track heat expansion

[jockellis]

Anyone know how the Austrailian railroad with the nearly 300-mile straight track deals with heat expansion or cold contraction whichever the case may be?

[Anonymous]

when I find a guy's forum name I'll be back.

[M636C]

Jock,

That track is laid with 60kg/m (120lb/yd) rail on concrete ties with spring clip fastenings. I don't think they have any special expansion joints. While it is a desert, and is hot in summer (maybe 40 degrees celcius, 105 Fahrenheit), temperatures would not get much below 0 degrees celcius (32 degrees Fahrenheit) even at night in winter.

I've travelled across twice, and the weather was overcast at Cook, the station stop on the long straight. There are maybe four active stations on the straight, which would have insulated joints for signals, which might take up some expansion.

If they have carried out the welding at an appropriate neutral temperature, it should all work. But you don't want a major derailment 150 miles from the nearest town, either!

Peter

[Modelcar]

...Never thought of that issue before it was raised by the above post...[Jock], and that is a real interesting situation. First off, I thought the temps. extremes would be much more than Peter noted. That's surprising to me, as I thought the desert temp would be much higher in sunlight and summer. Our desert areas sure can be.
Just for the thought of it...What would be the normal expansion it could experience if the numbers were added up for the total 300 miles....? We all know by observing a length of 39' rail between summer and winter the gap is noticeably different....say at least 1/2"....so how much would all this [by theory], add up to in length if this expansion was totaled on out for the 300 miles....Anyone care to do the math...Must be yards and yards and then some....! It really is interesting when one gives this situation some thought how it really is kept under control.

[Anonymous]

You're going to make me dust off my engineering text books!

This is going to be a ridiculously over-simplified analysis, so please bear with me and feel free to make additions or corrections.

The governing theory here is the linear thermal expansion of a material. Note that by "linear expansion" we're already simplifying the problem to one dimension, when in fact the real world exists in three dimensions. The three dimensional problem is highly complex and well beyond my capacities, so fortunately the one dimensional problem yields a reasonable approximation. Here's the governing equation:

(alpha) = (change in length) divided by (original length) times (change in temperature)

We're curious about the (change in length), so we'll solve the equation for it:

(change in length) = (alpha) times (original length) times (change in temperature)

Now we insert our three known quantities. Original length is easy, that's 300 miles. Change in temperature can be determined from M636C's information. He gives us a range of 0 to 40 C. We'll assume the rail was welded (or installed) at a neutral temperatue of 20 C. Thus, the maximum change in temperature is 20 C in either direction (warming from 20 to 40 or cooling from 20 to 0).

Alpha is the linear thermal expansion coefficient for the material. For steel, we'll use 12 x 10^-6 (that's 0.000012). The units here are inverse degrees C. This is only an approximation, as the exact number would depend on the specific type of steel.

Plugging these numbers into our equation gives:

(change in length) = 0.000012 x 300 miles x 20 C
(change in length) = 0.072 miles = 380 feet

So, if we have a solid, continuous piece of uniform steel that's 300 miles long, it would grow by 380 feet in the heat of a 40 C day or shrink by 380 feet on a cold 0 C night.

Again, please bear in mind this is a grossly over-simplified approximation. A more precise answer would require a three dimensional calculation (since steel expands in all three dimensions, not just length), specifics on the rail itself, information on the weld and insulating joints and their expansion properties, etc.

Hope this was a useful exercise,

Scott Lothes
Cleveland, Ohio

[Hugh Jampton]

They'll have expansion joints near Switches or every few miles or so on plain line.
Plus the average track temperature is higher than the average air temperature because rails are usually dark in colour on the sides from rust and or oil.
In the UK the average track temperature is 27 Centegrade (80F) and it hardly ever gets that hot here.

[oltmannd]

The rail won't expand or contract if you keep it from doing so. The track structure and rail anchors hold the rail in compression or tension instead of letting it expand or contract. Imagine it this way. You take a length of rail and let it expand 1/2 throug heating. Now, you apply a large enough longitudinal force to squeeze the raila 1/2" back to it's original length. Then you apply rail anchors to hold it there, in compression.

In the hot weather, if the compressive forces get too high, the track will "sun kink" as the whole track displaces sideways to relieve the strain. In cold weather, if the tension forces get too high, the rail will break.

Hope that helps.

[Modelcar]

...Thanks Scott for bringing out the book and doing a bunch of figuring for us...Your analyses was great and interesting. I just don't see how rail anchors contain a rail from expanding when the sun is beating down on it....One would think forces such as when a train travels over it and causes movement the rail would stretch [expand] through it's anchors...But I know for the most part, it does work some how because it is a reality every day in the hot summer sun and only sometimes does the system get into trouble. And of course it does have the opportunity to expand in width and height.

