Tyre for a vehicle wheels with self support-functions, and a rim for said tyre

A tyre for vehicle wheels comprising:

• a carcass structure (2) having at least one carcass ply (3) with axially-opposite circumferential edges in engagement with respective annular reinforcing structures (4) which are disposed in coaxial relationship with a rotation axis of the tyre (1) at positions axially spaced apart from each other and which are each incorporated into a tyre bead (5);
• a belt structure (6) applied to the carcass structure (2) at a radially external position thereof;
• a tread band (7) applied to the belt structure (6) at a radially external position thereof;
• at least one pair of sidewalls (8) each extending between one of said beads (5) and a side edge (7a) of the tread band (7), at an axially external position with respect to the carcass structure (3), characterized in that each of said beads (5), at a radially internal position thereof, has a rest surface (5a) that, in a diametrical section plane of the tyre, defines a profile converging towards the rotation axis of the tyre (1) away from an equatorial plane of the latter,
• with said carcass structure (2) being in addition associated at least one circumferential centring ridge (20) radially jutting out inwardly of the tyre (1) from a crown portion of the carcass structure itself, axially confined between the opposite side edges (7a) of the tread band (7).