2.1 doubly reinforcement beams (week 2)

8/11/2019 2.1 Doubly Reinforcement Beams (Week 2)

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DOUBLYREINFORCEDBEAMS

Lecture2

DrEeLoonTan

Lectureoutline

1. Learningoutcomes

2. Doublyreinforcedbeams

3. Tbeams

4. Examples


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Learningoutcomes

Bytheendofthislectureyouwillbeableto:

Analysisdoublyreinforcedconcreteforconcrete

beamsinflexureaccordingtoAustralianStandard

AS3600and

AnalysisT beamsinflexureaccordingto

AustralianStandardAS3600

Increasingthecapacityof

reinforcedconcretebeams

Increasetheleverarmbyincreasingthedepthofthebeam

Increasethecompression(C)andtensionforces(T)throughadditionalreinforcingbarsorincreasingtheconcretecompressionstrength(fc)

C

T

z


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Usingdoublyreinforced

beams

DoublyreinforcedbeamsareusedwhenthereisarestrictioninthedepthofbeamsDepthrestrictionsmaybeasaresultofmechanical

installationssuchasductingorpiping

Alimiteddepthofbeammeansthattheconcreteincompressionbecomesrelativelysmalltobalancethetensionforceinsteel

ReinforcingbarsincompressionareusedtoassisttheconcreteincompressiontobalancethetensionforceinsteelAresultantincreaseinmomentcapacityoccurs

Otheradvantagesofusing

compressionsteel

Compressionreinforcementhastheadvantagethatitreduceslongtermdeflectionofbeams

Compressionsteelisalsousefulinitssupportofshearreinforcement(stirrups)

stirrups


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Stressstraindistribution

forreinforcingsteelbars

Assumption

Case1:Assumingthatcompressive

reinforcementyields:

Case2:Assumingthatcompressive

reinforcementdidnotyield:

D

Ast

b

dscdn=kud

st

u=0.003

fsy

dkud/2

T=Ast

fsy

Cc

d

dkud

dst

kud

Cs=Ascsc

Asc

sc


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Case1(sc=fsy)

Forequilibrium:

Assumingthatcompressivereinforcement

yields:

systscscuc

sc

fAAbdkf

TCC

'

2

bdf

fAAk

f

c

syscst

u

sysc

'

2

Case1(sc=fsy)

Fromthestraindiagram,checkifyielding

occursforcompressionsteel:

Fromthestraindiagram,checkifyielding

occursfortensilesteel:

u

u

st

u

u

u

st

k

dkdkd

11

u

u

scsc

u

u

scu

sc

dkd

dkddk

1


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Case1(sc=fsy)

Case1:Ifsc>sy,thenassumptioniscorrect

sc=fsy

Momentcapacity:

scsyscu

ucu ddfAdk

dbdkfM

2

'

2

Case2(sc


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Case2(sc


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Example

IntroductiontoTbeams

Inbuildingconstruction,concreteslabsare

builtmonolithicallywithsupportingbeams

Theslabactsintegrallywiththebeamsectionto

resistbending


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Effectivewidthofflange

(bef)Cl.8.8

Theeffectivewidthdependsonthestressesalreadyinthefloorslabduetoitsbending

Italsodependsontheproximityoftheportiontothebeaminquestion

AccordingtoAS3600Cl.8.8

Tbeams:bef=bw+0.2a

Lbeams:bef=bw+0.1a

Whereaisthedistancebetweenpointsofzeromoment

Effectivewidthofflange

(bef)Cl.8.8

ef

w 0.1a0.1a b

bef

w0.1a

ef

0.1abw

b b

b 0.1a

L

a = 0.7L


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AnalysisofTbeams

TheanalysisofTbeamsissimilartothatof

rectangularsections

Withtheexceptionthattheflangemustbe

accountedforintheequilibriumequations

Assumption

Therearetwocasestoconsider:

Case1:Depthofcompressionblockwithinthe

flange

Case2:Depthofcompressionblockbelowthe

flange


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Case1(Withintheflange)

Thissectioncanbetreatedasasingly

reinforcedsectionwith:

Effectivedepth,dand

Widthequaltotheflangewidth,b=bf

Ast

bf

dn=kud

st

u=0.003

fsy

dkud/2

T=Astfsy

C

dkud

kud

2fc

d

Case2(Belowtheflange)

Ast

bf

dn=kud

st

u=0.003

fsy

dkud/2

T=Astfsy

Cf

dkud

kud

2fc

d

flange flangeweb

Cw

bw

tf dtf/2


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Case2(Belowtheflange)

Compressionforceintheflange:

Compressionforceintheweb:

Forequilibrium:

fwfcf tbbfC '

2

dkbfC uwcw '

2

dbf

tbbffAk

fAdkbftbbf

fACC

wc

fwfcsyst

u

systuwcfwfc

systwf

'

2

'

2

'

2

'

2

Example

2.1 doubly reinforcement beams (week 2)

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