The invention concerns a method for making a section of a support strut member of an offshore oil-drilling rig comprising steps which consist in: a) machining each longitudinal edge of a semi-cylindrical stiffener (13) to provide along the longitudinal edge, a lip (18) for support on a main surface (12A) of a main plate (12), by producing along the longitudinal edge an outer bevel (20) on the side opposite the conduit (17) defined by the stiffener (13); b) applying a base plate (22) of the support lip (18) to weld it with main surface (12A) of the plate (12); heating the support lip (18) to weld it with the plate (12) and constitute a support weld joint; and d) forming a weld bead with filler metal from outside the conduit (17) in the space delimited between the support weld joint, the outer bevel (20) and the main surface (12A) of the main plate (12).