# Experimental and Theoretical Study on Anchorage Loss of Prestressed CFRP-Reinforced Concrete Beams
## 1 Introduction  
Carbon fiber-reinforced polymer (CFRP) tendons exhibit high modulus, light weight, fatigue resistance, and corrosion resistance. The development of external prestressing CFRP tendon reinforcement technology has revealed significant advantages over other reinforcement techniques. It enhances bridge durability without substantially increasing structural weight. Additionally, it provides crack closure, combined flexural and shear reinforcement, and high efficiency. Therefore, it has been widely used in flexural reinforcement in bridge engineering [1; 2; 3; 4; 5]. To ensure effective reinforcement, prestress loss has become a key research focus, with anchorage loss being a significant component of the total prestress loss. Anchorage loss occurs due to the deformation of components within the prestressed tendon-main beam connection system. This deformation reduces the prestress in the tendons. In bridge structures, the calculation method for anchorage loss of externally prestressed CFRP tendons typically follows the method used for steel bars and strands [6]. However, significant differences in practical anchoring methods prevent simple interchangeability [7]. The anchorage loss of externally prestressed CFRP tendons primarily originates fromanchoring deformation, which depends on the type of anchoring device and tensioning method. These anchoring devices include the clamp type, the bonding type, and the combination type [8; 9; 10; 11; 12; 13; 14]. [PERSON] et al. [15] designed a small-sized variable-stiffness wedge (VSW) for BFRP tendons. This anchorage resulted in a deformation of 0.6 mm due to short-term losses, causing approximately 29 MPa of prestress loss. The prestress loss structure of externally prestressed CFRP tendons, similar to that of steel strands, is divided into short-term and long-term losses [10]. [PERSON] [16] proposed a simplified method to evaluate prestress loss, improving design efficiency and accuracy. This method includes both long-term and short-term losses, with short-term losses involving factors such as elastic shortening, concrete shrinkage, and initial losses in prestressing steel. [PERSON] et al. [17] found that in the Near-Surface Mounted (NSM) post-tensioning method, CFRP relaxation, a long-term loss, is the primary source of prestress loss, while short-term loss is mainly due to the anchoring set. [PERSON] et al. [18] highlighted the similarity in the loss structure between CFRP tendons and steel strands. Comparing test and calculation values of anchoring loss for clamp-bonding anchoring devices revealed that the difference does not exceed 15%. [PERSON] et al. [19] introduced the main components of prestress loss in CFRP tendon-reinforced concrete beams. [PERSON] et al. [20] studied CFRP tendon reinforcement, finding that anchoring loss accounts for 45.9% of the total loss, while concrete elastic shrinkage loss is negligible. A report by the Research Committee on Continuous Fiber Reinforcing Materials [21] indicates that under long-term prestressing, CFRP tendons relax, with a creep fracture stress coefficient of 0.85 after 100 years. Additionally, some scholars [22; 23] researched the prestress loss of carbon fiber cloth and sheets, concluding that early loss is rapid, but prestress stabilizes over time. [PERSON] et al. [24] reinforced concrete beams with CFRP and studied the impact of anchoring deformation on prestress loss. The test results showed that anchor deformation and slippage between the anchor and CFRP fabric cause an instantaneous prestress loss rate of approximately 12.6% to 18.2%. [PERSON] et al. [25] established a mechanical model, examined the anchoring effect of CFRP plates, and predicted the magnitude of short-term loss in their anchoring system, suggesting that short-term prestress loss should be 10% of the applied prestress. [PERSON] et al. [26] found that prestressing CFRP-reinforced plates on RC beams of different sizes affects both short-term and long-term prestress losses, with smaller sizes resulting in higher losses. [PERSON] et al.