M. SLIVANSKÝ

EXPERIMENTAL VERIFICATION OF THE RESISTANCE OF GLASS BEAMS

KEY WORDS

• structural glass,• laminated glass,• beams• reinforcement,• post – breakage structural capacity.

ABSTRACT

Experimental research at the Department of Steel and Timber Structures at SUT in Bratislava focused on the verification of the behavior of modern glass structures. Four types of glass beams were tested - laminated beams made of annealed (ANG) and fully tempered glass (FTG) in interactions with or without steel elements (as reinforcement). The results of the experimental research were also compared with theoretical models using FEM calculations.

Miloš SLIVANSKÝemail:milos.slivansky@stuba.skResearchfield:structuralglass

Address:DepartmentofSteelandTimberStructures,FacultyofCivilEngineering,SlovakUniversityofTechnology,Radlinského11,81368Bratislava

Vol. XX, 2012, No. 1, 21 – 28

1. INTRODuCTION

The nature of unpredictable and brittle failures is the crucialdisadvantageoftheuseofglassasastructuralmaterial.Improvingthe resistance of glass elements has often been realized bymulti-layeringglasssheetswithPVBfoilinthepast,anditwasessentialto overdimension the glass structure. The load-bearing capacityof the partly damaged laminated glass element at a reduced levelof stress was considered. Fully tempered glass was usually used,becauseasaresultofheattreatment,itdemostratesahighertensilestrength[8],[2].Theconceptof reinforcedglassbeams focusesonways toensurethe plastic (ductile) failure behaviour of the element.This ductilefailure behaviour is obtained by bonding a reinforcement profilein the tensile zone along the edge of the glass beam. Exceedingthe tensile strength of glass causes the initial formation of tensilecracks,butthegrowthofthecracksislimited.Thefracture‘senergy

ispartlyusedfordeformationofthereinforcement,whichtransfersthe tensile forces at the point of the crack. Together with thecompressionforcesintheuncrackedglass,aninternalcouplingoftheforces iscreated,and thereinforcedbeamisstillable tocarrytheload.Therehavebeenseveralresearchprojectsrealizedabroaddedicatedtoreinforcedorcompositeglassbeams.Exceptforsteelreinforcement

Fig. 1.1 Schematic overview of the distribution of the force after the failure of glass [8].

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profiles,acombinationofglasswithothermaterialshasalsobeenused.AbriefoverviewofthemostrecentworksisgiveninFig.1.2.Theseworksexaminedglassbeamsreinforcedwithsteelstrapsorprofiles [8], [9], carbon-fiber reinforced glass beams [10], glass-concrete composite beams [4], glass-timber composite beams [7],[6],andalsoglassbeamswithsteelflanges[11],[3],[5].

2. TYPES OF BEAMS, MATERIAL AND GEOMETRY

The first part of the experimental research focused on the basicmechanical properties of glass as astructuralmaterial. The effectoftheheattreatmentofglass(tempering)onitsstrengthintensionandtheimprovementof thebendingresistanceof theglassbeamswereexamined.In the second part of the experimental research the behavior ofglassbeams reinforcedwith stainless steelprofiles (as strips)wasexamined. Reinforcing profiles were attached to the bottom edgeon both surfaces of the glass by means of an epoxid glue. Theexperimental resultswere evaluated in terms of the nature of thecollapse at different stress levels and the different states of theoperationofthereinforcedglassbeam.

The glass beam specimens had dimensions of 1500 x 130 mm,and laminated glass (annealed or fully tempered) was used fortheirproductionwithasheetthicknessof5mmandPVBfoilwithathicknessof0.76mm.Thetheoreticalthicknessofthelaminatedglasspanewastherefore10.76mm.AstainlesssteelprofileoftheEN1.4301material‘squality,respectivelySTN17240,wasusedasareinforcingprofile.Aprofileof15x3mmwasattachedtobothsurfaces of the glass pane along the tension edge. Details of thereinforcedglassbeamwithastainlesssteelprofileareshowninFig.2.1.The two-component LoctiteHysol 9466 epoxy adhesivewasusedforbondingthereinforcingprofile.

