Anchorage and Development Length

Development Length - Tension Where, α = reinforcement location factor β = reinforcement coating factor γ = reinforcement size factor λ = lightweight aggregate concrete factor K t r = 0 as a design simplification c = spacing or cover dimension for further information and values, see page 31a, notes transverse reinforcement index Excess reinforcement: l d may also be modified by (A s required/ A s provided)

Development Length - Compression l dc may be modified by the following: Reinforcement in excess of that required by analysis ………..A’ s required/A’ s provided Spirally reinforced column bars and bars surrounded by closely spaced ties………..0.75

Standard Hooks When sufficient embedment length is not available for tensile reinforcing bars, they may be bent into the shape of a hook (hooks are not effective in compression). basic hook development length for uncoated rebar in normal weight concrete: l dh ≥ l hb (modification factors) ≥ 8 db ≥ 6 in. Modification factors: For side cover ≥ 2 ½ in. normal to plane of hook, and for 90° hook with cover on extension beyond hook ≥ 2 in. …………………..0.7 If the hook is enclosed vertically or horizontally within ties space ≤ 3 d b along the full length l dh ……………………………………….0.8 When anchorage for full development is not specifically required, and there is excess reinforcement…………………A s required/A s provided

Standard Hooks

Critical points, c, occur at points of maximum moment. All reinforcement must be anchored distances l d or l dh on both sides of these points. Critical points, x, are formed in bars that continue past bars that are stopped. The points x are to be taken as the theoretical stopping point of bars that actually are stopped further along the beam in accord with Code requirements. The continuing bars must extend ≥ l d beyond the points x. The bars being stopped must continue the greater of d, 12 d b or, when the last ⅓ of top reinforcement is being stopped, l n /16 beyond the point where they are theoretically no longer needed.

Zero Positive Moment Locations At points of zero positive moment a minimum A s is required: l a = greater of d or 12 d b

Reinforcement Stopped in a Tension Zone Flexural reinforcement may not be stopped in a tension zone unless one of the following conditions is satisfied: a.Shear at the cutoff point is ≤ ⅔Ф(V c +V s ) b.Excess stirrups are provided form the cutoff point for a distance = 3/4d past it. (see notes p. 33) c.The continuing reinforcement provides double the As required at the cutoff point and Vu ≤ ¾Ф(V c +V s )

Maximum Moment Diagrams

Reinforcement Layout WWF 3 #5 bars 50” 97” 37”8.3” 2#5 bars 60” 3 #5 bars