## 5 Conclusions  
This paper studies the simplified equation for predicting tendon stress increment and flexural capacity in a precast segmental concrete beam with internally un-bonded prestressed CFRP tendons. Based on the developed numerical model, the effects of segmental joints and tendon type on flexural behaviors are analyzed. A parametric study containing  
Figure 17: Failure modes of the analysis beam with different prestressing ratios.  
162 numerical models is conducted, and the analysis results are used to evaluate the widely used prediction equations for the PSCB-IUCFRP. Based on the failure mechanism analysis, new equations are put forward for predicting tendon stress increment, flexural capacity, and balanced prestressing reinforcement ratio for PSCB-IUCFRP. The main conclusions are as follows:  
1. The comparisons between segmental and monolithic beams show that plastic deformation in the segmental beam is concentrated at the failure joint cross-section, which differs from the monolithic beam's distributed modes. With the same conditions, the monolithic beam's stress increment, flexural capacity, and ultimate deflection are more significant than those of the segmental beam.
2. The parametric study shows that the loading types have a minor influence on the tendon stress increment and flexural capacity of PSCB-IUCFRP. The factors \(L/d_{\text{P}}\), \(A_{\text{P}}\), and \(\sigma_{\text{pe}}\) are negatively correlated with tendon stress increment. However, the factor \(f_{\text{c}}\) has the opposite effect. The flexural capacity decreases with an increase in \(L/d_{\text{P}}\), and an increase in \(A_{\text{P}}\), \(\sigma_{\text{pe}}\), and \(f_{\text{c}}\) improves the flexural capacity.
3. The equations of the ACI 440.4R model, based on the bond-reduction method, show the best prediction accuracy for tendon stress increment with a mean index value of 0.98 and COV index value of 0.24. It underestimates the results of cases under one-point loading but overestimates those under two-point loading. The predictions of the ACI 318-14 model and the AASHTO LRFD model are all conservative.
4. The predictions of the proposed equation, derived according to the failure mechanism and deformation analysis, show good agreement with the numerical model results for both tendon stress increment and flexural capacity. The simplified plastic hinge length for PSCB-IUCFRP is recommended to be 2.1 \(d_{\text{P}}\). The balanced prestressing reinforcement ratio of PSCB-IUCFRP is smaller than that of the bonded prestressed members, and the suggested equations are put forward.  
Conceptualization, methodology, software and validation, writing--original draft preparation, formal analysis, investigation, resources, data curation, writing--review and editing, W.Y.; visualization, writing--review and editing, Y.S.; supervision, writing--review and editing, L.C.; project administration, funding acquisition, writing--review and editing, F.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Project of the Ministry of Housing and Urban-Rural Development No. K20200641; Fundamental Research Funds for the Central Universities, funding number 2022 JBMC047; Project of Science and Technology Research Development Plan of China Railway, funding numbers N2021G046 and K2021G013; National Natural Science Foundation of China, funding number 51708020.  
Not applicable.  
The authors declare no conflict of interest.