GATE 2016 ME (ME2) – Question 45
A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200o C, the axial stress developed in the rod is __________ MPa. Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10−5 per oC.
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Correct answer: 239 to 241 OR -241 to -239
Explanation
Free thermal expansion would be αLΔT=1e−5·250·200=0.50mm. Only0.20mm is available, so restrained expansion is0.30mm and compressive mechanical strain is−0.30/250=−0.0012. Stress is200000·(−0.0012)=**−240MPa**. The final key also accepts the positive magnitude240MPa; both ranges are retained.