COLUMNS & STABILITY
Calculate elastic critical load, buckling stress and slenderness for an ideal column with common end restraints.
Values are calculated locally in your browser.
Theoretical result · verify applicability below
Schematic illustration · not to scale
Euler assumes elastic buckling. Verify the critical stress is below the material proportional limit; yield strength alone does not establish validity.
A straight, slender column can lose stability before its material yields. Euler’s equation balances bending stiffness against effective length. Use the least second moment of area and the corresponding restraint for the governing buckling axis.
For E = 200 GPa, I = 100,000 mm⁴, A = 400 mm², L = 1,000 mm and K = 1, Pcr = 197.392 kN, σcr = 493.480 MPa and λ = 63.246. The high stress illustrates why the proportional limit must be checked.
The initial inputs reproduce this example. Material values are illustrative inputs, not a material database or certified design values.
Straight, prismatic, centrally compressed column; linear elastic material, ideal end restraints and no initial imperfections. This is a theoretical bifurcation load, not an allowable load. Verify elastic range and check both axes, local buckling and code reduction factors.
No factor of safety or design-code allowance is applied unless explicitly stated. Read the engineering disclaimer before applying these results.
Confirm the load direction and units first. Check the schematic against your actual supports and geometry, then compare the worked example with your own independent calculation. A valid numerical result does not establish that the model is appropriate for a real component.
For background, consult the Air Force Stress Analysis Manual’s column analysis and MIT’s Mechanics of Materials learning modules. Use applicable design standards and certified material data for real designs.