Scope of the check
This calculator provides a fast, design-assist screen of column strength for axial load with biaxial moments. It is intended for preliminary sizing and comparison of alternatives, not final stamped design. Results depend on the assumptions shown on the page, including simplified interaction and simplified second‑order magnification.
Required project inputs
Prepare consistent units, a realistic column height, and end condition factors Kx and Ky. Enter service loads by type (dead, live, wind, seismic) for axial force and for moments about each principal axis. For reinforced concrete, provide f’c, fy, cover, bar diameter, tie diameter, and total longitudinal steel area Ast.
Section properties computed
From the selected shape, the tool computes gross area Ag and second moments of area Ix and Iy. It then derives radii of gyration rx and ry to estimate slenderness through K·L/r. For circular sections, properties are taken as identical about both axes; for rectangular sections, each axis is evaluated independently.
Axial capacity screening
For reinforced concrete, nominal concentric axial capacity is screened using a common expression: Pn0 = 0.85 f’c(Ag − Ast) + fyAst. A simplified strength factor φ is applied based on confinement type (tied versus spiral) to produce φPn. For steel and timber modes, the axial capacity shown is a simplified placeholder and must be verified using the relevant standard.
Biaxial moment interaction
Combined loading is checked using a linear interaction: Pu/φPn + |Mx|/φMn,x + |My|/φMn,y ≤ 1.0. For reinforced concrete, φMn is estimated using a simplified rectangular stress block approach with symmetric reinforcement assumptions. This is conservative for many cases but does not replace a full interaction diagram or code-specific biaxial reduction methods.
Slenderness and second-order effects
Slenderness is flagged when K·L/r becomes moderate to high. A simplified Euler buckling reference Pcr = π²EI/(KL)² is used to estimate a magnification factor δ = 1/(1 − Pu/Pcr), capped to prevent instability in the display. If your project is unbraced, has significant sway, or has high utilization, use a rigorous second‑order analysis.
Load combinations and governing case
A built‑in LRFD-style combination set is evaluated, and you can prepend one custom combination by supplying factors for D, L, W, and E. The governing case is the combination with the highest utilization. Use this output to focus your design effort: identify which load type or moment axis is driving the column sizing.
Interpreting utilization and next steps
Utilization below 1.0 indicates the section passes the simplified screen for the evaluated combinations. Utilization above 1.0 suggests increasing section size, increasing reinforcement, improving bracing to reduce effective length, or reducing applied moments through framing changes. Always confirm detailing limits (cover, spacing, minimum steel) and run code-compliant interaction and stability checks before finalizing.
FAQs
1) Does this replace code design for columns?
No. It is a preliminary screening tool that uses simplified strength and stability checks. Final design should follow your governing standard with full interaction diagrams, detailing rules, and second‑order analysis where required.
2) What does the utilization value mean?
Utilization is a combined demand-to-capacity indicator. This tool uses Pu/φPn + |Mx|/φMn,x + |My|/φMn,y. Values at or below 1.0 pass the simplified screen; higher values indicate the section likely needs revision.
3) Why are moments magnified for slender columns?
Slender columns can develop additional bending due to second‑order deflections (P‑Δ effects). The calculator applies a simplified magnification based on Pu relative to an Euler buckling reference to reflect that increased moment demand.
4) How should I choose Kx and Ky?
K depends on end restraints and frame stability. Typical values include about 1.0 for pinned-pinned, about 0.7 for fixed-fixed, and up to 2.0 for cantilevers. Use a code-aligned alignment chart or structural analysis for accuracy.
5) What is Ast, and how do I enter it?
Ast is the total longitudinal reinforcement area in the column. Enter the sum of all bar areas. The moment model assumes symmetric reinforcement and uses half of Ast as effective tension steel for each bending direction.
6) Can I model eccentric axial load directly?
Yes, by converting eccentricity into moments: M = P·e about the relevant axis. Add those moments into the appropriate load type fields (D, L, W, or E) so the combinations capture your intended eccentric loading.
7) Why do steel and timber look “simplified” here?
This file focuses on a consistent workflow across materials and includes placeholders for steel and timber axial capacity. For real projects, use steel section properties, code buckling curves, and timber stability factors from your governing standard.