For "FOOT TRAFFIC"you could laminate or use solid stock with plate's on the joints.
For looks the laminated may give a nicer look as it could be made with a continuous arch. Consider fabricateing a one piece gluelam type beam from solid stock. Say 1x3 inch material that does not have to be full lenght but has stagered joints. Suggest about 10/12 inches deep using resorcinol or best; epoxy glue. Thouroughly paint the finished beam with a wood presrvative.
To make the beam build a frame to which the first few layers could be clamped and the arch set. Then screws and clamping for the remainder.
The beams may be easier to fabricate than you think. The base frame is the important part. Construct it on the flat at a convienient location. For a natural curve fix the end points and set the mid height desired. use some very thin material to bend over this to define the curve and then set up some braces that the can be used as clamp points. Make it at least a foot longer on each end so it can be trimmed.
Most of the bridge could be built offsite and then moved into position. Consider concrete for the end support piers
Please note: I have never done this so the advice and technology may/is questionable.
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