Resistance of partially protected steel beams in fire

Intumescent coating is often used as a fire protection on steel members due to its attractive appearance and ease of use. In the case when the member is fully covered by the coating, the response during the fire can be predicted rather accurately. However, if the member is covered only partially, the member's temperature profile and the structural response during the fire are not trivial to define. Partially covered members appear e.g. in cases in which the member is coated on the building site, but some previously installed adjacent structures disturb the coating process. Such partially covered members have been studied in the literature mainly from the temperature point of view, but in the present paper, also the structural behavior during the fire is considered. The paper presents a general procedure how to define the resistance of a partially protected steel member during the fire. As a result, time‐resistance curves are defined for bending, shear and torsion and standard IPE and HEA profiles are used in the example simulations and the results are compared to fully protected and unprotected cases. The finite element method is adopted both for the thermal and structural analyses. The expansion of the intumescent coating is taken into account using the so called effective thermal conductivity, hence the same model can be used for both analyses. The simulated temperature results are validated against experimental and simulation results from previous researches. The results for bending, shear and torsion resistance show, that when compared to the unprotected case, the partial protection increases the resistances and the improvement is at its height during 15‐30 minutes from the beginning of the standard fire.


Introduction
In some situations, when a steel beam is protected with intumescent coating, the profile cannot be covered on all sides. The Eurocode introduces some methods for calculating the bending and shear resistances of steel beams with non-uniform temperature gradients. Unfortunately, they are all for passive fire protection methods, and none of the protection cases apply to a beam with an unprotected flange [1].
The behaviour of steel columns in non-symmetrical fire has been studied by [13] and [14], and concrete filled steel tube columns in non-symmetrical fire were researched by [15][16][17][18]. Additionally, Schaumann et al. [19] have studied the temperature behaviour of a steel beam, which is protected by intumescent coating, but supports a trapezoidal steel sheet, which partially inhibits the coatings expansion. None of these examples include both the thermal and structural analysis of a partially protected steel profile. The studies done by Hautala et al. [20] and Kangashaka [21] presented in this paper aim to remedy this.
The profiles studied in this paper are IPE 200 and HEA 200. Three levels of fire protection are simulated for each profile; a fully protected, a partially protected, and an unprotected case. In the partially protected case the upper surface of the top flange is left unprotected. With each level of fire protection bending, shear, and torsion resistances are determined. From these results the effect of partial protection are compared to the protected and unprotected cases as a function of time. The simulations are done with ANSYS Workbench 19.2 [22].

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The FEM-models

Material models and fire model
The effective thermal conductivity of the intumescent coating was calculated by dividing the equivalent thermal conductivity by Schaumann et al. [2] by a thermal expansion factor. The expansion factor ( Figure 1) is the ratio between the thickness of the coating at time i and the original thickness [2]. The equivalent thermal conductivity is given in Equation (1) as

Abstract
Intumescent coating is often used as a fire protection on steel members due to its attractive appearance and ease of use. In the case when the member is fully covered by the coating, the response during the fire can be predicted rather accurately. However, if the member is covered only partially, the member's temperature profile and the structural response during the fire are not trivial to define. Partially covered members appear e.g. in cases in which the member is coated on the building site, but some previously installed adjacent structures disturb the coating process. Such partially covered members have been studied in the literature mainly from the temperature point of view, but in the present paper, also the structural behavior during the fire is considered. The paper presents a general procedure how to define the resistance of a partially protected steel member during the fire. As a result, time-resistance curves are defined for bending, shear and torsion and standard IPE and HEA profiles are used in the example simulations and the results are compared to fully protected and unprotected cases. The finite element method is adopted both for the thermal and structural analyses. The expansion of the intumescent coating is taken into account using the so called effective thermal conductivity, hence the same model can be used for both analyses. The simulated temperature results are validated against experimental and simulation results from previous researches. The results for bending, shear and torsion resistance show, that when compared to the unprotected case, the partial protection increases the resistances and the improvement is at its height during 15-30 minutes from the beginning of the standard fire.
where α is the thermal expansion factor [-]. The effective thermal conductivity λeff of the intumescent coating is calculated as where λeq is the equivalent thermal conductivity [W/(mK)] and α is the thermal expansion factor [-]. The density is ρIC = 1400 kg/m 3 , and the specific heat of the coating was defined according to Figure 2   The specific heat, thermal conductivity, Young's modulus Ea, yield strength fy of steel S 355 are from [1], as well as its temperature independent density ρa = 7850 kg/m 3 . Steel is assumed to be linear elastic with linear strain hardening material. Tangent modulus is calculated as Ea/100 [24]. Poisson's ratio is υa = 0.3 [25].
The fire model used in the simulations is the ISO-834 standard fire curve, the coefficient of heat transfer by convection being αc = 25 W/(m 2 K) [27]. The emissivities are εIC = 0.8 for the intumescent coating [23], and εa = 0.7 for the unprotected steel surface [1].

