Question

The steel rails of a railroad track (E_s = 200 GPa, α_s = 11.7 × 10^–6/°C) were laid at a temperature of 6°C. Determine the normal stress in the rails when the temperature reaches 48°C, assuming that the rails (a) are welded to form a continuous track, (b) are 10 m long with 3-mm gaps between them.

Answer 1

(a) Calculate the normal stress developed in continuous steel railroad track, due to change in temperature using the equation

…… (1)

Here, is the young’s modulus of steel. is the coefficient of thermal expansion for steel. is the change in temperature.

Calculate using the equation,

Here are the initial and final temperatures

Substitute for and for

Substitute 200 GPa for, for in equation (1)

Therefore, normal stress developed in the continuous track is

(b) Calculate the change in lengthin the railroad tracks due to change in temperature using the equation,

Here, L is the length of the rod.

Substitute 10 m for L

Since there is a gap between the railroad tracks is less than, the change in length will be restricted. Calculate the original change in length using the equation,

Here, is the gap between the railroad tracks.

Substitute, 3 mm for

Calculate strain using the equation

Calculate the normal stress developed in railroad track with restricted elongation using the equation

Therefore, the normal stress developed in railroad track, 3m long and with 3 mm restricted elongation is