An anchoring device including two reinforcements for applying a hooping stress to a tubular structure, each of the reinforcements having a main binding portion which bears against the surface of the structure over 2 turns, a first end arranged at the end of a first end portion, and a second end arranged at the end of a second end portion. The anchoring device includes a spacer including a main body and two pairs of anchoring openings for the two ends of each reinforcement. The first and second end portions extend from a radial plane, where the reinforcements are tangential to the surface, then extend away from the surface from the radial plane as far as the anchoring openings so as not to exert a harmful point force on the structure.