Concrete Modulus of Rupture fr (ACI 318-19 19.2.3)
The tensile stress at which plain concrete first cracks.
Example
You enter
- Concrete strength f'c (psi) 4000
- Lightweight factor lambda (1.0 NW, 0.75 LW) 1
You get
- Modulus of rupture fr = 7.5 lambda sqrt(f'c) 474 psi
- As a fraction of f'c 0.1186 x f'c
Checked against published worked examples from: Expanded Shale, Clay and Slate Institute (ESCSI).
Details, formula, and sources
Scopefr = 7.5 x lambda x sqrt(f'c) psi (ACI 19.2.3.1), the tensile stress at which plain concrete first cracks, setting the cracking moment behind deflection and minimum-reinforcement checks. 4000 psi normalweight -> 474 psi (~0.119 f'c); all-lightweight (lambda 0.75) -> 356 psi. A design aid; the engineer of record's stamped design governs.
Formula or tablefr = 7.5 x lambda x sqrt(f'c) psi; lambda = 1.0 normalweight, 0.75 all-lightweight.
Source and editionThe ACI 318-19 19.2.3.1 modulus of rupture of concrete, by name.
Free accessACI 318 is readable free through the ACI online reading room at concrete.org; the 19.2.3 rupture provisions are in the published code.
What governsEstimate. AHJ and licensed professional govern.
API field namesfc_psi, lambda, fr_psi, fr_fraction
- Rupture stress fr = 7.5 x lambda x sqrt(f'c) psiACI 318-19 19.2.3.1
- Lightweight factor lambda = 1.0 normalweight, 0.75 all-lightweightACI 318-19 19.2.4
- Design value conservative cracking stress; test strength scatters above itscope of this tile