Column Modelling Setup

To investigate the interactions of thermal waves at corner junctions, the two-dimensional modelling of a simple square column cross-section is conducted. Experimental results from a column tested at MFPA Leipzig are used for validation, as discussed by Werther et al. (2012).

The column dimensions in the model were 156 mm x 156 mm, and this was exposed to the standard ISO 834 fire on all sides for 90 minutes. In order to optimise the available computer power, the symmetry of the column was used to reduce the overall area modelled, as discussed in 4.6.2. The area modelled was discretised into square plate elements of a 1 mm mesh size.

Similar measurement points were used to the one-dimensional analysis for comparison, however some intermediate points differ to align with the experimental results used for validation. The measurement points were taken at 0, 6, 10, 20, 30, 42 and 54 mm, and these were located at 60 mm in from the edge of fire impact to determine the influence of the thermal wave interaction. A depiction of these points on the column edge is shown in Figure 4-7.

Figure 4-7: Setup of the 2D thermal modelling and experiments

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Figure 4-8 shows the comparison between experimental results and the thermal modelling effort. For this comparison, only aligning points of temperature measurement are shown for the modelling output.

Figure 4-8: Comparison between experimental and 2D modelling

Due to the single set of experimental data for this two-dimensional case, the experimental results show a significant level of “noise” which reduces as the measurement points regress further into the timber column, the experimental values show a faster increase in temperature up to 150°C for all measurement points. Despite this, the modelling output does coincide relatively well with the experimental data, most notably at higher temperatures.

The experiment was terminated at approximately 43 minutes, but the modelling output is shown for 90 minutes as a comparison between the one and two-dimensional cases. It can be seen when comparing Figure 4-6 and Figure 4-8 that the influence of two-dimensional behaviour becomes apparent at different depths, however for this particular case with the temperature measurement points located 60 mm in from the heated surface the interaction has become apparent by 40 minutes. This is discussed further in Section 4.8.3.

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To determine whether a simple one-dimensional approximation is appropriate for use in thermal timber modelling checks must be made to ensure that the fire duration modelled will not incur significant isotherm interaction on the member in question. This is a function of the shape of the member, the relevant fire duration which determines the depth at which isotherms will interact, and the desired time to which the member is being designed for. In other words, the one-dimensional assumption is completely geometry and time dependent, and its use must be assessed on a case by case basis. Examples in which one-dimensional assumption would be appropriate are in the case of modelling slabs, sufficiently large beams or wide rectangular columns. Cases in which the members are more slender (including many different beam configurations) will most likely require the consideration of two or three-dimensional heating.

A comparison between the output for the one and two-dimensional modelling conducted is shown in Figure 4-9. For ease of comparison only the 6, 30 and 54 mm depths have been presented, with the one-dimensional results represented by solid lines and the two-dimensional results by dashed lines.

Figure 4-9: Comparison between 1D and 2D modelling

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The graph shows that the interaction is apparent at about 40 minutes of fire exposure, and the influence of the two-dimensional behaviour has a significant impact on the thermal performance of the timber. This highlights the importance of checking whether one-dimensional behaviour assumptions are appropriate when modelling timber members to ensure fundamental errors are not made in design and analysis.

4.8.4 2D Interaction

A similar model was conducted for the column case changing the depth of measurement to determine the influence of the two-dimensional interaction with timber depth. Figure 4-10 shows a comparison between the original modelling results of the column experiment, and output where the distance from the heated surface is changed to 30 and 90 mm. These are shown for 6, 30 and 54 mm depths into the timber, represented as red, green and purple lines respectively. As the distance from the heated surface increases the lines are represented by dotted, dashed and solid lines.

Figure 4-10: Comparison between depths of 2D modelling interaction

The measurement points spaced 30 mm from the heated surface record the most noticeable increases in temperature during the simulation, and the influence of the two-dimensional

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thermal wave is evident for each point as the temperature increases rapidly at each respective stage of the simulation. For the 6 mm deep measurement point (red lines) this effect is almost instantaneous, occurring at about 10 minutes into the simulation. The 30 mm deep measurement point (green lines) spaced 30 mm from the hot surface records a greater initial growth to 100°C than the 60 and 90 mm deep points, with a large rate of change of temperature at approximately 25 minutes. The 54 mm deep measurement point (purple lines) spaced 30 mm from the hot surface measures the most notable difference to its 60 and 90 mm counterparts, with a temperature of over 300°C at 41 minutes. This is due to the increasing thermal interaction of the two-dimensional heat source, and this effect increases with the duration of burning as the interaction becomes more significant. This is seen from the figure as the spacing between the temperature curves for each measurement point becomes greater with the depth into the timber.

The 60 mm measurement points display similar trends to the 30 mm points, however with a lower rate of increase in temperature for the points closer to the surface. The 54 mm measurement point has a much greater rate of increase in temperature due to its physical location in the simulation which is almost equidistant from the two heated surfaces. This infers that by 60 minutes into the simulation the effect of the two-dimensional thermal wave interaction has become significant, and is greatest at this point. This measurement point is highlighted in Figure 4-11 in red, where the thermal contours are compared for both 30 and 60 minutes of simulation run time on the left and right of the figure respectively.

Figure 4-11: 2D column thermal contour at 30 minutes (left) and 60 minutes (right)

The contours vary linearly from blue representing 20°C ambient temperature, to red which signifies 1000°C. The level of the char layer is at the cyan to green boundary. The figure shows

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the extent of amplification of the two-dimensional interaction over a 30 minute period, being much more significant at 60 minutes with a greater level of rounding of the thermal waves. It can be seen from Figure 4-10 that the temperature measurement at 90mm in is virtually identical to the one-dimensional case (Figure 4-6) for the first 70 minutes of exposure, with a noticeable influence of two-dimensional behaviour occurring at this stage of the simulation.

The major aspect which can be derived from Figure 4-10 is that the trends for each measurement depth are extremely consistent, showing that the two-dimensional behaviour of the timber can be predicted based on an estimated fire duration time. The analysis of the two-dimensional interaction above reinforces the requirement for the validity of a one-two-dimensional assumption for timber assemblies to be thoroughly checked. As previously iterated, this is highly dependent on the scope of the problem to be solved and should be considered on a case by case basis.