# Fire Performance of Self-Tapping Screws in Tall Mass-Timber Buildings
## 2 Materials and Methods
### Methodology
#### 2.3.3 Numerical Modelling  
In an attempt to validate the obtained test data, namely, the heat transfer within the glulam specimen and along the fasteners, as well as to predict the heat transfer when exposed to the standard temperature-time curve CAN/ULC S101 [6], a three-dimensional transient heat transfer model using the finite element method (FEM) was developed in  
Figure 4: Vertical load test: (**a**) Experimental setup; (**b**) STS connections with full-length penetration.  
ANSYS software. The heat transfer to the surface of the gulam was calculated using the values stipulated in EN 1991-1-2 [31] for the resultant emissivity of the fire by radiation \(\varepsilon_{\mathrm{f}}=0.8\) and the coefficient of heat transfer by convection \(\alpha_{\mathrm{c}}=25\) W/m\({}^{2}\)-K at the exposed surface. The convective heat flux coefficient at the unexposed face is taken as 9 W/m\({}^{2}\)-K for considering the convective and radiative losses [31]. As indicated in Clause B2 of EN1995-1-2 [10], thermal properties should be used only for a standard temperature-time curve, unless validated otherwise. As such, the thermal properties used for small-scales fire tests were taken from Konig & Walleij [32] with an initial density of 480 kg/m\({}^{3}\) and an initial moisture content of 12%. Otherwise, an initial density of 470 kg/m\({}^{3}\) and an initial moisture content of 12% were considered as specified for the standard condition of spruce-pine gulam in accordance with CSA O86-19 [8]. The mass transfer of moisture into or out of the wood was neglected given the thermal properties from EN1995-1-2 [10] and Konig and Walleij [32] are calibrated accordingly. For steel, the thermal properties are relatively well-known and are given by EN1993-1-2 [33]. Figure 5 presented the thermal properties used as a function of the materials' density, thermal conductivity, and heat capacity.  
During the small-scale fire experiments, the top surface of the gulam specimen and the head of the fastener were subjected to a constant heat flux of 50 kW/m\({}^{2}\), which corresponds approximately to the same incident heat flux after 10 min of the standard temperature-time curve [34]. Once the thermal response model was verified and validated, a second thermal model was made using the standard temperature-time curve CAN/ULC S101 [6]. Figure 6 shows the temperature-time curves used in the FEM modeling for the standardized fire standard CAN/ULC S101 [6] and the temperature-time curve replicating a constant heat flux of 50 kW/m\({}^{2}\). Due to the symmetry of the middle part of the fastener and in an attempt to reduce the computational time, the transient thermal model is performed for one quarter of the specimen and from modeling a cylindrical shank only (i.e., no threads), as  
Figure 5: Thermal proprieties of wood used for the heat transfer model: (**a**) Temperature–density relationship based on gulam specimen; (**b**) Temperature–thermal conductivity relationship for wood; (**c**) Temperature–specific heat relationship for wood. Solid line for thermal properties under a standard fire curve and dashed line for thermal properties under a constant heat flux [10;32].  
shown in Figure 6. [PERSON] [35] reported that neglecting the threaded portion of the shank reduced the computational time due to the greater quantity of hexahedrons and did not significantly affect the heat transfer responses of the model. According to [PERSON] [35] and [PERSON] et al. [36], the three-dimensional temperature fields were divided into elements with a length of 3 mm using three-dimensional hexahedral elements (see Figure 6).