## 3 Validation of the Simplified Design Method
### Parametric Study on Asymmetric Double-T Cross-Section  
We considered 81 geometrical configurations of asymmetric slim beam cross-sections (Table 5), using the numerical model validated in Section 2. Four types of asymmetric double-T steel profile were assessed, as shown in Figure 3 (ASB type, welded steel cross-section, IFB type, and SB type). Each geometrical configuration was considered twice, with composite and non-composite behavior. For all cases, the model was evaluated for four different fire resistances (R30, R60, R90, R120) resulting in a total of 648 analyses. The varying parameters are explained in Table 5, using the notations from Figure 9b. The ranges proposed by [PERSON] et al. [21], presented in Table 2, were respected and even extended as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline
**Coefficient** & **R30** & **R60** & **R90** & **R120** \\ \hline A\({}_{\rm i}\) & 0.113 & 0.130 & 0 & 0 \\ B\({}_{\rm i}\) & \(-\)12.80 & \(-\)11.80 & \(-\)2.60 & \(-\)1.25 \\ C\({}_{\rm i}\) & 760 & 980 & 990 & 1025 \\ A\({}_{\rm w}\) & \(-\)140.70 & \(-\)103.80 & \(-\)108.60 & \(-\)70.44 \\ B\({}_{\rm w}\) & 832.42 & 968.60 & 1146.70 & 1124.40 \\ C\({}_{\rm w}\) & 0.0317 & 0.0232 & 0.0198 & 0.0158 \\ D\({}_{\rm w}\) & \(-\)0.230 & \(-\)0.182 & \(-\)0.154 & \(-\)0.134 \\ A\({}_{\rm r}\) & 0 & 0.0954 & 0.0548 & 0.0381 \\ B\({}_{\rm r}\) & 0 & \(-\)19.254 & \(-\)15.130 & \(-\)12.797 \\ C\({}_{\rm r}\) & 300 & 1105.4 & 1135.9 & 1138.1 \\ \hline \end{tabular}
\end{table} 
Table 4: Coefficients for the simplified analytical method [15; 16]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Steel** \\ **Profile** \\ **Type**\({}^{\text{\text{\textdagger}}}\) \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Slab** \\ **Type**\({}^{\text{\textdagger}}\) \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **h** \\ **Type**\({}^{\text{\textdagger}}\) \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **b\({}_{\text{\text{\textdagger}}}\)** \\ **(mm)** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular}{c} **b\({}_{\text{\text{\textdaggerThe bending resistance was determined numerically, considering a simply supported beam with a uniform load. The value of the applied load was determined in order to obtain the requested fire resistance demand of 30, 60, 90, or 120 min. The simplified method has been applied in all 648 cases. The results obtained analytically were compared against the numerical results, in terms of bending resistance, for composite (Figures 10 and 11) and non-composite behavior (Figures 12 and 13). Figure 10 shows the comparison of composite behavior configurations, for R30 (**a**), R60 (**b**), R90 (**c**), and R120 (**d**), respectively. Figure 12 shows the comparison of non-composite behavior configurations, for R30 (**a**), R60 (**b**), R90 (**c**), and R120 (**d**), respectively. As Figures 10 and 12 suggest, the considered configurations cover a large interval of bending resistance values. The simplified method offers good results in comparison with the numerical values. The results obtained for R30 are underestimated by the simplified method up to 15%, due to the concrete thickness simplification, i.e., only the concrete thickness above the top flange is taken into consideration, while the plastic neutral axis is still in the steel profile height. The results obtained for R60 provide the closest results (up to 10%), as the PNA is close to the interface between the top steel flange and the concrete topping. The values for R90 and R120 demonstrate higher differences compared to the numerically results (up to about 30%, 40%, respectively), due to the simplification made to the temperature on the steel profile web which, in the simplified method, is considered to be uniform throughout the height.