# Study on the Fire Resistance of Axially Restrained H-Shaped Steel Beams Under Real Fire
## 3 Analysis of Fire Resistance of Steel Columns Based on Quasi-Real Fire Heating Curve
### Establishment of Finite Element Model of H-Section Steel Beam
#### 3.1.2 High-Temperature Mechanical Properties of Steel  
For this paper, the yield strength and elastic modulus of the steel are taken as 460 MPa and 200 GPa, as measured by [PERSON] et al. [30] through room temperature tensile tests. The mechanical properties of steel in fires gradually decrease as temperature rises, and in China's _Technical Code for Fire Protection of Building Steel Structures_ (GB 51249-2017) [31], the steel properties are only 50% of those at room temperature when the temperature reaches 600 \({}^{\circ}\)C. However, the domestic scholars [PERSON] et al. discovered in their study on the high-temperature mechanical properties of Q460 steel that the reduction factors in the code are somewhat conservative; thus, to obtain more precise simulation results, this paper adopts the reduction factors for yield strength and elastic modulus at different temperatures from [PERSON] et al.'s [32] research, as shown in Table 6.  
\begin{table}
\begin{tabular}{c c c|c c c} \hline \hline
**Temperature** & \begin{tabular}{c} **Elastic Modulus** \\ **Reduction Factor** \\ \end{tabular} & \begin{tabular}{c} **Yield Strength** \\ **Reduction Factor** \\ \end{tabular} & **Temperature** & \
\begin{tabular}{c} **Elastic Modulus** \\ **Reduction Factor** \\ \end{tabular} &
\begin{tabular}{c} **Yield Strength** \\ **Reduction Factor** \\ \end{tabular} \\ \({}^{\circ}\)**C** & \(\mathbf{E_{\text{T}}}\)/\(\mathbf{E}\) & \(\mathbf{f_{\text{y}}}\)-\(\mathbf{T}\)/\(\mathbf{f_{\text{y}}}\) & \({}^{\circ}\)**C** & \(\mathbf{E_{\text{T}}}\)/\(\mathbf{E}\) & \(\mathbf{f_{\text{y}}}\)-\(\mathbf{T}\)/\(\mathbf{f_{\text{y}}}\) \\ \hline
20 & 1.000 & 1.000 & 500 & 0.836 & 0.855 \\
100 & 0.983 & 0.879 & 550 & 0.809 & 0.744 \\
200 & 0.960 & 1.072 & 600 & 0.764 & 0.730 \\
300 & 0.928 & 1.143 & 700 & 0.636 & 0.362 \\
400 & 0.862 & 1.058 & 800 & 0.480 & 0.177 \\
450 & 0.862 & 1.058 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Reduction coefficients for elastic modulus and yield strength of Q460 steel at high temperatures.  
\begin{table}
\begin{tabular}{c c|c c} \hline \hline
**Temperature** & \begin{tabular}{c} **Thermal Conductivity of** \\ **Q460 Steel** \\ \end{tabular} & **Temperature** & \begin{tabular}{c} **Thermal Conductivity of** \\ **Q460 Steel** \\ \end{tabular} \\ \({}^{\circ}\)**C** & \
\begin{tabular}{c} **W/(m.\({}^{\circ}\)C)** \\ \end{tabular} & \({}^{\circ}\)**C** &
\begin{tabular}{c} **W/(m.\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline
25 & 50.971 & 600 & 36.820 \\
100 & 49.125 & 700 & 34.359 \\
200 & 46.664 & 800 & 31.898 \\
300 & 44.203 & 900 & 29.437 \\
400 & 41.742 & 1000 & 29.437 \\
500 & 39.281 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Thermal conductivity coefficients of Q460 steel.  
\begin{table}
\begin{tabular}{c c|c c} \hline \hline
**Temperature** & \begin{tabular}{c} **Specific Heat Capacity of** \\ **Q460 Steel** \\ **J/(kg.\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Temperature** \\ **Temperature** \\ **Q460 Steel** \\ \end{tabular} \\ \({}^{\circ}\)**C** & \
\begin{tabular}{c} **J/(kg.\({}^{\circ}\)C)** \\ \end{tabular} & \({}^{\circ}\)**C** &
\begin{tabular}{c} **J/(kg.\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline
25 & 462.40 & 600 & 733.57 \\
100 & 495.55 & 700 & 895.14 \\
200 & 529.10 & 800 & 840.68 \\
300 & 559.68 & 900 & 628.41 \\
400 & 597.27 & 1000 & 595.00 \\
500 & 651.90 &The Poisson ratio of Q460 steel in this paper is assigned as v = 0.3. To simplify calculations, the stress-strain model used for simulating Q460 steel in this paper also adopts a bilinear model, ignoring the strain-hardening segment of Q460 steel at high temperatures, as shown in Figure 9.