Cellular Theses

7/27/2019 Cellular Theses

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Master thesis

CELLULAR BEAM-COLUMNS

IN

PORTAL FRAME STRUCTURES

J.G. VerweijNovember 2010


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Master thesis

CELLULAR BEAM-COLUMNS

IN

PORTAL FRAME STRUCTURES

Thesiscommittee:

Chairman

Prof.Ir.F.S.K.Bijlaard,SectionSteel andTimberStructures

Committeemembers

Dr.A.Romeijn,SectionSteel andTimberStructures

Ir.R.Abspoel,SectionSteel andTimberStructures

Dr.Ir.P.C.J.Hoogenboom,SectionStructuralMechanics

Ir.L.J.M.Houben,SectionRoadandRailwayEngineering

Externalcommitteemember

Dr.O.Vassart,ArcelorMittalR&D

J.G.Verweij

1155482

DelftUniversityofTechnology

CivilEngineering

SectionSteelandTimberStructures

November2010


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Preface 5

PREFACE

Thepresentdocumentformsthefinalreport

ofmyMasterThesisProjectentitledCellular

beamcolumnsinportalframestructures.This

MasterThesishasbeencarriedoutasbeing

partoftheMastersdegreeprogrammein

CivilEngineering,SectionSteelandTimber

Structures,atDelftUniversityofTechnology.

Althoughinthepastalreadyalargedealof

researchwasperformedintothesubjectofthe

behaviourof(non)compositecellularbeams,

almostnoattentionhasbeenpaidtotheapplicationofcellularmembersascolumns.

Especiallytheuseinportalframestructures

seemsattractiveforreasonsofaestheticsand

thereforetheinvestigationofitsstructural

behaviourisrelevant.Forthatreasonthe

presentworkisdevotedtotheresearchofthe

behaviourofcellularbeamcolumns.

Partsofthisresearchhavebeenperformed

whilebeingincompany.First,attheresearchdepartmentofArcelorMittalinEschsur

Alzette,Luxembourg,whichenabledmeto

makeuseoftheirknowledgeandsoftware.Second,attheofficeofIBTIngenieursin

Bouwtechniek afirmofconsulting

engineersinVeenendaal,TheNetherlands,

thelastperiodwhilebeingonafulltime

contractalready.

IwouldliketothankrespectivelyDr.O.

VassartandIr.A.vantLandfortheir

willingnesstoprovidemethesefacilities.

Moreover,Iwouldliketoexpressmygratitudetotheotherpersonsofthethesis

committee:Prof.Ir.F.S.K.Bijlaard,Dr.A.

Romeijn,Ir.R.AbspoelandDr.Ir.P.C.J.

Hoogenboom.

Finally,thanksgotoallwhohavesupported

meatanytime,atanyplaceduringmy

studiesatDelftUniversityofTechnology.

Ede,November

2010

J.G.Verweij


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Tableofcontents 7

TABLE OF CONTENTS

PREFACE.......................................................... ........................................................... ..................................................... 5

1 INTRODUCTION ................................................... ........................................................... ............................... 15

1.1 MOTIVATION .................................................. ........................................................... ............................... 15

1.2 OBJECTIVES ..................................................... ........................................................... ............................... 15

1.3 SCOPE.................................................... ........................................................... ......................................... 15

1.4 LIMITATIONS................................................... ........................................................... ............................... 16

1.5 OUTLINE ......................................................... ........................................................... ............................... 16

PARTI LITERATURESTUDY ......................................................... ........................................................... ............ 19

2 INTRODUCTIONTOCELLULARBEAMCOLUMNS....................................................... ..................... 21

2.1 OPEN

WEB

SECTIONS.......................................................... ........................................................... ........... 212.2 PRODUCTIONMETHODS ..................................................... ........................................................... ........... 21

2.3 APPLICATIONAREA.................................................. ........................................................... ..................... 23

2.4 CURRENTRESEARCHSTATUS ....................................................... ........................................................... . 26

2.5 FUTUREDESIGNDEVELOPMENT................................................... ........................................................... . 32

2.6 ADVANTAGESANDDISADVANTAGES.................................................... .................................................. 32

3 MECHANICALBEHAVIOUROFBEAMSWITHWEBOPENINGS ............................................... ..... 33

3.1 INTRODUCTION ........................................................ ........................................................... ..................... 33

3.2 GLOBALBENDINGANDSHEAR..................................................... ........................................................... . 33

3.3 LATERALTORSIONALBUCKLING ........................................................... .................................................. 34

3.4 WEBPOSTFAILUREMECHANISMS ......................................................... .................................................. 35

3.5 ADDITIONALFAILUREMODES...................................................... ........................................................... . 36

3.6 SERVICEABILITYPERFORMANCE................................................... ........................................................... . 36

3.7 BEHAVIOURATELEVATEDTEMPERATURE...................................................... ......................................... 37

3.8 SUMMARYOFFAILUREMECHANISMS .................................................... .................................................. 37

4 DESIGNMETHODSFORCELLULARBEAMS.......................................................... ............................... 39

4.1 INTRODUCTION ........................................................ ........................................................... ..................... 39

4.2 LWODESIGNMETHOD....................................................... ........................................................... ........... 39

4.2.1 INTRODUCTION...................................................... ........................................................... ........... 39

4.2.2 SECTIONCLASSIFICATION.......................................................... .................................................. 40

4.2.3 GLOBALBENDINGRESISTANCE .......................................................... ......................................... 41

4.2.4 SHEARRESISTANCE.......................................................... ........................................................... . 41

4.2.5 SHEARBUCKLINGCAPACITY ..................................................... .................................................. 43

4.2.6 VIERENDEELBENDINGRESISTANCE ................................................... ......................................... 43

4.2.7 BENDINGRESISTANCEOFTEES ........................................................... ......................................... 44

4.2.8 INTERACTIONWITHNORMALFORCE ........................................................... ............................... 45

4.2.9 WEBPOSTHORIZONTALSHEAR ......................................................... ......................................... 45

4.2.10 WEBPOSTBUCKLING..................................................... ........................................................... . 45

4.2.11 PATTERNLOADING........................................................ ........................................................... . 47

4.2.12 SERVICEABILITYBEHAVIOUR ................................................... .................................................. 47

4.2.13 STIFFENERREQUIREMENTS ...................................................... .................................................. 48

4.2.14 GEOMETRICALLIMITATIONS ................................................... .................................................. 49

4.2.15 GENERALDESIGNCONSIDERATIONS.......................................................... ............................... 49

4.2.16 SOFTWARETOOL ............................................................ ........................................................... . 51

4.3 BACKGROUNDSOFTHEACBPROGRAM ......................................................... ......................................... 51


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8 Tableofcontents

4.3.1 INTRODUCTION...................................................... ........................................................... ........... 51

4.3.2 VIERENDEELBENDING..................................................... ........................................................... . 51

4.3.3 LATERALTORSIONALBUCKLING ....................................................... ......................................... 52

4.3.4 WEBPOSTBUCKLING....................................................... ........................................................... . 52

4.3.5

SERVICEABILITY

BEHAVIOUR ..................................................... .................................................. 54

4.4 COMPLEMENTARYUSAGE ............................................................ ........................................................... . 55

5 PORTALFRAMEDESIGNACCORDINGTOTHEEUROCODES....................... ................................ 57

5.1 INTRODUCTION ........................................................ ........................................................... ..................... 57

5.2 STANDARDS .................................................... ........................................................... ............................... 57

5.2.1 INTRODUCTION...................................................... ........................................................... ........... 57

5.2.2 DUTCHTGB1990SERIES ........................................................... .................................................. 57

5.2.3 HONGKONGSTEELCODE ........................................................ .................................................. 57

5.3 GLOBALANALYSIS.................................................... ........................................................... ..................... 58

5.3.1 INTRODUCTION...................................................... ........................................................... ........... 58

5.3.2 GEOMETRICALNONLINEARITY ......................................................... ......................................... 58

5.3.3 MATERIALNONLINEARITY....................................................... .................................................. 59

5.3.4 IMPERFECTIONS...................................................... ........................................................... ........... 60

5.3.5 STRUCTURALSTABILITY................................................... ........................................................... . 62

5.4 DESIGNOFBEAMCOLUMNS......................................................... ........................................................... . 64

5.4.1 CROSSSECTIONALRESISTANCE.......................................................... ......................................... 64

5.4.2 BUCKLINGRESISTANCE.................................................... ........................................................... . 65

5.5 NONUNIFORMMEMBERS................................................... ........................................................... ........... 71

5.6 CONCLUSION.................................................. ........................................................... ............................... 73

PARTIINUMERICALRESEARCH ............................................................... ....................................................... 75

6 INTRODUCTION ................................................... ........................................................... ............................... 77

7 DESCRIPTIONOFTHEFINITEELEMENTSOFTWAREANDTOOLS ............................................. 79

7.1 INTRODUCTION ........................................................ ........................................................... ..................... 79

7.2 FINITEELEMENTSOFTWARESAFIR............... ........................................................... ............................... 79

7.2.1 CAPABILITIESANDPROGRAMSTRUCTURE ................................................... ............................... 79

7.2.2 ELEMENTTYPES ..................................................... ........................................................... ........... 82

7.2.3 MATERIALLAWS.................................................... ........................................................... ........... 84

7.2.4 SAFIRSHELL........................................................... ........................................................... ........... 84

7.3 PREPROCESSORS ...................................................... ........................................................... ..................... 84

7.3.1 INTRODUCTION...................................................... ........................................................... ........... 84

7.3.2 CRYSTALPRO......................................................... ........................................................... ........... 84

