## 4 Results
### Rotational Stiffness of Connections  
Scaffolding design typically focuses on providing adequate structural integrity, stability, and load-carrying capacity while adhering to recognized industry standards, codes, and regulations. In the case of general scaffolding design, there is no need to consider the yield deformation capacity of connections where the connections are assumed to be hinges. However, in the case of investigating the accurate ultimate behavior of the scaffolding and identifying vulnerable components under various loads, it is necessary to consider the plastic deformation capacity of connections. The moment-rotation curves of the pocket-type connections do not show any initial rotation angle looseness [13] owing to the shape of the connections and the method of tightening by hammering the members, etc. Therefore, in this study, the rotational stiffness models for the pocket-type connections were assumed to have a bilinear form similar to the actual moment-rotation curves. Figure 14 defines the rotational stiffness values (\(k_{1}\), \(k_{2}\)) and reference rotation angles (\(\beta_{1}\), \(\beta_{2}\)) that are parameters of the assumed bilinear rotational stiffness model. If the simple mean of the \(\beta_{1}\) values of each specimen's bilinear rotational stiffness model are used as the mean value of \(\beta_{1}\), which is the reference for changing rotational stiffness, the continuity of each rotational stiffness cannot be guaranteed. Therefore, as shown in Equation (4), the mean of \(\beta_{1}\) was calculated as a weighted mean using the initial rotational stiffness (\(k_{1}\)) as a weight value. \[\left(\beta_{1}\right)_{Mean}=\frac{\sum\left(k_{1}\right)_{n}\times\left( \beta_{1}\right)_{n}}{\sum\left(k_{1}\right)_{n}} \tag{4}\]  
Figure 14: Bilinear rotational stiffness model. Figure 15 and Table 5 show the major parameters of the bilinear rotational stiffness model for each rotation direction of the pocket-type connections, which were derived from the results of experiments in this study and the authors' previous study [17]. Research has been conducted on the reliability analysis of scaffolding structures [20; 21; 22]. In order to provide statistical characteristics of random variables for the rotation stiffness that can be used in the reliability analysis of scaffolding structures, the derived bilinear rotational stiffness model for pocket-type connections also includes the rotational stiffness' (\(k_{1},k_{2}\)) coefficient of variation and 5 th and 95 th percentiles, along with the mean values of the parameters. In the rotational stiffness model of the downwardly rotated connections, the mean of the initial rotational stiffness (\(k_{1}\), rotation range: 0.000-0.025 rad) was 28.378 kNm/rad, and the mean of the post-yield rotational stiffness (second rotational stiffness, \(k_{2}\), rotation range: 0.025-0.196 rad) was 1.450 kNm/rad. In the rotational stiffness model of the upwardly rotated connections, the mean of the initial rotational stiffness (\(k_{1}\), rotation range: 0.000-0.035 rad) was 47.138 kNm/rad, and the mean of the second rotational stiffness (\(k_{2}\), rotation range: 0.035-0.169 rad) was 2.461 kNm/rad. In the rotational stiffness model of the laterally rotated connections, the mean of the initial rotational stiffness (\(k_{1}\), rotation range: 0.000-0.073 rad) was 3.144 kNm/rad, and the mean of the second rotational stiffness (\(k_{2}\), rotation range: 0.073-0.197 rad) was 0.577 kNm/rad. However, the coefficient of variation of the initial rotational stiffness of the laterally rotated connections was very large compared to the other rotational stiffness values, indicating some uncertainty. However, it can be considered a nominally pin connection when performing analyses according to Eurocode 3 [19].