By your use of the term cantilever, I assume there will be no other support except at the ceiling? If there is support at walls at the ends and the span isn't too great, there may be no problem other than sagging at the center.
I'm a bit concerned about your attachment at the ceiling. You're correct in the approach of using a triangle to provide efficient support, but I think the area of support is insufficient. You appear to be projecting about 18" and relying perhaps on support at the about the first 4" or so. I'm not sure that is enough.
Even if all your little parts were fastened rigidly enough by glue & screw, the screws or bolts holding the 2X4 to the rafter need to be sufficient to avoid a long hinge line along the 2x4. I would use a double row of lag bolts to prevent the 2x4 ledger from rolling.
I'm assuming that cutting the sheetrock away is not an option. If it were, I would suggest using 1x3's as your horizontal piece, butted directly to the side of the rafter up to the underside of the roof deck, fasten a piece of scrap to the rafter above the 1x3 and gluing and screwing a triangular plywood gusset to each side of the rafter and 1x3. This would give more substantial area of support.
Why not omit the "L-Girder" to keep weight down and just use a strip of some thin facia material instead? The Girder offers nothing in the way of support. In fact, I'd further reduce the weight byomitting the plywood and use a single layer of 1" foam over such a small area, but that's just my preference.
If you forge ahead with this design, I'd try a short 4' section and give it a few firm tugs to test it out before building the whole layout. Report back and tell me I'm wrong. (Wouldn't be the first time.
)
Wayne
