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Development LengthDevelopment Length

CE A433 CE A433 –– RC DesignRC DesignT. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.

Revised Spring 2009Revised Spring 2009

Consider a bar embedded in a Consider a bar embedded in a mass of concretemass of concrete

P = τ*[Lb*π*db]

P = σ * [π*db2/4]

d

τ = P / [Lb*π*db] < τmax

P < τmax * [Lb*π*db]

σ = P/ [π*db2/4] < σmax

P < σmax * [π*db2/4]

To force the bar to be the weak link: τmax * [Lb*π*db] > σmax * [π*db2/4]

Lb > (σmax / τmax)* [db/4]

Lb

db

Development LengthDevelopment LengthLLdd = development length= development length

the shortest distance over which a bar can achieve it’s the shortest distance over which a bar can achieve it’s full capacityfull capacityThe length that it takes a bar to develop its full The 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

Steel Limit, Steel Limit, σσmaxmax

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

σσmaxmax = = + ffyy

Lb > (fy / τmax)* [db/4]

Lb > fy * db / (4*τmax)

Concrete Bond Limit, Concrete Bond Limit, ττmaxmax

There are lots of things that affect There are lots of things that affect ττmaxmaxThe strength of the concrete, f’The strength of the concrete, f’ccType 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 barThe surface condition of the rebarThe surface condition of the rebarThe concrete cover on the barThe concrete cover on the barThe proximity of other bars transferring stress to the The proximity of other bars transferring stress to the concreteconcreteThe presence of transverse steelThe presence of transverse steel

Concrete Strength, f’Concrete Strength, f’cc

Bond strength, Bond strength, ττmaxmax, tends to increase with , tends to increase with concrete strength.concrete strength.Experiments have shown this relationshipExperiments have shown this relationshipExperiments have shown this relationship Experiments have shown this relationship to be proportional to the square root of to be proportional to the square root of f’f’cc..

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Type of ConcreteType of Concrete

Light weight concrete tends to have less Light weight concrete tends to have less bond strength than does normal weight bond strength than does normal weight concrete.concrete.ACI 318ACI 318--08 introduces a lightweight 08 introduces a lightweight concrete reduction factor, concrete reduction factor, λλ, on , on sqrtsqrt((f’f’cc) in ) in some equations.some equations.

See ACI 318See ACI 318--08, 8.6.1 for details08, 8.6.1 for details

Amount of Concrete Below BarsAmount of Concrete Below Bars

The code refers to “top The code refers to “top bars” as being any bar bars” as being any bar which has 12 inches or which has 12 inches or more of fresh concrete more of fresh concrete b l th b h thb l th b h thbelow the bar when the below the bar when the member is poured.member is poured.If concrete > 12” then If concrete > 12” then consolidation settlement consolidation settlement results in lower bond results in lower bond strength on the bottom side strength on the bottom side of the barof the barSee ACI 318See ACI 318--08, 12.2.4(a)08, 12.2.4(a)

Surface Condition of RebarSurface Condition of RebarAll rebar must meet ASTM requirements All rebar must meet ASTM requirements for deformations that increase pullout for deformations that increase pullout strength.strength.Bars are often surface coated is inhibit Bars are often surface coated is inhibit corrosion.corrosion.

Epoxy Coating Epoxy Coating The major concern!The major concern!GalvanizingGalvanizing

Epoxy coating significantly reduces bond Epoxy coating significantly reduces bond strengthstrengthSee ACI 318See ACI 318--08, 12.2.4(b)08, 12.2.4(b)

Proximity to Surface or Other BarsProximity to Surface or Other BarsThe size of the concrete “cylinder” tributary to The size of the concrete “cylinder” tributary to each bar is used to account for proximity of each bar is used to account for proximity of surfaces or other bars.surfaces or other bars. 2D 3D

