Concrete Cracking Moment Mcr (ACI 318-19)
The bending moment at which a plain concrete section first cracks - the value the modulus-of-rupture tile names as its purpose but does not compute: 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.
Formula and source
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.
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