developmentlength.08 (1)

8/7/2019 DevelopmentLength.08 (1)

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Development LengthDevelopment Length

CE A433CE A433 RC DesignRC Design

T. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.Revised Spring 2009Revised Spring 2009


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Consider a bar embedded in aConsider a bar embedded in a

mass of concretemass of concrete

P = X*[Lb*T*db]

P = W * [T*db2/4]

X = P / [Lb*T*db] < Xmax

P < Xmax * [Lb*T*db]

W = P/ [T*db2/4] < Wmax

P < Wmax * [T*db2/4]

To force the bar to be the weak link: Xmax * [Lb*T*db] > Wmax * [T*db2/4]

Lb > (Wmax / Xmax)* [db/4]

Lb

db


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Development LengthDevelopment Length LLdd = development length= development length

the shortest distance over which a bar can achieve itsthe shortest distance over which a bar can achieve itsfull capacityfull capacity

The length that it takes a bar to develop its fullThe length that it takes a bar to develop its full

contribution to the moment capacity, Mcontribution to the moment capacity, Mnn

Cc

Ts

Mn = (C or T)*(dist)

Mn

0

Ld


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Steel Limit,Steel Limit, WWmaxmax

Using the bilinear assumption of ACI 318:Using the bilinear assumption of ACI 318:

WWmaxmax == + ffyy

Lb > (fy / Xmax)* [db/4]

Lb > fy * db / (4*Xmax)


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Concrete Bond Limit,Concrete Bond Limit, XXmaxmax

There are lots of things that affectThere are lots of things that affectXXmaxmax The strength of the concrete, fThe strength of the concrete, fcc Type of concrete (normal weight or light weight)Type of concrete (normal weight or light weight)

The amount of concrete below the barThe amount of concrete below the bar

The surface condition of the rebarThe surface condition of the rebar

The concrete cover on the barThe concrete cover on the bar

The proximity of other bars transferring stress to theThe proximity of other bars transferring stress to theconcreteconcrete

The presence of transverse steelThe presence of transverse steel


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Concrete Strength, fConcrete Strength, fcc

Bond strength,Bond strength, XXmaxmax, tends to increase with, tends to increase withconcrete strength.concrete strength.

Experiments have shown this relationshipExperiments have shown this relationshipto be proportional to the square root ofto be proportional to the square root of ffcc..


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Type of ConcreteType of Concrete

Light weight concrete tends to have lessLight weight concrete tends to have lessbond strength than does normal weightbond strength than does normal weightconcrete.concrete.

ACI 318ACI 318--08 introduces a lightweight08 introduces a lightweightconcrete reduction factor,concrete reduction factor, PP, on, on sqrtsqrt((ffcc) in) in

some equations.some equations. See ACI 318See ACI 318--08, 8.6.1 for details08, 8.6.1 for details


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Amount of Concrete Below BarsAmount of Concrete Below Bars

The code refers to topThe code refers to topbars as being any barbars as being any barwhich has 12 inches orwhich has 12 inches ormore of fresh concretemore of fresh concretebelow the bar when thebelow the bar when themember is poured.member is poured.

If concrete > 12 thenIf concrete > 12 then

consolidation settlementconsolidation settlementresults in lower bondresults in lower bondstrength on the bottom sidestrength on the bottom sideof the barof the bar

See ACI 318See ACI 318--08, 12.2.4(a)08, 12.2.4(a)


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Surface Condition of RebarSurface Condition of Rebar

All rebar must meet ASTM requirementsAll rebar must meet ASTM requirementsfor deformations that increase pulloutfor deformations that increase pulloutstrength.strength.

Bars are often surface coated is inhibitBars are often surface coated is inhibitcorrosion.corrosion. Epoxy CoatingEpoxy Coating The major concern!The major concern!

GalvanizingGalvanizing Epoxy coating significantly reduces bondEpoxy coating significantly reduces bond

strengthstrength

See ACI 318See ACI 318--08, 12.2.4(b)08, 12.2.4(b)


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Proximity to Surface or Other BarsProximity to Surface or Other Bars

The size of the concrete cylinder tributary toThe size of the concrete cylinder tributary toeach bar is used to account for proximity ofeach bar is used to account for proximity ofsurfaces or other bars.surfaces or other bars.

