)
tensilecapacityofthescrews
f , f 240N/mm
forverticalloads
F , 7,22 ⋅ 240 ⋅ π ⋅82
/1000 87,2kN
forhorizontalloads
F , 7,94 ⋅ 240 ⋅ π ⋅82
/1000 95,8 kN
fullythreadedscrewsareused,thereforepull‐throughoftheheaddoesnotneedtobeconsidered
loads
vertical
F 11,43kN
horizontal
F 20,88kN
beam2.4ontheside
internalforces
vertical
V 5,94kN
horizontal
V 12,15kN
ULSCO5/6
k 1,1
vertical
F 1,2 ⋅11,43sin 45
19,4kN
F , 1,1 ⋅87,21,3
73,7kN
η19,473,7
0,26
a)FrameConstruction
EurocodeDesign‐LucasBienert 52
horizontal
F 1,5 ⋅20,88sin 45
44,3kN
F , 1,1 ⋅95,81,3
81,1kN
η44,381,1
0,55
η 0,26 0,55 0,81 1,0checkfortensionperpendiculartothegraininthebeam
vertical
V 1,2 ⋅ 5,94 7,13kN
F 14 ⋅ 160 ⋅ 1 ⋅340
13446
/1000 80,9kN
F 1,1 ⋅80,91,3
68,4kN
η7,1368,4
0,10 1,0
horizontal
V 1,5 ⋅ 12,15 18,23kN
F 14 ⋅ 460 ⋅ 1 ⋅80
1816
/1000 81,5kN
F 1,1 ⋅81,51,3
68,9kN
η18,2368,9
0,26 1,0
η 0,10 0,26 0,37 1,0
a)FrameConstruction
EurocodeDesign‐LucasBienert 53
ConnectionDiagonal4toColumn1.2or1.4
Theprinciplethatisshownherecanbeappliedtoallconnectionsofthediagonalwithacolumn.
system
fasteners
10M20dowels
inthediagonal
α 0°
n 5 ⋅ 2 , ⋅136
13 ⋅ 207,93
inthecolumn
α 54°
n 5 ⋅ 2 , ⋅102
13 ⋅ 206,74
f 240N/mm
f 400N/mm
material
glulamGL24h
ρ 385kg/m
strengthclass4.6
minimumdistances
diagonal
a)FrameConstruction
EurocodeDesign‐LucasBienert 54
a 3 2 ⋅ cos 0 ⋅ 2,0 10cm
a 3 ⋅ 2,0 6cm
a max 7 ⋅ 2,0 14; 8 14cm
a 3 ⋅ 2,0 6cm
column
a 3 2 ⋅ cos 54 ⋅ 2,0 9,24cm
a 3 ⋅ 2,0 6cm
amax 2 2 ⋅ sin 54 ⋅ 2,0 6,51; 3 ⋅ 2,0
6 6,51cm
capacityperfastenerpershearplane
M , 0,3 ⋅ 400 ⋅ 20 , /1000 289,6 Nm
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
k 1,35 0,015 ⋅ 20 1,65
f , ,25,26
1,65 ⋅ sin 54 cos 5420,62N/mm
diagonal
F ,
25,26 ⋅ 100 ⋅ 20
⋅ 24 ⋅ 289,6 ⋅ 100025,26 ⋅ 20 ⋅ 100
1 /1000
24,9kN
column
F , 21,0kN
failuremodegbecomesdecisive
dowelshavenoaxialcapacity
loads
F , 530,9kN
V 20,2kN
see8Frame
ULSCO5/6
k 1,1
F 1,5 ⋅ 530,9 796,4kN
diagonal
F . 7,93 ⋅ 6 ⋅ 24,9 1185,8kN
F , 1,1 ⋅1185,81,3
1003,4kN
10boltsand6shearplanes
a)FrameConstruction
EurocodeDesign‐LucasBienert 55
η796,41003,4
0,79 1,0
column
F . 6,74 ⋅ 6 ⋅ 21,0 850,9kN
F , 1,1 ⋅850,91,3
720,0kN
η796,4720,0
1,11 1,0 additionalstrengtheningisrequired,e.g.byfullythreadedscrewsperpendiculartothegraintoincreasethecapacityoftheconnection
checkfortensionperpendiculartothegraininthecolumn
V 1,5 ⋅ 20,2 30,3kN
F 14 ⋅ 400 ⋅ 1 ⋅160
11660
/1000
82,7kN
F 1,1 ⋅82,71,3
70,0kN
η30,370,0
0,43 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 56
b)PanelConstructionElementReferenceOverview
referenceno element page
1 floorjoists
1.1 floorjoistsmodules3,4 57
1.2 floorjoistsmodules1,2,6,7 61
1.3 floorjoistsmodules5 63
2 floorbeam 65
3 walls/studs 75
5 columns 87
6 beam 77
connections 90
Remarks
Forthecalculationoftheinternalforcesinthestuds,theFEsoftwareRFEMwasused.
