Standard Hook Development Length (ACI 318-19 25.4.3)
Where 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 the straight-bar rc-development-length. Standard 90/180 hooks; headed bars separate. A design aid, not the engineer of record's stamped detailing.
Formula and source
psi_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).
The 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.
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