I need to run two ducts in my first floor ceiling perpendicular to the joists.  The ceiling is framed with 2x6s, 16″oc with an eleven foot span.  Ideally, I’d like to remove a 2′ section from the middle of one of the joists and bridge the opening on both sides with a doubled up 2×6.  Similar to the framing for access to an attic.  This would allow me to jog the ducts over from a wall on the second story to a nearby wall on the first floor.  Can I do this with 2×6 joists?  If so, any recommendations for making sure the inspector won’t take issue with anything.

Thanks for the input.