Beams & Columns — Bending & Buckling

Columns — buckling, the sneaky failure

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: a slender column doesn't crush — it suddenly bows out sideways at a load far below its crushing strength. Euler's formula gives that critical load P_cr = π²·E·I / L² (for pinned ends). It depends on stiffness and length squared, not on strength at all.

d_{col} := 30 mm

= 30 mm a round column

I_{col} = \frac{\pi \cdot d_{col}^{4}}{64}

= 39761 mm^4 second moment for a circle

L_{col} := 2 m

= 2 m column length

P_{crit} := \pi ^2 * E_{beam} * I_{col} / L_{col}^2 in kN

= 19.621 kN buckling load ≈ 19.6 kN

✓ pass

P_{crit} > 0 kN

the load at which it bows out (longer column ⇒ much smaller P_crit)

Real-world hook: buckling is why a soda can crushes flat, why scaffolding is cross-braced, and why you can't hold up a load with a length of cooked spaghetti.

Where next: the track shifts from solids to energy — Thermodynamics governs engines, heat, and efficiency.