Standard Hook Development Length (ACI 318-19 25.4.3)

ScopeWhere a straight bar cannot fit - a beam bar anchoring into a column - the detailer hooks it, and the hook develops in ldh = (fy psi_e psi_r psi_o psi_c / (55 lambda sqrt(f'c))) db^1.5, never less than max(8 db, 6 in). A #8 Grade 60 bar in 4,000 psi concrete needs 14.9 in; a #5 only 7.4 - the db^1.5 scaling a hook = multiple-of-db rule of thumb gets wrong. Companion to straight-bar development length. Standard 90/180 hooks; headed bars separate. A design aid, not the engineer of record's stamped detailing.

Formula or tablepsi_c = f'c/15,000 + 0.6 (f'c < 6,000 psi, else 1.0); ldh = (fy psi_e psi_r psi_o psi_c / (55 lambda sqrt(f'c))) db^1.5; ldh = max(ldh, 8 db, 6 in).

Source and editionThe ACI 318-19 Eq. 25.4.3.1a hooked-bar tension development length with the 25.4.3.2 modification factors and the max(8 db, 6 in) minimum, by name.

Free accessACI 318 is readable free through the ACI online reading room at concrete.org; Eq. 25.4.3.1a and the 25.4.3.2 factor table are in the published code.

What governsEstimate. AHJ and licensed professional govern.

API field namesdb_in, fy_psi, fc_psi, psi_e, psi_r, psi_o, lambda, psi_c, ldh_in

• Hook equation ldh scales with db^1.5 - not linearly - through Eq. 25.4.3.1aACI 318-19 25.4.3.1
• Modification factors psi_e epoxy, psi_r confinement, psi_o location/cover, psi_c strength (f'c/15,000 + 0.6 under 6,000 psi)ACI 318-19 25.4.3.2
• Floor never less than 8 bar diameters nor 6 inACI 318-19 25.4.3.1(b)/(c)
• Special moment frame joint (option, added 2026-10-08) ldh = fy db / (65 lambda sqrt(f'c)), at least 8 db and 6 in (10 db and 7.5 in lightweight), No. 3-11, no psi factors; a straight bar needs 2.5 ldh, or 3.25 ldh with over 12 in of concrete below. Equation as quoted in PCI Journal, March-April 2024 (Ghosh).ACI 318-19 18.8.5.1 / 18.8.5.3