## 5 Comparison of Design Equations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Specimen** & \multirow{2}{*}{\(R_{1\times D}\) (kN)} & \multirow{2}{*}{\(R_{3\times D}\) (kN)} & \multirow{2}{*}{\(R_{3\times D}\)/\(R_{1\times D}\)} & \multirow{2}{*}{\(R_{max}\) (kN)} & \multirow{2}{*}{\(R_{max}\)/\(R_{3\times D}\)} & **Det.** \\  & **(\(F_{y}\)-2)-\(\eta\)-\(U\)** & & & & & & \\ \hline
1 & 1100-22.4-1-00 & 626.0 & 1569.5 & 2.51 & 2146.6 & (8.5) & 1.37 & F.P. \\
2 & 1100-22.4-2-00 & 870.1 & 2185.7 & 2.51 & 2901.0 & (9.1) & 1.33 & F.P. \\
3 & 1100-22.4-3-00 & 1125.1 & 2824.8 & 2.51 & 3676.7 & (8.9) & 1.30 & F.P. \\
4 & 1100-22.4-4-00 & 1383.0 & 3479.9 & 2.52 & 4477.4 & (8.5) & 1.29 & F.P. \\
5 & 1100-28.0-1-00 & 349.5 & 912.3 & 2.61 & 1324.8 & (9.5) & 1.45 & F.P. \\
6 & 1100-28.0-2-00 & 467.3 & 1228.2 & 2.63 & 1791.3 & (10.8) & 1.46 & F.P. \\
7 & 1100-28.0-3-00 & 594.2 & 1566.8 & 2.64 & 2256.0 & (10.4) & 1.44 & F.P. \\
8 & 1100-28.0-4-00 & 723.2 & 1911.1 & 2.64 & 2736.8 & (9.8) & 1.43 & F.P. \\
9 & 1100-37.3-1-00 & 167.3 & 449.5 & 2.69 & 697.5 & (10.6) & 1.55 & F.P. \\
10 & 1100-37.3-2-00 & 213.0 & 578.1 & 2.71 & 958.7 & (11.8) & 1.66 & P.W. \\
11 & 1100-37.3-3-00 & 264.0 & 720.4 & 2.73 & 1203.5 & (11.8) & 1.67 & P.W. \\
12 & 1100-37.3-4-00 & 316.8 & 869.7 & 2.75 & 1455.6 & (12.2) & 1.67 & P.W. \\
13 & 1100-56.0-1-00 & 64.1 & 174.0 & 2.72 & 286.5 & (11.6) & 1.65 & P.W. \\
14 & 1100-56.0-2-00 & 75.7 & 208.7 & 2.76 & 412.7 & (14.7) & 1.98 & P.W. \\
15 & 1100-56.0-3-00 & 89.7 & 247.7 & 2.76 & 527.1 & (15.8) & 2.13 & P.W. \\
16 & 1100-56.0-4-00 & 105.0 & 290.9 & 2.77 & 639.2 & (16.3) & 2.20 & P.W. \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Parametric analysis results of S900 (\(F_{y}=900\) MPa). Table 12 shows the comparison of the design equations [2; 3; 4], with the ultimate deformation limit load divided by the yield strength and square of the chord thickness. The design equations show only the value related to \(\eta\) independently of the yield strength, but the \(R_{3\%D}\) gradually decreases as the yield strength increases. This is because the \(R_{3\%D}\) determined by the ultimate deformation limit is moved to the elastic region as the yield strength increases and is determined to be lower than the \(R_{max}\). This is remarkable in the results of S900 and S1100 steel. The \(R_{3\%D}\) of those (see Tables 10 and 11) is almost the same, thus, the normalized \(R_{3\%D}\) gradually decreases. The mean values of the design strength of the AISC [2] to \(R_{3\%D}\) ratio and the coefficient of variation (CoV) are 0.79 and 0.101 at yield stresses of 460 MPa, 0.88 and 0.168 at 650 MPa, 1.10 and 0.206 at 900 MPa, and 1.32 and 0.223 at 1100 MPa, respectively. Figure 13 shows the ratio of the design equations to the \(R_{3\%D}\) and \(R_{max}\) according to the nominal yield stress. In AISC [2], the nominal yield strength is limited to 360 MPa, which is the reason that the design joint strength is overestimated in high-strength steels. In Eurocode 3 [3] and ISO 14346 [4], the design equations would be estimated properly until nominal yield strength limitations of 700 MPa and 460 MPa, respectively. As the nominal yield strength and \(2\gamma\) value increase, the design equations are overestimated. However, the ratio of the current design equations to \(R_{max}\) is less than 1.0 and the CoV is not large, as shown in Figure 13.  
Figure 14 shows the strength reduction effect according to the utilization ratio (\(U\)). As shown in Table 1, AISC [2] and Eurocode 3 [3] apply the same relational expression considering the reduction effect when compressive force is applied, and there is no reduction effect when tensile force is applied to CHS. ISO 14364 [4], on the other hand, considers the reduction effects in both compressive and tensile conditions. Figure 14a,b and Figure 14c,d show the chord stress function (\(Q_{f}\)) using \(R_{3\%D}\) and \(R_{max}\), respectively. Compared with the design equations in compressive force acting on the chord, the tendency of the design equation is slightly conservative.