The procedure consists of cutting out a flat shape from a carbon fiber material with several primary plies that are able to slide relative to one another. As the shape is rolled into a tube (110) the sliding plies form chamfered edges (112) that are overlapped and joined together. The initial fabric contains at least 28 weft fibers and 12 warp fibers, and the initial shape is cut out with the weft fibers of the primary plies extending along its axis of symmetry. After injecting with resin the rolled shape is polymerised.