# Effect of Wood Densification and GFRP Reinforcement on the Embedment Strength of Poplar CLT
## 2 Materials and Methods
### Embedment Strength Equations  
Currently, a number of distinct models of computation for CLT embedment strength are available. The most important calculation models are discussed in this part so that a comparison can be made between them. The [PERSON] (1974), [PERSON] (1975), [PERSON] (1976), [PERSON] (2007), and CSA (1977) equations were used in this study to predict the embedment strength of CLT. These equations were developed based on various factors, such as density, loading direction, and so on. [PERSON] et al. conducted a comprehensive study including about 720 embedment tests on Canadian cross-laminated timber (CLT) using lag screws, as well as 360 tests using self-drilling screws. The experiments included a range of screw sizes from 6.0 mm to 19.1 mm. A regression model that is not influenced by the panel layup and fastener diameter was constructed. According to [PERSON]'s model, the embedment strength is calculated as follows:  
\[f_{\theta,avg,Ken}=\frac{80(\rho_{12}-0.12)^{1.11}}{1.07(\rho_{12}-0.12)^{-0.07 }sin^{2}\theta+cos^{2}\theta} \tag{1}\]  
where \(f_{\theta,avg}\) is average embedment strength (MPa), \(\rho_{12}\) is density at 12% moisture content (g/cm\({}^{3}\)), and \(\theta\) is loading angle relative to the grain of face layer (\({}^{\circ}\)). Based on the NDS model, the strength of the face layer's embedment is linked to the \"effective\" bearing length of the fastener. This bearing length is changed proportionally based on the embedment strengths of both the transverse layer and the longitudinal layer. According to the NDS model, the embedment strength is calculated as follows:  
\[f_{\theta,avg,NDS}=\frac{\mathrm{t_{\parallel}}}{\mathrm{t_{\rho}}}.\frac{77G _{0}}{0.36G_{0}{}^{-0.45}d^{0.5}sin^{2}\theta+cos^{2}\theta}+\frac{\mathrm{t_ {\perp}}}{\mathrm{t_{\rho}}}.\frac{77G_{0}}{0.36G_{0}{}^{-0.45}d^{0.5}cos^{2} \theta+sin^{2}\theta} \tag{2}\]  
where \(G_{0}\) is measured relative density for the species or species group based on oven-dry mass and volume; \(\mathrm{t_{\parallel}}\) is the lag screw embedment length in parallel layer (s); \(\mathrm{t_{\perp}}\) is the lag screw embedment length in cross layer (s); \(\mathrm{t_{\rho}}\) is the embedment length of the lag screw in CLT specimen; and \(d\) is fastener diameter (mm). [PERSON] and [PERSON] conducted pioneering research on the lateral loading behavior of dowel-type fasteners in cross-laminated timber (CLT) panels. The researchers conducted experiments on smooth dowels ranging in diameter from 8 mm to 24 mm. These dowels were tested in both three- and five-layer cross-laminated timber (CLT) components. The dowels were strategically placed at gaps of one to three layers and subjected to loading at angles of 0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) with respect to the grain orientation of the face layer. The model is formulated as a mathematical expression that incorporates the variables of fastener diameter, overall wood density of the panel, and loading direction in relation to the strength axis of the panel, namely the grain direction of the surface layers of the cross-laminated timber (CLT) panel. According to [PERSON] and [PERSON]'s model, the embedment strength is calculated as follows:  
\[f_{\theta,avg,UB}=111.7(1-0.016d)\;\rho_{12}^{1.16}\times\left[\frac{\sum_{i=1}^{ n}t_{0,i}}{t\left(1.2 sin^{2}\theta+cos^{2}\theta\right)}+\frac{\sum_{j=1}^{n-1}t_{90, j}}{t\left(1.2 cos^{2}\theta+sin^{2}\theta\right)}\right] \tag{3}\]  
where \(t_{0,i}\) is the thickness of the CLT longitudinal layer \(i\), and \(t_{90,j}\) the thickness of the CLT transverse layer \(i\). According to [PERSON]'s model, the embedment strength is calculated as follows:  
\[f_{\theta,avg,Dong}=336.4(0.45-0.02d)\;\rho_{12}\times(\frac{R_{t}}{1.41 cos^{2 }\theta+sin^{2}\theta}+\frac{1-R_{t}}{1.41 sin^{2}\theta+cos^{2}\theta}) \tag{4}\]  
where \(R_{t}\) the ratio between the total thickness of the transverse layers and the CLT thickness.