Tagging of tied-arch and through-arch bridges?

Arch bridges where the the arch is above the road support (tied-arch bridges and through-arch bridges) are frequent, and notably different from deck-arch bridges where the road support is on top of the arch (see Wikipedia), but it seems that OpenStreetMap does not support a way to distinguish between them. Am I missing something?

I had drafted and tried to use some ideas for it

Should distinguish between arch vs deck. The deck attribute can be reused for trusses.