Comparedtothepreliminarydesign,thecross‐sectionsofthejoists,thebeamsandthecolumnswereadapted.Undertheroof,largercross‐sectionswererequired,whilethecross‐sectionsinthefloorscouldbedecreased.Thestudswerenotchanged.
b)PanelConstruction
EurocodeDesign‐LucasBienert 57
1.1RoofJoists
system
l 5,15m
cross‐section
b/h 16/24
e 60cm
A 384cm
I 18432cm
W 1536cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g 1,69kN/m
s 4,66kN/m
q 1044N/m
c I 0,2
g 1,69 ⋅ 0,6 1,01 kN/m
s 4,66 ⋅ 0,6 2,80 kN/m
w 0,2 ⋅ 1,044 0,21 kN/m
q H 0,75kN/m
w 0,21 ⋅ 0,6 0,13 kN/m
q 0,75 ⋅ 0,6 0,45 kN/m
Q 1,5 kN
ULSCO3
k 0,9
p 1,20 ⋅ 1,01 1,50 ⋅ 2,80 5,41kN/m
Q 1,50 ⋅ 0,70 ⋅ 1,5 1,58kN
M 0,125 ⋅ 5,41 ⋅ 5,15 0,250 ⋅ 1,58 ⋅ 5,1519,97kNm
σ19971536
1,30kN/cm
f 0,9 ⋅2,41,15
1,88 kN/cm
b)PanelConstruction
EurocodeDesign‐LucasBienert 58
η1,301,88
0,69 1,0
V 0,500 ⋅ 5,41 ⋅ 4,64 1,58 15,51kN
τ 1,5 ⋅15,51
0,67 ⋅ 3840,09kN/cm
f 0,9 ⋅0,351,15
0,27kN/cm
η0,090,27
0,33 1,0
nolateraltorsionalbuckling,becausethesheathingsecuresthecompressionflangeofthejoists
SLSCO9/10
w ,
1,04100 ⋅ 515
76,8 ⋅ 1150 ⋅ 184320,438cm
w , 1,208cm
w , 0,054cm
w ,1,5 ⋅ 515
48 ⋅ 1150 ⋅ 184320,201cm
instantaneousdeformation
w0,438 1,208 0,6 ⋅ 0,054 0,7 ⋅ 0,2011,82cm
maxw515300
1,72cm
η1,821,72
1,06 1,0
finaldeformation
w0,438 ⋅ 1 0,6 1,208 ⋅ 1 0,2 ⋅ 0,60,054 ⋅ 0,6 0 0,201 ⋅ 0,7 0,3 ⋅ 0,62,26cm
maxw515150
3,43cm
η2,263,43
0,66 1,0
maxreactionforces
A 0,5 ⋅ 1,01 ⋅ 5,15 2,61kN
A 0,5 ⋅ 2,80 ⋅ 5,15 7,20kN
A 0,5 ⋅ 0,13 ⋅ 5,15 0,32kN
A 0,5 ⋅ 0,45 ⋅ 5,15 1,16kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 59
1.1FloorJoists
system
l 5,15m
cross‐section
b/h 16/20
e 60cm
A 320cm
I 10667cm
W 1067cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g 1,39kN/m
s 0
w 0
g 1,39 ⋅ 0,6 0,83 kN/m
q A 2,5kN/m
q 2,5 ⋅ 0,6 1,5 kN/m
Q 1,5 kN
ULSCO2
k 0,8
p 1,20 ⋅ 0,83 1,50 ⋅ 1,5 3,25kN/m
M 0,125 ⋅ 3,25 ⋅ 5,15 10,78kNm
σ10781067
1,01kN/cm
f 0,8 ⋅2,41,15
1,67 kN/cm
η1,011,67
0,61 1,0
V 0,500 ⋅ 3,25 ⋅ 4,64 8,37kN
τ 1,5 ⋅8,37
0,67 ⋅ 3200,06kN/cm
nolateraltorsionalbuckling,becausethesheathingsecuresthecompressionflangeofthejoists
b)PanelConstruction
EurocodeDesign‐LucasBienert 60
f 0,8 ⋅0,351,15
0,24 kN/cm
η0,060,24
0,24 1,0
SLSCO7/8
w ,
0,83100 ⋅ 515
76,8 ⋅ 1150 ⋅ 106670,623cm
w , 0
w , 0
w , 1,120cm
instantaneousdeformation
w 0,623 1,120 0 0 1,74cm
maxw515300
1,72 cm
η1,741,72
1,02 1,0
finaldeformation
w0,623 ⋅ 1 0,6 1,120 ⋅ 1 0,3 ⋅ 0,60 0 2,32cm
maxw515150
3,43cm
η2,323,43
0,68 1,0
thisisstillOK,becauseamongstothersthebeneficialeffectofthesheathingwasnotconsideredyet
maxreactionforces
A 0,5 ⋅ 0,83 ⋅ 5,15 2,15kN
A 0
A 0
A 0,5 ⋅ 1,5 ⋅ 5,15 3,86kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 61
1.2RoofJoists
Theroofjoists1.2havethesameloadsanddimensionsastheroofjoists1.1butasmallerspan,theyarethereforenotdecisive,andacheckisnotnecessary.
