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

Previous year question for MECHANICS OF SOLIDS.

Question

A steel rod $20\text{ mm}$ diameter passes centrally through a copper tube of $25\text{ mm}$ internal diameter and $35\text{ mm}$ external diameter. Copper tube is $800\text{ mm}$ long and is closed by rigid washers of negligible thickness which are fastened by the nut threaded on the rod. The nuts are tightened till the load on the assembly is $20\text{ KN}$. Calculate initial stresses in the copper tube and steel rod. Calculate the increase in the stresses when one nut is tightened by one quarter of a turn relative to the other. Take pitch of the thread as $1.6\text{ mm}$. Take $E$ for steel and copper as $200\text{ GPa}$ and $100\text{ GPa}$ respectively.

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