COMPOSITE BEAMS.pdf

OUTLINE:
Introduction
Shoring Process
Effective Beam Flange Width
Shear Transfer
Strength Of Steel Anchors
Partially Composite Beams
Moment Capacity Of Composite Sections
Deflection
Design Of Composite Sections

1. COMPOSITE CONSTRUCTION:
COMPOSITE BEAM
1
Presented By
Eng. ZEINAB AWADA
Email
[email protected]
MASTER OF CIVIL ENGINEERING -LEBANON
ADVANCED STRUCTURAL SYSTEMS COURSE
Sat, Oct 16-2021

2. OUTLINE
2
❑Introduction
❑Shoring Process
❑Effective Beam Flange Width
❑Shear Transfer
❑Strength Of Steel Anchors
❑Partially Composite Beams
❑Moment Capacity Of Composite Sections
❑Deflection
❑Design Of Composite Sections

3. ❖What is a composite section !
1. INTRODUCTION
•Acompositestructureismadeupofmaterialswithdifferent
strengthactingtogether.
•Ifaconcreteslabissupportedbysteelbeams&Ifthereisno
provisionforsheartransferbetweentheslabandthebeam
→ Non-composite section
•Whennobondexistsbetweenboth,theloadcarriedbytheslabis
smallandmaybeneglected.
3

4. ❖Advantages of composite construction
•Thefloorservesasalargecoverplatefortheupperflangeofthesteel
beam→increasingthebeam’sstrength.
•Longerspansforsamesections.
•Compositesectionshavegreaterstiffnessthannon-compositesections.
•Thesesectionshavesmallerdeflections.
•Abilityofcompositestructuretotakeoverloadisdecidedlygreaterthanfor
non-compositestructure.
•Increasingtheload-carryingcapacityofanexistingfloorsystemcanbe
handledbyweldingcoverplatesontothebottomflangesofthebeam.
•Possibilityofhavingsmalleroverallfloordepths–thisisimportantfortall
buildings
4
1. INTRODUCTION

5. ❖Some types of composite constructions
5
A. Composite building floors:
i. Floors encasedin concrete: very rare due to expense.
ii.Non-encasedwithshearconnectors:mostlyusednowadays.
iii.Formedsteeldeck:usedforalmostallcompositebuildingfloors
1. INTRODUCTION

6. 6
1. INTRODUCTION
❖Composite vs non composite beam !
•For non composite beam:
Slipbetween two materials occursdue
to horizontal shear
•For composite beam:
No slip between 2 materials because
the shear studs resists the horizontal
shear

7. 7
❖Elastic stresses in composite Beams !
1. INTRODUCTION
•Availablestrengthofcompositebeamsisusuallybasedonconditionsat
failure.
•Insomecasestheavailablestrengthisbasedonlimitstateatfirstyield.
•Flexuralandshearingstressesinbeamsofhomogenousmaterialscanbe
computedfromtheformulas:
•Butacompositesectionisnothomogeneous,sotheseformulasarenot
valid.
•Tobeabletousethem,anartificeknownastransformedsectionis
employedtoconverttheconcreteintoamountofsteelthathasthesame
effectastheconcrete.
•Thisprocedurerequiresthestraininthefictitioussteeltobesameasthose
inconcreteitreplaces.
•Ec= modulus of elasticity of concrete
•n= Es/Ec= modular ratio

8. 8
❖Elastic stresses in composite Beams !
1. INTRODUCTION
•“nin2”ofconcretearerequiredtoresistthesameforce
as“1in2”ofsteel.
•Todeterminethisareaofsteelthatwillresistthesame
forceastheconcrete,dividetheconcreteareabyn,
replaceAcbyAc/n,theresultisthetransformedarea.
•IntheDeterminationoftheeffectiveflangewidth“b”,
firstweshouldtransformtheconcreteareaAc,the
mostconvenientwaytodothisistodividethewidth
“be”bynandleavethethicknessunchanged.
•Tocomputestressesinthehomogenoussteelsection,
wecalculatetheneutralaxisofthisshapeandcompute
thenthecorrespondingmomentofinertia.
•M = applied bending moment
•Itr= moment of inertia about neutral axis
•Yt= distance from the neutral axis to the top of steel
•yb= distance from the neutral axis to the bottom of steel
•Ybar= distance from neutral axis to the top of concrete
•The bending stresses at the top of steel:
•The bending stresses at the bottom of steel:
•The stress in the concrete :

