The paper describes a two-step finite element formulation for the thermo-mechanical non-linear analysis of the behaviour of the reinforced concrete columns in fire. In the first step, the distributions of the temperature over the cross-section during fire are determined. In the next step, the mechanical analysis is made in which these distributions are used as the temperature loads. The analysis employs our new strain-based planar geometrically exact and materially non-linear beam finite elements to model the column. The results are compared with the measurements of the full-scale test on columns in fire and with the results of the European building code EC 2. The resistance times of the present method and the test were close. It is also noted that the building code EC 2 might be non-conservative in the estimation of the resistance time.

A family of new beam finite elements for geometrically and materially non-linear static analysis of reinforced concrete planar frames is derived, in which strain measures are the only interpolated unknowns, and where the constitutive and equilibrium internal forces are equal at integration points. The strain-localization caused by the strainsoftening at cross-sections is resolved by the introduction of a 'short constant-strain element'. Comparisons between numerical and experimental results on planar frames in pre-and post-critical states show both good accuracy and computational efficiency of the present formulation.

A two-step formulation, consisting of separate thermal and mechanical analyses, is presented for the thermo-mechanical analysis of reinforced concrete planar frames subject to fire conditions. The heating and the cooling phases are considered. Standard planar, four-node quadrilater finite elements are employed in the non-linear time-dependent thermal analysis of cross-sections, while the recently proposed strainbased planar beam finite elements are used in the non-linear mechanical analysis of the frame [Bratina S, Saje M, Planinc I. On materially and geometrically non-linear analysis of reinforced concrete planar frames. International Journal of Solids and Structures 2004;41:7181-7207]. The formulation includes both exact geometric and material non-linearities, and considers the temperature dependence of thermal and material parameters, the plastic, creep and thermal strains in concrete and steel, the transient strain in concrete, and the strain localization as a consequence of softening of material at high temperatures. A so called 'constant strain element' is introduced to resolve numerically the loss of uniqueness of strain measures at the point of localization. The formulation is validated by comparing some of the present numerically predicted results with the data, measured in experiments. Although the present model is essentially 1D stress-strain model, and is thus simple in terms of the number of degrees of freedom used and ignores transfer of water in concrete during heating, the comparisons with the measured data are found to be satisfactory. In particular, the agreement of the fire resistance times and critical deflections between the predicted and the experimental values was found very satisfactory. In contrast, a disagreement was found in distributions of temperature over the beam cross-sections. The results make it possible to draw several conclusions concerning behaviour of structures in fire. In particular, it is established that the consideration of creep and transient strains in concrete has little effect on the fire resistance time of statically determinate beams under bending or unconstrained centrically loaded columns; their effect on displacements is, however, remarkable.