End condition & section
Material & load
Results
Critical stress curve
Buckled mode shape
Theory & key formulas
$$P_{cr}=\frac{\pi^2EI}{(KL)^2}$$
$$\sigma_{cr}=F_y\left(1-\frac{F_y}{4\pi^2E}\left(\frac{KL}{r}\right)^2\right)$$
Choose end conditions and cross-section geometry, then compute Euler or Johnson critical load, slenderness ratio, and safety factor with live buckled-shape visualization.
A slender column may fail by instability before the material reaches its yield stress. Euler's formula dominates for long columns, while Johnson's parabola gives a practical estimate for intermediate columns.
$$P_{cr}=\frac{\pi^2EI}{(KL)^2}$$The stress curve shows where the current column falls on the slenderness axis. The shape plot shows the assumed buckled mode for the selected end condition, making the role of the effective length factor easier to see.
Use the simulator for early sizing of columns, braces, struts, and machine frames. Real designs should also check imperfections, eccentric loading, connection stiffness, local buckling, and the governing building or machine-design code.