7.3.3 MAILLEURPORTIQUE ...................................................... ........................................................... . 867.4 POSTPROCESSORDIAMOND ........................................................ ........................................................... . 86

8 GLOBALBUCKLINGOFCELLULARMEMBERS..................................................... ............................... 87

8.1 INTRODUCTION ........................................................ ........................................................... ..................... 87

8.2 THEORETICALANALYSIS .................................................... ........................................................... ........... 87

8.3 FINITEELEMENTMODEL..................................................... ........................................................... ........... 89

8.3.1 INTRODUCTION...................................................... ........................................................... ........... 89

8.3.2 SUPPORTCONDITIONS ..................................................... ........................................................... . 89

8.3.3 USEOFIMPERFECTIONS ................................................... ........................................................... . 91

8.3.4 LOADAPPLICATION......................................................... ........................................................... . 94

8.4 PARAMETERSTUDY .................................................. ........................................................... ..................... 948.4.1 SETUP .......................................................... ........................................................... ..................... 94

8.4.2 BASEPROFILEIPE140 ...................................................... ........................................................... . 98


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Tableofcontents 9

8.4.3 BASEPROFILEIPE330 ...................................................... .......................................................... 101

8.4.4 BASEPROFILEIPE600 ...................................................... .......................................................... 103

8.4.5 BASEPROFILEHE200A.................................................... .......................................................... 107

8.4.6 BASEPROFILEHE650M................................................... .......................................................... 107

8.5

CONCLUSION

.................................................. ........................................................... ............................. 108

9 WEBPOSTBUCKLINGINCOMPRESSEDCELLULARMEMBERS ................................................. 111

9.1 INTRODUCTION ........................................................ ........................................................... ................... 111

9.2 THEORETICALANALYSIS .................................................... ........................................................... ......... 111

9.2.1 LWOMODEL ......................................................... ........................................................... ......... 111

9.2.2 ARCELORSMODEL .......................................................... .......................................................... 112

9.2.3 COMPARISONANDCONCLUSION....................................................... ....................................... 113

9.3 FINITEELEMENTMODEL..................................................... ........................................................... ......... 114

9.3.1 INTRODUCTION...................................................... ........................................................... ......... 114

9.3.2 SUPPORTCONDITIONS ..................................................... .......................................................... 114

9.3.3 USEOFIMPERFECTIONS ................................................... .......................................................... 115

9.3.4 LOADAPPLICATION......................................................... .......................................................... 115

9.4 PARAMETERSTUDY .................................................. ........................................................... ................... 115

9.4.1 SETUP .......................................................... ........................................................... ................... 115

9.4.2 BASEPROFILEIPE140 ...................................................... .......................................................... 117

9.4.3 BASEPROFILEIPE330 ...................................................... .......................................................... 118

9.4.4 BASEPROFILEIPE600 ...................................................... .......................................................... 120

9.4.5 BASEPROFILEHE200A.................................................... .......................................................... 122

9.4.6 BASEPROFILEHE650M................................................... .......................................................... 123

9.5 CONCLUSION.................................................. ........................................................... ............................. 125

PARTIIICASESTUDY......................................................... ........................................................... ...................... 127

10 PORTALFRAMESTRUCTURESUSINGCELLULARMEMBERS...................................................... 129

10.1 INTRODUCTION ........................................................ ........................................................... ................... 129

10.2 DESIGNUSINGTHELWOMETHOD........................................................ ................................................ 129

10.2.1 STRUCTUREOFTHEEXCELTOOL...................................................... ....................................... 129

10.2.2 ANALYSISPROCEDURE ............................................................ ................................................ 129

10.3 DESIGNUSINGFEAINSAFIR ..................................................... .......................................................... 133

10.3.1 INTRODUCTION.................................................... ........................................................... ......... 133

10.3.2 SECONDORDERNONLINEARINPLANEANALYSISWITH2DBEAMELEMENTS ....................133

10.3.3 SECONDORDERNONLINEAR3DFINITEELEMENTANALYSISWITHSHELLELEMENTS......... 134

10.4 CASESTUDY .................................................... ........................................................... ............................. 135

10.4.1 STRUCTURALSYSTEM..................................................... .......................................................... 13510.4.2 LOADCASE1:DISTRIBUTEDVERTICALLOAD ....................................................... ................... 135

10.4.3 LOADCASE2:HORIZONTALPOINTLOADS .......................................................... ................... 136

10.4.4 LOADCASE3:COMBINATIONOFBOTHVERTICALANDHORIZONTALPOINTLOAD .............. 138

10.5 CONCLUSION.................................................. ........................................................... ............................. 139

11 CONCLUSIONSANDRECOMMENDATIONS......................................................... ............................. 141

11.1 INTRODUCTION ........................................................ ........................................................... ................... 141

11.2 CONCLUSIONS .......................................................... ........................................................... ................... 141

11.3 RECOMMENDATIONS.......................................................... ........................................................... ......... 142

REFERENCES .................................................. ........................................................... ................................................. 143

ANNEXES ........................................................ ........................................................... ................................................. 151

A EUROPEANSTANDARDS....................................................... ........................................................... ......... 153


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10 Tableofcontents

A.1 INTRODUCTION ........................................................ ........................................................... ................... 153

A.2 EUROCODE3:PART11 ...................................................... ........................................................... ......... 154

A.3 EUROCODE3:PART15 ...................................................... ........................................................... ......... 154

B FEMRESULTSOFPARAMETERSTUDYINTOGLOBALBUCKLING............................................ 157

B.1 INTRODUCTION ........................................................ ........................................................... ................... 157

B.2 BASEPROFILEIPE140......................................................... ........................................................... ......... 157

B.2.1 BUCKLINGABOUTTHEWEAKAXIS .................................................... ....................................... 157

B.2.2 BUCKLINGABOUTTHESTRONGAXIS ........................................................... ............................. 160







B.5 BASEPROFILEHE200A ...................................................... ........................................................... ......... 178



B.6 BASEPROFILEHE650M...................................................... ........................................................... ......... 185



C FEMRESULTSOFPARAMETERSTUDYINTOWEBPOSTBUCKLING........................................ 191

C.1 INTRODUCTION ........................................................ ........................................................... ................... 191

C.1.1 ARCELORMODELFORWEBPOSTBUCKLING ......................................................... ................... 191

C.1.2 ARCELORMODELFORVIERENDEELBENDING ...................................................... ................... 193

C.1.3 LWOMODELFORBOTHWEBPOSTBUCKLINGANDVIERENDEELBENDING........................... 196

C.2 BASEPROFILEIPE140......................................................... ........................................................... ......... 198

C.2.1 WEBPOSTWIDTHS0=50MM.................................................... ................................................ 198

C.2.2 WEBPOSTWIDTHS0=100MM........................................................... ....................................... 199







C.5 BASEPROFILEHE200A ...................................................... ........................................................... ......... 204


C.5.2 WEBPOSTWIDTHS0=100MM........................................................... ....................................... 205C.6 BASEPROFILEHE650M...................................................... ........................................................... ......... 206



D LISTOFCONTENTSDATADVD ................................................... .......................................................... 209

E ARCELORPROFILLUXEMBOURG....................................... ........................................................... ......... 211

F IBTINGENIEURSINBOUWTECHNIEK .......................................................... ....................................... 213

G ADDRESSES .................................................. ........................................................... ....................................... 215


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Listofsymbols 11

LIST OF SYMBOLS

Thefollowingsymbolsareusedthroughoutthisreport.Someofthesearedifferentfromthatare

usedinthereferredpublicationsinordertopreventmisunderstandings.Furthermorenotethatthesubscripttisusedthroughoutthisreport,whenaformulaappliestoboththebottomandtoptee.

Thesubscript referstopropertiesorforcesactingonaninclinedsection.Additionalsymbolsare

definedwheretheyfirstoccur.

a throatthicknessofthefilletweld

fA crosssectionalareaoftheflange

sA crosssectionalareaofahorizontalstiffener

bA crosssectionalareaofthebottomtee

tA crosssectionalareaofthe(top)tee

wA crosssectionalareaoftheweb

vA shearareaofanunperforatedsection

v ,oA shearareaofaperforatedsection

v, tA shearareaofateesection

b flangewidth

w shearbucklingfactorforcontributionoftheweb

add additionaldeflectionduetoasingleopeningatpositionx

b purebendingdeflectionofthebeam

sw deflectionduetopermanentloads

od depth(ordiameter)ofawebopening

bd b fh t ,depthofthewebofthebotto= mtee

b, effd effectivedepthofthewebofthebottomtee(tomeetclassificationlimits)

td t fdistanceofthecriticalsectionfromthejointbetweenthetwohalfposts

h t= ,depthofthewebofthe(top)tee

wd

y235 with f in

2N / m m ,coefficientforsecti/ f= onclassificationy

modifiedcoefficientforsectionclassification(toallowfortheeffectofaxialtension)1 *e equivalentgeometricalimperfection

se offsetdistanceofcentreofstiffenerfromtipoftheweb

E elasticmodulusofsteel

fM0

naturalfrequency partialfactorforresistanceofcrosssections

M1 partialfactorforresistanceofmemberstoinstabilityassistedbymemberchecks shapefactorforsheararea

h heightofthesection

bh depthofthebottomtee

th depthofthe(top)tee

wh depthofthewebofthesection

i radiusofgyration

angle(ofinclinedsectiontotheverticalthroughthehole)

