Thermo-mechanical beahvior of steel-concrete composite columns under natural fire
including heating and cooling phases
Soumia Sekkiou,Med Salah Dimia, Noureddine Lahbari
Department of Civil Engineering University of Batna, Algeria [email protected]
Fabrice Bernard
Laboratoire de Génie Civil et Génie Mécanique (LGCGM)
Institut National des Sciences Appliquées, Rennes , France
[email protected] Abstract—In recent years, concrete filled tubular
(CFT) columns have become popular among designers and structural engineers, due to a series of highly appreciated advantages: high load-bearing capacity, high seismic resistance, attractive appearance, reduced column footing, fast construction technology and high fire resistance without external protection. In a fire, the degradation of the material properties will cause CFT columns to become highly nonlinear and inelastic, which makes it quite difficult to predict their failure. In fact, it is possible to fail during heating or cooling phase of fire. In this paper, the behavior of axially loaded concrete filled square hollow section columns subjected to natural fire conditions has been studied. The main objective of this study is to highlight the phenomenon of delayed collapse of this type of columns during or after the cooling phase of a fire, and then analyze the influence section size. The results show that critical conditions with respect to delayed failure arise much more for massive sections.
Keywords—Natural fire, Fire resistance, composite column, cooling phase, residual strength
1.
INTRODUCTIONThe fire behavior of composite columns and especially concrete filled hollow steel sections has been studied extensively in various countries.
Almost all essential parameters influencing their resistance have been identified: Section shape and dimensions [1,2,3], concrete filling [4,5,6], reinforcement rate, steel tube thickness, column slenderness [7.8], thermal and mechanical properties of steel and concrete [9,10], and even the contact problem at the steel-concrete interface [11,12]. Most of these works was done under standard fire conditions (ISO), which is represented by an increasing temperature continuously over time. It is thus not really a curve reflecting a natural fire which includes not only a heating phase but also a cooling phase during which the temperature of the fire is decreasing back to ambient temperature.
So in the prescriptive approach based on the standard ISO fire, the fire resistance of a structural element has to be guaranteed for a determined
duration and no verification has to be made about the performance of the element thereafter.
However, if the behavior of a structure or structural element is evaluated in a performance-based environment, a more realistic representation of the fire should be used, and an acceptable risk of failure under the effect of natural fire for the entire duration has to be ensured. The influence of such realistic fire scenarios in the evaluation of the fire resistance is a key issue in the performance-based approach, as presented for example by Fike et al.
[13] for concrete-filled hollow structural section columns. The required duration of stability may be longer than the duration of the heating phase; it may even be required that the structure survives the total duration of the fire until complete burnout. In that case, the load-bearing capacity of the structure to still decreases after the maximum gas temperature is attained, finally reaching a minimum value and eventually recovering partially or completely when the temperatures in the structure are back to ambient.
Under standard fire conditions, the designer is thus faced one problem which is to ensure the stability of the structural element or the entire structure during a specified period of fire. However, under real fire conditions, verification should necessarily be performed in the entire time domain by a step by-step iterative method. Some authors have been interested in the residual load bearing capacity of structural elements after exposure to fire, for example Han et al. [14,15,16] for composite columns, and they even developed formulas for calculating the index of the residual strength.
However, no study has been performed, to the authors’ knowledge, on the risk of collapse during the cooling phase of a fire.
However, structural failure that would occur at a later stage, when the temperatures in the compartment are back to ambient, may be an even greater threat because it would occur at the time of first inspection, not only by the fire brigades but also possibly by other people. Such a tragic incident occurred in Switzerland in 2004 when seven members of a fire brigade were killed by the sudden collapse of the concrete structure in an underground
car park in which they were present after having successfully fought the fire [17].
This type of collapse also occurred during the cooling phase of a fire in a full-scale fire test conducted in 2008 by Wald [18] in the Czech Republic.
