In this safety support comprising a segmented ring (6), whose segments (6a, . . . , 6f) are connected by linking means (9), at least one of the linking means (9) comprising at least one male element (26) and at least one female portion (27) suitable for fitting one inside the other by a relative movement of two segments in the circumferential direction of the ring, the at least one linking means (9) also comprises a lever mechanism (28) comprising at least two link arms (29, 31) of different lengths articulated on one another and each at one respective end of the two segments so that the lever mechanism acts so as to bring the two segments closer to one another when the male element (26) is partially engaged in the female portion (27) and when an articulation (38) common to two link arms of the lever mechanism (28) is moved substantially radially relative to the center (C) of the ring (6) in response to an axial movement of the ring relative to the rim.