# Anchor Design of a Ring Joint Based on Reliability in a Precast Shear Wall Structure
## 4 Bearing Capacity Model
### Parametric Study  
Five factors were considered for the parametric analysis based on the models of the anchoring and dowel actions, as listed in Table 3. Rebar fracture was observed in all models, and the load, \(f_{\text{y-R}}\), was recorded when the ring rebar yielded and the horizontal rebar was still in the elastic phase. In bearing capacity analysis, only the yield strength of the ring rebar was increased to yield the horizontal rebar, and the corresponding load, \(f_{\text{y-HR}}\), was recorded. The ratio of \(f_{\text{y-HR}}\)/\(f_{\text{y-R}}\) was used to evaluate the capacity reserve and results are summarised in Table 4.  
In group L1-L4, the horizontal rebar diameter is 10 mm, and the reserve decreases from 95.13% to \(-\)14.24%, at which there is no reserve, as the diameter of the up-ring rebar increases from 8 mm to 14 mm. In group P1-P4, the diameter of the up-ring rebar is 10 mm, and the reserve increases from 29.99% to 69.44% as the diameter of the horizontal rebar increases from 8 mm to 14 mm. In group Q1-Q4, the up-ring rebar is consistent with the horizontal rebar, and the reserve decreases from 110.70% to 24.76% as the diameter increases from 8 mm to 14 mm, demonstrating a high safety reserve. Research has shown that the reserve is low or zero when the diameter of the ring rebar is larger than  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{6}{c}{**Model List**} & \multicolumn{6}{c}{**Reserve Analysis**} & \multicolumn{6}{c}{**Bearing Capacity Analysis**} \\ \cline{2-13}  & \(\mathbf{d_{\text{r}}}\) & **C** & **CH** & \(\mathbf{W_{\text{r}}}\) & \(\mathbf{d  
that of the horizontal rebar. However, the reserve is improved when the diameter of the ring rebar is larger or equal to that of the horizontal rebar. The diameter thus plays a critical role in the bearing capacity, and it is recommended that the diameter of the ring rebar should be consistent with that of the horizontal rebar considering the bearing capacity reserve and economic factors. As the concrete grade increases from C25 to C40 in group M1-M4, the reserve increases from 32.32% to 50.78%. The reserve increases from 16.85% to 74.43% as the composite height increases from 75 mm to 150 mm in group N1-N4. As the width of the ring rebar increases from 125 mm to 200 mm in group O1-O4, the reserve increases from 25.50% to 52.37%. Therefore, the connection is safe and reliable with an improved reserve under a reasonable design.  
Based on the parametric analysis and bearing capacity reserve analysis, some suggestions are proposed: the diameter of the horizontal rebar should be consistent with that of the ring rebar; at least two rows of the horizontal rebar should be arranged at the corner of the closed area; the composite height and the width of the ring rebar should be at least 100 mm and 125 mm, respectively. The concrete grade should be better than C25, and the concrete grade of the connection area should be one level higher than that of the components.  
In-depth analysis were conducted based on models that satisfy the above suggested conditions, and the bearing capacity analysis results are summarised in Table 4. A bearing capacity model was proposed through linear fitting by considering the anchoring and dowel actions comprehensively, as given in Figure 14 and Equation (6).  
\[P\ =\ F_{\mathrm{u}}+0.45D_{\mathrm{c}} \tag{6}\]  
By substituting Equations (2)-(5) into (6) and ignoring the small effect of other factors, the bearing capacity model is obtained, as shown in Equation (7).  
\[P=\ 2\pi d(l_{\mathrm{v}}+l_{\mathrm{h}})\tau_{\mathrm{u}}+0.58d\ ^{2}\!\left(f_{ \mathrm{c}}\!\cdot\!f_{\mathrm{y}}\right)^{\frac{1}{2}} \tag{7}\]