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No. 8 Grade 60 bottom bar in 4,000 psi concrete: tension development length from cover, spacing and stirrups, hook, headed bar and Class B lap (ACI 318-19 Chapter 25)

Tool	Rebar Development and Splices
Source	American Concrete Institute (2019). Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary. American Concrete Institute, Farmington Hills, MI, Sections 25.3 to 25.6 (equations used as mathematics). The same equations are worked in Federal Emergency Management Agency (2021), 2020 NEHRP Recommended Seismic Provisions: Design Examples, FEMA P-2192-V1, pp. 161 and 167-168, which the tool reproduces (38.2 in and about 55 in).
Level	Professional

Problem

Three No. 8 Grade 60 bottom bars at 3.5 in on centre in a beam of 4,000 psi normalweight concrete, 1.5 in clear cover to No. 4 stirrups at 8 in (two legs, A_tr = 0.40 in²), uncoated. Find the tension development length by the general equation and by the simplified table, the compression development length, the 90 degree standard hook, the headed-bar length, the tension and compression lap lengths, and check a 36 in straight embedment.

Inputs to Enter

Bar No. 8: d_b 1.000 in, A_b 0.79 in²; f_y 60 ksi; f′_c 4,000 psi; λ 1.0; single bar
Cover 1.5 in to the stirrup, stirrup diameter 0.5 in, bar spacing 3.5 in, A_tr 0.40 in², s 8 in, n 3, stirrups at least the code minimum
ψ_t 1.0, ψ_e 1.0, ψ_s and ψ_g blank (by size and grade); no excess-steel reduction; compression ψ_r 1.0
Hook: ACI 318-19 equation, 90 degrees, ψ_e 1.0, ψ_r 1.6, ψ_o 1.25, ψ_c blank; head ψ_p 1.6, bearing area 3.16 in²
Splice: A_s,prov / A_s,req 1.0, 100 % spliced, column factor 1.0; embedment check: straight bar in tension, 36 in available; code coefficients at their defaults

Open the Rebar Development and Splices tool (loaded with this example)

Answers

c_b = lesser of 2.0 + 0.5 = 2.5 in and 3.5/2 = 1.75 in = 1.75 in; K_tr = 40 · 0.40/(8 · 3) = 0.667 in; (c_b + K_tr)/d_b = 2.417 (limit 2.5)
General equation: l_d = (3/40)(60,000/63.25)(1.0/2.417)(1.0) = 29.44 in; simplified table (first row, divisor 20): 47.43 in
Compression: greater of 18.97 in and 18.00 in: l_dc = 18.97 in
Standard hook (318-19): ψ_c = 4,000/15,000 + 0.6 = 0.867; l_dh = 60,000 · 1.6 · 1.25 · 0.867/(55 · 63.25) · 1.0^1.5 = 29.90 in; bend diameter 6 d_b = 6 in, extension 12 d_b = 12 in
Headed bar (318-19): l_dt = 21.93 in; head conditions satisfied
Tension lap: Class B, 1.3 · 29.44 = 38.27 in; non-contact spacing at most 6 in; compression lap 0.0005 · 60,000 · 1.0 = 30.00 in
Embedment: 36 in available against 29.44 in required, M.S. = +0.22 (ACI); the bar develops the full f_y

Notes

The tool's default inputs are this case; press Submit. The case is illustrative (stated on the page), not a printed example. Checked by test_rebar_development_splice.php (1,668 checks) against an independent numpy implementation and against the printed development lengths of FEMA P-2192-V1 and FEMA P-751. With ψ_r = ψ_o = 1.0 (a bar hooked into a confined column core) the hook shortens to 14.95 in; the ACI 318-14 hook equation gives 18.97 in.