## 5 Strength Evaluation
### Comparison Between Theoretical and Test Strengths  
Figures 6-8 compare the test and theoretical strengths of the truss connections. The theoretical strengths \(V_{CP}\) (chord face plastification) and \(V_{slip}\) (connection slip) are represented as the horizontal solid and dotted lines. \(V_{SB}\) (post-slip ultimate strength, = 723 kN) is not included in the figures, as the strength value is over 700 kN. The behavior of the unstiffened and stiffened plate-to-RHS K-connections, such as governing limit states and related connection strengths, can be summarized as follows. Note that, since the truss connections did not develop their strength fully under positive loading due to torsional effects, the theoretical strengths were compared with the test strengths under negative loading only.  
1. In all specimens, the maximum loads \(V_{u}\) were greater than \(V_{slip}\) (=190 kN), which was the slip resistance of the bolted joint of the branch members. Thus, in the load-displacement curves in Figures 6-8, the stiffness degradation or slip behavior occurred roughly at the load levels of \(V=\pm 190\) kN. However, the post-slip ultimate strength \(V_{SB}\) (= 723 kN) was greater than the maximum loads. This explains why hole bearing failure did not occur at the bolted joint while threaded marks or dents were left on the inner face of the hole (see Figures 7b and 8b).
2. For N00-150, \(V_{CP}\) of AISC 360-10 and CIDECT Design Guide 3 (= \(-149\) kN and \(-132\) kN, respectively) was less than \(V_{slip}\) (=190 kN). This indicates that the behavior of the unstiffened plate-to-RHS K-connection was governed by chord face plastification. Basically, the chord face plastification was a ductile failure mode accompanying hardening behavior, as reported in the previous studies by [PERSON], [PERSON], and [PERSON] [6,7]. Thus, during negative loading, the strength significantly increased with increasing displacement. Consequently, the maximum load in the negative direction, \(V_{u}=-402\) kN, was much larger than \(V_{CP}\).
3. For S15-150 and S25-200 with the stiffened plate-to-RHS K-connections, the overall behavior was governed by chord face plastification after connection slip at the bolted joint of the branch members. Overall, both AISC 360-10 and CIDECT Design Guide 3 gave reasonable estimates on the chord face plastification strengths \(V_{CP}\) of the stiffened connections. AISC 360-10 overestimated the connection strength; the test-to-theoretical strength ratio was \(V_{u}/V_{CP}\) = 1.13 for S15-150 (= \(-593\) kN/\(-525\) kN) and 0.93 for S25-200 (= \(-602\) kN/\(-644\) kN). On the other hand, the CIDECT Design Guide 3 underestimated the connection strength; \(V_{u}/V_{CP}\) = \(-593\) kN/\(-394\) kN = 1.51 for S15-150 and \(V_{u}/V_{CP}\) = \(-602\) kN/\(-463\) kN = 1.30 for S25-200.  
As compared above, considering that the test strengths included over-strength effects due to post-yield hardening behavior, the CIDECT Design Guide 3 results in safe and conservative design for stiffened plate-to-RHS K-connections, whereas AISC 360-10 may result in less- or nonconservative design. When designing the plate-to-RHS connections stiffened by chord face stiffener, it is necessary to satisfy the limits of applicability presented in Table 1. Although some of the limits, such as yield strength (\(F_{y}\leq 360\) MPa), wall width-to-thickness ratio of the connecting chord face (\(b/t\leq 40\)), and plate length-to-chord width ratio (\(b/l_{p}\leq 4\)), etc. were violated, test data are not sufficient to investigate the effects of such variables on the connection behavior. Further study on the limits of applicability for RHS truss connections is required.