The seismic assessment of reinforced concrete (RC) structures is commonly carried out neglecting potential previous damage induced by other phenomena, for example those related to the actions of slow-moving settlements. Many efforts are dedicated by the research community in properly considering multi-hazard actions and their inter-relations on the structure, instead of a reductionist approach, to be included in the numerical models adopted for the assessment of the seismic vulnerability. Such a consequences are increasingly becoming an important issue in the structural assessment, since several structures have an age close to, or higher than their design life. In this work a typological 3D case study RC building, including also infills, is created according to gravity loads design. The seismic assessment of the building structural elements, caused by the design seismic action, is initially shown. Then, the seismic assessment is repeated, considering as point zero of the analysis the "damaged" building as consequence of known slow-moving settlements. Finally, an interesting comparison in terms of fragility curves is proposed between the safety condition of the building expected in both cases, with or without the consideration of the precedent induced displacements.