A primary fuselage structure for an aircraft, including circumferential frames, a floor structure having lateral ends connected to the circumferential frames, at least one strut supporting the floor structure and including a lower end fixed on a circumferential frame and an upper end fixed on the floor structure, and at least one failure-initiating element associated with the strut, including a first arrangement for fastening the strut to a circumferential frame, at a distance from the lower end of the strut, as well as a second arrangement for attaching the circumferential frame to the strut, away from the ends of the strut. A fuselage segment and aircraft, such as an airplane, including the primary fuselage structure are also provided.