Adding joists in garage to drywall

[DKAudio]

I have a typical 2 car detached garage that I want to insulate the drywall. The joists right now are 2X6s at 24" OC. There are 3 spots however that the span is 48" (almost like a joist is missing). One is at the way front and then the next span and the last is at the way back. Therefore, I need to add joists to these spots in order to secure the drywall. The roof type is hipped (angled on all 4 sides). How can I add 2X6s at this point? I can't fit a whole joist span in since the roof is in the way. I think I need to install (2) 1/2 span pieces and join them in the middle somehow.

[Kman]

The only way I can think of that you could do this is to add a cross piece between the two existing joists at mid-point of the span, then put in two joists that are half the span connected to the cross piece in the middle. Some of the weight will be transferred to the two existing joists, but as long as you are just adding insulation and not putting any serious weight up there, it should be okay. Doubling up the cross piece might be in order, since they'll be spanning four feet. Doubling up would also give you a little more to nail into.