Fires following earthquakes are considered one major threat in seismic regions. In fact, according to modern seismic codes, ordinary structures are designed to suffer damage to some extent during strong earthquakes, exploiting the structure own ductility to avoid collapse and safeguard human lives. Then, a fire coming soon after an earthquake will find a different, more vulnerable, structure with respect to the initial, undamaged, one. Depending on the extent of damage, the fire resistance rating of the structure could be significantly reduced. This paper is devoted to obtaining some quantitative information about this topic, with reference to steel moment-resisting frames, even if the adopted methodology could also be extended to either different structural types or structural materials. As a first step, a simplified modelling of earthquake-induced structural damage, based on the superposition of geometrical and mechanical effects, is proposed. Then, a wide numerical analysis is performed with reference to a single-bay single-storey frame structure, allowing the main parameters affecting the problem to be identified. Finally, two multi-storey plane frames, designed in accordance with methods specified by Eurocodes, are analysed as a case study.