The total applied load of will be carried partly by the aluminum and partly by the brass. In other words, the internal force in the tube plus the internal force in the core will add up to .
Force applied to an axial member produces an axial deformation (either elongation or contraction). Since the aluminum tube and the brass core are bonded together, the deformations that occur in the tube and the core must be exactly the same.
These two observations will be used to determine the force carried by each of the components. Once these internal forces are known, the corresponding normal stresses can be computed.