How this calculator works
Euler theory describes a perfectly straight, slender, elastic column with centred axial load and ideal end restraints. Use the second moment for the buckling direction and the correct unbraced length. The reported Euler-Johnson transition sqrt(2 pi^2 E/sigma_y) is a screening measure, not a code capacity curve. Imperfections, residual stress, local buckling and inelastic behaviour reduce real capacity.
Formula
Pcr = pi^2 E I/(K L)^2; r = sqrt(I/A); lambda = K L/r; lambda_transition = sqrt(2 pi^2 E/sigma_y).
Worked example
For E = 200 GPa, I = 0.000001 m4, L = 2 m and pinned ends, Euler load is 493480.22 N. Changing to fixed-free ends reduces it to 123370.06 N.
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Frequently asked questions
Can Euler load exceed yield load?
It can mathematically. That indicates that elastic Euler theory is outside its useful regime, so use a suitable inelastic column method.
Which length factor should I use?
The presets describe ideal isolated restraints. Use a factor from the actual frame analysis where end rotation or sidesway differs.
Does the tool include an imperfection allowance?
No. It reports the ideal bifurcation load, not a factored design resistance.