"Throwing down" bridges seems to be a common human activity, it seems. Remember, after the Nazgul cross the Anduin at Osgiliath, Boromir and crew throw down that bridge (as he recounts during the Council of Elrond), the last bridge that was used to cross the river. How was this done? One would think that a city built with a river running through it would have substantial bridges between the two halves.
And yet they fell.
**And yet we know that this was folly as (1) Sauron wasn't really attacking at the time, just didn't have the money to pay the toll for all Nine Nazgul, and so feinting with a large force did the trick and (2) we all know about the
sewer system that runs beneath the river, as shown by Peter Jackson, and so the bridgeless river was of little defense.