HOLLOW SECTIONS INSTRUCTURAL APPLICATIONSJ. Wardenier, J.A. Packer, X.-L. Zhao and G.J. van der Vegte ISBN 978-90-72830-86-9 CIDECT, Geneva, Switzerland, 2010 Thepublisherandauthorshavemadecarefuleffortstoensurethereliabilityofthedatacontainedinthis publication,buttheyassumenoliabilitywithrespecttotheuseforanyapplicationofthematerialand information contained in this publication. Printed by Bouwen met Staal Boerhaavelaan 40 2713 HX Zoetermeer, The Netherlands P.O. Box 190 2700 AD Zoetermeer, The Netherlands Tel. +31(0)79 353 1277 Fax+31(0)79 353 1278 E-mailinfo@bouwenmetstaal.nl iiPREFACE The global construction market requires a world-wide coordination of product-, testing-, design- and execution-standards,sothatcontractsfordeliveryofproductsandforengineering-andconstructionservicescanbe agreed on a common basis without barriers. The mission of CIDECT is to combine the research resources of major hollow section manufacturers in order to create a major force in the research and application of hollow steel sections world wide. This forms the basis of establishing coordinated and consistent international standards. For the ease of use of such standards, it is however necessary to reduce their content to generic rules and to leavemoreobject-orienteddetailedrulestoaccompanyingnon-conflictingcomplementaryinformation,that have the advantage to be more flexible for the adaptation to recent research results and to be useable together with any international code. ThebookbyJ.Wardenier,J.A.Packer,X.-L.ZhaoandG.J.vanderVegte"Hollowsectionsinstructural applications"issuchasource,developedinaninternationalconsensusofknowledgeonthetopic.It incorporatestherecentlyreviseddesignrecommendationsforhollowsectionsjointsoftheInternational Institute of Welding, IIW (2009) and CIDECT (2008 and 2009). Both are consistent with each other and are the basisfortheDraftISOstandardforHollowSectionJoints(ISO14346)andmayformthebasisforfuture maintenance, further harmonisation and further development of Eurocode 3 (EN 1993-1-8), AISC (ANSI/AISC 360) and the CISC recommendations. FortheusetogetherwithEN1993-1-8andANSI/AISC360,bothbeingbasedonthepreviousIIW(1989) recommendations, the main differences to these rules are highlighted. Theauthorsareallinternationallyrecognizedexpertsinthefieldoftubularsteelstructures,threeofthem having been chairmen of the IIW-Subcommission XV-E on "Tubular Structures" since 1981. This committee is thepre-eminentinternationalauthorityproducingdesignrecommendationsandstandardsforonshoretubular structures. This book should therefore be an invaluable resource for lecturers, graduate students in structural, architectural and civilengineering,explainingtheimportant principlesinthebehaviouroftubularsteelstructures.Itisalso addressedtodesignersofsteelstructureswhocanfindinitthespecialitemsrelatedtotheuseofhollow sections, in particular joints, their failure modes and analytical models as supplements to more general design codes. Aachen, Germany, August 2010 Prof. Dr.-Ing. Dr.h.c. Gerhard SedlacekiiiivACKNOWLEDGEMENTS This book gives the background to design with structural hollow sections in general and in particular for joints to hollow sections. For the latter, the recently updated recommendations of the International Institute of Welding (IIW, 2009) and CIDECT (2008 and 2009) are adopted. Thebackgroundtodesignrecommendationswiththerelevantanalyticalmodelsisespeciallyimportantfor students in Structural and Civil Engineering, whereas the design recommendations themselves serve more as anexample.Sincethe availablehours forteaching SteelStructures,andparticularlyTubularStructures,vary fromcountrytocountry,thisbookhasbeenwritteninamodularform.Thepresentationgenerallyfollows European codes, but the material is readily adapted to other (national) codes. Sincethefirsteditionofthisbookwasusednotonlybystudentsbutalsobymanydesigners,thissecond editionwasneededduetotherecentupdateoftherecommendationsbyIIWandthesubsequentrevisionof the CIDECT Design Guides Nos. 1 and 3 in 2008 and 2009. The new IIW (2009) recommendations and the revised CIDECT Design Guides Nos. 1 and 3 (2008 and 2009) areconsistentwitheachotherandarethebasisfortheDraftISOstandardforHollowSectionJoints(ISO 14346).AlthoughthecurrentEurocode3(EN1993-1-8,2005)andAISC(2010)recommendationsarestill basedonthepreviousIIW(1989)andCIDECT(1991and1992)recommendations,itisexpectedthatinthe next revision these will follow the new IIW and CIDECT recommendations presented in this book. Besidesthestaticdesignrecommendationsandbackgroundforhollowsectionjoints,informationisgivenfor memberdesigninChapter2,compositestructuresinChapter4,andfireresistanceinChapter5.These chapters fully comply with the latest versions of the Eurocodes (EN 1993 and EN 1994). Further, fatigue design of hollow section joints is covered in Chapter 14. WewishtothankourcolleaguesfromtheIIWSub-commissionXV-E"TubularStructures"andfromthe CIDECT Project Working Group and the CIDECT Technical Commission for their constructive comments during the preparation of this book. We are very grateful that Prof. J. Stark and Mr. L. Twilt were willing to check Chapters 4 and 5 respectively on composite members and fire resistance. AppreciationisfurtherextendedtotheauthorsofCIDECTDesignGuidesNos.1to9andtoCIDECTfor making parts of these Design Guides or background information available for this book. Finally, we wish to thank CIDECT for the initiative to update this book. Delft, The Netherlands, September 2010 Jaap Wardenier Jeffrey A. Packer Xiao-Ling Zhao Addie van der Vegte CONTENTS 1.Introduction1 1.1History and developments1 1.2Designation2 1.3Manufacturing of hollow sections2 2.Properties of hollow sections9 2.1Mechanical properties9 2.2Structural hollow section dimensions and dimensional tolerances10 2.3Geometric properties11 2.4Drag coefficients14 2.5Corrosion protection14 2.6Use of internal void15 2.7Aesthetics15 3.Applications29 3.1Buildings and halls29 3.2Bridges29 3.3Barriers29 3.4Offshore structures30 3.5Towers and masts30 3.6Special applications30 4.Composite structures37 4.1Introduction37 4.2Design methods37 4.3Axially loaded columns37 4.4Resistance of a section to bending39 4.5Resistance of a section to bending and compression39 4.6Influence of shear forces39 4.7Resistance of a member to bending and compression39 4.8Load introduction41 4.9Special composite members with hollow sections41 5.Fire resistance of hollow section columns49 5.1Introduction49 5.2Fire resistance50 5.3Unfilled hollow section columns52 5.4Concrete filled hollow section columns53 5.5Water filled hollow section columns55 5.6Joints56 6.Design of hollow section trusses65 6.1Truss configurations65 6.2Joint configurations65 6.3Limit states and limitations on materials66 6.4General design considerations67 6.5Truss analysis68 7.Behaviour of joints75 7.1General introduction75 7.2General failure criteria77 7.3General failure modes77 v7.4Joint parameters77 8.Welded joints between circular hollow sections81 8.1Introduction81 8.2Modes of failure81 8.3Analytical models81 8.4Experimental and numerical verification83 8.5Basic joint strength formulae83 8.6Evaluation to design rules84 8.7Other types of joints85 8.8Design charts86 8.9Relation to the previous recommendations of IIW (1989) and CIDECT (1991)87 8.10Concluding remarks87 9.Welded joints between rectangular hollow sections103 9.1Introduction103 9.2Modes of failure103 9.3Analytical models104 9.4Experimental and numerical verification106 9.5Basic joint strength formulae106 9.6Evaluation to design rules107 9.7Other types of joints or other load conditions107 9.8Design charts109 9.9Concluding remarks109 10.Welded joints between hollow sections and open sections129 10.1Introduction129 10.2Modes of failure129 10.3Analytical models129 10.4Experimental verification131 10.5Evaluation to design rules131 10.6Joints predominantly loaded by bending moments131 11.Welded overlap joints141 11.1Introduction141 11.2Modes of failure141 11.3Analytical models for RHS overlap joints141 11.4Analytical models for CHS overlap joints143 11.5Analytical models for overlap joints with an open section chord143 11.6Experimental and numerical verification143 11.7Joint strength formulae144 12.Welded I beam-to-CHS or RHS column moment joints151 12.1Introduction151 12.2Modes of failure151 12.3Analytical models151 12.4Experimental and numerical verification153 12.5Basic joint strength formulae153 12.6Concluding remarks154 13.Bolted joints161 13.1Flange plate joints161 13.2End joints161 13.3Gusset plate joints162 13.4Splice joints162 vivii13.5Beam-to-column joints162 13.6Bracket joints163 13.7Bolted subassemblies163 13.8Purlin joints163 13.9Blind bolting systems163 13.10Nailed joints163 14.Fatigue behaviour of hollow section joints175 14.1Definitions175 14.2Influencing factors175 14.3Loading effects176 14.4Fatigue strength177 14.5Partial factors177 14.6Fatigue capacity of welded joints177 14.7Fatigue capacity of bolted joints179 14.8Fatigue design180 15.Design examples193 15.1Uniplanar truss of circular hollow sections193 15.2Uniplanar truss of square hollow sections197 15.3Multiplanar truss (triangular girder)197 15.4Multiplanar truss of square hollow sections199 15.5Joint check using the joint resistance formulae199 15.6Concrete filled column with reinforcement200 16.References209 Symbols221 CIDECT229 viii1. INTRODUCTION Designisaninteractiveprocessbetweenthe functionalandarchitecturalrequirementsandthe strength and fabrication aspects. In a good design, all theseaspectshavetobeconsideredinabalanced way.Duetothespecialfeaturesofhollowsections andtheirjoints,itishereevenofmoreimportance thanforsteelstructuresofopensections.The designershouldthereforebeawareofthevarious aspects of hollow sections. Manyexamplesinnatureshowtheexcellent propertiesofthetubularshapewithregardtoloading incompression,torsionandbendinginalldirections, seeFigs.1.1and1.2.Theseexcellentpropertiesare combinedwithanattractiveshapeforarchitectural applications(Figs.1.3and1.4).Furthermore,the closed shape withoutsharpcornersreducesthearea tobeprotectedandextendsthecorrosionprotection life (Fig. 1.5). Anotheraspectwhichisespeciallyfavourablefor circular hollow sections is the lower drag coefficients if exposed to wind or water forces. The internal void can be used invariousways,e.g.toincreasethebearing resistancebyfillingwithconcreteortoprovidefire protection.Inaddition,heatingorventilationsystems sometimes make use of the hollow section columns. Althoughthemanufacturingcostsofhollowsections arehigherthanthoseforothersections,leadingto higherunitmaterialcost,economicalapplicationsare achievedinmanyfields.Theapplicationfieldcovers all areas, e.g. architectural, civil, offshore, mechanical, chemical,aeronautical,transport,agricultureand otherspecialfields.Althoughthisbookwillbemainly focused on the background to design and application, in a good design not only does the strength have to be considered,butalsomanyotheraspects,suchas materialselection,fabricationincludingweldingand inspection,protection,erection,inserviceinspection and maintenance. Oneoftheconstraintsinitiallyhamperingthe applicationofhollowsectionswasthedesignofthe joints.However,nowadaysdesignrecommendations exist for allbasictypesofjoints,andfurtherresearch evidence is available for many special types of joints. Basedontheresearchprogrammescarriedout, CIDECT (Comit International pour le Dveloppement et l'Etude de la Construction Tubulaire) has published DesignGuidesNos.1to9forusebydesignersin practice.SincethesenineDesignGuidesareall together too voluminous for educational purposes and do not give the theoretical background, it was decided towritethisbookespeciallytoprovidebackground information for students and practitioners in Structural and Civil Engineering. Thisbookiswritteninalimitstatesdesignformat (also known as LRFD or Load and Resistance Factor Design in the USA). This means that the effect of the factoredloads(thespecifiedorunfactoredloads multipliedbytheappropriateloadfactors)shouldnot exceed the factored resistance of the joint or member. Thefactoredresistanceexpressions,ingeneral, alreadyincludeappropriatematerialandjointpartial safetyfactors(M)orjointresistance(orcapacity) factors (). This has been done to avoid interpretation errors,sincesomeinternationalstructuralsteelwork specificationsuseMvalues1,0asdividers(e.g. Eurocodes),whereasothersusevalues1,0as multipliers(e.g.inNorthAmericaandAustralia).In general, the value of 1/M is almost equal to . 