Rebar Tension Development Length (ACI 318-19)

The straight-bar tension development length from the ACI 318-19 general equation.

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Example

You enter

Concrete strength f'c (psi) 4000
Bar yield fy (psi) 60000
Bar diameter db (in, #8 = 1.00) 1
Casting position psi_t (1.3 top bar, 1.0 other) 1
Coating psi_e (1.5 / 1.2 epoxy, 1.0 uncoated) 1
Bar size psi_s (0.8 for #6 and smaller, else 1.0) 1
Grade psi_g (1.0 Gr 60, 1.15 Gr 80, 1.3 Gr 100) 1
Lightweight factor lambda (1.0 normalweight) 1
Confinement (cb + Ktr)/db (max 2.5) 2.5

You get

psi_t x psi_e (capped 1.7) 1.00
Confinement term used (capped 2.5) 2.50
Development length ld (12 in floor) 28.5
In bar diameters 28.5 db

Details, formula, and sources

ld = (3/40) x fy x psi_t x psi_e x psi_s x psi_g / (lambda x sqrt(f'c) x (cb + Ktr)/db) x db, with the confinement term capped at 2.5, the psi_t x psi_e product capped at 1.7, and the 12 in floor. A #8 Grade 60 bottom bar in 4,000 psi concrete, well confined, develops in 28.5 in; cast as a top bar the 1.3 casting-position factor stretches it to 37 in -- the trap the 40-bar-diameter rule of thumb papers over. Straight-bar tension only; hooks, compression bars, and lap splices are separate checks. A design aid, not a substitute for a licensed engineer's detailing.

ld = (3/40) x fy x psi_t x psi_e x psi_s x psi_g / (lambda x sqrt(f'c) x (cb + Ktr)/db) x db; (cb + Ktr)/db capped at 2.5; psi_t x psi_e capped at 1.7; ld >= 12 in.

ACI 318-19 (Building Code Requirements for Structural Concrete), by name: §25.4.2.3 (general tension development equation), §25.4.2.4 (confinement cap), Table 25.4.2.5 (modification factors), §25.4.2.1 (12 in minimum).

ACI 318-19 is viewable through ACI's online public-access reader; the (3/40) x fy / (lambda sqrt(f'c)) x db arithmetic and the psi-factor table values are public.

Estimate. AHJ and licensed professional govern.

Field names used by the API: fc, fy, db, psi_t, psi_e, psi_s, psi_g, lambda, conf, te, conf_eff, ld_in, ld_db

Psi factors user-selected psi_t / psi_e / psi_s / psi_g and the confinement term are entered from Table 25.4.2.5 and the actual detailing; the tool does not compute cb or Ktr from cover and stirrupsACI 318-19 Table 25.4.2.5
Caps and floor (cb + Ktr)/db is capped at 2.5, psi_t x psi_e at 1.7, and ld is never less than 12 inACI 318-19 §25.4.2.1 / .4 / .5
Straight tension bars only hooked-bar (ldh, §25.4.3), headed-bar, compression (§25.4.9), and lap-splice (§25.5) lengths are separate calculationsACI 318-19 §25.4