calcnote ACI 318-19
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Column design calculator

Project metadata
Geometry

Nonsway frames only (ACI 318-19 §6.6.4.3). For a sway column this result does not apply.

Section shape

Horizontal dimension of the section.

Vertical dimension of the section.

X Y

Clear distance between lateral supports.

Use 1.0 unless an alignment chart or frame analysis gives a lower value (nonsway range 0.5 to 1.0).

Max factored sustained axial load ÷ max factored axial load (ACI §6.6.4.4.4). Required only when kl/r exceeds the short-column limit; leave blank for short columns.

Materials

Normal weight: Ec = 57,000√f′c psi (§19.2.2.1(b)). Lightweight: Ec = wc^1.5 · 33 · √f′c psi (§19.2.2.1(a)).

Used in clear spacing checks: bar spacing (ACI §25.2.3) and spiral spacing (§25.7.3.1) require at least (4/3) times the maximum aggregate size.

Concrete weight
Reinforcement

Clear spacing between bars must be at least max(1.5 times the bar diameter, 1.5 in, (4/3) times the maximum aggregate size).

Tie arrangement and crossties (§25.7.2.3) are not checked.

Concrete surface to outside of tie. Not to bar centroid; δ is computed from this.

All-face: bars distributed across all four faces. Two-face: bars on the top and bottom faces only (physical faces, independent of bending axis).

Confining ties. Must be #4 for #11 longitudinal bars (ACI §25.7.2.2).

Upper limit: min(16·d_bar, 48·d_tie, b, h) per ACI §25.7.2.1. Engine checks.

Loads

Factored loads per ACI 318-19 load combinations, not service loads. Axial compression only: combinations with net axial tension cannot be checked. Add multiple load cases; the governing case (highest D/C) is reported.

Transverse load between supports

No transverse load between supports. Cm from end-moment ratio per ACI 318-19 §6.6.4.5.3(a).

Axis choice

About X: bending about the horizontal axis, depth = h. About Y: bending about the vertical axis, depth = b. The section drawing above shows which face is in compression.

Curvature

Single: column bends in one direction. Double: column reverses between its ends.

Case Pu (kip) M2 (kip-ft) M1 (kip-ft)
LC1
1/25

M1 ≤ M2. Enter as positive (zero permitted for moment).

What this calculator checks

This calculator evaluates a reinforced-concrete column section against ACI 318-19 for combined axial load and uniaxial bending (about X or Y). It covers rectangular sections with rectilinear ties and circular sections with ties or continuous spirals, under non-sway (braced) framing conditions.

The check runs a strain-compatibility analysis at the operating point on the P-M interaction diagram and reports a demand-to-capacity ratio (D/C). Capacity is reduced by the strength-reduction factor φ per §21.2.2, interpolated between compression-controlled (0.65 tied, 0.75 spiral) and tension-controlled (0.90) limits based on net tensile strain. Maximum nominal strength is capped at Pn,max = 0.80Po (tied) or 0.85Po (spiral) per §22.4.2.1.

Beyond the capacity check, the calculator evaluates:

  • Slenderness: effective slenderness ratio kl/r against the short-column limit of min(34 − 12M1/M2, 40) per §6.2.5, with moment magnification for slender columns per §6.6.4
  • Materials: normal-weight or lightweight concrete with Ec from §19.2.2.1(a) or §19.2.2.1(b); separate transverse steel grade (fyt) for spiral reinforcement
  • Clear bar spacing against aggregate size per §25.2.3
  • Transverse-load Cm factor: when loads act between supports, Cm = 1.0 per §6.6.4.5.3(b) instead of the end-moment formula
  • Detailing conformance: tie arrangement per §25.7.2, spiral pitch and ratio per §25.7.3 (Eq. 25.7.3.3), and clear spacing limits
  • Minimum eccentricity (M2,min) per §6.6.4.5.4, applied as advisory for short columns and binding for slender columns

D/C ratios are rounded conservatively: PASS results floor (toward zero) and FAIL results ceiling (away from zero), so a marginal section is never reported as passing due to rounding.

