## 2 Design Models for Post-Tensioning Anchorage Zone Bearing Strength  
Essentially, the strength of anchorage devices and anchorage zones must be sufficient for the transfer of tendon force to the concrete, and the formation of cracks in the anchorage zone must not impair the function of the anchorage device [23; 24]. AASHTO [25] classifies anchorage devices as basic and special anchorages. For a basic anchorage device with a simple bearing plate, as shown in Figure 1, prestressing force is transferred from prestressing steel to concrete only through the bearing plate on the supporting concrete surface and the bearing resistance (\(P_{r}\)) is expressed as a function of the relative size of the proportional supporting concrete surface area (\(A\)) to the gross area (\(A_{g}\)) of the anchorage bearing plate and the nominal concrete strength at the time of application of the tendon force (\(f_{ci}^{r}\)). A special anchorage device with one or more horizontal ribs to increase the net bearing area (\(A_{b}\)) could be used based on test qualification even though the bearing resistance, as determined by Equations (1) and (2), is lower than the required strength. Equations (1) and (2) do not consider the strength enhancement due to confinement of concrete by spiral rebars around the anchorage device, and they often lead to highly conservative designs for special anchorage devices with spiral rebars [16]. Furthermore, Equation (2) limits the effective supporting concrete surface area to 10.33 times the gross bearing area (\(A\leq 10.33A_{g}\)) without respect to reinforcement condition. \[P_{r}=f_{n}A_{b} \tag{1}\]  
where  
\[f_{n}=0.7f_{ci}^{\prime}\sqrt{\frac{A}{A_{g}}}\leq 2.25f_{ci}^{\prime} \tag{2}\]PTI [5] presented an equation for the allowable stress (\(f_{cpi}\)) for a basic anchorage bearing plate that adopted coefficients, \(\alpha\) and \(\kappa\), to consider lateral rebar confinement, as shown in Equation (3). The concrete stress under the maximum allowable tendon force should be equal to or less than \(f_{cpi}\) when \(\alpha\) and \(\kappa\) are 0.5 and 1, respectively, and the lateral rebar volume ratio (\(p_{s}\)) is zero. \(\alpha\) and \(\kappa\) are 0.75 and 1.5, respectively, when \(p_{s}\) is larger than 2%. Between \(p_{s}=0\)% and 2%, \(\alpha\) and \(\kappa\) are determined by interpolation. Equation (3) implies that \(A/A_{g}\) is limited to 4. \[f_{cpi}=\alpha f_{cci}^{\prime}\sqrt{A/A_{g}}\leq\kappa f_{ci}^{\prime} \tag{3}\]  
Eurocode [23] specifies additional rules for the design of anchorage zones for multiply anchored tendons along with the qualification test in accordance with EAD 160004-00-0301 [22]. The rectangular supporting concrete block associated with each anchorage device should satisfy Equation (4), and the reinforcement (\(A_{s}\)) should not be less than the value determined by Equation (5) to prevent bursting and spalling of the concrete. \[\frac{P_{max}}{c\cdot c^{\prime}}\leq 0.6f_{ck}(t) \tag{4}\]  
where \(P_{max}\) is the maximum applied tendon force, \(c,c^{\prime}\) are the dimensions of the rectangular concrete block, and the rectangle should have approximately the same aspect ratio as the anchorage bearing plate. That is, \(c/a\) and \(c^{\prime}/a^{\prime}\) should not be greater than \(1.25\sqrt{\frac{c^{\prime}}{a\cdot a^{\prime}}}\) where \(a\) and \(a^{\prime}\) are the dimensions of the smallest rectangle, including the bearing plate of the anchorage device. In addition, the maximum distribution area is limited to 9 times the loaded area (\(A\leq 9.0A_{g}\)), and \(f_{ck}(t)\) is the characteristic compressive cylinder strength of concrete at the time of tensioning. \[A_{s}=0.15\frac{P_{max}}{f_{y}}\gamma_{p,unfav}\text{ with }\gamma_{p,unfav}\geq 1.20 \tag{5}\]  
where \(f_{y}\) is the design strength of the reinforcing steel, \(\gamma_{p,unfav}\) is the partial factor for prestress in unfavorable situations. The design model by [PERSON] [5] for special anchorage zones is shown in Equation (6). PTI [5] also includes the design model for special bearing plates.