Atrsch existing to new ceiling joist

[Heavydrop68]

My polebarn is 60'x29' and I ripped out the old drop ceiling and I'm going to put drywall up. I'm going to use 2"x6"x16's for my new ceiling joist. My new ceiling joist will be 40" below my existing, how do I properly attach the new to the old for weight & support reasoning? Do I just attach a 2"x4" from existing to new 4 times across 1 joist?