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

TensileMembraneActionofCompositeSlabsinFire

ArethecurrentmethodsreallyOK?

IanBurgess

UniversityofSheffield,UK

Cardington

Maxbeamtemperature~1150°Ccf.Codecriticaltemperature~ 680°C

2

Thebasisofallcurrentsimplifiedmethods:Hayes(1968)

3

Small-deflectionyield-linemechanism– slabonly

L=al

l

nL

gHoggingrotationsaboutedgesof

panel

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

“Membraneforce”enhancements:

e1m Momentofmembraneforcesabout11/totalresistance

momentaboutx-axisatinitialYL.

e2m Momentofmembraneforcesabout22/totalresistance

momentabouty-axisatinitialYL.

Thesestartatzeroforzerodeflection

Resistancemomentenhancement(reduction)

e1b Proportionalchangeofresistancemomentaboutx-axisdue

tomembranecompression.

e2b Proportionalchangeofresistancemomentabouty-axisdue

tomembranecompression.

Partialenhancementfactors– bothcases- Hayes

7

8

Bending“enhancements”- Hayes

Wood’sequationforreductionofmomentcapacityofarectangularRCcross-

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

Thesedon’tincludeanyverticalshearbetween

thefacets.Iftheseareincludedthereisonly

oneenhancementfactor.

(TonyGillies2015)

Newenhancement

Factorequivalentto ! = !" −!" − !'

1 + 2+n,'

Forminganoverallenhancementfactor- Hayes

10

Anyproblemssofar?

• Themembranetractiondistributionisanassumption.

Itcorrespondstounfractured meshandeither:

• Nothrough-depthcracksalongyieldlines.

• Partialthrough-depthcracksalongyieldlines.

• Bothofthesedistributionsapplyonlytothecasewherea

lateralthrough-depthcrackhasformedacrosstheshort

spanthroughtheYLintersection.

• Distributionisfixedforeachcase.Enhancementfactor

startsbelow1.0– actuallyatzero.

• Internalforcesdon’tdependondeflection.

Structuralfireresistancemethodsforcompositefloors

11

BREMethod(Bailey2000)• AmendedversionofHayes’s

method.

• FireSafeDesign(SCIP288)checkedusingBRE-Baileydesign

method.

NewZealandSPM(Clifton2006)FRACOF(2011)• BasedonaEuropeanproject.

• AlmostidenticaltoBREmethod.

Afewchangestosafetyfactors,

extradeflectioncheck.

TypicaldesignstrategyforTMA

• Protectmemberson

columngridlines.

• Leaveintermediate

secondarybeams

unprotected.

• Designindividualpanels

withoutcontinuity.

12

BRE/FRACOFmethod

13

• Unprotectedcomposite

beamsathightemperature

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).

• Separate“membrane”

enhancementse1mande2m by

momentsaboutlongandshort

edges.

• Add“bending”enhancements

e1bande2b tomakee1ande2.• Overallenhancementfactor

! = !" −./0.1"2'341

• …orGillies! = !" −./0.1

"2'3641

• Cutoff atenhancement1.0for

aspectratios>1.0.

17

78 =9.;<=>?=

@A1

B�

7D =E F' − F" G'

16ℎ

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

µtt

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.

• Asdeflectionincreasesconcretecompressionblocks

concentratetowardsslabcorners,rebarfractureswhen

itsstrainexceedsitsductility.

• Notensionwithincompressionblocks

21


lines.





Changeofstressblocks– ductiley-reinforcement

Compression

Tension

z

y

x

y

a1

22


lines.





Changeofstressblocks – ductiley-reinforcement

Compression

Tension

z

y

x

y

a1

23


lines.






Compression

Tension

z

y

x

y

a1

24


lines.






Compression

Tension

z

y

x

y

b1

25


lines.






Compression

Tension

z

y

x

y

b1

26


lines.






Compression

Tension

z

y

x

y

b2

27


lines.






Compression

Tension

z

y

x

y

c

28

Withdifferentrebar

ductility,meshcan

eitherfractureabruptly

orprogressivelyatany

stage.

Changeofstressblocks– possibilitieswithlessductility

Tension

z

y

x

y

Unfractured

MidYLfractured

Diagonalsunzipping

29

Withdifferentrebar

ductility,meshcan



stage.


Tension

x

y

Unfractured

MidYLfractured

Diagonalsunzipping

z

y

30

Withdifferentrebar

ductility,meshcan



stage.


x

y

Unfractured

MidYLfractured

Diagonalsunzipping

z

y

Tension

31

a1x

b1x

b1x'

b1x**

b1x***

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 6 7 8

Enhancementfactor

d/d1

Garstontestcomparison

• A142mesh(142mm2 permetre,580MPa

steelat200mmspacinginxandy

directions)at69mmeffectivedepth;

• Meshductility12%.

• Slabaspectratio1.4706(6.360mx

9.353).

• 120mmthick,52MPaconcrete;

• Edgesverticallysupported.

