Tensile Membrane Action of Composite Slabs in Fire nbsp; Tensile Membrane Action of Composite Slabs in Fire Are the current methods really OK? Ian Burgess University of Sheffield,

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  • TensileMembraneActionofCompositeSlabsinFire

    ArethecurrentmethodsreallyOK?

    IanBurgess

    UniversityofSheffield,UK

  • Cardington

    Maxbeamtemperature~1150Ccf.Codecriticaltemperature~ 680C

    2

  • Thebasisofallcurrentsimplifiedmethods:Hayes(1968)

    3

  • Small-deflectionyield-linemechanism slabonly

    L=al

    l

    nL

    gHoggingrotationsaboutedgesofpanel

    Saggingrotationsaboutinternalyield

    lines

    Yield-linepatternisoptimized

    forminimumconcreteslab

    failureload.

    4

    Large-deflectionfailurecrack

    sometimesobservedintests

    andusedbyHayes.

  • Equilibrium1 nothrough-depthYLcracks- Hayes

    kbKT0

    bKT0

    Rationale: Superpositionofrebar

    tensionandconcretecompression

    force/unitlength.

    Tension

    Compression

    5

    T0l/2

    E

    Criterion: Cracksfrom

    intersection.Moment

    equilibriumaboutE.Findsbandk.

  • Equilibrium2 somethrough-depthYLcracks- Hayes

    kKT0

    KT0

    Tension

    6

    Rationale: Superpositionofrebar

    tensionandconcretecompression

    force/unitlength.

    Compression

    Bothb andk areconstant foreachofthe2cases.No

    variationwithdeflection.

  • 1 12

    2

    Membraneforceenhancements:

    e1m Momentofmembraneforcesabout11/totalresistancemomentaboutx-axisatinitialYL.

    e2m Momentofmembraneforcesabout22/totalresistancemomentabouty-axisatinitialYL.

    Thesestartatzeroforzerodeflection

    Resistancemomentenhancement(reduction)

    e1b Proportionalchangeofresistancemomentaboutx-axisduetomembranecompression.

    e2b Proportionalchangeofresistancemomentabouty-axisduetomembranecompression.

    Partialenhancementfactors bothcases- Hayes

    7

  • 8

    Bendingenhancements- Hayes

    WoodsequationforreductionofmomentcapacityofarectangularRCcross-

    sectionduetoaxialcompression:

    2

    0 0 0

    1M N NA BM T T

    = +1.Long-spanreinforcement:

    2

    0 0 0

    1 ' 'M N NA BM KT KT

    = +2.Short-spanreinforcement:

    Theseareintegratedinx- andy- directionsrespectivelyforthebending

    momentsacrosstheyieldlinesforPortions1and2.

    T0

    T0

    T0

    T0N

  • 9

    !" = !"$ + !"&!' = !'$ + !'&

    ! = !" !" !'1 + 2+,'

    Thesearenearlyalwaysunequal

    (WHY?).Puttogetheras

    Overallenhancementfactor

    x

    y

    z

    V

    V

    Verticalshear

    resultantsacross

    yieldlines

    Thesedontincludeanyverticalshearbetween

    thefacets.Iftheseareincludedthereisonly

    oneenhancementfactor.

    (TonyGillies2015)

    Newenhancement

    Factorequivalentto ! = !" !" !'

    1 + 2+n,'

    Forminganoverallenhancementfactor- Hayes

  • 10

    Anyproblemssofar?

    Themembranetractiondistributionisanassumption.Itcorrespondstounfractured meshandeither:

    Nothrough-depthcracksalongyieldlines. Partialthrough-depthcracksalongyieldlines.

    Bothofthesedistributionsapplyonlytothecasewherealateralthrough-depthcrackhasformedacrosstheshort

    spanthroughtheYLintersection.

    Distributionisfixedforeachcase.Enhancementfactorstartsbelow1.0 actuallyatzero.

    Internalforcesdontdependondeflection.

  • Structuralfireresistancemethodsforcompositefloors

    11

    BREMethod(Bailey2000) AmendedversionofHayess

    method.

    FireSafeDesign(SCIP288)checkedusingBRE-Baileydesign

    method.

