Concentrically braced frames are one of the most common seismic force resisting systems because of their high strength and stiffness. In current practice, the gusset plates that connect the brace to the adjacent beams and columns can increase the strength and stiffness of the connection significantly. This strength and stiffness can provide a reserve of lateral force resisting capacity during a large earthquake, which may play a role in the seismic collapse behaviour of the braced frame. An alternative connection has recently been proposed as a means of ensuring that brace buckling occurs only in-plane, that no field welding is required, and that all damage is confined to a replaceable brace module. However, the proposed connection does not include a gusset plate that can provide a similar stiffness and reserve capacity. In order to investigate the potential influence of the range of possible beam-column-gusset plate designs, this paper assesses the effect of the fixity of these connections on the behavior of a six-storey special concentrically braced frame. Nonlinear dynamic analyses have been conducted to determine the seismic performance of the frame with this connection modelled using three different assumptions (pinned, shear tab and fixed), and the collapse risk is assessed using the FEMA P695 methodology. The results show that when the gravity framing is not modelled, the fixity of the beam-column connections is important in avoiding the formation of a soft storey under extreme earthquakes, thereby reducing the probability of collapse of the building.