bracket 20 may be made by just cutting the h beam or i beam to a given size without having the side plates 25 connected to the upper plate 21 and the lower plate 23 as shown in fig6 a and 6 b furthermore the connecting brackets 20 of the present invention are provided in the longitudinal direction of the steel girder 10 and in this case the connecting brackets 20 positioned at both sides to support both end portions of the cover plate 30 have inclined portions 28 formed on the outside surfaces thereof in such a manner as to have given inclination from an external direction toward the internal direction thereof that is the inclined portion 28 of the connecting bracket 20 has the upper plate 21 longer than the lower plate 23 the side plate 25 positioned at the inside surface thereof is vertically connected and the side plate 25 positioned at the outside surface thereof and forming the inclined portion 28 is slantly welded to the upper plate 21 and the lower plate 23 in such a manner as to have the given inclination in case where the sections of the connecting brackets 20 positioned at both side portions of the steel structure are drastically varied stress is locally collected to the drastically varied portions to cause the material to be destructed and cracked which results in the reduction of the.