We don't need no stinkin' bridge shoes...

[James Costello]

I guess that I expected that some sort of math was involved, especially since we are in the 21 Century, where computer simulations seem to be done for lots of applications. Even in the 2nd half of the 20th Century, I would have expected some sort of scientific (read mathematical) approach, rather than just experimenting. After all, we don't live in the age of the Romans. 

You'd be surprised how late empirical calculations have been used in engineering history.

I do know that things like load limits of a bridge are calculated - why not expansion?  Or, are bridges and skyscrapers just built haphazardly, by trial and error?  If they crumble - no big deal?    Was Geo. Washington, or Brooklyn Bridge (in NYC) built using trial and error?!

Definitely, especially if you measure the Brooklyn Bridge in terms of human life. The Brooklyn Bridge was pioneering in many ways, especially for the use of caissons for underwater construction, where the pressurised environment resulted in the injury and death of workers from "caissons disease" or as we know it today, the bends.

http://www.history.com/topics/brooklyn-bridge
http://www.eyewitnesstohistory.com/brooklynbridge.htm

The BBC released a great mini-series on the Seven Wonders of the Industrial World and is worth checking out for the episode on the Brooklyn Bridge, let alone the Hoover Dam or the Transcontinental Railroad.
http://www.bbc.co.uk/history/british/victorians/seven_wonders_01.shtml

Computers, and more to the point, mathematical models, are a relatively "new" engineering technology.

[Pennsy]

I think everyone is also forgetting another very important type of mathematics for figuring how bridges are built.

Budget math and existing economic costs. It's a lot cheaper to leave expansion joints and bridge shoes.

Money still rules over all.

Jim

[pnolan48]

Roebling had a mini-scale Brooklyn Bridge to practice on. It's in Cincinnati, and still in use. I agree with James Costello that engineering calculations came later than many people expect, although I agree that Roebling had the mathematical tools to do the calculations manually. I am very aware of the streams of calculations that led to the atomic bomb; there were two or three geniuses (or four or more) behind the sequencing of those calculations.

I still think the original image just shows a bridge that is so over-designed that, bridge shoes or not, it will still be standing when the sun explodes and wipes everything else out. I can imagine, a zillion years from now, that bridge floating by a civilized planet and its engineers remarking, "Well, we don't know what it is, but it certainly is sturdy."