Development Length of Tension Bars

The development length is defined as that length of embedment necessary to develop the full tensile strength of the bar, controlled by either pullout or splitting.
For Modern deformed bars, tests indicate that splitting occurs when the total bond force U=u∑o per inch of length of bar, which is transmitted from steel to concrete, reaches a critical value.
• In the above fig, the moment, and therefore the steel stress is maximum at point ‘a’ and zero at the supports, if the bar stress is fs at ‘a’, then the total tension force Abfs must be transferred from the bar to the concrete in the distance l by bond forces.
• To fully develop the strength of the bar, Abfy, the distance l must be at least equal to the development length of the bar.
• However, if the actual available length is inadequate for full development, special anchorage, such as by hooks, must be provided.
Basic Equation For Development length of Tension Bars
• According to ACI code, for deformed bars or deformed wire
shall not be taken greater than 2.5
Î± = reinforcement location factor
•        Horizontal reinforcement so placed that more than 12” of fresh concrete is cast in the member below the development length or splice 1.3
•        Other reinforcement 1.0
Î² = Coating factor
•        Epoxy-coated bars or wires with cover less than 3db or clear spacing less than 6db 1.5
•        All other epoxy-coated bars or wires 1.2
•        Uncoated reinforcement 1.0
•        However, the product of Î±Î² need not be taken greater than 1.7
C = spacing and cover dimensions, in.
•    Use the smaller of either the distance from the center of the bar to the nearest concrete surface or one-half the center-to-center spacing of the bars being developed.
Ktr=Transverse reinforcement index =

•        Atr=Total cross-sectional area of all transverse reinforcement that is placed with in the spacing ‘S’ and that crosses the potential plane of splitting through the reinforcement being developed, in2
•        fyt = specified field strength of transverse reinforcement, psi
•        S = Maximum spacing of transverse reinforcement within ld center-to-center, in.
•        n = Number of bars or wires being developed along the plane of splitting.  It shall be permitted to use Ktr=0 even if transverse reinforcement is present.
•        Values of (f'c)^1/2 are not to be taken greater than 100 psi because of lack of experimental evidence on bond strengths obtainable with concretes having compressive strengths in excess of 10,000 psi
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