An innovative, simplified, and accurate model is proposed and developed to enable simplified yet realistic time history analysis of multi-storey buildings with moment resisting connections using friction energy dissipaters in the commonly used structural analysis and design program, SAP2000. The analyses are rapid to undertake, thereby enabling detailed study of the influence of many building system effects on the overall response. This paper presents the outcome of dynamic analysis of a complete 13-storey moment resisting steel building with Sliding Hinge Joints as the beam-column connections, considering the influential self-centring factors such as MRF and gravity columns continuity as well as column base and diaphragm flexibilities. The building is one of the Te-Puni towers, which are structural steel apartment buildings with steel-concrete composite floors, designed according to the low damage design philosophy, built in Wellington, New Zealand in 2008 and which have already been subjected to two significant earthquakes. The key objectives of the research have been to take the design of the 13-storey building and convert that into the proposed simplified model required for time history seismic analysis, to undertake analysis under scaled El-Centro earthquake record, investigate the peak inter-storey drift and the residual drift of the building, and determine the influence of column base rotational stiffness, floor slab out of horizontal plane displacement, type of friction damper, and MRF and gravity column continuity. It is concluded that the response of the building is stable and predictable, as expected, and that the post-earthquake state of the building, particularly from the self-centring point of view, is well within the limits for maintaining operational continuity following an ULS level design earthquake.