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    Calculates locally in your browser · ACI 318 tied column
    Concrete / compression

    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.

    TiesTiedSteel1–8%VerdictPass
    Axial capacity
    2312 kN
    φPn,max for a tied column
    Utilisation
    64.9%
    Within capacity
    Steel provided
    1608 mm²
    1.01% of the gross area
    Slenderness
    26.0
    Above 22 — second-order effects
    Capacity build-up
    Concrete plus steel, reduced by the tied-column factor and φ.
    2312 kN
    Capacity build-up
    TermValue
    Gross area Ag1.600e+5 mm²
    Steel Ast1608 mm²
    Net concrete area1.584e+5 mm²
    0.85 f′c (Ag − Ast)3770 kN
    fy Ast676 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.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Utilisation against axial load
    The column is adequate while the line stays under 100%.
    Utilisation against axial load0.00029.0758.1487.21116.29145.360030030060060090090012001200150015001800180021002100240024002700270030003000Utilisation %
    Canonical equations
    The exact relationships implemented by this engine.

    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.

    engineering methodology

    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.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the section width and depth.
    2. Choose the number and diameter of bars.
    3. Set f′c and fy.
    4. Enter the factored axial load and the unsupported length.

    The formula

    ϕPn,max=0.65⋅0.80[0.85fc′(Ag−Ast)+fyAst]\phi P_{n,max} = 0.65 \cdot 0.80 \left[0.85 f'_c (A_g - A_{st}) + f_y A_{st}\right]

    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

    Inputs
    • 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.
    Calculation path
    1. 1

      Ag = 160,000 mm²; steel ratio 1.0%.

    2. 2

      φPn,max = 0.65 × 0.80 × [0.85 × 28 × 158,392 + 420 × 1,608] = 2,310 kN.

    3. 3

      Utilisation: 1,500 / 2,310 = 64.9%.

    4. 4

      Slenderness klu/r = 3,000/115.5 = 26.0, above 22 — the column is slender.

    Result

    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.