2D 3D


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Presence of Transverse SteelPresence of Transverse Steel

The bond transfer tends to cause a splitting planeThe bond transfer tends to cause a splitting plane

Transverse steel will increase the strength of theTransverse steel will increase the strength of thesplitting plane.splitting plane.

See text for other possible splitting locationsSee text for other possible splitting locations


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The ACI 318The ACI 318--08 Development08 Development

Length Equation (ACI 318Length Equation (ACI 318--08 12.2)08 12.2)

b

b

trb

set

c

y

d d

d

Kcf

fL

d!

5.2,min

)7.1,min(

40

3 ]]]

P

sn

AK trtr

40!


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The ModifiersThe Modifiers

]]tt, Modifier for reinforcement location, Modifier for reinforcement location

1.3 for top bars, 1.0 for other bars1.3 for top bars, 1.0 for other bars

]]ee, modifier for epoxy coated bars, modifier for epoxy coated bars

1.5 when cover < 3d1.5 when cover < 3dbb or clear spacing < 6dor clear spacing < 6dbb 1.2 for other epoxy coated reinforcing1.2 for other epoxy coated reinforcing

1.0 for non1.0 for non--epoxy coated reinforcingepoxy coated reinforcing

The product,The product, ]]tt]]

ee, need not exceed 1.7, need not exceed 1.7


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More ModifiersMore Modifiers

]]ss, Modifier for bar size, Modifier for bar size

0.8 for #6 and smaller0.8 for #6 and smaller

1.0 for #7 and larger1.0 for #7 and larger

PP, Modifier for lightweight concrete, Modifier for lightweight concrete ACI 318ACI 318--08, 8.6.108, 8.6.1

PP= 1.0 for normal weight concrete= 1.0 for normal weight concrete

PP as low as 0.75 for the lightest weightas low as 0.75 for the lightest weightconcreteconcrete


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The Transverse ReinforcementThe Transverse Reinforcement

Index,Index, KKtrtr (ACI 318(ACI 318--08 Eq. 1208 Eq. 12--2)2) AAtrtr = total cross sectional area of= total cross sectional area of

all transverse reinforcement whichall transverse reinforcement whichis within the spacing, s, and whichis within the spacing, s, and which

crosses the potential plane ofcrosses the potential plane ofsplitting through thesplitting through thereinforcement being developed.reinforcement being developed.

s = maximum Cs = maximum C--C spacing ofC spacing oftransverse reinforcement withintransverse reinforcement withinthe development lengththe development length

n = number of longitudinal barsn = number of longitudinal barsbeing developed along the planebeing developed along the planeof splitting.of splitting.

sn

tr

tr

40

!


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The outer bars are #10, the center one is #6, the others are #8


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Other Development LengthsOther Development Lengths

Development in Compression: ACI 318Development in Compression: ACI 318--080812.312.3

Development of standard hooks inDevelopment of standard hooks intension: ACI 318tension: ACI 318--08 12.508 12.5 There are some very specific cover and/orThere are some very specific cover and/or

confinement requirementsconfinement requirements

Mechanical connectors (such as bearingMechanical connectors (such as bearingplates at the beam ends) may also beplates at the beam ends) may also beused.used.


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Effect on Moment CapacityEffect on Moment Capacity

Moment Capacity,Moment Capacity, JJMMnn, is a function of x, is a function of x

If different bars develop differently thenIf different bars develop differently thenyou need to look at the contribution thatyou need to look at the contribution thateach bar makes to the moment capacityeach bar makes to the moment capacity


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Moment Capacity DiagramMoment Capacity Diagram

Moment Capacity

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X (in)

phiPm(ft-k)


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Cutting BarsCutting Bars TheThe JJMMnn diagram can be made to more closelydiagram can be made to more closely

fit the Mfit the Muu diagram by terminating or cutting barsdiagram by terminating or cutting barswhen they are no longer needed. (ACI 318when they are no longer needed. (ACI 318--080812.10.3)12.10.3)

Mom

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X

m

End of #6 bar

End of #8 bars

End of #10 bars

> max(d, 12db)

> max(d, 12db)


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Beam Profile Showing Bar CutoffBeam Profile Showing Bar Cutoff

LocationsLocations

developmentlength.08 (1)

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