## 2 Fire-Resistance Performance of A60 BPP
### Transient Heat Transfer Analysis and Fire Test  
In the transient heat transfer analysis of the A60 BPP, the maximum temperature and contour were calculated using ABAQUS/implicit [16], a general-purpose finite element analysis program. The transient heat transfer analysis model generated based on both the design configuration of the A60 BPP in Figure 2 and the fire test specimen in Figure 3 is shown in Figure 4, and the detailed specifications of the analysis model are summarized in Table 1.  
Figure 4: Configuration of the fire test specimen. Figure 3: Configuration of the fire test specimen. In order to improve the accuracy of the transient heat transfer analysis, the temperature-dependent material properties for both thermal conductivity and specific heat were applied according to the existing research results [17; 18; 19; 20]. The FTP code regulates that the A60 BPP should be heated gradually to the temperature of 940 \({}^{\circ}\)C for 60 min using a fire test furnace and control temperature, as shown in Figure 5.  
As shown in Figure 5a, the fire test specimen for A60 BPP was installed in the vertical direction, and the side of the insulation was placed on the opposite side of the furnace inside. The enclosed internal temperature of the fire test furnace was heated up to 940 \({}^{\circ}\)C for 60 min according to the furnace control temperature curve with the heat at the flaming point. The furnace control temperature curve shown in Figure 5b is defined by the following equation [2]:  
\[T\ =340\log_{10}(8t+1)+20, \tag{1}\]  
where \(T\) is the heating temperature (\({}^{\circ}\)C), and \(t\) is the heating time (minutes). The heat input condition of the transient heat transfer analysis was set the same as the fire test furnace conditions specified in the FTP code, as represented in Figure 5. Regarding the temperature measurement, the maximum temperature was measured on the body of the A60 BPP in the unexposed ambient domain, and it was decided that the FTP regulation was satisfied only as the measured temperature was 180 \({}^{\circ}\)C or less. Since the furnace heating condition specified in the FTP code is a method of increasing the atmosphere temperature inside the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Part** & **Dimension (Tube/Body)** & **Material Type** \\ \hline
1 & Penetration piece & \(\phi\)8/\(\phi\)20 & SUS316L \\
2 & Penetration piece & \(\phi\)8/\(\phi\)20 & S45C \\
3 & Penetration piece & \(\phi\)12/\(\phi\)25 & SUS316L \\
4 & Penetration piece & \(\phi\)12/\(\phi\)25 & S45C \\ A & Fire test specimen & & S400 \\ B & Insulation & & A60 class \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detail specification of the analysis model. Figure 5: Fire test furnace condition. enclosed fire test furnace, the following equations for calculating the convection coefficient (\(h\)) were applied in the transient heat transfer analysis [21]:  
\[h\ =\frac{k}{L}\ Nu\ \left(W/m^{2}K\right) \tag{2}\]  
\[Nu\ =\ \left\{0.825+\ \frac{0.387\ R^{1/6}}{\left[1+\left(\frac{0.492}{Pr} \right)^{\frac{1}{6}}\right]^{8/27}}\right\} \tag{3}\]  
\[R\ =\frac{\wp\beta(T_{s}-T_{\infty})L^{3}}{v^{2}}\ Pr, \tag{4}\]  
where \(Nu\) is Nusselt number, \(R\) is Rayleigh number, \(Pr\) is Prandtl number, \(k\) is the thermal conductivity of the fluid, \(L\) is geometry characteristic length, \(v\) is dynamic viscosity coefficient of the fluid, \(g\) is gravity acceleration, \(\beta\) is volumetric expansion coefficient, \(T_{s}\) is face temperature assuming a vertical plate, and \(T_{\infty}\) is fluid temperature away from the face. Figure 6 shows the temperature distribution results measured on the fire test specimen of A60 BPP from the transient heat transfer analysis at the heating time of 60 min.