maxreactionforces
A 0,5 ⋅ 1,01 ⋅ 4,38 2,22kN
A 0,5 ⋅ 2,80 ⋅ 4,38 6,12kN
A 0,5 ⋅ 0,13 ⋅ 4,38 0,27kN
A 0,5 ⋅ 0,45 ⋅ 4,38 0,99kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 62
1.2FloorJoists
Thefloorjoists1.2havethesameloadsanddimensionsasthefloorjoists1.1butasmallerspan,theyarethereforenotdecisive,andacheckisnotnecessary.
maxreactionforces
A 0,5 ⋅ 0,83 ⋅ 4,38 1,83kN
A 0
A 0
A 0,5 ⋅ 1,5 ⋅ 4,38 3,29kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 63
1.3RoofJoists
Thedimensionsfortheroofjoists1.3couldbedecreasedtob/h 8/24.
b)PanelConstruction
EurocodeDesign‐LucasBienert 64
1.3FloorJoists
Thedimensionsforthefloorjoists1.3couldbedecreasedtob/h 8/20.
b)PanelConstruction
EurocodeDesign‐LucasBienert 65
2RoofBeam
Thebeamundertheroofinaxis3–5/Cbecomesdecisive.
system
maxl 2,10m
cross‐section
b/h 12/24A 288cm I 13824cm
W 1152cm
material
glulamGL24hf 24N/mm k 0,67f 3,5N/mm E , 11500N/mm k 0,6
loads
g2,610,6
4,35kN/m
s7,200,6
12,0kN/m
w0,320,6
0,54kN/m
q1,160,6
1,93kN/m
b)PanelConstruction
EurocodeDesign‐LucasBienert 66
reactionforces,internalforcesanddeformations
constantload
loadingandreactionforces
bendingmoment
shearforce
deformations
b)PanelConstruction
EurocodeDesign‐LucasBienert 67
unfavourableloads
loadingandreactionforces
bendingmoment
shearforce
loadingandreactionforces
b)PanelConstruction
EurocodeDesign‐LucasBienert 68
deformations
ULSCO3
k 0,9
p 1,20 ⋅ 4,35 1,50 ⋅ 12,0 23,2kN/m
q 1,5 ⋅ 0,7 ⋅ 1,93 2,03kN/m
M 23,2 ⋅ 0,4243 2,03 ⋅ 0,436710,74kNm
σ10741152
0,93kN/cm
f 0,9 ⋅2,41,15
1,88 kN/cm
η0,931,88
0,50 1,0
V 23,2 ⋅ 1,252 2,03 ⋅ 1,258 31,6kN
τ 1,5 ⋅31,6
0,67 ⋅ 2880,25kN/cm
f 0,9 ⋅0,351,15
0,27kN/cm
η0,250,27
0,90 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
SLSCO9/10
w , 4,35 ⋅ 0,0087 0,038cm
w , 12,0 ⋅ 0,0087 0,104cm
w , 0,54 ⋅ 0,0087 0,005cm
w , 1,93 ⋅ 0,0089 0,017cm
instantaneousdeformation
w0,038 0,104 0,6 ⋅ 0,005 0,7 ⋅ 0,0170,157
maxw210300
0,70cm
η0,1570,70
0,22 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 69
finaldeformation
w0,038 ⋅ 1 0,6 0,104 ⋅ 1 0,2 ⋅ 0,60,005 ⋅ 0,6 0 0,017 ⋅ 0,7 0,3 ⋅ 0,60,195cm
maxw210150
1,40cm
η0,1951,40
0,14 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 70
2FloorBeam
Thebeaminaxis3–5/Cbecomesdecisive.
system
maxl 2,10m
cross‐section
b/h 8/24A 192cm I 9216cm
W 768cm
material
glulamGL24hf 24N/mm k 0,67f 3,5N/mm E , 11500N/mm k 0,6
loads
g2,150,6
4,35kN/m
s 0
w 0
q3,860,6
6,44kN/m
reactionforces,internalforcesanddeformations
constantload
loadingandreactionforces
b)PanelConstruction
EurocodeDesign‐LucasBienert 71
bendingmoment
shearforce
deformations
unfavourableloads
loadingandreactionforces
b)PanelConstruction
EurocodeDesign‐LucasBienert 72
bendingmoment
shearforce
loadingandreactionforces
deformations
ULSCO2
k 0,8
g 1,20 ⋅ 3,58 4,30kN/m
q 1,5 ⋅ 6,44 9,66kN/m
M 4,30 ⋅ 0,4243 9,66 ⋅ 0,4367 6,04 kNm
b)PanelConstruction
EurocodeDesign‐LucasBienert 73
σ604768
0,79kN/cm
f 0,8 ⋅2,41,15
1,67 kN/cm
η0,791,67
0,47 1,0
V 4,30 ⋅ 1,252 9,66 ⋅ 1,258 17,53kN
τ 1,5 ⋅17,53
0,67 ⋅ 1920,20kN/cm
f 0,8 ⋅0,351,15
0,24kN/cm
η0,200,24
0,84 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
SLSCO7/8
w , 3,58 ⋅ 0,01935 0,069cm
w , 0
w , 0
w , 6,44 ⋅ 0,01987 0,128cm
instantaneousdeformation
w 0,069 0,128 0 0 0,20cm
maxw210300
0,70cm
η0,200,70
0,28 1,0
finaldeformation
w0,069 ⋅ 1 0,6 0,128 ⋅ 1 0,3 ⋅ 0,60 0 0,26cm
maxw210150
1,40cm
η0,261,40
0,19 1,0
Thefloorbeaminaxis1–3/Abecomesdecisivefortheconnectiontothestuds(cf.ConnectionFloorBeam2toStuds3).
