CE A433 – RC Design T. Bart Quimby, P.E., Ph.D. Revised Spring 2009 Development Length CE A433 – RC Design T. Bart Quimby, P.E., Ph.D. Revised Spring 2009

Consider a bar embedded in a mass of concrete P = s * [p*db2/4] P = t*[Lb*p*db] db Lb t = P / [Lb*p*db] < tmax s = P/ [p*db2/4] < smax P < tmax * [Lb*p*db] P < 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]

Development Length Ld = development length the shortest distance over which a bar can achieve it’s full capacity The length that it takes a bar to develop its full contribution to the moment capacity, Mn Ld Mn Cc Mn = (C or T)*(dist) Ts

Lb > (fy / tmax)* [db/4] Steel Limit, smax Using the bilinear assumption of ACI 318: smax = + fy Lb > (fy / tmax)* [db/4] Lb > fy * db / (4*tmax)

Concrete Bond Limit, tmax There are lots of things that affect tmax The strength of the concrete, f’c Type of concrete (normal weight or light weight) The amount of concrete below the bar The surface condition of the rebar The concrete cover on the bar The proximity of other bars transferring stress to the concrete The presence of transverse steel

Concrete Strength, f’c Bond strength, tmax, tends to increase with concrete strength. Experiments have shown this relationship to be proportional to the square root of f’c.

Type of Concrete Light weight concrete tends to have less bond strength than does normal weight concrete. ACI 318-08 introduces a lightweight concrete reduction factor, l, on sqrt(f’c) in some equations. See ACI 318-08, 8.6.1 for details

Amount of Concrete Below Bars The 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 See ACI 318-08, 12.2.4(a)

Surface Condition of Rebar All rebar must meet ASTM requirements for deformations that increase pullout strength. Bars are often surface coated is inhibit corrosion. Epoxy Coating  The major concern! Galvanizing Epoxy coating significantly reduces bond strength See ACI 318-08, 12.2.4(b)

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

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

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

The Modifiers yt, Modifier for reinforcement location 1.3 for top bars, 1.0 for other bars ye, modifier for epoxy coated bars 1.5 when cover < 3db or clear spacing < 6db 1.2 for other epoxy coated reinforcing 1.0 for non-epoxy coated reinforcing The product, ytye, need not exceed 1.7

More Modifiers… ys, Modifier for bar size 0.8 for #6 and smaller 1.0 for #7 and larger l, Modifier for lightweight concrete ACI 318-08, 8.6.1 l = 1.0 for normal weight concrete l as low as 0.75 for the lightest weight concrete

The Transverse Reinforcement Index, Ktr (ACI 318-08 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. s = maximum C-C spacing of transverse reinforcement within the development length n = number of longitudinal bars being developed along the plane of splitting.

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

Other Development Lengths Development in Compression: ACI 318-08 12.3 Development of standard hooks in tension: ACI 318-08 12.5 There are some very specific cover and/or confinement requirements Mechanical connectors (such as bearing plates at the beam ends) may also be used.

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

Moment Capacity Diagram

Cutting Bars The fMn diagram can be made to more closely fit the Mu diagram by terminating or cutting bars when they are no longer needed. (ACI 318-08 12.10.3) > max(d, 12db) > max(d, 12db) End of #6 bar End of #8 bars End of #10 bars

Beam Profile Showing Bar Cutoff Locations