You can pick up Ted Benson's book 'Building the Timber Frame House.' In the back of the book there are all the formulas, tables, and example calculations for sizing sawn beams. Maybe if you integrated some arched gussets. Even with your light load, you are pushing at 20' plus the uplift and side shear for the wind. Any professional carpenter will tell you the same thing.Ī 6 x 8 will span 12' for flooring. Stop agonizing over it and add a mid-span post. An 8x8 (even with no load) would sag under its own weight at that distance. Seems to me you're trying to talk yourself into a full span of twenty feet or more. There are span tables based on load and species. Get a copy of the UBC or code that is relevant in your area. The plan I imagine is that the 8x8 will be the center beam of a pergola with bamboo covering the top from the beam to the end of the pergola. The tables are usually based on allowed deflection, not ultimate strength. There are tables for stress rated lumber that show allowed sizes. Much of what the width is doing is keeping the beam from rolling sideways (why a 2x12 that is only 1.5' wide can span 16'). Too many things missing! Are the 8x8's used as joists? How far apart? What is the deck? What is the live load? Any codes involved? The width of a joist/beam is not nearly as important as the depth.