vwf designshearstrengthofafilletweld

yf yieldstrengthofsteel


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12 Listofsymbols

y,redf reducedyieldstrengthtoaccountforhighshearforce

r

ss

ysf yieldstrengthofstiffener

ywf designstrengthoftheweld

s,

s

EdF designaxialforceinstiffene

,RdF axialresistanceofstiffener

ok modificationfactorforthedeflectionforlongopenings

slendernessofwebpost

1 slendernessvaluetodeterminetherelativeslenderne nondimensional(relative)slendernessofwebpost

ectionclassification)

ndingmomentresistancedueto

post

ions

gs

localshearstress

t ced

fM criticalsection

e

o

A effectivelengthofwebpostforwebpostbuckling

actuallengthofopeningA

o ,

v ,

effA effectivelengthofopeningforstabilityoftheweb(s

effA effectivelengthofopeningforVierendeelbending

w,effA

effectivelengthofwebpostforwebpostbucklingw

A widthofthewebpostatthecriticalsectionlocation

L lengthofthebeam

n numberofsidesofthestiffener(singlesidedstiffener:1,doublesidedstiffener:2)

numberofopeningsalongthebeamoN

shearutilisationfactor(todeterminethereducedbehighshearforce)

actingonthewebc (design)compressivestress

c,Rd designcompressivestrengthofthewebpost

w,Rd principalstressresistance

ctw,Sd principalcompressivestressatthecriticalseings centretocentrespacingofadjacentopen

inos edgetoedgespacingofadjacentopen

openingtobeamendes enddistancefrom

Ed designvalueofthe

sft flangethicknes

st stiffenerthickness

wt webthickness

w,eff effectivewebthickness,redu

EdM designbendingmoment

hM webpostbendingmoment

h ,eM elasticbendingresistanceofthewebpost

theh,ef effectivewebpostbendingmoment,actingat

pl,tM plasticbendingmomentresistanceofthetoptee

bM bendingmomentresistanceofthebottomtee

b, redM reducedbendingmomentresistanceofthebottomtee(duetoaxialandshearforce)

fthe(top)tee

entresistanceofthetoptee(duetoaxialandshearforce)tM bendingmomentresistanceo

t,redM reducedbendingmom

vM appliedVierendeelmoment

EdN

designnormal

force

bN normalforceinbottomtee

tN normalforcein(top)tee


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Listofsymbols 13

pl,tN plasticnormalforceresistanceofatee

pl,fN plasticnormalforceresistanceoftheflange

b, RdV shearbucklingcapacity

bw, RdV contributionofthewebtotheshearbucklingcapacity

bw, o, RdV contributionofthewebtotheshearbucklingcapacityofaperforatedweb

EdV designshearforce

bV shearforceinbottomtee

tV shearforcein(top)tee

hV horizontalshearforceinthewebpost

h,RdV shearresistanceofthewebpost

pl,RdV plasticshearresistanceofunperforatedsection

hW sectionmodulusofthewebpostatthecriticalsectionlocation

elasticneutraldepthofteefromouteredgeofflange

plasticneutraldepthofteefromouteredgeofflange

ey

py


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Introduction 15

1 INTRODUCTION

1.1 Motivation

CellularmemberssteelIshapedstructuralelementswithcircularwebopeningsat

regularintervalshavebeenusedasbeams

formorethan30yearsnow.However,in

certaincountries,liketheNetherlandsand

Belgium,applicationseemstolackbehind.

Thiscanprobablybeattributedtoacombi

nationoffactors:unfamiliaritywiththese

beams,thepresentconcretemindedpractise

formultistoreybuildings,andalackof

localiseddesignguides.

Althoughcellularcolumnsarelesscommon,

examplesareavailable.However,inresearch

publicationsnoattentionispaidtothistopic.

Structuralengineersthereforehavetobase

theirdesignsonsimplifiedmethodsof

analysisandgoodengineeringjudgement.

Inordertoexploitthefullcapacityofcellular

columnsasoundbasisisneededandthusa

desireexistsforamorerefinedapproach.

Thesubjectofcellularmemberscametomy

attentionmainlybecauseoftworeasons.

Firstly,anopenthesissubjectwasavailable

forresearchingthepossibilityofusingplate

girderswithcircularopeningsinbridges.

Secondly,atthefirmofconsultingengineers

whereIdidmyworkplacement,Ingenieurs

burovoorBouwtechniek,theyonceapplied

cellularcolumnsinacarshowroom.Becauseofalackofexistingdesignguidance,

theyhadtofindtheirownwayinmakingthe

calculations.Admittedlythesewerequite

conservative.Knowingthis,Ithoughtittobe

worthwhiletogetamorerefinedpredictionof

thecapacityofthesemembers.

Inmysearchforinformationonthesubjectof

cellularmembersIcontactedIr.J.Naessens

fromtheStaalinfocentruminBelgium.

Headvisedmetogetintouchwithsome

peoplewithinArcelorMittal,aworldwideoperatingsteelcompany.Thisresultedinan

invitationtocometotheirresearch

departmentinEschsurAlzette,Luxembourg.

Itwasaconsiderationofparticularinterest

thattomakereliablepredictionsbasedwith

FEMcalculations,realtestdataisneededfor

calibratingthemodels.Becausethesetest

resultsareconfidential,andthecalculation

modeltobeproposedneedstobeverified,itwasdecidedthatitwouldbebesttocarryout

apartoftheresearchworkatArcelorMittals

offices.

1.2 Objectives

Theobjectivesofthisresearcharetwofold:

toinvestigatethebehaviourofcellularmembersunderaxialload

todevelopasuitableandeasytouse

calculationmethodforportalframesusingcellularbeamsandcolumns

1.3 Scope

Thepresentinvestigationdealswiththe

behaviourofasinglebaypitchedroofportal

frameusingcellularbeamcolumns.Although

someapplicationexamplesareavailable

wherecellularmembershavebeenusedas

columnsandinportalframestructures,no

guidanceexistsforthedesignofthese.Furthermoreexperimentalandnumericaltest

evidencelacksandthedesignexperienceis

limitedtothesellerstechnicalassistance.

Theuseofcellularbeamsinportalframe

structureshasbeenrecognisedasatopicof

interestwithinArcelorMittalalready,but

workonaprojecttoinvestigateitsbehaviour

andapplicationpossibilitieswaspostponed

duetoashiftinresearchpriorities.


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16 Introduction

Inthisresearchasimpleandstraightforward

calculationmethodforportalframes

consistingofcellularbeamcolumnshasbeen

developedandimplementedinMicrosoft

ExcelusingVisualBasicforApplications.

Firsttheliteraturestudydiscussesexisting

designmethodsforcellularbeamsandfor

portalframes.Inthesubsequentnumerical

researchcellularcolumnbehaviourhasbeen

studiedinordertorevealpossibledifferences

withthatofplainwebbedsections.3Dfinite

elementportalframeanalyseswerecarried

outtoverifyboththeproposedcalculation

methodanditsimplementation.Finallythecalculationmethodhasbeenappliedtoa

portalframestructureusingcellularmembers,

andtheresultshavebeencomparedwith3D

finiteelementcalculations.

1.4 Limitations

Thisstudyislimitedtothestudyofthe

structuralbehaviourofcellularbeams

columnsincoldsituationonly(normal

temperaturerange,notinfireconditions).Furthermorethefollowinglimitationshold:

onlysymmetricalsections nocompositedesign nocurvedbeams notaperedbeamsandcolumns onlycircularandelongatedwebpost

openingsarecovered

Thelastlimitisbasedonthemostcommon

fabricationprocessandtheexpectedreasonof

application:aesthetics.

1.5 Outline

Thepresentreportisdividedintothreeparts,

eachsubdividedinanumbersofchapters.

PARTILITERATURESTUDY

Chapter2givesageneralintroductionto

cellularbeamcolumnswithinformationon

productionmethods,applicationareaandthecurrentstateoftheartinresearch.

Chapter3paysattentiontothevariousfailure

mechanismsthatmightoccurforbeamswith

webholes.Theinteractionbetweenbending

momentandshearforcearoundweb

openingsisdiscussedqualitatively,andtheadditionalpossiblefailuremodesthatare

introducedbythepresenceofwebholesare

presented.Furthermoretheserviceability

behaviourisdealtwith.

Chapter4addressesexistingcalculation

methodsforcellularbeams.Theadditional

checksrequiredforbeamswithregularweb

openingsarepresented.

ThereaftertheapproachasdevelopedintheECSCprojectLargewebopeningsforservice

integrationincompositeconstructionis

comparedwiththetheoreticalbackgroundsof

thededicatedcomputerprogramARCELOR

CellularBeams.

Thetreatmentofthesebothmethodshasbeen

limitedtothecaseofnoncompositesimply

supportedcellularbeams,whereofthe

openingsareplacedatthecentreline.

Chapter5dealswiththeEurocoderegulations

forthestructuraldesignofpitchedroofportal

frames.Itdiscusseshowbothmaterialand

geometricalnonlinearityaredealtwith,both

onaglobalandalocallevel.Furthermorethe

rulesthatrelatetononuniformmembersare

explained.

PARTIINUMERICALRESEARCH

Chapter6introducesthesecondpartofthis

report,namelythenumericalinvestigation

intothestructuralbehaviourofcellularbeam

columns.

Chapter7firstexplainsthebackgroundsof

thespecialisedfiniteelementcodeSAFIRthat

hasbeenusedthroughouttheresearch,

followedbyadiscussionoftheaccompanying

toolsneededforpre andpostprocessingtheresults.


