You also need to consider the flow of the stream and how high off the water you will be. If you get flash floods or high flows it can wash your bridge downstream if it is not anchored to the abutments.
As for the design I would suggest using three posts (railroad tie) at each abutment one at each end and one in the center. Then lay one tie across these posts parallel to the stream and anchor it to the posts. This will be the support system. Then lay your railroad tie deck perpendicular to the stream. If you can drill holes through the ties at 3rd points that line up all the way across and put a threaded rod through it and put a nut and washer on each end. This will make them act as one beam and you won't have to worry about the extra load of the deck on top of your beams.
Dave
As for the design I would suggest using three posts (railroad tie) at each abutment one at each end and one in the center. Then lay one tie across these posts parallel to the stream and anchor it to the posts. This will be the support system. Then lay your railroad tie deck perpendicular to the stream. If you can drill holes through the ties at 3rd points that line up all the way across and put a threaded rod through it and put a nut and washer on each end. This will make them act as one beam and you won't have to worry about the extra load of the deck on top of your beams.
Dave