Project ForgeStrength of Materials
Stress & Strain
GATE 2014
Easy
A circular rod of length 'L' and area of cross-section 'A' has a modulus of elasticity 'E' and coefficient of thermal expansion 'α'. One end of the rod is fixed and the other end is free. If the temperature of the rod is increased by ΔT, then
- Astress developed in the rod is EαΔT and strain developed in the rod is αΔT
- Bboth stress and strain developed in the rod are zero
- stress developed in the rod is zero and strain developed in the rod is αΔT
- Dstress developed in the rod is EαΔT and strain developed in the rod is zero
Explanation
With one end free, the rod is completely free to expand — no external constraint develops any internal stress, so stress=0. The rod still physically elongates due to the temperature rise, giving a free thermal strain of αΔT.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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