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A howe truss bridge design includes vertical members and diagonals that slope up towards the center. Its diagonals are under compression under balanced loading. It was invented in 1840 by Massachusetts millwright William Howe. Howe truss design proved to be instrumental not only in the development of several notable bridges at the end of an era of fully wooden bridges but also as an inspiration for the creation of other popular designs.
Suspension bridge is a very old type of bridge. It allows spanning of obstacles like rivers and chasms that other, more conventional, bridge types don't. But it didn't appear in the shape that we know today until more modern materials didn't appear.
Cable-stayed bridge is a variant of a suspended bridge that is more economic that other types of bridges on middle distances and for middle loads. It also allows for some rather interesting designs.
Tied-arch bridge is a bridge that carries itself and can be constructed at places that have problems with unstable soil. It can be problematic if it is not maintained properly but there are tied-arch bridges that are over a century old and are still in use.