Project ForgeA cylindrical bar has length L=5m and cross-section area S=10m². It is made of a linear elastic material with density ρ=2700 kg/m³ and Young's modulus E=70 GPa. The bar is suspended from its top and is in uniaxial tension due to its own self-weight. The elastic strain energy stored in the bar equals ______ J. (Rounded to two decimal places, g=9.8 m/s²)
Explanation
At height y above the free (bottom) end, axial stress σ(y)=ρgy (weight of bar below, divided by area). Strain energy U=∫₀ᴸ [σ(y)²/(2E)]·S dy=(Sρ²g²)/(2E)·∫₀ᴸy²dy=(Sρ²g²L³)/(6E). Plugging in S=10, ρ=2700, g=9.8, L=5, E=70×10⁹: U≈2.08 J.
Source: GATE ME 2023 Official Paper (2023)
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