Question on basement ceiling framing

What Kirk said would work, your 2 x 4 on the flat would work. I usually use 1 x 6 t & g knotty pine to span the ducts and wrap the vertical sides. You still have to build a wall on either side, but you only have to have it drop about a 1/2" below the low point of the ductwork. Its a nice look and breaks up the drywall look.

I had a supply and return duct running down the middle of mine. I am far from a professional, but I built ladder bulkheads on each side, laid the 2X4 flat running across and then stood a 2X4 vertical down the center, screwed it to each crossmember and every 4 feet ran a short piece of 2X4 up to the floor joist above. This gave me about 2 more inches of headroom. Once it was all fastened, I grabbed the crossmembers and hung my body weight from them (about 190 lbs). They didn't move. This was probably over kill, but I'm known for that. I used 5/8th drywall on the ceilings and was a little worried it would sag.