## 3 Flexural Capacity Prediction Methods and Applicability Analysis
### Applicability Evaluation of the Widely Used Prediction Equations  
The deformation-based method was usually considered the most rational of these three prediction methods due to its clear physical significance. In the early version of AASHTO specifications [51], the bond-reduction method proposed by [PERSON] and [PERSON] [39] was recommended for the prediction of un-bonded tendon stress increment. However, the related provisions were replaced by the deformation-based method of [PERSON] et al. [43] in the revised specifications. All the methods were devised without considering the discontinuity of segmental joints. The applicability of these methods for PSCB-IUCFRP is here evaluated based on the 162 numerical model results.  
Figure 12 shows the comparisons between predictions and FE numerical model results. The indexes Mean(Pre./FE) and COV(Pre./FE) are employed to evaluate the prediction accuracy and scattering. Mean(Pre./FE) is defined as the mean value of the ratios of predictions to numerical model results, and COV(Pre./FE) is defined as the related coefficient of variation (COV). When the index Mean(Pre./FE) is closer to one and COV(Pre./FE) is smaller, the applicability of the prediction equation is better.  
The predictions of tendon stress increment made by the ACI 318-14 model [40] are conservative and scattered, with a mean value of 0.67 and a COV value of 0.28. It is likely due to the fact that the equation was built based on a statistical analysis without any clear mechanism analysis. Moreover, the results from experimental tests of PSCB-IUCFRP were not included in the regression data. Even so, the ACI 318-14 model's flexural capacity predictions seem acceptable. Although the tendon stress is underestimated, the length of the force arm (\(d_{\mathrm{P}}-a/2\)) is overestimated according to the axial force balance condition. As a result, the effects of the underestimation of tendon stress increment are reduced for flexural capacity prediction. However, this is not always guaranteed.  
The predictions of the AASHTO LRFD method, derived from the failure mechanism analysis, are the most conservative and have a very poor correlation with the numerical analysis results. For the beams with the same \(L/d_{\mathrm{P}}\), the tendon stress increment predictions are almost the same. We find that, with the assumed plastic hinge length \(l_{\mathrm{P}}=10.5\,c_{\mathrm{u}}\) by [PERSON] et al. [43], Equation (4) is transformed into Equation (6), and \(\Delta\sigma_{\mathrm{P}}\) is approximate to 0.031 \(E_{\mathrm{P}}d_{\mathrm{P}}/L_{0}\). We can infer that the assumption of plastic hinge length \(l_{\mathrm{P}}=10.5\,c_{\mathrm{u}}\) may not be suitable for PSCB-IUCFRP.  
Unexpectedly, the bond-reduction method of [PERSON] and [PERSON] [39], which is replaced by the AASHTO LRFD specifications [50], gives a more accurate prediction than the other two methods. However, the predictions of tendon stress increment also showapparent variability. The cases under one-point loading tend to be underestimated, and those under two-point loading tend to be overestimated. The equations should be modified further, and the physical significance should be clarified.  
Figure 12: Predictions of tendon stress increment and flexural capacity of the widely used equations: (**a**) ACI 318-14 model, (**b**) ACI 440.4R model, (**c**) AASHTO LRFD model. (circles represent the results of tendon stress increment and triangles denote the results of flexural capacity).