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Introduction 17

Chapter8givesadetaileddescriptionofthe

studyofglobalflexuralbucklingofcellular

members,madeinordertoconfirmthe

theoreticalresultsacquiredintheliterature

study.Afteranelaborateexplanationofthesetupoftheparameterstudyperformed,its

resultsarepresentedanddiscussed.From

theseitisconcludedthattheproposed

simplifiedrulefordeterminingtheflexural

bucklingcapacityofcellularcolumnscanbe

appliedsafely.

Chapter9presentstheresultsofanother

parameterstudyintowebpostbucklingof

cellularbeamcolumnswhileloadedinaxialcompression.Theimplicationsonboththe

LWOmodelandArcelorsownmodelfor

webpostbucklingarefirstanalysed

analytically,andthesetheoreticalresultsare

validatedagainsttheresultsofthefinite

elementparameterstudy.

PARTIIICASESTUDY

Chapter10illustratestheknowledgegainedinthepreviousparts.TheLWOmethodis

appliedtothedesignofportalframesusing

cellularmembers.Thereforeadesigntoolis

developedinMicrosoftExcelusingVBA.

Fordifferentloadcases,thepredictedfailure

behaviouriscomparedwith2Dand3Dfinite

elementanalyses,andtheExceltool

developedisfoundtodeliversaferesults.

Finallychapter11summarizestheconclusionsthatcanbedrawnfromtheresearchper

formed,andgivesrecommendationsfor

furtherresearch.

Thereportisconcludedbyalistofreferences

andanumberofannexes,givingsome

backgroundsontheEuropeanstandardsas

appliedinthisresearchandmoredetailed

resultsofthebothparameterstudies.

Furthermoreadatadvdisattachedtothereportwhichcontainsallanalysisdataandthe

spreadsheetsandsoftwarethathasbeenused.


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19/215

Literaturestudy 19

PART I-

LITERATURE STUDY


20/215


21/215

Literaturestudy 21

2 INTRODUCTION TO CELLULAR BEAM-COLUMNS

2.1 Open-web sections

Cellularbeamcolumnsshortlycellularbeamsbelongtothelargergroupofsteel

sectionswithwebopenings,thuscreatinga

highermomentofinertiatoweightratio.

Whenusedasfloorbeams,openwebsections

ontheirturnareapartofthegroupoffloor

systemswhichprovideameanstoincorporate

buildingserviceswithinthestructuraldepth

ofthefloor.Basicallyspeakingtwooptions

existforhighlyservicedofficebuildings:

eitherminimisethestructuralzonesothatthebuildingservicescanpassbeneath,or

integratethestructuralmembersandthe

buildingserviceswithinthesamehorizontal

zone[Chung2002].

Integratedfloorsystemscompriseamongst

othersfabricatedbeamswithtaperedwebs,

haunchedbeams,trusses,stubgirders,slim

floorsystemsandbeamswithsingleor

multiplewebopenings.Becauseinthese

systemstheavailabledepthforconstructionisalmostequaltothefloordepth,areduced

overallheightofthebuildingcanbeachieved,

therebyreducingcladdingcosts.Nowadays,

inmostcasesthedesignoffloorbeamswith

webopeningsiscarriedoutrecognisingthe

compositeactionbetweenthesteelbeamand

theconcreteslabontopofit.

Figure2.1 Serviceintegrationthroughweb

openingsincellularfloorbeams

Figure2.2

Variousopeningshapesincellularfloorbeams

of

g

.Alldimensionscanbeadjusted,butnobeneficial

filletweldeffectispresent.

Morecommonlyappliedisanotherprocess,

thatconsistsofflamecuttingthewebofan

existingHorIshapedhotrolledsection,and

thenweldingtheseparatedsectionstiptotip

together.Thematerialthatgetscutoutbythe

twowayflamecuttingprocessisreusedinthe

steelmills.AmongstothersArcelorMittal

(Luxembourg)andWestok(UK)usethismethodtoproducetheircellularbeams.

Steelmemberscanbeequippedwithsingle

multiplewebopenings,whichcantake

differentshapes.Whentheseopeningsare

circularandregularlyspaced,themembers

aredesignatedcellular.Dependingonthe

fabricationprocessotheropeningshapesare

possible,includingsquare,rectangular,

hexagonal(standardcastellatedsection)andoctagonalshapes.

2.2 Production methods

Cellularbeamsareproducedbyarangeof

steelmanufacturers,usingtheirownpatented

processes.TheprocessappliedbyFabsec(UK)

istofabricatethewholegirderbywelding

profiledsteelplatestoformtheflangesand

thewebofthesection.Priortotheweldin

process,openingsarecutinthewebplate


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22 PartI

Figure2.3 Fabricationprocess:flame

cuttingofhotrolledprofiles

Figure2.4 Fabricationprocess:weldingthe

separatedteesectionstogether

Manufacturersofcellularbeamsinother

countriesareCMCSteelProducts(USA),

beprecamberedsuchthatthedeathload

deflectionswillnotgovernthedesign.

Producingcurvedorta

MacsteelTrading(SouthAfrica),Peiner

TrgerGmbH(Germany)andGrnbauerBV

(TheNetherlands).Somemanufacturers(e.g.

Westok,MacsteelTrading)produceexclusivelycellularbeams,whileforothers(e.g.

ArcelorMittal,PeinerTrgerGmbH)theyonly

formapartoftheirwholeproductrange.

Whenproducingcellularbeamsbyflamecut

tingandwelding,thetopandbottomsections

donothavetobethesame:byusingdifferent

basesectionsitispossibletoproducean

asymmetriccellularsection.

Bothproductionprocessesallowtheheightof

theresultingsectiontobeadjustedtoagreat

peredsectionsisalso

thecentroidalline.Curved

ng

tees.

ness

esupports

r

ora

imple(vertical)flat.Whereconcentrated

loadsareintroducedsimpleplatescanbe

weldedabovetheopeningstoavoidlocal

plasticdeformation(ovalisation).

Itispreferablethough,toavoidinfillsand

stiffenersasmuchaspossiblebyadjustingthera

extend.Allbeamsaremadeaccordingtothe

specificationsofthedesigner.Theycaneasily

providedinthesameprocessflow.Tapered

cellularbeamsareproducedbycuttingthewebatanangleto

beamsareproducedbyadjustingthecutti

patterntocreatedifferentbottomandtop

Thentheseteesarebenttotherequiredradii

andweldedtogether.

Curvinginplanisalsopossible,butcaremust

betakenofthefactthatthetorsionalstiff

isrelativelylow.

Whenthechosensectionfailstoperform

satisfactory,thebeamcanbereinforcedlocally.Inhighshearareasnearth

itmaybenecessarytofillorreinforceoneo

moreopenings.Bucklingofawebpostcanbe

avoidedbyaddingtwoparthoops,

s

cellconfigu tion,toreducecosts.

Figure2.5 Circularreinforcedopenings

Figure2.6 Arrangementofsimplepla

avoidlocalplasticdeformation

testo


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Literaturestudy 23

Figure2.7

Filledwebopeningsatsuppforincreasedshearresist

ortance

Figure2.8

Webpoststiffenersandheadedstudsforcompositeapplica

isreallyaviablealternative,moreover,that

integrateddesignmayleadtoalowerpr

tion

a

beamsthanwhenusewould

her

k

causesto

erthanthatofstandard

olledprofiles.

Ithashoweverbeenshownbymanysuccessfuldesigns(especiallyintheUK,butamong

othersalsoinGermanyandFrance)thatsteel

iceof

r

eatly

ellularbeamscontributetoasoundand

Comparedtocastellatedbeamswithhex

gonalopeningshapes,andthusnomaterial

losstheflexibilityinsteadofstandard

dimensions,isamajoradvantage.Therefore

theuseofoptimisedcellularsectionswill

resultinlighter

bemadeofthemostefficientcastellated

sections.Cellularbeamsareavailableindifferentsteel

grades.Usuallyfloorbeamsrequirehigher

steelgradeslikeS355andS460,wherethe

standardgradeS235sufficesforroofbeams.

2.3 Application area

Cellularbeamsarewidelyusednowadays.

However,incertaincountries,liketheNet

lands(andBelgium),applicationseemstolac

behind.Itseemsthatthereisalotofunfamiliarityandalackoflocaliseddesign

guidesforpracticewiththesebeams.

Buttherearemorefundamental

pointout.First,intheNetherlandsmulti

storeybuildingswithmorethanfourfloors

aretraditionallythedomainofconcrete[BmS

2002].Second,thepriceofindividualcellular

beamsisindeedhigh

r

thetotalbuilding,notwithstandingthehighe

priceoftheindividualcellularbeams.

Theuseofcellularbeamsforfloorstructures

iswelldeveloped.Compositeconstruction

makesshallowerandlighterconstruction

possible.Boththeloadbearingcapacityandthestiffnessofthebeamareenhancedgr

bycompositeaction.Cellularfloorbeamsmay

beusedaslongspansecondarybeams,or

heavilyloadedprimarybeams.

Flexibilityintheuseofthefloorareaand

reductionofthestoreyheightandthusofthe

costforthefaadearethemainreasonswhy

c

economicaldesign.

Figure2.9 Hotelatrium


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24 PartI

Designproceduresandprogramsare

availablenowadays,whichenableeasy

calculationforawiderangeofpossibilities.

dandunstiffenedopenings,regularand

b red.

Calculationproceduresfordeterminingthe

fireresistanceofthesesectionshavebeen

developedtoo.Ingeneralafireengineering

calculationusingfiniteelementmethodswill

benecessary.Althoughmethodsforamore

straightforwardassessmentoftherequired

thicknessesofintumescentcoatingsare

available,usuallytheyrelyonconfidentialtestresultsandthereforehavealimitedrangeof

application.Furthermorepublictestresultson

thebehaviourofcellularbeamsprotected

withintumescentcoatingssuggestthatitwill

rulesto

ercurvedorflat.

