I've been trying to bone up a bit on the development of engineering in the "why buildings fall down" sense. I've come up with an insight, new to me at least, about the relation of theory and practice in, I guess, the development of any science. Not sure how well I can articulate this, but bear with me here...
Start with the Tacoma Narrows Bridge, which collapsed just four months after it was opened in 1940, perhaps the nation's most spectacular bridge failure ever. Apparently we know (now!) what did it in--"torsional vibration," i.e., "twisting," from uneven loads in a steady wind.
But here is where it gets interesting. Evidently engineers had known for a long time that suspension bridges go bollywackers from uneven loads. Eighty-six years before, a bridge over the Monongahela River at Wheeling West Virginia, had fallen down for the same reason. The question then arises: okay, so why not put up some kind of stiffener to keep the bridge from doing its little dance? The answer is, we had done that too: when they rebuilt the Wheeling bridge, they included stiffeners, on a system already developed by the great John Roebling, who himself went on to build (and stiffen) the Brooklyn Bridge?
So why did we ignore Roebling and make the old mistake all over again? Ah, here is where it gets interesting. Evidently engineering, at least in modern times, has involved a constant interplay between "theory" and "practice." No question that modern analytical techniques (than you, Newton and Euler), have helped us to make strides in the attempt to solve engineering problems. But it remains a marvel how much of engineering, even modern engineering, is the work of "empiricists"--self-taught or untaught builders, unencumbered by--often even contemptuous of--theoretical knowledge.
I know what you're thinking but here's the thing. Roebling who got it right was the empiricist. Evidently it was after Roebling that the "theorists" took over, and brushed empiricism aside. The trouble was, their theory wasn't up to it. They didn't have the conceptual apparatus to explain why Roebling's solution worked and so they went ahead and ignored it. Except actually, it's worse than that. They didn't just ignore empiricism: they developed some wrong theory (about the relation of mass and inertia) that powered them straight into disaster.
As I read about the Tacoma Narrows bridge, it sank into me that I'd heard a version of this story before. Years ago, my friend Paul told me the sad tale of Hagia Sophia Cathedral in Istanbul, perhaps the world's greatest dome (or compare the Pantheon in Rome and the Cathedral in Florence). The way Paul told me, they built Hagia Sophia on the instructions of the greatest mathematicians of their time. And it fell down. They rebuilt it on the instructions of a team of master builders, and it has lasted for 900-plus years.
So it looks like it has happened more than once. Now honest, I don't mean to get too anti-intellectual here: I love theory. But it does make you wonder: what kind of mistake are we making today, with all good intentions but simply because we lack the conceptual apparatus to get it right?
Biblio: For an introduction to the theory-practice issue (and a discussion of Tacoma Narrows) go here.
Another kind of engineering problem: Not really the same thing, but I'm remembering the story of the building of the B-2 stealth bomber. Way I got it, they set out to determine how to proportion the volume between wing and fuselage so as to maximize range. They took a derivative of range with respect to volume. But on second look, they chose the wrong derivative and so picked the design that would minimize range. So W. Biddle, "Skeleton Alleged in the Stealth Bomber's Closet," Science, May 12, 1989; link (paywall).