# Flexural Performance of Novel Nail-Cross-Laminated Timber Composite Panels
## 3 Experimental Results and Analysis
### Ultimate Bending Capacity
#### 3.4.2 Calculation for 5-Layer CLT Panels  
As shown in Figure 15: \(b=705\) mm, \(h_{1}=h_{2}=h_{3}=38\) mm, \(\overline{h_{1}}=\overline{h_{2}}=38\) mm, \(h_{tot}=190\) mm, \(L=2150\) mm, \(E=11,200\) MPa, \(f_{b}=11.8\) MPa, \(G_{R}=50\) MPa. In this case \(E_{1}=E_{2}=E_{3}\), \(A_{i}=b_{i}\)\(h_{i}\), \(I_{i}=\frac{b_{i}h_{i}^{3}}{12}\), \(\gamma_{2}=1\), \(\gamma_{1}=\frac{1}{1+\left(n^{2}\frac{E_{1}A_{1}}{I^{2}}\frac{\overline{h_{1} }}{G_{R}^{2}}\right)}\), \(\gamma_{3}=\frac{1}{1+\left(n^{2}\frac{E_{2}A_{2}}{I^{2}}\frac{\overline{h_{2} }}{G_{R}^{2}}\right)}\), \(a_{1}=\frac{h_{1}}{2}+\overline{h_{1}}+\frac{h_{2}}{2}-a_{2}\), \(a_{3}=\frac{h_{2}}{2}+\overline{h_{2}}+\frac{h_{3}}{2}+a_{2}\). Since, \(A_{1}=A_{2}=A_{3}=A\), \(a_{2}=0\), \(I_{1}=I_{2}=I_{3}=I\)  
Hence, \(A=b\times h=705\times 38=26,790\) mm\({}^{2}\), \(a=\frac{38}{2}+38+\frac{38}{2}=76\) mm  
\(\gamma_{1}=\gamma_{3}=\frac{1}{1+\frac{n^{2}\times 11200(705.38)}{2150^{2}}}=0.59\)  
\(\text{I}=\frac{bl^{3}}{12}=\frac{705\times 38^{38}}{12}=3.22\times 106\) mm\({}^{4}\)  
Hence, \(E_{Ieff}=\sum\limits_{i=1}^{3}\left(E_{i}l_{i}+\gamma_{i}E_{i}A_{i}a_{i}^{2} \right)=E\left[\left(l_{1}+\gamma_{1}A_{1}a_{1}^{2}\right)+l_{2}+\left(l_{3}+ \gamma_{3}A_{3}a_{3}^{2}\right)\right]=E\left(3+\frac{2\gamma A^{2}}{I} \right)=11,200\times 3.22\times 106\times\left(3+\frac{2\times 50.59\times 26790 \times 76^{2}}{3.22\times 106}\right)=2153\times 109\) N\(\cdot\)mm\({}^{2}\). \(I_{eff}=192.234\times 106\) mm\({}^{4}\)  
Hence, \(M_{r}=\varphi f_{b}\frac{I_{eff}}{(\gamma_{1}a_{1}+0.5 bl_{1})}=0.9\times 11.8 \times\frac{192\cdot 234\times 10^{6}}{0.59\times 76+0.55\times 38}\times 10^{-6}=31.98\) kN\(\cdot\)m  
Table 5 summarizes the ultimate bending moment of test specimens using the ultimate bearing capacity of each test specimen listed in Table 4. For the three-layer NCLT panels, the measured ultimate bending moment of specimen 4 was 15.41 kN\(\cdot\)m, slightly larger than the theoretical value \(Mr=15.11\) kN\(\cdot\)m. Due to the large size of the 5-layer NCLT panel, the probability of wood defects increased. Figure 14: Illustration of 3-layers CLT panels. Figure 15: Illustration of 5-layers CLT panels. In addition, cracks between plates caused by processing were also larger, and the NCLT panels were slightly warped. Therefore, the 5-layer NCLT panels test values were lower than the corresponding theoretical values, but the difference was within error range. It can be observed that the difference between theoretical and measured ultimate bending moment values of the three-layer panel bending moment were large, with error ranging between 15.26% and 46.90%. This indicates that the bending moment calculated according to the mechanical connection theory Formula (7) was larger compared to corresponding experimental values, and thus needs to be corrected. It can be observed from the test results that the nail connection scheme improved the bending capacity of NCLT panels. Hence, a nail connection influence coefficient \(\alpha\) as a mathematical adjustment was introduced in the bearing capacity formula to correct for the bending moment value of the limit state, as shown in Equation (9). The adjustments are shown in Table 6.  
\[M_{r}=\alpha\varphi f_{b}\frac{I_{eff}}{(\gamma_{1}a_{1}+0.5h_{1})} \tag{9}\]  
After this correction was implemented, the error was greatly reduced, and ratio between the average value of the measured bending moment and the corresponding theoretical bending moment was \(\overline{x}=1.006\). Based on this, the theoretical calculation formula of the mechanical connection was modified as:  
\[M_{r}=1.33\varphi f_{b}\frac{I_{eff}}{(\gamma_{1}a_{1}+0.5h_{1})} \tag{10}\]  
The European standard \"Eurocode 1\" [22] stipulates that the standard value of the live load of building floors for domestic and residential activities is 2 kN/m\({}^{2}\). The ultimate bearing capacity of NCLT panels made with screws, which is the smallest, was converted to its plane load value of 26.1 kN/m\({}^{2}\), which is 13 times the value required by the standard.