GATE ME 2020 Set 2 — Question 40
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Strength of Materials → Stress, Strain & Elastic Constants → Thermal Stresses
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Question
A thin-walled cylinder of radius and thickness is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure. The material of the cylinder has Young's modulus , Poisson's ratio , and coefficient of thermal expansion . What is the minimum rise in temperature of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of above the atmosphere?
Correct answer
(C) Δ T = (pr)/(α t E)
Solution
To prevent gas leakage, the cylinder must remain in contact with the rigid walls. This means the net axial strain must be zero or positive (tending to expand against the walls).
The internal pressure causes a hoop stress . Due to the Poisson effect, this causes an axial strain .
The rise in temperature causes a thermal axial strain .
For the cylinder to just maintain contact (prevent leakage), the total axial strain must be at least zero:The minimum rise in temperature is , which matches option (C).
The internal pressure causes a hoop stress . Due to the Poisson effect, this causes an axial strain .
The rise in temperature causes a thermal axial strain .
For the cylinder to just maintain contact (prevent leakage), the total axial strain must be at least zero:The minimum rise in temperature is , which matches option (C).
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