Roof Design for an Octagon Shaped Pergola

There are two considerations: 1) Structural, and 2) Aesthetics.

1) The pergola is small enough that you could span it with a 2x6. However, it will look weeny.

2) I’d use 4x6 (minimum) beams to match the posts. If you bolt them together they will want to “splay” outward. So, I’d use a gusset plate at the peak to help it keep its shape. Remember, steel connectors are basically “hinges”, so provide plate supports for rigidity or provide cross-ties at the top of your posts. (I like the gussets near the top so it has a “vaulted” appearance.)

Then you could install 2x6 decking on top of the beams. Install each section so the decking is parallel to the bottom edge.