## 2 Test Scheme Design and Implementation
### Loading Scheme  
Before conducting the tests, theoretical calculations determine the ultimate load values. These values are used to design the hierarchical and cyclic loading rationally, ensuring experiment safety. The loading process of prestressed reinforced concrete beams P2 and P3 generally consists of three stages until failure: (1) loading until the neutralization of prestress, (2) continued loading until cracking occurs in the lower part of the test beam, and (3) cracking in the lower part of the test beam until failure occurs at the top of the beam span. Non-prestressed reinforced concrete beam P1 generally experiences stages (2) and (3) only. The calculation of critical loads for the failure process of test beams P2 and P3 is as follows:  
1. The stress at the mid-span section during the neutralization of prestress is denoted as \(\sigma_{0}\), and the moment for decompression is denoted as \(M_{0}\). \[\sigma_{0}=\frac{N_{p}}{A}\pm\frac{N_{p}ey}{I}\] (1) \[M_{0}=\sigma_{0}\omega_{0}\] (2)  
In the equation, \(N_{p}\) represents prestress, \(e\) denotes eccentricity, \(A\) stands for the cross-sectional area of the test beam, \(y\) represents the distance from the centroid of the section to the calculated fiber, \(I\) represents the moment of inertia, and \(\omega_{0}\) represents the flexural modulus of the converted section for the tension side. Figure 3: Acoustic emission detection system. \[F_{1}=\frac{8M_{0}-ql^{2}}{2l} \tag{3}\]  
In the equation, \(F_{1}\) represents the critical load at the stage of neutralizing prestress, \(q\) denotes the gravity equivalent uniformly distributed load, and \(l\) represents the length of the beam. (2) The cracking moment \(M_{f}\) and critical load \(F_{2}\) at the stage of continued loading until cracking occurs in the lower part of the test beam are determined as follows:  
\[M_{f}=\sigma_{f}\omega_{0} \tag{4}\]  
\[F_{2}=F_{1}+\frac{8M_{f}-ql^{2}}{2l} \tag{5}\]  
In the equation, \(\sigma_{f}\) represents the cracking stress of C40 concrete, which is assumed to be 2.4 N/mm\({}^{2}\). (3) The ultimate flexural capacity \(M_{u}\) and critical load \(F_{3}\) at the stage of continued loading until failure occurs at the top of the beam span can be expressed as follows:  
\[M_{u}=f_{cd}bx\left(h_{0}-\frac{x}{2}\right)+f^{\prime}_{y}A^{\prime}_{s}(h_{ 0}-a^{\prime}_{s}) \tag{6}\]  
\[x=\frac{f_{pd}A_{p}+f_{y}A_{s}-f^{\prime}_{y}A^{\prime}_{s}}{f_{cd}b} \tag{7}\]  
\[F_{3}=F_{1}+F_{2}+\frac{4M_{u}}{l} \tag{8}\]  
In the equation, \(f_{cd}\) represents the design value of compressive strength of concrete. \(b\) denotes the width of the structural section. \(x\) represents the height of the compressed concrete zone. \(h_{0}\) is the effective height of the section. \(f^{\prime}_{y}\) is the design value of compressive strength of the steel reinforcement. \(A^{\prime}_{s}\) is the cross-sectional area of ordinary reinforcement in the compressed zone. \(a^{\prime}_{s}\) is the distance from the resultant force of longitudinal ordinary reinforcement in the compressed zone to the edge of the section. \(A_{p}\) represents the cross-sectional area of longitudinal the prestressed reinforcement in the tension zone. \(A_{s}\) denotes the cross-sectional area of ordinary reinforcement in the tension zone. \(f_{y}\) represents the design value of tensile strength of the steel reinforcement, and \(f_{pd}\) represents the design value of tensile strength of the prestressed reinforcement. The critical load \(F_{2}\)' for the P1 test beam is calculated using Equations (4) and (5). At the stage of neutralizing prestress, no loading is applied, and F1 in Equation (5) is set to 0. The ultimate flexural capacity \(M_{u}\)' and critical load \(F_{3}\)' at the stage of continued loading until failure occurs at the top of the beam span can be expressed as follows:  
\[M^{\prime}_{u}=f_{y}A_{s}\left(h_{0}-\frac{x}{2}\right) \tag{9}\]  
\[M_{0}=\sigma_{0}\omega_{0}\]0  
In the equations, the parameters have the same meanings as mentioned above.