Many building departments have pre-approved handouts for designing simple structures. Loads can be determined from tables in the code. Codes assign live load and dead load requirements. In 40 years of residential construction and design I have never seen dead loads calculated, but simply based on a standard per square foot load usually 10 pounds or so, this has plenty of wiggle room built in. There are span tables for joists and rafters, which is the most difficult part of gravity calculations. For your posts, footings and hangers just add your per square foot dead and live loads and figure the tributary area.
Yeah, that sounds reasonable. Basically, my thoughts about providing the full calculations started with the fact that I don't know- and the Building Department doesn't know or have a table for- what 2x2 Doug-Fir, spaced 4"o.c. weighs per square-foot. After my research this morning, I now do.
Like for my Patio-Cover, with the concrete-tile roof, we use a dead-load of 14 lbs/sf. Per the California Residential Code, for a patio-cover, we have to add snow-load (which, locally, we do not have) and 10 lbs/sf live-load. For non-patio-covers (i.e.: house) we have to add 20 lbs/sf.
Mine is a different design, being that the 4x8 main-joists hang off the house fascia, which are attached to the tails of the house with (2) 16d's, an SDS screw, and an A-34 (this means nothing to you non-construction folks reading this-- sorry- esoteric)- there's a detail on my plans Sheet-2 showing this. And I am actually a little concerned with that connection; so I wanted to calculate the load and see how I felt about it.
Also, at the Trellis I think I can fall under a section of the CRC specific to patio-covers that states if the load at the post isn't more than 700 lbs., a footing is not required (we have 0" frost-line) and I can bear directly on the existing 3Â½" concrete slab (there's a copy of that code on my Sheet-2, as well).
I guess what I'm getting at: I don't think- and I don't know if the Building Department is going to think- that this falls under the realm of "simple structure"; it definitely doesn't look like anything on their prescriptive patio-cover drawings and details.
Thanks for the input Mike. It's always nice conversing with a fellow TurboCAD/residential construction person.