I suppose there are two approaches to this. You can try to "optimize" your design by having the members carrying near the same force, or you can try to "optimize" it by choosing different size members so that the ratio of force to cross-sectional area of the members would be close to each other.andrewwski wrote: ...
That wouldn't be my design of choice, as you're supporting up to four times the load in some members and greater than the load in almost all of them. While it's the ratio of loads between members that I find the most helpful, you may find designs that lower the load but do not use substantially more members.
For example, for the bridge that AlphaTauri posted above, a top member carries a compression force of 262, and one of the members at the base of the bridge on either leg carries a force of 85. One approach to "optimization" would be to modify the bridge geometry so that these member forces would be closer together, and then use the same size wood (say 1/4" by 1/4") for both members. Alternatively, you can keep the geometry as is, but use different size wood for each member (say 1/4 x 1/4 for the top member and 1/4 x 1/8 for the leg member).
Here is another important point that you need to keep in mind when designing your bridge. There are two primary reasons why forces are created in structural members. The obvious one is that the structure is subjected to a load, like the bridge being subjected to a load of 15 kg. The less obvious one, the one that probably makes most of SO bridges fail prematurely, is excessive displacement of the joints of the structure. Such displacements could produce rather unanticipated internal stress in members causing them to fail. For example, A few millimeters of lateral displacement at the base of the bridge could result in significant (bending) stress in a member along the top of the bridge. So, when you are designing your bridge take displacement into consideration and try to minimize it as best as you can.