RC Column Longitudinal Steel for a Target Load
The longitudinal steel a target factored axial load needs for a given tied column.
Example
You enter
- Target factored axial load phi Pn (kip) 639
- Column width b (in) 16
- Column depth h (in) 16
- Concrete strength f'c (psi) 4000
- Steel yield fy (psi) 60000
You get
- Ast required (in²) 6.333
- Rho g 0.0247
Details, formula, and sources
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.
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.
ACI 318 is readable free through the ACI online reading room at concrete.org; the 22.4 axial provisions and 10.6.1 limits are in the published code.
Estimate. AHJ and licensed professional govern.
Field names used by the API: target_load_kip, b_in, h_in, fc_psi, fy_psi, ast_required_in2, rho_g
- Required steel Ast = (phi Pn / 0.52 - 0.85 f'c Ag) / (fy - 0.85 f'c), the inverse of the axial capACI 318-19 22.4.2
- 1% minimum governs reported Ast = max(strength requirement, 0.01 Ag)ACI 318-19 10.6.1.1
- 8% maximum a strength requirement over 0.08 Ag means the section is too small; enlarge itACI 318-19 10.6.1.1