Project ForgeStrength of Materials
Bending of Beams
GATE 2019
Hard
Consider a prismatic straight beam of length L=π m, pinned at both ends, with a square cross-section of side p=6 mm. E=200 GPa, and the coefficient of thermal expansion α=3×10⁻⁶ K⁻¹. The minimum temperature rise required to cause Euler buckling of the beam is ___ K.
1 K(± 0.05 accepted)
Explanation
Euler critical load for a pinned-pinned column: Pcr=π²EI/L². The fully-restrained thermal compressive force is P_thermal=EAαΔT. Setting them equal and using I/A=p²/12 for a square section: ΔT = π²(p²/12)/(αL²) = π²(0.006²/12)/(3×10⁻⁶×π²) = (0.006²/12)/(3×10⁻⁶) = 1.0 K.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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