# Numerical Analysis of a Moderate Fire inside a Segment of a Subway Station
## 4 Thermomechanical Simulation at Selected Time Instants
### Structural Response under Thermomechanical Loading  
The comparison of experimental data and simulation results refers to the strain increments caused by the application of the thermal loading. As regards the numerical results, there are strain increments from four different simulations. They refer either to the linear-elastic (label: LE) or to the elasto-plastic (label: EP) material behavior of concrete and either to a spatially-uniform prescription of one surface temperature history (label: U) or to a piecewise spatially-uniform prescription of three different surface temperature histories (label: P). As regards the outer reinforcement both at the midspan of the left cell of the top slab and at the center of the right wall, the two different types of thermal boundary conditions have little influence on the simulation results; see Figure 20a,c. This follows from the fact that the outer reinforcement layers were not experiencing a temperature change during the experiment. The material model used for concrete, in turn, has a much larger influence. The linear-elastic model results in larger strain increments as compared to the elasto-plastic model. The differences increase with increasing duration of the thermal loading, and they are larger at the top slab as compared to the right wall; compare Figure 20a,c. In addition, both types of simulations underestimate the measured strain increments. In this context, the uncertainties regarding the thermal boundary conditions and the material behavior of concrete must be mentioned. On the one hand, there are strong indications that the inner surface of the tested structure was exposed to significant temperature gradients. Given that there were only two thermocouples positioned very close to the heated surface, the thermal boundary conditions are affected by considerable uncertainties. On the other hand, the material behavior of concrete was accounted for as suggested by current standards and pertinent guidelines. Nevertheless, some aspects deserve special attention. It is likely that concrete was damaged prior to testing because of restrained shrinkage. Moreover, time-dependent viscous material behavior in the form of creep and load induced-thermal strains (LITS) could also have influenced the structural performance considerably. As regards the inner reinforcement at the midspan of the left cell of the top slab, the differences of the strain increments obtained with different thermal boundary conditions are significantly larger than described above; compare Figure 20b with Figure 20a,c. This follows from the fact that the inner reinforcement layers were experiencing a significant temperature change during the experiment. It is also interesting to note that the elasto-plastic simulations deliver larger strains than the linear-elastic simulations. This indicates that inelastic material behavior of concrete, in particular tensile cracking, had a significant influence on the structural performance during the fire test. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Analysis Type** & **RW Outer Layer (10\({}^{-6}\))** & **TS Outer Layer (10\({}^{-6}\))** & **TS Inner Layer (10\({}^{-6}\))** \\ \hline Measured & \(-48.9\) & \(-49.4\) & \(3.72\) \\ LE & \(-45.9\) & \(-68.9\) & \(29.2\) \\ EP & \(-47.6\) & \(-69.4\) & \(30.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Measured and simulated strains of steel rebar, positioned at the inner and the outer reinforcement at midspan of the left cell of the top slab and at the outer reinforcement at the center of the right wall: additional strains, resulting from application of the mechanical loading, considering linear-elastic (LE) or elasto-plastic (EP) material behavior of concrete. The elasto-plastic material model for concrete improved the quality of the simulations, albeit with a significant increase in computational effort. The brittle nature of the structure caused abrupt local failures in specific regions where the tensile stresses were particularly large; see Figures 21-26.