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I'd like to make a veranda over our patio at the back of the house to have a sheltered eating/sitting space.
It will be in front of some bi-fold doors so I'd like to avoid putting a post in the middle. This means the span needs to be 4.8m. The depth will be about 4.
It may eventually have some poly carbonate sheet 'glazing' on the roof, but it's pretty expensive so I might just put a waterproof sun sail over it. could even do oak, but gets pretty heavy
Whats the best way to make the span? Bolt two beams together? get a really deep section for stiffness? I am considering pressure treated timber or western cedar.
I can't bolt anything to the house - it's timber framed and clad and even with plates behind, it's a faff.
If it needs too much engineering, I may just have to bite the bullet and put a central support post in, but i'd like to see if it's possible without. Rough sketch(up) below

I don't think 4.8m would be a problem for an oak beam. You need to have an idea of the maximum roof load e.g. your sail is up and there's 2ft of wet snow on it.
Your sketch doesn't have much to stop lozenging except the screws holding it together. I'd add some webs in both directions to stop that as it's essentially a free standing structure. You also need to anchor it solidly to the ground.
If it's not going to be bolted to the house will there be a gap? I'm not sure that having a free standing structure swaying against it is a good idea.
We have a slightly smaller, but similar setup, and used plained larch with a 4.7 span. Ours is connected to the house though, and does have a glass roof. Best thing we did, other than extending the house, means we can have the back doors (need a bi-fold door next) open most of the spring/summer/autumn & the dogs love it
Just watch the wind loading if you cover it....... a strong wind can create a big lifting force that would love to pull it up.
Otherwise that span doesn't seem too much just go bigger than you think! Quick google reveals this as a starting point (this is for a flat roof):
5m span - 75×220 @ 400c/c
(if it's freestanding then you're going to have to think about how to stop it wobbling)
Needs triangulation.

Yes! will have 45degree wind braces as shown in this sketch and posts will be anchored to the patio - not sure if bolt down shoes on the pavers is enough, or I need to put something solid underneath and chemfix some rebar and a shoe for each post.
Last year I made a 3x3 green oak frame with 100mm square rails and that's fine, just wasn't sure if the extra span would cause it to sag too much
Based on your sketch, you'll need professional advice as currently you have two of the rafters "floating" and only being held up by blocking.
On this end away from the house you either need a face mount or dropped beam so the rafters are all doing the same thing. Suitable hardware required too.
13ft span is pretty big. I'd think at least 2x8 alone for rafters just to stop them sagging under their own weight. Double up 2x8 as a Dropped beam carried on the outside posts let's you reduce the span further with increased cantilever.
Consider that doubled up material is less preferable to a thicker single piece if unroofed as water will get in between the faces of sistered material and stay wet.
Cedar and pressure treated lumber (softwood) are less strong than oak also
As above, uplift concerns if you roof it. A post foot bolted to your patio wouldn't do anything to stop it..do it properly and do a concrete footing
I would probably look to use Douglas Fir or Larch rather than Cedar, similar weather resistance but a more structural timber (based on my observations from felling them).
Sharkbait's dimensions sound about right as I planned to do something similar at a previous house. Didn't do it in the end as was going to be a pretty thick beam cutting through our view to the hills as being a bungalow we were limited on how high the wall plate could go.