A steel-concrete composite structure (1) is described. The steel-concrete composite structure comprises a steel member (2) having an upper surface (5) and a plurality of shear connector elements (6) upstanding from the upper surface and a concrete slab (4) having upper and lower surfaces (7, 8). The slab is supported on its lower surface by the upper surface of the steel member. The slab comprises a plurality of through holes (9) between the upper and lower surfaces, each through hole tapering towards the lower surface so as to form an inverted frustally-shaped seating surface (10). The concrete slab is configured and positioned with respect to the steel member such that at least one shear connector element projects into each through hole. The steel-concrete composite structure comprises a plurality of removable inverted frustoconical plugs (15), each plug having top and bottom surfaces (18, 19; Fig. 6) and an inverted frustoconically-shaped plugging surface (20; Fig. 6). Each plug has at least one through hole (16) between the top and bottom surfaces. At least one plug (15) is seated in a corresponding through hole (9) of the concrete slab. Each plug is configured such that at least one of the least one shear connector elements (6) projecting into the corresponding through hole (9) is received by a corresponding though hole (16) of the plug. The structure also comprises a plurality of fasteners (17, 29), each fastener coupled to a corresponding shear connector element and arranged to discourage removal of a plug (15) from a through hole (9) of the concrete slab.