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 at the end of the turn-up and spreads through the polymer coating, edging and filling materials. According to the invention, a transition element, made of a polymer transition material, is at least partially in contact, on its axially outer face, with the polymer edging material and, on its axially inner face, with a polymer filling material, the radially outer and radially inner ends of the transition element are respectively radially on the outside and radially on the inside of the end of the turn-up 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 edging material and of the polymer filling material with which the transition element is in contact.