1. Rails are laid such that there is no stress in them at 24°C. If the rails are 32 m long, determine:

A. The stress in the rails at 80°C when there is no allowance for expansion.

B. The stress in the rails at 80°C when there is an expansion allowance of 8 mm per rail.

C. The expansion allowance for no stress in the rails at 80°C.

D. The maximum temperature for no stress in the rails when the expansion allowance is 8 mm.

* Given:
- Coefficient of linear expansion, [tex]\alpha = 11 \times 10^{-6}/°C[/tex]
- Young's Modulus, [tex]E = 205 \text{ GPa}[/tex].

To calculate the stress in the rails at different temperatures, we use the formula stress = α * ΔT * E, where α is the coefficient of linear expansion, ΔT is the temperature difference, and E is the modulus of elasticity.

By plugging in the given values, we can find the stress in the rails at 80°C with and without an expansion allowance.
To find the expansion allowance, we use the formula ΔL = ΔT * α * L, where ΔL is the expansion allowance, ΔT is the temperature difference, α is the coefficient of linear expansion, and L is the length of the rails. By plugging in the given values, we can determine the expansion allowance for no stress in the rails at 80°C.

To find the maximum temperature for no stress in the rails when there is an expansion allowance, we use the formula ΔT = ΔL / (α * L), where ΔT is the temperature difference, ΔL is the expansion allowance, α is the coefficient of linear expansion, and L is the length of the rails. By plugging in the given values, we can determine the maximum temperature for no stress in the rails.Remember to convert units consistently throughout the calculations to ensure accurate results.

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