1.1 HISTORY AND DEVELOPMENTS Theexcellentpropertiesofthetubularshapehave been recognised for a long time; i.e. from ancient time, nice examples are known. An outstanding example of bridgedesignistheFirthofForthBridgeinScotland (1890)withafreespanof521m,showninFig.1.6. Thisbridgehasbeenbuiltupfromtubularmembers madeofrolledplateswhichhavebeenriveted together,becauseatthattime,otherfabrication methods were not available for these sizes. Inthesamecentury,thefirstproductionmethodsfor seamlessandweldedcircularhollowsectionswere developed.In1886,theMannesmannbrothers developedtheskewrollpiercingprocess (Schrgwalzverfahren), shown in Fig. 1.7, which made itpossibletorollshortthickwalledtubulars.This process,incombinationwiththepilgerprocess (Pilgerschrittverfahren,Fig.1.8),developedsome yearslater,madeitpossibletomanufacturelonger thinner walled seamless hollow sections. In the first part of the previous century, an Englishman, Whitehouse,developedthefireweldingofcircular hollowsections.However,theproductionofwelded circularhollowsectionsbecamemoreimportantafter the development of the continuous welding process in 1930bytheAmerican,FretzMoon(Fig.1.9). EspeciallyaftertheSecondWorldWar,welding processeshavebeenperfected,whichmadeit possibleforhollowsectionstobeeasilywelded 1 together. Theendcuttingrequiredforfittingtwocircularhollow sectionstogetherwasconsiderablysimplifiedbythe development of a special end preparation machine by Mller (Fig. 1.10). For manufacturers who did not have such end cutting machines,theendpreparationofcircularhollow sections remained a handicap. Awayofavoidingtheconnectionproblemswasthe useofprefabricatedconnectors,e.g.in1937 MengeringhausendevelopedtheMerosystem.This systemenabledthefabricationoflargespace structures in an industrialized way (Fig. 1.11). In 1952, the rectangular hollow section was developed byStewartsandLloyds(nowCorusTubes).This section,withnearlythesamepropertiesasthe circular hollow section, enables the connections to be made by straight end cuttings. Inthefifties,theproblemsofmanufacturing,end preparation and welding were all solved and from that point of view the way to a successful story was open. Theremainingproblemwasthedeterminationofthe strength of unstiffened joints. Thefirstpreliminarydesignrecommendationsfor trussconnectionsbetweencircularhollowsections were given by Jamm in 1951. This study was followed byseveralinvestigationsintheUSA(Bouwkamp, 1964;Natarajan&Toprac,1969;Marshall&Toprac, 1974),Japan(Togo,1967;Natarajan&Toprac, 1968),andEurope(Wanke,1966;Brodka,1968; Wardenier,1982;Mang&Bucak,1983;Puthli,1998; Dutta, 2002). Researchonjointsbetweenrectangularhollow sectionsstartedinEuropeinthesixties,followedby manyotherexperimentalandtheoretical investigations.Manyoftheseweresponsoredby CIDECT. Besidestheseinvestigationsonthestaticbehaviour, in the last 25 years much research was carried out on thefatiguebehaviourandotheraspects,suchas concretefillingofhollowsections,fireresistance, corrosionresistanceandbehaviourunderwind loading. 1.2 DESIGNATION Thepreferreddesignationsforstructuralapplications are: -Circular hollow sections (CHS) -Rectangular hollow sections (RHS) -Square hollow sections (SHS) In Canada and the USA, it is common to speak about Hollow StructuralSections(HSS),whereasinEurope alsothetermStructuralHollowSections(SHS)is used. 1.3 MANUFACTURING OF HOLLOW SECTIONS Asmentioned,hollowsectionscanbeproduced seamlessorwelded.Seamlesshollowsectionsare madeintwophases,i.e.thefirstphaseconsistsof piercinganingotandthesecondstepconsidersthe elongation of this hollow bloom into a finished circular hollowsection.Afterthisprocess,thetubecango throughasizingmilltogiveittherequireddiameter. More information about other processes, most of them based on the same principle, is given by Dutta (2002). Nowadays, welded hollow sections with a longitudinal weldaremainlymadeemployingeitherelectrical resistanceweldingprocessesorinductionwelding processes,showninFig.1.12.Astriporplateis formedbyrollersintoacylindricalshapeandwelded longitudinally. The edges are heated, e.g. by electrical resistance,thentherollerspushtheedgestogether, resultinginapressureweld.Theweldprotrusionon theoutsideofthetubeistrimmedimmediatelyafter welding. Rectangularhollowsectionsaremadebydeforming circularhollowsectionsthroughformingrollers,as shown in Fig. 1.13. This forming process can be done hotorcold,usingeitherseamlessorlongitudinally weldedcircularhollowsections.Althoughitis commonpracticetouselongitudinallyweldedhollow sections,fortheverythicksections,seamless sections may be used. Squareorrectangularhollowsectionsaresometimes madebyformingasinglestriptotherequiredshape andclosingitbyasingleweld,preferablyinthe middle of a face. Large circular hollow sections are also made by rolling platesthroughaso-calledU-Opressprocessshown inFig.1.14.Afterformingtheplatestotherequired 2 shape, the longitudinal weld is made by a submerged arc welding process. Anotherprocessforlargetubularsistousea continuouswidestrip,whichisfedintoaforming machine at an angle to form a spirally formed circular cylinder,seeFig.1.15.Theedgesofthestripare welded together by a submerged arc welding process resulting in a so-called spirally welded tube. Moredetailedinformationaboutthemanufacturing processes and the limitations in sizes can be obtained from Dutta (2002). 3 Fig. 1.1 Reeds in the wind Fig. 1.3 Airport Bangkok, Thailand Fig. 1.2 Bamboo Fig. 1.4 Ripshorster Bridge, Germany 4 Fig. 1.5Paint surface for hollow sections vs open sections Fig. 1.7Skew roll piercing process (Schrgwalzverfahren) Fig. 1.6 Firth of Forth Bridge, Scotland Fig. 1.8 Pilger process (Pilgerschrittverfahren) 5 forming rollersheatingwelding rollerswelded CHSheatingcoilforming rollersheatingwelding rollerswelded CHSheatingcoil Fig. 1.9 Fretz Moon process Fig. 1.11 Mero connector Fig. 1.10 End cutting machine Pressure rollersinductorWelded CHSPressure rollersinductorWelded CHSPressure rollersinductorWelded CHS Fig. 1.12 Induction welding process 6 Fig. 1.13 Manufacturing of rectangular hollow sections Fig. 1.14 Forming of large CHS Fig. 1.15 Spirally welded CHS 7 8 2. PROPERTIES OF HOLLOW SECTIONS 2.1 MECHANICAL PROPERTIES Hollow sections are made of similarsteelasusedfor othersteelsections,thusinprinciplethereisno difference in mechanical properties. Tables2.1aand2.2ashow,asanexample,the mechanicalpropertiesaccordingtotheEuropean standard EN 10210-1 (2006) for hot finished structural hollowsectionsofnon-alloyandfinegrainstructural steels.ThecoldformedsectionsaregiveninEN 10219-1 (2006): Cold formed welded structural hollow sectionsofnon-alloyandfinegrainstructuralsteels (seeTables2.1band2.2b).Asshown,the requirementsofEN10210-1andEN10219-1are almost identical. Hollowsectionscanalsobeproducedinspecial steels, e.g. high strength steel with yield strengths up to690N/mm2orhigher,weatheringsteelsandsteel with improved or special chemical compositions, etc. Generally,thedesignofmembersisbasedonthe yieldstrength.InthischaptertherecommendedM0 and M1 factors of 1,0 are adopted for the design yield strength fyd. Instaticallyindeterminatestructures,sufficient deformationcapacityorrotationcapacityisrequired forredistributionofloads.Inthiscase,yieldingof membersoryieldinginthejointsmayprovidethe requiredrotationcapacity.Atensilemembermadeof ductile steel can be brittle if a particular cross section isweakened,e.g.byholes,insuchawaythatthis cross section fails before the whole member yields. It isthereforerequiredthatyieldingoccursfirst.This shows that the yield-to-ultimate tensile strength ratio is alsoimportant,especiallyforstructureswithvery non-uniformstressdistributions,whichisasituation thatoccursintubularjoints.Somecodes,suchas Eurocode 3 (EN 1993-1-1, 2005), specify the following requirement for the minimum ratios: 1 , 1ffydu> (2.1a) TheIIW(2009)recommendationsandmanyoffshore codes require a higher ratio between fu and fyd: 8 , 0ffor 25 , 1ffuydydus > (2.1b) Thisisonlyoneaspectforductility.Inthecaseof impactloading,thesteelandmembersshouldalso behaveinaductilemanner.Hence,Tables2.1aand 2.2aalsogiverequirementsbasedonthestandard Charpy test to ensure adequate notch toughness. Nowadays,morerefinedcharacterisationmethods existtodescribetheductilityofcrackedbodies,e.g. the CTOD (Crack Tip Opening Displacement) method. Thesecharacterisationmethodsaregenerallyused for pressure vessels, transport line pipes and offshore applications, which are beyond the scope of this book. Anothercharacterisationissometimesrequiredfor thickwalledsectionswhichareloadedinthe thicknessdirection.Inthiscase,thestrengthand ductilityinthethicknessdirectionshouldbesufficient to avoid cracking, called lamellar tearing, see Fig. 2.1. Thistypeofcrackingiscausedbynonmetallic manganese-sulphideinclusions.Thus,ifthesulphur contentisveryloworthesulphurisjoinedwithother elements such as calcium (Ca), such a failure can be avoided.Indirectlythisisobtainedbyrequiringa certainreductionofareaRAZinthetensiletest.For example,RAZ=35meansthatinthetensiletestthe crosssectionalareaatfailurehasbeenreducedby 35% compared to the original cross sectional area. Inmoststructuralsteelspecificationstheminimum requiredyieldstrength,ultimatetensilestrength, elongationandtheCharpyV-notchvaluesare specified.Designstandardsorspecificationsgive further limitations for the fu/fy ratio, whereas depending ontheapplication,morerestrictiverequirementsmay begivenrelatedtoCTODvaluesorthepropertiesin the thickness direction (Z quality). Anotheraspectistheeffectofcoldformingonthe mechanical properties of the parent steel. In the case ofcoldformingofhollowsections,theyieldstrength and to a lesser extent the ultimate tensile strength are increased, especially in the corners, asshowninFig. 