## 4 Discussions
### Existing Design Equations for Stud Anchors and Fully-Welded Channel Anchors
As shown in Figure 8a, for stud anchors, the current design codes provided quite good predictions (the ratio \(V_{\text{pred}}/V_{\text{test}}=V_{n}/V_{m}\) of prediction-to-test was close to 1 for all codes). On the other hand, as shown in Figure 8b,c for channel anchors, \(V_{\text{pred}}/V_{\text{test}}\) was scattered widely, but unexpectedly, each equation \begin{table}
\begin{tabular}{c l} \hline \hline
**Design Code or Authors** & **Design Equation, \(Q_{n}\) [N] 1** \\ ANSI/A3C 360-16 ([PERSON] et al., 2016) & \(0.5A_{sat}\sqrt{f^{\prime}_{c}E_{c}}\leq R_{g}R_{p}A_{sat}F_{u}\) for stud anchor \\  & where \(R_{g}\) = 1.0 and \(R_{p}\) = 0.75 throughout the present study \\  & \(0.3\bigl{(}t_{f}+0.5t_{w}\bigr{)}L_{ca}\sqrt{f^{\prime}_{c}E_{c}}\) for C-channel anchor \\  & \(0.5A_{sat}\sqrt{f^{\prime}_{c}E_{c}}\leq A_{sat}F_{u}\) for stud anchor \\  & \(45\bigl{(}t_{f}+0.5t_{w}\bigr{)}L_{ca}\sqrt{f^{\prime}_{c}}\) for C-channel anchor \\  & \(\min\left\{0.8F_{u}A_{sa}:\ \ 0.29 ad_{sat}^{2}\sqrt{f^{\prime}_{c}E_{c}}\right\}\) for stud anchor \\  & where \(\alpha=0.2(h_{sat}/d_{sa}+1)\) for \(3\leq h_{sat}/d_{sa}\leq 4\) or 1 for \(h_{sat}/d_{sa}>4\) \\  & \(88\sqrt{t_{w}}L_{ca}\sqrt{f^{\prime}_{c}}\) for C-channel anchor \\  & \(65\sqrt{t_{w}}L_{ca}\sqrt{f^{\prime}_{c}}\) for L-channel anchor \\ Maleki and Mahoutian (Maleki and Mahoutian, 2013) & \(27.2\bigl{(}t_{f}+0.5t_{w}\bigr{)}L_{ca}\sqrt{f^{\prime}_{c}}\) for C-channel anchor \\  & \((336t_{w}^{2}+5.24L_{ca}t_{ca})\sqrt{f^{\prime}_{c}}\) for C-channel anchor \\  & \(\xi^{3}\frac{h_{sat}}{h_{sat}}+1.6\) & \(\sqrt{f^{\prime}_{c}}L_{ca}t_{ca}\) for L-channel anchor \\  & \(0.25(7-0.023L_{ca})(1.5-0.005h_{ca})f^{\prime}_{c}L_{ca}t_{ca}+\frac{2\xi^{2}L_ {ca}}{h_{sa}}F_{u}\) for C-channel anchor \\  & \(0.213L_{ca}\sqrt{u_{sf}^{\prime}_{c}}\times 10^{3}\) for L-channel anchor \\  & \(\min\left\{31A_{sat}\sqrt{(h_{sat}/d_{sa})f^{\prime}_{c}}+10000;\ A_{sat}F_{u}\right\}\) for stud anchor \\  & \(\min\left\{0.0056h_{ca}L_{ca}\sqrt{f^{\prime}_{c}}L_{k}R_{k}3:\ \ 0.001t_{sc}L_{ca}F_{u}/\sqrt{3}\right\}\) for L-channel anchor \\  & where \(k_{1}=2.2(t_{sc}/h_{ca})^{2/3}\leq 1.0\), \(k_{2}=0.4\sqrt{t_{p}/t_{sc}}+0.43\leq 1.0\), \\  & \(k_{3}=\sqrt{s_{sa}/10}\times R_{ca}\leq 1.0\) \\  & \(k_{k}k_{2}k_{3}195.894(t_{w})^{0.425}(f^{\prime}_{c})^{0.383}\times L_{ca}\) for L-channel anchor \\  & where, \(k_{h}=\exp(-1.918t_{w}/h_{ca})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Existing Design Equations for Stud Anchors and Channel Anchors with Full-length Welding. showed a similar tendency for both fully-welded channel anchors and partially-welded channel anchors. Among the predictions, the combination of the equation of [PERSON] and Mahoutian [13] and Equations (1) and (2) best matched with the test results (mean and standard deviation of \(V_{\text{pred}}\)/\(V_{\text{test}}\) was \(m\pm\sigma\) = 0.80 \(\pm\) 0.13 for fully-welded channel anchors or 0.77 \(\pm\) 0.15 for partially-welded channel anchors). It is noted that the overall average of the calculated concrete contribution \(V_{nc}\) by Equation (2) was 6.6% of \(V_{n}\cdot(V_{nc}/V_{n}\) was in the range of 3.0-12.1% for all cases). Although some of the equations showed relatively good and conservative predictions suitable for design purpose, this is limited only to the test results of the present study. Fundamentally, it is not appropriate to apply the existing design equations for fully-welded channel anchors to the design of partially-welded channel anchors, because the failure mode and shear strength are strongly affected by the shape and welding condition of steel anchors [4,5,12].