Concrete Section Depth for a Target Cracking Moment
The total section depth that reaches a target cracking moment for a given width.
Example
You enter
- Target cracking moment Mcr (kip-ft) 31.62
- Section width b (in) 12
- Concrete strength f'c (psi) 4000
- Lightweight factor lambda (1.0 NW, 0.75 LW) 1
You get
- Required total depth h 20.00 in
- Modulus of rupture fr 474 psi
Details, formula, and sources
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.
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.
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: target_mcr_kipft, b_in, fc_psi, lambda, h_in, fr_psi
- Section depth h = sqrt( 6 Mcr / (fr b) ), the inverse of Mcr = fr b h^2/6ACI 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; the flexure/shear/deflection design still governs the depthscope of this tile