The paper presents two complementary materials, reinforced concrete and structural steel, and shows how their composite action is achieved in the case of composite beams, composite slabs and composite columns. There are listed the advantages and disadvantages of such constructions compared to reinforced concrete and structural steel used separately. Emphasis is placed on composite beams. The designing of the composite floor construction was carried out on the example of the Children's House, which is located in the center of the city of Rijeka and is part of the former complex "Rikard Benčić". To show the design, the first and second floor construction were selected because of the different static systems of composite beams. The composite beams of the first floor construction are made as continuous beams over three spans of 5.15 m, 4.95 m and 5.15 m, and the composite beams of the second floor construction are made as simple beams over a span of 15.25 m. During the construction, the composite beam is propped and the composite action in beams is achieved by headed studs. Action effects are calculated by elastic global analysis, and the resistance of s crosssection is based on its plastic resistance. The design of the floor constructions was made accordingly to eurocode series of European standards and National Annexes.