I started to create a chase from the crawl space up to the second floor. The chase is located in a non-bearing wall. It will be used to provide hot air to a bonus room. I gained access to the top of the chase on the second floor. As I look down, the chase is free and clear for rectangular metal duct. However, at the bottom of the chase there is a joist that is parallel and directly below the non-load bearing wall. In this situation, when a 2"x10" joist is in the way of a new chase, is the appropriate solution to temporary support the joist then cut a section out then nail in 2"x10"s short cross joists using hangers?