Presence of Transverse SteelPresence of Transverse SteelThe bond transfer tends to cause a splitting planeThe bond transfer tends to cause a splitting planeTransverse steel will increase the strength of the Transverse steel will increase the strength of the splitting plane.splitting plane.See text for other possible splitting locationsSee text for other possible splitting locations

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

f ⎟⎟⎞

⎜⎜⎛

)71min(3 ψψψb

b

trb

set

c

yd d

dKcf

fL

⎟⎟⎟⎟

⎠⎜⎜⎜⎜

⎝⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ +′=

5.2,min

)7.1,min(403 ψψψ

λ

snAK tr

tr40

=

3

The ModifiersThe Modifiers

ψψtt, Modifier for reinforcement location, Modifier for reinforcement location1.3 for top bars, 1.0 for other bars1.3 for top bars, 1.0 for other bars

ψψ modifier for epoxy coated barsmodifier for epoxy coated barsψψee, modifier for epoxy coated bars, modifier for epoxy coated bars1.5 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 reinforcing1.0 for non1.0 for non--epoxy coated reinforcingepoxy coated reinforcing

The product, The product, ψψttψψee, need not exceed 1.7, need not exceed 1.7

More Modifiers…More Modifiers…

ψψss, Modifier for bar size, Modifier for bar size0.8 for #6 and smaller0.8 for #6 and smaller1.0 for #7 and larger1.0 for #7 and larger1.0 for #7 and larger1.0 for #7 and larger

λλ, Modifier for lightweight concrete, Modifier for lightweight concreteACI 318ACI 318--08, 8.6.108, 8.6.1λ λ = 1.0 for normal weight concrete= 1.0 for normal weight concreteλλ as low as 0.75 for the lightest weight as low as 0.75 for the lightest weight concreteconcrete

The Transverse Reinforcement The 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 which all transverse reinforcement which is within the spacing, s, and which is within the spacing, s, and which crosses the potential plane of crosses the potential plane of splitting through thesplitting through the sn

AK trtr

40=

splitting through the splitting through the reinforcement being developed.reinforcement being developed.s = maximum Cs = maximum C--C spacing of C spacing of transverse reinforcement within transverse reinforcement within the development lengththe development lengthn = number of longitudinal bars n = number of longitudinal bars being developed along the plane being developed along the plane of splitting.of splitting.

sn

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

Other Development LengthsOther Development Lengths

Development in Compression: ACI 318Development in Compression: ACI 318--08 08 12.312.3Development of standard hooks in Development of standard hooks in pptension: ACI 318tension: ACI 318--08 12.508 12.5

There are some very specific cover and/or There are some very specific cover and/or confinement requirementsconfinement requirements

Mechanical connectors (such as bearing Mechanical connectors (such as bearing plates at the beam ends) may also be plates at the beam ends) may also be used.used.

Effect on Moment CapacityEffect on Moment Capacity

Moment Capacity, Moment Capacity, φφMMnn, is a function of “x”, is a function of “x”If different bars develop differently then If different bars develop differently then you need to look at the “contribution” thatyou need to look at the “contribution” thatyou need to look at the contribution that you need to look at the contribution that each bar makes to the moment capacityeach bar makes to the moment capacity

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Moment Capacity DiagramMoment Capacity Diagram

Moment Capacity

500

600

0

100

200

300

400

0 50 100 150 200 250 300 350 400

X (in)

phiP

m (f

t-k)

Cutting BarsCutting BarsThe The φφMMnn diagram can be made to more closely diagram can be made to more closely fit the Mfit the Muu diagram by terminating or cutting bars diagram by terminating or cutting bars when they are no longer needed. (ACI 318when they are no longer needed. (ACI 318--08 08 12.10.3)12.10.3)

Moment Capacity

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X (in)

phiP

m (f

t-k) End of #6 bar

End of #8 bars

End of #10 bars

> max(d, 12db)

> max(d, 12db)

Beam Profile Showing Bar Cutoff Beam Profile Showing Bar Cutoff LocationsLocations