## 5 Comparison of Test Results and Design Equation Results  
Among previous design equations, Equations (6)-(8) by [PERSON] and [PERSON] [4; 5] are generally used to estimate the ultimate bearing strength of the post-tensioning anchorage zone. The intended use of these equations concerns strength interpolation or extrapolation for anchorage bearing plates that were not qualified through testing. However, there is some ambiguity in each of the variables in the equations, such as \(A_{b}\) of a  
Figure 11: Fracture mode of group 3 specimens: (**a**) A12H-8; (**b**) A12H-9; (**c**) A12H-10; (**d**) A12H-11.  
special anchorage with horizontal ribs. In addition, the average area loss in lateral confinement by the anchorage bearing plate (\(A_{anchorage}\)) should be substituted for \(A_{duct}\), as shown in Equations (9) and (10), when a cone-shaped special anchorage bearing plate is used. In this paper, the model by [PERSON] et al. [16] was adopted for the computation of \(A_{b}\), and \(A_{anchorage}\) was used instead of \(A_{core}\). In this paper, the coefficients representing the effect of \(A/A_{g}\) and lateral confinement for a specimen larger than the minimum anchorage spacing were proposed from Equation (18) through Equation (23). The test results were compared with those of Equations (6)-(8) and Equations (18)-(23) (Figure 12). When applying the two design equations, identical values of \(A_{b}\) and average area loss in lateral confinement (\(A_{anchorage}\)) were used.  
As seen in Figure 12, for the minimum anchorage spacing, both Equations (6)-(8) and Equations (18)-(23) present conservative estimations, and Equations (18)-(23) show better agreement with the test results than Equations (6)-(8). The difference between the two sets of equations for this group lies in limiting the lateral confinement pressure to 8.3 MPa in Equations (6)-(8). Therefore, for the minimum anchorage spacing, the limitation of the lateral confinement pressure could be revised to 13 MPa or more for Equations (18)-(23). For the specimens larger than the minimum anchorage spacing, Equations (18)-(23) estimate the strength well overall except for A12H-5 and -7, which were reinforced with \(\varnothing\)10 spiral rebars. Meanwhile, Equations (6)-(8) greatly overestimates the strength of A12H-7, which could lead to an unsafe design. This is because the large spiral diameter led to overestimation of the effective core area, \(A_{core}\), resulting in an overestimation of strength. Considering that anchorage zone designs such as A12H-5 or -7 are generally avoided by engineers, both design equations might be used to estimate the anchorage zone without respect to \(A/A_{g}\). However, to ensure safe and efficient design, the proposed equations are more effective, according to the comparison in Figure 12. Table 6 shows error rate comparisons between design equations. Each column in Table 6 presents the absolute value of prediction error for both design equations. Even though Equations (6)-(8) predicted very precisely for some specimens with errors less than 5%, but the average error was larger, and the error deviated much more than the proposed equation. Therefore, it can be concluded that the proposed equation provides a more reliable prediction of the bearing strength of the post-t  
Figure 12: Comparison of test results and results of design equations.