Concrete Section Depth for a Target Cracking Moment
The inverse of the concrete-cracking-moment tile: the total section depth that reaches a target cracking moment for a given width, h = sqrt( 6 Mcr / (fr b) ) with fr = 7.5 lambda sqrt(f'c). A 12 in wide section at 4000 psi needs about a 20 in depth to crack at 31.6 kip-ft. A common use is to enter 1.2 Mcr for the minimum-reinforcement check. Gross rectangular section; the flexure/shear/deflection design still governs the final depth. A design aid; the engineer of record governs.
Formula and source
fr = 7.5 x lambda x sqrt(f'c); h = sqrt( 6 x Mcr / (fr x b) ), the inverse of Mcr = fr b h^2/6; S = b h^2/6; Mcr_lbin = Mcr_kipft x 12000.
The ACI 318-19 cracking moment Mcr = fr Ig/yt (19.2.3.1 modulus of rupture), solved for the section depth, by name.
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