Project ForgeThe rod PQ of length L with flexural rigidity EI is hinged at both ends: hinged to a wall at P, and hinged at Q to a roller resting on the ground. A horizontal force F is applied at Q (the rod makes a 45° angle with the vertical). For what minimum force F is it expected to buckle?
- Aπ²EI/L²
- B√2π²EI/L²
- π²EI/(√2L²)
- Dπ²EI/(2L²)
Explanation
Since the rod is pin-connected at both ends with no other transverse load, it's a two-force member: the internal axial force acts along the rod. At joint Q, horizontal equilibrium requires F=P_axial·cos45°, so P_axial=F/cos45°=F√2. Buckling occurs (pin-pin, effective length L) when P_axial=π²EI/L², i.e. F√2=π²EI/L² ⟹ F=π²EI/(√2L²).
Source: GATE ME 2008 (2008)
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