Euler buckling load of a pinned column

A 3 m steel column is pinned at both ends (K = 1). Its least second moment of area is 2.5 × 10⁶ mm⁴ and E = 200 GPa. Find the Euler buckling load and the factor of safety for a 120 kN axial service load.

Given

Solution

1. 1.Euler critical load
   $$P_{cr}=\frac{{\pi }^{2}EI}{(KL{)}^2}$$
   $$P_{cr}=548.3\mathrm{kN}$$
2. 2.Factor of safety against buckling
   $$FS=\frac{P_{cr}}{P_{service}}$$
   $$FS=4.57$$

Worked in ProveCalc

The effective length factor is a given you can change, so pinned, fixed and fixed-free cases are one edit apart, and every dependent result is marked stale until it is recomputed.

The results above were evaluated by ProveCalc's compute engine (SymPy and Pint), the same engine the desktop app runs on your machine.

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