## 5 Conclusions  
In this paper, a new beam-tendon hybrid model consisting of fiber beam elements and slipping cable element is proposed to analyze the flexural behaviors of EPCBs. The mechanical characteristics of EPCBs, including the material and geometric nonlinearities, interfacial slip effects, and the unbonded effects of the external tendon are all considered in the model. The FE formulations of the proposed elements are presented and the computational procedure is developed in the OpenSees framework as the new element classes. The proposed model is validated by comparisons with experimental tests and the parametric analysis is conducted. The main conclusions can be summarized as follows:  
1. Interfacial slip effects are inevitable for steel-concrete composite beams during their service life, even when they are designed with full shear connections. The structural stiffness, capacity and failure modes are all affected. The proposed fiber beam element model considering interfacial slip effects can be used to predict the capacity, deformation and failure mode, which are all verified to agree well with the experimental results.
2. Ignoring the friction at the deviators, the external tendon has equal traction along its whole length. The conventional truss element could not satisfy the strain-compatibility property in multiple segments, causing some overestimation of the stress increments and flexural capacity. The proposed slipping cable element is built considering the strain-compatibility property, which shows better agreement with the experimental results.
3. The parameter analysis results reveal that the deviator spacing, external tendon effective height, interfacial shear capacity and loading type all affect the flexural capacity of EPCBs. An increase in the deviator spacing decreases the ultimate effective height of the external tendon, which then leads to a decrease in the flexural capacity. The increased external tendon effective height increases the ultimate stress increments and flexural capacity. With an increase in the interfacial shear capacity, the flexural capacity increases gradually but the stress increments and effective height of the tendon do not vary monotonously. The proposed model provides an effective method for predicting the flexural behaviors of EPCBs.  
Figure 21: Effects of interfacial slip on flexural responses of EPCB.  
**Author Contributions:** Conceptualization, methodology, software, validation, writing--original draft preparation, W.Y.; project administration, L.C.; supervision, writing--review and editing, B.H.; data curation, H.X.; visualization, Y.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Funds of China Railway Economic Planning and Research Institute, funding number 2021 BSH01; Project of Science and Technology Research Development Plan of China Railway, funding numbers K2021G013 and N2021G046; Project from Key Laboratory of Transport Industry of Bridge Detection Reinforcement Technology (Beijing), funding number C21M00030.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.