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ACI 318-19 Deflection — Effective Ie and Long-Term
Rectangular section, uniform service load, simple span or cantilever. ACI 318-19 replaced Branson's Ie with the Bischoff–Scanlon expression using (2/3)Mcr (Table 24.2.3.5); many tools still use Branson. Long-term multiplier λΔ = ξ/(1 + 50ρ′) and the Table 24.2.2 limits. Branson's value is shown for comparison only.
Member
Service loads
Results
Ig · Icr in⁴—
Mcr · (2/3)Mcr kip-ft—
Ie (D) · Ie (D+L) Table 24.2.3.5—
Branson Ie (D+L) — removed in 318-19—
ΔD · ΔD+L · ΔL in—
λΔ · long-term additional in—
Checked deflection vs limit—
Table 24.2.3.5Ma ≤ (2/3)Mcr: Ie = Ig; otherwise Ie = Icr / [1 − ((2/3)Mcr/Ma)²(1 − Icr/Ig)] ≤ Ig — Bischoff & Scanlon; Branson's equation was removed (R24.2.3.5)
§24.2.3.5 · §19.2Mcr = fr·Ig/yt, fr = 7.5√f′c; Ec = 57,000√f′c (normalweight)
§24.2.4.1Additional long-term deflection = λΔ·Δsustained, λΔ = ξ/(1 + 50ρ′); ξ = 1.0 / 1.2 / 1.4 / 2.0 for 3 / 6 / 12 months / ≥ 5 years
Table 24.2.2ℓ/180 (flat roof, immediate L) · ℓ/360 (floor, immediate L) · ℓ/480 or ℓ/240 (after attachment of nonstructural elements)
VerificationNo fully worked ACI 318-19 numerical deflection example was found in a published source. The engine is checked by: Ie = Ig exactly at Ma = (2/3)Mcr; Ie → Icr as Ma → ∞; Bischoff Ie < Branson Ie (published finding); Icr by independent numerical integration; and a full hand calculation of the default case.
ScopeUniform load, prismatic rectangular section, simple span or cantilever. For continuous members ACI permits averaging Ie at critical sections (§24.2.3.6) — not included.
Preliminary calculation tool. Final design requires the full text of ACI 318 and review by a licensed PE. This tool follows ACI 318-19, the edition referenced by the 2021 and 2024 IBC; ACI CODE-318-25 was published in January 2025 and is expected in the 2027 IBC (changes include development length equations and seismic provisions).