# Thermomechanical Analysis of Steel-to-Timber Connections under Fire and the Material Density Effect
## 2 Materials and Methods
### Material Properties and Fire Curve  
As described in our previous work [17], the material properties are defined according to the standards. For mechanical and structural analysis, the material properties involved in the study are the mechanical properties of wood and steel material (with elastic and plastic behavior) and the thermal properties of both materials (conductivity, specific heat density, and emissivity). For the wooden members, three different species of glued laminate were considered: GL20H, GL24H, and GL32H [5; 6; 7; 18]. The wood stiffness and strength properties vary as a function of the orientation between longitudinal, tangential, and radial directions. Stiffness and strength are greatest in the longitudinal direction. For this reason, only the properties parallel-to-grain were considered according to the direction the applied tensile load. The mechanical properties of the glued laminated wood chosen for use in this study, at approximately 12% moisture content, have a Poisson ratio value equal to 0.4 and a coefficient of thermal expansion equal to 4 \(\times\) 10\({}^{-6}\)/K in all species considered. In tests of both hardwoods and softwoods, the parallel-to-grain values ranging from 0.000031 to 0.0000045 per \({}^{\circ}\)K were considered [18; 19; 20]. The other mechanical properties can vary significantly among the glued laminated species. For GL20H, the yield strength parallel-to-grain is equal to 16 MPa, the Young's modulus is equal to 8.4 GPa, and the density is equal to 370 kg/m\({}^{3}\). For GL24H, the yield strength parallel-to-grain is equal to 19.2 MPa, the Young's modulus is equal to 11.5 GPa, and the density is equal to 420 kg/m\({}^{3}\). For GL32H, the yield strength parallel-to-grain is equal to 25.6 MPa, the Young's modulus is equal to 14.2 GPa, and the density is equal to 480 kg/m\({}^{3}\). For the connectors and plate elements, steel material S275 was considered, according to the Eurocode 3 part 1-1 [21], where the yield strength is equal to 275 MPa, the ultimate tensile strength is equal 430 MPa, the Young's modulus is 210 GPa, the Poisson's ratio is 0.3, the density is equal to 7850 kg/m\({}^{3}\), and the coefficient of thermal expansion was considered constant equal to 12 \(\times\) 10\({}^{-6}\)/K. The stress-strain curves for the steel and wood material at elevated temperatures are defined as multilinear with isotropic hardening plasticity (see Figures 2-5). Figure 2: Strain–stress of steel at different temperatures. Figure 4: Strain–stress of GL24H wood at elevated temperatures. Figure 5: Strain–stress of GL32H wood at elevated temperatures. Figure 3: Strain–stress of GL20H wood at different temperatures. The fire starts with a transient thermal analysis, resulting in the thermal response of the connection during the fire exposure. The nominal temperature-time standard curve ISO 834 is the one that has been used in fire tests to rate structural and separating elements [12], which is described by Equation (1) and shown in Figure 6.  
\[\theta_{\infty}=20+345\log_{10}(8t+1) \tag{1}\]  
where \(t\) is the time in min and \(\theta_{\infty}\) is the gas temperature in the fire compartment expressed in \({}^{\circ}\)C.  
The initial temperature in the steel-to-timber connection was considered equal to 20 \({}^{\circ}\)C. The external surface of the connection is exposed to the standard fire curve ISO 834 and the convection coefficient is 25 W/m\({}^{2}\)K [13]. The emissivity of the flames is considered constant and equal to 1 [13]. For thermal analysis, heat transfer is governed by material density, thermal conductivity, and specific heat. The wood properties are temperature dependent, being defined by Eurocode 5, part 1-2 [14] and presented in Figures 7-9. The emissivity is also defined as equal to 0.8, Eurocode 5, part 1-2 [14]. Figure 6: Nominal temperature–time curve ISO 834. Figure 7: Density of wood.