2.2.Further,theyield-to-ultimatetensileratiois increased and the elongation slightly decreased. Ifthestandards,e.g.EN10210-1andEN10219-1, specifythepropertiesataparticularcrosssection locationbasedonthefinishedproduct,these propertieshavebeenalreadypartlytakeninto account. Thus, this generally applies in Europe. 9 However, some standards outside Europe specify the material properties of the parent material. In this case, the increased yield strength can be taken into account fordesign.Asmallcornerradiusproducesasmall cold formed area withalargecoldformingeffectand consequentlyalargeincreaseinyieldstrength,while alargecornerradiusdoesjusttheopposite. AccordingtoresearchworkofLind&Shroff(1971), the product of area and increase in yield strength can approximatelybetakenasconstant.Lind&Shroff assumed that in every corner of 90 the yield strength of the parent material fyb is increased over a length of 7ttotheultimatetensilestrengthoftheparent material fu. The total increase over the section 4(7t)t(fu - fyb)canbeaveragedoverthesection,resultingina design yield strength fya, as shown in Fig. 2.2. It is noted that the cold formed sections should satisfy therequirementsforminimuminsidecornerradiusto guaranteesufficientductility,seeTable2.3forfully aluminum killed steel (steel with limited Si content). Part 10 of Eurocode 3 (EN 1993-1-10, 2005) specifies thematerialselection.Here,apermissiblethickness can be determined based on a reference temperature, thesteelgradeandqualityandthestresslevel.The referencetemperaturecovers,besidestheair temperature, also cold forming effects, strain rate, etc. However, the current rules cannot be adopted to cold formedhollowsectionsbecausethedeterminationof theeffectofcoldformingforcoldformedhollow sections is not yet clearly specified. Based on the data obtainedbySoininen(1996),Kosteskietal.(2003), Bjrk (2005), Khn (2005), Puthli & Herion (2005) and Sedlaceketal.(2008),presentlyaproposalisbeing workedoutforanamendmentofEN1993-1-10.In this proposal of CEN/TC 250/SC 3-N 1729 (2010), it is recommendedthatforcoldformedhollowsections accordingtoEN10219,theprocedureforhotformed materialcanbeusedprovidedthatforthecold formingeffectsthereferencetemperatureisreduced byATcf.ForCHS,ATcfvariesfrom0Cto20C depending on the thickness and the d/t ratio. For RHS with steel qualities according to EN 10219, ATcf varies from35Cto45Cdependingonthethicknessand theratiobetweentheinsidecornerradiusandthe thickness.Forcoldformedhollowsectionswith Charpyimpactstrengthssignificantlyexceedingthe requirementsofEN10219,alowervalueofATcfis allowed. 2.2 STRUCTURAL HOLLOW SECTION DIMENSIONS AND DIMENSIONAL TOLERANCES Thedimensionsandsectionalpropertiesofstructural hollowsectionshavebeenstandardisedinEN(EN 10210-2, 2006; EN 10219-2, 2006) and ISO standards (ISO657-14,2000;ISO4019,2001)forhotfinished andcoldformedstructuralhollowsections respectively. ThetwoapplicablestandardsinEuropeareEN 10210-2(2006)"Hotfinishedstructuralhollow sectionsofnon-alloyandfinegrainsteelsPart2: Tolerances, dimensions and sectional properties" and EN10219-2(2006)"Coldformedweldedstructural hollowsectionsofnon-alloyandfinegrainsteels Part2:Tolerances,dimensionsandsectional properties". However, the majority of manufacturers of structural hollow sections do not produce all the sizes showninthesestandards.Itshouldbefurthernoted that other sizes, not included in these standards, may be produced by some manufacturers. ThemajorityofthetolerancesgiveninEN10219-2 arethesameasthoseinEN10210-2,seeTables 2.4a and 2.4b. Internationally,thedeliverystandardsinvarious countriesdeviateconsiderablywithrespecttothe thicknessandmasstolerances(Packer,1993).In mostcountriesbesidesthethicknesstolerance,a masstoleranceisgiven,whichlimitsextreme deviations.However,insomeproductionstandards, e.g. in the USA, the thickness tolerance is not always compensatedbyamasstolerance.Thishasresulted inassociateddesignspecificationswhichaccountfor this, by designating a lower "design wall thickness" of 0,9 or 0,93 times the nominal thickness t. In Eurocode 3, where design is based on nominal thicknesses, the thicknesstolerancesinEN10210-2andEN10219-2 are(partly)compensatedbythemasstolerance.Itis foreseen that in the next revision these tolerances will be tightened. Althoughthecircular,squareandrectangularhollow sections are the generally-used shapes; other shapes aresometimesavailable.Forexample,sometube manufacturersdelivertheshapesgiveninTable2.5. Ofthese,theellipticalhollowsectionshavebecome more popular for architectural designs. These shapes are not dealt with further in this book. However, more informationaboutellipticalhollowsectionscanbe foundinBortolottietal.(2003),Chan&Gardner (2008),Chooetal.(2003),Martinez-Saucedoetal. 10 (2008), Packer et al. (2009b), Pietrapertosa & Jaspart (2003),Theofanousetal.(2009),Willibaldetal. (2006) and Zhao & Packer (2009). 2.3 GEOMETRIC PROPERTIES 2.3.1 Tension ThedesigncapacityNt,Rdofamemberundertensile loadingdependsonthecrosssectionalareaandthe designyieldstrength,andisindependentofthe sectional shape. In principle, there is no advantage or disadvantageinusinghollowsectionsfromthepoint of view of the amount of material required. The design capacity is given by: yd Rd , tAf N = (2.2) If the cross section is weakened by bolt holes or slots, thenetcrosssectionshouldalsobechecked,ina similarwayasforothersections,e.g.accordingto Eurocode 3 (EN 1993-1-8, 2005): 9 , 0f AN2 Mu netRd , t= (2.3) where the partial safety factor M2 = 1,25. Thefactor0,9mayvaryfromcountrytocountry depending on the partial factor M used. Where ductile behaviour is required (e.g. under seismic loading), the yieldresistanceshallbelessthantheultimate resistance at the net section of fastener holes. 2.3.2 Compression Forcentrallyloadedmembersincompression,the criticalbucklingloaddependsontheslenderness and the section shape. The slenderness is given by the ratio of the buckling length b and the radius of gyration i. ib= (2.4) Theradiusofgyrationofahollowsection(inrelation tothemembermass)isgenerallymuchhigherthan that for the weak axis of an open section. For a given length,thisdifferenceresultsinalowerslenderness forhollowsectionsandthusalowermasswhen compared with open sections. Thebucklingbehaviourisinfluencedbyinitial eccentricities, straightness and geometrical tolerances aswellasresidualstresses,non-homogeneityofthe steel and the stress-strain relationship. BasedonextensiveinvestigationsbytheEuropean ConventionforConstructionalSteelwork(ECCS)and CIDECT,"Europeanbucklingcurves"(Fig.2.3and Table2.7)havebeenestablishedforvarioussteel sectionsincludinghollowsections.Theyare incorporated in Eurocode 3 (EN 1993-1-1, 2005). The reduction factor ; shown in Fig. 2.3 is the ratio of thedesignbucklingcapacityNb,Rdtotheaxialplastic capacity. ydRd , bRd , plRd , bffNN= = ; (2.5) where: fb,Rd = ANRd , b(2.6) Thenon-dimensionalslenderness isdetermined by: E= (2.7) where: yEfEt = (Euler slenderness)(2.8) Thebucklingcurvesforthehollowsectionsare classifiedaccordingtoTable2.6.Mostopensections fallundercurves"b"and"c".Consequently,forthe caseofbuckling,theuseofhotformedhollow sectionsgenerallyprovidesaconsiderablesavingin material. Fig.2.4illustrates,forabucklinglengthof3m,a comparisonbetweentherequiredmassofopenand hollow sections for a given load. It shows that in those casesinwhichloadsaresmall,leadingtorelatively slendersections,hollowsectionsprovideagreat advantage(considerablyloweruseofmaterial). However,ifloadsarehigher,resultinginlow slenderness, the advantage (in %) will be less. Theoverallbucklingbehaviourofhollowsections improveswithincreasingdiameter-orwidth-to-wall 11 thicknessratio.However,thisimprovementislimited bylocalbuckling.Topreventlocalbuckling,d/torb/t limitsaregivene.g.inEurocode3(EN1993-1-1, 2005),seeTable2.7.Inthecaseofthinwalled sections, interaction between global and local buckling should be considered. In addition to the improved buckling behaviour due to thehighradiusofgyrationandtheenhanceddesign bucklingcurve,hollowsectionscanofferother advantages in lattice girders. Due to the torsional and bending stiffness of the members in combination with jointstiffness,theeffectivebucklinglengthof compressionmembersinlatticegirderscanbe reduced(Fig.2.5).Eurocode3(EN1993-1-1) recommendsaneffectivebucklinglengthforhollow section brace members in welded lattice girders equal to or less than 0,75, in which represents the system length, see also Rondal et al. (1992). Forchords,0,9timesthesystemlengthforin-plane buckling or 0,9 times the length between the supports forout-of-planebuckling,istakenastheeffective buckling length. Thesereductionsarealsobasedonthefactthatthe chordandbracemembersaregenerallynotfully optimised.Ifforexamplethechordwouldbefully utilizedwithdifferentmembersforeverypanelthen these reductions would not be allowed. Laterallyunsupportedcompressionchordsoflattice girders(seeFig.2.6)haveareducedbucklinglength due to the improved torsional and bending stiffness of thetubularmembers(Baar,1968;Mouty,1981). Thesefactorsmaketheuseofhollowsectionsin girders or trusses even more favourable. 2.3.3 Bending Ingeneral,IandHsectionsaremoreeconomical underbendingaboutthemajoraxis(Imaxlargerthan for hollow sections). Only in those cases in which the designresistanceinopensectionsislargelyreduced bylateralbuckling,hollowsectionsofferan advantage. Itcanbeshownbycalculationsthatlateralinstability isnotcriticalforcircularhollowsections,square hollowsectionsandforthemostcommonlyused rectangularhollowsectionswithbendingaboutthe strong axis. Table 2.8 shows allowablespan-to-depth ratiosforthemostcommonlyusedsections(EN 1993-1-1, 2005). According to a study of Kaim (2006) these limits can be taken considerably larger. Itisapparentthathollowsectionsareespecially favourablecomparedtoothersectionsifbending about both axes is present. Hollowsectionsusedforelementssubjectedto bending can be more economically designed by using plasticdesign.However,thenthesectionshaveto satisfymorerestrictedconditionstoavoidpremature localbuckling.Likeothersteelsectionsloadedin bending,differentmoment-rotationbehaviourcanbe observed. Fig.2.7showsvariousmoment-rotationdiagramsfor a member loaded by bending moments. Themoment-rotationcurve"1"showsamoment exceeding the plastic moment Mpl and a considerable rotationcapacity.Moment-rotationcurve"2"showsa momentexceedingtheplasticmomentcapacityMpl, butafterthemaximum,themomentdrops immediately,sothatlittlemoment-rotationcapacity exists.Moment-rotationcurve"3"representsa capacitylowerthantheplasticmomentcapacity, which,however,exceedstheyieldmomentcapacity Mel.Inthemoment-rotationcurve"4"thecapacityis evenlowerthantheyieldmomentcapacityMeland failureisbyelasticbuckling.Theeffectofthe moment-rotationbehaviourisreflectedinthe classificationofcrosssectionsasshowninFig.2.8 andTable2.7.Thecrosssectionclassificationis giveninlimitsforthediameter-orflat width-to-thickness ratio. Thelimitsarebasedonexperimentsandcanbe expressed as: ydf235ctd=for CHS(2.9) f235c 3tbyd= for RHS(2.10a) ydf235c 3th= for RHS(2.10b) withfydinN/mm2andcdependingonthesection class, the cross section and the