Something interesting I ran accross in a book- In the 1880’s, an engineer named Theodore Cooper developed a baseline of sorts, to uniformly apply design weights when engineering a bridge. The Cooper Class E10 design is based on the concentrated wheel loads of two Consolidation ( 2-8-0 ) steam locomotives,followed by a loaded train of uniform loading. The “10” comes from the 10,000# loading on the drive wheels of a consolidation locomotive. From this basic standard, bridges are designed on multiples of this value. An E50 loading, for example, would be 5 times the loading of an E10 value. Apparantly, this system is still used to this day. If I understand it correctly, modern bridges are designed for E72, if they’re concrete, and E80 if they are steel.
Is anyone familiar with this system of design? Why is, (or how could) a 125 year old standar, based on equipment loadings, be used and relevent today? Why the different loadings on concrete verses steel?
The Cooper rating as you point out is an axle-loading rating based on the loading pattern of double-headed 2-8-0s. The number in the rating is the axle loading of the driving axle; e.g., E40 = 40,000 lb. maximum weight on the driving axle. It allows for closely spaced axle loadings to derive a live load that replicates the static weight of the locomotive and train on the bridge. Additional factors have to be added to the static live load for dynamic loading (acceleration, deceleration, impact, nosing, as well as snow/ice and wind load).
The Cooper rating was an excellent empirically derived method of estimating live loads on railroad bridges, and it worked well for diesel-electric, too. Recently AREMA changed recommended practice to include acceleration and deceleration longitudinal loading, which stemmed from the introduction of A.C. locomotives and concern about their high adhesion and tractive effort. It consists of a simple percentage increase to the Cooper rating.
I don’t know where you’re finding the difference between steel and concrete, as far as I know we’re using E80 for all new construction including culverts. I’ll ask one of our bridge engineers in the morning.
Cooper was a brilliant engineer that greatly advanced the science of bridge engineering in the late 19th century, and while his name lives on in Cooper ratings he was also the consulting engineer for the first Quebec cantilever bridge – the one that collapsed during construction because the dead load of the bridge was greater than the ability of the bridge to carry it.
Bridge design is an iterative process and in large bridges the dead load is most of the load. In order to start design the engineer has to make an assumption about the dead load. The engineer uses experience to estimate the weight of the steel in the bridge. From that number he can calculate the stresses on each member, then sizes each member for that stress, and designs the connections.&
The “center section” is the suspended truss span between the two cantilever arms. The failure occurred in the design of the cantilever arms. They were complete re-engineered (with a proper budget) using stresses that were within the capabilities of steel. The suspended span of the 2nd bridge fell into the river during lifting into place due to a poor construction detail, not a design detail. A new suspended span had to be fabricated and lifted into place.
The bridge you are thinking of in Scotland that failed was the Firth of Tay Bridge, which was conventional truss spans on piers. The engineer did not take proper consideration of wind loadings and the center spans blew off their piers one night, with an express train inside them. The construction details were inadequate too, so the entire bridge was torn down and a new bridge constructed.
Actually, although there are still conflicting theories, the most likely cause of the Tay Bridge collapse was probably a combination of poor design and materials choices, metal fatigue, and poor maintenance. The bridge was very top-heavy at the section that collapsed (the “high girders”), and there was a kink at the south end, which transferred momentum from northbound trains to the bridge. The piers were basically sets of paired latticework towers, held together by a latticework of thin wrought iron bars that were connected to the main towers by weak cast iron lugs, which suffered repeated damage whenever a train’s passage caused the bridge to oscillate. Over the course of the bridge’s life the lugs gradually lost strength, and on the night of the accident, the passage of two fast, heavy passenger trains broke the last connections between two of the towers on a pier, reducing the amount that a pier could move out of center to a mere three feet, and the oscillation (abetted to some degree by the wind) pushed one of
The information was in a book Landmarks on the Iron Highway, by Bill Middleton, si I can’t say if it’s good or bad, ad far as E72/E80 information. I just didn’t understand why there would be a difference. Thanks for the book recommendation. I’ll add it to my list. I’m 1/3 through Castles of Steel. Invincible and Inflexible just pulled into Port Stanley, and there might be some excitement in the near future.[;)]
Using an E80 rating would give you axle loadings of 80,000#, locomotive total weight of 1,112,000# over 100’, and a uniform trainload of 80,000# per lineal foot of following train. I can see where the uniform loading becomes a moot point, after a structure is designed for the concentrated loads. I was perplexed over the idea of an 1880’s rule of thumb still being applicable today, but just using a multiplication factor. Is it just a case of making the E number match the axle loading, and everything else works out, because it would be overbuilt?
