Limit fire analysis of 3D frame structures

This work introduces a mathematical problem named limit fire analysis for estimating the structural safety of 3D frames in case of fire, taking into account the stress redistribution. It is a generalization of the classic limit analysis to a fire event, where the load factor is replaced by the time of fire exposure that reduces the strength of the materials. A lower bound theorem is derived, making it possible to define the limit fire duration, i.e. the maximum time of exposure for which the structure is safe, unaffected by initial plastic deformations, loading history, thermal strains and variations of elastic properties. A numerical framework is also given for evaluating the limit time. The structure is discretized using an equilibrated mixed finite element for each beam and column. The time-dependent admissibility of the stress is imposed through a fiber approach at multiple sections along the elements. An arc-length continuation method with the fire duration as additional unknown provides a sequence of safe time of exposure converging to the limit one. Newton's iterations are used at each step to determinate the element state and to impose global equilibrium, with all tangent operators obtained analytically. Reinforced concrete frames are considered as example of application. Numerical tests show an efficient analysis also for large buildings.