## 3 Thermo-Structural Numerical Model
### Nonlinear Thermal FEM Model  
To simulate thermal conduction in transient 3D thermal analysis, the profile steel decking was modelled with a 4-node shell heat transfer element (SHELL131) and the concrete slab was modelled with a 20-node solid heat transfer element (SOLID90) from the ANSYS software library [32]. The proposed numerical model took into account the nonlinear thermal contact between the steel decking and the concrete slabs, using surface-to-surface contact elements (TARGE170 and CONTA174) [32]. The mesh density was controlled to have a maximum element size of 5 cm with a uniform mesh. The thermal model had 86,094 nodes and 20,597 elements. The average element quality and the average orthogonal quality of the thermal FEM model were 0.9883 and 0.9928, respectively. The numerical model took into account the temperature-dependent thermal properties of all the materials. Nonlinear thermal properties of LWC, such as thermal conductivity and specific heat, were defined using the following procedures and experimental tests. Thermal conductivity of LWCs at ambient temperature was experimentally measured, as indicated in Table 2. Based on the Eurocode 4, nonlinear thermal conductivity was obtained using the following Equation (1). \[ \begin{array}{l}k(\theta_{c})=k_{20^{\circ}\mathrm{C}}-\frac{\theta_{c}}{1 00}\qquad 20\leq\theta_{c}\leq 800\ ^{\circ}\mathrm{C}\\ k(\theta_{c})=0.5\qquad\qquad\qquad\theta_{c}>800\ ^{\circ}\mathrm{C}\end{array}  \tag{1}\]  
Heat transfer in porous LWC is greatly influenced by the moisture content [33]. Movement of water within the concrete is accompanied by significant energy transfer. This is associated with the latent heat of water and the heats of hydration and dehydration. It is known that the temperature increases at a slower rate above 100 \({}^{\circ}\mathrm{C}\). This effect is more significant for higher values of moisture content, constituting latent heat due to a vaporization process that consumes a lot of heat [11]. Thus, it leads to longer delays in the temperature rise within the concrete, and a plateau in the temperature history becomes evident for the moisture content of 7% or higher. After most of the moisture has evaporated (at temperatures exceeding about 150 \({}^{\circ}\mathrm{C}\)), the temperature in the concrete rises more rapidly. This nonlinear effect of moisture vaporization is taken into account, modifying the specific heat in the range of 90 \({}^{\circ}\mathrm{C}\) to 250 \({}^{\circ}\mathrm{C}\), following Equation (2). \[ \begin{array}{l}ce(\theta_{c})=0.84\ \mathrm{kJ}/\mathrm{kgK}\qquad 20\leq \theta_{c}\leq 90\ ^{\circ}\mathrm{C}\\ ce(\theta_{c})=5\ \mathrm{kJ}/\mathrm{kgK}\qquad\qquad\quad\quad\quad 90<\theta_{c} <250\ ^{\circ}\mathrm{C}\\ ce(\theta_{c})=0.84\ \mathrm{kJ}/\mathrm{kgK}\qquad\qquad 250\ ^{\circ}\mathrm{C}\leq \theta_{c}\end{array}  \tag{2}\]  
Finally, temperature-dependent thermal properties in steel and NC such as specific heat and thermal conductivity are obtained from chapter 3 of Eurocode 4. It should be noted that the upper limit specified in Eurocode 4 is used for thermal conductivity of NC. Figure 9 shows the nonlinear thermal properties, both thermal conductivity and specific heat, for the three LWCs and NC. Steel-Concrete Interaction  
Debonding between the steel decking and the concrete slab was experimentally observed, as shown in Figure 6. This phenomenon caused a decrease in contact area at the interface and an increased resistance to heat flow. To take into account the increasing gap between steel decking and concrete, the thermal resistance at the contact interface was modified using APDL programming. APDL is a scripting language that is used to perform operations and parametric design analyses. Convective heat transfer occurs through the air gap, whereas conductive heat transfer occurs through metal contact points. If radiation heat transfer is neglected, the conductive heat transfer between two contacting surfaces is defined in Equation (3).