## 4 Discussions  
### Existing Design Equations for Stud Anchors and Fully-Welded Channel Anchors  
For the nominal shear strength \(Q_{n}\) of a steel anchor (stud anchors and fully-welded channel anchors) embedded in a solid concrete slab, current design codes such as ANSI/AISC 360-16 [9] provide design equations. Table 4 summarizes existing design equations including current code equations and the other design equations available in the literature [3; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. It is noted that for direct comparisons among those design equations, some of symbols were modified from the original expressions and the design factors such as strength reduction factors and partial factors were not included in the equations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Yielding of Steel Anchors**} & \multicolumn{2}{c}{**Maximum Strength**} & \multicolumn{2}{c}{**Ultimate Slip**} \\ \cline{2-7}
**Specimen** & \(\mathbf{V_{y}}\) & \(\delta_{y}\) & \(K_{i}=\mathbf{V_{y}}/\delta_{y}\) & \(\mathbf{V_{m}}\) & \(\delta_{u}\) & \(\mathbf{\mu}=\delta_{u}/\delta_{y}\) \\  & **(tN)** & **(mm)** & **(tN/mm)** & **(tN)** & **(mm)** & **(mm)** & **\\ \hline H-S & 640.0 & 3.4 & 190.9 & 1024.6 & 22.5 & 6.7 \\ UI-S & 901.5 & 3.2 & 284.2 & 1262.5 & 21.6 & 6.8 \\ UO75-S & 718.6 & 3.7 & 195.4 & 900.0 & 27.5 & 7.5 \\ UOI00-S & 584.0 & 3.1 & 189.7 & 834.1 & 26.3 & 8.5 \\ H-Z130 & 566.3 & 2.2 & 260.3 & 861.2 & 17.8 & 8.2 \\ H-Z230 & 1008.3 & 2.6 & 389.9 & 1246.5 & 9.7 & 3.8 \\ UI-Z130 & 876.8 & 2.6 & 335.1 & 963.5 & 6.9 & 2.6 \\ UO75-Z230 & 1411.2 & 3.9 & 363.0 & 1473.3 & 8.4 & 2.1 \\ UO100-Z230 & 1362.7 & 4.6 & 297.9 & 1401.2 & 10.0 & 2.2 \\ H-C130 & 857.7 & 2.2 & 392.4 & 1077.0 & 10.9 & 5.0 \\ H-C230 & 1191.0 & 2.2 & 553.9 & 1541.8 & 8.4 & 3.9 \\ UI-C130 & 1025.3 & 2.7 & 384.0 & 1409.8 & 10.4 & 3.9 \\ UO100-C230 & 1340.5 & 2.9 & 456.2 & 1740.9 & 11.7 & 4.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test Results. Figure 7: Comparisons of Behavior: (**a**) in terms of Steel Anchors; (**b**) in terms of Steel Beams. Although the design equations for channel anchors in Table 4 are for a specific shape with full-length welding, all of those equations were applied to the test specimens of the present study to verify their applicability. The elastic modulus of concrete was calculated as \(E_{c}=4700\sqrt{f^{\prime}_{c}}\)([PERSON] et al., 2016) in all equations for direct comparison, and the contribution \(V_{nc}\) of the concrete inside the UH-beam, which was cast monolithically with concrete slabs, was taken into account in the calculation of the design shear strength \(V_{n}\) as follows. \[V_{n}=\Sigma Q_{n}+V_{nc} \tag{1}\]  
\[V_{nc}=0.66\times\min\biggl{\{}\sqrt{2/(1+0.004d_{c})};\ \ 1\biggr{\}}\times(\rho_{w})^{1/3} \sqrt{f^{\prime}_{c}}b_{c}d_{c}\times 2 \tag{2}\]  
where, \(V_{nc}\) = nominal shear strength provided by the concrete, which was calculated in accordance with ACI 318-19 ([PERSON] et al., 2016) (for the case of normal-weight concrete, non-prestressed members, not providing the minimum amount of shear reinforcement, and having no axial load); \(\rho_{w}\) = longitudinal reinforcement ratio; and \(b_{c}\), \(d_{c}\) = width and depth of concrete measured at the interface between the monolithically cast beam and slab (\(b_{c}\) = clear distance between top flanges of U-section, \(d_{c}\) = net length excluding the width \(b_{ca}\) of channel anchors). The factor of 2 in Equation (2) is for double-sided push-out testing, and the vertical reinforcement in the concrete slab (4-D13) was considered as longitudinal tension reinforcement ([PERSON] et al., 2016) in the calculation of \(\rho_{w}\). Figure 8 shows the comparison (in this figure, each design equation is identified by an abbreviated name of the design code or authors, and C or L behind the abbreviated name indicates C- or L-channel anchor).