maxreactionforces
A 3,04 ⋅ 1,817 5,53kN
A 0
b)PanelConstruction
EurocodeDesign‐LucasBienert 74
A 0
A 5,475 ⋅ 1,88 10,29kN
maxinternalforces
V , 0,9393 ⋅ 3,04 2,86kN
V , 0
V , 0
V . 0,9785 ⋅ 5,475 5,36kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 75
3Studs
Becausethecross‐sectionofthestudsdecreasesinthehigherstoreys,checksmustbeperformedateverytransition,i.e.inthe11.,the6.andthe1.floor.Still,the1.floorbecomesdecisive.TheinternalforcesweredeterminedusingtheFEMsoftwareRFEM.
system
decisivestud
generalglobalsystem(wall)
cross‐section
b/h 20/20
b)PanelConstruction
EurocodeDesign‐LucasBienert 76
A 400cm
I I 13333cm
i i16
√125,77cm
material
glulamGL24h
f 24N/mm
ULSCO6
k 1,1
N 460,8kN
σ460,8400
1,27kN/cm
f 1,1 ⋅2,41,15
2,30kN/cm
flexuralbuckling
λ319,55,77
55,3
λ55,3π
⋅249600
0,88
k 0,5 ⋅ 1 0,1 ⋅ 0,88 0,3 0,880,92
k1
0,92 0,92 0,880,853
η1,27
0,853 ⋅ 2,300,67 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 77
6Beam(Roof)
system
maxl 2,32m
cross‐section
b/h 12/24
A 288cm
I 13824cm
W 1152cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g2,220,6
3,70kN/m
s6,120,6
10,21kN/m
w0,270,6
0,46kN/m
q0,990,6
1,64kN/m
reactionforces,internalforcesanddeformations
b)PanelConstruction
EurocodeDesign‐LucasBienert 78
constantload
loadingandreactionforces
bendingmoment
shearforce
deformations
b)PanelConstruction
EurocodeDesign‐LucasBienert 79
unfavourableloads
loadingandreactionforces
bendingmoment
shearforce
loadingandreactionforces
b)PanelConstruction
EurocodeDesign‐LucasBienert 80
deformations
ULSCO3
k 0,9
p 1,20 ⋅ 3,70 1,50 ⋅ 10,21 19,75kN/m
q 1,5 ⋅ 0,7 ⋅ 1,64 1,72kN/m
M 19,75 ⋅ 0,5382 1,72 ⋅ 0,629711,72kNm
σ11721152
1,02kN/cm
f 0,9 ⋅2,41,15
1,88 kN/cm
η1,021,88
0,54 1,0
V 19,75 ⋅ 1,392 1,72 ⋅ 1,431 29,96kN
τ 1,5 ⋅29,96
0,67 ⋅ 2880,23kN/cm
f 0,9 ⋅0,351,15
0,27kN/cm
η0,230,27
0,85 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
SLSCO9/10
w , 3,70 ⋅ 0,01254 0,046cm
w , 0,128cm
w , 0,006cm
w , 1,64 ⋅ 0,01801 0,030cm
instantaneousdeformation
w 0,046 0,128 0,6 ⋅ 0,006 0,7 ⋅ 0,300,199cm
maxw232300
0,77 cm
b)PanelConstruction
EurocodeDesign‐LucasBienert 81
η0,1990,77
0,26 1,0
finaldeformation
w0,046 ⋅ 1 0,6 0,128 ⋅ 1 0,2 ⋅ 0,60,006 ⋅ 0,6 0 0,030 ⋅ 0,7 0,3 ⋅ 0,60,247cm
maxw232150
1,55cm
η0,2471,55
0,16 1,0
maxreactionforces
A 3,70 ⋅ 0,928 3,43kN
A 9,47kN
A 0,42kN
A 1,64 ⋅ 1,044 1,71kN
B 3,70 ⋅ 2,552 9,45kN
B 26,04kN
B 1,17kN
B 1,64 ⋅ 2,784 4,57kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 82
6Beam(Floor)
system
maxl 2,32m
cross‐section
b/h 8/24
A 192cm
I 9216cm
W 768cm
material
glulamGL24h
f 24N/mm
k 0,67
f 3,5N/mm
E , 11500N/mm
k 0,6
loads
g1,830,6
3,04kN/m
s 0
w 0
q3,290,6
5,48kN/m
b)PanelConstruction
EurocodeDesign‐LucasBienert 83
