how to make a spaghetti bridge that wont break with no glue?

Answer 1

Cook the spaghetti, form your bridge and then let it dry out.

or

use some cooked spaghetti to bind some dry spaghetti together to construct your bridge.
I would make some box girders out of lasagna noodles held together with cooked spaghetti "ropes"

Answer 2

We always used glue.

Could you use the starch in the spagetti to stick it together.
Try getting two peices wet and holding them together until they dry. They might fuse together.