2.1 Preparation of the experiment

All the types of glass beamswere tested using a4-point bendingtest.Thetheoreticaldistancebetweenthesupports(span)was1400mmwith1500mmasthetotallengthofthebeams.Thespecimenswere loadedsymmetricallyat twopointsatadistanceof200mmfrom the middle of their spans. The total distance between thesupportsoftheloadinggirderwastherefore400mm.Theloadinggirder and the test samples were fitted together in aZDMU 30stationaryhydraulictestingmachinewithamaximumloadingforceof100kN(Fig.2.2).ThecourseoftheloadingtestwasrecordedusingaHBMSpider8measuringstation,andthedatawerestoredinaPC(notebook)viatheCatman utility software.Themeasured datawere exported toaMicrosoftExcelfileformataftertheloadingtesthadfinished.Thefollowingdataweremeasured:• verticaldeformationoftheglassspecimen 5x• horizontaldeformationoftheglassspecimen 1x• trajectoryofthetestingmachinejack 1x• loadingforce 1x• strainmeasurementoftheglassspecimen 4x

3. EVALuATION OF THE MEASuREMENTS

Sixteen glass beam samples were tested in the laboratory of theDepartment of Steel andTimber Structures at SUT in Bratislava.Thespecimensweresortedaccordingtothetypeofglass(ANGfloatglassorFTGfullytemperedglass)andthebeamtype(unreinforcedorreinforced=Reinforced)into4basicgroups.

3.1 Testing of the unreinforced beams

Thebrittlebreakingbehaviorof theglasselements forboth typesof beams (ANG and FTG) occurred through their total collapse,whichhadnotbeenprecededbyanynoticeableformationofcracks,

Fig. 1.2 Similar structural glass composite beam concepts [8].

Fig. 2.1 Glued reinforcing profile (detail), scheme and actual performance.

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23EXPERIMENTAL VERIFICATION OF THE RESISTANCE OF GLASS BEAMS

so the beams suddenly failed. For the beamsmade of float glassthe final damagewas strictly of alocal character (one crack andintact compact parts); the beams made of fully tempered glasswerebrokenintomanysmallpiecesduetotheheattreatment,andsomeofthefragmentswereejectedforquiteadistance.Thebrokenspecimens showedno residual resistance,despite the fact that thebrokenpartswereconnectedbyPVBfoil.

3.2 Testing the reinforced beams of float glass

Themainobjectiveoftheexperimentalresearchpreparedwastestingthereinforcedbeamsmadeoffloatglass.Themeasurementresultsprovedtherelationshipbetweentheloadandverticaldeflectionuntilthecrackformsisalmostperfectlylinear.Theextensionofthesizeandnumberofcracksresultsinadecreaseinthebendingstiffnessandanincrease

Fig. 3.1Typical breaking behavior of ANG (left) and FTG specimens (right).

Fig. 2.2Loading girder, scheme and installation of the hydraulic testing machine.

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in theverticalbeam‘sdeflection.Thetypicalbrittlebreakingbehaviorof the glass elementswas transformed to aductile (plastic) behavior,whichshowedagradualdecline in thebendingstiffnessof thebeam.Thedecreaseinthebendingstiffnessofthereinforcedbeamiscausedbytwocrucialfactors–theformationandprogressoftensilecracksintheglassandtheplasticdeformationofthereinforcementinthecrack.Allofthereinforcedbeamsmadeoffloatglasswereabletocarrytheincreasingload,andnoneofthemcollapsedafterthefirstcrackhad occurred. The initial crack was formed on the tension edge

of thebeams.The crackshad aslightlybranched shape andwereorientedperpendicularly to theedgeof thebeam.Theyformed inboth layersof the laminatedglassalmost simultaneously; inmostcasestheywereintheareaofthemaximumbendingmoment.Theinitial crack‘slength was limited to amaximum 3/5s of the totalheightofthebeam‘scross-section.Newcrackswereformedundertheincreasingload,andtheexistinginitialcracksgrew.Themechanismofthefinalcollapsedifferedaccordingtowhetherthebeamswithorwithoutasecondarylateralrestraint(stabilisation

Fig. 3.2Graphs of the P - w relationship for the ANG-R beams.

