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GATE 2020 ME (ME2) – Question 40

Mechanics of Materials · Thermal stresses, strain gauges and rosettes · 2 marks · Multiple choice

A thin-walled cylinder of radius r and thickness t is open at both ends and fits snugly between rigid walls at ambient conditions. Material has Young’s modulus E, Poisson ratio ν and thermal expansion α. For uniform cylinder temperature and no buckling, find minimum temperature rise ΔT needed to prevent gas leakage when storing gas at gauge pressure p.

Diagram for GATE 2020 ME (ME2) question 40
  1. $\Delta T=3\nu pr/(2\alpha tE)$
  2. $\Delta T=(\nu-1/4)pr/(\alpha tE)$
  3. $\Delta T=\nu pr/(\alpha tE)$
  4. $\Delta T=(\nu+1/2)pr/(2\alpha tE)$

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Correct answer: (C) $\Delta T=\nu pr/(\alpha tE)$

Explanation

Hoop stress is pr/t. At the limiting condition the axial contact force is zero, so axial stress is zero. Axial strain is then $\epsilon_z=-\nu pr/(tE)+\alpha\Delta T$. Preventing separation requires εz≥0, hence **ΔTmin=νpr/(αtE),C**. Closed-end axial pressure stress must not be added to this open-ended shell.