Development & Lap Length Calculator (ACI 318-19)

How the development length is calculated

ACI 318-19 Eq. 25.4.2.4a gives ℓd = fy·ψt·ψe·ψs·ψg / (1.1λ√f′c·(cb + Ktr)/db) · db, not less than 300 mm. ψt = 1.3 for top bars with more than 300 mm of fresh concrete below, ψe accounts for epoxy coating (ψt·ψe ≤ 1.7), ψs = 0.8 for bars up to Ø20, and the new grade factor ψg is 1.0 for Grade 420, 1.15 for Grade 550 and 1.3 for Grade 690. The confinement term (cb + Ktr)/db is capped at 2.5. The simplified Table 25.4.2.3 is shown for comparison; it is usually more conservative.

Hooks under ACI 318-19

The hooked-bar equation changed in 2019: ℓdh = fy·ψe·ψr·ψo·ψc·db^1.5 / (23λ√f′c), not less than 8db or 150 mm. ψr = 1.6 unless confining ties are provided (then 1.0), ψo = 1.25 unless the hook ends inside a column core with enough side cover (then 1.0), and ψc = f′c/105 + 0.6 for f′c below 42 MPa. Because of db^1.5, large bars need much longer hooks than before.

Lap splices

Tension laps are Class B (1.3ℓd) unless the area provided is at least twice the area required over the whole lap and no more than half the bars are spliced, which allows Class A (1.0ℓd). Compression laps are 0.071·fy·db for fy ≤ 420 MPa, or (0.13fy − 24)·db above that, not less than 300 mm.

Worked example

Ø20 bottom bar, f′c 32 MPa, fy 420 MPa, 50 mm clear cover, 100 mm clear spacing, Ø10 stirrups @ 150 (2 legs), 4 bars in the layer. cb = min(50 + 10, (100 + 20)/2) = 60 mm; Ktr = 40 × 157.1/(150 × 4) = 10.5; (cb + Ktr)/db = 3.52, capped at 2.5. ℓd = 420 × 1.0 × 0.8 × 1.0 / (1.1 × 5.657 × 2.5) × 20 = 432 mm, and the Class B lap is 562 mm. The simplified table would give 707 mm, so the full equation saves about 40%.

FAQ