    NewZealandSPM(Clifton2006)FRACOF(2011) BasedonaEuropeanproject. AlmostidenticaltoBREmethod.

    Afewchangestosafetyfactors,

    extradeflectioncheck.

  • TypicaldesignstrategyforTMA

    Protectmembersoncolumngridlines.

    Leaveintermediatesecondarybeams

    unprotected.

    Designindividualpanelswithoutcontinuity.

    12

  • BRE/FRACOFmethod

    13

    Unprotectedcompositebeamsathightemperature

    carrysomeoftheloadas

    simplysupported.

    Concreteslabcarriesremainingloadintensile

    membraneaction.Needs

    enoughdeflection.

    +

  • Small-deflectionyield-linemechanism slabonly

    BRE/FRACOF

    L=al

    l

    nL

    gHoggingrotationsaboutedgesofpanel

    Saggingrotationsaboutinternalyield

    lines

    Theanalysisisbasedonthe

    optimalyield-line patternfor

    theconcreteslabwithout

    consideringthesteelbeams.

    14

    Tensilecrackacross

    shortmid-span

    Large-deflectionfailurecrack

    observedintestsandusedin

    Bailey/BRE,FRACOFandNZ

    SPM.

  • Forceequilibrium nothrough-depthYLcracks BREetc

    kbKT0

    bKT0

    15

    E

    Criterion: Crackacross

    mid-long-span.Moment

    equilibriumaboutE.

    Findsb andk.

    (Ultimatestrength

    ofreinforcement

    acrossFracture)1.1T0l/2

    Thisistheonlymechanism

    noseparationofconcrete

    alongtheyieldlines.

  • 0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    0 1 2 3 4 5 6 7 8

    Enhancementfactor

    d/d1

    BRE1.0 Gillies1.0

    BRE1.5 Gillies1.5

    BRE2.0 Gillies2.0

    BRE3.0 Gillies3.0

    16

    TMAenhancementcalculations BRE/FRACOF

    SimilarlytoHayes: Horizontalforceequilibrium

    assumingmid-spancrack.(But

    onlythelinearmembrane

    tractiondistribution).

    Separatemembraneenhancementse1mande2m bymomentsaboutlongandshort

    edges.

    Addbendingenhancementse1bande2b tomakee1ande2.

    Overallenhancementfactor! = !"

    ./0.1"2'341

    orGillies! = !" ./0.1

    "2'3641

    Cutoff atenhancement1.0foraspectratios>1.0.

  • 17

    78 =9.;?=

    @A1

    B

    7D =E F' F" G'

    16

    wE wq

    Limitingdeflection(centralcracking) criterion

    +

  • Backtobasics

    18

  • Increasingdeflectionofyield-linemechanism

    Yield-linemechanismisaplasticbendingmechanismat

    smalldeflections.Yieldlines

    areessentiallydiscretecracks.

    Asdeflectionsstarttoincreasetheyield-linepatternincreases

    therotationsofitsflatfacets,

    withtherebaryieldinguntilit

    fractures.

    Sotheinitiallarge-deflectionmechanismisthisone.

    MechanismB

    19

  • h

    x

    tt

    s

    yx

    zf

    qy

    x

    DxDy

    TOPSURFACEOFSLABCRACK OPENING AT REBAR LEVEL

    x

    Asdeflectionsstarttoincreasetheyield-linepatternincreasestherotationsofitsflatfacets,and

    rebaryieldsacrosscracksuntilitfractures.

    Geometryofyield-linecrack opening

    20

  • ForceequilibriumofMechanismB

    S

    C1T1T2 C2

    M1 M2

    M3

    Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks21

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    a1

    22

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    a1

    23

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    a1

    24

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    b1

    25

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    b1

    26

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyield-

    lines.

    Asdeflectionincreasesconcretecompressionblocksconcentratetowardsslabcorners,rebarfractureswhen

    itsstrainexceedsitsductility.

    Notensionwithincompressionblocks

    Changeofstressblocks ductiley-reinforcement

    Compression

    Tension

    z

    y

    x

    y

    b2

    27

  • Shapeofconcretecompressionblocksisdictatedbycompatibilityandequilibrium: Initiallytensionandcompressionateverypointofyie