GATE ME 2019 Set 1 — Question 31
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Strength of Materials → Stress, Strain & Elastic Constants → Elastic Constants & Poisson's Ratio
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Question
A solid cube of side is kept at a room temperature of . The coefficient of linear thermal expansion of the cube material is and the bulk modulus is . If the cube is constrained all around and heated uniformly to , then the magnitude of volumetric (mean) stress (in MPa) induced due to heating is ______.
Correct answer
59.5 to 60.5
Solution
1.When a solid cube is constrained in all directions and heated uniformly, it experiences a state of hydrostatic stress.
2.The volumetric strain that would occur if the cube were free to expand is:
where is the coefficient of linear thermal expansion and is the change in temperature.3.Since the cube is fully constrained, the net volumetric strain is zero. This induces a compressive volumetric (mean) stress such that:
where is the bulk modulus.4.Given:
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