The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap delta so that the rails just touch one another when the temperature is increased from T1, = - 20°F to T2 = 90°F. Using this gap, what would be the axial force in the rails if the temperature were to rise to T3 = 110 degree F?

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.