Heat-related temporary speed restrictions (TSRs)

The rail is subjected to a range of temperatures, from the coldest temperatures in winter to the hottest days in summer. In continental US or Europe this can easily be − 10 to + 30°C (ΔT = 40°C), giving a thermal strain αΔT of 12 × 10− 6 × 40, or 0.48 × 10− 3 (α value of steel taken from Table 31.1). Over a 3-km length of CWR, this would produce a length change of 1.44 m! Clearly, something has to be done to stop the rail expanding/contracting.

For each km of track, there will approximately 2000 ties, so there are 2000 clips bearing down on each rail. The combined friction of all these clips stops the rail sliding over the ties. The ties themselves are very heavy, and are set in tightly packed ballast consisting of self-locking chips of broken stone (e.g., granite). This means that the ties do not move over the ground either, so the track is unable to expand or contract. The thermal strain is neutralized by an equal and opposite elastic strain, which produces a locked-in thermal stress given by
(31.7)σ=EαΔT

For ΔT = 40°C, σ = 200 × 103 MN m− 2 × 0.48 × 10− 3 = 96 MN m− 2 (E value of ferritic steel taken from Table 3.1). This is much less than the yield stress of the steel, so the rail stays elastic.