The present invention relates to a system for producing composite beams and floor structures of buildings by means of bent sections made of steel and another material attached by means of connectors formed in the section made of steel, made up of sections (1) made of steel obtained by means of bending or shaping steel sheet of little thickness and an upper slab or board (2) made of another material such as concrete, wood or resin fibreboard. The sections (1) made of steel are special shapes and incorporate in the sheet itself connectors (3) obtained by means of cutting, drawing and bending the sheet in certain areas of the metal section (1) which are attached to the slab or board (2) made of the other material. The metal sections (1) incorporate a groove (4) :in their design which allows the attachment to other metal beams (5) or metal supports (6) by means of special parts formed by flat bars (7, 8 and 9).