Development LengthCE A433 RC DesignT. Bart Quimby, P.E., Ph.D.Spring 2007

Consider a bar embedded in a mass of concreteP = t*[Lb*p*db]P = s * [p*db2/4]t = P / [Lb*p*db] < tmaxP < tmax * [Lb*p*db]s = P/ [p*db2/4] < smaxP < smax * [p*db2/4]To force the bar to be the weak link: tmax * [Lb*p*db] > smax * [p*db2/4] Lb > (smax / tmax)* [db/4]Lbdb

Development LengthLd = development lengththe shortest distance over which a bar can achieve its full capacityThe length that it takes a bar to develop its full contribution to the moment capacity, MnCcTsMn = (C or T)*(dist)Mn0Ld

Steel Limit, smaxUsing the bilinear assumption of ACI 318:smax = + fy

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

Concrete Bond Limit, tmaxThere are lots of things that affect tmaxThe strength of the concrete, fcType of concrete (normal weight or light weight)The amount of concrete below the barThe surface condition of the rebarThe concrete cover on the barThe proximity of other bars transferring stress to the concreteThe presence of transverse steel

Concrete Strength, fcBond strength, tmax, tends to increase with concrete strength.Experiments have shown this relationship to be proportional to the square root of fc.

Type of ConcreteLight weight concrete tends to have less bond strength than does normal weight concrete.

Amount of Concrete Below BarsThe code refers to top bars as being any bar which has 12 inches or more of fresh concrete below the bar when the member is poured.If concrete > 12 then consolidation settlement results in lower bond strength on the bottom side of the bar

Surface Condition of RebarAll rebar must meet ASTM requirements for deformations that increase pullout strength.Bars are often surface coated is inhibit corrosion.Epoxy Coating The major concern!GalvanizingEpoxy coating significantly reduces bond strength

Proximity to Surface or Other BarsThe size of the concrete cylinder tributary to each bar is used to account for proximity of surfaces or other bars.

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

The ACI 318-05 Development Length Equation (ACI 318-05 12.2)

The Modifiersyt, Modifier for reinforcement location1.3 for top bars, 1.0 for other barsye, modifier for epoxy coated bars1.5 when cover < 3db or clear spacing < 6db1.2 for other epoxy coated reinforcing1.0 for non-epoxy coated reinforcingThe product, ytye, need not exceed 1.7

More Modifiersys, Modifier for bar size0.8 for #6 and smaller1.0 for #7 and largerl, Modifier for lightweight concrete1.3 for lightweight concrete1.0 for other concrete

The Transverse Reinforcement Index, Ktr (ACI 318-05 Eq. 12-2)Atr = total cross sectional area of all transverse reinforcement which is within the spacing, s, and which crosses the potential plane of splitting through the reinforcement being developed.fyt = the yield strength of the transverse reinforcings = maximum C-C spacing of transverse reinforcement within the development lengthn = number of longitudinal bars being developed along the plane of splitting.

Other Development LengthsDevelopment in Compression: ACI 318-05 12.3Development of standard hooks in tension: ACI 318-05 12.5There are some very specific cover and/or confinement requirementsMechanical connectors (such as bearing plates at the beam ends) may also be use.

Effect on Moment CapacityMoment Capacity, fMn, is a function of xIf different bars develop differently then you need to look at the contribution that each bar makes to the moment capacity

Moment Capacity Diagram

Chart1

0

303.6513970588

303.6513970588

303.6513970588

481.7673529412

481.7673529412

481.7673529412

512.7555247149

512.7555247149

X (in)

phiPm (ft-k)

Moment Capacity

Sheet1

Determine Development Lengths

f'c3000psialpha1.3

fy60000psiBeta1

lamda1

#3 Stirrups at 10" O.C. over the development length

BarsdbGammasncAtrKtrldld

(in)(in)(in)(in^2)(in)(in)(ft)

#10 bars:1.25011051.380.2200.176107.608.97

#8 bars:1.00011051.380.2200.17668.865.74

#6 bar:0.7500.81051.380.2200.17630.992.58

Determine contribution of bars to the moment capacity

b16in

d30in

ConditionIIIIII

#10 bars222

#8 bars022

#6 bars001Span30ft

As2.544.124.56in^2

d27.5027.5027.50inXMn

a1.873.033.35in00

phi*Mn303.65481.77529.90ft-k107.60303.65

Contribution to pMn303.65178.1248.13ft-k360303.65

Cutoff Location, x000in0303.65

Ld107.6068.8630.99in68.86481.77

360481.77

0481.77

30.99512.76

360512.76

Sheet1

X (in)

phiPm (ft-k)

Moment Capacity

Sheet2

Sheet3

MBD00260F92.unknown

MBD0025C07E.unknown

Cutting BarsThe fMn diagram can be made to more closely fit the Mu diagram by terminating or cutting bars when they are no longer needed. (ACI 318-05 12.10.3)End of #6 barEnd of #8 barsEnd of #10 bars> max(d, 12db)> max(d, 12db)

Chart2

0

303.6513970588

303.6513970588

303.6513970588

481.7673529412

481.7673529412

481.7673529412

512.7555247149

512.7555247149

X (in)

phiPm (ft-k)

Moment Capacity

Sheet1

Determine Development Lengths

f'c3000psialpha1.3

fy60000psiBeta1

lamda1

#3 Stirrups at 10" O.C. over the development length

BarsdbGammasncAtrKtrldld

(in)(in)(in)(in^2)(in)(in)(ft)

#10 bars:1.25011051.380.2200.176107.608.97

#8 bars:1.00011051.380.2200.17668.865.74

#6 bar:0.7500.81051.380.2200.17630.992.58

Determine contribution of bars to the moment capacity

b16in

d30in

ConditionIIIIII

#10 bars222

#8 bars022

#6 bars001Span30ft

As2.544.124.56in^2

d27.5027.5027.50inXMn

a1.873.033.35in00

phi*Mn303.65481.77529.90ft-k107.60303.65

Contribution to pMn303.65178.1248.13ft-k360303.65

Cutoff Location, x0120200in120303.65

Ld107.6068.8630.99in188.86481.77

360481.77

200481.77

230.99512.76

360512.76

Sheet1

X (in)

phiPm (ft-k)

Moment Capacity

Sheet2

Sheet3

MBD00260F92.unknown

MBD0025C07E.unknown

Beam Profile Showing Bar Cutoff Locations