GATE CE 2017 Set 1 — Question 4
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Structural Engineering → Stress, Strain & Beams → Thermal Stress
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Question
An elastic bar of length , uniform cross sectional area , coefficient of thermal expansion , and Young's modulus is fixed at the two ends. The temperature of the bar is increased by , resulting in an axial stress . Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be
Correct answer
(A) σ
Solution
Thermal stress in a bar fixed at both ends is given by the formula . This expression is independent of the length of the bar. When the temperature increases, the bar tries to expand by . Since the ends are fixed, a compressive force develops to counteract this expansion, such that . Solving for stress , we get . Since cancels out, doubling the length has no effect on the axial stress.
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