This article analyzes steel-concrete composite columns subjected to natural fires in order to verify that the possibility of structural collapse during or after the cooling phase is real and, if so, what are the parameters and conditions that more likely lead to this undesirable behavior.
2.
ANALYSIS PROCEDUREA sequentially coupled thermal-stress analysis is used to conduct the numerical simulations, thus two different models are needed: a heat transfer model and a mechanical model. The analysis was performed by first conducting a pure heat transfer analysis for computing the temperature field and afterwards a stress/deformation analysis for calculating the structural response. Nodal temperatures are stored as a function of time in the heat transfer analysis results and then read into the stress analysis as a predefined field.
A. Thermal analysis
A non-linear heat transfer analysis is first conducted for all the columns under study. The temperature curves considered in input data are taken from the parametric fire model of Annex A in Eurocode 1 part 1-2 [19], that represents the action of a natural fire with the cooling phase. These temperature curves are applied to the four exposed surfaces of the columns as a thermal load, through the convection and radiation heat transfer mechanisms.
The factor Γ that appears in Equation (A.2 a) [19] is taken equal to 1.0, which makes the heating phase of the time temperature curve of this natural fire model approximate the beginning of the standard curve as shown in figure 1.
Fig. 1. Various fire curves considered.
Figure 1 shows the various fire curves that have been used, differing from each other by the duration of the heating phase, from 30 to 120 min.
In each curve, the fire is divided into three phases:
Phase 1 is the heating phase of the fire, when the gas temperature is increasing from 20°C to the maximum temperature. The duration of phase 1 is tpeak;
Phase 2 is the cooling phase of the fire, when the gas temperature is decreasing from the maximum temperature to 20°C. The end of phase 2 takes place at time, t20 (where 20 refers to the gas temperature);
Phase 3 is the phase after the fire, when the gas temperature is constant equal to 20°C.
The nonlinear finite element software SAFIR developed at the University of Liège [20] for the simulation of structures subjected to fire is used. A uniform temperature has been assumed over the height of the column. Thus, thermal analysis can be reduced to a two-dimensional problem.
The temperature distribution in the sections is determined by 2D nonlinear transient analyses, as shown in Figure 2.
The non-steady-state 2D temperature distribution within any cross-section is determined by the Fourier thermal conductivity equation:
t c T y Q
T x k T
22 22 . . (1)
Where k is the thermal conductivity of the material, T is the temperature, Q is the amount of heat generated in the material per unit volume, ρ is the density, c is the heat capacity, t is the time and x, y are the position coordinates.
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740,40 652,54 564,68 476,81 388,95 301,09 213,23 125,36 37,50
Fig. 2. Isotherms after 30 min in a section heated on four sides (1/4 modeled).
The temperature fields within a given network are established by a finite element method in conjunction with an integration method for time steps. It is assumed that conduction is the main heat transfer mechanism in the hollow steel section and concrete core. Convection and radiation act
essentially as heat transfer from the environment to the external hollow steel section. The influence of moisture (assumed uniformly distributed in the concrete) is treated in a simplified way : the transient temperatures in the concrete are calculated assuming that all moisture evaporates, without any transfer, at temperatures situated within a narrow range, with the heat of evaporation giving a corresponding change in the enthalpy-temperature curve. Therefore during the period of evaporation, all the heat supplied to an element is used for the moisture evaporation until the element is dry. The discretization for plane sections of different shapes is possible by using triangular and/or quadrilateral elements. For each element the material can be defined separately. Any material can be analyzed provided that its physical properties at elevated temperatures are known. The variation of material properties with temperature can be considered.
In square sections, there are two axes of symmetry, therefore only one quarter of the section has to be discretized. Figure 3 shows an example of such a discretization.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
11
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SILCONCEC2 STEELEC2 STEELEC3 Fire30.fct 1
Fig. 3. Discretization of one-quarter of a square section.
B. Structural analysis
A non-linear stress analysis had been subsequently conducted using the same FEA package [20], accounting for the nodal temperature–time curves previously calculated in the thermal model. The columns are discretized longitudinally by means of Bernoulli beam type elements and the cross sections of the beam elements are divided into fibers that match the 2D elements of the thermal analysis.
