Tyre for a civil engineering vehicle, comprising: - a crown reinforcement, radially on the inside of a tread and radially on the outside of a carcass reinforcement, - the crown reinforcement comprising at least a crown bilayer made up at least partially of two radially superimposed crown layers (211, 212), each made up of reinforcers coated in an elastomeric material, - each crown bilayer being made up of a circumferential zigzag winding of a strip of width W, in a circumferential direction (XX') of the tyre and on a substantially cylindrical surface of revolution positioned at a radial distance R from the axis of rotation (YY') of the tyre, - the trajectory of the circumferential zigzag winding being a periodic curve having a period P and an amplitude L, - the periodic curve forming, with the circumferential direction (XX'), an angle A measured at the points on the curve positioned in an equatorial plane passing through the centre of the tread and perpendicular to the axis of rotation (YY'), - the periodic curve extending over a number N of periods P distributed over a number T of circumferences 2IIR, - the trajectory of the circumferential zigzag winding generating strip crossovers between a radially outer portion of strip and a radially inner portion of strip, - a strip crossover being outer when the radially outer portion of strip forms a positive angle B with the circumferential direction (XX') in an axial plane, - a strip crossover being inner when the radially outer portion of strip forms a negative angle B with the circumferential direction (XX') in an axial plane, characterized in that the crown layer reinforcers (211, 212) are made of metal, in that the periodic curve of the trajectory of the circumferential zigzag winding satisfies the following relations: N* W / sinA = 2 Π R * t, where 0.6<=t<=1, N * P = 2 Π R * T, and in that, for at least 40% of the strip crossovers axially positioned, relative to the equatorial plane, at an axial distance L1 equal to not more than 0.25 times the amplitude L of the periodic curve, the circular bilayer portion centred on the strip crossover and having a radius R1 equal to twice the width W of a strip, comprises Ne outer strip crossovers and Ni inner strip crossovers, such that |Ne-Ni|/(Ne+Ni)<= 0.3. - a crown reinforcement, radially on the inside of a tread and radially on the outside of a carcass reinforcement, - the crown reinforcement comprising at least a crown bilayer made up at least partially of two radially superimposed crown layers (211, 212), each made up of reinforcers coated in an elastomeric material, - each crown bilayer being made up of a circumferential zigzag winding of a strip of width W, in a circumferential direction (XX') of the tyre and on a substantially cylindrical surface of revolution positioned at a radial distance R from the axis of rotation (YY') of the tyre, - the trajectory of the circumferential zigzag winding being a periodic curve having a period P and an amplitude L, - the periodic curve forming, with the circumferential direction (XX'), an angle A measured at the points on the curve positioned in an equatorial plane passing through the centre of the tread and perpendicular to the axis of rotation (YY'), - the periodic curve extending over a number N of periods P distributed over a number T of circumferences 2IIR, - the trajectory of the circumferential zigzag winding generating strip crossovers between a radially outer portion of strip and a radially inner portion of strip, - a strip crossover being outer when the radially outer portion of strip forms a positive angle B with the circumferential direction (XX') in an axial plane, - a strip crossover being inner when the radially outer portion of strip forms a negative angle B with the circumferential direction (XX') in an axial plane,