32

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 6 7 8

Enhancementfactor

d/d1

1.0 BRE1.0

1.4706 BRE1.4706

2.0 BRE2.0

3.0 BRE3.0

Garstoncomparisonfordifferentaspectratios

33

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

Bendingstress(MPa)

d/d1

StressQ

StressR

StressS

Garston– applytensilestrengthtochangemechanism

Q R

S

EC2tensile

strengthforC52

[0.3fc0.67]

34

b

DyDx

Dxy x

y

2

1

1

20x

xu z

v

=

=

22

2

2

2

2

2

2

y

x

y

u yyv x z

x Gap

y Gap

xy z

yx z

=

= +

=

=

+ +

+ +42

4

2

2

4

2 2 2 2

y

y

lu

lv x z

ly Gap x z

=

= +

= + +

32

3 2 2

2 2

y

xy

u yyrlv z

x Gap y

=

= +

=

3' 2 xu y= +

Newmechanism– centralthrough-depthcrack

35


z

y

x

y

36


z

y

x

y

37


z

y

x

y

38

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 6

Enhancementfactor

d/d1

Frombasicmechanismtocentrallycracked

39

Withattachedsteelbeams…

…theyield-linemechanismchanges.

40

l

rlnxl

gx

Forcesonthex-alignedmechanism

SC1Cy2

Tx1

Ty1

Ty2

Tb, t°

Tb, t°

A B

Unprotectedbeamsat

hightemperature

41

SC1

Cx2

Tx1

Ty1

Tx2

Tb, t°

Tb, t°

A

B

nyl

rl

l

gy

Forcesonthey-alignedmechanism

Unprotectedbeamsat

hightemperature42

Combinationsofcompressionblockandrebarfracture

CompressionblockReinforcementmeshfracturelevel(x-alignedmechanism)

None Centraly Diag.xCentral+

Diag.y

Central+

Diag.x

Central+

Diag.x,y

Full abovemesh a1 a1’ a1* a1** a1*’ a1***

belowmesh a2 a2’ a2* a2** a2*’ a2***

Triangular abovemesh b1 b1’ b1* b1** b1*’ b1***

belowmesh b2 b2’ b2* b2** b2*’ b2***

Trapezoidal c1 c1’ c1* c1** c1*’ c1***

y

x

43

Exampleofapplication:9mx6mcompositeslab

9m

6m

• 130mmthickslab,30MPa

concrete;

• A142mesh(142mm2 per

metre,500MPasteelat

200mmspacinginxandy

directions)at60mmeffective

depth;

• Mesheffectiveductility(over

200mmlength)1%:fracture

crack-width2mm;

• Onecentraldownstandsteel

beam,305x165UKB40,Grade

S275- unprotectedagainst

fire;

• Edgesverticallysupported.

305

60

130

16510

6

44

ny

0.6

0.4

0.2

0 2 4 6 8 10 12

0.8

n xorn y

Loadcapacity(kN/m2)

nx

Initialyield-lineparameterfordifferentloadcapacities

nx

ny

45

x

Criticaltemperature(°C) 900

600

300

0

Loadcapacity(kN/m2)

2 4 6 8 10 12

1200

y-mechanism

x-mechanism

Criticaltemperaturevariationwithloadcapacity

46

x

y

1200

1000

800

600

400

200

0 20 40 60 80 100

1400Unprotectedbeamtemperature(°C)

Slabdeflection(mm)

10

8

6

5

3

2.0

2.772.4

2.2

(Nofailureofnon-compositeslab)

(Ambient-temperaturefailureofcompositeslab)

4

Enhancementofcriticalsteeltemperaturewithdeflection

47

800

700

0 20 40 60 80 100

900

Unprotectedbeamtemperature(°C)

Slabdeflection(mm)

3kN/m2

Enhancementofcriticalsteeltemperaturewithdeflection

a1y

b1y’

b1y

b1y***b1y’*

48

MaximumsteeltemperatureenhancementsTemperatureenhancement(°C)

120

80

40

0 2 4 6 8 10

160

y-mechanismx-mechanism

b1y’

B1y*

b1y’*

b1y’*

Loadcapacity(kN/m2)

b1x’

B1x**

49

MaximumtensilestressatsectionA

5

Stress(M

Pa)

3

2

1

0 20 40 60 80 100

Slabdeflection(mm)

A

5kN/m2

A

B

50

Insummary…

Existingsimplifiedmethods:Forconcreteslabs:

• Fixedmembranetractiondistribution– independentofslab

deflection.

• Membranetractiondistributiononlyvalidwhileconcretehas

compressionalongwholeyieldlines.

• Assumescentralcrackfullyformed.Rebaratultimatestrength

(+10%)

• Enhancementfactorstartsbelow1.0.

Forcompositeslabsinfire:

• Yield-linepatternbasedonnon-compositeslab.

• Superposeshigh-temperaturecompositebeamcapacityand

deflection-controlledslabenhancement.

• Criterionformid-spanthrough-depthcrackismeaningless.

51

Insummary…

Thenewapproach:Forallslabs:

• Basedonthekinematicsofdeflectingflatfacetsofthesmall-deflection

yieldlinemechanism,togetherwithin-planeequilibriumofthe

concreteandsteelforces.

• Allowsconcretestressblockstomoveandmeshtofractureacross

yieldlines.

Forcompositeslabsinfire:

• Keepsloadconstant,allowsbeamstemperaturetoincreaseuntilyield

linemechanismforms.

• Enhancementofsteelbeamtemperaturewithdeflection.

Biggestproblemstobesolved:• Fractureductilityofrebaracrossdiscretecracks- yieldlinesor

through-depthmid-spancrack.

• Concretetensilestresstoinitiatethemid-span(orintersection)crack.

52

Thankyou

53

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

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