GATE ME 2026 Set 1 — Question 51
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Strength of Materials → Stress, Strain & Elastic Constants → Elastic Constants & Poisson's Ratio
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Question
A cylindrical pressure vessel made of steel has diameter of and wall thickness of . For steel, Young’s modulus and Poisson’s ratio are and , respectively. The cylinder is designed such that the allowable normal strain at the outer cylindrical surface is equal to . The permissible pressure in the tank is ________ kPa (rounded off to 1 decimal place).
Correct answer
838 to 842
Solution
1.Identify Stresses in Thin Cylinder:
For a thin-walled cylindrical pressure vessel with internal pressure , diameter , and thickness :Hoop stress:
Longitudinal stress:
2.Strain Formulas:
The normal strains on the outer surface are:Hoop strain:
Longitudinal strain:
Since , the hoop strain is larger and will be the limiting factor.
3.Substitute Given Values:
, , , , .The permissible pressure is .
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