The basis of the mechanical analysis of structures undergoing large displacements is in the incremental form of the principle of virtual work.
The formulation used in the model and the assembly of finite elements are based on the principle of virtual work expressed in a corotational description. In the model, a whole composite column is built up by means of several 2-D beam elements which are based on the following formulations and hypotheses:
Displacement type element in a total corotational description;
The displacement of the node line is described by the displacements of three nodes, two nodes at each end of the element supporting two translations and one rotation plus one node at mid-length supporting the non-linear part of longitudinal displacement. The longitudinal displacement of the node line is a second-order power function of the longitudinal co-ordinate. The transversal displacement of the node line is third-order power function of the longitudinal co- ordinate;
The Bernoulli hypothesis is considered, i.e., the cross section remains plane under bending moment;
The hypothesis of Von Karman is used : the strains are small;
The rotations are assumed to be small (note that they are evaluated in the co- rotated configuration);
The longitudinal integrations are numerically calculated using Gauss’
method;
The integration of the longitudinal stresses and stiffness on the section is based on the fiber model; the section is supposed to be made of a certain number of parallel fibers. In fact, the same discretization as the one used for the thermal analysis is used. Each finite element of the thermal analysis, with its known material type and temperature, is considered as a fiber;
The mechanical interaction between the steel tube and concrete infill was modelled as perfect i.e. no slip at the steel-concrete interface;
The columns are simply supported at both ends. A sinusoidal imperfection with maximum amplitude of L/500 [6,21] has been introduced in the direction of the thermal gradient (leading to bending along one single axis).
3.
MATERIAL MODELS AT ELEVATED TEMPERATURESThe numerical model takes into account the temperature dependent thermal and mechanical properties of the materials.
A. Thermal models
The thermal properties of steel and concrete in the heating phase have been extracted from EN1994-1-2 [22]. This means that thermal conductivity of concrete was taken with the upper limit in the sense of EN 1992-1-2 [23]. Siliceous concrete was chosen, with a density of 2300 kg/m³ and a water content of 92 kg/m³. Thermal properties of steel were considered as fully reversible during cooling. The specific mass of concrete, which decreases during heating because
of the release of water, has been considered as constant during cooling, with a value that corresponds to the one of the maximum temperature. When the temperature increases in the concrete, the thermal conductivity has a tendency to decrease [22]. It has been considered that the decrease of thermal conductivity is not reversible and, during cooling, the thermal conductivity of concrete keeps the value corresponding to the maximum temperature.
As previously said, the thermal boundary conditions are a mixture of thermal radiation and forced convection. The thermal radiation id defined by the steel emissivity which is taken equal to 0.7 whereas the forced convection coefficient is assumed to be 35 W/m²K.
B. Mechanical models
The mechanical properties of the steel have been considered as reversible, which means that stiffness and strength are recovered to full initial values during cooling. In the thermal elongation curve, the plateau corresponding to the phase change that occurs around 800°C at a level of 11 x 10-3 during heating occurs at slightly lower temperatures, around 700°C, at a level of 9 x 10-3 during cooling.
When steel is back to ambient temperature, there is no residual thermal expansion.
For concrete, a residual thermal expansion or shrinkage has been considered when the concrete is back to ambient temperature. The value of the residual value is a function of the maximum temperature and is taken from experimental tests made by Schneider in 1979 and mentioned in [24].
Compressive strength of concrete does not recover during cooling. According to EN 1994-1-2, an additional loss of 10% has been considered during cooling. This means that, for example, if the compressive strength has decreased from 1,00 to 0,50 at a given temperature, it will decrease to 0,45 when cooling back to ambient temperature. This assumption is of course the key for all the predictions presented in this paper and thus the reliability of the conclusions. In a recent paper, Yi- Hai and Franssen [25] have shown, from the analysis of hundreds of experimental results reported in the literature, that the additional reduction during cooling may be even higher than the 10% reduction considered in Eurocode 4. In the stress-strain relationship of concrete, the strain corresponding to the peak stress is considered during cooling as fixed to the value that prevailed at the maximum temperature (Figure. C.2 of Eurocode 4).
