## 4 Design of CFS Screw Connection with Gypsum Sheathing  
### Shear Strength Design  
Based on the all-steel design method of CFS wall studs in AISI S100-2012 [1], the bearing capacity of a wall stud with small slenderness can be determined by the shear strength of the screw connection with sheathing. In addition, the degeneration of the lateral performance of a CFS wall is usually caused by the shear failure of screw connections [15; 16]. The current AISI design manual [25] gives the maximum nominal load per screw connection with gypsum sheathing at ambient temperature. However, the effects of the loaded sheathing edge, double-layer sheathing and elevated temperatures were not yet considered. Therefore, for CFS walls with double-layer gypsum sheathing or increased loaded edge distance, both the axial and lateral design could be overly conservative. This paper recommends including the favorable effects of the loaded sheathing edge and double-layer sheathing on the shear behavior of the screw connection at ambient and elevated temperatures based on reliable construction. A unified prediction formula for \(F_{\mathrm{mT}}\) was proposed by non-linear regression, as shown in Equation (1), where \(d\) represents the loaded edge distance; \(\alpha\) is the coefficient that considers the effect of double-layer gypsum sheathing at ambient temperature, as shown in Equations (2) and (3); and \(R_{\mathrm{mT}}\) is the reduction factor of shear strength, defined as the ratio of the shear strength at elevated temperatures to that at ambient temperature. \(R_{\mathrm{mT}}\) is developed by the multi-segment polynomials, as shown in Equation (4). The values of the coefficients in Equation (4) are given in Table 3. Based on the previous thermal physical experiments of fire-resistant gypsum plasterboard at elevated temperatures [21], the dehydration of gypsum plasterboard (CaSO4-2H2O) occurred from approximately 85 \({}^{\circ}\)C to 160 \({}^{\circ}\)C. Therefore, \(R_{\mathrm{mT}}\) is assumed to be 1.0 for temperatures below 80 \({}^{\circ}\)C in Table 3. The \(R_{\mathrm{mT}}\) predicted by Equation (4) is in good agreement with the values obtained from the present experiments, as shown in Figure 13.  
\[F_{mT}=316e^{0.04d}\cdot\alpha\cdot R_{mT},\quad 10\leq d\leq 20\;\mathrm{mm} \tag{1}\]  
where the units of \(F_{\mathrm{mT}}\) are \(N\). For single-layer gypsum sheathing,  
\[\alpha=1.0 \tag{2}\]  
For double-layer gypsum sheathing,  
\[\alpha=0.0028d^{2}-0.085d+1.98,\quad 10\leq d\leq 20\;\mathrm{mm} \tag{3}\]  
\[R_{mT}=aT^{2}+bT+c \tag{4}\]  
where \(a\), \(b\) and \(c\) are the coefficients of Equation (4). Figure 14 compares the values of \(F_{\mathrm{mT}}\) predicted by Equation (1) to those obtained from the present 200 experiments. The average ratio of the predicted \(F_{\mathrm{mT}}\) to the experimental results is 98.8%, and the Pearson product-moment correlation coefficient is 0.995. Thus, Equation (1) is able to accurately evaluate the shear strength of the screw connection with single- or double-layer gypsum sheathing and different edge distances at ambient and elevated temperatures. In structural engineering design, if the loaded edge distance exceeds 20 mm, Equation (1) can still be used with the loaded edge distance of 20 mm to obtain a conservative prediction of the shear strength of the screw connection, and a factor of safety [25] can be applied to the maximum allowable axial strength of the screw connection, as shown in Equation (5). \[F_{aT}=F_{mT}/\Omega \tag{5}\]  
where \(F_{aT}\) is the maximum allowable axial strength of the screw connection with sheathing and \(\Omega\) is the factor of safety for the screw connection [25]. Figure 14: Predicted shear strength compared to experimental results. Figure 13: Comparison of \(R_{\text{mT}}\) obtained from Equation (4) and experimental results: (**a**) single-layer gypsum; and (**b**) double-layer gypsum sheathing.