A method, and associated apparatus, for assembling a structural frame from elongate, tubular columns having plural sides, and a selected style of elongate beams, with respect to which, the method includes the steps of (a) pre-fitting the sides of such columns and the ends of such beams with attached, gravity-set, complementary interconnect structures (either collar-form or non-collar form in nature), including column-side-fitted interconnect structures and beam-end-fitted interconnect structures, (b) utilizing gravity, bringing interconnect-structure pre-fitted beams and columns into correct, predetermined, relative design dispositions relative to one another, and (c) through the performing of the bringing step alone, and on the resulting occurrence of the achievement of the mentioned correct, predetermined, relative design dispositions between a beam and a column, simultaneously and immediately thereby establishing (1) a full-moment load-bearing connection, and (2) a relatively positionally gravity-set-and-stabilized condition, between that beam and column.