Connection end piece of a flexible pipe, and associated flexible pipe

The invention relates to a pipe comprising at least one tubular sleeve (20) and at least one layer (24, 25) of traction shielding arranged outside the tubular sleeve (20). Said shielding layer (24, 25) comprises a plurality of filiform shielding elements (29), and the end piece (14) comprises a plurality of end sections (34) of each shielding element (29), an end collar (50), and a cover (51) fixed to the end collar (50), the end collar (50) and the cover (51) defining between them a chamber (52) for receiving the end section and at least one anchoring support (62, 64) for each shielding layer (24, 25), which is mounted in a fixed manner according to an axis (A-A') of the pipe in relation to the end collar (50) and/or in relation to the cover (51). Each end section (34) is anchored to the anchoring support (62, 64) by a pivoting connection or a ball-and-socket connection.