Project ForgeUniaxial compression test data for a solid metal bar of length 1 m shows a linear elastic response from O to yield point P (σ=100 MPa at ε=0.002), followed by nonlinear response up to Q (130 MPa) and R. The rod is pinned at both ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is __________ mm (round off to one decimal place).
Explanation
E=σ/ε at P = 100/0.002 = 50,000 MPa = 50 GPa. For buckling not to precede yielding, the Euler critical stress must equal the yield stress: σcr=π²E·d²/(16L²) [since I=πd⁴/64, A=πd²/4, Pcr/A=π²EI/(AL²)]. Setting σcr=σyield: d²=16σyieldL²/(π²E)=16×100×10⁶×1²/(π²×50×10⁹)≈0.003243 m², d≈0.0569 m ≈ 56.9 mm.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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