## 2 Theoretical Strength of Plate-to-RHS Connections
### Connection Without Sififener  
The governing limit state of plate-to-RHS connections without stiffener is chord face plastification. According to AISC 360-10 and CIDECT Design Guide 3, the chord face plastification strength (\(N_{CP}\)) of plate-to-RHS T- or Y-connections can be computed as follows (see Figure 2a).  
For AISC 360-10 (T- or Y-connections),  
\[N_{CP}=\frac{F_{y}t^{2}}{1-t_{p}/b}\Bigg{[}\frac{2l_{p}}{b}+4\sqrt{1-\frac{t_{p }}{b}}\ Q_{f}\Bigg{]} \tag{1}\]  
For CIDECT Design Guide 3 (T- or Y-connections),  
\[N_{CP}=F_{y}t^{2}\Bigg{[}\frac{2l_{p}}{b}+4\sqrt{1-\frac{t_{p}}{b}}\Bigg{]}Q_{f} \tag{2}\]  
where \(F_{y}\) = steel yield strength of the chord member; \(b\) and \(t\) = wall width and thickness of the chord member; \(l_{p}\) and \(t_{p}\) = length and thickness of the longitudinal plate; and \(Q_{f}\) = chord member stress function. The \(Q_{f}\) functions depending on the type of truss connections are presented in Table 2. Note that the connection strength is expressed in terms of various symbols such as \(P\), \(N\), or \(V\) in Figures 2 and 3, depending on the force direction to be considered; \(P\) is the connection strength represented as the tensile or compressive force of the branch member, while \(N\) and \(V\) are the components of \(P\) decomposed in the transverse and longitudinal directions of the chord member, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline Design code & AISC 360-10 & CIDECT Design Guide 3 \\ \hline \multirow{4}{*}{Chord member} & Yield strength & \(F_{y}\leq\) 360 MPa & \(F_{y}\leq\) 460 MPa [3] \\ \cline{2-3}  & Yield ratio & \(F_{y}/F_{u}\leq\) 0.8 & \(F_{y}/F_{u}\leq\) 0.8 [4] \\ \cline{2-3}  & Width-to-thickness ratio & \(b/t\leq\) 40 [1] & b/t \(\leq\) 40 and \(b/t\leq\) 40 [5] \\ \cline{2-3}  & Height-to-width ratio & - & 0.5 \(\leq\) h/b \(\leq\) 2.0 \\ \hline \multirow{2}{*}{Longitudinal plate} & Yield strength & \(F_{yp}\leq Fu\) (\(t/t_{p}\)) [2] & \(F_{yp}\leq F_{y}\) \\ \cline{2-3}  & Length & - & 1 \(\leq\eta_{p}\) (=\(l_{p}/b\)) \(\leq\) 4 \\ \hline \end{tabular}  
* This is given in Table K1.2A in AISC 360-10. [2] This is given in Equation K1-3 in AISC 360-10 to prevent punching shear failure under plate shear load. [3] For 355 MPa \(\leq F_{y}\leq\) 460 MPa, joint strength shall be reduced to 90%. [4] For \(F_{y}\) /\(F_{u}>\) 0.8, \(F_{y}\) shall be taken as 0.8\(F_{u}\). [5] For compression, only class 1 and 2 sections are allowed.  
\end{table}
Table 1: Limits of applicability for plate-to-RHS truss connections.  
Figure 3: Longitudinal plate-to-RHS K-connection with bolted joint of chord members: (**a**) Longitudinal plate-to-RHS K-connection; (**b**) Failure modes in bolted joint of branch member.  
If the angle between the chord and branch members is \(\theta\) (\(\leq\)90\({}^{\circ}\)) in Y-connections, the connection strength \(P_{CP}\) in the branch axis can be computed by dividing \(N_{CP}\) by sin \(\theta\).  
\[P_{CP}=\frac{N_{CP}}{\sin\theta}\text{ for Y-connections} \tag{3}\]  
Equation (3) applies to the Y-connections where only one branch member is joined with the chord member. For K-connections where both tensile and compressive branch members are joined with the chord member (see Figure 3), the transverse components of the tensile and compressive branch forces cancel out each other, and thus, the connection strength \(V_{CP}\) in the longitudinal direction of the chord member is determined as follows.  
\[V_{CP}=\frac{2N_{CP}}{\tan\theta}\text{ for K-connections} \tag{4}\]  
According to the previous studies by [PERSON], [PERSON], etc. [5; 6; 7; 8; 9], the behavior of plate-to-RHS connections is governed by deformation-controlled action and the strength increases with increasing deformation. In this case, if the tensile and compressive branch members are not too close to be overlapped (or gap K-connection), it is possible to superpose the resistances of the tensile and compressive branch members that are independently determined.