An assembly (1) for a tire comprises a first structure (10), a second structure (12) and bearing cord elements. The assembly comprises a gimped securing element (18) comprising a core (18a) around which a gimp yarn (18b) is wound. The core (18a) exhibits an elongation at rupture Arupture_core and the gimp yarn (18b) exhibits an elongation at rupture Arupture_gimp such that: Arupture_core A1=h/(E+e1+e2) in which h is the conformation height of the assembly, e1 is the thickness of the first structure (10), e2 is the thickness of the second structure (12), and E is the lock length.