GATE 2026 ME – Question 51
A cylindrical pressure vessel made of steel has diameter of 3 m and wall thickness of 15 mm. For steel, Young's modulus and Poisson's ratio are 210 GPa and 0.3, respectively. The cylinder is designed such that the allowable normal strain at the outer cylindrical surface is equal to 0.00034. The permissible pressure in the tank is ________ kPa (*rounded off to 1 decimal place*).
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Correct answer: 835.80 to 844.20
Explanation
The hoop stress is $\sigma_h = \frac{pd}{2t}$ and the longitudinal stress is $\sigma_l = \frac{pd}{4t}$. The strain in the hoop direction is $\varepsilon_h = \frac{\sigma_h - \nu\sigma_l}{E} = \frac{pd}{2tE}(1 - 0.5\nu) = \frac{pd}{2tE} \times 0.85$. Setting $\varepsilon_h = 0.00034$ gives $p = \frac{0.00034 \times 2 \times 0.015 \times 210 \times 10^9}{3 \times 0.85} = 840{,}000$ Pa, which is 840.0 kPa.