## 4 Experimental Results and Discussion  
Figure 4 shows the results of five cyclic loadings of the strand. In this work, the unloading is omitted when discussing longitudinal modulus because of the buckling effect. During the cyclic loading test, the length and diameter of both the strand and the rope changed after each loading cycle. The change in the length led to a change in the linear density (tex). Thus, we recalculated a new linear density of both the strand and rope before each cycle by dividing the weight with new length. This increases the accuracy of the data and allows for separating discussion of the effects of strand modulus and strand angle to the rope modulus. Figures 5 and 6 show the relationship between specific stress and strain of the strand and rope for the loading part of five cyclic tests. The longitudinal specific modulus (unit of N/tex) of the strand and rope in each cycle were calculated by fitting data. Figure 3: Effect of packing factor (\(PF\)) on the modulus of the rope. The specific modulus of the strand (cycles 1-5), and the rope (cycles 2-5) were determined using the data across the entire range of strain because the specific stress vs. strain graphs are almost perfectly linear. The specific modulus of the rope at the first cycle could not be determined since a non-linear relationship was observed between specific stress and strain. As mention in the previous section, three samples of rope and strand were conducted in the experiment and the average errors in longitudinal specific modulus from one sample to another are approximately 3% and 5% for strand and rope, respectively. Therefore, the results presented in this section are based on experimental data of the first test. The specific modulus of the strand and rope in each cycle are presented in Table 3; values in parentheses indicate the specific modulus when the change of linear density with respect to the cycle numbers is not taken into account. The specific modulus of the strand largely changed from the first to the second cycle which may have been caused by the molecular alignment. After the second cycle, the degree to which the specific modulus changed was lessened. A similar trend was observed for the rope after the second loading, as the modulus gradually changed with the number of cyclic loadings. Figure 4: Five cyclic loading of a strand at 20% MBL. Figure 5: Loading portion of the strand under five cyclic loadings. Figure 7 shows the measured braided angle and diameter of the rope at the first cycle. The angle and diameter decreased by approximately 7\({}^{\circ}\) and 0.23 mm, respectively, with strain. This result implies that the construction geometry of the rope changes significantly when the rope experiences the first cyclic loading. Figures 8 and 9 depict the change in angle and diameter of the rope, respectively, with strain, from the second to the fifth cycle. During these periods, both the angle and diameter of the rope changed less than during the first cycle and remained at near constant values. This means that the construction geometry of the rope does not change following the first cycle, with the same loading level, which probably resulted from the friction between fibers. These measured values are used to predict the specific modulus of the rope using CLT and to discuss the applicability of CLT when using the unit of N/tex. Table 4 shows the change in linear density (tex) and cross-sectional area of the rope during the test. The change in tex denotes the change in length of the rope due to deformation (elongation). When the rope is extended (from L\({}_{1}\) to L\({}_{2}\)) by deformation, the area of the rope is reduced (from A\({}_{1}\) to A\({}_{2}\)). When the change in voids is ignored and there is a constant volume deformation, the ratio of A\({}_{1}\) to A\({}_{2}\) (or MPa\({}_{1}\) to MPa\({}_{2}\)) becomes the same as L\({}_{1}\) to L\({}_{2}\) (or tex\({}_{1}\) to tex\({}_{2}\)).