A tire 10 comprises a radial carcass reinforcement 2 surmounted radially on the outside by a crown reinforcement 31, the carcass reinforcement 2 being formed of a plurality of metal reinforcing elements 21. The tire also includes two sidewalls 1, at least one of the sidewalls comprising an additional reinforcing reinforcement 5 wherein the additional reinforcement 5 comprises, in the circumferential direction, on the tire a plurality of first parts 51 and of second parts 52 that have rupture strengths, that is to say, forces that rupture per unit width of reinforcement, that are such that the rupture strength of the second parts 52 is lower than the rupture strength of the first parts. The first parts 51 and the second parts are arranged such that they alternate in the circumferential direction.