## 4 Results
### Moment-Rotation Curve  
To find the moment-rotation curves of the pocket connections, moment (\(M\)) was calculated using Equation (1). The rotation angles (\(\theta\), rad) of the downwardly rotated specimens and the upwardly rotated specimens were calculated from Equation (2), and the rotation angles of the laterally rotated specimens were calculated using Equation (3). To avoid reflecting the error that occurs owing to the bending of the horizontal member when calculating the connections' rotation angles, the actuator's displacement data were not considered in the calculations. Diagrams of each symbol are shown in Figure 12.  
\[M=P\times L \tag{1}\]  
\[\theta=\tan^{-1}\left(\frac{d_{h,\,1}-d_{h,\,2}}{l_{h,\,1}-l_{h,\,2}}\right)- \tan^{-1}\left(\frac{d_{v,\,1}-d_{v,\,2}}{l_{v,\,1}+l_{v,\,2}}\right) \tag{2}\]  
\[\theta=\tan^{-1}\left(\frac{d_{h,\,1}-d_{h,\,2}}{l_{h,\,1}-l_{h,\,2}}\right)- \tan^{-1}\left(\frac{d_{v,\,1}}{l_{v,\,1}}\right) \tag{3}\]  
where \(P\) is the load; \(L\) is the distance from the vertical steel pipe's central axis to the load point; \(d_{h,\,1}\), \(d_{h,\,2}\), \(d_{v,\,1}\), \(d_{v,\,2}\) are the displacement measurements from each displacement gauge; and \(l_{h,\,1}\), \(l_{h,\,2}\), \(l_{v,\,1}\), \(l_{v,\,2}\) are the distances from the steel pipe's central axis to each displacement gauge. Figure 13 shows the moment-rotation relationships calculated for all specimens, and Table 4 shows the means and standard deviations of the maximum moment for each connection rotation direction. In the literature, connections are classified as rigid, semi-rigid, and nominally pin according to their rotational stiffness. These classifications correspond to the three regions divided by the dotted lines in the moment-rotation curve graph in Figure 13. The dotted lines are defined according to Eurocode 3 [19]. The specimens' moment-rotation curves each show differences according to the rotation direction. The specimens that showed the maximum moment were the upwardly rotated specimens, and  
Figure 12: Symbol designation for rotation calculation: (**a**) downward and upward rotation; (**b**) lateral rotation. the mean was 1.942 kNm. In the case of upward rotation, the moment-rotation curves rapidly decreased after the maximum moment occurred (approximately 0.19-0.27 rad). It seems that the rotational stiffness, which corresponds to the slope of the moment-rotation curve, rapidly decreased at around 0.03 rad before the maximum moment occurred. The rotation angle of 0.03 rad indicates the time at which denting occurred in the vertical steel pipe, and the vertical steel pipe significantly affected the rotational stiffness of the upwardly rotated connection. There was no noticeable deformation of the pocket during the loading of upward rotation. When the contact section of the vertical steel pipe with the end of the horizontal steel pipe yielded, the moment-rotation curve showed the yielding. The maximum capacity was derived from the ultimate capacity of vertical steel pipe in local bending. On the other hand, in downward rotation, which resists rotation relying on the low strength of pins and pockets without interference in the vertical pipe, the rotational stiffness decreased at small angles (about 0.01 rad) compared to upward rotation, and gradual deformation occurred in the upper part of the pocket after about 0.01 rad. When the top part of the pocket in contact with the pin started to yield, the moment-rotation curves showed the yielding state. As the load increased, the moment gradually increased, affecting the pocket capacity, and the mean maximum load was 0.934 kN. The lateral rotation case showed the smallest moment capacity with a mean moment of 0.321 kNm, and it had a moment-rotation curve that was gradual overall. The rotation angle in the yield state was the biggest among the specimens. In the rotation range of about 0.05 rad to 0.10 rad, the pocket that maintained a rectangular cross-section was changed to a parallelogram due to the yield of the pocket bend.