(New)Development of Reinforcement

Symbols

ψ_e = factor used to modify development length based on reinforcement coating
ψ_g = factor used to modify development length based on grade of reinforcement
ψ_s = factor used to modify development length based on reinforcement size
ψ_t = factor used to modify development length for casting location in tension
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength
K_tr = transverse reinforcement index, in.
A_tr = total cross-sectional area of all transverse reinforcement within spacing s that crosses the potential plane of splitting through the reinforcement being developed, in.²
d_b = nominal diameter of bar, wire, or prestressing strand, in
f'_c = specified comprehensive strength of concrete, psi
f_y = specified yield strength of nonprestressed reinforcement, psi
l_d = development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, in.
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.

Development of reinforcement

Determined tension or compression in reinforcement at each section of a member should be adopted by the fact embedment length; hook, head deformed bar, mechanical device, or a combination according to 25.4.1.

Heads and hooks should not be used to develop bars in compression according to 25.4.1.2.

The values of √f_c^‘ used to calculate development length should not exceed 100 psi. It’s automatically controlled according to 25.4.1.4.

Development of deformed bars and deformed wires in tension

Development length l_d for deformed bars and deformed wires in tension is controlled the greater of below:

• Length calculated in accordance with 25.4.2.3 or 25.4.2.4 using the applicable modification factors of 25.4.2.5

• 12 in

For deformed bars or deformed wires, l_d is calculated in accordance with Table 25.4.2.3. All of the modification factors for development of deformed bars and wires is choosen automatically according to Table 25.4.2.5.

Alternatively, l_d can be calculated with Eq. 25.4.2.4a and 25.4.2.4b.

(c_b + K_tr)/d_b is not exceed 2.5,

where n is the number of bars or wires being developed or lap spliced along the plane of splitting. It is permitted to use K_tr = 0 reinforcement is present or required.

When Eq. 25.4.2.4a is calculated with the prerequisite (c_b + K_tr)/d_b = 2.5 is used with the development length can be determined less than calculated according to Table 25.4.2.3.

25.4.3 Development of standart hooks in tension

Development length l_dh for deformed bars in tension terminating in a standard hook is the greater of

• 8db

• 6 in.

25.4.3.3 The total cross-sectional area of ties or stirrups confining hooked bars A_th shall consist of (a) or (b):
(a) Ties or stirrups that enclose the hook and satisfy 25.3.2.
(b) Other reinforcement enclosing the hook, that extends at least 0.75􀆐dh from the enclosed hook in the direction of the bar in tension, and is in accordance with (1) or (2).
For members with confining reinforcement that is both parallel and perpendicular to l_dh, it shall be permitted to use the value of A_th based on (1) or (2) that results in the lower value of l_dh.
(1) Two or more ties or stirrups shall be provided parallel to l_dh enclosing the hooks, evenly distributed with a center-to-center spacing not exceeding 8d_b, and within 15d_b of the centerline of the straight portion of the hooked bars, where db is the nominal diameter of the hooked bar.
(2) Two or more ties or stirrups shall be provided perpendicular to l_dh, enclosing the hooked bars, and evenly distributed along l_dh with a center-to-center spacing not exceeding 8d_b, where d_b is the nominal diameter of the hooked bar.

References: ACI 318-19

According to 25.4.3.4, for bars being developed by a standard hook at discontinuous ends of members with both side cover and top (or bottom) less than 2-1/2 in., and the rules belowed should be supplied:

• The hook is enclosed along l_dh within ties or stirrups perpendicular to l_dh at s≤3d_b

• The first tie or stirrup tenclose the bent portion of the hook within 2d_b of the outside of the bend

where d_b is the nominal diameter of the hooked bar.

25.4.9 - Development of deformed bars and deformed wires in compression

Development length l_dc for deformed bars and deformed wires in compression is the gerater of
- Length calculated in accordance with 25.4.9.2
- 8 in.

According to 25.4.9.2, l_dc is the greater of (a) and (b), using the modification factors at Table 25.4.9.3

ψ_r is permitted to be taken as 1.0.