Simulated models for bending, shear and torsion
A cantilever beam is used to model the bending, shear and torsion resistances. To determine the resistances, a fixed rotation or displacement was introduced at the free end of the beam, and the resistance was calculated from the beam's moment or force reaction at the supported end. In the bending model, the rotation φz ( Figure  3a) around the z-axis was introduced, for the torsion model the rotation φx (Figure 3c) was around the x-axis, and in the shear model a displacement v (Figure 3b) in y-direction was used. In the torsion model, warping of the profile should be taken into account depending on the case, and in the current study, the warping is restrained in both ends of the model. For bending and torsion cases, the length L of the beam is 0.02 m. In case of shear resistance, the length must be so short that it eliminates the effect of the bending moment on the shear failure of the beam. This was checked using Equation 4 (when M =FL, and Q = F at the support). * 100% = * 2 * * 100% = 2 * 100% = 2 * 100% , (4) where σavg is the average bending stress on the cross section  For each loading case (bending, shear, torsion) three models are made, a fully protected, a partially protected, and an unprotected model. The ISO-834 fire curve is applied on the beams, and a thermal analysis is performed. After this, the temperature gradients of each beam at heating times t = 0 s, 300 s, 450 s, 600 s, 900 s, 1200 s, 1500 s, 1800 s, 2100 s, 2400 s, 2700 s, 3000 s, 3300 s and 3600 s are used as body loads in structural analyses to determine the resistances at different heating times for each level of fire protection. Each model comprises of two bodies, one for the steel profile and the other for the intumescent coating. Since the mechanical behavior is not of interest, the intumescent coating body is suppressed during the structural analyses. For each of the loading cases one end of the beam is supported so that the translation and rotation degrees-offreedom are fixed. In the models for bending, translation is set to zero at the free end along the z-axis, and rotation is not allowed around the x-and y-axes. In the free end of the shear models, rotation is suppressed around all axes, and translation along the z-axis.
In the torsion models, neither rotation nor translation was restricted at the free end. A rotation or a displacement is applied on the beams, which linearly changes from 0 to 0.6 degrees, or 0 to 0.06 mm during 0.6 s. The resulting moment or force reaction at the support are measured as a function of time. Additionally, for bending the plastic strain at the flanges, for shear the plastic strain at the web, and for torsion the plastic strain of the beam is measure as a function of time. Finally, the moment or force reaction is plotted as a function of the rotation or displacement. In the shear model for the partially protected HEA 200 at heating times 600 s, 900 s, 1200 s, 1500 s and 1800 s the beam was loaded for longer, since the plastic strain did not begin until after 0.6 s.

Elements and meshing
The elements used in this study are SOLID70 for thermal analysis and SOLID185 for structural analysis. The mesh size was determined from a sensitivity analysis ( Figure 4). It was carried out by comparing the bending results of a fully protected IPE 200 beam at a heating time 1800 s. The mesh sizes were 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm. The difference in results between 5 mm/4 mm meshing was significantly larger than between other meshes, which yielded relatively similar differences. Therefore, meshing size of 4 mm was chosen. Since none of the loads on the beams varied along the beams' lengths, there is only one element across the beam length. The meshes of the beams are depicted in Figures 5 and 6.

Validation of thermal simulation models
In their work, Schaumann et al. simulated the expansion of the intumescent coating and used the equivalent thermal conductivity [2]. The proposed simulation method was validated using their data, as well as test data from Tabeling [23]. They are shown in Figure 7. It also shows the ISO-834 fire curve and the temperature of the furnace in the Tabeling tests. As can be seen, the curves of the data from this study closely follow the data from previous studies. The maximum difference in temperature between the data from Schaumann et al. [2] and the proposed method with standard fire is 88.3 °C, and between the tests by Tabeling [23] and the proposed method with furnace fire it is 57.8 °C. The data can be assumed to validate the IPE 200 models, and since the profiles are so similar, the HEA 200 models are also validated.

Temperatures
The results of the thermal analyses of the IPE 200 models are depicted in Figure 9.

Bending resistance
As mentioned earlier, the moment reactions of the supported end of the beam are plotted as a function of rotation. For the fully protected, partially protected, and unprotected IPE 200 beams they are shown in Figures 10, 11 and 12, respectively. From these curves the bending resistance at a certain heating time is read when the plastic strain reaches 0.2 %. These resistances are plotted as a function of heating time in Figure 13. The same is done for the HEA 200 beam, and the results are shown in Figure 14. To compare the results, the halving times (the time it takes for the resistance to reduce 50 %) of the resistances are shown in Table 1.     The difference in halving times between the fully protected beams follows from the fact that the IPE 200 beam heats up faster. However, the difference disappears when examining the partially protected beams. The partially protected beams heat up faster than the fully protected beams, and since the HEA 200 beam has larger flanges than the IPE 200 beam does, the increase in heating speed is also larger.

Shear resistance
Similarly to bending, the force reactions are plotted as a function of displacement for all three fire protection levels and for both beam types. From these curves, the shear force resistances are read when the plastic strain reaches 0.2 %, and they are plotted as a function of heating time (Figures 15 and 16). The halving times of the shear resistances are once again compared in Table 2.   As for bending, the difference between the halving times of the fully protected beams is quite large because IPE 200 is heating up faster. However, the halving times of the partially protected beams are no longer the same. This is likely due to the fact that shear is manly carried by the web of the cross section.

Torsion resistance
Finally, the torsion resistance curves as a function of heating time are plotted as before. They are presented in Figure 17 and 18. The halving times are compared in Table 3.  Once again, the difference between the halving times of the fully protected beams is explained with the fact that the IPE 200 is heating up faster. After this, however, the differences for partially protected and unprotected beams are rather similar. After the increase in heating speed caused by removing the intumescent coating from the upper flange, it seems that the shape of the cross section affects the halving time more than the higher and more even temperature distribution caused by removing all intumescent coating. Since the torsion modulus of the HEA 200 beam is higher, its halving times are also higher.

Conclusions
In this study, the effect of partial fire protection on the bending, shear and torsion resistances of IPE 200 and HEA 200 beams in a standard fire was studied. Based on previous studies partially protected beams have lower resistances than fully protected beams, but their resistances do not decrease quite as quickly as those of unprotected beams. In this paper it was found that the halving times of the partially protected beams were several minutes longer than those of the unprotected beams. The proposed method provides information on the performance of partially protected structures more broadly, and can thus be used in design universally, and not just in designing cantilever beams. Therefore, the advantage provided by partial protection should be utilized when designing the fire performance of structures.