Here's how I created a cardboard poster backing, that when full size will support a 24"x36" poster, and when folded in half will support an 18"x24" poster.
Cut two pieces of cardboard from an old box of size 18"x24". Place them side by side, along the 24" length. Using any packaging tape (I like Uhaul's "Box / Packaging Paper Tape" http://www.uhaul.com/MovingSupplies/Tape/Box-Packaging-Paper-Tape-%2855-yard-roll%29?mid=143&id=822 - it is strong, sticky, and can be torn by hand, and it blends well with the cardboard color), tape the two sides along the seam, and smooth down with a ruler or something to make sure it adheres well.
Fold it in half along the seam. Using more packaging tape, tape along the inner seam of the hinge to make it stronger and provide more support.
Voila! You have a poster backing board that is versatile, and will easily support two sizes of posters, 18"x24" AND 24"x36"!