Jean-Marc Franssen

Failure temperature of a system comprising a restrained column submitted to fire

The problem of columns submitted to fire is discussed in the introduction with an emphasis on the differences between the case of a column acting as a single element or being part of a frame. In the latter case, failure of the column does not necessarily lead to the failure of the structure. The basic principles of the arc-length technique are given, first for the way it is applied traditionally at room temperature, then for the way it can be applied to extend a numerical simulation beyond the moment of local failures in case of fire. The technique is then applied to the case of restrained columns and it is shown how it is possible to obtain a safe estimate of the critical temperature of the column leading to the failure of the structure, even if the degree of restraint applied to the column is unknown.

A Simple Model for the Fire Resistance of Axially-Loaded Members According to Eurocode 3

A general model, i.e. a non-linear computer code, has been extensively used to determine the buckling load of axially-loaded members according to the hypotheses of Eurocode 3, Part 10 or Part 1.2. Two yield strengths, two buckling axes, six ultimate temperatures and 10 different lengths have been considered for 339 different steel H-sections. The numerical results have been statistically sorted and compared to the simple models presented in Eurocode 3, Part 10 and Eurocode 3, Part 1.2. The simple models that have been proposed up to now can lead to different safety levels when compared to the general model, the safety level depending mainly on the buckling length. A new proposal has thus been made for a simple model that systematically ensures a conservative result when compared to the general model.

The unloading of building materials submitted to fire

Abstract The unloading of building materials is considered in uniaxially oriented structures. It is shown how the uncertainty encountered in numerical simulations between loading or unloading can be resolved when using the principle of Duhamel and assuming that the plastic strain is not affected by a temperature variation. A solution is also proposed to consider the inelastic behaviour of a material with a non-linear stress-strain relationship like the linear-elliptic one that is often used for steel. The analysis of three composite steel-concrete elements tends to prove that the consideration of inelastic behaviour is not critical in simply supported beams. It seems to be of more importance in an hyperstatic beam and even more in a centrically loaded composite column.

A new proposal of a simple model for the lateral-torsional buckling of unrestrained steel I- beams in case of fire: experimental and numerical validation

Abstract The behaviour of Steel I-Beams exhibiting lateral-torsional buckling at elevated temperature has been studied by means of experimental and numerical analysis. The authors in an earlier paper have presented an analytical formula for the buckling resistance moment in the fire design situation. This new proposal, different from the actual proposal of the Eurocode 3 Part 1.2 has been validated in this work by comparison with the results from a set of 120 experimental and numerical tests performed on IPE 100 beams, submitted to temperatures varying from room temperature to 600 °C. The numerical simulations have been based on the measured geometrical dimensions of the cross-sections, the longitudinal imperfections, i. e. the out of straightness of the beams, the residual stresses and the yield strength. The Eurocode simple model promotes ultimate loads that depend mainly on the non-dimensional slenderness of the beams. The analytical results provided by the Eurocode 3, for a certain range of the slenderness, appear to be unsafe when compared with the numerical and experimental results. It is shown that the new proposal is safer than the Eurocode 3 formulas.

A tool to design steel elements submitted to compartment fires - OZone V2. Part 1: pre- and post-flashover compartment fire model

Abstract The computer code OZone V2 has been developed to help engineers in designing structural elements submitted to compartment fires. The code is based on several recent developments, in compartment fire modelling on one hand and on the effect of localised fires on structures on the other hand. It includes a single compartment fire model that combines a two-zone model and a one-zone model. In this paper, the description of this compartment fire model is given. The main model is first presented. It consists of the usual zone model equations fully coupled with the partition model equations. The partitions are modelled by the finite element method. The switch from the two-zone to the one-zone model is then explained. The vertical, horizontal and forced vent sub-models are presented, followed by the fire source and the combustion models. A comparison between this code and another compartment fire model NAT is made. The OZone calculations are then compared to full scale fire tests. Considerations as to how this model is used for the design of steel elements will be presented in a companion paper (Fire Saf. J., this issue).

