Long-Term Deflection Multiplier (ACI 318-19 24.2.4)
Why bottom-only beams sag and doubly-reinforced ones hold.
Example
You enter
- Immediate deflection from sustained load (in) 0.4
- Sustained-load duration (months, >=60 = 5 yr) 60
You get
- Time factor xi 2.00
- Creep multiplier lambda 2.000
- Additional long-term deflection 0.800 in
- Total deflection (immediate + long-term) 1.200 in
Details, formula, and sources
a concrete beam keeps deflecting for years from creep and shrinkage. ACI 24.2.4.1.1 multiplier lambda = xi / (1 + 50 rho'), where xi is 2.0 at 5+ years and rho' is the compression-steel ratio. A bottom-only beam (rho' = 0) with a 0.4 in immediate deflection gets the full lambda = 2.0 -> 0.80 in additional -> 1.20 in total, sagging triple its snapshot value; add compression bars so rho' = 0.01 and lambda drops to 1.33 -> 0.93 in total, 22% less. This long-term total is what the L/240 and L/480 limits are actually checked against. A design aid; the engineer of record governs.
xi = 2.0 (>=60 mo) / 1.4 (>=12) / 1.2 (>=6) / 1.0 (else); lambda = xi / (1 + 50 rho'); additional = lambda x immediate; total = immediate + additional.
The ACI 318-19 24.2.4.1.1 additional time-dependent (creep and shrinkage) deflection multiplier lambda = xi / (1 + 50 rho'), with the 24.2.4.1.3 time factor xi, by name.
ACI 318 is readable free through the ACI online reading room at concrete.org; the 24.2.4 deflection provisions are in the published code.
Estimate. AHJ and licensed professional govern.
Field names used by the API: immediate_defl_in, duration_months, xi, lambda, additional_defl_in, total_defl_in
- Time factor xi = 2.0 at 5 years or more, 1.4 at 12 months, 1.2 at 6 months, 1.0 at 3 monthsACI 318-19 24.2.4.1.3
- Compression steel rho' = As'/(b d) reduces the multiplier; a doubly-reinforced beam creeps far lessACI 318-19 24.2.4.1.1
- Sustained load the multiplier applies to the immediate deflection from the sustained load onlyACI 318-19 24.2.4.1