## 4 Parametric Analysis  
The material properties used for parametric analysis are shown in Table 6. [PERSON] et al. [25] and [PERSON] et al. [21] reported the yield stress of 460 (HSB600) and 650 MPa (HSA800) steel. The yield stress of steel grades S900 and S1100 was studied by [PERSON] et al. [18]. The simplified bi-linear stress-strain curves were adopted, and true stress-strain curves were used as shown in Figure 6.  
The CHS XP-joint for parametric analysis was selected as the shape currently used for the HSS type of AISC [37]. HSS14 \(\times\) 0.625, 14 \(\times\) 0.5, 14 \(\times\) 0.375, and 14 \(\times\) 0.25 have a diameter of 14 inches (355.6 mm) and nominal thicknesses of 0.625 (15.875 mm), 0.5 (12.7 mm), 0.375 (9.525 mm), and 0.25 inches (6.35 mm), respectively. As shown in Table 7, the parameters are as follows: a nominal yield strength (\(F_{y}\)) of 460, 650, 900, and 1100 MPa, the chord diameter-to-thickness ratio (2\(\gamma\)), the longitudinal plate width-to-chord diameter ratio (\(\eta\)), and the utilization ratio (\(U\)). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Steel** & \(F_{y}\) **(MPa)** & \(E\) **(MPa)** & \(\sigma_{0.2}\) **(MPa)** & \(\sigma_{u}\) **(MPa)** & \(\varepsilon_{u}\) **(\%)** \\ \hline HSB600 & 460 & 205,000 & 486 & 606 & 10 \\ HSA800 & 650 & 205,000 1 & 798 & 914 & 4.2 1 \\ S900 & 900 & 210,000 & 1054 & 1116 & 2.26 \\ S1100 & 1100 & 207,000 & 1152 & 1317 & 2.20 \\ \hline \end{tabular} 1  
\end{table} 
Table 6: Material properties for parametric study. Figure 5: Chord length effect on the joint strength. Figure 6: True stress–strain curves for parametric analysis. The utilization ratio is the chord preload ratio, and axial force is applied to the chord in the parametric analysis. The 2\(\gamma\) of HSS14 \(\times\) 0.25 is 56.0, thus, it is out of the application range of the current design equations. This shape was, however, included for parametric analysis because it is currently manufactured and used in the field. The thickness of the longitudinal plate (\(t_{b}\)) was equal to the thickness of CHS (\(t\)). The weld size (s) was determined considering the minimum fillet weld size of American Welding Society (AWS) [38]. The configuration and plan of the parametric analysis model are shown in Figure 7.  
In order to determine the joint strength, design guides [3,4] are normally based on the ultimate limit state corresponding to the maximum load carrying capacity. This maximum load-carrying capacity is defined by the lower end of the ultimate joint strength and the load corresponding to an ultimate deformation limit. In contrast, AISC [2] adopts the strength limit state only, but suggests that designers should be aware of the potential for relatively large connection deformations in HSS joints. Figure 8 shows two methods for obtaining the joint strength in load-indentation curves: the ultimate deformation limit states and ultimate joint strength. In order to show the joint strength in the curves clearly, the normalization of the ordinate by dividing the yield strength and the square of the thickness is adopted. The out-of-plane deformation of the connecting CHS of 3% diameter (3%\(D\)) is generally used as the ultimate deformation limit [33]. This ultimate deformation limit restricts the joint deformation at a service load less than 1%\(D\). The ultimate deformation limit-to-service load ratio was assumed to be 1.5 or 1.67 [2]. The ultimate joint strength could be determined by selecting the