Height within the bridge

As far as the rectangle and the cylinder are concerned, the rectangle is the easiest to calculate measurements. All I really need to do is allow for about a 2.5m clearance space and the 3m for the width of the path and that's taken care of.

The cylinder is a little more difficult, and relies more on approximation (in a sense). I've allowed for a 4m wide cylinder that should fit the path in line with that of the rectangle in the diagram below. If the path is 3m wide, it allows a headspace of a little over 3m, but this will shrink depending on structure.