# Experimental and Theoretical Study on Anchorage Loss of Prestressed CFRP-Reinforced Concrete Beams
## 3 Experimental Study
### Results and Discussion  
The measured data show that jack rebounding during the experimental (EXP) process made it difficult to precisely control the set tension value. By substituting the data into Equation (4), with L set to 11,600 mm and E\({}_{\text{cfrp}}\) to 160,000 MPa, the deformation magnitude was calculated, as shown in Table 4.  
The EXP results indicate a relationship between anchorage loss and factors such as prestress magnitude, dimensions of the front end of the steel reaction frame, connecting rod dimensions, and clearance in threaded connections. For instance, in the control group, anchorage loss constituted about 1.54% of the total applied prestress, resulting in a total deformation of approximately 1 mm. By using EXP data from seven conditions and the TCS, the anchorage loss was calculated, as shown in Table 5. Data from both sources are summarized in Figure 14.  
Comparing the data revealed significant differences in the seven deformation values (a) obtained from the experiments. The analysis indicated that the discrepancies were due to gaps between the anchorage and the connecting screw and between the fixed nut and the connecting screw during the experiments. These gaps increased actual deformation (a), causing a greater decrease in the prestress of the CFRP tendon. The magnitude of prestress, thread length, and screw diameter do not directly affect gap size; rather, they relate to the torque applied to the nut and the number of threaded connections. To address this, a \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & \(\sigma_{\text{a}}\) **(MPa)** & \(\sigma_{\text{b}}\) **(MPa)** & \(\sigma_{\text{1}}\) **(MPa)** & **Deformation (a/mm)** \\ \hline
1 & 948.51 & 933.88 & 14.63 & 1.061 \\
2 & 951.52 & 941.65 & 9.87 & 0.716 \\
3 & 947.98 & 935.71 & 12.27 & 0.890 \\
4 & 486.86 & 476.28 & 10.58 & 0.784 \\
5 & 485.58 & 472.43 & 13.16 & 0.954 \\
6 & 975.28 & 957.20 & 18.08 & 1.311 \\
7 & 962.36 & 941.14 & 21.22 & 1.539 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Anchorage loss of prestressed CFRP tendon. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & **Steel Reaction Frame** & **Connection Screw** & **Deformation** & \(\sigma_{\text{1}}\) **(MPa)** \\ \hline
1 & 0.267 & 0.364 & 0.631 & 8.70 \\
2 & 0.112 & 0.355 & 0.467 & 9.196 \\
3 & 0.111 & 0.359 & 0.470 & 11.995 \\
4 & 0.057 & 0.471 & 0.528 & 10.046 \\
5 & 0.057 & 0.465 & 0.522 & 12.719 \\
6 & 0.118 & 0.978 & 1.097 & 17.888 \\
7 & 0.113 & 0.936 & 1.049 & 19.988 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Theoretical calculation value of anchorage loss. correction was applied. Based on experimental data and standard construction processes, a gap value of 0.2 mm was assumed for each threaded connection. For groups 2, 4, and 6, where special treatments were applied, a gap value of 0.1 mm was used. We integrated the conclusions of the above analysis into the TCS and added a calculation section for the gap values caused by threaded connections in the TCS, resulting in a modified theoretical calculation system (MTCS). The MTCS for the total deformation \(\sigma_{1}\) at the tensioning end was derived from this analysis, yielding the formula for anchorage loss shown below:  
\[\mathrm{a}=\omega_{1}+\omega_{2}+\mathrm{n}\omega_{3}, \tag{5}\]  
\[\sigma_{1}=\frac{\mathrm{a}\times\mathrm{E}_{\mathrm{cfrp}}}{\mathrm{L}}, \tag{6}\]  
where \(\omega_{1}\) is the deformation caused by prestress on the steel reaction frames, \(\omega_{2}\) is the deformation caused by prestress on the connecting screw, \(\omega_{3}\) is the gap value present at each threaded connection point, n is the number of threaded connections, l is the length of the CFRP tendon, and \(\mathrm{E}_{\mathrm{cfrp}}\) is the modulus of elasticity of the CFRP tendon. The adjusted comparative data are shown in Figure 15. The results of EXP and MTCS are basically consistent, with an error controlled within approximately 5%, demonstrating high accuracy.