The pvc pipe goes all the way thru to provide support for the entire gun. All the cardboard is glued at various points to the pipe. Also, I put crosspieces of cardboard inside the gun to further brace it.
The strength of the cardboard comes from cutting/building against the corrugation. If you cut along the pleats in the corrugation, it'll bend on those pleats. Make them go vertical and they'll hold up to the stress. It's like cutting wood against the grain versus along the grain; along the grain is more prone to bending or splitting.
Looking good so far, definitely one of the better homemade guns I've seen. I don't know if you want to know this when you're this far in, but...the part behind the frontmost piece of the barrel (forgot the term; it's 3 A.M.) is actually triangular, not rectangular...
Ah crap, you're right. Finally looked at a good front view and it is indeed wider along the bottom than on the top. Damn. Fortunately, it looks like it'll be an easy thing to fix; the exterior isn't structural to the gun, so I can rip it off and try again with little damage to the actual body of the gun. Will need some more paint though, all out