Some other ideas: Cut the curves from an already curvy branch (this will be stronger), cut the curves from a larger piece of wood (say ply). Steam bending.

Steam bending is the traditional way for load bearing beams, but that was before the invention of power tools and cross linking PVA glue.

You won't be able to get a good curve using only the columns (and you'll have trouble with them moving under the force). Better to make a curved former out of ply or MDF and use lots of clamps (like 1 every foot). There will be a lot of force applied for the first few laminates, so you'll need the former to be very strong. A good idea is to cut the shape in thick board then drill 1inch holes every foot to put your clamp in.

I'm surprised that you can bend 1 inch wood, but my US friends tell me that your hardwood is lot less stiff than here, so it might work.

how much of a curve?

I'm guessing a radius of about 6 feet - nathanhurst is right, 3/4" is too thick to make that turn, unless it's green and steamed. I guess what I'm looking at is 1/4" boards, built up to a beam of about 3 1/2", unless you've got another suggestion.

(I might try wandering in the woods to see if I find something natural to work, but that's a long shot. I've tried steam bending wood for a snoeshoe project and I don't really see that working out for this application.)

Thanks,

Bill

Steambending would work well for this project, assuming a radius of 6, (I have no idea what a pergola is) I can definitely see 1/2" ash making that kind of a bend id steamed, they do it in boat building all the time, Ash is the wood of choice for mking a fair curve like the one you want/need. I also like the idea of cutting it out of a large curved branch or trunk, I suggest Titebond III, I've read Rave revieds in a few wood working publications including Tautons Fine woodworking.

Does anyone know of places you can -buy- curved beams?

Would you consider using Trex for at least this portion of the project? Trex isn't great for really heavy loads but should be able to handle the load of a Pergola. I do know that it bends easily as we have done that on a playground project I worked on. I would also like to build a curved front pergola and Trex seems to be the easiest solution so long as I don't want a white pergola (which, of course, I do).

Can you bend trex with a heat gun?