Circular Joints?

I'm currently working on a project where (similarly to many "bridge building" games) the user is allowed to create a structure. This structure consists of rods (cylinders) and nodes (spheres) that are attached to each other. Each rod is attached to exactly two nodes (unless it is the predefined rod standing on the ground) but a node can have a possibly unlimited number of rods attached to it. Currently I am using two fixed joints at the rods to connect with the nodes. It works well unless I try to create any kind of closed structure (at the moment any rectangular shape). In those cases my whole structure starts to fly around, violating any joints that are created. My question is if this is even possible with FixedJoint? I tried to use other joints as well but the node always fell of the tip of the rod.