Go here to figure your spans. With a pergola what you are actually looking at is more of a ceiling joist where the dead load is only the weight of the joist itself. Don’t put in rafter or you will get a much greater span.
My guess would be that 2x6’s will probably start to sag in very short order, not to mention how bouncy they will be. Play around with the span chart and I bet you’ll find 2x8’s are sufficient though. However, if you are planning on notching them I would definitely stay with the 2x10’s as you are creating a real weak point here. If you go with something smaller you can always just put some hurricane ties on instead. You also might consider some cross-bracing.
A true (2)2x12 beam and notched posts will be much stronger than the example more pain posted, but 18’ is an awful long beam. Probably fine for a purgola, but you’d hate to see it sag. You may want to go for a 3-2x12 or add a post. Beam calculations are more difficult than joist span so you can’t really just look up a chart.
I think you are probably fine, the only thing about your plan that really worries me is your hole depth. First you need to check where the frost line is for NE Ohio. Second, you have to remember that you’re going to have 13’ sticking out of the ground and there will be a lot of leverage at this point. You get some soggy ground and streamline winds and those joists are just going to be windbreaks. I could easily see a purgola going over in such conditions. If you’re going to be that tall, I’d probably go a bit deeper. Also definitely make sure to use a good form so you don’t end up with a bowl-shaped footing.
*Not a building engineer, just have some knowledge on the subject.
Thanks for the reply.
I have used that chart before, thanks for the link.
I originally was thinking 2x10 for the header but sag was a possible issue. I was thinking the 2x12 for the 18’ span to eliminate any possible sag. I don’t want the third post, just want to keep it at the corners want a clear view.
The notching would be no more than an inch. Just something to lock it all in place add a little stability.