9. 9
❖Flexural strength !
1. INTRODUCTION
•Inmostcasesthenominalflexuralstrengthwillbereachedwhenthe
entiresteelsectionyieldsandtheconcretecrushesincompression
(plasticstressdistribution).
•Forshapeswithcompactwebsthatis
ThenominalstrengthMnisobtainedfromtheplasticstressdistribution
•Forshapeswiththatis
Theelasticstressdistributioncorrespondingtofirstyieldofthesteel
•ForLRFD.Φb=0,9&ForASDΩ=1,67
•Whenacompositebeamhasreachedtheplasticlimitstate,thestresses
willbedistributedinoneofthethreewaysshowntotheright.

10. 10
2. SHORING PROCESS
Case 1
no shoring is used
steel beams must support all the loads as well
as their own weights.
Case 2
shoring is used
shoring supports the weight of wet concreteand
other construction loads
•Beamsmustbedesignedwithenough
strengthandstiffnesstosupportwet
concreteandconstructionloads.
•Mostspecificationssaythatafterthe
concretehasgained75%ofits28-day
strength→thesectionhasbecome
composite
•Shoringdoesnotsupporttheweightofthe
steelbeams.
•Whenshoringisremoved(after75%)→weight
oftheslabistransferredtothecomposite
sectionandnotjusttothesteelbeams.
•willbepossibletouselighterandthuscheaper
steelbeams.

11. •Camberisacurvaturebuiltintoamemberorstructureso
thatwhenitisloaded,itdeflectstoadesiredshape.
•Camberisusuallydesignedtocompensatefordeflections
causedbypre-compositedeadloads.
•Camberingcanbedesignedtocompensateforeither:
i.Certainpercentageofdeadloaddeflection.
ii.Fulldeadloaddeflection.
iii.Fulldeadloaddeflectionaswellasa%ofliveloaddeflection.
•Deflectionsofun-shoredfloorsduetothewetconcrete
sometimescanbequitelarge.→usecambering.
11
2. SHORING PROCESS
❖Whatiscamberingofbeams!

12. Case 1
Beams are closely spaced
Case 2
Large spacing between beams
bending stresses in the slab will be fairly uniformly
distributed across the compression zone
bending stresses will vary quite a bit nonlinearly
across the flange.
•Thefurtheraparticularpartoftheslaborflangeisawayfromthesteel
beam→thesmallerwillbeitsbendingstress.
•Specificationsattempttohandlethisproblembyreplacingtheactual
slabwithanarroweroreffectiveslabthathasaconstantstress.
•Thisequivalentslabisconsideredtosupportthesametotal
compressionasissupportedbytheactualslab.
•Theportionoftheslaborflangethatcanbeconsideredtoparticipatein
thecompositebeamactioniscontrolledbythespecifications. 12
3. EFFECTIVE FLANGE WIDTH

13. 1.AISC specifications I3.1a
The effective width of the concrete slab on each side of the beam center
line shall not exceed the least of the values to follow.
•The distance from the beam center line to the edge of the slab.
•1/8ofthespanofthebeammeasuredC-Cofsupportsforbothsimpleandcontinuousspans.
•1/2ofthedistancefromthebeamcenterlinetothecenterlineoftheadjacentbeam(b/2).
❖Determination of effective flange width
13
3. EFFECTIVE FLANGE WIDTH
2.AASHTO
TheMaximumtotalflangewidthcouldbedistinguishedasfollows:
•Maynotexceed:(1/4ofthebeamspan,12xtheleastthicknessoftheslab,orthedistanceC-Cofthebeams).
•Iftheslabexistsonlyononesideofthebeam,henceItseffectivewidthmaynotexceed1/12ofthebeamspan,6x
theslabthickness,or1/2ofthedistancefromthecenterlineofthebeamtothecenterlineoftheadjacentbeam.
•Theportionoftheslaborflangethatcanbeconsideredtoparticipateinthe
compositebeamactionisknownaseffectiveflangewidth

