If you are building the bridge out of balsa wood cut out and glue gusset plates similar to what Andy McConnell did in his well built bridge shown above. Here is a connection detail of one of the spaghetti bridges. The lightest of the commercially available hardwoods, it grows naturally in the humid rain forests of Central and South America. The best stands of balsa usually appear on the high ground between tropical rivers where there is plenty of rainfall and good drainage. Balsa wood is so light because the cells of the wood are big and very thin walled, so that the ratio of solid matter to open space is very small.
Woods typically have a gooey cement, called lignin, holding the cells together.
In balsa, the lignin content is at a minimum. In a living balsa tree, the remainder of the volume is filled with water. That gives the tree, which can grow to 60 to 90 feet tall, the rigidity to stand. Each balsa cell is naturally pumped full of water until it becomes rigid much like a tire full of air. Green balsa wood must be kiln dried to remove most of the water before it can be sold.