pergola
I have a 20'x20' pergola on a concrete patio.
Construction is 8"x8" posts sandwiched with 2"x8" rafters.
I notice some swaying during some thunderstorms with heavy winds and I can push on a post with some effort, that moves the whole pergola.
What size knee bracing should I install (width and length)?
I would use titan post anchors for the posts.
For the ledger on the hollow block wall you can buy masonry anchors designed for that. Hilti makes tons of really good anchors. For hollow CMU walls, how they work is you drill the hole and insert a screen tube and fill it with the adhesive. Then when you insert the bolt it pushes the adhesive through the screen making it expand wider than the width of the hole.
Hilti
Simpson Strong Tie
You can easily span 12' with a 2x12 for a pergola as long as your load is not crazy. What is going on top of the 2x12's? 2x2's? I would set my posts on 12' centers and cantilever 4' on each side. I would also sandwich a 2x12 on each side of the post. There actually is enough information in your question but there are many online beam span charts. Here is one. Hope it helps. Make sure there is no earth to wood contact on your posts and you will enjoy your pergola for decades. http://www.decks.com/deckbuilding/beam_span_chart_table
Best Answer
That's a beautiful pergola, and to preserve its style I would use the same timbers as you used for your posts. I'd make the vertical and horizontal legs of the triangle 1/3 of the post height, unless that causes serious headroom interference, then reduce a bit to no less than 1/4 of post height. Much less than that and you won't see much benefit.
I'd make all the knee braces the same length, so that they interface with the posts at different heights due to the rafter height.
The connection between the rafters is fairly straight-forward. The connection at the post is less so. Large lag screws, countersunk and level, or carriage bolts all the way through would be good. That connection will have the most tendency to slip, reducing the effectiveness of your effort.
Here's a similar example courtesy of StrongTie. In this case the knee braces connect to the post at the same height, but I pictured yours being vertically offset (to match the height of the rafters). I would also deviate from this photo by running the bolts in horizontally. You'll need shorter bolts and I think you'll end up with a better connection.