Question

A welded railway line, of length 15 km, is laid without expansion joints 

in a desert where the night and day temperatures differ by 50°C. The 

cross-sectional area of the rail is 3.6 × 10−3 m2. The rails are made of 

steel, which has Y = 2.0 × 1011 N/m2. (a) What is the difference in the 

night and day tension in the rail if it is kept at constant length? (b) If 

the rail is free to expand, by how much does its length change between 

night and day?

Answer 1

(a) Tension will be equal to:

$F = αΔTEA$

Thermal coefficient

$α = 13 \times 10^{-6}$

A is the cross-sectional area

$E = Y \\ F = 13 \times 10^{-6} \times 50 \times 2 \times 10^{11}\times 3.6 \times 10^{-3} \\ F = 468 \;kN$

(b) The length change between night and day will be equal to:

$ΔL = αLΔT \\ ΔL = 13 \times 10^{-6} \times 15 \times 10^3 \times 50 \\ ΔL = 9.75 \;m$