- Conventional FEM chokes on this because it's (obviously) non-linear and recursive. No great surprise there.
- You tend to see this in sloped members simply because you tend to see this in roofs. Architects are usually a good deal less about the aesthetics of it in the underside of a floor. Also, you kinda need the oculus business for full dramatic effect. That's not unheard of in floors but pretty rare.
- I don't believe that axial/membrane effects are required for stability. If you've got a competent tension ring that'll certainly help. With no tension right, the slope exacerbates problems and lateral spread rears its ugly head.
- From a stability perspective, I believe this to be okay by inspection based on this observation: by definition, nothing here "grows without bound". The contributions to flexure and deflection get progressively smaller as you cycle round. Nothing runs away/amok on you.
- If you've got a vibration sensitive occupancy, that definitely warrants some attention.
- If you've got rain or concrete ponding potential, then there's a stability issue there. But that's a different animal and, other than trickier math, is little different than ponding issues in normally framed systems.
- This is actually quite a common morphology in old school heavy timber structures, particularly in the NE. Barns and churches where they mount a pergola on top and want no obstruction below. Back in my wood truss design days, I used metal plate wood connected trusses reciprocally to mimic these structures in certain applications.
- A useful way to think of these systems is as two, crossing beams, each constructed in two pieces that are moment spliced in a peculiar fashion.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.