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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.  After the design is complete, if he thinks it's necessary, he tots up all the weight in all the steel in all the members and re-runs the design to see that the original assumptions about the stresses on each of the members were correct.  Back in Cooper's day there wasn't computer support to do this very tedious process automatically -- basically it consists of designing the bridge twice, so engineers used experience and judgement to make assumptions about the dead load, and rarely did the back-check because it was time-consuming and expensive.  That method was fine so long as bridges got larger very slowly but the Quebec Bridge because of its immensely long main span was a leap into the unknown (only one bridge of comparable size existed, the Forth Bridge in Scotland).  The design budget was insufficient to pay Cooper and Peter Szlapka (the bridge designer) to do the check, with catastrophic consequences.  It was a grave error in professional judgement by Cooper and ended his until-then stellar career. He should not have taken the commission under the terms proffered by the bridge's promoter but apparently his ego got the better of him. Could I suggest you acquire "Engineers of Dreams," by Henry Petroski?  I think you would find it fascinating.S. Hadid
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