Fig. 3.3The initial cracks and their growth before the final collapse of the specimen.

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of the compression edge) were tested. For beams without anystabilization most of the cracks had adiagonal direction. Thecrackswerelinkedtoeachother,andtheyreachedthecompressionedge progressively. The total collapse of the beam was causedby the buckling and explosion of the compression edge, whichwas corrupted by alarge number of cracks. For the beams withasecondary lateral stabilization, the cracks had amostly irregularlayout.Therewere twodifferent formsof the final collapse - thebuckling and explosion of the compression edge between thesecondarylateralrestraintsortheformationofasignificantdiagonalcracknearthesupportsoftheloadinggirder.Adiagonalcrackwithaslopeofabout45° to60°damagedboth layersof the laminatedglassthroughthetotalheightofthebeam‘scross-section.Thetotalresistance of the beam was probably affected by the transverseforcesaccordingtothecharacterandlocationofthediagonalcracks.In both cases, the damaged beamswere unable to carry any loadsor forces. The ending parts of the beam (out of the area with themaximum bending moment) remained compact with avery smallnumberofcracks.Duetothefinalcollapse,theplasticdeformationanddelaminationofthereinforcementprofileoccuredinseveralcasesofthespecimenstested.Thetotalvaluesofthebendingresistanceofthe reinforcedbeamsmadeof floatglass (ANG-R)hadarelativelysmallvariance,despitethefacttherewasafinalcollapsecausedbythebucklingorbytheformationofasignificantdiagonalcrack.

3.3 Testing the reinforced beams of fully tempered glass

The reinforced beams made of fully tempered glass behavedidenticallyas thebeamsmadeof floatglassuntil an initial crackwasformed.Thefullytemperedglassbrokeimmediatelyintomanysmallpiecesorfragments;thus,therewasnoredistributionofthe

stressbetweenthecompressedglassandtensionedreinforcement.The collapse of the beams was not preceded by any noticeableformationofcracks,andthetotalfailurewassudden,whichwasthesameasfortheunreinforcedbeamsmadeoffullytemperedglass.

4. OWERVIEW OF THE EXPERIMENTAL RESuLTS OBTAINED

From the results of the experimental research, the followingconclusionscanbeformulated:• theextremlybrittlefailurebehavioroftheglasselements;• a positive effect of heat treatment (tempering) on the tensilestrength of glass; the fully tempered glass beams achieveda higher bending resistance from 2.5 to 4.5, compared to thebeamsmadeoffloatglass;

• themeasuredvaluesofYoung‘smoduluscorrespondedtoavalueof70GPa;

• apositiveeffectofthelateralrestraintofthecompressionedgeonthestabilityandtotalresistanceoftheglassbeams,

• theinteractionoftheglasswiththereinforcingprofilebymeansoftheepoxyadhesiveshowedsufficientresults;

• the aesthetics of the glued bond was satisfactory and notcontradictorytotheappearenceoftheglasselement;

• the technological process of preparing the reinforced beams isrelativelyinexpensiveandsimple;

• thetotalbendingresistanceofthereinforcedbeamsmadeoffloatglasswasfrom2.5to4timeshighercomparedtotheresistanceoftheunreinforcedbeamsmadeoffloatglass;

• theinitialbendingresistance(untilthefirstcrackwasformed)ofthereinforcedbeamsmadeoffloatglasswasfrom1.7to3.3timeshighercomparedtotheresistanceoftheunreinforcedbeamsmade

Fig. 3.4Total collapse of the beam caused by the buckling (left) and a collapse caused by the formation of a diagonal crack (right).

