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Question
A uniform steel rod of 5 mm2 cross section is heated from 0°C to 25°C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain.
(α for steel = 12 x 10-6/°C and γ for steel = 20 x 101ON/m2)
Solution
Given that α steel = 12 x 10-6 /°C, γ steel = 20 x 1010 N/m2
Area of cross-section of the rod, A = 5 mm2 = 5 × 10−6 m
Change in temperature (ΔT), (T2 − T1) = 25°C
Force exerted by the rod due to heating = Thermal stress × Area
Thermal stress = γ x Strain
= γsteel x αsteel x ΔT
Therefore, the force exerted by the rod due to heating is
= γsteel x αsteel x ΔT x A
= 20 x 1010 x 12 x 10-6 x 25 x 5 x 10-6
= 300 N
`"Strain" = "Change in length"/ "Original length"= alphaDelta"T"`
Strain = αsteelΔT
= 12 x 10-6 x 25
= 3 x 10-4
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