Abstract: A connection device of fixed point type between a pipework component and a support, which device is capable of absorbing the forces applied to the pipework in every direction in both normal operation and under emergency conditions. The device assures the connection, at a fixed point, of pipework equipped with a sleeve and a frame anchored to a structure. The sleeve includes two opposite shoulders applied against two parallel and opposite bearing surfaces on the frame, and at least one prismatic bearing surface consisting of at least two small plane faces parallel with the axis of the pipework. The frame comprises at least one prismatic seating consisting of small plane faces parallel with the axis of the pipework, arranged to be equal in number to the small faces of the bearing surface so as to form in cross-section a polygon similar to the polygon formed by a cross-section of the bearing surface, which engages with slight clearance in the seating so as to prevent rotation of the pipework.