## 3 New Numerical Parametric Models
### The Temperature Field  
The new parametric models were evaluated under the same conditions as the transient thermal analysis, with the same defined finite elements, type of mesh, and identical boundary conditions. Regarding the boundary conditions of the parametric models, these were like those admitted in the M4 model, referred to in the experimental validation. However, the new parametric models under study are subject to the standard fire curve, defined following ISO 834-1:199 [10]. The boundary conditions applied in the new parametric models are represented in Figure 6.  
Finally, a total simulation time of 240 min was considered, except for the study of the model with different gypsum board thicknesses, in which it was necessary to extend the simulation up to 300 min to calculate the residual cross-section. The temperature field evaluation at control points A, E, and F, in accordance with the consideration of the experimental validation model M4, is represented in Figure 7.  
In this way, descriptive curves of the time evolution of temperature were drawn up. The temperature fields obtained for the models related to the study of the distance between centers (D) are represented in Figure 7a. To compare the temperature evolution curves of the wood height (H) study, the temperature fields are represented in Figure 7b. The study of the wood width (W), referring to the models under analysis, is represented in Figure 7c. The study of gypsum board thickness (Tg) is represented in Figure 7d. Analyzing the results obtained for the study of the distance between centers (D), it is concluded that the temperature fields of the different models present a high similarity, with the slopes of the curves being approximately the same. However, it appears that a smaller distance between centers, in this case, equal to 400 mm, allows a slightly delayed increase in temperature to be obtained when compared to distances of 500 and 600 mm. Based on the results obtained for the temperature field resulting from the study of the wood height (H), the slopes of the curves in the three models are similar. Regarding \begin{table}
\begin{tabular}{c c c c c} \hline \hline
\begin{tabular}{c} **Parameter in** \\ **Study** \\ \end{tabular} & \multicolumn{2}{c}{**Dimension [H \(\times\) W + Tg] \(\times\) D**} & \multicolumn{2}{c}{**Best**} \\  & & **Performance** \\ \hline \multirow{2}{*}{D} & [70 \(\times\) 30 + 12.5] \(\times\) 400 & [70 \(\times\) 30 + 12.5] \(\times\) 500 & D1 \\ \hline \multirow{2}{*}{H} & [70 \(\times\) 30 + 12.5] \(\times\) D1 & [90 \(\times\) 30 + 12.5] \(\times\) D1 & [120 \(\times\) 30 + 12.5] \(\times\) D1 & H1 \\ \hline \multirow{2}{*}{W} & [H1 \(\times\) 30 + 12.5] \(\times\) D1 & [H1 \(\times\) 40 + 12.5] \(\times\) D1 & [H1 \(\times\) 50 + 12.5] \(\times\) D1 & W1 \\ \hline \multirow{2}{*}{Tg} & [H1 \(\times\) W1 + 12.5] \(\times\) D1 & [H1 \(\times\) W1 + 15] \(\times\) D1 & [H1 \(\times\) W1 + 25] \(\times\) D1 & Tg1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: New numerical parametric models. Figure 6: Boundary conditions for the new numerical model. The light blue color represents the wood, and the violet color represents the gypsum board. control point A, it is also possible to conclude that the temperature field at this point is not influenced by the variation in the wood height. Around points E and F, despite the curves having the same slope, the increase in the wood height causes a delay in the temperature evolution. Thus, it appears that the model with the best performance regarding the time evolution of temperature is the one defined by [120 \(\times\) 30 + 12.5] \(\times\) 400. Analyzing the results obtained for the temperature field referring to the study of the wood width (W), at points A and F, the results confirm the previous conclusions, there is a linear evolution of temperature between the exposed face to the fire and the top of the beam, which depends, mainly, on thermal conduction in the gypsum board.