A steel rod is lying horizontally on a frictionless table top as shown in the figure. the temperature starts rising from 293 K to 393 K. Calculate Thermal Stress developed in the steel rod. Coefficient of thermal conductivity of steel = 50 W/m K and E = 210 GPa. The length of the rod is 2000 mm.
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Length of the rod as a function of temperature L
′
=L(1+αΔT)
where α is the coefficient of thermal expansion.
ΔT is the change in temperature
∴ ΔL=L
′
−L=LαΔT
Strain
L
ΔL
=αΔT ............(1)
From Hooke's law, Y=
Strain
Stress
⟹Stress=Y×Strain
∴ Stress =Y×αΔT
⟹ Stress is independent of L
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