[rmxt]

Excuse my arcane units, but it is what I am familiar with:

ΔL=αΔtL; ΔL/L=αΔt; ϵ=ΔL/L; ϵ=αΔt; E=f/ϵ; f=ϵ/E; so f=αΔtE

ΔL = change in length due to temperature

L = restrained length

f = stress that arises due to full restraint

E = Young’s modulus

ϵ= strain

α= coefficient of linear thermal expansion

Using AASHTO numbers for structural steel:

f= 6.5x10^-6 (1/F)* 100 F * 29000 ksi = 18.85 ksi

That's a big chunk of the elastic 50 ksi range, and it's greater than a good portion of the allowable ranges from the table on page 41 of this PDF [1]. As you might already seem to know, AASHTO doesn't consider temperature loading for fatigue limit states, and in the Strength limit states it considers the force effects to be halved. (Though the displacement effects are multiplied by 1.2) Regardless, fully restraining these things at their ends doesn't seem like a good idea. Am I missing something in what you're talking about? Yes, the strain is low but fatigue generally works in terms of stresses.

[1] http://downloads.transportation.org/LRFDUS-6-Errata.pdf

[msandford]

So I guess it depends a lot on the kind of steel that you're using and what you're designing to. Do you need the full 100F range? Can you get a lower expanding steel for a nominal price increase if you're going to buy many mill run's worth? Are you going to have to build to bridge standards, or can you get away with something else? It's sort-of a bridge, but sort-of not. From a technical perspective you don't need as much safety factor since you've in total control of the vehicle load which isn't true on bridges. I don't know what the regulatory considerations on safety factor are especially since it would probably qualify for its own category since it bears little resemblance to anything that's man-rated like bridges or buildings.

You might also be able to get some nice double-whammy effects from using something like a514 since it's corrosion resistant, has a higher elastic yield, and may well have a reduced thermal expansion coefficient. If you increase the strength and decrease the expansion at the same time then instead of blowing 40% of your "budget" on thermal it might only be 10%. And since you're covering such a large range of climates you might be able to rate every 10 or 20 miles of loop based on the climatic averages in that region instead of looking at the absolute min and absolute max for the whole thing. It might add a few extra weeks of design but make things a lot more feasible.