The thermal stress in the rail is 8.8 × 10⁷ N/m² when the rail temperature is raised to 35°C.
Young's Modulus:
Given that the initial temperature of the rails is, T = -5°C,
The final temperature of the rails is, T' = 35°C
Young’s modulus for steel is Y = 20 × 10¹⁰ N/m²
According to Hooke's Law, we know that Young’s modulus is defined as:
Y = stress/strain
The strain developed due to an increase in temperature is :
strain = αΔT
where α is the coefficient of thermal expansion = 11×10⁻⁶ for steel
ΔT = temperature difference = T' -T = 35° - (-5°) = 40°C
so,
strain = 11×10⁻⁶×40
Now,
Y = stress/strain
20 × 10¹⁰ = stress/11×10⁻⁶×40
stress = 20×10¹⁰ × 11×10⁻⁶ × 40
stress = 8.8 × 10⁷ N/m²
Learn more about Hooke's Law:
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