OpenSpecEngineering

Finds how far a deformed reinforcing bar in tension must extend into concrete to develop its yield strength, by ACI CODE-318-25 [1]. It gives the straight-bar development length, the Class B tension lap splice and the development length of a standard hook. Detailers use it to set bar lengths, laps and hooks.

The development equations

ℓ_d = (3/40)·f_yψ_tψ_eψ_sψ_g / [λ√f′_c·(c_b + K_tr)/d_b] · d_b, at least 12 in.
ℓ_st = 1.3ℓ_d, at least 12 in.
ℓ_dh = f_yψ_eψ_s / (50λ√f′_c) · d_b, at least 8d_b and 6 in.

d_b is the bar diameter, f_y the bar yield strength and f′_c the concrete strength, both in psi, with √f′_c not taken above 100 psi. λ is 1.0 for normalweight concrete and less for lightweight. The ψ factors come from Code Tables 25.4.2.5 and 25.4.3.2 [1]:

• ψ_t, casting position: 1.3 for a top bar with more than 12 in. of fresh concrete cast below it.
• ψ_e, coating: 1.2 or 1.5 for epoxy-coated bars. ψ_tψ_e need not exceed 1.7.
• ψ_s, bar size: 0.8 for No. 6 and smaller straight bars; 1.0 to 1.5 for hooks, rising with size.
• ψ_g, grade: 1.0 for Grade 40 and 60, 1.15 for Grade 80, 1.3 for Grade 100.

(c_b + K_tr)/d_b is the confinement term: cover or bar spacing plus the effect of stirrups, capped at 2.5. The hook length takes ψ_cc = ψ_r = 1.0, which the Code permits. The Code’s equations are in inch-pound units, so the page converts the inputs exactly and evaluates them in psi and inches.

Limits and common mistakes

• The grade presets use the metric yield strengths (Grade 60 = 420 MPa = 60,916 psi), which give lengths about 1.5 % longer than 60,000 psi. Enter f_y in psi for the inch-pound numbers.
• ψ_t = 1.3 applies to the top bars of deep beams and thick slabs, not to every bar near the top.
• Lap splices of bars larger than No. 11 are not permitted in tension; the page says so.
• Diameters between bar sizes take the larger bar’s factors. Bars larger than No. 18 are rejected.
• These are tension lengths. Compression development and headed bars need other provisions.

Worked example

Detail the lap of #8 Grade 60 top bars in a 4000 psi beam with more than 12 in. of concrete below them. The bars are uncoated, with normal cover and stirrups.

1. Choose Bar Size #8 [No. 25] — 1.000 in, 25.4 mm and Rebar Grade ASTM A615 Grade 60 — fy = 420 MPa.
2. Choose Concrete Strength 4000 psi (27.6 MPa).
3. Choose Casting Position Factor ψt ψt = 1.3 and keep Coating Factor ψe ψe = 1.0.
4. Keep Confinement Term (c_b + K_tr)/d_b 1.5 and Concrete Type Normalweight concrete — λ = 1.00.
5. Press Solve. The Solution shows: ψs, straight bar: 1
   ψg: 1
   ψt·ψe: 1.3
   Tension development length ld: 1,590.18 mm
   Class B lap splice ℓst: 2,067.24 mm
   ψs, standard hook: 1
   Standard hooked development length ldh: 489.287 mm
   ld / db: 62.6057

Check: (3/40) × 60,916 × 1.3 / (√4000 × 1.5) = 62.6 bar diameters, or 1,590 mm for a 25.4 mm bar. At exactly 60,000 psi it would be 61.7 d_b. Specify a lap of about 2.1 m.