## 4 Discussions
### Comparison to Existing Design Equations for Channel Anchors with Partial-Length Welding  
As mentioned above, it is not suitable to apply the existing design equations for fully-welded channel anchors to the design of partially-welded channel anchors. For this reason, as given in Equation (3), AC495 [27] provides the design equation for L-channel anchors welded to U-shaped cold-formed steel beams, which is similar to the equation of ANSI-AASC 360-16 [9].  
\[Q_{n}=\frac{0.6\times 100^{3/2}\Big{(}t_{f}+0.5t_{w}\Big{)}\sqrt{f^{\prime} {}_{c}E_{c}}}{\sqrt{L_{bw}}} \tag{3}\]  
where, \(L_{bw}\) = web-to-web clear distance of the U-shaped cold-formed steel beam.  
Meanwhile, [PERSON] et al. [4] also proposed a design equation for inversed L-channel anchors with partial-length welding based on their push-out tests and parametric study of finite element simulations.  
\[Q_{n}=2(A_{cai}+A_{ca2})\frac{F_{u}}{\sqrt{3}}+2\Big{(}19-38.1\frac{b_{ca}}{d _{\text{slab}}}\Big{)}A_{cbf}f^{\prime}{}_{c} \tag{4}\]  
where,\(A_{ca1}\), \(A_{ca2}\), \(A_{cb}\) = shear plane areas, and bearing area of channel anchors, respectively. Those definitions are illustrated in the literature [4], but approximately \(A_{ca1}=t_{w}L_{ca,w}\), \(A_{ca2}=t_{f}b_{ca}\), and \(A_{cb}=t_{f}L_{ca,w}\) were used in the present study. \(b_{ca}\) = width of channel anchor; \(L_{ca,w}\) = welded length of channel anchor measured at one end; and \(d_{\text{slab}}\) = depth of concrete slab.  
Figure 8: Comparison of Predictions to Tests: (**a**) Stud Anchors; (**b**) Fully-welded Channel Anchors (H-beams); (**c**) Partially-welded Channel Anchors (UH-beams).  
Those two equations were applied to the test results for comparison. It is noted that unlike the design equations in Table 4, in Equations (3) and (4), the contribution \(V_{nc}\) of concrete was taken into account implicitly. Thus, the design shear strength was calculated as \(V_{n}=\Sigma Q_{n}\). To compare over a wider range of design parameters such as the type of steel anchors, the other test results available in the literatures [4; 5; 6] were also included. Some of information that was not clearly specified in the literature was assumed based on the figures in the literature, and the test parameters are summarized in Appendix A.  
Figure 9 and Table 5 show the comparison. In overall, the equation of [PERSON] et al. [4] (\(m\pm\sigma\) of \(V_{\text{pred}}/V_{\text{test}}\) = 0.94 \(\pm\) 0.28) gave the better prediction on average, but it scattered wider compared to the equation of AC495 [27] (1.32 \(\pm\) 0.23): to be more specific, 1.07 \(\pm\) 0.11 for C-channel anchors, 1.42 \(\pm\) 0.09 for L-channel anchors, 1.34 \(\pm\) 0.24 for inversed L-channel anchors, and 1.19 \(\pm\) 0.24 for Z-channel anchors in the case of the equation of AC495 [27], while 0.87 \(\pm\) 0.02 for C-channel anchors, 0.52\(\pm\)0.04 for L-channel anchors, 1.01 \(\pm\) 0.26 for inversed L-channel anchors, and 1.06 \(\pm\) 0.14 for Z-channel anchors in the case of the equation of [PERSON] et al. [4]. The equation of [PERSON] et al. [4] was derived for inversed L-channel anchors having no top flange, but it showed relatively good agreement for all anchor shapes because the uplift of concrete slabs was prevented by hoop reinforcement in their study.  
Although the number of samples used in the comparison was limited, both equations were considered applicable to design, considering the fact that the design factors such as strength reduction factors and partial factors are used in actual design. For safer and more economic design, further experimental studies with various parameters are required.  
Figure 9: Comparison of Predictions to Tests: (**a**) C-channel Anchors; (**b**) L-channel Anchors; (**c**) Increased L-channel Anchors; (**d**) Z-channel Anchors.