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offloatglass,butonly50to100%ofthetotalbendingresistanceoftheunreinforcedbeamsmadeoffullytemperedglass;

• allofthereinforcedbeamsmadeoffloatglassdidnotcollapseafterthefirstcrackhadoccurred;thus100%ofthepost-breakageload-bearingcapacitywasreached;

• theredistributionofthestressbetweenthecompressedglassandtensioned reinforcement developed after the crack‘s formation;amoresignificantincreaseinthenormalstresswasmeasuredinthereinforcement(stainlesssteelprofile);

• the typical brittle breaking behavior of the glass elementstransformed into ductile (plastic) behavior, which showedagradualdeclineinthebendingstiffnessofthebeam;

• a decrease in the bending stiffness of a reinforced beam iscausedby two crucial factors - the formation and extensionof

tensile cracks in the glass and the plastic deformation of thereinforcementatthepointofthecrack;

• noneofthespecimensfailedduetothedelaminationorruptureofthereinforcementprofile;allofthemcollapsedafterthefailureoftheglasspart,whichwascorruptedbyalargenumberofcracks;

• theapplicationofthereinforcementincombinationwiththefullytemperedglasswasineffectiveandhadnopracticalimportance;

• the increase in the total bending resistance of the reinforcedbeams compared to the unreinforced beams made of fullytemperedglasswasnegligibleinthetests(maximum10%);

• the total bending resistance of the reinforced beams made offully tempered glass compared to the reinforced beams of thefloatglasswasapproximately30%higher(thepositiveeffectoftemperingonthetensilestrengthoftheglass).

Fig. 4.2Maximal loading of the beams by total collapse (total resistance).

Fig. 4.1Total loading of the beams by the initial crack formation (initial resistance).

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5. THEORETICAL ANALYSIS

5.1 FEM models

Atotalof16modelswasanalysed in theFEMcalculationsusingtheDlubalRFEM4software.Thebehaviorofabeamwasanalysedboth in terms of the extent of abeam‘sdamage (without acrack,onecrack,anumberofcracks)andintermsoftheworkingdiagramofthereinforcementmaterial(thelinearandnon-linearrelationshipofσ - ε).Thenon-linearmaterialmodeloftheEN1.4301stainlesssteelusedasimplifiedworkingdiagramaccordingtoEC1993-1-4:2006(E).The original continuous dependence ofσ - ε was replaced in theFEMcalculationsbyapolygonal.ThelayerednatureofthelaminatedglasswasignoredintheFEMmodels; the laminatedglassandalso thereinforcingprofileswerereplacedbyashell element.Both theglass and reinforcement laytogetherononecommonplane.Inthecaseofthecrackedglassbeams,thetensilecrack/cracksweredefinedasFEMelementswith thenon-linearworkingdiagramoftheglassofawidthof5mm.Exceedingthenormalstressintensionover 1MPa caused arupture of the material, and these elementswerenolongercapableofcarryinganytensionforces.Inthecaseofnormalstressincompression,theunlimitedlinearbehaviorofthematerialwasdefined.

5.2 Overview of the theoretical results

The evaluation of the FEM calculations focused primarily onacomparisonoftheverticaldeflectionUz,thenormalstressSigmax

andthedistancebetweenthecompressionedgeandtheneutralaxisx.SeveralofthegraphicoutputsfromtheRFEM4softwareareshowninFig.5.1toillustratethetheoreticalresultsoftheFEMmodels.

5.3 Comparison of the results

The results of the FEM calculations proved that the number andextensionofcracksdonotaffectthebendingstiffnessofareinforced

Fig. 5.2Diagrams of the P – w relationship of the reinforced glass beams, a comparison of the theoretical and experimental results.

Fig. 5.1-Normal stress Sigmax in the glass and vertical deflection Uz for loading force P = 18kN (one crack, non-linear material model of the reinforcement).

