## 4 Nonlinear Finite Element Analysis Considering Fire Damage
### Parametric Analysis Results of Deflections  
Figure 19 shows the vertical deflections of the HCS according to the fire exposure time for each variable (i.e., HCS depth, span length, hollow ratio in a section, cover thickness of concrete, and load ratio). As shown in Figure 19a, the deflection tended to decreased as the HCS depth increased. This is because the heat transfer rate within the cross-section decreased as the heat capacity of the HCS section increased at the same time when the flexural stiffness of the section increased significantly as the depth increased. When the heat transfer rate in the section decreased, the mechanical properties of the concrete and prestressing strands deteriorated relatively slowly, as shown in Figures 14 and 15. In addition, the deflection showed a tendency to increase significantly with the span length, as shown in Figure 19b. However, when the vertical deflection of the HCS was normalized with the limit deflection calculated using Equation (1), similar values were obtained regardless of the HCS depth and span length. This is because the limit deflection calculation formula presented in ISO 834-1 [32] considers the section depth and span length reasonably. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Types**} & \multirow{2}{*}{**Analysis**} & \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**Ratio**} \\  & & & & & **(Analysis/Test)** \\ \hline \multirow{6}{*}{D200-T7} & \multirow{6}{*}{Temperature (\({}^{\circ}\)C)} & Unexposed surface & 55 & 52 & 1.06 \\ \cline{3-6}  & & 200 mm (\({}^{\circ}\)C) & 105 & 89.2 & 1.18 \\ \cline{3-6}  & & 150 mm (\({}^{\circ}\)C) & 161.4 & 148.5 & 1.09 \\ \cline{3-6}  & & 100 mm (\({}^{\circ}\)C) & 246.4 & 248.1 & 0.99 \\ \cline{3-6}  & & 50 mm (\({}^{\circ}\)C) & 393 & 379.9 & 1.03 \\ \cline{2-6}  & & Deflection (mm) & 97.23 & 97.20 & 1.00 \\ \hline \multirow{6}{*}{D265-T8} & \multirow{6}{*}{Temperature (\({}^{\circ}\)C)} & Unexposed surface (\({}^{\circ}\)C)} & 37 & 36.5 & 1.01 \\ \cline{3-6}  & & 200 mm (\({}^{\circ}\)C) & 69.4 & 67.8 & 1.02 \\ \cline{3-6}  & & 150 mm (\({}^{\circ}\)C) & 111.9 & 100.4 & 1.11 \\ \cline{3-6}  & & 100 mm (\({}^{\circ}\)C) & 109.9 & 104 & 1.06 \\ \cline{3-6}  & & 50 mm (\({}^{\circ}\)C) & 366.1 & 361.5 & 1.01 \\ \cline{2-6}  & & Deflection (mm) & 81.70 & 76.70 & 1.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of analysis and test results (at 120 min). Figure 17: Comparison of measured and computed deflections. Figure 18: Temperature behavior with respect to fire exposure time. Figure 19: _Cont_. As shown in Figure 19c, the vertical deflection of the HCS decreased slightly as the hollow ratio in the section increased. This is because within the hollow ratio range of 30-50%, heat release occurred relatively rapidly as the surface area inside the void increased with the hollow ratio. In addition, as shown in Figure 19d, it appeared that as the cover thickness of concrete increased, the deflection increased because the effective depth of the prestressing strands decreased with increasing the cover thickness of concrete at the same height of the section. However, the effects of the hollow ratio in a section and the cover thickness of concrete on the deflection of the HCS under fire were insignificant when the hollow ratio was 35 to 50% and the cover thickness of concrete was 30 to 50 mm, which are applied widely in practice. Figure 19e shows the deflection of the HCS according to the fire exposure time for each load ratio (i.e., the ratio of the external load to the ultimate load). It was discovered that the load ratio exerted a dominant effect on the deflection of the HCS compared with any other variables. As the load ratio increased, the neutral axis in the cross-section moved up due to flexural cracks, resulting in a decrease in flexural stiffness of the section. Therefore, the vertical deflection normalized to the limit deflection increased proportionally with increasing the load ratio.