It says in
The Hobbit, that:
Quote:
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Amid shrieks and wailing and the shouts of Men he [Smaug] came over them, swept towards the bridges and was foiled! The bridge was gone, and his enemies were on an island in deep water - too deep and dark for his liking. If he plunged into it, a vapor and a steam would arise enough to cover all the land with a mist for days; but the lake was mightier then he, it would quench him before he could pass through.
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So it seems to me from this that they destroyed the bridge to force the dragon in the air, denying him access to the bridge. Perhaps they hoped that they could knock him out of the sky into the water perhaps hoping that such a fall would be enough to harm the dragon.