Structural Concrete - Hassoun

262 Chapter 7 Development Length of Reinforcing Bars
and 7.5 becomes
l ( ) ( )(
)
d 3 f y ψt ψ
=
e ψ s
√ ( )
d b 40λ f
′ cb c
+ K tr ∕db
(7.7)
where
ψ t = bar location
ψ e = coating factor
ψ s = bar-size factor
λ = lightweight aggregate concrete factor (ACI Code, Section 19.2.4.2)
= 1.0 normal-weight concrete
= When lightweight aggregate is used, λ shall not exceed 0.75 unless splitting tensile strength is
specified, then
λ = f ct ∕(6.7 √ f ′ c ) ≤ 1 (ACI Code, Section 19.2.4.2) c b = spacing or cover dimension (in.); the
smaller of
(1) Distance from center of bar or wire being developed to the nearest concrete surface or
(2) One-half the center-to-center spacing of bars or wires being developed
K tr = transverse reinforcement index
= 40 A tr /sn
n = number of bars or wires being developed along the plane of splitting
s = maximum spacing of transverse reinforcement within l d , center to center (in.)
f yt = yield strength of transverse reinforcement (psi)
A tr = total sectional area of all transverse reinforcement within spacing s that crosses the potential
plane of splitting through to the reinforcement being developed (in. 2 )
Notes:
1. Let (c b - + K tr )/d b not exceed 2.5 to safeguard against pullout-type failures.
2. The value of √ f c ′ shall not exceed 100 psi (ACI Code, Section 25.4.1.4).
3. Let K tr = 0 be used as a design simplification (ACI Code, Section 25.4.2.3).
7.3.2 ACI Code Factors for Calculating l d for Bars in Tension
1. Ψ t = bar location factor
Ψ t = 1.3 for top bars defined as horizontal reinforcement, placed so that more than 12 in. of
fresh concrete is below the development length, or splice
Ψ t = 1.0 for all other reinforcement
2. Ψ e = coating factor
Ψ e = 1.5 for epoxy-coated bars or wires with cover less than 3d b or clear spacing less than
6d b
Ψ e = 1.2 for all other epoxy coated bars or wires
Ψ e = 1.0 for uncoated and zinc-coated (galvanized) reinforcement (However, the value of the
Ψ t Ψ e product should not exceed 1.7.)
3. Ψ s = bar size factor
Ψ s = 0.8 for no. 6 bars or smaller bars and deformed wires
Ψ s = 1.0 for no. 7 bars and larger bars