Forcurvedroofscellularbeamsaretheideal

solution,becausecurvingofthebeamsisalreadypartoftheproductionprocessandas

suchavailableatnoextracost.

Moreover,economiesareachievedin

comparisonwithplaincurvedbeamsdueto

weightsavings.Theradiusofthearchisnot

limitedbythefullspanlength,butbythe

partswhereofdetotalarchconsists.

Anotherwellappreciatedfacetofcurved

cellularbeamsistheirinherentaesthetical

valueandtheirlightimpression.Intherangeofroofspansofover30m,cellular

beamsareabletoserveasanalternativeto

latticegirders,havingtheadvantageoflower

costoflabour.Longspansofover50mhave

beenrealisedalready.

Compositeandnoncompositedesigns,

symmetricandasymmetricdesigns,stiffene

allowfortheincreasedwebposttemperature.

Inroofstructurescellularbeamsarealso

frequentlyapplied,eith

irregularwe openingsareallcove

bedifficultto

specifysimplegeneric

Figure2.10 Apartmentbuilding Figure2.11 Officebuilding

Figure2.13 CurvedroofbeamsFigure2.12 Parkinggarage


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Literaturestudy 25

Figure2.14 Industrialhall Figure2.15 Sportshall

Figure2.16 Roofstructurewithcurved

cellularbeams

Figure2.17 Cellularportalframestructure

withtaperedperforatedcolumns

practice,

.

columns:economicsandaesthetics.In

d

full

Inbeamstheloadingismostlyresistedby

bendingaction,whileincolumnsnormallyaxialforcesdominate.Becausetheweb

contributesmoretothe(pure)axialcapacity

thantothebendingmomentresistance(inthe

strongdirection),theinfluenceofweb

perforationsonthepureaxialcapacityismore

severe.

However,forslendercolumnsitisnotthe

pureaxialcapacitybutthebucklingresistance

(intheweakdirection)thatgovernscolumn

b amongstothe tion

f

e

reaxialload

ial

outperforations,butwith

reducedhorizontaldisplacements.

Contrarytotheconsiderableamountof

researchdevotedtothebehaviourofcellularbeams,resultingindesignguidesfor

nopublisheddesignguideexistsforthe

applicationofcellularmembersascolumns.

Despitethelackofsoundlaboratorytest

evidenceandtheabsenceofpracticaldesign

methods,stillprojectarerealisedinwhich

cellularmembersareappliedvertically

Thereseemtobetwoprimaryreasonstouse

cellular

tallsinglestructures,suchashighbaywarehousesandsocalledsupersheds,thechoice

ismainlydrivenbyeconomics.Theincreased

inertiaofcellularcolumnsisrequiredto

minimisethehorizontaldeflectionsinduce

bywindloads.Inlowerheightcolumnsthe

decisiontousecellularcolumnsismorelikely

tobedrivenbyaesthetics.

Obviouslytheaxialcapacityofcellular

columnsislessthanthatofsectionswitha

crosssectionalarea.Atfirstsighttheimpactofcreatingwebholesseemsmuchgreaterfor

columnsthanfor(longspan)beams.

design.This ucklingcapacitydepends,rs,ontheradiusofgyra

beingthesquarerootofthesecondmomento

inertiadividedbythearea.Bythepresenceof

awebopeningthisradiusincreases,andso

doesthebucklingfactor(ratiobetweenth

bucklingcapacityandthepu

capacity).Forslendercolumnsthisincrease

almostoutweighsthereductioninpureax

loadcapacity,sothatthebucklingloadofa

cellularcolumnisnearlyequaltothatofthesamememberwith


26/215

26 PartI

Figure2.18 Highbayportalframestructu

usingcellularmembers

re

Figure2.19 Cellularwindcolumnsto

supportaglassfaade

Lowerheightcolumnsusuallyhaveahigher

degreeofaxialloadcapacityutilisationand

sufferlessfrombucklinginstability,andthus

theapplicationofcellularcolumnsisnot

likelytoproveeconomical.Butalthoughthestructuralperformancemay

benotoptimalasisthecaseformany

solutionsthevisualattractiveappearanceo

cellularcolumnsmayverywellgivereas

usethemanyway.

Structuralefficiencyisjustoneofallpossib

f

onto

le

design ple,itisverywell

pos l nsofaestheticsitis

opriate.

But t willbethemo c lution,becausenoextra

trea e

:beamswitheitherindividual

urther

with

openingsontheelasticstressdistributionhas

[1974].

However,for

acquiredsolu

estimatingth am.

Suggesteddesignmethodsmostoftenhavea

criteria.Forexam

sib ethatforreaso

decidedthattaperedcolumnsareappr

in hatcaseacellulartaperste onomicalso

tm ntisrequired.

2.4 Current research status

Beamswithwebopeningshavebeena

popularresearchthemeoverthepastfew

decades.Themanyresearchprojects,com

prisingboththeoreticalandexperimental

investigations,canbesubdividedintotwo

maincategoriesorwithmultiple(regularlyspaced)web

openings.Theseopeningsmaybetreatedas

individualwhenthespacingbetweenthe

openingsissufficientlylargetoensurethat

adjacentopeningsdonotinteract.F

moreitispossibletodistinguishbetween

takingintoaccountthecompositeaction

theconcretefloorslabornot,andwhether

openingreinforcementisdealtwith.Inthe

pastallthesecategorieswereapproachedasseparatedesignproblems[Darwin2000].

Forover100yearstheinfluenceofcreating

beenstudied,e.g.byChan&Redwood

anumberofreasonsthe

tionsarenotveryusefulfor

eresistanceofaperforatedbe

verylimitedscopeofapplicability,andgive

onlyacoarseapproximationofthebeamssresistancebytodaysstandards.Elasticdesign

alsoignoresloadcapacityafterfirstyield,


27/215

Literaturestudy 27

andisthereforeespeciallyinappropriatefo

beamswithrectangularwebopenings,whe

largepeakstresseswilloccurduetolocal

bending.Thereforequitealotofresearchhas

beencarriedouttodevelopmoreconveniedesignmethods,andtopointoutwhichlimits

areapplicable.

Becauseofthehighspecificationsinbuilding

servicesinmodernbuildingcon

r

re

nt

struction,

rgeindividualopeningsareoftenformedin

thewebsofsteelbeamstoprovidepassageat

specificlocations.Theseopeningsmayhavea

severepenaltyontheloadcarryingcapacities

offloorbeams,theinfluencedependingonthe

shape,sizeandlocationofthewebopening.Inthe1980sand1990salargenumberoftests

onsteelandcompositebeamswithdiscrete

rectangularopeningswereconductedatdif

ferentuniversities.Asaresult,practical

designrecommendationsweredevelopedand

publishedeitherasseparatepublications:

CIRIA/SCIP068 Darwin1990

orasarticlesinthetechnicaljournals:

Redwood&Cho1993 ASCE1992

Thesedesign tional

rulesandcrit the

res

nin

ned

f

the

o&Chung2002].

la

Chung&Lawson2001methodsprovideaddi

eriatowhichthedesignin

openingsregionshastobetested.Procedu

fordeterminingtheincreaseindeflection

weredevelopedtoo,mosttimesbasedon

elementarybendingtheory,butwithsuitable

modificationtoaccountforthereductio

shearstiffness.Whilethesemethodsaregearedtothedesign

ofbeamswithrectangularopenings,beams

withcircularwebopeningsmaybedesig

byexploitingsimilaritiesinthebehaviouro

rectangularandcircularopenings.

Acommonlyusedruleistomultiplythe

diameterofacircularwebopeningbya

favourablefactorof0.450.50todetermine

lengthofanequivalentrectangularopening.

ThisrulewasfirstproposedbyRedwood[1973],anditprovidesasafethoughconser

vativeapproximation[K

Figure2.20 DealingwithVierendeel

bendingeitherbyanequiv

rectangularopeningorby

inclinedsectionverifications

Forotheropeningshapes,suchamo

alent

dificationpossibletoo.Inacomprehensiveparametric

studyusingthefiniteelementmethod,itwas

t

variousshap rly

beingthe

,

is

shownthats eelbeamswithwebopeningsof

esandsizesbehavesimila

amongsteachotherunderawiderangeof

appliedmomentsandshearforces,thekey

dimensionalparameterofinfluence

criticalopeninglength.Thisholdsforthe

failuremodes,theloaddeflectionbehaviour

theyieldpatternsaswellasfortheshapeofthemomentshearinteractioncurves[Liu&

Chung2003,Chungetal2003].

Figure2.21

Similarmomentshearinteractioncurvesfor

variousopeningshapes


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28 PartI

Castellatedbeamswereusedinthe1930s

already.Especiallyinthetimewhenmateri

costswerehighandlabourcostslow,itwas

attractivetodevisemethodswhichincr

thestiffnessofsteelmembers,withoutincreasingtheweightofsteelrequired.

Earlystudiesconcentratedoninplane

responseinboththeelasticandplasticra

Theoreticalsolutionswerederived,an

extensivemeasurementsweremadeof

stressdistributionsacrossthecrosssectio

al

ease

nges.

d

the

n.

s

al

ciably

is

of

g

Amongthevariousmethodsusedarephoto

elasticinvestigations,elementarybeam

theory,curvedbeamanalysis,Vierendeel

analogy,finitedifferencetechniques,variousfiniteelementschemes,etc.[Gibson&Jenkin

1957,Kolosowski1964,Nethercot&Kerd

1982,Nadjaietal2007].

