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GATE 2024 ME – Question 57

Mechanics of Materials · Thin-walled pressure vessels · 2 marks · Numerical answer

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha = 60°$ with the horizontal. The closed vessel has a wall thickness of 10 mm and diameter of 2 m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is __________ MPa (*rounded off to 1 decimal place*).

A horizontal thin cylindrical vessel with hemispherical ends. A weld line crosses the cylindrical part at an angle $\alpha$ of 60° to the horizontal axis.

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Correct answer: 12.44 to 12.56

Explanation

The hoop stress is $\sigma_h = \frac{pd}{2t} = \frac{200 \times 10^3 \times 2}{2 \times 0.01} = 20$ MPa and the axial stress is $\sigma_a = \frac{pd}{4t} = 10$ MPa. The weld line is at 60° to the axis, so the normal to the weld plane is at 30° to the axis. The normal stress on that plane is $\sigma_n = \sigma_a\cos^2 30^\circ + \sigma_h\sin^2 30^\circ = 10(0.75) + 20(0.25) = 12.5$ MPa.