## 3 Comparison of Steel Temperatures from the Model with Experimental Results
### Steel Temperatures in Central Columns
#### 3.2.2 Comparison of the Results  
To apply the model, some input parameters were directly defined from the test set-up:  
* The design fire load density \(\mathrm{q_{f,d}}=511\) MJ/m\({}^{2}\);
* The height of the fire load basis \(\mathrm{h_{base}}=0.325\) m;
* The net heat of combustion of the fire load H was estimated from a bomb calorimeter test (performed by the University of Edinburgh) as 16.8 MJ/kg;
* The total area of vertical openings \(\mathrm{A_{v}}=30\) m\({}^{2}\);
* The equivalent height of the openings \(\mathrm{h_{eq}}=1\) m.
* Other input parameters were taken from EN 1991-1-2:
* The combustion factor m = 0.8 (leading to an effective heat of combustion = 13.44 MJ/kg);
* The coefficient of convection heat transfer on the steel surface \(\mathrm{\alpha_{c}}=35\) W/m\({}^{2}\)K;
* The flame emissivity \(\mathrm{\varepsilon_{f}}=1\);
* The steel emissivity \(\mathrm{\epsilon_{m}}=0.7\);
* The time-steps dt = \(\Delta\)t = 5 sec. Finally, three parameters had to be defined based on some assumptions:  
* The rate of heat release density \(\mathrm{RHR_{f}}\) has been set to 400 kW/m\({}^{2}\), an evaluation made from the mass loss test measurement;
* Several fire spread rates v were considered and the present comparison was achieved with 3.2 mm/s which is representative of the fire spread rate observed in the first half of the compartment;
* The width of each band was set as \(\mathrm{d_{x}}=25\) cm (nearly identical results are obtained with a band width of 50 cm);
* The thickness of the flame layers \(\mathrm{d_{z}}=10\) cm (no sensitivity analysis was carried out for this parameter). It has to be noted that since the analytical model considers a fire load which is covering the whole floor area of the defined compartment, the compartment length and width were defined as 14 m and 4.2 m, respectively, to match the dimensions of the fire load used in the test. This configuration set up does not influence the criteria which verifies if the fire is air controlled. Indeed, Equation (3) does not depend on the compartment length and width but only on the openings sizes. The width of the two modelled openings is slightly  
Figure 10: Photographs of the large scale natural fire tests carried out by Ulster University in the frame of “TRAFIR” project: (**a**) unprotected steel column with thermocouples; (**b**) levels of the thermocouples. smaller (14 instead of 15 m in the experiment), but this does not influence the results as the fire is not air controlled in both cases (and R is therefore not modified). With the given input data, the time needed to burn the fire load within one band is 1277 s (21 min) while the time needed for the combustion front to cross a band is 78 s.  
Figure 11 presents the steel temperatures measured in column C11 at the five different levels while Figure 12 shows the corresponding steel temperatures obtained with the analytical model. On Figure 12, all the curves are overlapping except the one for level 5. Figures 13-17 present on common graphs the steel temperature for each level (with the label \"TEST\" for the experimental data and the label \"MODEL\" for the results of the analytical model). For the upper levels 4 and 5 (Figures 16 and 17), a third curve \"MODEL + ZONE\" is plotted, corresponding to the combination of the analytical model with a zone model. Indeed, such combination is needed to properly capture the effect of the hot smoke layer below the ceiling. In this case, the software OZone (Cadorin [30]) was applied, modelling the real compartment volume and the evolution of the fire as the one from the analytical procedure (i.e; the 4.2 m width band-by-band evolution with time). This combination was computed for level 5 (implying a smoke layer of at least 40 cm) and for level 4 (implying a smoke layer of at least 90 cm). When combination is considered, the maximum steel temperature of both calculation methods is plotted. Figure 14: Steel temperature—Test n°2 versus analytical model at level 2. Figure 13: Steel temperature—Test n°2 versus analytical model at level 1.