reactionforces,internalforcesanddeformations
constantload
loadingandreactionforces
bendingmoment
shearforce
deformations
b)PanelConstruction
EurocodeDesign‐LucasBienert 84
unfavourableloads
loadingandreactionforces
bendingmoment
shearforce
loadingandreactionforces
b)PanelConstruction
EurocodeDesign‐LucasBienert 85
deformations
ULSCO2
k 0,8
g 1,20 ⋅ 3,04 3,65kN/m
q 1,5 ⋅ 5,48 8,21kN/m
M 3,65 ⋅ 0,5382 8,21 ⋅ 0,6297 7,14kNm
σ714768
0,93kN/cm
f 0,8 ⋅2,41,15
1,67 kN/cm
η0,931,67
0,56 1,0
V 3,65 ⋅ 1,392 8,21 ⋅ 1,431 16,84kN
τ 1,5 ⋅16,84
0,67 ⋅ 1920,20kN/cm
f 0,8 ⋅0,351,15
0,24kN/cm
η0,200,24
0,81 1,0
nolateraltorsionalbucklingbecausethejoistssecurethecompressionflangeofthebeam
b)PanelConstruction
EurocodeDesign‐LucasBienert 86
SLSCO7/8
w , 3,04 ⋅ 0,0188 0,057cm
w , 0
w , 0
w , 5,48 ⋅ 0,02701 0,148cm
instantaneousdeformation
w 0,057 0,148 0 0 0,205cm
maxw232300
0,77cm
η0,2050,77
0,26 1,0
finaldeformation
w0,057 ⋅ 1 0,6 0,148 ⋅ 1 0,3 ⋅ 0,60 0 0,266cm
maxw232150
1,55cm
η0,2661,55
0,17 1,0
maxreactionforces
A 3,04 ⋅ 0,928 2,82kN
A 0
A 0
A 5,48 ⋅ 1,044 5,72kN
B 3,04 ⋅ 2,552 7,77kN
B 0
B 0
B 5,48 ⋅ 2,784 15,24kN
b)PanelConstruction
EurocodeDesign‐LucasBienert 87
5Columns
system
cross‐sectionscolumnA,D
b/h 16/20
A 320cm
I I 10667cm
i i16
√124,62cm
columnB,C
b/h 20/20
A 400cm
I I 13333cm
i i20
√125,77cm
materialglulamGL24hγ 3,7kN/m f 24N/mm
globalsystem(beam6)
localsystem
loads
columnA,D
g 3,7 ⋅ 0,16 ⋅ 0,2 0,037kN/m self‐weightofthecolumn
N 3,43 14 ⋅ 2,82 43,0kN
s 0
N 9,47kN
w 0
N 0,42kN
q 0
N 1,71 14 ⋅ 0,74 ⋅ 5,72 60,9kN
columnB,C
reactionforceA@6 theloadisaddedupfortheroofand14
storeys
g 3,7 ⋅ 0,2 ⋅ 0,2 0,046kN/m self‐weightofthecolumn
N 9,45 14 ⋅ 7,77 118,2kN
s 0
N 26,04kN
w 0
reactionforceB@6 theloadisaddedupfortheroofand14
storeys
b)PanelConstruction
EurocodeDesign‐LucasBienert 88
N 1,17kN
q 0
N 4,57 14 ⋅ 0,74 ⋅ 15,24 162,5 kN
ULSCO2
k 0,8
columnA,D
g 1,2 ⋅ 0,037 0,044kN/m
N1,2 ⋅ 43,0 0,044 ⋅ 16 ⋅ 3,195 1,5
⋅ 60,9 145,2kN
σ145,2320
0,45kN/cm
f 0,8 ⋅2,41,15
1,67kN/cm
flexuralbuckling
λ319,54,62
69,2
λ69,2π
⋅249600
1,10
k 0,5 ⋅ 1 0,1 ⋅ 1,10 0,3 1,101,15
k1
1,15 1,15 1,100,683
η0,45
0,683 ⋅ 1,670,40 1,0
columnB,C
g 1,2 ⋅ 0,046 0,055kN/m
N1,2 ⋅ 118,2 0,055 ⋅ 16 ⋅ 3,195 1,5
⋅ 162,5 388,4kN
σ388,4400
0,97kN/cm
f 0,8 ⋅2,41,15
1,67kN/cm
flexuralbuckling
λ319,55,77
55,3
b)PanelConstruction
EurocodeDesign‐LucasBienert 89
λ55,3π
⋅249600
0,88
k 0,5 ⋅ 1 0,1 ⋅ 0,88 0,3 0,880,92
k1
0,92 0,92 0,880,853
η0,97
0,853 ⋅ 1,670,68 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 90
Anchoring
Thehold‐downdeviceconsistsoftwointernalsteelplatesanddowelsinsidethecorrespondingstuds.Atstudswithsmallertensileforces,theconnectioncanbeadapted,e.g.byusingonlyoneinternalsteelplateand/orlessdowels.