14. ❖How is the longitudinal shear transferred?
Case 1
Beams are encased
Case 2
Beams are not encased
Itcanbetransferredbetweenthe
twobybondandshear(and
possiblysometypeofshear
reinforcing),ifneeded.
Mechanicalconnectorstransfer
theloads.
14
4. SHEAR TRANSFER
Case 3
Case of Bridges
steel anchors are designed to
resist all of the shear between
bridge slabs and beams

15. ❖Types of steel Anchors
•Varioustypesofsteelanchorshavebeentried,including
spiralbars,channels,zees,angles,andstuds.
•Economicconsiderationshaveusuallyledtotheuseofround
studsweldedtothetopflangesofthebeams.
•Thesestudsareavailableindiametersfrom½to1inandin
lengthsfrom2to8in,butAISCspecifications(I8.2)statesthat
theirlengthmaynotbelessthan4studdiameters.
•Thisspecificationalsopermitstheuseofhot-rolledsteel
channels,butnotspiralconnectors.
15
4. SHEAR TRANSFER

16. •Shopinstallationinitiallyismoreeconomical
•Anchorsmayeasilybedamagedduringtransportationandsettingofthebeam.
•Anchorsserveasahindrancetotheworkerswalkingalongthetop
flangesduringtheearlyphasesofconstruction.
16
4. SHEAR TRANSFER
❖Shopvsfieldinstallationofsteelanchors
•Iftheplasticneutralaxis(PNA)fallsintheslab
→maximumhorizontalshear(orhorizontalforceontheplanebetween
concreteandsteel)issaidtobeAsFy
•IfthePNAisinthesteelsection→maximumhorizontalshear
isconsideredtobeequalto0,85f’cAc.
❖Maximumhorizontalshear

17. AISC(I3.2d)statesthat:
Forcompositeaction,totalhorizontalshearbetweenthepointsofmaximum
negativemomentandzeromomentistobetakenastheleastofthefollowing,
whereƩQnisthetotalnominalshearstrengthofthesteelanchors:
•Forconcretecrushing:??????′=0.85??????′??????c
•Fortensileyieldingofthesteelsection:??????′=??????????????????�
Forhybridbeams:yieldforcemustbecalculatedseparatelyforeachofthe
componentsofcrosssection.
•Forstrengthofsteelanchors:??????′=Ʃ??????n
17
4. SHEAR TRANSFER
❖Shear to be taken by the anchors

18. Manual calculation:
•Nominal shear strength in kips of one stud steel anchors embedded in
a solid concrete slab is to be determined by this eq.
Normal shear strength:
•Fu : specified minimum tensile strength of the steel stud in ksi(MPa).
•Ec: modulus of elasticity of concrete in ksi(MPa).
•w: unit weight of concrete in lb/ft3.
•Asa: cross-sectional area of the anchors in (in2).
•f ’c : specified compressive stress of concrete in ksi.
•Rg: coefficient to account for group effect.
•Rp: position effect factor for shear studs.
18
5. STRENGTH OF STEEL ANCHORS
❖Steel headed stud anchors ! According to AISC specification I8.2a

19. Tabular Values
Values of Qnare listed in Table 3-21 in AISC manual.
Thesevaluesaregivenfordifferentstuddiameters,
for3and4ksinormalandlightweightconcrete
weighing110lb/ft3,andforcompositesectionswith
orwithoutsteeldecking.
19
❖Steel headed stud anchors !
5. STRENGTH OF STEEL ANCHORS

20. ❖Whatispartiallycompositesection!
20
6. PARTIALLY COMPOSITE BEAMS
•Thepartiallycompositesection,isonethatdoesnothavea
sufficientnumberofanchorstodevelopthefullflexuralstrength
ofthecompositebeamandtocompletelypreventslipbetween
theconcreteandsteel.
•forallpartialcompositebeams,thePNAislocatedwithinthe
steelmember.Sincethereisnotenoughshearstudstotransfer
thetotalcompressiveforceintotheslab,theremustbesome
steelincompressionandthereforemakingthePNAwithinthe
steel.
•Wheneverafullycompositebeamhasexcesscapacity,thedesign
canbefine-tunedbyeliminatingsomeofthestuds,thereby
creatingapartiallycompositebeam

