Electromagnetic and mechanical study for the $Nb_3 Sn$ cos-theta dipole model for the FCC

The Italian Institute for Nuclear Physics (INFN), in collaboration with CERN, is going to build the short model in Nb $_3$ Sn of the main bending dipole for the hadron-hadron Future Circular Collider (hh-FCC). The magnet will be developed on the basis of the baseline design presented in the FCC Conceptual Design Report (CDR) in the end of 2018. In particular, it will be based on cosine-theta design, with an internal aperture diameter of 50 mm and a Bladder & Key configuration for the mechanics. The main purpose of the model construction is to demonstrate the feasibility of a magnet dipole with field quality characteristic suitable for a collider and magnetic field above the LHC frontier.The mechanical structure, which is a critical aspect of the magnet design, especially for the brittleness of the Nb $_3$ Sn cables, will have to demonstrate the effectiveness to reach the highest performance achievable in terms of bore magnetic field. Here we present both the electromagnetic and mechanical design study of the model.