Expansion of rail for 20C temperature variation

[Julian Roberts]

I think it's worth having this as its own subject to assist anyone looking like me to know how much gap to leave for expansion.

It's a reminder that a metre length of rail is trying to expand about 0.4mm for 20 deg rise.

Dave was kindly answering this question on this thread viewtopic.php?f=89&t=8355&start=50

[Noel]

I have looked on the internet and found http://www.repairengineering.com/coefficient-of-thermal-expansion.html (other sources seem to be in the same ball-parks) which gives coefficients for carbon steels around 12*10^-6, for stainless steels and nickel-silver around 17*10^-6, which for 20C increase produce approximate results of .24mm/m and .32mm/m. I did the calculations in a spreadsheet, so the math is hopefully OK, but my input may not be. However, according to the table, the coefficient for NS is slightly more than one third greater than that for steel, so a difference of +150% given by Dave looks a bit high...

[davebradwell]

I was hoping someone would check it as it's easy to be out by X10, especially when using a bit of scrap paper and mental arithmetic while having breakfast. Suspect n/s varies according to type and form. My post certainly wasn't meant to be definitive - there was rounding and approximation. I think 0.36 was the figure which is a bit nearer to yours, Noel and that produced by multiplying a rounded up number.

It still explains why soldered joints break. Store your layout in a garage or standard shed and you might get at least twice this movement.

DaveB

[MPR]

I’ve given a quick check and the values calculated are definitely in the correct ball park.
But it is not the whole story - the substrate that the track is mounted on will also have its own thermal coefficient of expansion (typically around. 4x10-6/C for plywood) - which will reduce the differential expansion - but also introduce a significant length dependency on humidity, which will also be significant in a crowded exhibition hall!

Further, the linear expansion mismatch is in a very long, very thin bent (and effectively pre-buckled) beam. Even pinning the ends rigidly with solder joints won’t hugely increase the stress at the ends in this condition , as long as the rail is not massively pinned along its length. The small amounts of sideways movement in chairs etc will all act to reduce the stress and as rails are parallel, the movement will be in the same direction for both!
All of which is to say, the headline movement may not be as catastrophic as you might think, particularly if there is a little slop in the middle.

[jim s-w]

Personal experience of securing both ends of a meter length of rail (and not the middle) is it will buckle. Its best to secure it in only 1 place (i use 2 sleepers side by side with a dropper on each) and allow the rest to slide through the chairs.
Rail soldered to every sleeper has been absolutely fine.

[davebradwell]

I agree, Jim, you can't be too paranoid when dealing with this issue and I've had my share of disasters. In my world, when it's cold it's also very wet so there's a combination of short rails and long boards. If rail is attached both ends the results would be unpredictable as the restraints won't be in the same place each side - for "small sideways movement" read serious gauge error.

As a spin-off it would appear good practice to attach droppers near the fixed end of a piece of rail to reduce stresses on the joint.

DaveB