Tyre for a heavy construction plant vehicle, intended to carry a nominal load Zn, comprising a crown reinforcement radially on the inside of a tread and radially on the outside of a carcass reinforcement: - the crown reinforcement comprising a working reinforcement and a circumferential hoop reinforcement, - the working reinforcement having an axial width LT and being formed by a first and a second working layer (61, 62) each comprising inextensible metallic reinforcers having a tensile elastic modulus of more than 150 GPa, coated with an elastomer-based material and mutually parallel, and one working layer crossing the next such that the mean angle AM of the metallic reinforcers of the working reinforcement, defined as the geometric mean of the respective angles formed by the reinforcers of the first and second working layers (61, 62) with a circumferential direction (XX') tangential to the circumference of the tyre, is at least equal to 15° and at most equal to 45°, - the circumferential hoop reinforcement having an axial width LF at least equal to 0.3 times the axial width LT of the working reinforcement and comprising at least one circumferential hooping layer (71, 72) formed from elastic metallic reinforcers having a tensile elastic modulus of more than 150 GPa, coated with an elastomer-based material and mutually parallel, and forming with the circumferential direction (XX') an angle at most equal to 5°, - the elastic metallic reinforcers of the circumferential hoop reinforcement, removed from the tyre with their coating of vulcanised elastomer-based material, having a structural elongation As at least equal to 0.5% and a force at break Fr, these two characteristics being measured in accordance with the same standard ISO 6892 of 1984, characterized in that the axial width LF of the circumferential hoop reinforcement, the structural elongation As and the force at break Fr of the elastic metallic reinforcers of the circumferential hoop reinforcement, and the mean angle AM of the inextensible metallic reinforcers of the working reinforcement, satisfy the relationship: Zn / Z 0 * T 0 + a 1 + a 2 * As / AM + b * LF * AM − A 0 / A 0 + c * AM < Fr / CS where Zn: the nominal load (expressed in tonnes) applied to the tyre, Z0: reference load equal to 100 tonnes, T0: reference tension equal to 7000 N, a1 = -230,000 N*°, a2 = -160,000 N*°/%, b = -34,000 N/m, A0: mean reference angle of metallic reinforcers of the working reinforcement equal to 29°, c = 550 N/°, CS: safety coefficient at least equal to 1. - the crown reinforcement comprising a working reinforcement and a circumferential hoop reinforcement, - the working reinforcement having an axial width LT and being formed by a first and a second working layer (61, 62) each comprising inextensible metallic reinforcers having a tensile elastic modulus of more than 150 GPa, coated with an elastomer-based material and mutually parallel, and one working layer crossing the next such that the mean angle AM of the metallic reinforcers of the working reinforcement, defined as the geometric mean of the respective angles formed by the reinforcers of the first and second working layers (61, 62) with a circumferential direction (XX') tangential to the circumference of the tyre, is at least equal to 15° and at most equal to 45°, - the circumferential hoop reinforcement having an axial width LF at least equal to 0.3 times the axial width LT of the working reinforcement and comprising at least one circumferential hooping layer (71, 72) formed from elastic metallic reinforcers having a tensile elastic modulus of more than 150 GPa, coated with an elastomer-based material and mutually parallel, and forming with the circumferential direction (XX') an angle at most equal to 5°, - the elastic metallic reinforcers of the circumferential hoop reinforcement, removed from the tyre with their coating of vulcanised elastomer-based material, having a structural elongation As at least equal to 0.5% and a force at break Fr, these two characteristics being measured in accordance with the same standard ISO 6892 of 1984, Zn: the nominal load (expressed in tonnes) applied to the tyre, Z0: reference load equal to 100 tonnes, T0: reference tension equal to 7000 N, a1 = -230,000 N*°, a2 = -160,000 N*°/%, b = -34,000 N/m, A0: mean reference angle of metallic reinforcers of the working reinforcement equal to 29°, c = 550 N/°, CS: safety coefficient at least equal to 1.