[Anonymous]

Digging even deeper here. . . .

From oltmannd's good comments, it might be useful to find out just how much force the average tie clip must withstand. We'll start by determining how much force it would take to squeeze our heated rail that's expanded by 380 feet back to its original length of 300 miles even. The equation to use here is as follows (again, over simplified):

d = PL / EA
d is the change in length, 380 feet or .072 miles
P is the force, what we want to know
L is the original length, 300 miles
E is the modulus of elasticity, 30 million pounds per square inch (psi) for steel
A is the cross sectional area of the rail, 11.75 square inches for 120 lb/yd rail

Solving for P:

P = dEA / L = .072 * 30000000 * 11.75 / 300
P = 84,600 pounds

So it takes a force of 84,600 lbs to keep 300 miles of rail from expanding over a temperature change of 20 C. Assuming ties spaced 22 inches on center, there are about 864,000 ties in 300 miles of track. Thus, at each tie plate there only has to be 0.1 pounds of horizontal force applied to the rail to keep it in place (84,600 divided by 864,000).

But that's horizontal force -- the tie clips hold the rail to the ties using a vertical force. Translating that vertical force into a horizontal force introduces friction (isn't this stuff fun???). Clean steel (big simplification/assumption here) has a coefficient of friction of 0.8. That means 80% of the vertical force becomes horizontal force. However, if the steel gets lubricated (like from grease or oil on a passing train) the coefficient of friction drops all the way to 0.16. If we're going to play it safe, we can only assume that 16% of our vertical force translates to horizontal force.

Thus, the vertical force at each tie plate needs to be 0.1 pound / 0.16 = 0.625 pound.

Again, this analysis is incredibly over-simplified, but I hope it was still useful. I found some good information on welded rail forces at:

http://www.newscientist.com/lastword/article.jsp?id=lw437

Wow, that's the most action my engineering textbooks have seen in months! Thanks, guys.

Additions, corrections, questions, etc. welcomed as always,

Scott Lothes
Cleveland, Ohio

[M636C]

Guys,

I'd guess at the tie spacing being about 18". This is based on trying to walk along the track, and the ties are too close to step on each comfortably but too far apart to walk on alternate ties comfortably. I think the spacing is greater than common in the USA.

Hugh is right about the rail being dark and heating. Some rails locally are painted white on the side as an experiment. They also have put Armco guard rails into the ballast in one curve (on the outside) to give better support for the ties (but this is a long way from the long straight).

I haven't seen any special expansion joints on the Trans Australian (but I might have missed them!)

Peter

[Modelcar]

....Great stuff guys...!!! Really interesting. I'd say the Aussie engineers had the book out a good long time to really get it right....and I suppose they did as it's been around for some time. Very good and interesting forum stuff.

[Anonymous]

The new railway line from Alice Springs to Darwin (opened Jan 04) is about 1000 miles with no expansion joints. There were a number of letters in the local paper about this subject as the line was being built. The engineers assured it wasn't a proplem.

[Anonymous]

Found the following about Darwin Alice Railway construction

Answers to Frequently Asked Questions on Continuous Rail Welding - print from pdf print from word
What are the welding processes used on this project?
There are two welding processes used;


Flash Butt Welding - this method is used to weld 13 shortwelded rail sections (27.5 metres) together into longwelded rail sections (LWR) of 357.5 metres, which are then used in the tracklaying process; and
Aluminothermic (Thermit) Welding - this method is used on site to weld LWR sections together.
What is flash butt welding?
Flash Butt Welding aligns the rail, charges rails electrically and hydraulically forges the ends together. The welderhead automatically shears upset metal to within 1/8" of the rail profile. A base grinder removes the 1/8" flashing material from the rail, which leaves a smooth base and greatly reduces the likelihood of stress risers, which shorten the life of the rail. The sides and head of the rail are also ground to the profile of the parent rail. As a final step in the welding process, a mag particle test is performed. These quality checks, plus two separate checks with a straight-edge and taper gauge, contribute to the complete job that makes a quality weld.
(Source: www.cn.ca/safetyenvironment/safety/technology/en_SEFlashButtWelding.shtml)

What is aluminothermic (Thermit) welding?
Thermit welding is a welding process, which produces coalescence of metals by heating them with superheated liquid metal from a chemical reaction between metal oxide and aluminium with or without the application of pressure.

Filler metal is obtained from an exothermic reaction between iron oxide and aluminium. The temperature resulting from this reaction is approximately 2500° C. The superheated steel is contained in a crucible located immediately above the weld joint. The superheated steel runs into a mould which is built around the parts to be welded. Since it is almost twice as hot as the melting temperature of the base metal, melting occurs at the edges of the joint and alloys with the molten steel from the crucible. Normal heat losses cause the mass of molten metal to solidify, coalescence occurs, and the weld is completed. (Source: www.Key-to-Steel.com)

Why is the Alice Springs to Darwin railway constructed with continuous weld line?
To provide a low maintenance cost railway. The development of Continuously Welded rail was undertaken in Europe during the 1950's and 1960's and has been progressively introduced into Australia since that time until now it is the standard practice. Most of the rail tracks in Australia are constructed using this technique.