loading. For RHS, it is conservativelyassumedthatthewidthofthe"flat"is equaltotheexternalwidthbordepthhoftheRHS minus 3t. 12 Thecrosssectionclasses1and2candevelopthe plastic moment capacity up to the given b/t or d/t limits withbi-linearstressblocks,whereasthemoment capacity of the cross section classes 3 and 4 is based onanelasticstressdistribution(seeFig.2.8).The difference between the cross section classes 1 and 2 is reflected in the rotation capacity. After reaching the plastic moment capacity, the cross section class 1 can keepthiscapacityafterfurtherrotation,whereasthe capacityofthecrosssectionclass2dropsafter reachingthiscapacity.Asaconsequence,the momentdistributioninthestructureorstructural componentshouldbedeterminedbyelasticanalysis forstructuresmadeofsectionswithcrosssection classes 2, 3 or 4. For structures made of sections with cross sections in class 1 a plastic moment distribution canbeadopted,butanelasticmomentdistributionis stillpermissible(andinsomecountriesmore common). Foraclass1beamfullyclampedatbothendsand subjectedtoauniformlydistributedloadingq,the plasticmomentdistributionimpliesthatafterreaching theplasticmomentcapacityattheends,thebeam canbeloadeduntilafurtherplastichingeoccursat mid span (see Fig. 2.9). Fortheclass4crosssection,themaximumstressis determinedbylocalbucklingandthestressinthe outerfibreislowerthantheyieldstrengthfy. Alternatively,aneffectivecrosssectionalareabased on the yield strength may be determined. Detailedinformationaboutthecrosssectional classification is given by Rondal et al. (1992). ResearchbyWilkinson&Hancock(1998)showed that especially the limits for the side wall slenderness ofRHSneedtobereducedconsiderably.E.g.for class 1 sections, they suggest reducing the Eurocode 3 limits (EN 1993-1-1) for the side wall slenderness to: 6t) 2r 2t 5(b70t2r) 2t (h s (2.11) with30tr 2 t 2 bs For r = t, this can be simplified to: tb83 , 0 77th s with34tbs (2.11a) Intheabsenceofshearforcesoriftheshearforces donotexceed50%oftheshearcapacityVpl,Rd,the effectofshearmaybeneglectedandthebending moment capacity about one axis is given by: yd pl Rd , cf W M = for cross section classes 1 or 2(2.12) yd el Rd , cf W M = for cross section class 3(2.13) yd eff Rd , cf W M = for cross section class 4(2.14) Whentheshearforceexceeds50%oftheshear capacity, combined loading has to be considered, see Eurocode 3 (EN 1993-1-1). 2.3.4 Shear Theelasticshearstressincircularandrectangular hollowsectionscanbedeterminedwithsimple mechanics by: 3ft I 2S Vyd Eds = t (2.15) Fig.2.10showstheelasticstressdistribution.The design capacity based on plastic design can be easily determinedbasedontheHuber-Hencky-VonMises criterion by assuming the shear yield strength in those parts of the cross section active for shear. 3fA Vydv Rd , pl= (2.16) where: h bhA Av+= for RHS(2.17) (or just 2 h t) with V in the direction of h. A2Avt= for CHS(2.18) 2.3.5 Torsion Hollowsections,especiallyCHS,havethemost effective cross section for resisting torsional moments, because the material is uniformly distributed about the polar axis. A comparison of open and hollow sections ofnearlyidenticalmassinTable2.9showsthatthe torsionalconstantofhollowsectionsisabout200 times that of open sections. 13 Thedesigncapacityfortorsionalmomentsis described by: 3fW Mydt Rd , t= (2.19) or circular hollow sections:F t ) t d (2 t dI 2Wttt== (2.20) here:w ( ) t t d4I3tt~ (2.21) or rectangular hollow sections (Marshall, 1971):F AmttA2 tIW+= (2.22) here:w AA3tt A 43tI2m+ ~ (2.23) ) (2.24) (2.25) or thin walled rectangular hollow sections, eq. (2.22) (2.26) hefirsttermineq.(2.23)isgenerallyonlyusedfor heexact,morecomplicatedequationsforthecross .3.6 Internal pressure hedesigncapacityperunitlength,showninFig. ( ) ( t + = 4 r 2 b h 2m m m A( ) t = 4 r h b A2m m m mFcan be approximated by: t b h 2 Wm m t =Topen sections. However, research by Marshall (1971) showedthatthegivenformulaprovidesthebestfit with the test results. TsectionalpropertiesaregiveninEN10210-2(2006) and EN 10219-2 (2006). 2 hecircularhollowsectionismostsuitabletoresistTan internal pressure p. T2.11, is given by: t 2 dt 2f pyd= (2.27) M0 ectionalclassification, .4 DRAG COEFFICIENTS hollowsections, .5 CORROSION PROTECTION tructuresdesignedinhollowsectionshavea20to eq. (2.27), = 1,0, but for transport pipelines, theInM0valuemaybeconsiderablylargerthanforother cases,dependingonthehazardoftheproduct,the effect of failure on the environment and inspectability. ThedesigncapacitiesforRHSsectionssubjectedto internalpressurearemuchmorecomplicated; referencecanbemadetotheDeutscher Dampfkesselausschu (1975). 2.3.7 Combined loadings ariouscombinationsofloadingsarepossible,e.g.Vtension, compression, bending, shear and torsion. Dependingonthecrosssvariousinteractionformulaeshouldbeapplied. Reference can be made to Eurocode 3 (EN 1993-1-1). Itisbeyondthescopeofthisbooktodealwithall possibleformulae;however,theinteractionbetween the various loads in the cross section can be based on theHuber-Hencky-VonMisesstresscriterion(Roik& Wagenknecht,1977).Forthememberchecks,other interaction formulae apply, see e.g. EN1993-1-1. 2 iallycircularHollowsections,espechaveastrikingadvantageforuseinstructures exposedtofluidcurrents,i.e.airorwater.Thedrag coefficientsaremuchlowerthanthoseofopen sectionswithsharpedges,seeFig.2.12(Schulz, 1970; CIDECT, 1984; Dutta, 2002). 2 tructuresmadeofhollowsectionsofferadvantagesSwithregardtocorrosionprotection.Hollowsections haveroundedcorners(Fig.2.13)resultinginabetter protectionthanthatforsectionswithsharpcorners. Thisisespeciallytrueforthejointsincircularhollow sectionswherethereisasmoothtransitionfromone sectiontoanother.Thisbetterprotectionincreases the protection period of coatings against corrosion. S50% smaller surface to be protected than comparable structuresmadeofopensections.Many 14 investigations,summarizedbyTissier(1978),have beenconductedtoassessthelikelihoodofinternal corrosion. These investigations, carried out in various countries, show that internal corrosion does not occur in sealed hollow sections. Eveninhollowsectionswhicharenotperfectly .6 USE OF INTERNAL VOID he possibilities of using the internal space are briefly .6.1 Concrete filling wallthicknessesarenot veryimportantreasonforusingconcretefilled oncrete filling of hollow sections contributes not only .6.2 Fire protection by water circulation nothermethodforfireprotectionofbuildingsisto he columns are interconnected with a water storage ordertopreventfreezing,potassiumcarbonate .6.3 Heating and ventilation heinnervoidsofhollowsectionsaresometimes .6.4 Other possibilities ometimeshollowsectionchordsoflatticegirder .7 AESTHETICS rationaluseofhollowsectionsleadsingeneralto sealed, internal corrosion is limited. If there is concern aboutcondensationinanimperfectlysealedhollow section, a drainage hole can be made at a point where water can drain by gravity. 2 heinternalvoidinhollowsectionscanbeusedinTvariousways,e.g.toincreasethecompressive resistancebyfillingwithconcrete,ortoprovidefire protection.Inaddition,heatingorventilationsystems aresometimesincorporatedintohollowsection columns. Tdescribed below. 2 thecommonly-available Ifsufficient to meet the required load bearing resistance, thehollowsectioncanbefilledwithconcrete.For example, it may be preferable in buildings to have the sameexternaldimensionsforthecolumnsonevery floor.Atthetopfloor,thesmallestwallthicknesscan bechosen,andthewallthicknesscanbeincreased withincreasingloadforlowerfloors.Ifthehollow section with the largest available wall thickness is not sufficientforthegroundfloor,thehollowsectioncan befilledwithconcretetoincreasetheloadbearing resistance. Ahollowsectionsisthatthecolumnscanberelatively slender.Designrulesaregivenine.g.Eurocode4 (EN 1994-1-1, 2004). Ctoanincreaseinloadbearingresistance,butitalso improvesthefireresistanceduration.Extensivetest projectscarriedoutbyCIDECTandtheEuropean CoalandSteelCommunity(ECSC)showedthat reinforcedconcretefilledhollowsectioncolumns withoutanyexternalfireprotectionlikeplaster, vermiculitepanelsorintumescentpaint,canattaina firelifeofeven2hoursdependingonthecross sectionratioofthesteelandconcrete,reinforcement percentageoftheconcreteandtheappliedload,see Fig. 2.14 (Twilt et al., 1994). 2 Ause water filled hollow section columns. Ttank.Underfireconditions,thewatercirculatesby convection,keepingthesteeltemperaturebelowthe criticalvalueof450C.Thissystemhaseconomical advantages when applied to buildings with more than about8storeys.Ifthewaterflowisadequate,the resulting fire resistance time is virtually unlimited. In(K2CO3)isaddedtothewater.Potassiumnitrateis used as an inhibitor against corrosion. 2 Tusedforairandwatercirculationforheatingand ventilation of buildings. Many examples in offices and schoolsshowtheexcellentcombinationofthe strengthfunctionofhollowsectioncolumnswiththe integrationofheatingorventilationsystems.This systemoffersmaximizationoffloorareathrough elimination of heat exchangers, a uniform provision of warmth and a combined protection against fire. 2 Sbridges are used for conveying fluids (pipe bridge). In buildings,therainwaterdownpipesmaygothrough the hollow section columns or in other cases electrical wiringislocatedinthecolumns.Theinternalspace can also be used for prestressing a hollow section. 2 Astructureswhicharecleanerandmorespacious. Hollowsectionscanprovideslenderaesthetic columns,withvariablesectionpropertiesbutflush externaldimensions.Duetotheirtorsionalrigidity, hollowsectionshavespecificadvantagesinfolded structures, V-type girders, etc. 15 16 oftenmadeofhollow sections directly connected to one another without any stiffenerorgussetplate,isoftenpreferredby architectsforstructureswithvisiblesteelelements. However, it is difficult to express aesthetic features in economiccomparisons.Sometimeshollowsections areusedonlybecauseofaestheticappeal,seee.g. Fig.2.15,whilstatothertimesappearanceisless important. Latticeconstruction,whichis Table 2.1a Hot finished structural hollow sections Non-alloy steel properties (EN 10210-1, 2006) Minimum yield strength (1) (N/mm2) Minimum tensile strength (N/mm2) Longitudinal (2) minimum elongation (%) on gauge o oS 65 , 5 L =Charpy impact strength (10 x 10 mm) Steel designation t s 16 mm 16 < t s 40 mm 40< t s 63 mm t < 3 mm 3 s t s 100 mm 3 < t s 40 mm 40 < t s 63 mm Temp. C J S235JRH235225215360-510360-51026252027 S275J0H S275J2H 275265255430-580410-5602322 0 -20 27 27 S355J0H S355J2H S355K2H 355345335510-680470-6302221 0 -20 -20 27 27 40 (3)(1)For thicknesses above 63 mm, these values are further reduced. (2) In transverse direction 2% lower. (3)Corresponds to 27 J at -30 C. Table 2.1b Cold formed welded structural hollow sections Non-alloy steel (EN 10219-1, 2006) Steel properties different from EN 10210-1 (2006) Steel designation Minimum longitudinal elongation (%), all thicknesses, tmax = 40 mm S235JRH24 (1) S275J0H S275J2H 20 (2) S355J0H S355J2H S355K2H 20 (2) (1)For t > 3 mm and d/t < 15 or5 , 12t 2h b 10 > 3,0 > 2,0 > 1,5 > 1,0 s 2 s 5 s 14 s 20 s 25 s 33 any any 24 12 8 4 any 16 12 10 8 4 any any 24 12 10 6 18 Table 2.4a Hot finished structural