Answer:
Ф = 0.02838 ft
F = 1,032 N
Explanation:
To find out gap delta,
As it is case of free thermal expansion,
First we start with, some assumptions we have to made to solve this problem.
1. Thermal Expansion Coefficient of Steel is ∝= 6.45 ×10^(-6)
2. Modulas of elasticity for A-36 steel is E= 200 GPa
3. Area of rail is assumed to be unit area.
The gape required can be given by,
Ф = ∝ × ΔT × L ... where Ф= Gap Delta in ft
ΔT= Temperature rise in F
= 90- (-20)
= 110 F
Ф = 6.45 ×10^(-6) × 110 × 40
Ф = 28,380 × 10^(-6) ft
Ф = 0.02838 ft .... total gape required for expansion of steel rails
Stress induced in rails is given by,
σ = ∝ × ΔT × E
= 6.45 ×10^(-6) × 110 × 200
σ = 1,41,900 Pa
Now, let's find axial force in rails,
Here,we have to consider ΔT= 20 F.
As due to temperature change, axial force generated in rails can be find by,
F = A × ∝ × ΔT× E × L
F = 1 × 6.45 × 10^(-6) × 20 × 200 × 10^(-9) × 40
F = 25,800 × 40 × 10^(-3)
F = 10,32,000 × 10^(-3)
F= 1,032 N
Finally, due to temperature change, rail is subjected to axial force, axial stress.
