RC Column Longitudinal Steel for a Target Load
The inverse of the rc-column-axial tile: the longitudinal steel a target factored axial load needs for a given tied column, Ast = (phi Pn / 0.52 - 0.85 f'c Ag) / (fy - 0.85 f'c). A 16 in square 4,000 psi column carrying a 639 kip design load needs about 6.33 in^2 (2.47%). Reports the larger of the strength requirement and the ACI 1% minimum, and flags a load that needs more than 8% (section too small). Concentric short tied column; no P-M interaction. A design aid; the engineer of record governs.
Formula and source
Ag = b x h; Ast = (phi Pn / 0.52 - 0.85 f'c Ag) / (fy - 0.85 f'c), the inverse of phi Pn = 0.80 x 0.65 x [0.85 f'c (Ag - Ast) + fy Ast]; reported Ast = max(strength, 0.01 Ag); flag over 0.08 Ag.
The ACI 318-19 22.4.2 concentric tied-column axial strength (22.4.2.1 cap 0.80 phi Po, phi = 0.65) with the 10.6.1 ratio limits, solved for the longitudinal steel, by name.
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