The invention relates to improving the endurance of the beads of a radial tire for a heavy vehicle of construction plant type by reducing the cracking that starts on the axially outer face of the turn-up and spreads through the polymer coating and filler materials. According to the invention, a transition element made of a polymer transition material, is in contact, via its axially inner face, with the polymer coating material of the axially outer face of the turn-up and, via its axially outer face, with the polymer filler material, and the elastic modulus at 10% elongation of the polymer transition material is somewhere between the respective elastic moduluses at 10% elongation of the polymer coating material and of the polymer filler material.