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AbstractThe paper describes a two-step finite element formulation for the thermo-mechanical non-linear analysis of thebehaviour of the reinforced concrete columns in fire. In the first step, the distributions of the temperature over thecross-section during fire are determined. In the next step, the mechanical analysis is made in which these distributionsare used as the temperature loads. The analysis employs our new strain-based planar geometrically exact and materiallynon-linear beam finite elements to model the column. The results are compared with the measurements of the full-scaletest on columns in fire and with the results of the European building code EC 2.52594
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The resistance times of the presentmethod and the test were close. It is also noted that the building code EC 2 might be non-conservative in the estimationof the resistance time. 2005 Elsevier Ltd. All rights reserved.Keywords: Fire resistance; Finite element method; Reinforced concrete column; Thermal strain; Creep strain; Transient strain;Eurocode 21. IntroductionThe fire resistance analysis of reinforced concrete structures constitutes an important part in their design.In the analysis an engineer usually employs various formulae for the fire resistance of structures offered bybuilding codes, without really understanding the thermo-mechanical behaviour of a structure duringfire. Much about the behaviour of a structure in fire may be found out experimentally. The experiments areperformed in specially designed furnaces in which the temperature of the surrounding air changes with timeaccording to the prescribed law. Due to reasons of economy the furnaces are often small, so that the major-ity of experiments have to be limited to testing of single structural elements of small to medium size, e.g.reinforced or prestressed simply supported or continuous beams (Lin et al., 1988) and columns (Linet al., 1992). Such a method is time consuming and the scatter of results can be wide, so that only if thenumber of specimens is sufficiently large, the results are statistically reliable, which makes the experimentexpensive. The experiments often give a rather good picture of the overall behaviour of the structure, par-ticularly its resistance time and the deformed shape, but cannot directly provide several other data, such as,e.g. stress distributions or transient strains during fire, which are also important for an engineer to under-stand the behaviour of the structure. Such data can be provided by the numerical models if they are suffi-ciently accurate.To overcome these drawbacks, a considerable amount of research has been directed towards the devel-opment of numerical methods which enable the behaviour of a structure to be predicted by much lessexpensive computer simulations. An example of the simulations is the problem of the decision whetherit is more advisable to demolish and rebuild than to repair the building which has sustained a fire (Cioniet al., 2001). The numerical analysis of the behaviour of a structure in fire requires the deduction of afirm theoretical model of the interaction between the fire and the structure which is a very complex task.
A number of simplified models for the evaluation of the fire resistance of simple reinforced concretestructures have already been presented (e.g. Dotreppe et al., 1999; Eurocode 2, 2002; Lie and Celikkol,1991), as well as the more advanced models which account for the non-linear behaviour of material infire (Dotreppe et al., 1999; Ellingwood and Lin, 1991; Eurocode 2, 2002; Huang et al., 1999; Lie andIrwin, 1993; Sidibe ´ et al., 2000; Zha, 2003). These models use the simplification of piding the interactionbetween the fire and the structure into three separate consecutive steps. In the first step, we estimate thechanging of the surrounding air temperature with time (the fire scenario ). In the second step, we deter-mine the changing of temperature with time in the concrete structure as the result of the time and spacedependent heat transfer from hot air into the structure. We have to perform a transient thermal analysisof the structure in which the heat conduction problem is solved, which is governed by the partial differ-ential equation of the heat conduction, often augmented by the moister and pressure terms and equa-tions. The effects of the heat radiation and the heat convection from air to the structure surface areaccounted for via the boundary conditions. The final step consists of the determination of the timedependent (but with inertial forces disregarded) mechanical response of the structure due to the simulta-neous actions of mechanical and temperature loads. The advanced non-linear mechanical models basedon the 3D continuum finite element method would be perfect for this task. Unfortunately, such modelsare computationally too demanding for the analysis of skeletal buildings and are at present limited to theprediction of the fire response of only simple concrete members or their details. For the practical workand parametric studies, the simplified models which are based on beam and plate theories need be used,as in Cai et al. (2003); Lie and Irwin (1993); Sidibe ´ et al. (2000).