[msandford]

> Thermal is an issue that gets worse with distance.

I would respectfully disagree. The rail industry has figured out how to do Continuous Welded Rail (CWR) quite well, using the elasticity of steel.

http://blogs.agu.org/landslideblog/2011/03/08/distorted-rail...

Similarly the tube for the Hyperloop doesn't HAVE to free-float against its foundations. It might be easier or harder depending on various factors to work on expansion joints or doing the tube equivalent of CWR. You'd probably work on both to figure out which is easier in the long run.

Considering that it's a 9-11ft diameter tube with about 1" wall thickness, it's going to be pretty stiff, especially relative to traditional rails. The moment of inertia means that it should be very resistance to bending or buckling under compression and under tension steel is usually very good.

Given that there are going to be plenty of turns that the track has to make, I would look at doing a combination of two things:

1. Working towards a CWR style solution

2. Allow some movement so that the corners can take up the slack as the tube expands

The turns are very gradual and sweeping. But you could imagine that there's a virtual intersection between two straight portions that you determine by drawing lines from the straight portions until they meet. The actual turn will take place far from here, but it's instructive. So as the tube expands, the actual curve is going to move ever so slightly from the neutral position towards the virtual intersection. So long as there is enough room on the pylons to accommodate this, things will be pretty good. The tube will go from being curved 0.1 degrees per 100 feet to 0.105 degrees per 100 feet (or something like this) but this can be designed for and ensured that it doesn't cause the tube to buckle or collapse. It's engineering, not the utter unknown.

[HCIdivision17]

That is one of the coolest articles on field engineering I've seen in a while. Thanks a lot for sharing it - it really brings out how something like the hyperloop can be tackled. So far, thermal effects have been my main point of curiosity, but the idea of calibrating the steel to take care of it will likely be the ... easiest? way around the problem.

At their desired vacuum pressures, the steel doesn't need to be anything special, so I would love to see the mechanical engineering that goes into designing the 5 mile track's materials.

[msandford]

The engineering to do a 5 mile section is pretty straightforward. It's only 5 miles long (25000 feet) and around 250 joints.

1. Giant foundations and just handle the thermal stress by not letting anything move

2. Figure out the slip joints really well to soak up the ~125 feet of travel and still hold a good vacuum

3. Figure them out OK and just install extra vacuum pumps since there are only ~250 joints

4. Try out some/all of these options on 500 feet of tube in parallel to see how it all performs and don't make a final decision on the whole 5 miles until you have real cost numbers

The other thing I'll mention is that you don't need the steel to be continuous in order to hold a vacuum. You need the inside face of the tube to be smooth in order to not jerk around the vehicles, but all the sealing could be done on the outside with clamp-on seals. If the average continuous tube piece is 100 feet long and the max thermal expansion is 0.5% then you only need a half-inch gap between the tube pieces.

If your air bearings are say 3 feet long each and divided into 10 sections internally which are fed through orifices so that no one section can rob all the pressurized air flow then you're never going to lose more than 10% of your bearing force and you should be able to glide right over these 1/2" gaps with no problems. And if there are some problems a few accumulators (plain air tanks or pressurized bladders) inline with the supply lines would probably increase the momentary recharge capabilities enough to negate the problem.

700mph is 1000 feet per second or 12 inches per millisecond. That means a 1/2" gap is crossed in just 40 microseconds or so.

[rmxt]

Thank you for the additional info. I am skeptical merely because they were quite hand-wavy about temperature accommodations, and it certainly is/was simplistic to think that ALL thermal movements can be accommodated for only at stations. (Especially if it's a direct and exclusive SF-LA route) Yes, the cross-sectional properties of the tube are going to be phenomenal, but I've always operated under the assumption that you don't try to resist thermal movements, regardless of the strength of the cross-section. You let them dissipate and design for the deflection (e.g., at the bearings and abutments), rather than the stress (buckling/tensile) in the beam. If we start allowing stress to develop in the superstructure tube, I can't imagine what the cyclic fatigue impacts of that temperature stress will be. (Maybe it's not significant...)

I am no rail expert (though I am a civil/structural guy), but even continuous welded rail isn't always continuous for hundreds of miles. [1] I think that there are two factors at play: continuity in the maglev/rail structures, and continuity in the superstructure/tube. I do not know what maglev devices look like, but if they do look like traditional rail, then agreed that a CWR solution seems to be the way to go. That being said, no matter how stiff the tube is, it too will have to accommodate thermal movement. My gut reaction is to call everything tube related simply supported, allow for (6.5x10^-6x100ft.x100deg = 0.065 feet) ~= 0.75" of expansion or contraction at each pier, and surround this expansion zone with a metal sleeve of 2"+ greater diameter than the main tube. Simply supported, multi-span structures are a well-studied problem. Adding in the continuity of the rail/maglev structures are what make it hairy, IMO, and the interplay between seismic considerations and thermal considerations becomes important. As far as I can see, it's very important for the maglev structures to be continuous to ensure for smoothness and speed of the ride.

For example, given that you make the superstructure spans simply supported, you have these nearly perfect "mass-on-a-stick" seismic models with well defined, and relatively short periods. Then, you have much longer continuous sections of rail/maglev equipment that contain releases on a far fewer number of span segments. These will have much longer periods of vibration. Maybe I'm stretching here, but the connections between the maglev/rail and superstructure seem like a place that is rife with potential for failure and stress during a seismic event. (I would not want a life-safety issue being my most prominent failure point.)

[1] http://boards.straightdope.com/sdmb/showthread.php?t=471152

[msandford]

If you're dealing with bridges or buildings then you're right of course, you don't stress anything and you just let the stress dissipate through various movements.

But thermal stresses are very small, for "normal" steel it's 13e-6 per degree C. If you figure that the temperature variations in CA aren't going to be more than say 40C (and that's probably too much) then you're looking at 520e-6 or basically 5e-4.

As far as strain goes, that's not a terribly big number at less than 0.1% especially considering that most of the stress/strain graphs will go up to 10% or more and the first 1% are usually WELL within the linear elastic region. That means that you're talking about doing perhaps only using a few ksi of the steel's strength for the thermal effects.

[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.

[tcpekin]

Correct me if I'm wrong, but the linear elastic region usually ends somewhere around 0.2-5%, meaning 1% strain is not well within the linear elastic region. If you just do σ_y/E, you'll get the yield strain. Using rmxt's numbers you get 0.17% yield strain. Using [1] for 1018 steel you get 0.155% yield strain. The strains you calculated are not insignificant.

[1]http://www.matweb.com/search/datasheet.aspx?matguid=3f2ce033...

[msandford]

I guess it depends on the material you're looking at. The system designer would probably be the best person to ask. Are you going to make it out of 1018 or a36, or are you going to use something that's higher performance? Does the increased cost of the stronger steel get offset by the reduced weight?

You can get a36 for about $1/lb in small quantities. You can get corten (a588) for about $2/lb in small quantities. But the a588 has a yield strength about 50% higher than the a36, so strength-for-strength it's a pretty decent deal.

If you need 1" of a36 then you're going to need only 2/3" of a588 so it's only 33% more expensive. Combine that with the weathering properties which can reduce your maintenance intervals substantially (this is the same steel they make sea containers out of) and your lifetime cost might well be lower.

Further since your tubes now weigh less you might be able to get away with either smaller pylons or greater pylon spacing, both of which might be advantageous.

So you're right that the strain is non-trivial but that's only if you pick basically the toughest, least strong steel available. It's pretty easy to go stronger and to not lose too much toughness and gain other desirable features such as corrosion resistance, and in the process make the strain less significant relative to the elastic region.