Headed Bar Development Length (ACI 318-19 25.4.4)

How far a headed deformed bar must run past the critical section to develop its yield in tension.

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Checked against published worked examples from: Dextra Group.

Details, formula, and sources

Scopeldt = (fy psi_e psi_p psi_o psi_c / (75 sqrt(f'c))) db^1.5, never less than 8 db or 6 in. A head bearing on the concrete replaces most of the bond length and the congestion of a hook: an uncoated #8 at 60 ksi in 4,000 psi concrete develops in 11.0 in, where a standard hook needs 14.9 in. Parallel ties and a head inside a column core keep the factors at 1.0; without them the length grows by 1.6 and 1.25. Heads are limited to No. 11 bars and smaller in normalweight concrete. ACI 318-25 prints 90 in place of 75. The engineer of record governs.

Formula or tableldt = max[(fy psi_e psi_p psi_o psi_c / (75 sqrt(f'c))) db^1.5, 8 db, 6 in]; psi_c = f'c/15,000 + 0.6 below 6,000 psi, else 1.0; sqrt(f'c) <= 100 psi; ACI 318-25 uses 90 in place of 75.

Source and editionACI 318-19 Eq. 25.4.4.2(a)-(c) with the Table 25.4.4.3 modification factors and the 25.4.4.1 conditions, by name; the ACI 318-25 coefficient as printed in Dextra's ACI 318-25 headed bar calculation (free PDF at dextragroup.com).

Free accessACI 318 is free to view in ACI's read-only online edition; the 318-19 equation and the psi_p table are reproduced in PCI Journal, March-April 2024 (Ghosh), and the Dextra calculation is a free PDF.

What governsEstimate. AHJ and licensed professional govern.

API field namesdb_in, fy_psi, fc_psi, psi_e, psi_p, psi_o, edition, ldt_in, psi_c

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