# Fire Performance of Self-Tapping Screws in Tall Mass-Timber Buildings
## 4 Design Proposal  
### Characterization of the Heat-Affected Layer  
Based on the results presented herein, the combination of the insulation effect of the timber and the favorable geometries of fastener shanks provided a lower heat transfer response for screw-type fasteners than bolt-type fasteners at elevated temperatures. The smaller heated behavior has limited thermal conduction along the cross-section area and maintained the temperature profiles relatively low along the STS shanks for long fire exposures. Although STS represent an encouraging alternative for connections in timber construction, the determination of their load capacity under fire conditions must consider the heat-affected layer, which is the temperature profile behind the char layer [12] that impacts the fastener's effective length of penetration. The design principles should rely on the residual length of penetration that will provide adequate strength such that the fasteners are within timber that properly retains its structural capacity. Several researches have provided guidelines to characterize the heat-affected layer [40; 41]. However, most of these studies were for the temperature profiles of timber sections tested for less than two hours, with the relationship proposed by [PERSON] [41] being the closest model predicting the temperature development in a glulam exposed to a heat flux from three sides [48]. [PERSON] [41] calculate the temperature profile in a wood member subject to the standard fire curve from one side using Equations (6) and (7). \[\Theta(x)=20+180\left(\frac{\beta t}{x}\right)^{\alpha} \tag{6}\]  
\[\alpha(t)=0.025t+1.75 \tag{7}\]  
where \(\Theta\) is the temperature in \({}^{\circ}\)C as a function of the depth x, \(\beta\) is the charring rate in mm/min, \(t\) is the time in min, and x is the depth measured from the surface of the cross-section in mm. Equations (6) and (7) were derived assuming a char line at the 200 \({}^{\circ}\)C isotherm and an ambient temperature of 20 \({}^{\circ}\)C. The design method in CSA O86-19 [8] followed a thermal model developed by Janssen & White [49], with assumptions of a charring rate of 0.70 mm/min for glulam, a char line at 300 \({}^{\circ}\)C isotherm, an ambient temperature of 20 \({}^{\circ}\)C and thermal penetration depth of 35 mm. Substituting these assumptions into Equation (6) results in the following Equation (8):  
\[\Theta(x)=20+280\left(1-\frac{x}{35}\right)^{2} \tag{8}\]  
where \(\Theta\) is the temperature in \({}^{\circ}\)C as a function of the depth x, and x is the depth measured from the surface of the cross-section in mm. Considering the average char rating of 0.58 mm/min obtained from the small-scale fire tests of the STS with the head exposed to the constant heat flux for one hour, the temperature profiles using Equations (6)-(8) (with \(\beta\) = 0.58 mm/min and t = 60 min) can be calculated and compared to the measured temperatures at mid-length (45 mm) and at the tip (125 mm) of the tested STS with the head exposed. A depth of 35 mm from the char layer is deducted from the initial positions (e.g., 160-35 = 125 mm), as shown in Figure 13. As expected, the measurement STS temperatures are much higher than the timber temperature profiles predicted by Equations (6)-(8), namely, due to the high conductivity of the fastener shank and the effect of a longer exposure. Both calculated temperature profiles are applicable to the timber alone and did not include a fastener being inserted into it. Indeed, the heating rate through the steel element increases the temperature profiles along their shanks while the glulam inside would remain at ambient temperatures without fastener inserted, as demonstrated by [PERSON] et al. [47]. Additionally, Equation (8) implied in CSA O86-19 [8] does not include the effect of the fire duration on the thermal penetration depth, which is the distance from the char line to the part of wood that is still at an ambient temperature.