Beam crack control verification: Cl 24.3.2 bar spacing

This page walks through the complete ACI 318-19 Cl 24.3.2 crack control check for test case C1: a 12×24 in beam with 3-#8 bars, cover = 1.5 in, #3 stirrup, Grade 60 steel. The check verifies that bar spacing does not exceed the code limit for crack width control. Every intermediate value is pinned by a regression test. This is one of 30 cases in the beam verification report.

Case definition

Section	12 × 24 in
Reinforcement	3-#8, 1 layer
Cover	1.5 in clear + #3 stirrup (0.375 in)
Materials	Grade 60 (f_y = 60 ksi)

Step 1: Clear cover to bar surface

The clear cover c_c in Cl 24.3.2 is measured from the nearest concrete surface to the surface of the flexural tension reinforcement, not to the stirrup:

c_c = \text{cover} + d_{\text{stirrup}} = 1.5 + 0.375 = 1.875\ \text{in}

Step 2: Stress in steel (Cl 24.3.2.1)

ACI 318-19 Cl 24.3.2.1 permits using (2/3)f_y as the calculated stress in reinforcement closest to the tension face, instead of computing from elastic cracked-section analysis:

f_s = \frac{2}{3}\,f_y = \frac{2}{3} \times 60 = 40.0\ \text{ksi}

Step 3: Maximum bar spacing (Cl 24.3.2)

The spacing of reinforcement closest to the tension face shall not exceed the lesser of the two expressions in Cl 24.3.2, with f_s in psi:

s_{\max} = \min\!\left(15\,\frac{40{,}000}{f_s} - 2.5\,c_c,\; 12\,\frac{40{,}000}{f_s}\right)

With f_s = 40,000 psi and c_c = 1.875 in:

\text{Term 1} = 15 \times \frac{40{,}000}{40{,}000} - 2.5 \times 1.875 = 15.0 - 4.6875 = 10.3125\ \text{in}

\text{Term 2} = 12 \times \frac{40{,}000}{40{,}000} = 12.0\ \text{in}

s_{\max} = \min(10.3125,\; 12.0) = 10.3125\ \text{in}

Step 4: Actual bar spacing

With 3 bars in a single layer, the center-to-center spacing is:

s_{\text{actual}} = \frac{b - 2\,(\text{cover} + d_{\text{stirrup}} + r_{\text{bar}})}{n_{\text{bars}} - 1} = \frac{12 - 2 \times 2.375}{3 - 1} = \frac{7.25}{2} = 3.625\ \text{in}

where the edge distance = cover + stirrup + half bar = 1.5 + 0.375 + 0.5 = 2.375 in.

Result

s_actual = 3.625 in < s_max = 10.3125 in: PASS.

Skin reinforcement (Cl 24.3.2.1): h = 24 in < 36 in, so skin reinforcement is not required.

Pinned values

These values are locked by regression tests. A drift beyond tolerance fails the build before it can deploy.

Quantity	Value	ACI reference
c_c (clear cover to bar)	1.875 in
f_s	40.0 ksi	Cl 24.3.2.1
s_max	10.3125 in	Cl 24.3.2
s_actual	3.625 in
Status	PASS
Skin reinforcement	Not required (h < 36 in)	Cl 24.3.2.1