Given that the continents are shifting an inch or two every year could this ever end up straining the structural supports until they collapse? If for example, Long Island started drifting east away from Manhattan, would the Brooklyn Bridge ever snap?
Heh, about 180 million years too late to worry about plate tectonics messing with greater NYC.
The Palisades over in New Jersey are flood basalts from when North America and Eurasia parted ways during the break-up of Pangea. Once that was over, things have been pretty stable geologically.
The plates move at about the same rate one's fingernails grow, which is about 2 cm/year. So if one did have a bridge spanning a plate boundary, it would be possible to design it so that it could accommodate that type of change over a ~100 year life span.
If you spanned, say, Gibraltar the ends of your bridge would be inching toward each other, but given that the bridge is gonna last a max of 2 or 3 centuries, you're only accommodating ~6 feet per century of movement.
Worth noting, though, that the tectonic plates are thick; many miles. The little bit on the surface we might be punching foundations into can behave differently than the larger plate. In practice, you're getting less movement from the layers on the surface because their forward movement, in the case of Gibraltar, is resisted by the surface layers on each side of the plate boundary. This means a lot of the surface movement is actually vertical instead of horizontal.
Bottom line, I think this only a minor problem on the time scale of a bridge's lifespan. By the time tectonic movement would become a problem, you've already exceeded the bridge's lifespan and it will need replacement anyway.
