# Experimental and Theoretical Study on Anchorage Loss of Prestressed CFRP-Reinforced Concrete Beams
## 2 FEM Calculation and Theoretical Analysis  
### Mechanism of Anchorage Loss  
Figure 2 illustrates the externally prestressed CFRP tendon reinforcement system for concrete beams. The reinforcement system is fixed to the bottom of the beam via chemical anchors and mechanical connections. During reinforcement, prestress is applied to the CFRP tendons to actively close any cracks that develop in the bottom span of the beam during normal use, thereby extending the bridge's service life.  
Figure 1: Schematic diagram of research process.  
Figure 2: Schematic diagram of simply supported beam bridge strengthened with externally prestressed CFRP tendons.  
The reinforcement system consists of CFRP tendons and the CFRP tendon-main beam connection system. As shown in Figure 3, the CFRP tendon-main beam connection system includes a CFRP tendon anchorage, a connecting screw, a fixed nut, and a steel reaction frame. Prestressing is applied to the CFRP tendons by using a jack, achieving active reinforcement.  
As shown in Figure 4, when applying prestress to the CFRP tendons, the tensioning device must be placed at the end of the steel reaction frame, i.e., the tensioning end. Subsequently, the hydraulic jack moves the CFRP tendons and the front steel plate towards the front end of the steel reaction frame via a screw. This elongates the CFRP tendon, generating prestress to resist deformation. Once the desired prestress level is reached, the fixation nuts are tightened to complete the prestressing process of the CFRP tendons, and the strengthening procedure is finished as illustrated in steps 1 to 3 in Figure 4.  
Before completing CFRP tendon reinforcement, the main causes of prestress loss are anchorage loss, CFRP tendon friction loss, and concrete elastic compression loss. After reinforcement is completed, under the long-term action of prestress, there occur CFRP tendon relaxation loss, CFRP tendon temperature difference loss, and concrete shrinkage creep loss.  
This research study examines the phenomenon of anchoring loss, which occurs when the stressed region at the tensioning end changes before and after unloading. Due to the alteration in the stressed region (illustrated in the red area in Figure 5), before unloading, the anchorage and the rear end of the steel reaction frame are under compression. After unloading, the anchorage, the connection screw, and the front section of the steel reaction frame experience tensile stress, whereas the fixed nut undergoes compressive stress. This modification causes distortion in the components, which is then transmitted to the CFRP tendon, resulting in relaxation and loss of prestress, commonly referred to as anchorage loss. To calculate anchorage loss, some assumptions are taken into account.  
1. The stress conditions between the CFRP tendon anchor and the front plate only impact the outward deformation of the anchor, not the loss of prestress in the CFRP tendon, both before and after unloading. The effect is disregarded in later computations.  
Figure 4: Schematic diagram of prestressed CFRP tendon tensioning.  
Figure 3: Schematic diagram of CFRP tendon–main beam connection system.  
2. Since only a little amount of deformation is sent to the anchors at both ends, it can be disregarded. Thus, it is inferred that all the deformation is transferred to the CFRP tendon.  
To summarize, the loss of anchorage in the CFRP tendon may be categorized into four components: deformation at the connecting screw, the front end of the steel reaction frame, the fixed nut, and the rear end of the anchor.