Abstract: This T-assembly of the tenon and mortise type for two perpendicular metal tubes comprises a mortise formed in one tube and having an omega shape in cross section, through the local distortion of the tube wall, by depressing said wall towards its opposite lateral wall, without breaking the continuity of the tube surface, the tenon being obtained on the other hand by simply crushing to a slightly dovetail configuration the end of the other tube, the tenon comprising at least one collar-shaped external protrusion adapted notably to engage the outer portion of the mortise.