Concrete Immediate Deflection from Ie (ACI 318-19)
The short-term (immediate) deflection of a reinforced concrete beam or slab under service load.
Example
You enter
- Effective inertia Ie (in⁴, from the Ie tile) 4662
- Concrete strength f'c (psi) 4000
- Service load w (kip/ft) 0.8
- Span L (ft) 24
- Support and loading simple_udl
You get
- Immediate deflection 0.355 in
- Span / deflection L/810
- Modulus Ec 3605 ksi
Details, formula, and sources
ACI 318-19 §24.2.3 elastic beam deflection: delta = K w L^4 / (Ec Ie), with Ec = 57000 sqrt(f'c) the normalweight modulus and Ie the effective (Bischoff) moment of inertia. K is the support/loading coefficient - 5/384 simply supported under a uniform load, 1/384 fixed both ends, 1/8 cantilever, ~1/185 propped cantilever. With Ie 4,662 in^4 (the Ie for a 12 x 20 in beam at f'c 4000), a 0.8 kip/ft service load on a 24 ft simply supported span deflects 0.355 in (L/810); the same beam fixed at both ends deflects 0.071 in (L/4052), five times stiffer. The span/deflection ratio L/delta is what the ACI Table 24.2.2 limits (L/180, L/240, L/360, L/480) are checked against. Feed the immediate deflection into a long-term check for creep and shrinkage. Prismatic member, uniform-load cases; a point load or non-prismatic member is separate. A design aid; the engineer of record governs.
delta = K w L^4 / (Ec Ie); Ec = 57000 sqrt(f'c). K = 5/384 simply supported UDL, 1/384 fixed-fixed UDL, 1/8 cantilever UDL, ~1/185 propped cantilever UDL. L/delta is checked against ACI Table 24.2.2 (L/180, L/240, L/360, L/480).
ACI 318-19 §24.2.3 immediate deflection by elastic analysis with the effective (Bischoff) moment of inertia Ie (§24.2.3.5), and Ec = 57000 sqrt(f'c) (§19.2.2.1), by name; the elastic beam coefficients K are standard mechanics-of-materials results.
ACI 318 is readable free through the ACI online reading room at concrete.org; the §24.2.3 deflection provisions and the §19.2.2.1 modulus are in the published code. Ie, f'c, load, span, and support case are the user's inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: ie_in4, fc_psi, w_klf, span_ft, support, immediate_defl_in, span_over_defl, ec_ksi
- Deflection delta = K w L^4 / (Ec Ie); Ec = 57000 sqrt(f'c)ACI 318-19 §24.2.3, §19.2.2.1
- Support coefficient K 5/384 simple UDL, 1/384 fixed-fixed UDL, 1/8 cantilever UDL, ~1/185 propped cantilever UDLelastic beam theory
- Serviceability / scope L/delta checked against ACI Table 24.2.2 (L/180 to L/480); prismatic member, uniform load (point load is separate)ACI 318-19 Table 24.2.2