GATE ME 2014 Set 1 — Question 16
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Strength of Materials → Stress, Strain & Elastic Constants → Thermal Stresses
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Question
A circular rod of length ‘’ and area of cross-section ‘’ has a modulus of elasticity ‘’ and coefficient of thermal expansion ‘’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by , then
Correct answer
(C) stress developed in the rod is zero and strain developed in the rod is α Δ T
Solution
When a rod is heated, it undergoes thermal expansion. The free thermal strain is given by .
Thermal stress is only developed if the expansion is restricted. In this case, one end of the rod is free, meaning the rod can expand freely without any constraint.
Thermal stress is only developed if the expansion is restricted. In this case, one end of the rod is free, meaning the rod can expand freely without any constraint.
1.Since expansion is free, no internal resistive force is generated, so stress developed = 0.
2.The rod undergoes expansion, so the strain developed = .
Thus, option (C) is correct.Continue learning with Success Tracker
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