This paper investigates the influence of typical gravity connections on the seismic demands of steel concentrically braced frame (CBF) buildings with friction dampers as dissipative floor connectors. The investigated connections include (i) typical shear tab, (ii) clip angle, (iii) flush end-plate and (iv) shear tab connections with bottom T-stub. It is shown that the seismic behavior of the gravity framing system (GFS) is practically insensitive to the gravity connection type because the supplemental damping provided by the dissipative floor connectors dominates the seismic response of the GFS. While flush end-plate and shear tab connections with bottom T-stub generally exhibit smaller rotational demands than more flexible gravity connections, the resultant lateral drift demands in the GFS are more-or-less identical in all cases due to the elastic contribution of the gravity columns. A simplified method is proposed to evaluate the influence of the damper activation forces on the seismic response of multi-story CBF buildings equipped with floor sliding friction dampers. First, the building is transformed into an equivalent single-degree-of-freedom system. Subsequently, dual graphics called P-spectra are generated through nonlinear response history analysis. These graphics allow to estimate the peak floor absolute acceleration demands and peak/residual roof displacements of the GFS as a function of the activation forces of the sliding friction dampers. An application example demonstrates that the proposed method can be reliably employed in a pre-design phase to identify the range of damper activation forces through which an optimal performance of the steel CBF building may be anticipated.