hollow sections Tolerances (EN 10210-2, 2006) Section typeSquare/rectangularCircular Outside dimensionthe greater of 0,5 mm and 1% (1) the greater of 0,5 mm and 1% but not more than 10 mm Welded-10% Thickness Seamless-10% and -12,5% at maximum 25% cross section Welded 6% on individual lengths Mass Seamless-6%; +8% Straightness0,2% of the total length and 3 mm over any 1 m length Length (exact)+10 mm, -0 mm, but only for exact lengths of 2000 to 6000 mm Out of roundness-2% for d/t s 100 Squareness of sides90 1- Corner radiiOutside3,0t maximum- Concavity/convexity 1% of the side- Twist2 mm + 0,5 mm/m (1)- (1)For elliptical hollow sections with h s 250 mm, the tolerances are twice the values given in this table. Table 2.4b Cold formed welded structural hollow sections (EN 10219-2, 2006) Tolerances different from EN 10210-2 (2006) Section typeSquare/rectangularCircular Outside dimension b < 100 mm: the greater of 0,5 mm and 1% 100 mm s h, b s 200 mm: 0,8% b > 200 mm: 0,6% 1%,minimum 0,5 mm maximum 10 mm ThicknessWelded t s 5 mm: 10% t > 5 mm: 0,5 mm for d s 406,4 mm: t s 5 mm: 10% t > 5 mm: 0,5 mm for d > 406,4 mm: 10% with maximum 2,0 mm Mass 6% 6% Straightness 0,15% of the total length and 3 mm over any 1 m length Outside corner radii (profile) t s 6 mm:1,6 to 2,4t 6 mm < t s 10 mm:2,0 to 3,0t t > 10 mm:2,4 to 3,6t - Concavity/convexitymaximum 0,8% with a minimum of 0,5 mm- Table 2.5 Special shapes available TriangularHexagonalOctagonalFlat - ovalEllipticalHalf-elliptical Shape 19 Table 2.6 European buckling curves according to manufacturing processes (EN 1993-1-1, 2005) Cross sectionManufacturing processBuckling curves Hot finished 420 N/mm2 < fy s 460 N/mm2 a0 Hot finished fy s 420 N/mm2 a Cold formedc hbFlangeWebthbFlangeWebhbhbFlangeWebthbFlangeWebthbFlangeWebhbhbFlangeWebtbt dtdtdthbFlangeWebthbFlangeWebhbhbFlangeWebthbFlangeWebthbFlangeWebhbhbFlangeWebtbt dtdtdthh Table 2.7 Limits for b/t, h/t and d/t for cross section classes 1, 2 and 3 (EN 1993-1-1, 2005) Class123 fyd (N/mm2)fyd (N/mm2)fyd (N/mm2) Cross section Load type Considered element 235275355460235275355460235275355460 3f235ctbyd+ sc = 33c = 38c = 42 RHS b/t (1) CompressionTop face 36,0 33,5 29,8 26,6 41,0 38,1 33,930,245,041,8 37,2 33,03f235cthyd+ sc = 72c = 83c = 124 RHS h/t (1) BendingSide wall (2) 75,0 69,6 61,6 51,8 86,0 79,7 70,562,3127,0117,6 103,9 91,6ydf235ctdsc = 50c = 70c = 90 CHS d/t Compression and/or bending tttt50,0 42,7 33,1 25,5 70,0 59,8 46,335,890,076,9 59,6 46,0(1) ForallhotfinishedandcoldformedRHS,itisconservativetoassumethatthewidth-to-thicknessratioofthe"flat"is 3tbt2r - 2t - b = or3tht2r - 2t - h = . (2)Wilkinson & Hancock (1998) suggested reducing the Eurocode limits (EN 1993-1-1) for the side wall slenderness of RHS considerably, e.g. for class 1 in a simplified form to: tb83 , 0 77th s with34tbs . 20 Table 2.8 Allowable span-to-depth ratios L/(h-t) to avoid lateral buckling based on EN 1993-1-1 (2005) s t hL t ht b S235S275S355S460 0,573,763,048,837,7 0,693,179,561,647,5 0,7112,596,274,557,5 0,8132,0112,887,467,4 0,9151,3129,3100,277,3 1,0170,6145,8112,987,2 hbFlangebthbFlangebhbhbFlangebthbFlangebthbFlangebhbhbFlangebtbht hbFlangebthbFlangebhbhbFlangebthbFlangebthbFlangebhbhbFlangebtbht Table 2.9 Torsional strength of various sections Section Mass (kg/m) Torsion constant It (104 mm4) or (cm4) UPN 20025,311,9 INP 20026,213,5 HEB 12026,713,8 HEA 14024,78,1 140 x 140 x 624,91475 168.3 x 624,02017 21 Fig. 2.1 Lamellar tearing Actual fymeanafter cold formingActual fymeanafter cold formingActual fymeanafter cold forming Fig. 2.2 Influence of cold forming on the yield strength for a square hollow section of 100 x 100 x 4 mm 01,000,750,500,2500 0,5 1,0 1,5 2,0001,000,750,500,2500 0,5 1,0 1,5 2,0 Fig. 2.3 Eurocode 3 buckling curves (EN 1993-1-1, 2005) 22 Bucklingstress (N/mm2)Bucklingstress (N/mm2) Fig. 2.4 Comparison of the masses of hollow and open sections under compression in relation to the loading Fig. 2.5 Restraints for the buckling of a brace member Fig. 2.6 Bottom chord laterally spring supported by the stiffness of the members, joints and purlins 23 MplMelMeMplMelMe Fig. 2.7 Moment-rotation curves Fig. 2.8 Stress distribution for bending Fig. 2.9 Moment distribution in relation to the cross section classification 24 Fig. 2.10 Elastic shear stress distribution tfydt fydt fydt d - 2t Fig. 2.11 Internal pressure Fig. 2.12 Wind flow for open and circular hollow sections 25 paint layerssteelsteelcorner protection for RHS and open sectionspaint layerssteelsteelcorner protection for RHS and open sectionspaint layerssteelsteelcorner protection for RHS and open sectionspaint layerssteelsteelcorner protection for RHS and open sections Fig. 2.13 Painted corners of RHS vs. open sections Fig. 2.14 Fire resistance of concrete filled hollow sections RHS 304,8x304,8x9,5111 min.14 min.onlyRHSnon-reinforcedconcrete filling50min.steel fibrereinforcedconcrete fillingworking load (kN)firelife(min.)1650. 3150. 3150.120.60.RHS 304,8x304,8x9,5111 min.14 min.onlyRHSnon-reinforcedconcrete filling50min.steel fibrereinforcedconcrete fillingworking load (kN)firelife(min.)1650. 3150. 3150.120.60.RHS 304,8x304,8x9,5111 min.14 min.onlyRHSnon-reinforcedconcrete filling50min.steel fibrereinforcedconcrete fillingworking load (kN)firelife(min.)1650. 3150. 3150.120.60. 26 Fig. 2.15 Aesthetically appealing structures 27 28 3. APPLICATIONS Theapplicationsofstructuralhollowsectionsnearly cover all fields. Hollow sections may be used because ofthebeautyoftheirshapeortoexpresslightness, whileinothercasestheirgeometricalproperties determinetheirapplication.Inthischapter,examples aregivenforthevariousfieldsandtoshowthe possibilities of constructing with hollow sections. 3.1 BUILDINGS AND HALLS In buildings and halls, hollow sections are mainly used forcolumnsandlatticegirdersorspaceframesfor roofs.Inmodernarchitecture,theyarealsousedfor other structural or architectural reasons, e.g. facades. Fig.3.1showsa10-storeybuildinginKarlsruhe, Germanywithrectangularhollowsectioncolumns 180x100.Specialaspectsarethatthecolumnsare madeofweatheringsteelandarewaterfilledto ensuretherequiredfireprotection.Thecolumnsare connectedwithwaterreservoirstoensurecirculation. Besides the fire protection, a further advantage is that duetothewatercirculationinthecolumns,the deformationofthebuildingduetotemperature differences by sunshine is limited. Fig.3.2showsanexampleoflatticegirdertrusses used in a roof of an industrial building. For an optimal cost effective design, it is essential that the truss joints are made without any stiffening plates. AnespeciallyappealingapplicationisgiveninFig. 3.3,showingatree-typesupportoftheairport departurehallinStuttgart,Germany.Forthejoints, streamlined steel castings are used. Fig.3.4showstheroofoftheterminalofKansai InternationalAirportinOsaka,Japanwithcurved triangular girders of circular hollow sections. Fig.3.5showsadomeunderconstruction,whereas Fig. 3.6 illustrates a special application using columns and beams in the faade for ventilation assuring clean windows in the swimming pool. Fig.3.7showsaverynicearchitecturalapplicationin BushLaneHouseinthecityofLondon,UK.The externalcircularhollowsectionlatticetransfersthe faadeloadsandtheloadsonthefloorstothemain columns.Thehollowsectionsarefilledwithwaterfor fire protection. Veryattractiveapplicationscanbefoundinthehalls andbuildingsfortheOlympicGamesinAthens,e.g. Fig. 3.8. Ellipticalhollowsectionsarebecomingmoreand morepopularamongarchitectsandalreadyseveral examplesexist,seeforexampleFig.3.9,theairport building in Madrid. Nowadays,manyexamplesoftubularstructuresare foundinrailwaystations(Figs.3.10and3.11)and roofs of stadia and halls (Figs. 3.12 to 3.14). Indeed,asstatedbyoneoftheformerCIDECTvice presidents,JimCran,attheTubularStructures Symposium in Delft (1977) "The sky is the limit", whilst presentingbeautifulapplicationsofstructuralhollow sections. 3.2 BRIDGES Asmentionedintheintroduction,theFirthofForth Bridgeisanexcellentexampleofusingthehollow sectionshapeforstructuralapplicationsinbridges. Nowadays, many modern examples exist (IISI, 1997). Figs.1.4,3.15to3.17and3.20showvarious examplesofpedestrianbridges;someoftheseare movable bridges. Circular hollow sections can also be used as a flange for plate girders, as shown in Fig. 3.17 for a triangular box girder. Averyniceexampleofaroad-pedestrianbridgeis illustratedinFig.3.18,beingacomposite steel-concrete bridge with hollow sections for the arch and braces and a concrete deck. Fig. 3.19 shows a railway bridge near Rotterdam, The Netherlands with circular hollow section arches. 3.3 BARRIERS Thereareafewaspectswhichmakehollowsections increasinglysuitableforhydraulicstructures,suchas barriers.Duetoenvironmentalrestrictions,the maintenanceofhydraulicstructuresrequiressevere precautions,makingdurabilityanimportantissue. Structuresofhollowsectionsarelesssusceptibleto corrosionduetotheroundedcorners.Furthermore, especiallycircularhollowsectionshavelowerdrag coefficients,leadingtolowerforcesduetowave loading.Fig.3.21showsabarrierwithasupport 29 structureofcircularhollowsections.Fig.3.22shows thestormsurgebarriernearHookofHollandwith triangular arms made of circular hollow sections and a length (250 m) equal to the height oftheEiffelTower in Paris. 3.4 OFFSHORE STRUCTURES Offshore,manyapplicationexamplesareavailable; mostofthemincircularhollowsections.Forthe supportstructure,thejacketortower,notonlyisthe waveloadingimportant,butalsootheraspectsare leadingtotheuseofcircularhollowsections.E.g.in jackets,thecircularhollowsectionpilesareoften driventhroughthecircularhollowsectionlegsofthe jacket,thusthepileisguidedthroughtheleg. Sometimestheinternalvoidisusedforbuoyancy. Further,thedurabilityandeasymaintenancein severe environments are extremely important. Hollowsectionmembersareusedinjackets,towers, thelegsanddiagonalsintopsidestructures,cranes, microwavetowers,flaresupports,bridges,support structuresofhelicopterdecksandfurtherinvarious secondary structures, such as staircases, ladders, etc. Figs. 3.23 and 3.24 show two examples. 3.5 TOWERS AND MASTS Consideringwindloading,corrosionprotectionand architectural appearance, there is no doubt that hollow sectionsaretobepreferred.However,inmany countries,electricpowertransmissiontowersare made of angle sections with simple bolted joints. Nowadays,architecturalappearancebecomesmore important,whilestringentenvironmentalrestrictions makeprotectionandmaintenanceincreasingly expensive.Thesefactorsstimulatedesignsmadeof hollow sections (Figs. 3.25 and 3.26). 3.6 SPECIAL APPLICATIONS The field of special applications is large, e.g. along the roads,petrolstations(Fig.3.27),soundbarriers(Fig. 3.28),trafficinformationgantries(Fig.3.29),guard rails, parapets and sign posts. Further,excellentapplicationexamplesarefoundin radiotelescopes(Fig.3.30),inmechanical engineering,cranes(Fig.3.31)androllercoasters (Fig. 3.32). Intheagriculturalfield,glasshouses(Fig.3.33)and agriculturalmachineryaretypicalexamples.Alsoin transport,manyexamplesexistbuttheseareoutside the scope of this book. Indeed, the sky is the limit. 30 Fig. 3.2 Roof with lattice girdersFig. 