Continuous Welded Rail Thermal Force and Neutral Temperature

Above its neutral temperature it is in compression and can buckle; below it, in tension and can pull apart. The force does not depend on the length of the rail, only on its area, its modulus, and how far it is from neutral, which is why a mile of CWR and a hundred feet of it develop the same force per degree. For a 13.0 sq in rail section at 30,000,000 psi and a coefficient of 0.0000065 per degF, that force is 2,535 pounds per degree per rail. The field number worth carrying alongside it is that rail in direct sun runs roughly 20 to 30 degF hotter than the air, and it is rail temperature that matters, not air temperature. Rail laid at a 95 degF neutral, on a 95 degF afternoon with a 25 degF sun adder, is sitting at 120 degF -- 25 degrees above neutral, 63,375 lb of compression in each rail and 126,750 lb in the track. That is what a sun kink is: the ballast section and the fastenings resist that force laterally, and when the resistance drops because the track was freshly surfaced, the shoulders were disturbed, or the ballast is thin, the track buckles. It is why hot-weather work that disturbs ballast carries slow orders, and why neutral temperature is set deliberately when rail is laid or destressed rather than being whatever the day happened to be. The winter case is the mirror: the same rail at 10 degF is 85 degrees below neutral and carries 215,475 lb of TENSION, which is what pulls a broken weld or a defect apart. This assumes FULLY restrained rail, which is the design intent for CWR but is not true near rail ends, at joints, at bridge expansion arrangements, or where fastenings have degraded; partially restrained rail develops less force and more movement. It does not predict the buckling temperature, which depends on lateral resistance from the ballast and fastenings, alignment imperfections, curvature, and vertical load, and which requires a track buckling analysis rather than a force calculation. It does not determine the correct neutral temperature for a location, decide whether rail needs destressing, or address rail adjustment procedures, and it does not evaluate rail defects or welds. This is a derailment-hazard subject: the FRA Track Safety Standards at 49 CFR 213 including the CWR plan requirements, the railroad's own CWR procedures, and the track owner govern.

F = A x E x alpha x (T rail - T neutral), in lb from sq in, psi, and per degF; force in the track = 2 x force per rail; rail temperature = air temperature + sun adder.

The restrained thermal force relation for continuous welded rail, by name, with 49 CFR 213 named for the CWR plan requirements. Rail area, modulus, and coefficient of expansion are entered. The railroad's own CWR procedures and the track owner govern.

49 CFR 213 is US federal regulation and public domain; the force relation is elementary mechanics on user-entered section properties.

Estimate. AHJ and licensed professional govern.

Field names used by the API: rail_area_in2, modulus_psi, alpha_per_degf, neutral_temp_f, air_temp_f, sun_adder_f, force_per_degf_lb, rail_temp_f, differential_f, force_per_rail_lb, force_track_lb

• Force is independent of length only area, modulus, and the differential from neutral enterrestrained thermal expansion
• Rail runs hotter than air roughly 20 to 30 degF above air temperature in direct sun; rail temperature is what governsrailroad CWR procedures
• Fully restrained is an assumption not true near rail ends, at joints, at bridge expansion arrangements, or with degraded fastenings49 CFR 213 CWR plan