## 6 Analytical Results and Discussion  
The specific modulus of the rope was predicted from the specific modulus of the strand in the axial direction and the braided angle of the strand using CLT. Because five cyclic loadings were conducted, five specific modulus and braided angles were needed to predict those moduli. The braided angles were selected as the beginning of each cyclic test. This means that at the first cycle input angle is the angle before testing, and input angle for second cycle is the angle at the end of the first cycle, and so on. These input parameters were substituted into Equations (5)-(9) and the results obtained are summarized in Table 5. The predicted longitudinal specific modulus (\(E\prime_{11}\)) of the unit cell has the smallest value at the first cycle due to the smallest modulus of the strand (\(E_{11}^{s}\)) and the largest braided angle (\(\theta\)). From the second cycle, the moduli remained at nearly constant values, exhibiting a change rate of only 5.21%, as the modulus and angles of the strands constituting the rope were almost stable. The predicted longitudinal specific modulus (\(E\prime_{11}\)) of the unit cell were compared with that of the rope obtained from the experiment. Table 6 shows the comparison results for the second to fifth cyclic tests. Moduli obtained from the prediction were larger than moduli of the rope measured via experimentation. This difference mainly has been caused by strand undulation in the rope; this was neglected in this study for simplicity, due to the complexity of the rope structure. However, it is important to note that both the predicted and experimentally-measured specific modulus remained nearly constant after the second loading cycle when the strand modulus and slope were not changing very much (Table 5). This result shows that the specific modulus and the slope of the strand are dominant to the modulus of the real rope, similar to our simplified model. With respect to the longitudinal modulus for the first cyclic test, as the relationship between specific stress and strain of the strand at the first cyclic test is linear (Figure 5), the strand modulus (\(E_{11}^{s}\)) is constant during the test. On the other hand, the relationship between the specific stress and strain of the rope at the first cyclic test (Figure 6) is nonlinear; this is considered to be influenced by the change in the angle of the strand (\(\theta\)) since the strand modulus is constant. As the angle of the strand changed with strain in a linear manner (Figure 7), a linear fit of the data was conducted. The result of the data fitting is shown in Figure 11. As a result, the braided angle-strain relationship is described using Equation (10):  
\[\theta=a*\epsilon_{11}+b \tag{10}\]  
where \(\theta\), \(\epsilon_{11}\), \(a\), and \(b\) are the angle, strain, and constant values, respectively. As mentioned above, strand modulus (\(E_{11}^{s}\)) is constant during the first cyclic test. When substituted into Equations (5)-(9), the specific modulus of the rope at every braiding angle in the first cyclic test (\(29.15^{\circ}\leq\theta\leq 22.90^{\circ}\)) (Table 5) can be obtained. The data shows that the specific modulus of the rope at the first cyclic test is linear with the braided angle in this limited range. This linear relationship between the specific modulus and braided angle can be expressed as follows:  
\[E_{11}=c_{1}*\theta+c_{2} \tag{11}\]  
where \(E_{11}\), \(\theta\), \(c_{1}\), \(c_{2}\) represent the longitudinal specific modulus, braided angle, and constant value, respectively. In this study, we used unit of N/tex for the modulus and stress and did not need to consider _PF_, which is a function of strain, in Equation (2). Thus, the relationship between specific stress and strain can be expressed as follows:  
\[\sigma_{11}=E_{11}*\epsilon_{11} \tag{12}\]  
where \(\sigma_{11}\), \(E_{11}\), \(\epsilon_{11}\) are the specific stress, specific modulus, and strain at the first cyclic loading of the rope, respectively.