25.4 Development of Reinforcement

Calculated tension or compression in reinforcement at each section of a member shall be developed on each side of that section by embedment length; hook, headed deformed bar, mechanical device, or a combination thereof.

Hooks and heads shall not be used to develop bars in compression.

Development lengths do not require a strength reduction factor ϕ.

The values of used to calculate development length shall not exceed 100 psi.

Development length ℓ_d for deformed bars and deformed wires in tension shall be the greater of (a) and (b):

For bars with f_y ≥ 80,000 psi spaced closer than 6 in. on center, transverse reinforcement shall be provided such that K_tr shall not be smaller than 0.5d_b.

For deformed bars or deformed wires, ℓ_d shall be calculated in accordance with Table 25.4.2.3.

For deformed bars or deformed wires, ℓ_d shall be calculated by:

(25.4.2.4a)

(25.4.2.4b)

For the calculation of ℓ_d, modification factors shall be in accordance with Table 25.4.2.5.

Development length ℓ_dh for deformed bars in tension terminating in a standard hook shall be the greater of (a) through (c):

For the calculation of ℓ_dh, modification factors Ψ_e, Ψ_r, Ψ_o, Ψ_c, and λ shall be in accordance with Table 25.4.3.2. At discontinuous ends of members, 25.4.3.4 shall apply.

The total cross-sectional area of ties or stirrups confining hooked bars A_th shall consist of (a) or (b):

1. Ties or stirrups that enclose the hook and satisfy 25.3.2.
2. Other reinforcement enclosing the hook, that extends at least 0.75ℓ_dh from the enclosed hook in the direction of the bar in tension.
   
   A_th shall be in accordance with (c) or (d). 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 (c) or (d) that results in the lower value of ℓ_dh.
3. 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 d_b is the nominal diameter of the hooked bar.
4. 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.

For bars being developed by a standard hook at discontinuous ends of members with both side cover and top (or bottom) cover to hook less than 2-1/2 in., (a) and (b) shall be satisfied:

Use of a head to develop a deformed bar in tension shall be permitted if conditions (a) through (f) are satisfied:

Development length ℓ_dt for headed deformed bars in tension shall be the longest of (a) through (c):

For the calculation of ℓ_dt, modification factors Ψ_e, Ψ_p, Ψ_o, and Ψ_c shall be in accordance with Table 25.4.4.3.

For beam column joints, the total cross-sectional area of parallel tie reinforcement A_tt shall consist of ties or stirrups oriented parallel to ℓ_dt and located within 8d_b of the centerline of the headed bar toward the middle of the joint, where d_b is the nominal diameter of the headed bar.

For anchorages other than in beam-column joints, tie reinforcement, A_tt, shall not be considered, and Ψ_p shall be taken as 1.0 provided the spacing is at least 6d_b.

If beam negative moment reinforcement is provided by headed deformed bars that terminate in a joint, the column shall extend above the top of the joint a distance at least the depth h of the joint, where h is the horizontal dimension of the joint in the direction of the forces being considered. Alternatively, the beam reinforcement shall be enclosed by additional vertical joint reinforcement providing equivalent confinement to the top face of the joint.

Any mechanical attachment or device capable of developing f_y of deformed bars shall be permitted, provided it is approved by the building official in accordance with 1.10. Development of deformed bars shall be permitted to consist of a combination of mechanical anchorage plus additional embedment length of the deformed bars between the critical section and the mechanical attachment or device.

Development length ℓ_d for welded deformed wire reinforcement in tension measured from the critical section to the end of wire shall be the greater of (a) and (b), where wires in the direction of the development length shall all be deformed D31 or smaller.

For welded deformed wire reinforcement, ℓ_d shall be calculated from 25.4.2.3 or 25.4.2.4, times welded deformed wire reinforcement factor Ψ_w from 25.4.6.3 or 25.4.6.4. For epoxy-coated welded deformed wire reinforcement meeting 25.4.6.3, it shall be permitted to use Ψ_e = 1.0 in 25.4.2.3 or 25.4.2.4.

For welded deformed wire reinforcement with at least one cross wire within ℓ_d that is at least 2 in. from the critical section, Ψ_w shall be the greater of (a) and (b), and need not exceed 1.0:

(a)
(b)

For welded deformed wire reinforcement with no cross wires within ℓ_d or with a single cross wire less than 2 in. from the critical section, Ψ_w shall be taken as 1.0.

Where any plain wires, or deformed wires larger than D31, are present in the welded deformed wire reinforcement in the direction of the development length, the reinforcement shall be developed in accordance with 25.4.7.

Zinc-coated (galvanized) welded deformed wire reinforcement shall be developed in accordance with 25.4.7.

Development length ℓ_d for welded plain wire reinforcement in tension measured from the critical section to the outermost cross wire shall be the greater of (a) and (b) and shall require a minimum of two cross wires within ℓ_d.

ℓ_d shall be the greater of (a) and (b):

Development length ℓ_d of pretensioned seven-wire strands in tension shall be in accordance with (a) and (b):

(a)	(25.4.8.1)

Seven-wire strand shall be bonded at least ℓ_d beyond the critical section except as provided in 25.4.8.3.

Embedment less than ℓ_d shall be permitted at a section of a member, provided the design strand stress at that section does not exceed values obtained from the bilinear relationship defined by Eq. (25.4.8.1).

Development length ℓ_dc for deformed bars and deformed wires in compression shall be the greater of (a) and (b)

ℓ_dc shall be the greater of (a) and (b), using the modification factors of 25.4.9.3:

For the calculation of ℓ_dc, modification factors shall be in accordance with Table 25.4.9.3, except Ψ_r shall be permitted to be taken as 1.0.

Reduction of development lengths defined in 25.4.2.1(a), 25.4.6.1(a), 25.4.7.1(a), and 25.4.9.1(a) shall be permitted by use of the ratio (A_s,required)/(A_s,provided), except where prohibited by 25.4.10.2. The modified development lengths shall not be less than the respective minimums specified in 25.4.2.1(b), 25.4.6.1(b), 25.4.7.1(b), and 25.4.9.1(b).