Calculator Inputs
Use section properties or direct radii of gyration. The input grid is responsive: three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
This example uses section properties to illustrate a typical calculation workflow.
| Parameter | Example value |
|---|---|
| Unsupported length about x-axis | 3.5 m |
| Unsupported length about y-axis | 3.0 m |
| End condition about x-axis | Pinned - Pinned (K = 1.0) |
| End condition about y-axis | Fixed - Pinned (K = 0.7) |
| Area | 12,000 mm² |
| Ix | 67,500,000 mm⁴ |
| Iy | 27,648,000 mm⁴ |
| Elastic modulus | 200,000 MPa |
| Computed rx | 75.000 mm |
| Computed ry | 48.000 mm |
| Slenderness ratio about x-axis | 46.667 |
| Slenderness ratio about y-axis | 43.750 |
| Governing axis | X-axis |
| Euler critical load about x-axis | 10,876.707 kN |
| Euler critical load about y-axis | 12,375.275 kN |
Formula Used
1) Radius of gyration: r = √(I / A)
2) Effective length: Le = K × L
3) Slenderness ratio: λ = Le / r = KL / r
4) Euler critical stress: σcr = π²E / λ²
5) Euler critical load: Pcr = π²EI / (KL)²
How to Use This Calculator
- Select whether you want to enter section properties or direct radii of gyration.
- Choose units for length, area, inertia, radius, modulus, yield strength, and service load.
- Enter unsupported lengths for both axes. Use separate values if restraint differs by direction.
- Select end conditions for each axis or enter custom K factors.
- Enter area and either Ix/Iy or rx/ry, depending on the chosen mode.
- Add elastic modulus. Yield strength and service load are optional enhancements.
- Press the calculation button to show results above the form and below the header.
- Review the governing axis, slenderness ratio, Euler stress, critical load, and the Plotly graph. Export data with CSV or PDF buttons.
FAQs
1) What does column slenderness ratio tell me?
It compares effective length to radius of gyration. A higher value means the column is more likely to buckle before material crushing or yielding governs.
2) Why are there separate x-axis and y-axis values?
Columns can buckle about either principal axis. The weaker axis usually governs because it often has a smaller radius of gyration or a less favorable restraint condition.
3) What is the effective length factor K?
K adjusts the unsupported length to reflect end restraints. Fixed ends reduce effective length, while cantilever behavior raises it and increases buckling sensitivity.
4) Should I use section properties or direct radii?
Use section properties when you know area and moments of inertia. Use direct radii when a catalog or steel table already provides rx and ry values.
5) Is Euler critical load always the design load capacity?
No. Euler load is an ideal elastic buckling benchmark. Real design capacity also depends on code provisions, imperfections, residual stresses, material strength, and load combinations.
6) Why compare Euler stress with yield strength?
The comparison helps indicate whether elastic buckling may occur before yielding. If Euler stress exceeds yield strength, material yielding may control earlier than ideal Euler buckling.
7) What happens if the service load is entered?
The calculator estimates a simple Euler factor of safety by dividing governing Euler critical load by the entered service load. It is informative, not a code check.
8) Can I use this for final structural approval?
Use it for screening, comparison, and education. Final approval should always follow the governing structural code, project details, connection behavior, and licensed engineering review.