Oh laddie – don’t knock 1880’s rules of thumb! If it ain’t broke, don’t fix it, and Cooper’s work was sufficiently brilliant that it ain’t broke; the physics hasn’t changed a bit (except as 1435 pointed out the new AREMA recommendation for longitudinal accelera
I would imagine that seismic loading has also been added since Cooper’s time. Of course, new contsruction methods need new earthquakes to properly validate the design - e.g. concrete bridge columns in California (original designs didn’t provide enough horizontal rebar to keep the columns intact).
Petroski’s writings came to mind when reading the earlier part of your post - and I also found “Engineers of Dreams” to be a very interesting and informative book. One of his observations was that really major bridge failures occurred about every thirty years and he postulated that was due to the bridges being designed by engineers with no direct experience in failures of the bridge type the
I might add one other thing about the Cooper system – which applies particularly to the comment on seismic loadings (which is quite correct). The Cooper system gives you the load, and the distribution of that load. What it does NOT do is tell you how to hold it up. That is, there is no prescription for the design and construction (unlike highway work in the US, where there is a handbook which basically says things like 'if the span is 40 feet and you are holding up an interstate, use 6 beams of such and such a shape and construction). In railway work, once you know what the loading is (Cooper, plus add-ons such as the longitudinal and seismic) it is up to the engineer designing the structure to figure out what members, whether concrete or steel or wood or whatever, arranged and connected in what ways, will hold the load up. This is not to say that the various railroads don’t have standard designs – they do, and it saves a lot of time.
It’s not the AC part of the locomotives that adds on the extra safety factor to Cooper’s System, it’s the “high adhesion tration motors & wheelsets” …You ought to see what happens on some old timber trestles when there is a predominant direction of tonnage and the stringers start walking off the bents & pile caps!
Or forward (if it’s in dynamic braking at that point). Think of it as a force applied longitudinally to the rail. The rail doesn’t slide and ball up in a wad somewhere because it is anchored against longitudinal movement, so it resolves the force into the ties, and the ties into the ballast. The force can cause the track to slide out on the curves or in this case to slide the stringers off the caps or the caps off the piles.
For historical accuracy, Golden Spike NHS has a stub switch and the approach rail has no tie plates or rail anchors - just held by spikes. Three times a day the engine makes run, crossing the switch several times. Each west bound crossing - the locomotive is accelerating. Each east bound crossing the locomotive is braking. After 6 months of this, one rail has crept about 1/2 to 3/4ths of an inch further east. Now this is one small 30 ton locomotive. Imagine the reaction forces of the eingines pulling a 10,000 ton train.
As pointed out, the Cooper E-rating system is not a rule of thumb for designing bridges; it is a system for describing the axle loadings and spacings on a train. Knowing what train weight (“live load”) you have to carry is the first step. Last I knew there was a large binder AREMA bridge design manual that offered suggestions and good practices for designing railroad bridges with adequate strength etc.
As a practical matter, I think that today, an E80 train is supposed to roughly represent a unit coal train, and is the standard design limit for most main lines. Formerly, lower standards were generally used (e.g., E65, E50). But there are exceptions: I have it on good authority that the double-track railroad bridge over the Mississippi River just upriver from New Orleans, origininally built in the 1930’s, was designed for two E65 trains (simultaneously) or a single E90 train.
As was aluded to, with a really big bridge, most of the strength of the bridge is used just to hold up its own weight (the “dead load”). For this reason, it is relatively easy to build a large bridge to a higher design load standard. (E.g., if you want to redesign a culvert to carry twice the axle load, you need to make it almost twice as strong, but if you want to design a long-span bridge to carry twice the axle load, you only need to make it slighly stronger.)
Yes - we had beans last Winter Fest day - cooked on the backhead of the 119. And I wish we got paid. Even $3 a week is better than nothing - but I wouldn’t trade the experience for anything. Come visit us - May 10th is just around the corner.
Because the Cooper E-rating system was based on axle loadings and spacings of an 1880 consolidation steam locomotive, wouldn’t the loading parameters be somewhat different for a 2007 SD-70? Or is that a non-issue?