GATE 2019 ME (ME1) – Question 31
A solid cube of side 1 m is initially at 32°C. Linear thermal-expansion coefficient is $10^{-5}/^\circ\mathrm C$ and bulk modulus 200 GPa. It is constrained on all sides and heated uniformly to 42°C. Find magnitude of induced mean volumetric stress (MPa).
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Correct answer: 59.5 to 60.5
Explanation
Full restraint prevents free volumetric strain $3\alpha\Delta T$. The opposing hydrostatic compressive stress is $3K\alpha\Delta T=3(200000)(10^{-5})(10)=\mathbf{60}$ MPa.