Keywords: beams, columns, structural members, composite structures, fire, fire analysis, thermal analysis, temperature distribution, numerical modelling, finite element method, software.

In this paper a general numerical model was developed based on the finite element method (FEM) in bi-dimensional domain, as well as the computational program PFEM_2D T. The model is capable of determining temperature fields for different types of structures and boundary conditions, accomplishing linear or non- linear analyses. Furthermore, the model carried out thermal analysis of structures under different situations (fire, hydration heat and ambient temperature and solar radiation - environmental action). The PFEM_2D T is based on the technique Object-Oriented Programming (OOP) [1]. The computational model PFEM 2D T was applied to the structural members under fire conditions and it has been validated using the comparison of its results of temperature distribution with those obtained by other thermal studies. The thermal numerical model is capable of predicting the temperature distribution of structural members under fire conditions and it is more an alternative by using advanced methods to determine thermal behaviour of structures under a fire situation.

The interest in the analysis and design structural members under fire situation has been increasing significantly in the last years. Several researchers have been working on the subject. In spite of the steel structures always being an option considered in most of the developed countries, it becomes important in the design phase to consider the performance of these types of structures under fire conditions.

With the progressive increase of the temperature, the mechanical properties of the steel are weakened, causing the steel structure to the collapse. In the concrete structures under fire conditions, the degeneration of the mechanical properties of the concrete can directly influence the use of a thicker cover than for the rebar of the reinforced concrete usual. Experimental and theoretical studies have been carried out to predict the fire resistance of the steel, concrete and composite structures such as: Refs. [2,3,4,5,6,7]. Based on fire safety and life risk it very important to develop and to improve models able to predict the field temperature of the structures under fire conditions in order to obtain more reliable results.

The thermal numeric model developed in the PFEM_2D T code using the finite elements method (FEM) allowed for the obtainment of coherent and satisfactory results for evaluation of structures under fire conditions and it facilitated the extraction of conclusions of certain relevance regarding the thermal behaviour of steel and composite structures under fire conditions.

The numeric results generated by program PFEM_2D T have demonstrated a good agreement with numeric-experimental results obtained by others authors. The results obtained by program were more conservative than those obtained in Refs. [2,3], probably due to the fact that model PFEM_2D T does not consider the evaporation of water in the concrete in the elaboration and modelling of the problem. Through the validation of the model, it is noticed the importance in improving the program, in order to take into account the interstitial evaporation water (moisture) in concrete.

The thermal numerical model is capable of predicting the temperature distribution of structural members in fire conditions and the model can also be used for the thermal calculus of structural members under fire conditions composed of different types of concretes (e.g., lightweight concrete, high-strength concrete). The model developed is another alternative for using advanced methods to calculate the thermal behaviour of structures under fire situation.

1

L. Yu, A. V. Kumar, "An object-oriented modular framework for implementing the finite element method", Computer & Structures. Pergamon, 79(9), pp. 919-928, Germany, 2001. doi:10.1016/S0045-7949(00)00192-9

2

T.T. Lie, R.J. Irwin, "Fire resistance of rectangular steel columns filled with bar-reinforced concrete", Journal of Structural Engineering, 121(5), pp. 797-805, USA, 1971. doi:10.1061/(ASCE)0733-9445(1995)121:5(797)

3

V.K.R. Kodur, T.T. Lie, "Fire Resistance of Circular Steel Columns Filled with Fiber-Reinforced Concrete", Journal of Structural Engineering, 122(7), pp. 776-782, USA, 1996. doi:10.1061/(ASCE)0733-9445(1996)122:7(776

4

R.M. Polivka, E.L. Wilson, "Dot/detect finite element analysis of nonlinear heat transfer problems", California: National Information Service. Report n^o ucb/sesm, 76(2), USA, 1976.

5

D. Hosser, T. Dorn, O. El-Nesr, "Experimental and numerical studies of composite beams exposed to fire", Journal of Structural Engineering, 120(10), pp. 2871-2892, USA, 1994. doi:10.1061/(ASCE)0733-9445(1994)120:10(2871)

6

Z. Ma, P. Mäkeläinen, "Behavior of Composite Slim Floor Structures in Fire", Journal of Structural Engineering, 126(7), pp. 830-837, USA, 2000. doi:10.1061/(ASCE)0733-9445(2000)126:7(830)

7

Y. Sakumoto, T. Yamaguchi, T. Okada, M. Yoshida, S. Tasaka, H. Saito, "Fire resistance of fire-resistant steel columns", Journal of Structural Engineering, 120(4), pp. 1103-1121, USA, 1994. doi:10.1061/(ASCE)0733-9445(1994)120:4(1103)

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