Bluey- I think in this case it's just for the aesthetics of a covered bridge. Originally covered bridges acted like a van body on a tractor-trailer. The sides acted like two shear walls resisting bending, this was (I assume) much more economical than having stonemasons build a structural arch. This bridge, as you can see, has no shear walls and its support comes from the I-beams visible underneath. Covering the bridge served both to keep the two shear walls from getting out of plane with the loading direction as well as keeping the wooden bridges serviceable for a long period.
Someone correct me if I'm off on this.
Early bridges were made of wood, especially where it was a plentiful resource. Wooden bridges tended to deteriorate rapidly from exposure to the elements, having a useful lifespan of only nine years. Covering them protected their structural members, thus extending their life to 80 years or more. Oregon, known for its timber resources, has the largest number of historical covered bridges of any state on the west coast of the United States.
Most wooden covered bridges employ trusses as their key structural design element. A popular design was the Brown truss, known for its simplicity, but others were also used.
Given the ready availability of steel, concrete, and other modern construction materials, most modern covered bridges are built either for the convenience of the user, rather than to protect the structure itself, or as a statement of style or design.
Quoted from wikipedia.
