Project ForgeStrength of Materials
Bending of Beams
GATE 2015
Medium
Consider a steel (Young's modulus E=200 GPa) column hinged on both sides. Its height is 1.0 m and cross-section is 10 mm × 20 mm. The lowest Euler critical buckling load (in N) is __________.
3290 N(± 6 accepted)
Explanation
Buckling occurs about the weak axis: I_min = (20×10³)/12 ≈ 1666.7 mm⁴ = 1.6667×10⁻⁹ m⁴. For a pin-pin column (K=1), Pcr=π²EI/L² = π²×200×10⁹×1.6667×10⁻⁹/1² ≈ 3290 N.
Source: GATE ME 2015 (Session 1) (2015)
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