Stiffening this module takes some creativity. Consider using hollow aluminum or steel rectangular bar to provide additional stiffness within a wood box as shown. This would provide the necessary strength and stiffness since the height of the module narrows through the gorge.
You may also want to incorporate metal bar surrounded by wood in the bridge decking to ensure they are sufficiently rugged and robust to withstand leaning children. The segment top could be slanted into the gorge for an even more striking presentation.