Whileelementarybeamtheory(witha

reducedwebsection)isthesimplestmethod

ofanalysisofacastellatedbeam,theresults

calculatedbythismethoddeviateappre

fromtheactualvaluesforstressesand

deflections.Thisisbecauselocalbending

neglectedinthisapproach[Handbookcastellatedbeams].

TheapplicationofthetheoryforVierendeel

beamstotheopeningregionsprovedmore

successfulandisstillbeingused.Atan

openinglocationthecrosssectionconsists

twoTsections.Theycarrytheglobalbendin

momentasaxialforceandtheshearcauses

additionallocalbendingmoments.

Figure2.22 Comparisonofexperimentaland

predictedflangestresses

Usuallythepointofcontraflexureisass

umed

ith

lar

kling

er

idual

uldbe

nal

failuremechanismsareintroducedlike

formationofaVierendeelmechanism,

bucklingofthewebposts,weldruptureand

horizontalshearfailureofthewebpost.

Quantitativedataonthelateralbuckling

behaviourofcastellatedbeamswasprovidedbyKerdal,whoshowedthatthisbehaviouris

similartothatofplainwebbedbeams[PhD

Kerdal,Nethercot&Kerdal1982].

Withtheincreaseofcalculationpossibilities

andtobeinlinewithnewbuildingcodes,

designmethodswereupdatedandrefinedto

allowamoreaccurate,andthusmore

competitivepredictionoftheultimateload

e

assessmentof na[Zaarour&Redwood1996,Redwood&

edwood2000].

90s.Their

intr u modernbuilding

pra s orsin

.

atmidlengthoftheTsections,togetherw

alinearvariationoverdeopening.

Becausewebholesincastellatedandcellu

beamsarecloselyspaced,theycaninteractwitheachother,whichmayleadtobuc

orcripplingoftheposts.Theseinteraction

effectsrequiredueattention,asforslend

webstheycangoverntheultimateload

capacity[Uenoyo&Redwood1978].

Effectivelyabeamcontainingwebholes

behaveslikeanassemblyofindiv

structuralcomponents,andthusitsho

checkedagainstdifferentpossiblefailure

modes.TheseweresummarisedbyKerdalinareviewofearliercarriedoutexperimental

programmes[Kerdal&Nethercot1984].

Comparedtoplainwebbedbeams,the

presenceofwebholesmeansthatadditio

capacity.Att ntionwaspaidtoanimproved

thewebbucklingphenome

Demirdjian1998]andtotheeffectof

compositeactiononcastellatedbeams

[Redwood&Cho1993,R

CellularbeamswerefirstusedinSwitzerland

inthe1970s[Stahlbau1970s],butapplication

becamecommonnotbeforethe19

od ction,togetherwith

cti es,liketheuseoflongspanflo

officesandthetendencytodesignmoreslenderstructures,causedarevivalinthe

researchtobeamswithwebopenings


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Literaturestudy 29

Ofcoursealotofresearch,boththeoreti

andnumerical,wascarriedoutbythemanu

facturersofcellularbeamsthemselves.

cal

CI)

r

n

g

crosssection.

low

Openingsinwebs

o

d,

sh

e

ngmoment,andtheHigh

e

l

atsat

In1990theSteelConstructionInstitute(S

intheUKpublishedaguidespecificallydirectedtowardsthecalculationofcellula

beams[SCIP100].Thecalculationmethodin

thisguide,entitledDesignofcompositeandno

compositecellularbeams,consistsincomparin

theappliedactionsonaninclinedsectionwith

theresistanceofthatsection,wherebythe

inclinationangleisvariedsothatiterations

arerequiredtolocatethecritical

Alinearinteractionformulaisusedtoal

forcoexistenceofshearforcesandbendingmoments.

Thismethodwaslaterincorporatedintothe

draftannexprestandardEurocode311

AmendmentA2:AnnexN

[ENV199311,AnnexN].Whenitcamet

convertingtheENVstoENs,itwasdecided

nottoconvertAnnexN,becausenoconsensus

couldbereachedbetweentheparticipating

countriesonthelevelofdetailtobeinclude

andalsotolimitthevolumeofEC3.Ithasbecomecommonpractisetodistingui

betweentheLowMomentSide(LMS),wher

thelocalbendingmomentcounteractsthe

globalbendi

MomentSide(HMS),wherethelocaland

globalmomentactinthesamedirection.

IntheapproachofSCIP100theultimate

capacityislimitedbytheformationofone

plastichingeattheLowMomentSide.

BecauseitwasexpectedthatfortruefailurbyaVierendeelmechanismfourplastic

hingesarerequired,thismechanismwas

investigatedinmoredetailbyChungeta

[2001]andasimpleempiricalmomentshear

interactioncurvewasproposed.

Itappearsthatshearyieldingisvery

importantasitpromotestheformationof

plastichingesattheHighMomentSide.Inthe

paperadesignmethodisproposedinwhich

loaddistributionacrossthewebopeningthresultsfromtheformationofplastichinge

boththeLMSandHMSisincorporated.

Figure2.23

LowMomentSide(LMS)and

hibited.

are

r

is

cal

arinteractioncurvesareoften

citts

its p

HighMomentSide(HMS)

Themethodisvalidforclass1/2(plastic/

compact)sectionsontheassumptionthat

instabilityispro

Chungrecognisestwodesignapproachesto

assessthestructuralbehaviourofbeamswith

webopenings[Chungetal2001]:

Tsectionapproach

perforatedsectionapproachIntheTsectionapproachallglobalactions

representedaslocalforcesandmomentsand

thesearecheckedagainstthesection

capacitiesoftheTsections,takinginto

accountthecombinedeffectofaxialandshea

forceonthebendingmomentcapacity.

Theperforatedsectionapproachaimsat

comparingtheglobalactionsdirectlywiththe

capacityoftheperforatedsectionunder

coexistingshearforceandbendingmoment,e.g.inASCE[1992]andChungetal[2001].

Thedesignprocedureinthefirstmethod

rathercomplicated.Duetothecomplexityof

theinteraction,usuallysimplificationsare

madeinordertolimitthecalculationeffort,

leadingtoconservativeresults.

Inthesecondmethodsimple,empiri

momentshe

used.Althoughthedesignrulesarerelatively

simple,theempiricalnatureoftheimpliallowancefortheVierendeelmomentlimi

sco eofapplicability.


30/215

30 PartI

The signsoftware

ng

Furthermorethemethodtoverifytheweb

postbucklingphenomenahasbeengreatly

improved,andalsothemethodtocalculate

deflections.

Sofaralmostallresearchdescribedtookplace

eitherintheUSAorCanadaorintheUnited

Kingdom(bySCI).Guidanceintendedforuse

inmainlandEuropehasbeenratherlimited.

Forexample,inDutchonlyinformationontheanalysisofcastellatedbeamsisavailable,

whichisentirelybasedonasmartapplication

methodsofc ndapplicationis

methodusedinthede

providedbyArcelorMittaltakesitsstarti

pointinthemethodasdescribedinSCIP100

andAnnexN(inclinedTsections).Itsscope

howeverhasbeenextendedtocoverasymmetricandcompositebeamsaswell.

ofthecurrent

Noreference

buildingcodes[BmSConstrA].

ismadetomoreadvanced

lculation,aa

limitedtostandardcastellatedbeamranges.

WhenitbecameclearthatAnnexNwouldnot

beincludedinthefinalEurocode,workwas

undertakenwiththeobjectivetoupdateand

improvetherulesoftheAnnex,towidenitsscopetocompositegirdersandtocometo

designrecommendationsatanEuropean

level.In2001theECSCprojectLargeweb

openingsforserviceintegrationincompositefloors

[LWO]startedandwasfinishedin2003.

Figure2.24 Oneoftheoutcomesofthe

LWO+project:designsoftware

Theaimoftheprojectwastoexperimentally

andtheoreticallyinvestigatethebehaviouro

steelandcompositebeamswithweb

openings.Alltestresultscouldbeverifiedby

adequatefiniteelementsimulations.Forpostbuckling,anewmodel

f

webwasproposed

al

f

edas

e

seof

ated.

te

d

w

old

realtest

fire

whichisabletodealwithrectangular,circular

andelongatedopeningsinaconsistent

mannerusingastrutanalogy.

LWOnotonlycoversdesignundernorm

(cold)conditions,butalsounderfire

conditions.Furthermoreworkwasperformed

tocontributetoimprovedmanufactureo

cellularbeams.

Theoutcomesoftheprojectareanextensivedesignguide,togetherwithacondensed

versioninEurocodestyleformat(propos

anewAnnexN),simplifieddesignaidsto

quicklyestimateasectionsizeinpredesign

stageandasoftwareforthecalculationof

compositebeamscontainingwebopenings.

Regardingthebehaviourinfireconditions,it

wasconcludedthatingeneraltheinneredge

ofopeningsshouldbeprotectedinorderto

avoidaspecificassessmentofthetemperaturfield.Becauseonlyoneloadedtestwas

conducted,nodefiniteguidanceontheu

sprayedprotectioncouldbeformul

In2005theLWOprojectwasfollowedbya

RFCSvalorisationproject[LWO+]topromo

theknowledgegained(finishedin2006).

TheresultsoftheECSCprojectwereupdate

anddisseminatedtopractitioners,andane

softwarewasdevelopedfordesigninc

condition,togetherwiththepreparationofStateof theArtreportsindifferent

languages.

Thebackgroundtheorytothedesignmethod

developedintheLWOprojectwasalso

presentedinanumberofjournalpapers:

Lawson&Hicks2005 Lawsonetal2006

Thesealsocomparetheoutcomesofthe

designmodeltoFEManalysesand

results.However,specifictopicsliketheresistanceandthevibrationalbehaviourof

thosebeamsarenotconsideredherein.


