What is the stability of a crane mounted on a barge?

You'll need specifics to calculate the stability of a crane mounted on a barge. The crane has a given mass, a given height (depending on the manner in which it is operated), and a given mechanical moment. This is based on the mass, size and shape of the crane as it is deployed, and also the size and shape of the barge. Certainly the manner in which the crane is placed on the barge will have to be considered.