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Euler Buckling Load of a Braced Column

Hardcolumnsbucklingeuler
A 4 m long steel column with a 40 mm × 120 mm solid rectangular section is pinned at both ends. It is braced against buckling about its weak axis at midheight only. Taking E = 200 GPa, the theoretical Euler buckling load is most nearly:
  1. A79 kN
  2. B316 kN
  3. C711 kN
  4. D1,422 kN
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Answer: B. 316 kN

Each axis must be checked with its own effective length. Weak axis: I = (120)(40)³/12 = 6.40×10⁵ mm⁴ with an effective length of 2.0 m because of the midheight brace, giving P = π²EI/L² = 316 kN. Strong axis: I = (40)(120)³/12 = 5.76×10⁶ mm⁴ over the full 4.0 m, giving 711 kN. Buckling occurs at the smaller value, so the column fails about the weak axis at 316 kN. Ignoring the brace and using 4 m for the weak axis gives 79 kN.
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