4.
PARAMETRIC STUDIESUsing SAFIR program, parametric studies have been performed by means of the numerical model described in the previous section. The main parameters affecting the fire resistance of hollow steel section columns filled with bar-reinforced concrete columns at elevated temperatures have
been investigated through these parametric studies.
The parameters studied are the outside dimension of square HSS columns (D), the thickness of the steel tube wall (th), the length of column (L), the amount of steel reinforcement (As) and the duration of the heating phase.
The variables that are considered in this research study are given below:
The outside dimension of square HSS columns (D) varies from 150mm to 300mm.
The amount of steel reinforcement varies from 0% to 10%;
The duration of the heating phase does not exceed 120 minutes.
The wall thickness thvaries from 5mm to 10mm and the ratio D/th is less than
fy 235
52 to neglect the effect of local buckling in the steel wall according to Eurocode 4-Part 1.1 [26].
Only the steel yield strengh fy 355MPa has been considered because it is now the most commonly used material for hollow steel sections.
Three concrete strengths, namely, MPa
fc 30 , fc 40MPa, fc 50MPa have been used;
Only the quality of reinforcing steel S500 ( fs 500MPa) has been considered in this study because it is now the most commonly used material for reinforcing steel;
Concrete cover which represents the distance between the axis of longitudinal reinforcements and the border of the concrete core has been fixed at a minimum value of 30 mm.
The following symbols have been used in the figures:
S150x5 stands for Square section with dimensionD
= 150 mm, steel wall thickness th = 5 mm C30 stands for compression strength of concrete on cylinder fc 30MPa,
e30 stands for concrete cover e = 30 mm
4D16 stands for the case where the reinforcement in the section consists of 4 bars with diameter 16mm
5.
INFLUENCE OF THE DURATION OF THE HEATING PHASEFigure 4 summarizes the analyses performed to examine the influence of the duration of the fire.
Each curve in the Figure is related to one of the fires shown in Figure 1 and is the result of numerous simulations performed with different load levels. From the load bearing capacity at time t=0, here 5066 kN, the load has been progressively reduced and numerous simulations have been performed, each one for a different load, yielding a fire resistance time that increases as the load is decreased. In a real building, the columns are
subjected to different loads of various levels which are not known by the fire fighters. As an example of results, for the curve marked as tpeak=30 min, if a column is subjected to a load of 2000 kN, it will fail after 40 min. Each of the presented curves shows whether there is a potential dangerous range of the load that could lead to collapse during or after the heating phase. If this is the case, the fact that a delayed collapse will occur or not in a building will depend on the actual load level on the columns.
The load that gives a fire resistance time equal to the duration of the heating phase tpeak is marked on the curve; for the fire with a heating phase of 30 min, this load is 2303 kN. If the load applied on the column is greater than 2303 kN, failure will occur during the heating phase of the fire. For loads less than 2303 kN, failure of the column occurs in the cooling phase of the fire; for the 30 min fire, this failure time of 43 min is obtained for a load of 1990 kN. Any load less than 1990kN will not lead to the collapse of the column, which is marked by the fact that the curve has a horizontal asymptote.
For the fire that has a heating phase of 120 min, any load greater than 313 kN will lead to collapse during the heating phase, that is, in less than 120 min. If the load happens to be between 297 and 313 kN, collapse will occur during the cooling phase. If the load is less than 297 kN, there will be no collapse of the column and indefinite stability is ensured. There is no possibility of collapse after the cooling phase for this fire duration and for this range of load levels.
It is thus possible, according to this model, to have in certain cases a structural collapse some time after the end of heating phase.
Fig. 4. Evolution of the load bearing capacity for a column subjected to natural fires of different duration of heating phase.
