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Question

An iron rod of length 1 m is fixed between two walls as shown in figure. Find thermal stress and thermal strain developed in the rod if it is heated by ΔT=20C
(Given: Coefficient of linear expansion of iron is 1.2×105 C1; Young's modulus of iron is 2×1011 N/m2).


A
24×107 N/m2, 48×105
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B
48×106 N/m2, 32×104
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C
32×107 N/m2, 48×104
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D
48×106 N/m2, 24×105
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Solution

The correct option is D 48×106 N/m2, 24×105
We know that,
Thermal strain =αΔT=ΔLLo
Where, α= Coefficient of linear expansion
ΔT= Change in temperature
Lo= Original length
ΔLLo=1.2×105×20=24×105

Also,
Thermal stress =YαΔT
=2×1011×1.2×105×20
=48×106 N/m2

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