## 4 Parametric Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Specimen (\(F_{y}\)-2)-\(\eta\)-\(U\) 1** & **2\(\gamma\) (D/t)** & **\(\eta\)** & **\(D\) (mm)** & \(t\)**, (s) (mm)** & \(l_{b}\) (mm)** \\ \hline
1 & \(F_{y}\)-22.4-1-\(U\) & & 1 & & & 355.6 \\
2 & \(F_{y}\)-22.4-2-\(U\) & & 2 & & & 711.2 \\
3 & \(F_{y}\)-22.4-3-\(U\) & & 3 & & & 1066.8 \\
4 & \(F_{y}\)-22.4-4-\(U\) & & 4 & & & 1422.4 \\
5 & \(F_{y}\)-28.0-1-\(U\) & & 1 & & & 355.6 \\
6 & \(F_{y}\)-28.0-2-\(U\) & & 2 & & & 711.2 \\
7 & \(F_{y}\)-28.0-3-\(U\) & & 3 & & & 1066.8 \\
8 & \(F_{y}\)-28.0-4-\(U\) & & 4 & & & 1422.4 \\
9 & \(F_{y}\)-37.3-1-\(U\) & & 1 & & & 355.6 \\
10 & \(F_{y}\)-37.3-2-\(U\) & & 2 & & & 711.2 \\
11 & \(F_{y}\)-37.3-3-\(U\) & & 3 & & & 1066.8 \\
12 & \(F_{y}\)-37.3-4-\(U\) & & 4 & & & 1422.4 \\
13 & \(F_{y}\)-56.0-1-\(U\) & & 1 & & & 355.6 \\
14 & \(F_{y}\)-56.0-2-\(U\) & & 56.0 & 2 & & 711.2 \\
15 & \(F_{y}\)-56.0-3-\(U\) & & 3 & & & 1066.8 \\
16 & \(F_{y}\)-56.0-4-\(U\) & & 4 & & & 1422.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters for CHS XP-joints made of HSB600, HSA800, S900, and S1100 steel. Figure 7: Parametric analysis plan of CHS XP-joints. maximum load in the load-indentation curve. [PERSON] and [PERSON] (2019), however, described three type of load-deformation relationships: (1) a curve in which the maximum load is clearly indicated by the decrease of the load after the maximum load; (2) a curve in which, after the first peak load, the load decreases and increases again; and (3) a curve in which the maximum load does not appear but continues to rise. The first and second types of the curves can determine the ultimate joint strength by selecting the maximum load or first peak load (F.P., see Figure 8), but the last type of curve does not facilitate determining the joint strength. [PERSON] et al. (2019) estimated the maximum strength of the CHS joints using the plastic-to-elastic work energy ratio when the maximum load did not appear in the curve. This plastic workload (P.W., see Figure 8) was defined by adopting the plastic-to-elastic work ratio of 3.0. Figure 9 and Table 8 show the results of HSB600 steel. The ultimate and serviceability deformation limits (3%\(D\) and 1%\(D\)) and the maximum strength determined by the first peak load or plastic workload are shown in Figure 9. In the deformation limit state, the ultimate deformation limit strengths (\(R_{3\%D}\)) are lower than 1.67 times the serviceability deformation limit strengths (\(R_{1\%D}\)) in models 2-4, but the other models are higher. As the 2\(\gamma\) increases, this ratio increases. The maximum strength (\(R_{max}\)) determined by strength limit state is entirely higher than \(R_{3\%D}\), but this difference is not significant in models 1-4. In these cases, \(R_{3\%D}\) could represent the joint strength of CHS XP-joints. Figure 8: Definition of the deformation limit and maximum load. Figure 9: Load–indentation curves of HSB600 (\(F_{y}\) = 460 MPa): (a) 2\(\gamma\) of 22.4 and 37.3; (b) 2\(\gamma\) of 28.0 and 56.0. Figure 11: Load–indentation curves of S900 (\(F_{y}\) = 900 MPa): (**a**) 2\(\gamma\) of 22.4 and 37.3; (**b**) 2\(\gamma\) of 28.0 and 56.0.