21. 8.MOMENT CAPACITY OF COMPOSITE SECTIONS
•Theplasticneutralaxismayfallintheslaborintheflange
ofthesteelsectionorinitsweb.
•h:thedistancebetweenthewebtoesofthefillet:h=d-2k
•tw:webthickness.
•Fyf:yieldstressofthebeamflange.
•E:modulusofelasticityofsteel=29000ksi(200GPa).
21
❖The nominal flexural strength of a composite beam !
•Thepositivenominalflexuralstrength,Mnofa
compositesectionistobedetermined,assuminga
plasticstress(Mn=Mp)distributionif:

22. ❖Neutral axis in concrete slab
•Ifaisequaltoorlessthantheslabthickness→PNAwillfallintheslab
•TheconcreteslabcompressionstressesvarysomewhatfromthePNAouttothetopoftheslab.
•Forconvenienceincalculations,theyareassumedtobeuniform,withavalueof0,85f’coveran
areaofdepthaandwidthbe(effectiveflangewidth).
•Thevalueofacanbedeterminedfromthe
followingexpression,wherethetotaltensioninthe
steelsectionissetequaltothetotalcompressionin
theslab:
T = C →
22
8.MOMENT CAPACITY OF COMPOSITE SECTIONS
plastic moment capacity

23. •Ifaiscalculatedandisgreaterthantheslabthicknesst
→PNAwillfalldowninthesteelsection.
•Ifthishappens→itwillbenecessarytofindoutwhether
PNAisintheflangeorbelowtheflange.
•Suppose,weassumethatit’satthebaseoftheflange.
•WecancalculatethetotalcompressiveforceCabovethe
PNA:
•Totaltensileforcecanbecalculatedasfollows:
Af: area of the flange → ????????????= �??????.???????????? 23
8.MOMENT CAPACITY OF COMPOSITE SECTIONS
❖Neutral axis in top flange of steel beam

24. ❖Neutral axis in top flange of steel beam
•IfC>T→PNAwillbeintheflange.
•IfC<T→PNAisbelowtheflange.
•AssumingthatwefindthePNAisintheflange,wecandetermineitslocation,letting??????bethe
distancetothePNAmeasuredfromthetopofthetopflange,byequatingCandT
•Ycanbecalculatedasfollows:
24
8.MOMENT CAPACITY OF COMPOSITE SECTIONS
•Thenthenominalorplasticmomentcapacityofthesection:

25. •Ifwefindthataislargerthantheslabthickness,andifwethenassume
thatthePNAislocatedatthebottomofthesteelflangeandwecalculate
CandTandfindTislargerthanC→PNAwillfallintheweb.
25
8.MOMENT CAPACITY OF COMPOSITE SECTIONS
❖Neutral axis in web of steel section
•Thenthenominalorplasticmomentcapacityofthesection:
•Ycanbecalculatedasfollows:

26. ➢For common cases of simple-span beams and I-shaped
members and channels, the maximum vertical deflection Δ:
❖Deflection !
26
•M=maximumserviceloadmoment,kip-ft
•L=spanlength,ft
•Ix=momentofinertia,in4
•C1=loadingconstantwhichincludesthe
numericalconstantsappropriateforthe
givenloadingpattern,E(29000ksi)
9.DEFLECTIONS
Case1:Unshoredcompositeconstruction:
•Finaldeflectionswillequaltheinitialdeflectionscausedbywet
concretecalculatedwithmomentsofinertiaofthesteel
beams,plusthedeflectionsduetotheloadsappliedafter
concretehardens,calculatedwithmomentsofinertiaofthe
compositesections.
Case2:Shoredcompositeconstruction:
•Alldeflectionswillbecalculatedwithmomentsofinertiaof
thecompositesection.

