I have a wall that has a vent right against it so I cannot frame up to the joist. I am considering using L-Brackets connected to the masonary wall. I have a drawing below.

I'd like some advise/comments on this plan:
Pre-build a traditional stud wall on the floor
Attach a few L-Brackets to the top plate
Raise up and attach to the masonary
Soffit down to the secured stud wall

Is this a sound approach? Can I get any comments or advise for me... much appreciated!

I see no reason why it shouldn't work. You'll want to close off the space between the top of the stud wall and the gap behind the duct to prevent fire and smoke spread. Do it so that if you had a fire in the wall, it couldn't travel into the soffit or into the joist cavity by going around the duct.

Only thing is maybe find a little lower place to put that bracket, maybe on the underside of the top plate rather than the top side, it'll make drilling in that concrete wall much easier.

Thanks to both for your comments-
Maintenance 6 - blocking the space sounds like a good idea. Are you talking about a sealant such as:


JayinMinnesota - thank you for the suggestion.

Please tell me, do people usually using furring strips in this situation?

thanks,

Most places allow just stuffing it tight with fiberglass insulation. The firecaulk option is better but a lot more expensive.