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The behaviour of a steel frame load-bearing structure with flexible beam-to-column joints when it is subjected to a fire is analyzed in detail in a current paper. In particular, both the qualitative and the quantitative evaluations are performed of the influence that the statical scheme, and especially the constraints placed upon the fire induced displacements of the considered frame members, exert on the redistribution of internal forces generated in such a structure as a consequence of the constrained thermal expansion. The obtained results clearly indicate that the growing deformation of the load-bearing structure is closely related to the way that this structure is loaded in a manner changing during a fire exposure. This relationship has to be considered, however, with taking into account the increasing flexibility of the heated joints. The identification of the frame failure modes potentially possible to occur under fire conditions as well as the evaluation of the risk of the occurrence of such the modes and also the assessment of their significance for structural safety are the main results of this investigation.