Let's see if I can come up with a simplified version:
First, If there is a problem with the zero stress temperature being too low (or high), you do not have to relay the track to change it. What you do is knock off the anchors if standard wood ties and spikes, make a cut and stretch the rail, either vibrating and pulling or heating, vibrating and pulling, then re-welding and re-apply the anchors. If it is on concrete ties with spring clips, then you knock the clip loose, the go through the cut and stretch, re-weld and knock the clips back in. Ever heard the expression, "you can't push a rope?" You really can't push a rail, either. (An anchor is a device that clips around the base of the rail. It is applied tight against the side of the ties to keep the rail from "running", that is moving longitudinally. Normally in welded rail (CWR) they are applied on both sides of every other tie. Anchoring on both sides of a tie is called box anchoring.
Installing rail expansion joint or lengths of jointed rail at intervals should not be done. If in doubt, the answer is, DO NOT INSTALL RAIL EXPANSION JOINTS AT ANY LOCATION FOR ANY REASON EXCEPT IN THE APPROACH TO DRAWSPANS. Expansion joints are maintenance problems. The maintenance cost for jointed rail track is roughly double that of welded rail. (Somebody else may have a better ratio than that, but for sure it is significantly more.)
Beyond a few hundred feet it does not matter how long the welded rail section is. It will not move due to sliding friction between rail and fastening or anchoring system. So, whether the length of CWR is 600 feet or 6,000 feet, or 600 miles, the movement of the free end will be the same.
Also, beyond this length of a few hundred feet, the stress in the rail is not related to how long the section of rail is. The stress is solely based on the difference between actual rail temperature and zero stress temperature.
The tensile strenght of rail is sufficiently high that there is not real problem with overstressing the rail at low temperatures. Remember, "You can't push a rope?" If you try to push a rope, all it does is go off to the sides. The desire is to keep the rail in tension most of the time. It might be better to think of the rail more in terms of it being a rubber band. It sags when you hold the ends closer together than what it takes to make the rubber band straight. It will stay straight as you pull it up to the point at which it breaks.
In the AREMA Manual the recommended neutral stress temperature for welded rail is (2H+L)/3 + 15 to 25 degrees F. The “H” is the high temperature of the rail over a year. It can be up to 30 degrees or so higher than the air temperature due to heating by the sun. Let’s take an example:
High Air Temp, 105F, so take High Rail Temp, 140 Low Temp, -10F. Set no stress at (2H+L)/3+20
(2x140+(-10))/3 =90. 90+20=110. Therefore we want to stretch the rail so that it has no stress when the rail temperature is 110 degrees F.
Notice that with this setup, the difference between zero stress temperature and low rail temperature is four times the difference between zero stress temperature and high rail temperature. Since temperature difference and internal stress are directly related, the maximum tensile stress is four times the maximum compressive stress.
When the rail is in compression it is kept straight by the ballast shoulders and the friction and interlocking between the ties and the ballast. This second force, the friction and interlocking between tie and ballast is more important than is frequently considered. To improve that connection is the primary reason that many concrete ties are now molded with a pattern on their sides so that they key into the ballast better.
One of the main reasons that a buckle will frequently occur under a train is because the passage of the train will shake things loose thereby reducing the stabilizing forces. Also, once the track is at all out of line, there will be a lateral force from the wheels passing over the misalignment further making the track want to go sideways.
A break is a much better form of failure for a couple of other reasons.
In signaled track a rail break will drop the signals, so that unless the train is already in the block when the break occurs the signal system will tell him to stop before he gets to the break. A buckle in the track does not announce itself to the signal system because the rail remains continuous.
If the rail ends stay in line, and they usually will, and if the gap is not too wide, and usually it is not, the wheel will simply bounce across the break and keep going. In transit and other systems where trains are light and short the train will most likely survive a trip across the break. This is much less likely under heavy freight trains, because even if the first few axles bounce across, the heavy impact can cause another nearby break which will result in everything from there back derailing. Heavy impacts can also cause a broken wheel which can also result in a trip off into the cornfieds.
The coefficient of thermal expansion of steel is not as high as that of several other metals, and is only one of many properties of concern. Rail steel metallurgy has been experimented with in many ways over the years, and probably will be some more.