3.1Faade of the Institute for Environment in Karlsruhe, Germany Fig. 3.3 Airport departure hall in Stuttgart, Germany31 Fig. 3.4Roof of Kansai International Airport in Osaka, Japan Fig. 3.6Faade with ventilation through the RHS columns and beams, Borkum, Germany Fig. 3.8Hall for the 2004 Olympic Games, Athens, Greece Fig. 3.5 Dome structure in Gothenburg, Sweden Fig. 3.7 Bush Lane House in London, UK Fig. 3.9 Airport Madrid with EHS sections, Spain 32 Fig. 3.10Railway station in Rotterdam, The Netherlands Fig. 3.12Barrel dome grid for the Trade Fair building in Leipzig, Germany Fig. 3.13Retractable roof for the Rogers Centre in Toronto, Canada Fig. 3.11TGV railway station at Charles de Gaulle Airport, France Fig. 3.14Stadium Australia for the 2000 Olympic Games, Sydney, Australia 33 Fig. 3.15Movable pedestrian bridge in RHS, The Netherlands Fig. 3.17 Pedestrian bridge in Houdan, France Fig. 3.19Railway bridge with CHS arches, The Netherlands Fig. 3.21 Eastern Scheldt barrier, The Netherlands Fig. 3.16Movable pedestrian bridge in RHS near Delft, The Netherlands Fig. 3.18Composite road bridge in Marvejols, France Fig. 3.20Movable pedestrian bridge in CHS near Delft, The Netherlands Fig. 3.22 Storm surge barrier, The Netherlands 34 Fig. 3.23 Bullwinkle offshore structure, Gulf of Mexico Fig. 3.25 Electric power transmission tower Fig. 3.27 Petrol station, The Netherlands Fig. 3.24Amoco P15 offshore platform with jack-up, North Sea Fig. 3.26 Mast, The Netherlands Fig. 3.28 Sound barrier, Delft, The Netherlands 35 Fig. 3.29 Traffic information gantry, The Netherlands Fig. 3.30 Radio telescope Fig. 3.31 Cranes Fig. 3.33 Green house, The NetherlandsFig. 3.32 Roller coaster 36 4. COMPOSITE STRUCTURES 4.1 INTRODUCTION Concretefilledhollowsections(Fig.4.1)aremainly usedforcolumns.Theconcretefillinggivesahigher loadbearingcapacitywithoutincreasingtheouter dimensions.Thefireresistancecanbeconsiderably increasedbyconcretefilling,inparticularifproper reinforcement is used. Duetothefactthatthesteelstructureisvisible,it allows a slender, architecturally-appealing design. The hollowsectionactsnotonlyastheformworkforthe concrete,butalsoensuresthattheassemblyand erection in the building process are not delayed by the hardening process of the concrete. CIDECTresearchoncompositecolumnsstarted alreadyinthesixties,resultinginmonographsand designrules,adoptedbyEurocode4(EN1994-1-1, 2004). CIDECT Design Guide No. 5 (Bergmann et al., 1995)providesdetailedinformationforthestatic design of concrete filled columns. To a large extent, this chapter follows theinformation giveninDesignGuideNo.5,butupdatedwiththe latest revisions to Eurocode 4 (EN 1994-1-1). 4.2 DESIGN METHODS Inthelastdecades,severaldesignmethodsfor composite columns were developed, e.g. in Europe by Guiaux & Janss (1970), Roik et al. (1975) and Virdi & Dowling(1976),finallyresultinginthedesignrules given in Eurocode 4 (EN 1994-1-1, 2004). Inthischapter,thedesignmethodgivenisbasedon the approach presented in Eurocode 4 (EN 1994-1-1). Thedesignofcompositecolumnshastobecarried out at the ultimate limit state, i.e. the effect of the most unfavourablecombinationofactionsshouldnot exceed the resistance of the composite member. Anexactcalculationoftheloadbearingcapacity considering the effect of imperfections and deflections (secondorderanalysis),theeffectofplastificationof the section, cracking of the concrete, etc. can only be carriedoutbymeansofacomputerprogram.With suchaprogram,theresistanceinteractioncurvesas shown in Fig. 4.2, can be calculated. Based on these calculatedcapacities,thefollowingsimplifieddesign methods have been developed. 4.3 AXIALLY LOADED COLUMNS FromtheworkofRoiketal.(1975),asimplified design method is given in Eurocode 4 (EN 1994-1-1), similartothedesignmethodadoptedforsteel columns, i.e.: Rd , pl EdN N ; s (4.1) where: NEddesign normal force (including load factors) reduction factor for the relevant buckling curve, i.e.curve "a" for s s 3% and curve "b" for 3% < s s 6% (see Fig. 2.3) Npl,Rdresistance of the cross section to normal force according to eq. (4.2) Npl,Rd = Aa fyd + Ac fcd + As fsd(4.2) where: Aa, Ac, Ascrosssectionalareasofstructuralsteel, concrete and reinforcement fyd, fcd, fsddesignstrengthsofsteel,concrete(see Table4.1)andreinforcementusingthe recommendedMfactorsaccordingto Eurocode2(EN1992-1-1,2004)and Eurocode 3 (EN 1993-1-1, 2005) being a = 1,0 for fy, c = 1,5 for fc, and s = 1,15 for fs TheloadfactorsfortheactionsFhavetobe determined from EN 1990 (2002). ConcreteclasseshigherthanC50/60shouldnotbe usedwithoutfurtherinvestigationandclasseslower thanC20/25arenotallowedforcomposite construction. Inconcretefilledhollowsections,theconcreteis confinedbythehollowsection.Therefore,the concretestrengthreductionfactorof0,85doesnot have to be considered. Thereductionfactorfollowsfromtherelative slenderness eff , crRk , plENN== (4.3) where: Npl,Rkresistanceofthecrosssectiontoaxialload according to eq. (4.2), however, with fyd, fcd and fsd replaced by fyk, fck and fsk Ncr,effelasticbucklingcapacityofthemember(Euler 37 critical load) Ncr,eff = 2beff) EI (2t(4.4) where: bbuckling length of the column (EI)effeffective stiffness of the composite section Thebuckling(effective)lengthofthecolumncanbe determinedbyfollowingtherulesofEurocode3(EN 1993-1-1). (EI)eff = Ea Ia + 0,6 Ec,eff Ic + Es Is(4.5) Ec,eff = tEdEd , GcmNN1Em +(4.6) where: Ia, Ic, Ismomentsofinertiaofthecrosssectional areas of structural steel, concrete (with the area in tension assumed to be uncracked) and reinforcement, respectively Ea, Ecm, Esmoduliofelasticityofstructuralsteel, concrete and reinforcement Ec,effmodulus of elasticity of concrete corrected for creep with Ecm according to Table 4.1 NEdacting design normal force NG,Edpermanent part of NEd tcreepfactoraccordingtoClause3.1of Eurocode 2 (EN 1992-1-1) The calibration factor 0,6 in eq. (4.5) is incorporated to consider,forexample,theeffectofcrackingof concreteundermomentactionduetosecondorder effects. 4.3.1 Limitations Thereinforcementtobeincludedinthedesign calculationsshouldnotexceed6%oftheconcrete area. There is no minimum requirement. Thecompositecolumnisconsideredas"composite" if: 0,2 s s 0,9(4.7) where: Rd , plyd aNf A= o (4.8) If the parameter is less than 0,2, the column shall be designedasaconcretecolumnfollowingEurocode2 (EN1992-1-1).Ontheotherhand,whenexceeds 0,9,thecolumnshallbedesignedasasteelcolumn according to Eurocode 3 (EN 1993-1-1). To avoid local buckling, the following limits should be observedforbendingandcompressionloading(EN 1994-1-1, 2004): -Forconcretefilledrectangularhollowsections(with hbeingthegreateroveralldimensionofthe section): h/t s 52(4.9) -For concrete filled circular hollow sections: d/t s 902(4.10) The factor accounts for different yield strengths: = ydf235(4.11) with fyd in N/mm2. Although the d/t and h/t values given in Table 4.2 are equal(forCHS)orhigher(forRHS)thanthoseof class3forunfilledsections,theplasticresistanceof the section can be used. However, for the analysis of theinternalforcesinastructure,anelasticanalysis shouldbeperformed.Furtherdiscussionson slendernesslimitsforunfilledCHSandRHSandthe effectofconcretefillingcanbefoundinZhaoetal. (2005). 4.3.2 Effect of long term loading Theinfluenceofthelong-termbehaviourofthe concrete on the load bearing capacity of the column is included by a modification of the concrete modulus of elasticity,sincetheloadbearingcapacityofthe columns may be reduced by creep and shrinkage. As shown in eq. (4.6) for a load which is fully permanent, themodulusofelasticityoftheconcretewillbe considerably reduced. 38 4.3.3 Effect of confinement For concrete filled circular hollow section columns with asmallrelativeslenderness< 0,5(forCHS,thisis approximately/ds12)ande/ds0,1,thebearing capacityisincreasedduetotheimpededtransverse strains.Thisresultsinradialcompressioninthe concreteandahigherresistancetonormalstresses, seeFig.4.3.Abovethesevalues,theconfinement effect is very small. Forconcretefilledrectangularhollowsections,any confinement effect is neglected. Detailed information can be found in Eurocode 4(EN 1994-1-1). 4.4 RESISTANCE OF A SECTION TO BENDING Forthedeterminationoftheresistanceofaconcrete filled section to bending moments, a full plastic stress distributioninthesectionisassumed(Fig.4.4).The concrete in the tension zone of the section is assumed to be cracked and is therefore neglected. The internal bendingmomentresultingfromthestressesand dependingonthepositionoftheneutralaxisisthe resistance of the section to bending moments Mpl,Rd. 4.5 RESISTANCE OF A SECTION TO BENDING AND COMPRESSION Theresistanceofaconcretefilledcrosssectionto bendingandcompressioncanbeshownbythe interactioncurvebetweenthenormalforceandthe internal bending moment. Figs.4.5to4.8showtheinteractioncurvesforRHS andCHScolumnsinrelationtothecrosssection parameter.Thesecurveshavebeendetermined without any reinforcement, but they may also be used forreinforcedsectionsifthereinforcementis consideredinthevaluesandinNpl,RdandMpl,Rd respectively. Theinteractioncurvehassomesignificantpoints, showninFig.4.9.Thesepointsrepresentthestress distributionsgiveninFig.4.10.Theinternalmoments and axial loads belonging to these stress distributions can be easily calculated if effects of the corner radius are excluded. Comparing the stress distribution of point B, where the normal force is zero, and that of point C with the same moment as in point B and axial force NC,Rd (Fig. 4.10), theneutralaxismovesoveradistance2hn.Hence, thenormalforceNC,Rdcanbecalculatedbythe additional compressed parts of the section with depth 2hn.BecausetheforceNC,Rddoesnotcontributeto the moment MC,Rd = MB,Rd. Furthermore,thenormalforceatpointCistwicethe value of that at point D: NC,Rd = 2ND,Rd. 4.6 INFLUENCE OF SHEAR FORCES Theinfluenceoftheshearstressesonthenormal stresses does not need to be considered if: VEd s 0,5 Vpl,Rd(4.12) The shear force on a composite column may either be assigned to the steel profile alone or be divided into a steelandareinforcedconcretecomponent.The componentforthestructuralsteelcanbeconsidered byreducingtheaxialstressesinthosepartsofthe steel profile which are effective for shear (Fig. 4.11). Thereductionoftheaxialstressesduetoshear stressesmaybecarriedoutaccordingtothe Huber-Hencky-VonMisescriterionoraccordingto Eurocode4(EN1994-1-1).Forthedeterminationof thecross-sectioninteraction,itiseasiertotransform thereductionoftheaxialstressesintoareductionof therelevantcrosssectionalareasequaltothatused for hollow sections without concrete filling: reduced Av = Av

||.|

