Garage Ceiling Joist Question
Could be with the proper bracing...run the 2X's like you're thinking. Then run some braces up to the rafter above the joist...nothing fancy, just tie the two together. I would brace each one in three places, the center and then half way between the center and the wall each direction. Braced up well you could probably get by using 2x4's.
You might be money ahead to purchase shorter 2X's and splice the center. The center brace would support the splice to keep everything in plane, the center brace should include a plywood gusset G&S to tie it all together. I would think it may be easier to install 2-10' 2x's that one long stick.