Numerical simulation of a full scale fire test on a loaded steel framework

This paper presents the results of a number of numerical simulations of the behaviour in a real fire of a full-size, loaded, two-dimensional, mainly unprotected steel frame. Data jS,om the fire test, reported in Steel Construction Today 1987, provides the benchmark. The application of one, two and three-dimensional heat flow models is discussed, and the basis of the structural model used is described. The influence of lateral restraint, frame continuity and thermal expansion is quantified using the compul:er model. In contrast the simple method in draft Eurocode 3 is used to calculate the frame stability assuming that the temperatures of the beam and columns are uniform across their sections, and good agreement with the test result is shown. It is suggested that a rigorous computer program, like that described in the paper, could be usefully employed to identify those types of structure which might be analysed safely by the simplified method.

Fire Tests and Calculation Methods for Circular Concrete Columns

The introduction sets the scene of the present paper, i.e. the extensive research works performed at the University of Liege in order to derive acceptable calculation methods for the fire design of concrete columns. It is explained that all previous works have been based on square or rectangular cross sections, for which corner spalling was observed very often, whereas circular section are nowadays becoming more and more popular.In order to examine the influence of the circular shape on the behavior under fire conditions, an experimental research study has been performed recently at the University of Liege. This paper describes the test procedure, the observations made, and the values obtained for the fire resistance. Theoretical methods have been developed for a quick, safe, and efficient design of concrete columns under fire conditions. These methods have been applied successfully to the recently tested circular columns.

CALCULATION METHOD FOR DESIGN OF REINFORCED CONCRETE COLUMNS UNDER FIRE CONDITIONS

The determination of the fire resistance of concrete columns is essentially based on tabulated data containing the dimensions of the cross section and values of the concrete cover. However, more scientific approaches such as analytical formulations should be proposed to consulting engineers for a quick and efficient design. A large number of experimental results have been examined; they have been performed at the Universities of Ghent and Liege in Belgium, at the Technical University of Braunschweig, and at the Fire Research Station in Ottawa, Canada. A computer code SAFIR, developed at the University of Liege for the simulation of the structural behavior under fire conditions, has been used for the analysis of the experimental results and for the progressive development of the formulation. The design formula has been obtained in three steps. The first step consists of determining the plastic crushing load of the column at elevated temperature on the basis of numerical simulations. The second step is the determination of the buckling coefficient for centrically loaded columns. The third step is the development of a nonlinear amplification term for eccentrical loads. The formula has been calibrated to take into consideration the particular effects of the concrete cover and the additional amplification appearing for the high values of the slenderness ratio.

A Simple Model for the Fire Resistance of Axially Loaded Members - Comparison with experimental results

Abstract A general model, i.e. a non linear computer code, has been extensively used to determine the buckling load of axially loaded members, considering that the material model behaves at elevated temperatures according to the hypotheses of Eurocode 3 Part 1.2, and the main results of this numerical investigation are summarised in this paper. The main parameters and the results of 59 experimental tests found in the literature are reported, as well as the results of 21 original tests made within this research project. Those test results are used to evaluate the severity factor of the analytical formula deduced from the numerical simulations. This factor is chosen in order to obtain an analytically calculated ultimate load which is, in the average, the same as the experimental load. The ultimate load or ultimate temperature can be determined by the proposed analytical formula or directly by interpolation in tables which give the ratio between the ultimate load and the plastic load at room temperature.

The use of numerical models for the fire analysis of reinforced concrete and composite structures

Abstract Numerical methods for the analysis of reinforced concrete and composite structures under fire conditions are presented. They are based on the finite element method using beam elements with subdivision of the cross-section in a rectangular mesh. The structure submitted to increasing temperatures is analysed step-by-step using the Newton-Raphson procedure. A comparison between theoretical and experimental results is made for a reinforced concrete and a composite beam. In both cases there is a good agreement between theoretical and experimental results. In this article we intend to show that, though the same type of model can be used for both reinforced concrete and composite structures, the difficulty of analysis increases substantially when going from reinforced concrete to composite structures.