A radially expandable building drum (1), intended for the manufacture of an adapter for mounting a tyre on a rim, comprises a central axis (X-X), and an assembly zone coaxial with the latter and comprising a first set (10) of segments (100) and a second set (20) of segments (200), all the segments being arranged circumferentially around the central axis, in which the segments (100) of the first set (10) and the segments (200) of the second set (20) face one another axially. The external circumferential face of each segment (100, 200) comprises a groove (103, 203) for accommodating a bead wire, and the said drum passes, in the said assembly zone, from a retracted first position of substantially cylindrical shape into an expanded second position of substantially frustoconical shape when the segments (100) are driven by a first cam (300) and the segments (200) by an adjacent second cam (400).

To form a tire carcass, a body ply is wound about a drum, which has two half-drums movable axially in opposite directions to and from a center plane of the drum, and having respective turn-up bladders, on each of which is laid a respective annular lateral portion of the body ply; each annular lateral portion being turned up about a respective bead bundle and onto a sidewall of a toroidal-shaped annular central portion of the body ply by inflating the relative turn-up bladder and controlling distension of a given annular portion of the turn-up bladder so that, when inflation is completed, the annular portion assumes a given final position, in which an intermediate portion of the turn-up bladder rolls outwards along the relative sidewall of the annular central portion of the body ply.

A bead-lock section for use in a first drum half between a crown-up section and a turn-up section, includes a bead-lock seal arranged to extend over and seal the bead-lock member in an air-tight or substantially air-tight manner. The bead-lock seal has a first end that is arranged to be mounted in an air-tight or substantially air-tight manner to the crown-up section and a second end that is arranged to be mounted in an air-tight or substantially air-tight manner between the bead-lock member and a mounting body directly adjacent to the bead-lock member. The bead-lock seal is arranged to slide along the mounting body when the bead-lock member is moved between the release position and the bead-lock position.