How ACI 318-19 controls cracking
ACI 318-19 does not calculate crack widths. It limits the spacing of flexural bars nearest the tension face: s ≤ 380(280/fs) − 2.5cc and ≤ 300(280/fs) (24.3.2), where cc is the clear cover to the bar and fs the service stress. The code lets you take fs = 2/3 fy, but a calculated fs from the cracked section is usually lower and allows wider spacing.
Crack width estimates
Where crack width matters – exposed, humid or aggressive environments – the tool estimates it two ways. Gergely–Lutz: w = 11×10⁻⁶·β·fs·∛(dc·A). Frosch (the basis of the current ACI spacing rule): w = 2(fs/Es)·β·√(dc² + (s/2)²). Both are compared with the ACI 224R guide values, from 0.41 mm (dry air) to 0.10 mm (water-retaining). Treat them as estimates – measured crack widths scatter widely.
Worked example
200 mm slab, Ø12 @ 150, 30 mm clear cover, f′c 30 MPa, Ms = 30 kN·m/m. As = 754 mm²/m, d = 164 mm, n = 7.77, k = 0.234, j = 0.922, so fs = 30×10⁶/(754 × 0.922 × 164) = 263 MPa. The spacing limit is min(380 × 280/263 − 75, 300 × 280/263) = 319 mm ≥ 150 mm. With β = 1.29 and dc = 36 mm, Gergely–Lutz gives w = 0.27 mm and Frosch 0.28 mm, below 0.30 mm for humid exposure.
FAQ
Which moment should I use?
The service (unfactored) moment. For building members D + L is usual; for liquid-retaining structures use the sustained load and ACI 350.
Why is β larger than 1?
β converts the crack width at the bar level to the tension face, because cracks are wider at the surface. It is (h − kd)/(d − kd), about 1.2 for beams and 1.35 for thin slabs.
How do I reduce crack width?
Use smaller bars at closer spacing, reduce cover where durability allows, or add steel to lower fs.