I don't think they'd sag. For a footbridge the support should be more than adequate. I'd put in a midway support to take any bounce out of it when I walk across it, but that's just me. There are lots of these being built for bike trails and ATV trails. If you need more support for vehicular traffic I've seen old flatbed trailers used to span creeks and ravines on mountain properties. A pretty cheap bridge that you just have to sit it in place.