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glassbeamsignificantlyinthecaseoftheunlimitedlinearbehaviorofthereinforcementmaterial(thedashedtracesshowaslightvariance,Fig.5.2).Ontheotherhand,theeffectofthenumberandextensionofthecracksinglassisstronglymanifestedforanon-linearmaterialmodel of the reinforcement (continuous traces).Aglass beam hasavery smallbending stiffness, and theverticaldeflection increasesbecauseoftheplasticdeformationofthereinforcementinthecrack.Thecomparisonofthetheoretical(FEManalysis)andexperimentalresults indicates aplastic deformation of the reinforcement duringtheexperimentafterthecrackswereformed;otherwise,theductile(plastic) P – w relationship of the real diagram (with an almosthorizontalsecondarypartition)isnotpossible(Figs.3.2and5.2).Inmostcasesthereinforcementworkselasticallybeforetheinitialcrackformation;therefore,theresultsofthetheoreticalandexperimentalresearchonthereinforcedglassbeamswithoutcracksaresimilar.

6. CONCLuSION

Theissueofglassbeamsisarelativelynovelfieldforload-bearingstructures. Experimental research at the Department of Steel andTimberStructureshasshownthatthereliabilityofglassstructurescan be significantly improved by means of combinations withmetallic materials. Reinforcing glass with aglued stainless steelprofile increases its total resistance and supplies avery importantresidual resistance to the damaged glass structure (post-breakageload-bearing capacity). The application of the reinforcing profile

bymeansofepoxyadhesivesistechnologicallyaverysimpleandrelativelyinexpensiveprocess,whichisnotcontradictionarytotheappearance of aglass element. The unpredictable and dangerousbrittlebreakingbehavioroftheglasselementsismodifiedtowardstheductile (plastic)behavior.The significantdamageof theglassand large deformations is noticeable before the final collapseof the reinforced glass element occurs. The application of thereinforcement in combination with fully tempered glass has nopractical importance, because it immediately breaks into manysmallpieces;thus,thereisnopossibleredistributionoftheinternalforces, which leads to asudden failure of the beam without anypost-breakageload-bearingcapacity.Thetheoreticalanalysisprovidedhelpsinunderstandingtheoperationofreinforcedglassbeamsinageneralway.ThedeviationsbetweentheresultsoftheFEMcalculationsandtheexperimentaldatamainlyoccur because the mechanical material properties of the stainlesssteelwereconsideredaccordingtothetheoreticalECvalues,andtherealworkingdiagramof the reinforcementwasnotexperimentallytested.TheresultsoftheexperimentaltestingofthereinforcedglassbeamsshowedthattherealelasticworkingintervaloftheEN1.4301stainlesssteelusedwasprobablyhigherthanthetheoreticalnominalvalueoftheyieldstrengthfy=210MPa,accordingtotheEC.ThecomputationalFEMmodelsusedaregenerallyapplicableinthedesignofreinforcedglassbeamsdespitethedeviationslistedabove.Usingthenominalmaterialproperties,thetheoreticalresults(totalbendingresistance,verticaldeflection,normalstress)representsafevalues.

REFERENCES

[1] Slivanský, M.: Experimental and theoretical verification oftheresistanceofglassbeams.DissertationworkSvF-3237-3702,CivilEngineering,SUTBratislava2010

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[8] Louter, C.: Adhesively bonded reinforced glass beams,HERONVol.52,Nos.1/2,2007

[9] Ølgaard, A. B., Nielsen, J. H., Olesen, J. F., Stang, H.:Properties of anAdhesive for StructuralGlassApplications,ChallengingGlass,ConferenceonArchitecturalandStructuralApplicationsofGlass,2008

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[11] Wellershoff, F., Sedlacek, G.: Structural Use of Glass inHybridElements,Steel–GlassBeams,Glass–GFRPPlates,GlassProcessingDays2003,pp.268-270