BOFIRE A FEM-programm for non-linear analysis of structural members under fire conditions Prof. P. Schaumann, Dipl.-Ing. F. Kettner DESCRIPTION BOFIRE is a transient, non-linear, incremental computer code based on the finite element method. The program includes two main calculation modules: one for calculating the development and the distribution of the temperature in the structural member (thermal response model) and another for considering the mechanical behaviour of the structure taking into account the change of material properties at elevated temperatures (mechanical response model). The mechanical actions in fire situations are taken into account in the first step, the thermal actions are applied by gas temperature-time curves e.g. ISO-fire curve. Time steps typically range between 5 and 15 seconds. In each time step the temperature distribution and the resulting stress-strain distribution in the structure are calculated. For the material properties the thermal and mechanical definitions of ENV 1994-1-2 [1] are implemented, thus concrete-, steel- and composite steel and concrete structures can be analysed. Failure of the structure may occur due to loss of equilibrium (instability, kinematics) or exceeding the material strengths. The model was developed by Schaumann (1984) [2] and updated by Upmeyer (2001) [4] and Kettner (2003). Verification of BOFIRE has been carried out by comparison to numerous fire tests of steel, concrete and composite structures. An overview of the operation of BOFIRE is illustrated in figure 1. DATA INPUT Interactive windows-surfaces can be used to define the cross section, the static system and the boundary conditions for the numerical calculation. Figure 2 shows the main input window of the user interface HAFRONT. The following input can be done: Geometry: o System: beam, column, plane frame o Cross section: Any
Material: Concrete, steel, composite mechanical loads: Single and distributed loads in/ out of plane thermal loads: any (prefix: ISO 884) THERMAL ANALYSIS For the thermal analysis the cross section is divided in finite elements as shown in figure 3. With the latest versions of BOFIRE all kind of cross sections can be modelled. With this finite element net a plane transient temperature calculation is done. Therefore different kind of gas temperatures can be imported. MECHANICAL ANALYSIS BOFIRE is able to calculate linear structures like beams, columns or plane frames. Hence beam elements with up to seven degrees of freedom are used (figure 5). The calculation of the equilibrium of the internal and external forces is a non-linear and incremental calculation process considering second order theory and the non-linear material behaviour. DATA OUTPUT The spreadsheet program EXCEL is the most popular way to interpret the thermal and mechanical calculation results of BOFIRE. But the code included data plotting library DISLIN provides the opportunity to produce colored countourplots of the temperature distribution or 3-dimensional graphics of stresses or strains as shown in figure 6. REFERENCES [1] CEN (European Committee for Standardization) (1994), ENV 1994-1-2 Eurocode 4 Design of composite steel and concrete structures, Part 1-2: General rules Structural fire design, CEN, Belgium [2] Schaumann P. (1984). Zur Berechnung stählerner Bauteile und Rahmentragwerke unter Brandbeanspruchung (To the Calculation of Steel Members and Frames exposed to Fire), Technisch-wissenschaftliche Mitteilungen Nr. 84-4, Institut für konstruktiven Ingenieurbau, Ruhr-Universität Bochum, Germany (in German) [3] Schaumann, P. and Upmeyer, J. (2000). Behavior of composite structures exposed to natural fires, 6th. ASCCS International Conference Steel-Concrete Structures, Los Angeles, USA [4] Upmeyer J. (2001). Nachweis der Brandsicherheit von kammerbetonierten Verbundbauteilen über Grenzbrandlasten (Fire Design of Partially Encased Composite Columns by Limit Fire Loads), Schriftenreihe des Instituts für Stahlbau der Universität Hannover, Heft 19, Shaker Verlag, Germany (in German)
F fi,d Static system and mechanical action Discretization of the cross section Thermal action ISO t u t [min] Thermal Problem Temperature distribution in the structural member at time t F fi,d Mechanical Problem Ultimate loadbearing capacity at time t u including the effects of temperature Failure Time t u Figure 1: Numerical analysis with BOFIRE
Figure 2: Main window of HAFRONT Figure 4: Finite element net of the cross section
y w, M y x ϑ, M T u, N v, Q y w, Q z z v, M z additionally for the warping of the crossection: ϑ, Mw Figure 5: Degrees of freedom for the beam element Stresses Temperature Time: Figure 6: Stress and temperature distribution over the cross section of a concrete filled tube with an embedded I-section