•Use of the Cloud Analysis for the development of probabilistic fire demand models.•The LOCAFI localised fire model was used to model the effect of hydrocarbon pool fires.•Development of fire fragility functions of a steel pipe-rack.•The interstorey drift ratio – average maximum heat flux pair results the most efficient. This paper proposes a new method to build a probabilistic fire demand model (PFDM) to investigate the structural behaviour of a steel pipe-rack located within an industrial installation and exposed to a localised fire. The PFDM will serve to develop fire fragility functions to be used either in a fire risk assessment or in a fully probabilistic structural fire engineering (PSFE) framework. The cloud analysis (CA) was exploited to build a PFDM based on different engineering demand parameters (EDP) – intensity measures (IM) pairs. In particular, the analysis was applied to a prototype steel pipe-rack integrating an industrial plant in Italy. In order to cover a wide range of plausible fire scenarios and to introduce uncertainties in the fire model, 539 fire scenarios were examined by varying the fire diameter, the fire-structure distance and the fuel. The selection of the fire diameters was based on parametric analyses quantifying liquid flow through orifices and pipes. The thermal impact of the pool fires on the structure was analysed using the LOCAFI localised fire model and the thermo-mechanical response of the pipe rack was evaluated by means of finite element analysis. Based on the structural analysis outcomes, it was found that the interstorey drift ratio (ISDR) – maximum average heat flux impinging the structure (HFavg) EDP-IM pair was the most efficient and was also characterised by the highest relative sufficiency among the other pairs. Moreover, it has to be noted that for this type of case study, the CA revealed to be a viable option to build a PFDM.