system
angleoftheforcetothegrain
α 0°
fasteners
8M20dowels
n 2 ⋅ 4 , ⋅200
13 ⋅ 206,52
strengthclass4.6
f 240N/mm
f 400N/mm
material
glulamGL24h
ρ 385kg/m
minimumdistances
a 3 2 ⋅ cos 0 ⋅ 2,0 10cm
a 3 ⋅ 2,0 6cm
a max 7 ⋅ 2,0 14; 8 14cm
a 3 ⋅ 2,0 6cm
capacityperfastenerpershearplane
M , 0,3 ⋅ 400 ⋅ 20 , /1000 289,6 Nm
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
F ,
25,26 ⋅ 67 ⋅ 20
⋅ 24 ⋅ 289,6 ⋅ 100025,26 ⋅ 20 ⋅ 67
1 /1000
19,8kN
failuremodegbecomesdecisive
dowelshavenoaxialcapacity
b)PanelConstruction
EurocodeDesign‐LucasBienert 91
ULSCO11/12
k 1,1
F 448,6kN cf.RFEManalysis
F . 19,8 ⋅ 6,52 ⋅ 4 516,2kN
F , 1,1 ⋅516,21,3
436,8kN
η448,6436,8
1,03 1,0
6,52boltsand4shearplanes
b)PanelConstruction
EurocodeDesign‐LucasBienert 92
ConnectionRoofJoists1toRoofBeam2
Thisconnectionhadtobechangedincomparisontothepreliminarydesign.Insteadofdiagonalfullythreadedscrews,joisthangersareused.
system
angleoftheforcetothegrain
α 90°
fasteners
JoistHangerSimpsonStrongtieBT4‐120orsimilar
material
glulamGL24h
ρ 385kg/m
capacity
F , 23,9kN
cf.technicaldatasheet[7]
loads
F 2,61kN
F 7,20kN
F 0,32kN
F 1,16kN
[email protected] theshearforcesinthejoistareequalto
thesupportforces
ULSCO3
b)PanelConstruction
EurocodeDesign‐LucasBienert 93
k 0,9
F 1,2 ⋅ 2,61 1,5 ⋅ 7,20 1,5 ⋅ 0,7 ⋅ 1,1615,1kN
F . 23,9kN
F , 0,9 ⋅23,91,3
16,5kN
η15,116,5
0,92 1,0
11boltsand2shearplanes
checkfortensionperpendiculartothegraininthebeam
V F 15,1kN
F 14 ⋅ 160 ⋅ 1 ⋅165
116,524
/1000
51,5kN
F 0,9 ⋅51,51,3
35,6kN
η15,135,6
0,43 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 94
ConnectionFloorJoists1toFloorBeam2
Forthisconnection,thesamesystemisused,buttheloadsarelowerfromthefloorthanfromtheroof,sothatthisconnectionisnotdecisive.
b)PanelConstruction
EurocodeDesign‐LucasBienert 95
ConnectionFloorBeam2toStuds3
Thefloorbeaminaxis1–3/AbecomesdecisiveatsupportC.
system
angleoftheforcetothegrain
floorbeam
α 90°
stud
α 0°
fasteners
4M20dowels
n 2 ⋅ 2 , ⋅100
13 ⋅ 202,94
f 240N/mm
f 400N/mm
material
glulamGL24h
ρ 385kg/m
strengthclass4.6
minimumdistances
floorbeam
a 3 2 ⋅ cos 90 ⋅ 2,0 6cm
b)PanelConstruction
EurocodeDesign‐LucasBienert 96
a 3 ⋅ 2,0 6cm
amax 2 2 ⋅ sin 90 ⋅ 2,0 8; 3 ⋅ 2,0 68cm
a 3 ⋅ 2,0 6cm
stud
a 3 2 ⋅ cos 0 ⋅ 2,0 10cm
a 3 ⋅ 2,0 6cm
a 3 ⋅ 2,0 6cm
capacityperfastenerpershearplane
M , 0,3 ⋅ 400 ⋅ 20 , /1000 289,6 Nm
floorbeam(member1)
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
k 1,35 0,015 ⋅ 20 1,65
f , ,25,26
1,65 ⋅ sin 90 cos 9015,3N/mm
stud(member2)
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
β25,2615,3
1,65
failuremodedbecomesdecisive
dowelshavenoaxialcapacity
F ,
1,05 ⋅15,3 ⋅ 80 ⋅ 202 1,65
⋅ 2 ⋅ 1,65 ⋅ 1 1,654 ⋅ 1,65 ⋅ 2 1,65 ⋅ 289,64 ⋅ 1000
15,3 ⋅ 20 ⋅ 801,65
13,1kN
loads
F 5,53kN
F 10,29kN
shearforcesinthebeamattheconnection
V 2,86kN
V 5,36kN
reactionforceC@2
ULSCO2
b)PanelConstruction
EurocodeDesign‐LucasBienert 97
k 0,8
F 1,2 ⋅ 5,53 1,5 ⋅ 10,29 22,08kN
F . 2,93 ⋅ 1 ⋅ 13,09 38,5kN
F , 0,8 ⋅38,51,3
23,7kN
η22,0823,7
0,93 1,0
2,94boltsand1shearplane
tensionperpendiculartothegrain
V 1,2 ⋅ 2,86 1,5 ⋅ 5,36 11,5kN
F 14 ⋅ 80 ⋅ 1 ⋅180
11824
/1000 30,1kN
F 0,8 ⋅30,11,3
18,5kN
η11,518,5
0,62 1,0
b)PanelConstruction
EurocodeDesign‐LucasBienert 98
ConnectionRoofBeam2toStuds3
This connection follows the same principle as the connection of the floor beam to the studs.Becauseofthehigherloadsfromtheroofthanfromthefloors,6dowelsarerequiredinsteadof4.Therefore,thestudsinthehigheststoreymustbe28/28(likethestudsinstorey1to5)toallowforenoughspaceforthe6dowels.
c)CLTConstruction
EurocodeDesign‐LucasBienert 99
c)CLTConstructionElementReferenceOverview
referenceno element page
1 floorslab 100
2,3 floorslab ‐
4 floorslab ‐
5 Walls 106
Anchoring 108
Remarks
Becauseofgoodlateraldistributionoftheloadsintheslabs,thesingleconcentratedforceQwillnotbecomedecisive.
