## 6 Finite Element Analysis  
For the unstiffened and stiffened plate-to-RHS K-connections, N00-150 and S15-150, finite element modeling (FEM) was implemented using ABAQUS (Dassault Systemes Simulia Corp., Providence, RI, USA). [11]. As shown in Figure 9a,b, the stress-strain relationships of steel materials used for the branch and chord members were idealized as the bilinear or trilinear relationships based on the actual stress-strain curves obtained from the material tensile tests. The yield and ultimate strengths(\(F_{y}\) and \(F_{u}\)) in Table 4 were used (\(E_{s}\) = 200,000 MPa and Poisson's ratio = 0.3), and the Von Mises yield criterion was applied to address the behavior under multiaxial stresses. For the high-tension bolts, the trilinear \(\sigma\)-\(\varepsilon\) relationships were idealized based on the yield and tensile strengths, \(F_{y}\) = 0.9\(F_{u}\) and \(F_{u}\), respectively (see Figure 9c). To model the material nonlinearity of the steels and bolts under cyclic loading, isotropic and kinematic hardening rules (i.e., combined hardening rule) were used with the Von Mises yield criterion and associated flow rule. The kinematic hardening modulus and the rate at which hardening modulus decreases with plastic strain were assumed as \(C_{k}\) = 700 MPa and \(\gamma_{k}\) = 75, respectively. For the infilled concrete of the branch member (\(f_{c}\)\({}^{\prime}\) = 57.4 MPa), the damaged plasticity model was applied. Under compression, a parabolic-linear model under compression was used as shown in Figure 9d. The tensile behavior of the concrete before cracking was assumed as a linear elastic relationship (\(f_{ct}\) = 0.21 \(\sqrt{c}\)\({}^{\prime}\) = 1.59 MPa), and then, the following softening behavior was also simplified as linear. To simulate the inelastic behavior of the concrete under multiaxial stress, the Drucker-Prager plasticity model was applied. Figure 10 shows the ABAQUS modeling image. All steel and concrete components of the plate-to-RHS K-connection specimens were meshed by the C3D8R element, a general-purpose linear brick element with reduced integration. The RHSs and filled concrete of the chord and branch member were divided by setting mesh size 20 mm. To account for stress flow with accuracy, the longitudinal plate and gusset plate at the joint were finely divided by setting mesh size as 7.5 mm. For the high-strength bolts and weld joints, the smallest mesh size 5 mm was applied. The interface of the weld joints was set to \"tie\". On the other hand, \"interaction\" was applied to the steel-to-steel and steel-to-concrete contact surfaces to account for bearing under compression, friction under shear, and separation under tension. The friction coefficient was assumed as \(\mu\) = 0.25 for the steel-to-steel contact surface and \(\mu\) = 0.47 for the steel-to-concrete contact surface [12; 13]. As shown in Figure 10, the ball jigs that were used for lateral supporting of the top chord member were also included in the analysis model. Note that, for N00-150 where the location of lateral supporting was different, the ball jigs in the analysis model were placed near the longitudinal plate at the center so that the distance between two ball jigs was 1000 mm. Figure 9: Stress-strain relationships of steel, high-tension bolt, and filled concrete: (**a**) Steel plate (15 mm); (**b**) Rectangular hollow steel sections; (**c**) High-tension M24 bolt; (**d**) Infilled concrete. As the boundary condition, the base plates at the bottom were considered as fixed in all directions or degrees of freedom. The analysis was performed in two phases. In the first phase, the preload of the high-tension bolts (\(T_{o}\) = 204 kN) was applied. Then, cyclic lateral loads were applied to the loading surface of the chord member. The analysis was performed by controlling the lateral displacement of the branch member. Geometric nonlinear was applied. Note that the preload of the bolts was kept constant during cyclic lateral loading, which was implemented by the \"fixed at current length\" option in ABAQUS.