Why is continuous weld line low maintenance?
There are no joints to be maintained. In the early history of railways the rails were joined by mechanical joints which were designed to allow the rail to expand and contract as the temperature rose and fell. These joints were a significant source of maintenance as the bolts and plates that joined the rails often broke, the rails were damaged by the bolts and plates and could crack, the track was harder to keep level and the sleepers would be damaged.

How strong are the welds?
When the rail is trying to contract, the rails are trying to pull themselves apart. The point where this is most likely to occur is at the welds. The strength and the quality of the welds are sufficient to prevent this happening. An ongoing program of ultrasonic rail flaw inspections will be carried out to check the integrity of both the welds and the rails.

Older generation railway workers are adamant that you must have expansion joints otherwise the rail will buckle. How does the continuous rail overcome thermal expansion and contraction in the temperatures between Darwin and Alice Springs?
In order to balance the forces between those which want to buckle the track during high temperatures and those which want to pull the rails apart during cold temperatures the rail is layed at what is called the neutral temperature of 40 degrees Celsius. The range of rail temperature expected throughout the course of the year is approximately -10°C to +65°C.

On a railway the length of the Alice Springs to Darwin railway (1420km) this movement would be 16.3 metres for every degree of temperature change. It has been calculated that the rails are subjected to a temperature range of 45 degrees in Darwin and 74 degrees in Alice Springs. This would mean that the rails would expand and contract up to 1.2 km between the coldest night and hottest day during the year.

If the rail were free to move when heated or cooled it would expand or contract like all other steel. A small amount of the stress developed along the rail can be taken up with expansion across the rail. Its height and width expand due to their own dimension as well as some distributed stress from the longer length. The rail bulges slightly. As long as the column is prevented from moving sideways along its length it is very stable.

How is the rail constrained?
The rails are held to the sleepers by strong spring clips and prevent the rail moving along the track. The sleepers are very heavy concrete. Their weight and the friction of the ballast stop any movement. There are 2 clips for each rail at each sleeper. Each clip exerts a load of about 2 tonnes onto the foot of the rail.

When the rail is constrained from moving along the track the only potential expansion the rail experiences at any single point, is the expansion that could occur between two sleepers. Over 700mm, between the sleepers, the rail will try to expand 0.0077mm, about 8 thousandths of one mm.

[Anonymous]

The last summer here in Germany was hot.

The mainline here in Limburg was complete overhauled. New ballast, new ties, new rails.

They wanted to lay the new rails at one very hot weekend and the problem was the temperature outside.
They couldn´t weld the rails together when the temperature was above I think 27 degrees Celsius.

[Modelcar]

Darwin Bob...Excellent report. Lots of technology obviously goes into modern railroad construction.

[Anonymous]

Many thanks for the excellent report, Darwin Bob! I found it very informative. The really scary thing is that it agrees with the back-of-a-napkin calculations from my first post:

QUOTE: Originally posted by Darwin Bob

On a railway the length of the Alice Springs to Darwin railway (1420km) this movement would be 16.3 metres for every degree of temperature change. It has been calculated that the rails are subjected to a temperature range of 45 degrees in Darwin and 74 degrees in Alice Springs. This would mean that the rails would expand and contract up to 1.2 km between the coldest night and hottest day during the year.

For one degree C of temp change,
change in length = 0.000012 * 1420km * 1 = 0.017 km = 17 meters

And for the full range of 74 degrees C,
change in length = 0.000012 * 1420km * 74 = 1.26 km

Now THAT's scary! I was even more interested in "Each clip exerts a load of about 2 tonnes onto the foot of the rail." That's WAY more than I calculated. Either my figures are way off (highly likely) or a very large factor of safety is employed (also highly likely). It would stand to reason that a much greater than average force should be used, as this type of situation could easily introduce stress concentrations.

Interesting stuff,

Scott Lothes
Cleveland, Ohio

[Hugh Jampton]

The main job of the clip is to prevent the rail from overturning when the train pass, so the clip force needs to withstand this most

[Anonymous]

QUOTE: Originally posted by Hugh Jampton

The main job of the clip is to prevent the rail from overturning when the train pass, so the clip force needs to withstand this most.

Well, yes -- a classic example of not seeing the forest for the trees. That happens to us engineer-folk quite a bit.

[Modelcar]

...But isn't the spike the item specifically installed to retain the rail in place and from overturning as the train weight and forces are applied and the clip a later application to do that plus retain the rail in place laterally from forces such as expansion, etc.....

