Assembly for a tyre comprising: - a first structure formed by first cord elements, the first structure having a longitudinal edge extending in a first direction which defines a first axis, - a second structure formed by second cord elements, the second structure comprising a longitudinal edge extending in a second direction which defines a second axis, the first axis and the second axis being parallel, - a bearing structure comprising bearing cord elements linking the first cord elements of the first structure and the second cord elements of the second structure, and - at least one cord securing element fixed to the first cord elements and to the second cord elements, the assembly being characterized in that the at least one securing element exhibits an elongation at rupture at least equal to a minimum elongation A min greater than or equal to the ratio (A 1) between a conformation height (h) of the assembly and the sum of a thickness (e 1) of the first structure, of a thickness (e 2) of the second structure and of a lock length: A min ≥ A 1 = h / E + e 1 + e 2 in which: h is the conformation height of the assembly, corresponding to a height between opposite faces of the first structure and of the second structure when the bearing cord elements are taut; e 1 is the thickness of the first structure; e 2 is the thickness of the second structure; E is the lock length, which is equal to the sum of a first curvilinear length of the portion of the securing element which is locked in the first structure and of a second curvilinear length of the portion of the securing element which is locked in the second structure, where the first curvilinear length is equal to half the curvilinear length of the securing element which is locked between two successive anchoring points in the first structure, and the second curvilinear length is equal to half the curvilinear length of the securing element which is locked between two successive anchoring points of the securing element in the second structure. - a first structure formed by first cord elements, the first structure having a longitudinal edge extending in a first direction which defines a first axis, - a second structure formed by second cord elements, the second structure comprising a longitudinal edge extending in a second direction which defines a second axis, the first axis and the second axis being parallel, - a bearing structure comprising bearing cord elements linking the first cord elements of the first structure and the second cord elements of the second structure, and - at least one cord securing element fixed to the first cord elements and to the second cord elements, in which: h is the conformation height of the assembly, corresponding to a height between opposite faces of the first structure and of the second structure when the bearing cord elements are taut; e 1 is the thickness of the first structure; e 2 is the thickness of the second structure; E is the lock length, which is equal to the sum of a first curvilinear length of the portion of the securing element which is locked in the first structure and of a second curvilinear length of the portion of the securing element which is locked in the second structure, where the first curvilinear length is equal to half the curvilinear length of the securing element which is locked between two successive anchoring points in the first structure, and the second curvilinear length is equal to half the curvilinear length of the securing element which is locked between two successive anchoring points of the securing element in the second structure.