## 1 Introduction  
Precast segmental concrete beam (PSCB) is a popular and widely used construction technique in bridge engineering due to its significant benefits of economy, high-quality control, fast construction, and low environmental impact [1; 2; 3; 4]. Especially for bridge constructions in mountainous and urban areas, PSCB is usually the preferred option [5]. In PSCB, the segments are assembled as a monolithic structure by prestressing forces, which have crucial influences on the structural performance. The steel strand is the tendon type most commonly employed to apply the prestressing force in PSCB, including internal bonded and external un-bonded steel tendons [6; 7; 8; 9]. However, the problem of corrosion in steel tendons [10; 11] at the joint location is of great concern for the durability of PSCB. Once the joint opens, the corrosion of the internal steel tendon will cause performance deterioration and even collapse of PSCB [12]. The externally arranged steel tendon is a possible solution because of its replaceable condition during service life. However, the new problem for externally prestressed PSCB is that the effective tendon depth decreases along with structural deformation (so-called second-order effects), causing the structural carrying capacity to be lower than the bonded members [13]. Better prestressing schemes are therefore always the focus of researchers and engineers. The carbon-fiber-reinforced polymer (CFRP) tendon is an optional alternative to steel tendons due to its lightweight, high strength, and corrosion-resistant [14; 15]. Previously, most research has focused on applying CFRP tendons to the monolithic beam [16; 17; 18; 19; 20]. [PERSON] et al. introduced the CFRP tendons into PSCB as internal un-bonded prestressing reinforcements [21; 22], generating a new scheme for PSCB called PSCB-IUCFRP. This newly developed scheme has three main advantages. One is that the tendon corrosion problem is solved, improving structural durability. Additionally, the segments can be directly assembled with keyed dry joints, which helps to accelerate construction. Most importantly, the structural flexural performance is improved compared to externally prestressed PSCB because the effective depth of the internal tendon in PSCB-IUCFRP can remain even at the ultimate states. [PERSON] et al. [21; 22] conducted two flexural performance tests on PSCB-IUCFRP specimens. The results showed that the flexural capacity of PSCB-IUCFRP was almost 71% of that of the bonded beams, and the structural ductility was better than that of bonded members. Based on this experimental study, [PERSON] et al. [23] and [PERSON] et al. [24] proposed a solid element-based finite element model for the flexural behavior analysis of PSCB-IUCFRP. The model showed satisfactory prediction accuracy for failure mode, carrying capacity, and structural deformation. Nevertheless, its computational efficiency is limited due to the complicated contact relation and poor convergence. To solve this problem, [PERSON] et al. [25] developed a nonlinear high-efficiency fiber beam-tendon hybrid model to analyze the flexural performance of a full-scale PSCB-IUCFRP. The results showed that the flexural capacity of PSCB-IUCFRP was 75% of that of bonded members, and was improved by 55% compared with externally prestressed beams. However, all of these models are iteration-calculated methods based on nonlinear finite element software, which is inconvenient for designers. A simplified method for predicting tendon stress increment and flexural capacity of PSCB-IUCFRP is needed. Flexural capacity prediction of the unbonded prestressed members has always been a complicated and widely focused problem due to the unbonded phenomenon of tendons. During the service, the whole section remains compressive and the tendon stress increment is very small. However, for the strength limit state, the unbonded tendon is usually not yielded but has a non-negligible stress increment. The stress increment depends on structural deformations rather than just a sectional analysis.