Concrete column calculator
A tied column carries load through the concrete and the longitudinal steel together. This calculator builds φPn,max from the ACI 318 expression, checks the 1–8% steel limits, and flags slenderness above the threshold where second-order effects start to matter.
| Term | Value |
|---|---|
| Gross area Ag | 1.600e+5 mm² |
| Steel Ast | 1608 mm² |
| Net concrete area | 1.584e+5 mm² |
| 0.85 f′c (Ag − Ast) | 3770 kN |
| fy Ast | 676 kN |
| φPn,max (0.65 × 0.80) | 2312 kN |
| Minimum steel (1%) | 1600 mm² |
Tied column, compression-controlled. Moment interaction and biaxial bending are separate checks.
φPn,max = 0.65·0.80·[0.85f′c(Ag−Ast) + fy·Ast] · Tied column, ACI 318 §22.4.2.
0.01Ag ≤ Ast ≤ 0.08Ag · §10.6.1.1.
klu/r · Above 22 the column is slender and moments magnify.
A clear path from inputs to results.
A tied column carries load through the concrete and the longitudinal steel together. This calculator builds φPn,max from the ACI 318 expression, checks the 1–8% steel limits, and flags slenderness above the threshold where second-order effects start to matter.
How to use
- Enter the section width and depth.
- Choose the number and diameter of bars.
- Set f′c and fy.
- Enter the factored axial load and the unsupported length.
The formula
Reference: ACI 318-19 §22.4.2 (tied columns), §10.6.1.1 (steel limits), §6.2.5 (slenderness).
Worked example
400 × 400 mm, 8 × 16 mm bars, 1,500 kN
- 400 × 400 mm section.
- 8 bars of 16 mm (Ast 1,608 mm²).
- f′c 28 MPa, fy 420 MPa.
- Pu 1,500 kN, unsupported length 3,000 mm.
- 1
Ag = 160,000 mm²; steel ratio 1.0%.
- 2
φPn,max = 0.65 × 0.80 × [0.85 × 28 × 158,392 + 420 × 1,608] = 2,310 kN.
- 3
Utilisation: 1,500 / 2,310 = 64.9%.
- 4
Slenderness klu/r = 3,000/115.5 = 26.0, above 22 — the column is slender.
φPn,max 2,310 kN · utilisation 64.9% · slender (klu/r 26).
Interpreting the result
Most columns fail in the detailing, not the axial check. The 1% minimum exists to control creep and provide continuity, and the slenderness flag matters more than the utilisation: a slender column can carry the axial load and still fail on magnified moments.
Assumptions & limitations
- Tied (not spiral) column, compression-controlled.
- Axial load only; moment interaction is a separate check.
- Effective length factor k = 1.
- No seismic confinement requirements.
Frequently asked questions
Why is the factor 0.80 applied?
It accounts for accidental eccentricity in a tied column.
Does this check biaxial bending?
No. Biaxial bending needs the interaction surface.
What if klu/r exceeds 22?
Moments must be magnified (ACI §6.6.4), which usually reduces capacity.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.