Viaduct construction (split from Why do things float?)

[Tony83]

Ok, on a related topic. During the 18th and 19th centuries, an incredible network of water canals was built in the UK. Due to geographical needs, sections of this network were actually built as viaducts, often a hundred or so feet above ground level.

The question is, how did the engineers of the time calculate whether or not a barge was going to be too heavy for the viaduct and thereby cause structural failure?

Is it a coincidence, or incredible good luck, that there is not one historical example of them getting it wrong?

Answers on a postcard please.

[Gary88]

because british engineers are just that damned good

imagine a stamp somewhere over that way >>>>>>

[Simetrical]

By the 18th and 19th century, basic structural principles had already been discovered. A large percentage of the math/physics stuff taught in engineering courses was already established by the 18th century; essentially all was established by the end of the 19th. Essentially, you measure certain stress properties of a given material, then you plug that into certain equations that had been derived (probably in some part from Newtonian physics, definitely using calculus). Then you did, I guess, somewhere between tens and thousands of pages of manual calculations (I don't know how big a workload we're talking here) to determine the results of the equations. This told you how much material you needed. Nowadays the same thing is done, but using computers instead of manual calculation.

Of course, the Romans and Egyptians and so on didn't have calculus or physics, but they managed to build strong structures too. This is even simpler: they overbuilt. Architects and engineers got a rough feeling of how much stone (or whatever) was used for a given type of structure, over generations. Then they used some basic empirical principles to figure out how much would be needed for variations on that structure. They had no real idea of the underlying principles, and since it's kind of a pain if your lovely expensive new palace or temple collapses under the first heavy snowfall, they erred heavily on the side of caution.

One interesting result of this essentially intuition-based approach may be the Bent Pyramid. According to one suggestion, the Egyptians started building it at the traditional slope of 55°, but then an inexplicable structural failure occurred in a pyramid (as I recall, a different one). They had no idea what went wrong, and until they could figure it out they switched to the more conservative angle of 43° (which distributes the same weight over a larger base, and so is more stable). Eventually they switched back to 55°, possibly having figured out the reason for the earlier issue. I don't know whether that's the reason they did it, but it's a thought-provoking possibility regardless of plausibility.

A more straightforward result of the approach is that because everything was built to withstand much higher stresses than necessary, it's tended to last. Roman bridges still exist today, surely at least in part because the Romans didn't know how cheaply they could build them without substantial risk of collapse. Now that engineers can carefully calculate the materials needed to sustain a given load, they don't overbuild by such a large factor, and opt to save on price and space instead. This might contribute to occasional building collapse, but probably not at a particularly large rate, I suppose, although I'm no engineer.