For the OP.
I have a solution for you.
Let's say you have 1200 pounds of stuff to store up there. And let's say some of it is bulky, so you want to put it in the middle where the height is greater.
So let us designate an area 8' wide by 12' long, or approx. 100SF. Spread the load across this area and you get 12 pounds per square foot of live load. The structure to hold this up will be another 7=10 pounds per square foot of dead load depending on whether you have a ceiling attached.
Using this joist calculator:
http://www.awc.org/codes-standards/calculators-software/spancalc
Set it to the following parameters:
Ceiling joist
L/240 (No finished ceiling attached to the bottom)
#2 Hem-Fir (Readily available lumber species and grade)
2x10's at 16" on center
This will span your 24'
Use 1/2" plywood for the decking material and use blocking between the joists where seams occur. Glue and screw the deck in place.
You could actually extend the decking all the way to the side walls for additional storage with the same capacity per square foot. It just wouldn't be as tall.
And you wouldn't have to stop at a 12' long space. Just add more 2x10 ceiling joists and decking to extend it. You could do the entire overhead area like this. But access becomes a problem, because it really isn't designed for walking on, and there isn't really space up there to do so anyway.
You could use 2x8's if the load was less per square foot by making the area larger and spreading the load out more.
Understand?
Btw, do you ever intend to have a ceiling in that space, or insulate it?
Bill