Thermal Expansion of A-36 Steel Rails: -20F to 90F

[gv3]

Homework Statement

The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional area of each rail is 5.10 in2.

So i was able to find out the deformation on the rail. My question is, does the .34848in get split between both ends of the rail since both sides are free ends? So each side would expand .17424in?

Homework Equations

δ=αΔTL[/B]

The Attempt at a Solution

δ=αΔTL= .34848 in[/B]

 

[Merlin3189]

Does it make any difference?
Consider having a large number of rails, as in reality you would. Then think about the total expansion of the rails, then the total gap required, then the gap between each rail.

 

[gv3]

Does it make any difference?
Consider having a large number of rails, as in reality you would. Then think about the total expansion of the rails, then the total gap required, then the gap between each rail.

well because i was thinking that not only will the rail in the middle expand, but the one on the left and right of it would also expand. So if the deformation wasn't split between both ends, the gap would have to be 2δ. Because the rail in the middle will expand by δ and the rails next to it will also expand by δ.

 

[Chestermiller]

Yes, one side would expand 0.1742, but the adjacent rail would also expand by that much.

 

[Merlin3189]

I think that is what is intended to happen. My point was simply about the calculation.

But I wonder if that may be a practical problem for RR engineers? The rail doesn't know which way it is supposed to move, so if the spikes and ties aren't uniform, the rail could move slightly asymmetrically when it expands and contracts. Over years perhaps the rails could creep and make the gaps vary in size?

Anyhow, over here we are moving to continuous welded rail, so there are no gaps any more. What happens when the rails warm up, I don't know. I think some CWR is laid hot, so that it lives in various states of tension. Maybe with stronger ties and fixings expansion forces can now be resisted and not cause buckling?