## 4 The Test Phenomena and the Result Analysis
### The Moment--Rotation Curve  
The vertical displacement of the beam was measured by the electronic displacement meters W3 and W4 as shown in Figure 10. The distance of the displacement meter away from the outer surface of the column was 710 mm. It was a symmetrical and synchronous loading, which was considered  
Figure 16: Load–displacement curve. to approximately represent the non-rotation of the columns. The measured results of displacement meters W5 and W6 also demonstrated that horizontal displacement basically did not occur to the column. The relative rotation \(\theta\) and the joint bending moment \(M\) are calculated as follows:  
\[\theta=\arctan\frac{\delta}{L} \tag{2a}\] \[M=PL \tag{2b}\]  
where \(\delta\) is the displacement of the measurement points W3 and W4, \(L\) is the distance between the displacement meter and the flange outer surface of the column, and \(P\) is the load at the beam end. The left sides of specimens S1 and S2 are chosen for analysis, and the bending moment-rotation curve is shown in Figure 17.  
Figure 17 shows that the bending moment-rotation curve slope of specimen S1 at the early stage is slightly smaller than that of S2; thus, the initial stiffness of specimen S1 is smaller than that of specimen S2. The yield bending moment of S1 is approximately 110 kN-m, and the corresponding yield rotation is approximately 0.0111 rad. S2 has a greater joint rigidity and its yield bending moment is approximately 140 kN-m, while the corresponding yield rotation is approximately 0.0125 rad. As the loading increases, the curve tends to become gentle and the joint rigidity is reduced until final failure occurs. When S1 is damaged, the ultimate bending moment is around 169 kN-m, while it is 209 kN-m for S2. When the size of diagonal stiffeners increases, the yield bending moment also increases by 27.3% and the ultimate bending moment increases by 23.7%. Thus, it may seem that the size of the diagonal stiffeners has a considerable impact on the performance of the joints. With analysis, it is found that this is mainly because the stiffeners also transmit the force from the beam to the column and take a share of the weld stress. The stress of the joint domain moves outward, and the stiffeners increase the integrity of the beam and the column, thus leading to increases in bearing capacity and stiffness. The ultimate rotation of S1 is 0.037 rad, while it is 0.047 rad for S2. The increase of the rotation of S2 may result from the buckling of the beam of S2, which provides the possibility for rotation, while a large deformation does not happen to the beam of S1. The limit rotation of both components is greater than 0.03 rad, which meets the requirement of the American FEMA that the limit rotation of joints should be no less than 0.03 rad. According to the joint stiffness classification method in Eurocode 3, the new connection stiffness classification can be determined. The span of the beam in the frame is set as 6 m. The calculation process is as follows:  
Region of rigid joints in braced frame:  
\[S_{j,mi}\geq 25 El_{b}/L_{b}=25\times 1.77\times 10^{8}\ \mathrm{kN/m^{2}} \times 1443\times 10^{-8}\ \mathrm{m^{4}}\div 6\ \mathrm{m}= \tag{3}\]  
Figure 17: Moment–rotation curve. Region of rigid joints in unbraced frame:  
\[S_{j,ini}\geq 8 EI_{b}/L_{b}=3405.48\;\mathrm{kN}\cdot\mathrm{m} \tag{4}\]  
Region of flexible joints:  
\[S_{j,ini}\leq 0.5 EI_{b}/L_{b}=212.8425\;\mathrm{kN}\cdot\mathrm{m} \tag{5}\]  
where \(S_{j,ini}\) is the slope in the moment-rotation curve, \(E\) is the elasticity modulus, \(I_{\mathrm{b}}\) is the inertial moment of the beam section, and \(L_{b}\) is the span of the beam. The other region is a semi-rigid joint. Since the connection has upper and bottom beams, the value of \(S_{j,ini}\) is twice as large. The partition results are shown in Figure 18. It can be seen that S1 and S2 are semi-rigid joints in the unbraced frame and are close to the rigid joints. Both S1 and S2 are rigid joints in the braced frame.