31/215

Literaturestudy 31

Figure coating

Fur ]

was r

prim r

in

.

ar

designandmanufactureofcellularbeams.

Whiletheassessmentofvibrationalbehaviour

offloorsusingcellularbeamsisanalogousto

thatoffloorswithplainwebbedbeam,see

VibrationGuide[2007],thebehaviourinfire

conditionsisfarmorecomplex.

Untilrecentlyalmostallresearchwascon

cernedwithdesignincoldsituation.Inmore

recentresearchattentionwaspaidtothe

behaviourinfireconditionstoo.

Fromafirstinvestigationitbecameclearthat

theopeningsgiverisetoincreasedwebpost

temperatures.Therebythestrengthofthe

webpostmayverywellbecritical[TN2002].

Theincreasedwebposttemperatureswere

validatedandconfirmedforprotectedbeams

byBailey[2004,UMIST].Forunprotectedsteel

cellularbeamsnoincreaseinwebpost

temperaturewasobserved.

ichsaysto

ut),

ndthenincreasethethicknessby20%.

fotherinformation,thisrulewas

ofte a h

intu e

Howev

results

cannot

We talshear)

oftencand is

zonere n.Therefore

further

theme

cellular andtoprovidemore

ealisticrulestodeterminetherequired

tumescentcoatings.

The h

dea s.

Gen iSCI nshave

beenissuedtointumescentmanufactures,

whichallowmorefavourablelimiting

temperaturesbasedontheactualperformance

oftheirparticularproduct.

Ithasbecomeapparentthatfailuremodesare

notnecessarilythesamefordesignatambient

temperatureandinfireconditions.Therefore

itisnotadequatetobasethefireprotection

requirementsonroomtemperaturestructuralanalysis,asispossibleforplainbeams,buta

separateanalysisatelevatedtemperatures

mustbeconducted[Simms2007].

Nowresearchiscarriedoutonthefire

behaviourofcompositecellularbeams.Ithas

beenpointedoutthatsomeaxialrestraintwill

enhancetheultimateloadcapacityofcom

positecellularbeamsinfireconditionsgreatly

[ThesisRini].Furthermoreworkisgoingonto

providequantitativedataonthestructuralwebpostfailuretemperatureofcomposite

cellularbeams[Nadjaietal2007].

2.25 Swellingofintumescent

duetofire

thermoreanAccessSteelresource[SN019

epared.Thisdocument,whichisp

a ilyaimedatpractisingengineers,

providestheapproachthatwasdeveloped

thescopeoftheLWOproject,andalsogives

simpledesignrulesforopeningsoflimited

sizeplacedatspecificlocations.

Asaresultanunifiedanalyticaldesign

methodforanalysisatambienttemperature

wasmadeavailabletotheEuropeanmarket

In2004theInternationalInstituteofCellul

BeamManufactures(IICBM)wasformed,with

theaimtohelpdevelopstandardsforthe

IntheUnitedKingdompassivefireprotection

(sprayed,board)forcastellatedbeamswas

usuallybasedonarulewh

determinetherequiredthicknessoffire

protectionmaterialfortheoriginalsection(fromwhichthecastellatedsectionwasc

a

Inabsenceo

n ppliedtocellularbeamsprotectedwit

m scentcoatings(active)also.

er,fromtheaforementionedtest

itbecameclearthatthis20%rule

besafelyappliedtocellularbeams.

bpostfailure(buckling,horizon

ontrolsthedesignofcellularbeams,thustheincreasedtemperaturesinth

quirethoroughattentio

researchwasconductedtounderstand

chanicsofthestructuralbehaviourof

beamsinfire,

r

thicknessofin

SCIpreparedanumberofreportswhic

lwiththefiredesignofcellularbeam

er cdesignguidanceexistsintheformofRT1085.Productspecificversio


32/215

32 PartI

2.5 Future design development

Inviewoftheresearchworkalreadydone,

someareasofinteresttobecoveredinfuture

developmentsare:

catenaryeffectinfireconditionsforcompositefloors

firebehaviourofbeamswithrectangularwebopenings

incorporationofaxialloadinganddifferenttypesofsupportconditions

behaviouranddesignoftaperedcellularmembers

Itisnotedherethatnoactivitiesfromthe

IICBMhavebeenseensince2005.Twomain

partnershowever,ArcelorMittalandWestok,haveagreedtocooperateinresearchactivities

andtodevelopanewsoftwareforthedesign

ofcellularbeamsjointly.Thissoftwarewill

alsocoverthedesignoftaperedbeams,

elongatedopenings,etc.Whenthefinal

versionsoftheEurocodeswillcomeinto

force,designersfromtheUnitedKingdomas

wellasthosefrommainlandEuropewillbe

abletousethesametool.

2.6 Advantages and disadvantages

Thissectionsummarizesthemainadvantages

anddisadvantagesofcellularmembers.

Advantages increasedspanspossible(flexibility) passageofservicesthroughweb

openingsfeasible(functionality)

specificationsareeasytoadjusttowardsspecificneeds(adaptability)

theofferofanewmeansofarchitecturalexpression(appearance)

availabilityofhighperformancedesigntools(support)

materialsavingsandreductionofthenumberoffoundations(sustainability

&economics)

Disadvantages

lesssuitableforconcentratedloads morecalculationeffortrequired severereductioninpureaxialcapacity increasedproductioncosts


33/215

Literaturestudy 33

3 MECHANICAL BEHAVIOUR OF BEAMS WITH WEB OPENINGS

3.1 Introduction

Thepresenceoftheholesinthewebmeansthatthebeamsstructuralbehaviourwillbe

differentinanumberofrespectsfromthatof

plain,uniformmembers.Notonlytherelative

importanceoftheusualmodesoffailureis

altered,butalsonewpossiblefailure

mechanismsareintroduced.Inthischapter

themechanicalbehaviourofbeamswithweb

openingsisdiscussed,togetherwitha

descriptionofthevariouspossiblefailure

mechanisms.Criteriatocheckagainstthesefailuremodesareprovidesinthenextchapter.

Mostattentionisgiveninthischaptertothe

behaviourandfailuremechanismsthatdiffer

fromthatofplainwebbedbeams.Failure

modesthatarelargelysimilartotheseof

standardsectionsareonlybrieflytouched.

Asnopublictestdataisavailableregarding

thebehaviourofcolumnswithwebopenings,

onlybeamsaredealtwithinthischapter.

3.2 Global bending and shear

Oneofthemostobviousobservationsfrom

testsisthelargedependenceofthebehaviour

ofbeamswithwebopeningsontheratioof

momenttoshear,theM/Vratio.

Forsimplysupportedbeamscarryinga

uniformdistributedload,thelocationof

maximumappliedmoment(midspan)differs

fromthemaximumshearposition(atthe

supports).Thereforefirstseparateattentionisgiventothebendingmomentcapacityandthe

verticalshearcapacity.

Astheglobalbendingmomentcapacityistoa

largeextenddeterminedbytheflanges,the

influenceofthewebperforationisrather

small.Globalbendingofthebeamwillbe

resistedpredominantlybytensioninthe

bottomteeandcompressionintheuppertee.

ItwasalreadydescribedbyToprac&Cooke

[1959]thatinaspan,subjectedtoapurebendingmoment,theTsectionsaboveand

belowtheholesyieldinamannersimilarto

thatofaplainwebbedbeam.Thespreadof

yieldtowardsthecentralaxiswasstoppedbythepresenceoftheholesbywhichtimethe

twothroatsectionshadbecomecompletely

plasticincompressionandintension.Halleux

[1967]wasthefirsttointroduceplastictheory

fortheanalysisofthebehaviourofcastellated

beams.Forfullybracedspecimensunderpure

bending,theoccurrenceofapureflexural

mechanismwasobservedindeed.Thusthe

behaviourisjustlikeaplainwebbedbeam.

Itisobviousthattheinfluenceofwebholesontheshearcapacityismorepronounced.

Generallyitisthewebthattransmitsthe

verticalshearforce.Theshearcapacityatan

openinglocationmaybecalculatedby

additionoftherespectiveshearcapacitiesof

thetopandbottomtee.

Whenthebendingandtheshearmechanisms

areconsideredseparately,theyarerarelythe

criticalmodesoffailureincellularbeams.

However,foropeningsintheregionwherebothshearforceandbendingmomentare

present,additionalbendingiscreateddueto

thetransferoftheshearforceacrossthe

opening.

ForlowM/Vratiostheeffectsofsecondary

bendingmayevendominatetotheextend

thatthesignofstressesattheLowMoment

Sideisreversed.

Figure3.1

Failureofacompositebeam:

b)lowmomenttoshearratio

a)purebending


34/215

34 PartI

Figure3.2 Vierendeelbendingover

byisan

llelogram.

ften

ties

the

losetothoseproducedinafullbendingsituation,andalsobecauseshortspans

usuallycarryhigherloadssoshearforce

bal)

r

ty.

inw

pport

rtis

ngs

s

rovisionsinthecodesforthedetermination

ofthelateralbucklingstrengthofplain

webbedbeamscouldalsobeusedfor

castellatedbeams,makinguseofthecross

sectionalpropertiesattheopeninglocation.

