Sorry, Jim. I misunderstood. I thought the image you created was of the final structure AFTER doing the beam sizing calculations.
To help with calculations, my internet search has come up with the following:
Avg weight of red cedar - 26 lb/cu. ft green 23.7 lb/cu ft. dry (12%)
Avg weight of douglas fir - 35 green 33 dry.
(Of course divide by 12 for board feet.)
Obviously fir is heavier, but also stronger.
Given that I live north of Seattle, can we assume it will spend much of its time closer to green than dry?
To complicate things further, because my wife wants a "Roman" gazebo with round decorative columns covering each post, knee braces are difficult (impossible). To prevent racking, can I use a large dowel (which is easiest for her non-timber framer husband) glued in place and 2 commercially available 7 guage angle brackets per post?
Earlier I had said I was planning to use 6x6 posts. That was because I assumed I needed that to allow for a sizable dowel. Using 4x4 posts would be lighter and allow more room inside the decorative post end caps for longler galvanized brackets.
While I'm asking for help - do I need the purlins/battens to tie everything together? Will they also help with the racking problem?
What makes this all confusing is I've found sites, such as
www.baldwinpergolas.com, which sell commercially made pergolas, some with 18 foot spans - simply using pairs of KNOTCHED 2x8 cedar members as the "entablature" (beam). Am I missing something?
I appreciate everyone's help. Thanks again, again,
Bob