Concrete Cracking Moment Mcr (ACI 318-19)
The bending moment at which a plain concrete section first cracks.
Example
You enter
- Section width b (in) 12
- Section total depth h (in) 20
- Concrete strength f'c (psi) 4000
- Lightweight factor lambda (1.0 NW, 0.75 LW) 1
You get
- Modulus of rupture fr 474 psi
- Gross section modulus S = b h²/6 800 in^3
- Mcr (kip-ft) 31.62
Details, formula, and sources
Mcr = fr Ig/yt = fr b h^2/6, with fr = 7.5 lambda sqrt(f'c). A 12 x 20 in section at 4000 psi normalweight (fr 474 psi, S 800 in^3) cracks at 31.6 kip-ft. This is the value behind the effective-moment-of-inertia (Ie) deflection analysis and the minimum-reinforcement check (design strength >= 1.2 Mcr). Gross rectangular section; a T-beam uses the transformed Ig. A design aid; the engineer of record governs.
fr = 7.5 x lambda x sqrt(f'c); S = b h^2 / 6; Mcr = fr x S (= fr Ig/yt); Mcr_kipft = Mcr_lbin / 12000.
The ACI 318-19 cracking moment Mcr = fr Ig/yt with the 19.2.3.1 modulus of rupture, by name.
ACI 318 is readable free through the ACI online reading room at concrete.org; the cracking-moment and 19.2.3 rupture provisions are in the published code.
Estimate. AHJ and licensed professional govern.
Field names used by the API: b_in, h_in, fc_psi, lambda, fr_psi, sm_in3, mcr_kipft
- Cracking moment Mcr = fr Ig/yt = fr b h^2/6 for a gross rectangular sectionACI 318-19
- Rupture stress fr = 7.5 x lambda x sqrt(f'c) psi (lambda 1.0 NW, 0.75 LW)ACI 318-19 19.2.3.1
- Gross section reinforcement transform neglected; a T-beam uses the transformed Igscope of this tile