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For K-12 Students · Column Buckling

Column Buckling for a stair stringer

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a stair stringer live below — adjust the inputs and watch it respond, right in your browser.

Column Buckling (Euler)Live

critical load & slenderness

Controls

Presets

Young's modulus E (GPa)

Moment of inertia I (10⁶ mm⁴)

Length L (m)

Cross-section area (mm²)

A slender column fails not by crushing but by buckling sideways at the Euler critical load Pcr = π²EI/(KL)². The effective-length factor K depends on the end restraints — fixing both ends quadruples the capacity versus pinned. Educational tool, not a substitute for code-based design.

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Data Inspector

Critical load Pcr2193 kN

Effective length3.00 m

Slenderness KL/r52

Critical stress731 MPa

Governing equation

P_{cr} = \frac{π ^{2} E I}{( K L ) ^{2}} = \frac{π ^{2} ( 200 GPa ) ( 10 \times 1 0 ^{6} mm ^{4} )}{( 1 \times 3 m ) ^{2}} = 2193 kN

Reading this result: Intermediate slenderness (KL/r = 52): buckling and yielding compete, so design codes blend the two rather than trusting Euler alone.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Column Buckling for a stair stringer" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.