[Anonymous]

Very slow spped prorably

DOGGY

[mudchicken]

l = 0.00007 x L x (change in temperature)

l = expansion length in feet

L = length in feet of subject rail

change in temperature in degrees farenheit

common knowledge for most american trackmen......but watch them all go nuts converting decimal feet to feet and inches![:D][:D][:D]


**** pandrol pretzel clips replace the cut-spikes AND rail anchors....if you did not lay the rail at the proper intermediate temperature, pandrols won't help with the sun-kinks or pull-aparts.....

Scott: If CTM / Cleveland Track Material (old Pettibone) ever does another open house at their Cleveland Plant, make a point to visit. Carl Axtelm and owner Bill Willoughby put on quite a show. One of the larger switch, OTM and frog manufacturers in the country.

Mudchicken / travelling feathers

[mudchicken]

Common tie spacing in US is 19 1/2 inches....

Think 24 ties every 39 foot rail length (UP used to allow 22 ties per rail in some light duty side tracks, not any more with 286K-315K loading and more 125Ton cars with extreme wheel loading showing up...

[kenneo]

[#offtopic]

BigBoy 4014

Was in Limburg a.d.L. this past June. Yes, it was hot from when I lived in Germany --- in Wiesbaden.

The Lahn area and the eastern Rhein on the North bank (Right Bank) up through Biebrich is as pretty as ever. Last time I saw the Frankfurt Opera House it was still a bombed out shell. What a restoration they have done! Memories. [^][^][8D][:)]

[DSchmitt]

QUOTE: Originally posted by oltmannd

The rail won't expand or contract if you keep it from doing so. The track structure and rail anchors hold the rail in compression or tension instead of letting it expand or contract. Imagine it this way. You take a length of rail and let it expand 1/2 throug heating. Now, you apply a large enough longitudinal force to squeeze the raila 1/2" back to it's original length. Then you apply rail anchors to hold it there, in compression.

In the hot weather, if the compressive forces get too high, the track will "sun kink" as the whole track displaces sideways to relieve the strain. In cold weather, if the tension forces get too high, the rail will break.

Hope that helps.

Basically the constrained welded rail willexp/contract in length much less than the same length of rail made up of short sections. The short sections expand/contract at every joint

[daveklepper]

The only locations I have seen rail expansion joints, basically tapered rails, like regular rails cut at a very shallow angle arranged so one of a pair slides along another, have been at bridges. Is this because the expansion and contraction forces that ties in ballast can restrain may cause problems on bridges? What is current experience with modern track construction on bridges? At one time the Chicago Transit Authority would not install welded rail on old elevated structures where we recommended it for noise control, but I believe they do use it on the upgraded structures now. Dave Klepper

[mudchicken]

Dave K.:

Look at the forces exerted on the track by the BRIDGE. Assume that the bridges that you notice most of the expansion joints on are open deck (no ballast, ties fixed to bridge members).....New large span bridges still require expansion joints, especially moveable spans....it's as much or more to prevent skew ties (reduced gage) as it is to stop structural kinks...

travelling feathers

[jchnhtfd]

QUOTE: Originally posted by daveklepper

The only locations I have seen rail expansion joints, basically tapered rails, like regular rails cut at a very shallow angle arranged so one of a pair slides along another, have been at bridges. Is this because the expansion and contraction forces that ties in ballast can restrain may cause problems on bridges? What is current experience with modern track construction on bridges? At one time the Chicago Transit Authority would not install welded rail on old elevated structures where we recommended it for noise control, but I believe they do use it on the upgraded structures now. Dave Klepper

Dave -- joints such as you describe are quite common along the Northeast Corridor on the moveable bridges. There, rather than being expansion joints, they are the joints which me***o create a smooth track when the bridge is closed, but un-mesh (first thing in the bridge operating sequence) to allow the bridge to move. It is possible that the design is restricted to former Penn and New Haven moveable bridges, as I know the moveable bridges on the CN and CP lines in central Ontario had (and have, on the ones which are left) square cut ends. They ride a lot rougher, as the alignment is never as good -- but they don't have the complicated machinery of the Northeast Corridor bridges.

[rrnut282]

Finally, those high school physics classes have paid off, I followed everything that was said.[:)] Just one thought, I remember alpha expressed as feet increase/foot orig length. Did your calcs already take that into account? I'm guessing you did, because the numbers I recall were smaller than what you stated.

[Modelcar]

....In observation from our "Depot" now [Trail Head], and noting the NS ROW parallel to it just a few days ago....I noted the heavy continous rail is held in place by one cut-spike, 2 bolts and I believe it is called a Pandrol clip....This is on a long sweeping curve and I don't know if all these items are used on tangent sections....I was surprised so many of these fasteners in use together.