1. 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

2. 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]

3. 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

4. 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)

5. 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

6. 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.

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

8. 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 , (a)

9. 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 , (b)

10. 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

11. 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

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

13. 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

14. 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 , 8.6.1
l = 1.0 for normal weight concrete
l as low as 0.75 for the lightest weight concrete

15. 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.

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

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

18. 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

20. Moment Capacity Diagram

21. 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 )
> max(d, 12db)
> max(d, 12db)
End of #6 bar
End of #8 bars
End of #10 bars

22. Beam Profile Showing Bar Cutoff Locations