\| 2Rd , plEd1VV 21 (4.13) 3fA Vydv Rd , pl= (4.14) For Av, see Chapter 2. 4.7 RESISTANCE OF A MEMBER TO BENDING AND COMPRESSION 4.7.1 Uniaxial bending and compression Fig.4.12showstheprincipleofthemethodforthe designofacompositememberundercombined compressionanduniaxialbendingusingthe 39 cross-sectioninteractioncurve.Duetoimperfections, the resistance of an axially loaded member is given by eq. (4.1) or on the vertical axis in Fig. 4.12. The moment capacity factor at the level of is defined as the imperfection moment. Having reached the load bearingcapacityforaxialcompression,thecolumn cannot resist any additional bending moment. Thevalueofdresultingfromtheactualdesign normalforceNEd(d=NEd/Npl,Rd)determinesthe momentcapacityfactordforthecapacityofthe member.Thisfactord givesthemomentcapacity includingtheimperfectionmoment,thusthe imperfection moment should be added to the external moment including second order effects. Thecapacityforthecombinedcompressionand bending of the member can now be checked by: M||,max s M d Mpl,Rd(4.15) where: M||,maxdesignbendingmomentofthecolumn, including the imperfection moment and second order effects M0,9forS235toS335and0,8forS420and S460 dto be obtained from the interaction diagrams in Figs. 4.5 to 4.8 The additional reduction by the factor M accounts for the assumptions of this simplified design method, e.g. theinteractioncurveofthesectionisdetermined assumingfullplasticbehaviourofthematerialswith no strain limitation. Note:Interactioncurvesofthecompositesections alwaysshowanincreaseinthebendingcapacity higherthanMpl,Rd.Thebendingresistanceincreases withanincreasingnormalforce,becauseformer regionsintensionarecompressedbythenormal force.Thispositiveeffectmayonlybetakeninto accountifitisensuredthatthebendingmomentand theaxialforcealwaysacttogether.Ifthisisnot ensured, and the bending moment and the axial force resultfromdifferentloadingsituations,therelated moment capacity d has to be limited to 1,0. Columns with equal end moments Theverificationprocedureforcolumnswiththesame endmomentsgiveninEurocode4(EN1994-1-1)is as follows: The second order moment MEd,|| can be approximated by: MEd,|| = k MEd(4.16) where: eff , crEdNN11k= (4.17) kistheamplificationfactortoincorporatethesecond order effects. Ncr,eff can be determined with eq. (4.4), however, with a modified (EI)eff,|| due to the simplifications mentioned before: (EI)eff,|| = 0,9 (Ea Ia + 0,5 Ec,eff Ic + Es Is)(4.18) Thetotalmomentincludingtheimperfectionmoment is: M||,max =eff , crEdNN11(MEd + NEd e0)(4.19) The capacity can now be checked with eq. (4.15). Columns with different end moments If the end moments are not equal (see Fig. 4.13), then thekfactorineq.(4.17)hastobecorrectedforthe external moment by a factor : eff , crEdNN1k |= (4.20) where: = 0,66 + 0,44rbut > 0,44(4.21) with r being the ratio between the smallest and largest end moment (Fig. 4.13). Thetotalmomentincludingtheimperfectionmoment is now: eff , crEd0 Edeff , crEdEdmax ||,NN1e NNN1MM+|= (4.22) Thismomenthastobeusedineq.(4.15).Ifthefirst ordermomentislargerthanMEd,||,thenthisvalue 40 should be used. 4.9 SPECIAL COMPOSITE MEMBERS WITH HOLLOW SECTIONS 4.7.2 Biaxial bending and compression Theprevioussectionsconsidercompositemembers consistingofahollowsectionattheoutersideand concreteinside.Theconcretemaybereinforcedor not.However,analternativeistoreinforcethe concretewithsteelfibresinsteadofreinforcingbars whichprovideadvantagesintheextensionofthefire resistance. Acompositememberunderbiaxialbendingand compressionhasfirsttobeexaminedforbothaxes under uniaxial bending and compression, see Section 4.7.1.Additionallythecombinedsituationhastobe verified.Theinfluenceoftheimperfectionisonly taken into account for the buckling axis which is most critical. 41 Thecheckcanbeexpressedbythefollowing condition: 0 , 1MMMMRd , z , pl dzEd , zRd , y , pl dyEd , ysu+u(4.23) Othertypesofreinforcementusedaresolidsections oranotherhollowsectioninsideacircularor rectangularhollowsectionwithconcreteinbetween. Fig.4.16showsanexampleofaCHSwithanother CHS member inside. Although many combinations are possible,thedesignisinprinciplesimilartothatfor thereinforcedconcretehollowsectioncolumns described in the previous sections (Zhao et al., 2010). Thevaluesdyanddzaredeterminedatthelevelof d. 4.8 LOAD INTRODUCTION Inthedesignofcompositecolumns,afullcomposite actionofthecrosssectionisassumed.Thismeans thatinthebondareanosignificantslipcanoccur betweenthesteelandtheconcrete.Atlocationsof loadintroduction,e.g.atbeam-columnconnections, this has to be verified. If no calculation is carriedout, thelengthofloadintroductionshouldbeassumedto betheminimumof2b,2dor/3,wherebordisthe minimumtransversedimensionofthecolumn,and is the column length. If the steel is not painted and is free of oil and rust, the maximumbondstress,basedonfrictionis(EN 1994-1-1, 2004): -Rd = 0,55 N/mm2 for CHS columns -Rd = 0,40 N/mm2 for RHS columns Theshearloadtransfercanbeincreased considerablybyshearconnectorsorsteel components, see Fig. 4.14. Forconcentratedloads,aloaddistributionaccording to Fig. 4.15 can be assumed. For such locally loaded partsofencasedconcrete,higherdesignvaluesfor the concrete strength can be used. Table 4.1 Strength classes of concrete, characteristic cylinder strength and modulus of elasticity for normal weight concrete Strength class of concrete fck,cyl/fck,cubC20/25C25/30C30/37C35/45C40/50C45/55C50/60 Cylinder strength fck (N/mm2)20253035404550 Modulus of elasticity Ecm (N/mm2)30000310003300034000350003600037000 Note: The recommended values a = 1,0, c = 1,5 and s = 1,15 should be used to determine the design values. Table 4.2 Limits for wall thickness ratios of concrete filled hollow sections for preventing local buckling under axial compression (EN 1994-1-1, 2004) Steel gradeS235S275S355S460 Rectangular hollow sections eq. (4.9) h/t52,048,142,337,2 Circular hollow sections eq. (4.10) d/t90,076,959,646,0 42 Fig. 4.1 Concrete filled hollow sections with notations NEde/Mpl,Rd1,000,750,500,2500,75 0,50 0,25 0 1,00S235 / C45d = 500 mmt=10 mmNEd/Npl,RdNEde/Mpl,Rd1,000,750,500,2500,75 0,50 0,25 0 1,00S235 / C45d = 500 mmt=10 mmNEd/Npl,Rd Fig. 4.2 Bearing capacity of a composite hollow section column 43 Fig. 4.3 Three dimensional confinement effect in concrete filled hollow sections Fig. 4.4 Stress distribution for the bending resistance of a section 1,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,4o = 0,450,400,2750,250,2250,200,300,90,80,70,60,5,,NEd/Npl,Rd MEd/Mpl,RdRd , plyd aNf Aparameter = o0,351,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,41,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,4o = 0,450,400,2750,250,2250,200,300,90,80,70,60,5,,NEd/Npl,Rd MEd/Mpl,RdRd , plyd aNf Aparameter = o0,35 Fig. 4.5 Interaction curve for rectangular hollow sections with bending about the weak axis, b/h = 0,5 44 1,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,4MEd/Mpl,Rdo = 0,450,400,350,2750,250,2250,200,90,80,70,60,5,1,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,40,90,80,70,60,5NEd/Npl,Rd ,Rd , plyd aNf Aparameter = o0,301,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,41,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,4MEd/Mpl,Rdo = 0,450,400,350,2750,250,2250,200,90,80,70,60,50,90,80,70,60,5,1,00,80,20,40,601,0 0,8 0,2 0,4 0,6 0 1,2 1,40,90,80,70,60,5NEd/Npl,Rd ,Rd , plyd aNf Aparameter = o0,30 Fig. 4.6 Interaction curve for square hollow sections with b/h = 1,0 o = 0,450,400,2750,250,2250,200,90,80,70,60,51,00,80,20,40,60NEd/Npl,Rd MEd/Mpl,Rd 1,0 0,8 0,2 0,4 0,6 1,2 1,4 0,Rd , plyd aNf Aparameter = o0,300,35o = 0,450,400,2750,250,2250,200,90,80,70,60,51,00,80,20,40,60NEd/Npl,Rd 1,00,80,20,40,60NEd/Npl,Rd MEd/Mpl,Rd 1,0 0,8 0,2 0,4 0,6 1,2 1,4 0MEd/Mpl,Rd 1,0 0,8 0,2 0,4 0,6 1,2 1,4MEd/Mpl,Rd 1,0 0,8 0,2 0,4 0,6 1,2 1,4 0,Rd , plyd aNf Aparameter = o0,300,35 Fig. 4.7 Interaction curve for rectangular hollow sections with bending about the strong axis, h/b = 2,0 0,400,350,2750,250,2250,30,1,00,80,20,40,600,90,80,70,60,5NEd/Npl,Rd MEd/Mpl,Rd1,0 0,8 0,2 0,4 0,6 0 1,2 1,41,00,80,20,40,60NEd/Npl,Rd 0,20,Rd , plyd aNf Aparameter = oo = 0,450,400,350,2750,250,2250,30,1,00,80,20,40,600,90,80,70,60,5NEd/Npl,Rd MEd/Mpl,Rd1,0 0,8 0,2 0,4 0,6 0 1,2 1,41,00,80,20,40,60NEd/Npl,Rd 1,00,80,20,40,60NEd/Npl,Rd 0,20,Rd , plyd aNf Aparameter = oo = 0,45 Fig. 4.8 Interaction curve for circular hollow sections 45 NE,RdNA,RdNC,RdND,RdNB,RdMA,RdMC,RdMD,RdMB,RdNE,RdNA,RdNC,RdND,RdNB,RdMA,RdMC,RdMD,RdMB,Rd Fig. 4.9 Interaction curve approached by a polygonal connection of the points A to E NC,RdND,Rd= 0,5NC,Rd-NE,RdME,RdND,Rd= 0,5NC,RdMD,Rd= Mmax,RdMC,Rd= Mpl,RdNC,RdMB,Rd= Mpl,RdNpl,RdNC,RdND,Rd= 0,5NC,RdNC,RdND,Rd= 0,5NC,Rd-NE,RdME,RdND,Rd= 0,5NC,RdMD,Rd= Mmax,RdMC,Rd= Mpl,RdNC,RdMB,Rd= Mpl,RdNpl,Rd Fig. 4.10 Stress distributions of selected positions of the neutral axis (points A to E) 46 Fig. 4.11 Reduction of the normal stresses due to shear ,ud,Rd , plEdNNRd , plEdMM,ud,Rd , plEdNNRd , plEdMM Fig. 4.12 Design for compression and uni-axial bending MEdr MEdMEdr MEd Fig. 4.13 Relation between the end moments (-1 s r s +1) 47 Fig. 4.14 Load introduction into hollow sections by inserted plates 1:2,5 1:2,5 1:2,5 1:2,5 Fig. 4.15 Load introduction in a composite column 0dt0concreteouter tubeinner tubediti Fig. 4.16 Tube-in-tube composite column concept 48 5. FIRE RESISTANCE OF HOLLOW SECTION COLUMNS 5.1 INTRODUCTION ThischapterisareducedversionofCIDECTDesign GuideNo.4(Twiltetal.,1994),however,updated withthelatestrevisionstoEurocodes3and4on structuralfiredesign(EN1993-1-2,2005;EN 1994-1-2, 2005). Unprotectedstructuralhollowsectionshavean inherentfireresistanceofapproximately15to30 minutes.Traditionally,itwasassumedthat unprotectedsteelmembersfailwhentheyreach temperaturesofabout450to550C.However,the temperatureatwhichasteelmemberreachesits ultimatelimitstatedependsonthemassivityofthe sectionandtheactualloadlevel.Iftheserviceload levelofacolumnislessthan50%ofitsresistance, the critical temperature rises to over 650 C, which, for baresteel,meansanincreaseinfailuretimeofmore than 20%. Whenhollowsteelsectionsarerequiredtowithstand extended amounts of time in fire, additional measures havetobeconsideredtodelaytheriseinsteel temperature. 5.1.1External insulation of the steel section External insulation of the steel section is a type of fire protection that can be applied to all kinds of structural elements(columns,beamsandtrusses).The temperaturedevelopmentinaprotectedhollowsteel sectiondependsonthethermalpropertiesofthe insulationmaterial(conductivity),onthethicknessof theinsulationmaterialandonthesectionfactor (massivity) of the steel profile. Externalfireprotectionmaterialscanbegroupedas follows: -Insulatingboards(basedmainlyongypsumor mineralfibreorlightweightaggregatessuchas perliteandvermiculite).Ifboardprotectionistobe used,caremustbetakentoensuretheintegrityof joints between the boards. -Spraycoatingorplaster(basedmainlyonmineral fibreorlightweightaggregatessuchasperliteand vermiculite) -Intumescentcoatings(paint-likemixturesapplied directlytothesteelsurfacewhich,incaseoffire, swell up to a multiple of their original thickness) -Suspendedceilings(mainlyprotectingroofs, trusses) -Heat radiation shielding In some countries, intumescent coatings are restricted toafireresistanceof30or60minutes,butthis technologyisrapidlydevelopingandnowadays considerably larger protection times are possible. 