GATE ME 2014 Set 1 — Question 50
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Strength of Materials → Stress, Strain & Elastic Constants → Thermal Stresses
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Question
A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250°C. If the Young’s modulus and coefficient of thermal expansion are 200 GPa and , respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _______
Correct answer
499 to 501
Solution
When a rod is held between two immovable rigid walls and its temperature is increased, it tries to expand but is prevented by the walls, leading to the development of thermal stress.The thermal strain that would have occurred if the rod were free is:Since the walls are rigid and immovable, the net strain is zero. Thus, the compressive stress developed is:Given:
- Young's modulus,
- Coefficient of thermal expansion,
- Temperature rise,
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