Development LengthDevelopment Length

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

Spring 2007Spring 2007

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

P = *[Lb**db]

P = * [*db2/4]

= P / [Lb**db] < max

P < max * [Lb**db] = P/ [*db

2/4] < max

P < max * [*db2/4]

To force the bar to be the weak link: max * [Lb**db] > max * [*db

2/4] Lb > (max / max)* [db/4]

Lb

db

Development LengthDevelopment Length LLdd = development length = development length

the shortest distance over which a bar can the shortest distance over which a bar can achieve it’s full capacityachieve it’s full capacity

The 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, maxmax

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

maxmax = = + f fyy

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

Concrete Bond Limit, Concrete Bond Limit, maxmax

There are lots of things that affect There are lots of things that affect maxmax The strength of the concrete, f’The strength of the concrete, f’cc 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 The proximity of other bars transferring stress

to the concreteto the concrete The presence of transverse steelThe presence of transverse steel

Concrete Strength, f’Concrete Strength, f’cc

Bond strength, Bond strength, maxmax, tends to increase , tends to increase with concrete strength.with concrete strength.

Experiments have shown this Experiments have shown this relationship to be proportional to the relationship to be proportional to the square root of f’square root of f’cc..

Type of ConcreteType of Concrete Light weight concrete tends to have Light weight concrete tends to have

less bond strength than does normal less bond strength than does normal weight concrete.weight concrete.

Amount of Concrete Below Amount of Concrete Below BarsBars

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 below 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 strength on the bottom side of the barside of the bar

Surface Condition of RebarSurface Condition of Rebar All rebar must meet ASTM All rebar must meet ASTM

requirements for deformations that requirements for deformations that increase pullout strength.increase pullout strength.

Bars are often surface coated is Bars are often surface coated is inhibit corrosion.inhibit corrosion. Epoxy Coating Epoxy Coating The major concern! The major concern! GalvanizingGalvanizing

Epoxy coating significantly reduces Epoxy coating significantly reduces bond strengthbond strength

Proximity to Surface or Other Proximity to Surface or Other BarsBars

The size of the concrete “cylinder” The size of the concrete “cylinder” tributary to each bar is used to account tributary to each bar is used to account for proximity of surfaces or other bars.for proximity of surfaces or other bars.

Presence of Transverse Presence of Transverse SteelSteel

The bond transfer tends to cause a splitting planeThe bond transfer tends to cause a splitting plane Transverse 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 318-05 Development The ACI 318-05 Development Length Equation (ACI 318-05 Length Equation (ACI 318-05

12.2)12.2)

b

b

trb

set

c

yd d

dKcf

fL

5.2,min

)7.1,min(403

snfA

K yttrtr 1500

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 < 6d or clear spacing < 6dbb 1.2 for other epoxy coated reinforcing1.2 for other epoxy coated reinforcing 1.0 for non-epoxy coated reinforcing1.0 for non-epoxy coated reinforcing

The product, The product, ttee, need not exceed 1.7, need not exceed 1.7

More Modifiers…More 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

, Modifier for lightweight concrete, Modifier for lightweight concrete 1.3 for lightweight concrete1.3 for lightweight concrete 1.0 for other concrete1.0 for other concrete

The Transverse Reinforcement The Transverse Reinforcement Index, KIndex, Ktr tr (ACI 318-05 Eq. 12-2)(ACI 318-05 Eq. 12-2)

AAtrtr = total cross sectional area = total cross sectional area of all transverse reinforcement of all transverse reinforcement which is within the spacing, s, which is within the spacing, s, and which crosses the potential and which crosses the potential plane of splitting through the plane of splitting through the reinforcement being developed.reinforcement being developed.

ffytyt = the yield strength of the = the yield strength of the transverse reinforcingtransverse reinforcing

s = maximum C-C spacing of s = maximum C-C spacing of transverse reinforcement within transverse reinforcement within the development lengththe development length

n = number of longitudinal bars n = number of longitudinal bars being developed along the being developed along the plane of splitting.plane of splitting.

snfA

K yttrtr 1500

Other Development LengthsOther Development Lengths Development in Compression: ACI Development in Compression: ACI

318-05 12.3318-05 12.3 Development of standard hooks in Development of standard hooks in

tension: ACI 318-05 12.5tension: ACI 318-05 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 Mechanical connectors (such as

bearing plates at the beam ends) may bearing plates at the beam ends) may also be use.also be use.

Effect on Moment CapacityEffect on Moment Capacity Moment Capacity, Moment Capacity, MMnn, is a function , is a function

of “x”of “x” If different bars develop differently If different bars develop differently

then you need to look at the then you need to look at the “contribution” that each bar makes “contribution” that each bar makes to the moment capacityto the moment capacity

Moment Capacity DiagramMoment Capacity DiagramMoment Capacity

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X (in)

phiP

m (f

t-k)

Cutting BarsCutting Bars The The MMnn diagram can be made to more diagram can be made to more

closely fit the Mu diagram by terminating closely fit the Mu diagram by terminating or cutting bars when they are no longer or cutting bars when they are no longer needed. (ACI 318-05 12.10.3)needed. (ACI 318-05 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 Beam Profile Showing Bar Cutoff LocationsCutoff Locations