A steel rod of $20\text{ mm}$ diameter passes centrally through a cop…

Question

A steel rod of $20\text{ mm}$ diameter passes centrally through a copper tube of $50\text{ mm}$ external diameter and $40\text{ mm}$ internal diameter. The tube is closed at each end rigid plates of negligible thickness. The nuts are tightened lightly home on the projecting parts of the rod. If the temperature of the assembly is raised by $50\text{ }^\circ\text{C}$, calculate the stresses developed in copper and steel, Take E for steel and copper as $200\text{ GN/m}^2$ and $100\text{ GN/m}^2$ and $\alpha$ for steel and copper as $12 \times 10^{-6}\text{ per }^\circ\text{C}$ and $23 \times 10^{-6}\text{ per }^\circ\text{C}$. [20]

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