COLUMNS & STABILITY
Evaluate the Johnson parabola and automatically switch to Euler above the transition slenderness.
Values are calculated locally in your browser.
Theoretical result · verify applicability below
Schematic illustration · not to scale
Johnson’s empirical parabola joins the compressive yield strength at zero slenderness to Euler’s elastic curve at Cc. Below the transition this tool uses Johnson; above it, the reported stress and load use Euler to avoid extending the parabola beyond its domain.
With E = 200 GPa, Sy = 250 MPa, r = 10 mm, L = 1,000 mm, K = 1 and A = 400 mm²: λ = 100, Cc = 125.664, σcr = 170.843 MPa and Pcr = 68.337 kN.
The initial inputs reproduce this example. Material values are illustrative inputs, not a material database or certified design values.
Ideal centrally loaded prismatic column and a ductile material for which Johnson’s empirical approximation is appropriate. Residual stress, eccentric loading, imperfections and local buckling are excluded. Stub columns still require a direct compression check.
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.