Forthecalculationoftheinternalforcesofthewalls,theFEsoftwareRFEMwasused.
BecauseofmissingrulesforCLTintheEC,thesamedesignfactorsasforglulamareapplied.
Comparedtothepreliminarydesign,thethicknessesofthewallshadtobeincreased.Nowwallswiththethicknesses145mm,170mmand246mmareused.Thereductionofthethicknessovertheheightofthebuildingwasadapted.
storeyno M N t t t‐ % % mm mm mm 0 100,00 100,00 145 170 2461 87,11 93,33 145 170 2462 75,11 86,67 145 170 2463 64,00 80,00 145 170 2464 53,78 73,33 145 170 246
5 44,44 66,67 120 120 1706 36,00 60,00 120 120 1707 28,44 53,33 120 120 1708 21,78 46,67 120 120 1709 16,00 40,00 120 120 170
10 11,11 33,33 95 95 9511 7,11 26,67 95 95 9512 4,00 20,00 95 95 9513 1,78 13,33 95 95 9514 0,44 6,67 95 95 9515 0,00 0,00 95 95 95
c)CLTConstruction
EurocodeDesign‐LucasBienert 100
1RoofSlab
system
maxl 4,38m
cross‐section
t 145mm
A 1450cm /m
I 25405cm /m
W 3504cm /m
material
CLTKL‐trä145
f 10,1N/mm
k 0,67
f 0,7N/mm
E , 5290N/mm
k 0,6
seetechnicalapproval[1]
loads
g 1,97kN/m
s 4,41kN/m
q 1044N/m
c I 0,2
w 0,2 ⋅ 1,044 0,21 kN/m
q H 0,75kN/m
reactionforces,internalforcesanddeformations
constantload
loadingandreactionforces
c)CLTConstruction
EurocodeDesign‐LucasBienert 101
bendingmoment
shearforce
deformations
unfavourableloads
loadingandreactionforces
c)CLTConstruction
EurocodeDesign‐LucasBienert 102
bendingmoment
shearforce
deformations
ULSCO3
k 0,9
p 1,20 ⋅ 1,97 1,50 ⋅ 4,41 8,97kN/m
q 1,50 ⋅ 0,7 ⋅ 0,75 0,79kN/m
M 8,97 ⋅ 2,311 0,79 ⋅ 2,31122,55kNm/m
σ22553504
0,64kN/cm
f 0,9 ⋅1,011,15
0,79 kN/cm
η0,640,79
0,81 1,0
V 8,97 ⋅ 2,718 0,79 ⋅ 2,718 26,52kN
τ 1,5 ⋅26,52
0,67 ⋅ 14500,041kN/cm
c)CLTConstruction
EurocodeDesign‐LucasBienert 103
f 0,9 ⋅0,071,15
0,055 kN/cm
η0,0410,055
0,75 1,0
SLSCO9/10
w , 1,97 ⋅ 0,1546 0,305cm
w , 0,681cm
w , 0,032cm
w , 0,75 ⋅ 0,2483 0,186cm
instantaneousdeformation
w0,305 0,681 0,6 ⋅ 0,032 0,7 ⋅ 0,1861,14cm
maxw438300
1,46cm
η1,141,46
0,78 1,0
finaldeformation
w0,305 ⋅ 1 0,6 0,681 ⋅ 1 0,2 ⋅ 0,60,032 ⋅ 0,6 0 0,186 ⋅ 0,7 0,3 ⋅ 0,61,43cm
maxw438150
2,92cm
η1,432,92
0,49 1,0
c)CLTConstruction
EurocodeDesign‐LucasBienert 104
1FloorSlab
system
maxl 4,38m
cross‐section
t 145mm
A 1450cm /m
I 25405cm /m
W 3504cm /m
material
CLTKL‐trä145
f 10,1N/mm
k 0,67
f 0,7N/mm
E , 5290N/mm
k 0,6
seetechnicalapproval[1]
loads
g 1,64kN/m
s 0
w 0
q A 2,5kN/m
reactionforces,internalforcesanddeformations
cf.1.1RoofSlab
ULSCO2
k 0,8
g 1,20 ⋅ 1,64 2,0kN/m
q 1,50 ⋅ 2,5 3,75kN/m
M 2,0 ⋅ 2,311 3,75 ⋅ 2,311 13,21kNm/m
σ13213504
0,38kN/cm
f 0,8 ⋅1,011,15
0,70 kN/cm
η0,380,70
0,54 1,0
V 2,0 ⋅ 2,718 3,75 ⋅ 2,718 15,54 kN
c)CLTConstruction
EurocodeDesign‐LucasBienert 105
τ 1,5 ⋅15,54
0,67 ⋅ 14500,024kN/cm
f 0,8 ⋅0,071,15
0,049kN/cm
η0,0240,049
0,50 1,0
SLSCO7/8
w , 1,64 ⋅ 0,1546 0,253cm
w , 0
w , 0
w , 2,5 ⋅ 0,2483 0,621cm
instantaneousdeformation
w 0,253 0 0 0,7 ⋅ 0,621 0,69cm