Thealternativeapproachofcalculatingthe

resistanceagainstlateralbucklingofthetee

sectionincompression,withtheeffectiven uate

lateralsuppo .

arectangularopening

Thismechanismwasfirstreportedby

Alffillischetal[1957](andalsodiscussed

Toprac&CookeandHalleux).Infactit

extensionoftheflexuremechanism,butnow

withV0.Itshowsaverypronounced

distortioninthemannerofapara

Becauseoftheanalogywiththestructural

responseofaVierendeelgirder,theoccur

renceofthesesecondaryeffectsiso

labelledVierendeelbehaviour.

Generallyfourplastichingesatthecorners

ofaholearerequiredforthemechanismtodevelop.Failureduetothissocalled

Vierendeelmechanism,orashearforce

mechanism,isalwaysaccompaniedby

excessiveplastificationattheplastichinge

locations.Forlargesinglewebopeningsthis

mechanismislikelybedecisive.

TheVierendeelmomenthastoberesistedby

Tsections,whosecapacityisreducedbythe

presenceofaxialandshearforces.

Fromthestudyofthegeometricalproperofcastellatedbeamswhichfailedduetothe

formationofaVierendeelmechanism,itis

clearthatthistypeofmechanismismore

likelytodevelopinbeamswithsomecombi

nationofashortspan,awidewebpostand

shallowteesections[Kerdal&Nethercot

1984].Thisisbecauseanincreasedsizeof

webpostwillproducealargersecondary

momentandthusstresseswhicharemore

c

becomedominantcomparedtothe(glo

bendingmoment.Withincreasingopening

lengththeVierendeelmomentwillfurthe

increase,reducingtheultimateloadcapaci

Enlargedopeningsarethereforebestplacedareaswhereshearforcesarerelativelylo

andthefullbendingresistanceisnotyet

utilised,i.e.intheareabetweenthesu

andmidspan(forsimplysupportedbeams).

3.3 Lateral-torsional buckling

Forbeamsthatarenotaxiallyloaded,theonly

globalbucklingmodeislateraltorsional

buckling.Ifnoadequatelateralsuppo

provided,thismodewillalmostalwaysbedominantovertheflexuremechanism.

Althoughithasbeenshownthatthelateral

torsionalbucklingcapacityisindeed

influencedbythepresenceofwebopeni

[Thevendran&Shanmugam1990],test

revealednofundamentaldifferencesin

behaviour:bothplainwebbedandcastellated

beamsexhibitedthesamelaterallybuckled

configurationconsistingofasmooth

continuousprofileandnodistortionofthewebpostswasobserved[Kerdal&Nethercot

1984].Thereforeitwasconcludedthatthe

p

lengthtake betweentwopointsofadeq

rt,isknowntobeconservative

Support

Yielding orbuckling

Cracking Concretecrushing

Yielding

Compression

Tension

Web-post buckling

Web buckling

Web-postbending

Web-postshear

spacedopenings(composite)

Figure3.3 Modesoffailureatclosely


35/215

Literaturestudy 35

3.4 Web-post failure mechanisms

Largesinglewebopeningsareusuallyspac

atsufficientdistancetoavoidinteraction.

However,forcloselyspacedopeningsthis

interactionisinevitableandsomenewfailure

ed

the

ng

ns

.In

in

thetopandbottomtees.

ive.

owever,failureismore

peningegion.Otherwisethebeamshouldbe

reinforcedlocally.

u isin

manycasest hanism.From

thehorizontalshearingforce,combinedwith

theverticalshearforcesthatactonthetees,

diagonaltensileandcompressiveactionis

developedinthewebpost,whichmaycause

(local)lateraltorsionalbuckling.

modesareintroduced.

Itfollowsfromhorizontalequilibriumthat

webposthastotransmitahorizontalsheari

force,beingequaltothedifferenceintensio

inthebottomchords(positivebending)

additionthewebpostsinasymmetricand

compositebeamswillalsobesubjecttoin

planebendingmomentsinordertomainta

equilibriumbetween

Fornarrowposts,thehorizontalshearcapacity,andforasymmetricopeningsthe

purebendingresistancemightbedecis

Forslenderpostsh

likelytooccurbywebpostinstability.

Ingeneraltwokindsofwebpostbuckling

exist:lateraltorsionalbucklingduethe

horizontalshearandwebcripplingunder

concentratedloads.

Thelattermodeisbestavoidedbynotplacing

anyconcentratedloadaboveanor

Webpostb cklingduetosheartransfer

hecontrollingmec

Figure3.4 Webpostyieldingdueto

horizontalshear

Figure3.5 Forcesinawebpostwithan

asymmetricallyplacedopening

Thetendencytobuckledependsonthewidth

andheightofthewebpostandthed/tratioof

theweb.Duetothecomplexityofthe

problem,severaldesignmethodshavebeen

proposed.ThemethodinSCIP100wasof

empiricalnature,withalimitedscopeof

y. ,

resultingfrom

simplebutmoregeneralstrutmodel,thatalso

n nings.

applicabilit Thepresentdesignmethod

theLWOprojects,isbasedona

coversrecta gularandasymmetricope

Figure3.6 Webpostbucklingbehaviour

Figure3.7 Webpostlateraltorsional

bucklingdueto(vertical)shear


36/215

36 PartI

Figure3.8 Horizontalweldrupture

IntheACBprogramanothermodelforweb

postbucklingisused,thatwasdevelopedaspartofanoptimisationstudytocellular

beamscarriedoutbyCTICMonbehalfof

Arcelor.Generallysaiditisamoreadvan

a

ced

werederivedfromalarge

ossiblefailuremodes.Inmanycases

ringhaveprovedtobethe

g

.

r,butlocalweb

ucklingispreventedbyusingthelimiting

valuesforaclass3webwhentheoutstandof

thewebofacompressedteeisclassifiedclass4,sothattheelasticpropertiesareused.

Shearbucklingcanoccurinhighshearareas

(e.g.nearsupports)andisalsoinfluencedby

thepresenceofwebopenings.Itmaygovern

thedesignofabeamwithsingleopenings,but

be uremodes

aredominant

ec

herearetwoeffectsduetowebperforations

h ,

inginsteadofby

lycalledadditional

canbesignificantfor

For l totaladditional

def t doesnotexceed20%.

Reg d haviouras

runperfo sothat

maybeestimatedbytheethods(allowingfor

the

model,whichalsocoversasymmetricsections

andtakesintoaccountthepostcriticalreserve

strength.However,thecoefficientsto

calculatethecriticalforcesinthewebpost

andintheTsectionsarenotavailablein

public,asthey

measurementprogrammeofwebpostimperfectionsinARCELORCellularBeams,

whereoftheresultsareproprietary.

3.5 Additional failure modes

Apartfromtheabovementionedfailure

mechanisms,therearesomeadditional

p

howevertheywillnotgovernthedesign.

Theweldbetweenthetwohalvesofacellular

beamthatisproducedfromhotrolledsectionsisalwaysassumednottoinfluence

theglobalandlocalstructuralbehaviour.The

requiredthicknessisdeterminedsuchthatthe

horizontalshearforcecanbetransmitted.

Ithasbeenshownthatitisnotnecessaryto

makefullbuttwelds.Twosidedfilletweld

withoutchamfe

mostefficientandeconomicalsolution.

Localflangebucklingispreventedbyusin

class3platepartsorlower.Cellularbeamsmadeoutofhotrolledsectionsmostoften

haveflangesthatareatleastclass2(compact),

sothatthefullplasticcapacitycanbeutilised

Thewebclassmaybehighe

b

forcellular amsusuallyotherfail

.

Forr tangularwebopenings,bucklingofthe

compressedteeshouldbechecked.Incellular

beamsthisfailuremechanismhasnotbeenobservedbeforereachingthecrosssectional

capacityofthetee.Elongatedopeningswere

showntobehavelikerectangularopenings,

andthusaresusceptibletoteebucklingtoo.

3.6 Serviceability performance

T

whic causeanincreaseindeflections.First

thesecondmomentofareaisreducedwhich

addstothepurebendingdeflection.Second,atanopeningpositionverticalloadhastobe

transferredbylocalbend

hear.Thistermisusuals

sheardeflectionand

lon pgo enings.

thece lularbeams

lec ionsusually

ar ingvibrations,thesamebe

ratedbeamsisobserved,fo

thenaturalfrequencysam ae pproximationm

effectoftheopenings).

Figure cklingabovea

rectangularopening

3.9 Teebu


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Literaturestudy 37

3.7 perature

As apter2,onbeforehand

itc herthefailuremodeat

creasedtemperaturewillbethesameasat

se

itions

3.8 Summary of failure mechanisms

Inconclusionsthereexistanumberoffailure

mechanismsforbeamswithwebopenings.

Fornoncompositecellularbeamstheycanbe

summarisedasfollows:

Globalfailuremodes

purebending pureshear interaction lateraltorsionalbuckling

Localinstabilitymodes

shearbuckling

localflangebuckling localwebbuckling

)

ckling

webcrippling weldrupture

Indesignitisnecessarytoensurethatall

relevantfailuremechanismsareaddressed.

However,thismayoftenbedoneinanimplicitway.Furthermore,itisnotedthatnot

allmodesoffailureareasimportant.While

theVierendeelmechanismhasbeen

researchedextensively(e.g.byChung),for

beamswithmultipleopeningsusuallyother

failuremodesdominate.Cellularbeamsare

likelytofailbywebpostbucklingandwhen

thisisprevented,bylateraltorsionalbuckling.

Optimisationisonlytobegainedwhen

calculationmethodsforgoverningfailuremechanismsarerefined.

Behaviour at elevated tem

alreadynotedinch

annotbesaidwhet

in

roomtemperature.Thewebopeningscauincreasedtemperaturesinthewebposts.

Thereforeasepa

Documents

Cellular Theses