a rigid member configured to be inserted inside a pipe to be bent and to tilt in a bending operation which is performed by a bending die in order to obtain a curve having a prefixed mean radius Rm as measured between a rotation centre of the bending die and a longitudinal axis of the pipe to be bent, said mean radius Rm and longitudinal axis lying in a central plane orthogonal to a symmetry plane of the pipe to be bent passing through its longitudinal axis,

said pipe to be bent having an internal dimension Di as measured transversally to the pipe's longitudinal axis,

wherein the rigid member has a proximal side profile with respect to the rotation centre of the bending die comprising at least a concave intermediate portion as generated by a radius Rci section of circumference rotating about a longitudinal central axis of the rigid member, and a distal side profile with respect to the rotation centre of the bending die comprising at least two convex, divided, end portions as generated by respective radius Rce sections of circumference, where Rci=Rm−(Di/2)+t, and Rce=Rm+(Di/2)−t, t varying according to an accuracy of dimensional characteristics of the pipe to be bent and of the curve to be obtained,

and wherein said pipe to be bent has a quadrangular cross-section, and said intermediate portion and said end portions of the rigid member are portions of an extrusion surface generated by said sections of circumference in their shift parallel to said symmetry plane of the pipe to be bent.