maxw438300
1,46cm
η0,691,46
0,47 1,0
finaldeformation
w0,253 ⋅ 1 0,6 0 0 0,621
⋅ 0,7 0,3 ⋅ 0,6 0,95cm
maxw438150
2,92cm
η0,952,92
0,33 1,0
c)CLTConstruction
EurocodeDesign‐LucasBienert 106
5.x9OuterWall
system
cross‐section
t 145mm
A 1450cm /m
I 25405cm /m
W 3504cm /m
i14,5
√124,19cm
material
CLTKL‐trä145
f 8,3N/mm
f 10,1N/mm
k 0,67
E , 5290N/mm
E , 2300N/mm
k 0,6
seetechnicalapproval[1]
internalforces
n 68,6kN/m
n 4,9kN/m
c)CLTConstruction
EurocodeDesign‐LucasBienert 107
n 222,1kN/m
n 50,7kN/m
windfromthesidebecomesdecisive
ULSCO6
k 1,1
n1,2 ⋅ 68,6 1,5 ⋅ 222,1 1,5 ⋅ 0,7 ⋅ 4,91,5 ⋅ 0,7 ⋅ 50,7 473,7kN/m
σ473,7
100 ⋅ 14,50,33kN/cm
f 1,1 ⋅0,831,15
0,79 kN/cm
flexuralbuckling
λ319,54,19
76,3
λ76,3π
⋅8,32300
1,46
k 0,5 ⋅ 1 0,1 ⋅ 1,46 0,3 1,461,62
k1
1,62 1,62 1,460,429
η0,33
0,429 ⋅ 0,790,96 1,0
c)CLTConstruction
EurocodeDesign‐LucasBienert 108
AnchoringWall5.y3
system
angleoftheforcetothegrain
α 90°
fasteners
7M20dowels/m
f 240N/mm
f 400N/mm
material
CLTKL‐trä170
ρ 385kg/m
strengthclass4.6
minimumdistances
a 4 ⋅ 2,0 8cm
a max 7 ⋅ 2,0 14 ; 8 14cm
capacityperfastenerpershearplane
M , 0,3 ⋅ 400 ⋅ 20 , /1000 289,6 Nm
f , , 0,082 ⋅ 1 0,01 ⋅ 20 ⋅ 38525,26N/mm
k 1,35 0,015 ⋅ 20 1,65
f , ,25,26
1,65 ⋅ sin 90 cos 9015,3N/mm
c)CLTConstruction
EurocodeDesign‐LucasBienert 109
F ,
15,3 ⋅ 170/2 ⋅ 20
⋅ 24 ⋅ 289,6 ⋅ 1000
15,3 ⋅ 20 ⋅ 170/21 /1000
15,3kN
failuremodegbecomesdecisive
theaxialcapacityofthefastenersisneglected
ULSCO11/12
k 1,1
F 138,4kN/m cf.RFEManalysis
F . 15,3 ⋅ 7 ⋅ 2 214,4kN/m
F , 1,1 ⋅214,41,3
181,5kN
η138,4181,5
0,76 1,0
7boltsand2shearplanesperm
checkfortensionperpendiculartothegraininthebeam
V 0,61 ⋅ 138,4 ⋅ 0,143 12,1kN
F 14 ⋅ 95 ⋅ 1 ⋅150
1150319,5
/1000
16,7kN
F 1,1 ⋅16,71,3
14,1kN
η12,114,1
0,85 1,0
theshearforceisestimatedassumingthewalltobeabeamsupportedbythedowelswiththeuniformloadF
Appendix
EurocodeDesign‐LucasBienert 110
Appendix
Attachments
Eurocodedesign(XLSX) RFEMresultsforthepanelconstruction(XLSX) RFEMresultsfortheCLTconstruction(XLSX) RFEMmodelsfortheframe,panelandCLTconstruction(RF5) technicalplansfortheframeconstructionPa1.2,Pa2(PDF) technicalplansforthepanelconstructionPb1–Pb3,Pa4.2(PDF) technicalplansfortheCLTconstructionPc1–Pc2,Pc3.2(PDF)
a)FrameConstruction
Elements
Appendix
EurocodeDesign‐LucasBienert 111
Appendix
EurocodeDesign‐LucasBienert 112
Connections
Appendix
EurocodeDesign‐LucasBienert 113
Appendix
EurocodeDesign‐LucasBienert 114
Appendix
EurocodeDesign‐LucasBienert 115
Appendix
EurocodeDesign‐LucasBienert 116
b)PanelConstruction
Elements
Appendix
EurocodeDesign‐LucasBienert 117
Appendix
EurocodeDesign‐LucasBienert 118
Connections
Appendix
EurocodeDesign‐LucasBienert 119
Appendix
EurocodeDesign‐LucasBienert 120
Appendix
EurocodeDesign‐LucasBienert 121
c)CLTConstruction
Elements
Appendix
EurocodeDesign‐LucasBienert 122
Connections