How to use it

  1. Choose a section shape (rectangular or circular) and enter the cross-section dimensions and unsupported length.
  2. Set the effective-length factor k (0.5 to 1.0, non-sway range). Use 1.0 unless an alignment chart or frame analysis gives a lower value.
  3. Specify materials. Select concrete strength (f’c) and type (normal-weight or lightweight). For lightweight concrete, enter the equilibrium density wc (90 to 120 pcf). Choose the maximum aggregate size for clear-spacing checks.
  4. Define reinforcement. Pick bar size, count and layout. For circular sections with spirals, specify the spiral bar size, pitch and transverse steel grade (fyt, 60 or 80 ksi).
  5. Enter loads. Enter factored axial load Pu and end moments M1 (smaller) and M2 (larger) as magnitudes. Select single or double curvature. If transverse loads act between supports, toggle the transverse-load option so the calculator uses Cm = 1.0.

The section drawing (rectangular shapes) updates as you change dimensions, showing axes, compression face and bar positions.

What you get

A result page showing the D/C ratio, PASS or FAIL verdict, the governing ACI clause, and a summary of all intermediate values (Ec, Ig, EI, Pc, δns, φPn, φMn). The page includes a P-M interaction diagram with the operating point plotted, and a detailing-conformance table listing tie arrangement, spiral ratio, and clear spacing results.

From the result page you can download a formatted Word (.docx) calc note containing all inputs, intermediate calculations, the P-M diagram and the verdict. The document is ready for review by the engineer of record or for project-file archival.

Verified against published references

The engine is cross-validated against 14 test cases drawn from Wight's Reinforced Concrete: Mechanics and Design (7th ed.) and StructurePoint spColumn v10.00, covering rectangular and circular sections, tied and spiral confinement, short and slender columns, single and double curvature, Grade 60 and Grade 80 steel, and bending about X or Y.

Full derivations, point-by-point comparisons and any deliberate divergences are published in the verification report. Every test case can be loaded directly into this calculator from its verification page.

Scope and limits

  • Non-sway only. The effective-length factor k is capped at 1.0. Sway (unbraced) columns with k > 1.0 are outside scope; for those, a second-order frame analysis per §6.7 or §6.8 is needed.
  • Uniaxial bending. The check evaluates bending about one axis at a time. Biaxial bending is not covered.
  • Non-seismic detailing. Tie and spiral rules follow Chapter 25 (non-seismic). Seismic detailing per §18 is not implemented.
  • No fire or sustained-load deflection. The calculation addresses strength at the ultimate limit state only.
  • Single load combination. Each run checks one (Pu, M1, M2) set. The engineer of record must verify all governing load combinations.

Frequently asked questions

Which ACI 318-19 clauses does this calculator implement?
Axial and flexural strength per §22.4, moment magnification for non-sway frames per §6.6.4, slenderness screening per §6.2.5, the strength-reduction factor per §21.2.2, minimum eccentricity per §6.6.4.5.4, and detailing checks per §25.7 (tie arrangement, spiral ratio, clear spacing). Seismic detailing (§18) is not covered.
Is this calculator free?
Yes. All checks, the P-M diagram and the downloadable Word calc note are available at no charge.
Does it support lightweight concrete?
Yes. Select "Lightweight" under concrete type and enter the equilibrium density. Ec is computed from §19.2.2.1(b) and the modification factor λ is applied per §19.2.4.
Can I check bending about the Y axis?
Yes. For rectangular sections, select the bending axis (X or Y). The calculator swaps depth and width, reorients the bar layout, and evaluates capacity about the chosen axis. Circular sections are axis-symmetric, so the axis choice does not apply.
How is the calculator verified?
Against 14 test cases from Wight (7th ed.) and StructurePoint spColumn v10.00. The full comparison, including point-by-point anchor values and any deliberate divergences, is published in the verification report.