## 2 Design Models for Post-Tensioning Anchorage Zone Bearing Strength
A special anchorage zone should be qualified based on  
Figure 1: Geometry of the post-tensioning anchorage zone with a basic anchorage device. an actual size test for typical sizes. The bearing strength of a special anchorage zone for which size has not been tested could be interpolated or extrapolated based on a comparison between the qualified test results and Equation (6). The ultimate bearing resistance, \(P_{n}\), comprises the bearing resistance by concrete, \(P_{c}\), and additional strength by confinement of spiral or stirrup rebar, \(P_{s}\). Equation (7) implies the bearing resistance of concrete by direct contact and confinement by the surrounding concrete, and the maximum relative bearing area of \(A/A_{g}\) is limited to 6.25. \[P_{n}=\eta(P_{c}+P_{s})\leq 3f_{ci}^{\prime}A_{b} \tag{6}\]  
\[P_{c}=0.8f_{ci}^{\prime}A_{b}\sqrt{A/A_{g}}\leq 2f_{ci}^{\prime}A_{b} \tag{7}\]  
\[P_{s}=4.1f_{lat}A_{core} \tag{8}\]  
where \(A_{b}\) is the net bearing plate area, \(f_{lat}\) is the lateral confinement pressure, \(\frac{2A_{g}f_{y}}{D\cdot s}(=f_{lat,sp})\) for spiral reinforcement and \(\frac{2A_{g}f_{y}}{T\cdot s}(=f_{lat,st})\) for stirrup reinforcement. \(f_{y}\) is the yield strength of rebar. The maximum effective lateral confinement pressure is limited to 8.3 MPa, \(D\), \(L\), and \(s\) are the diameter of spiral, side length of stirrup, and spacing of spiral or stirrup rebar, respectively, \(A_{core}\) is the effectively confined concrete core area, \(\frac{D^{2}\pi}{4}\left(1-\frac{s}{D}\right)^{2}-A_{duct}\) for spiral reinforcement (=\(A_{core,sp}\)) and \(\frac{1}{2}L^{2}-A_{duct}\) for stirrup reinforcement (=\(A_{core,st}\)), and the calibration factor, \(\eta\), which ranges from 0.85 to 0.95, was assumed to be 0.85 in this study. Unlike the basic anchorage bearing plate in Figure 1, the special anchorage bearing plates, as in Figure 2a, contains cones and ribs; thereby, those influences should be included in the contribution of lateral reinforcement (\(P_{s}\)). Considering that the behavior of the anchorage zone is highly dependent on the behavior of the concrete directly beneath the bearing plate, the above equation for \(A_{core}\) should be modified. In this study, average area loss (\(A_{anchorage}\)) by the anchorage bearing plate is substituted with \(A_{duct}\), and it was assumed to be a hollow column with a mid-point cone diameter of 115.5 mm. \[A_{core,sp}=\frac{D^{2}\pi}{4}\left(1-\frac{s}{D}\right)^{2}-A_{anchorage} \tag{9}\]  
\[f_{n}=0.7f_{ci}^{\prime}\sqrt{\frac{A}{A_{g}}}\leq 2.25f_{ci}^{\prime} \tag{2}\]0  
Meanwhile, the FEM-based research of [PERSON] and [PERSON] [8] revealed that the ultimate bearing strength is rarely affected by the dimensions of the concrete block if the dimensions are larger than the minimum spacing specified by the anchorage supplier and the spiral remains unchanged. In that study, \(A/A_{g}\) of the basic model was 2.8; it varied from 4.38 to 11.18 in additional FEM analysis. However, the authors stated that the design equation by [PERSON] and [PERSON] [5] estimated an increase in the ultimate strength of 12%, 23%, and 45% for \(A/A_{g}\) = 4.38, 6.25 and 11.18, respectively. Considering the design guides and research mentioned above, experimental verification is necessary to determine which design guide is more reasonable. The modified model by [PERSON] et al. [16] proposed a method of determining the net bearing area of a special anchorage with horizontal ribs. The reduction coefficient, \(R\), which is determined depending on the position and number of ribs, is factored into the additional net area by the ribs. In this study, a value of \(R=0.85\) was calculated, as a special anchorage device with a rib at the center in the longitudinal direction was used.