# Experimental and Theoretical Study on Anchorage Loss of Prestressed CFRP-Reinforced Concrete Beams
## 2 FEM Calculation and Theoretical Analysis
### Analysis of FEM Results  
The analysis results of the model are subdivided into the following six regions within the tensioning end, as illustrated in Figure 8: front end of the steel reaction frame (A), fixed nut (B), connecting screw at the location of the fixed nut (C), middle part of the connecting screw (D), connecting screw at the rear part of the anchor (E), and rear part of the anchor (F). The stress contour plot in Figure 9 illustrates the distribution of stress in the simulation results, indicating that the highest stress concentration arises at the points where the fixed nut engages with the connecting screw threads, with a peak value of 640 MPa. Additionally, significant stress is observed at the connection points of the connecting screw at the left and right ends, approximately three turns of threads away from the ends. In the case of the anchor screws, discernibly elevated stress levels are evident on the two screws proximal to the CFRP tendon in comparison to those positioned at the distant end. Consequently, it is \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Material** & **Elastic Modulus (MPa)** & **Poisson Ratio** \\ \hline Steel reaction frame & Q235 & 210,000 & 0.2 \\ Fixed nut & Grade 8.8 & 210,000 & 0.3 \\ Connecting screw & Grade 8.8 & 210,000 & 0.3 \\ Anchor & Q235 & 210,000 & 0.3 \\ CFRP tendon & CFRP & 160,000 & 0.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Corresponding relationship between components and materials in deformation area. Figure 8: Schematic diagram of division of deformation area at tensioning end. Figure 7: Schematic diagram detailing the steel reaction frame (unit: mm). deduced that the predominant loss of anchorage originates from the vicinity encompassing the fixed nut, the connecting screw, and the rear extremity of the anchor. The designated nodes within these regions are denoted as a-f (Figure 9), correlating with the corresponding deformation areas A-F (Figure 8). Table 2 presents the deformation magnitude at the tensioning end, where the connecting screw includes the contact part between the connecting screw and the fixed nut (a), the middle section of the connecting screw (b), and the contact part between the connecting screw and the back of the anchor (c). The analysis of the deformation percentages reveals that the primary contributors to deformation at the tensioning end are the steel reaction frame and the connecting screw. Deformation at the fixed nut and the rear section of the anchor screw accounts for only 4.04% of the total, rendering it negligible for subsequent calculations. Furthermore, it is noted that the deformations of the two connecting screws, situated at the fixed nut and the rear section of the anchor screw, are approximately equal, each measuring around 0.025 mm. This deformation predominantly manifests along the three threads of the stressed section, allowing for simplification in subsequent calculations. From the preceding analysis, it is deduced that the deformations within the anchorage area primarily stem from four components: (1) the front end of the steel reaction frame; (2) the fixed nut; (3) the connecting screw; (4) the rear section of the anchor screw. However, the deformations associated with components (2) and (4), specifically the fixed nut and the rear section of the anchor screw, are deemed negligible in comparison with those of the front end of the steel reaction frame and the connecting screw. Consequently, for optimization purposes, these negligible deformations are omitted from subsequent calculations. As such, the crux of the theoretical calculation revolves around establishing the computational