GATE 2022 ME (ME1) – Question 52
A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became $\bar{t}$. The corresponding change in the wall thickness of the cylindrical portion, i.e. $100 \times (\bar{t} - t)/t$, is ________% (round off to 3 decimal places).
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Correct answer: -0.070 to -0.050
Explanation
The perimeter changes by the hoop strain, so $\varepsilon_\theta = 0.001$. For a thin cylinder $\sigma_\theta = \frac{pr}{t}$ and $\sigma_L = \frac{\sigma_\theta}{2}$, with the radial stress neglected. Then $E\varepsilon_\theta = \sigma_\theta - \nu\sigma_L = \sigma_\theta\left(1 - \frac{\nu}{2}\right) = \frac{5}{6}\sigma_\theta$, and the thickness strain is $E\varepsilon_t = -\nu(\sigma_\theta + \sigma_L) = -\frac{1}{3} \times 1.5\sigma_\theta = -0.5\sigma_\theta$. So $\varepsilon_t = -\frac{0.5}{5/6}\varepsilon_\theta = -0.6 \times 0.001 = -0.0006$, which is a change of $-0.060\%$.