Figure 5 presents another illustration of these results. On the horizontal axis is the duration of the heating phase of the fire whereas the applied load is on the vertical axis. Each curve of Figure 4 is on a vertical line in Figure 5 but, in Figure 5, only the characteristic points of the curves of Figure 4 have been marked. The plan is divided into three regions.
Above the upper line is the region corresponding to failures in phase 1, the heating phase (e.g., above 2303kN for a fire duration of 30 min and above
313kN for a fire duration of 120 min). Under this line is the region of failures during phase 2, the cooling phase. Below the lowest line is the region that does not lead to collapse at all and the intermediate region.
As is seen on figure 5, the collapse in phase 3 does not exist in this case, it should be the intermediate region, it occurs when the compartment is back to ambient temperature conditions.
Fig. 5. Influence of the duration of the heating phase
6.
INFLUENCE OF THE SECTION OF THE COLUMN The analyses have been repeated for different section dimensions of the column with a length of 3m. The results are summarized in Figure 6 for different heating phases.Failures in phase 2 of the fire are observed in almost all sections except for smaller sections heated during 90 minutes and 120 minutes, when failure occurs during the first minutes of the beginning of the cooling phase, which leads to not consider late failure.
Fig. 6. Influence of the section of the column For tpeak = 30 minutes, delayed failure exists for all sections, it occurs about 11minutes after the end of heating, but this time of collapse is almost constant and does not vary from one smaller section to massive section; this is because short fire does not induce thermal gradients ranging in depth of the section, it is almost the same layer or thickness heated whatever is the section. Figure 7 shows thermal gradients almost similar under fire with tpeak = 30 minutes at the same points taken equidistant for three different sections,particularly
Collapse in phase 1
Collapse in phase 2
No Collapse
in the first three quarters of an hour when failure of all sections occurs.
When tpeak rises to 60 minutes , there is a little late collapse ( 5 minutes after tpeak ) for the smallest section , and higher for other sections ( between 13 and 17 minutes). For this fire, a jump of about 11 min in tcollapse may be noted, passing from a section of S150x5 (mm²) to a section of S180x5 (mm²). Beyond a section of S200x6.3 (mm²), the duration of fire resistance becomes insensitive to the dimension of the section, because temperatures at selected points approximate from the start of heating until the failure.
For longer duration fires, collapse tends to move away from the heating phase as the section size increases. It may even occur at more than 30 minutes from the beginning of cooling for a section of 300x300x8, heated during two hours.
For small sections, this can be explained by the fact that for longer duration fires, the sections are heated longer, thus allowing almost all the points to reach very high temperatures during the heating phase, so the temperatures reached are more important and significant degradation of material properties occur during this phase.
But for massive sections, even if the heating time is long, there will always be a central area that is not too affected during heating but in which the heat continues to spread and temperatures continue to increase a long time during cooling when the temperature of the gas tends to return to room temperature (figure 7) which explains the sensitivity of these sections to the delayed collapse.
(a) tpeak=120min
(b) tcollapse=152min
(c) t20=367min
(d) tcooling=2138min
Fig. 7. Isotherms in a section S300x8 heated during 120 minutes on 4 sides (1/4modeled).
7.
CONCLUSIONA numerical model has been used in this study for concentrically loaded simply supported composite steel-concrete columns heated on four sides to highlight the phenomenon of delayed collapse of this type of columns during or after the cooling phase of a fire. The results show that a failure during the cooling phase of a fire is a possible event even after several minutes after the end of the heating phase.
The main mechanisms for these delayed failures are to be found in the fact that temperatures in the central zones of the concrete core can keep on increased even after the gas temperature is back to ambient and also in the fact that concrete may lose additional strength during cooling compared to the situation at maximum temperature.
It has been shown that the most critical situations with respect to delayed failure arise for short fires, for columns with low slenderness (short length and/or massive section), for columns with small thickness and for concrete cores with important reinforcement rate.
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