GATE ME 2024 Set 1 — Question 57
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Strength of Materials → Stress, Strain & Elastic Constants → Mohr's Circle
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Question
The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle 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).
Correct answer
12.3 to 12.7
Solution
1.Calculate the principal stresses:
- Internal pressure kPa MPa.
- Diameter m mm.
- Thickness mm.
- Hoop stress MPa.
- Longitudinal stress MPa.
The weld line makes an angle with the longitudinal axis. The normal to the weld line makes an angle with the longitudinal axis.
The normal stress on a plane whose normal is at angle to the longitudinal axis is:
Thus, the normal stress acting on the weld is 12.5 MPa.
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