# Fire Resistance of Ultra-High-Strength Steel Columns Using Different Heating Rates
## 2 Methodology and Validation
### Model Validation for Hybrid Columns under Fire
#### 2.4.3 Nonlinear Structural Analysis at Elevated Temperatures  
Following the same procedure as with the CHS columns, GMNIA simulations at high temperatures were conducted, enabling validation. Six simulations were carried out, incorporating three load levels and two different heating rates. Each of these simulations was then compared with its respective experimental and numerical results, obtained from [PERSON] et al. [12], as illustrated in Figure 11.  
In Figure 11a, the test conducted with a heating rate of 5 \({}^{\circ}\)C/min, with a constant mechanical load corresponding to 30% of the load-bearing capacity, is presented. The numerical results obtained from Ansys match well with the experimental tests, diverging only after 65 min. On the other hand, Figure 11b presents the results obtained with a heating rate of 20 \({}^{\circ}\)C/min using the same mechanical load (30%). The results demonstrate good agreement during the initial 20 min but anticipate the failure or collapse of the column, when compared to the experimental tests.  
Figure 11c presents the results obtained with a heating rate of 5 \({}^{\circ}\)C/min using a mechanical load corresponding to 45% of the load-bearing capacity. Similar to previous cases, the results with this heating rate demonstrate good agreement during the initial 45 min but exhibit a more significant difference in the later stages of the analysis. Figure 11d presents the results for a higher heating rate (20 \({}^{\circ}\)C/min) and same load level. The results align until 17 min, after which ANSYS anticipates the collapse, when compared to the experimental test.  
Figure 11e presents the results for a heating rate of 5 \({}^{\circ}\)C/min with a load level corresponding to 60%. The results agree well until the 40 min mark but diverge afterwards. Lastly, in Figure 11f, the results are presented for a load level of 60% and a heating rate of 20 \({}^{\circ}\)C/min. The results agree well until the 12 min mark, after which they anticipate the collapse compared to the experimental test.  
The overall results of these simulations are summarised in Table 11 for R20 and Table 12 for R5. The accuracy of the model is well demonstrated by the very small RMSE during the simulation time, with RMSE varying between 0.4 mm and 2.61 mm.  
Figure 10: Validation of load-bearing capacity of hybrid column at room temperature [12].  
Figure 12 compares the experimental failure modes with those obtained by Ansys. As demonstrated, there is a good agreement in the deformed shape modes.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Load Level** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Load-Bearing** \\ **Capacity (kN)** \\ \end{tabular} & \begin{tabular}{c} **Load** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **Critical Temperature** \\ **Ansys (°C)** \\ \end{tabular} & \
\begin{tabular}{c} **Relative ERROR** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **RMSE** \\ **(mm)** \\ \end{tabular} \\ \hline U0.30 & 30 & 1298.52 & 1298.52 & 579.4 & 0.38 & 1.95 \\ U0.45 & 45 & 1947.78 & 1947.78 & 527.9 & 2.91 & 2.61 \\ U0.60 & 60 & 2597.04 & 2597.04 & 503.2 & 3.76 & 0.92 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Results for hybrid column with R20.  
Figure 11: Validation for hybrid columns at high temperatures. Displacement and rate of displacement over time [12].