5.1.2 Concrete filling of the section Usually,fireprotectionthroughconcretefillingofthe sectionisappliedtocolumnsonly.Fillinghollow sectionswithconcreteisaverysimpleandattractive wayofenhancingfireresistance.Thetemperaturein theunprotectedoutersteelshellincreasesrapidly. However,asthesteelshellgraduallylosesstrength andstiffness,theloadistransferredtotheconcrete core. Apartfromthestructuralfunction,thehollowsection also acts as a radiation shield to the concrete core, in combination with a steam layer between the steel and the concrete core. Dependingonthefireresistancerequirements,the concreteinthehollowsectioncanbeplainconcrete (fireresistance30minutesupto60minutes)or concretewithreinforcingbarsorsteelfibres.New researchaimedatincreasingthefireresistanceof concrete filled hollow sections is focused on the use of high strength concrete. 5.1.3 Water cooling Watercoolingisatypeoffireprotectionthatcanbe appliedtoallkindsofhollowsections,butismostly used for columns. The hollow section acts both as the loadbearingstructureandasthewatercontainer. This protection system is quite sophisticated; it needs a thorough design and proper hydraulic installations. Thecoolingeffectconsistsoftheabsorptionofheat by water, the removal of heat by water circulation and itsconsumptioninthevaporizationofwater.In practicalapplications,theseeffectsarecombined.A suitablydesignedwaterfilledsystemwilllimitthe average steel temperature to less than 200 C. Two different systems can be used: permanently filled elementsorelementsfilledonlywhenafirebreaks out.Inthelattercase,protectiondependsonafire 49 detectionsystemandashortwaterfillingtime.In unreplenishedsystems,theattainablefireresistance time depends on the total water content (including any reservoirtank)andontheshapeoftheheated structure.Insystemswherethewaterisconstantly renewed,thefireresistanceisunlimited.Water coolingbynaturalflowismainlyusedforverticalor inclinedelementsinordertoensurethecirculationof the water. 5.2 FIRE RESISTANCE 5.2.1 Concept Fire safety precautions are specified with the intent of avoidinganycasualtiesandreducingeconomicfire damagetoanacceptablelevel.Asfarasbuilding constructionisconcerned,itisimportantthatthe constructionelementscanwithstandafirefora specifiedamountoftime.Inthisrespect,oneshould bearinmindthatthestrengthanddeformation propertiesofthecommonlyusedbuildingmaterials deterioratesignificantlyatthetemperaturesthatmay beexpectedunderfireconditions.Moreover,the thermalexpansionofmostbuildingmaterialsis considerable. As a result, the structural elements and assembliesmaydeformorevencollapsewhen exposed to fire conditions. Theamountoftimethataconstructionelementcan resistafirelargelydependsontheanticipated temperaturedevelopmentofthefireitself.This temperaturedevelopmentdepends,amongother aspects,onthetypeandamountofcombustible materialspresent,expressedintermsofkgofwood perm2floorsurfaceandcalledthefireloaddensity, see Fig. 5.1, and on the fire ventilation conditions. Inpracticalfiresafetydesign,however,itis conventionaltouseaso-called"standardfirecurve", definedinISO834-1(1999),whichismoreorless representativeforpostflash-overfiresinbuildings with relatively small compartments, such as apartment buildings and offices. Alternative standard fire curves, withsmalldifferencesfromtheISO-curve,areinuse in the USA. Theamountoftimeabuildingcomponentisableto withstand heat exposure according to the standard fire curve,iscalledthe"fireresistance".Inordertobe abletodeterminethefireresistanceofabuilding component,properperformancecriteriahavetobe determined.Thesecriteriaaredefinedinrelationto theanticipatedfunctionoftherespectivebuilding elementduringfire.Formoredetails,seeTwiltetal. (1994). For building components such as columns, with a load bearingfunction,theonlyrelevantperformance criterion is "stability". Asfarasthedeterminationofthefireresistanceis concerned,therearebasicallytwopossibilities:an experimental approach and an analytical approach. Theexperimentalapproach,i.e.thedeterminationof thefireresistanceofcolumnsbasedonstandardfire tests,isthetraditionalapproach.Althoughemploying differentnationaltestingprocedures,theconceptof firetestingis,byandlarge,thesameinthevarious countries. Theanalyticalapproachisthemodernapproachand has become possible by the development of computer technology. On an international level, calculation rules forthefireresistanceofbothsteelandcomposite steelconcretecolumns,includingconcretefilled hollowsectioncolumns,areavailable.Theanalytical approachofferssignificantadvantages,when compared with the experimental one. Importantfactorsinfluencingthefireresistanceof columns are: -Load level -Shape and size of the cross section -Buckling length -Concrete filling and reinforcement Baresteelcolumns(i.e.hollowsectioncolumns without external protection or concrete filling) possess onlyalimitedfireresistance.Dependingontheload levelandthesectionfactor(massivity),afire resistance of 15 to 20 minutes is usually attainable. A 30minutesfireresistancecanonlybeachievedin moreexceptionalcases.Thissituationmaybe dramaticallyimprovedbyapplyingthermalinsulation tothecolumn.Dependingonthetypeandthickness oftheinsulationmaterial,fireresistancesofmany hourscanbeachieved,althoughmostrequirements today are limited to 120 minutes. Hollowsectioncolumnsfilledwithconcretehavea muchhigherloadbearingcapacityandahigherfire resistancethanunprotected,emptyhollowsection columns.Providedtheconcreteisofgoodquality (over,say,acrushingstrengthof20N/mm2)andthe cross sectional dimensions are not too small (not less than150x150mm),afireresistanceofatleast30 minuteswillbeachieved.Sectionswithlarger 50 dimensionswillhaveahigherfireresistanceandby addingadditionalreinforcementtotheconcrete,the fire resistance may be increased to over 120 minutes. Infinite fire resistance can be achieved by water filling, provided an adequate water supply is available. Improvedfireperformanceofhollowsectioncolumns canalsobeachievedbyplacingthecolumnsoutside the building envelope an expedient sometimes used forarchitecturalpurposes.Bypreventingdirectflame impingementonthemember,theneedforadditional fireprotectionmeasurescanbesignificantlyreduced or even become unnecessary. Sincefiresafetyrequirementsforcolumnsare normallyexpressedintermsofthefireresistanceto be attained, this emphasizes the need to consider the fireresistancerequirementsfromthebeginningina structural design project. 5.2.2 Requirements Firesafetyinbuildingsisbasedonachievingtwo fundamental objectives: -Reducing the loss of life -Reducingthepropertyorfinanciallossin,orinthe neighbourhood of, a building fire Inmostcountries,theresponsibilityforachieving these objectives is divided between the government or civicauthoritieswhohavetheresponsibilityforlife safetyviabuildingregulations,andtheinsurance companies dealing with property loss through their fire insurance policies. Theobjectivesoffiresafetymaybeachievedin various ways. For example: -Byeliminatingorprotectingpossibleignition sources (fire prevention). -Byinstallinganautomaticextinguishingdevice,in ordertopreventthefirefromgrowingintoasevere fire (operational or active measures, e.g. sprinklers). -By providing adequate fire resistance to the building components using passive measures to prevent fire spreadingfromonefirecompartmenttoadjacent compartments. Oftenacombinationoftheabovemeasuresis applied. Requirementswithregardtofireresistanceclearly belong to the passive measures. To date, the use of a conventional fire scenario employing the ISO standard firecurve(ISO834-1,1999)iscommonpracticein Europeandelsewhere.Thestandardfiretestisnot intended to reflect the temperatures and stresses that wouldbeexperiencedinrealfires,butprovidesa measureoftherelativeperformanceofelementsof structuresandmaterialswithinthecapabilitiesand dimensionsofthestandardfurnaces.Ingeneral, uncertaintiesaboutstructuralbehaviourinrealfires aretakenintoaccountbymakingconservativefire resistance requirements. RequiredsafetylevelsarespecifiedinCodesand normally depend on factors like: -Type of occupancy -Height and size of the building -Effectiveness of fire brigade action -Active measures, such as vents and sprinklers Anoverviewoffireresistancerequirementsasa functionofthenumberofstoreysandrepresentative for European countries is given in Table 5.1. The following general features may be identified: -Nospecifiedfireresistancerequirementsfor buildingswithlimitedfireloaddensity(say,15-20 kg/m2)orwheretheconsequencesofcollapseof the structure are acceptable. -Fire resistance for a specified but limited amount of time, where the time requirement is mainly intended toallowforsafeevacuationoftheoccupantsand intervention by rescue teams. -Extendedfireresistanceofthemainstructureto ensure that the structure can sustain afullburnout ofcombustiblematerialsinthebuildingsora specified part of it. Sometimesunprotectedsteelmaybesufficient,for exampleforsituationswheresafetyissatisfiedby othermeans(e.g.sprinklers)and/orifrequirements withrespecttofireresistancearelow(i.e.notover, say, 30 minutes). Afullfireengineeringapproach(NaturalFire Concept),inwhichcompartmentandsteel temperature are calculated from a consideration of the combustiblematerialpresent,compartmentgeometry andventilation,isnowadaysmoreacceptedandhas shown considerable savings in fire protection costs in specific cases. 5.2.3 Performance criteria Thefundamentalconceptbehindallmethods designedtopredictstructuralstabilityinfireisthat 51 constructionmaterialsgraduallylosestrengthand stiffnessatelevatedtemperatures.Thereductionin theyieldstrengthofstructuralsteelandthe compressionstrengthofconcretewithincreasing temperatureaccordingtoEurocode3(EN1993-1-2) andEurocode4(EN1994-1-2)isgiveninFig.5.2.It shows that there is not much difference in the relative reduction in strength of concrete and steel under high temperatures.Thereasonforthedifferenceinthe structuralbehaviourofsteelandconcreteelements under fire conditions is that heat propagates about 10 to12timesfasterinasteelstructurethanina concrete structure of the same massivity, because the thermalconductivityofsteelishigherthanthatof concrete. Normally,thefireresistancedesignofstructuresis basedonasimilardesignapproachasusedfor designunderambienttemperature.Inamulti-storey bracedframe,thebucklinglengthofeachcolumnat roomtemperatureisusuallyassumedtobethe columnlengthbetweenfloors.However,such structuresareusuallycompartmentedandanyfireis likelytobelimitedtoonestorey.Therefore,any columnaffectedbyfirewillloseitsstiffness,while adjacentmemberswillremainrelativelycold. Accordingly,ifthecolumnisrigidlyconnectedtothe adjacentmembers,built-inendconditionscanbe assumed in the event of fire. Investigations by Twilt & Both(1991)showedthatinthecaseoffireonone storeythebucklinglengthofcolumnsinbraced framesisreducedtobetween0,5and0,7timesthe column length, depending on the boundary conditions, see Fig. 5.3. There is an increasing tendency toward assessing the fireresistanceofindividualmembersor sub-assemblesbyanalyticalfireengineering.The Eurocodesonstructuralfiredesign(EN1993-1-2, 2005;EN1994-1-2,2005)definethreelevelsof assessments: -Level 1: Tabulated data -Level 2: Simple calculation models -Level 3: Advanced calculation models "Advancedcalculationmodels"isthemost sophisticatedlevel.Suchcalculationprocedures includeacompletethermalandmechanicalanalysis ofthes