An assembly including a tire having beads, said bead axially including outside the turn-up a layer of a material defining a bead outer profile, such that the distance A, between the carcass frame and the bead outer profile, is as defined in formula (Z), B being the distance between the end of the turn-up, said bead including first and second profiles between the carcass frame and the turn-up, the first profile extends from the bead wire and is made of a material having an extension secant modulus at a 10% elongation higher than 20 MPa, a second profile arranged in the bead such as to be in contact with a surface of the first profile and the turn-up, made of a material having an extension secant modulus at a 10% elongation of at least 7 MPa and an extension secant modulus at a 100*% extension of at least 4.5 MPa.