27. 27
•WhenWsectionisinsufficienttosupporttheloadsanticipatedforcertainspan,
severalpossiblealternativesmaybetaken,Perhapsthemosteconomicalsolution:
1.theuseofoneofahigherstrengthsteelWsection.
•Ifthisisnotfeasible,wemaymakeuseofoneofthefollowing:
1.twoormoreregularWsectionsside-by-side(anexpensivesolution)
2.acover-platedbeam
3.abuilt-upgirder
4.asteeltruss.
10.DESIGN OF COMPOSITE SECTIONS
❖Cover plates Why!

28. 28
•An expression for the required area of one flange cover plate can be
developed as follows
•The total Z of the built-up section must at least equal the Z required.
•It will be furnished by the W shape and the cover plate as follows:
10.DESIGN OF COMPOSITE SECTIONS
❖Cover plates Area!

29. ❖Lower bound moment of inertia !
Manual
•Thelowerboundmomentofinertiaiscomputedasfollows:
29
10.DESIGN OF COMPOSITE SECTIONS
Tabular
•atableoflowerboundmomentofinertiavalues
ispresentedtotheright.

30. THANK YOU
30
THANK YOU
Hope you enjoyed my presentation !
Contactmeforanyhelp
[email protected]

31. ✓Structural steel design,5
th
edition, jack C.McCromac,StephanF. Csernak
✓American institute of steel construction, Steel construction manual, 14
th
edition
✓Chapter 9
❖References
31

32. 32
•Note,however,thesenumerousadvantagesforcompositebeamsisonlytruewhentheconcreteissubjectto
compressiveforces.Concreteisabrittlematerialwhosetensilestrengthisquitevariableandfractures(or
cracks)withlittleornowarning.Asaresult,concreteisassumedtohavenotensilestrengthandisignored
whenitisintension.
•Ontheotherhand,concreteisverygoodincompression.Thismeansthatcompositeactionisonlyofbenefit
inPOSITIVEmomentregionswhereconcreteisonthecompressionsideofthebeam.
•Innegativemomentregions,wheretheconcreteisonthetensionsideofbeam,theconcreteaddsnothing
tothestrengthorstiffnessofthesteelbeam.
•Sincecompositeactionisofmostbenefittosimplysupported,singlespanbeamswhereallthemomenton
thesectionispositive.
•Forcontinuousbeams,themaximummomentstendtobenegativeandlocatedoversupports.Beamssized
forthesenegativemomentswilltendtomorethanadequatetohandlethepositivemomentssocomposite
actionisnotrequired.
NOTES

33. 33
•Thecoverplatemustextend,ataminimum,overthe
distancewherethemomentdemandexceedsthe
momentcapacityprovidedbybasesectionwithoutthe
coverplates.
•Intheexampleshownthemomentcapacityofthebase
sectionissufficientneartheendsofthememberwhere
themomentislowbutneedstobeenhancedwhere
momentdemandexceedsthecapacityofthebase
section.Theintersectionofthemomentdemandand
momentcapacitycurvescangenerallybedetermine
mathematicallysinceitispossibletowriteequationsfor
bothcurves
NOTES

34. 34
•Bystatics,V'equalsC
cand/orT
s.Whentheplasticneutralaxisisinthesteelbeam,C
cisatits
maximumvalue(C
c=.85f'
cA
c)sinceA
cisatitsmaximumvalue.Whentheplasticneutralaxisis
intheslab,T
sisatitsmaximumvalue(T
s=A
gF
y)sincetheentiresectionisintension.Since
C
calwaysequalsT
swhentheplasticneutralaxisisintheslabandisatitsmaximumwhenthe
plasticneutralaxisislocatedinthebeam,themaximumvalueofV'willbethelesserofthe
maximumvaluesofC
corT
s.Thesmallervaluecontrols.
•Forasectiontobe"fullycomposite"theshearconnectorsmustprovidestrengththatequalsor
exceedsthemaximumV'resultingfromconcretecrushing(C
cmax)ortensileyielding(T
smax)as
discussedabove.Iftheshearstrengthprovidedbytheshearconnectors(V'=sumofthe
strengthoftheshearconnectorslocatedbetweenthelocationofmaximumandzeromoments)
islessthanwhatcanbedevelopedbyconcretecrushingortensileyieldingthenthesectionis
saidtobe"partiallycomposite"andit'sstrengthmustbedeterminedbythelimitimposedby
theshearconnectorstrength.
NOTES