I absolutely love structural steel studs. I built one of these before patio v1 (at my old house) and last year i built a cantilevered deck  off my backyard so I'm a somewhat capable armchair engineer. However, I don't understand trusses (their bearings and cantilevered!) and know my limits when to ask for help.

This is a project years in the making and the footings are already there: 2' reinforced concrete caissons 3' deep on 3x3' footers. (poured a couple years ago)  with 4x1" embedded bolts 

 

I wanted to keep the trees, hence half open, but calculate everything as if it's a solid roof.

Construction wise, It's just me, so that kinda influences the design. 

I made some posts for railings and i really like the design, I'm into fractals and based the the columns on:  are 20pieces of 2x2x16ga?? steel, with 1/4"??  plate CNC cut and welded at various intervals for aesthetics and bar joist bearings. *note it'd be great to cleverly space them so they're all the same layout. Intuitively they seem stiff enough, but I couldn't prove it :(

 

Naively, I'd pick a 20K(something) bar joist, but I have no idea. I'd like to minimze the depth. 

As far as the actual structural steel studs, i think? i can get by with 800S300-113's but would also consider sandwiching smaller ones but I dunno. with a corrugated corten roof (and some fiberglass panels for light). 

Hopefully this will get us started and I look forward to hearing from you soon.