## 4 Calculation Formula of Shear Behavior Capacity  
In Section 3, an in-depth investigation was conducted on the influence of multiple factors on the shear behavior of strengthened beams. Through the analysis of the finite element model, it was found that these factors are closely related to the strain of the FRP grid. The stress distribution and deformation capacity of the FRP grid under stress have a significant impact on the shear contribution of the composite strengthening system. Figure 13: Effect of shear reinforcement ratio. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Beam ID**} & \multirow{2}{*}{\begin{tabular}{c} **Reinforcement** \\ **Ratio (\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Ultimate** \\ **Load** \\ **(kN)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Change** \\ **Rate (\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **FRP Grid** \\ **Effective** \\ **Strain** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Change** \\ **Rate** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Failure** \\ **Mode** \\ \end{tabular} } \\ \hline B-1 & 0.19 & 328.27 & & 0.0054 & & SF \\ B-S1 & 0.15 & 320.47 & \(-\)2.38 & 0.0050 & \(-\)7.85 & SF \\ B-S2 & 0.13 & 313.48 & \(-\)4.51 & 0.0047 & \(-\)13.03 & SF \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Effect of shear reinforcement ratio on reinforced beams. So far, based on the research on the calculation models and methods of shear behavior capacity, scholars from various countries have proposed a variety of theoretical models. Among them, the truss model is the most widely used due to its clear mechanical model, simple calculation, and good universality. China's structural design code [18] also adopts this model, calculating the shear behavior capacity of the inclined section of the beam as the superposition of the shear contributions of concrete and stirrups. This model is also applicable to RC beams strengthened with FRP grid-PCM composites, and the shear behavior capacity is calculated as the superposition of the shear contributions of concrete, stirrups, the FRP grid, and PCM. Currently, the basic forms used to calculate the behavior capacity of beams shear-strengthened with FRP grids are quite similar. This paper refers to the calculation formula proposed in the ACI 440.2R-08 code [22] to quantify the contribution of the FRP grid in the shear process. Section 2.2.1 analyzes that both the PCM and concrete belong to cementitious composite materials. Therefore, the calculation method used for the shear resistance contribution of the PCM is the same as that for concrete. Due to the unclear influence mechanism of FRP strengthening on the shear contributions of concrete and stirrups and the limited research on quantifying the shear contributions of each part of the original beam, the shear contribution of the original beam in this paper is still calculated according to China's code. Based on the above analysis, in this section, a mathematical model of the effective strain of the FRP grid is established using regression analysis. Then, this model is substituted into the ACI 440.2R-08 code to quantify the shear contribution of the FRP grid. Finally, combined with the shear contributions of other parts, the shear behavior capacity formula for RC beams strengthened with FRP grid-PCM composites is derived, aiming to provide an accurate theoretical basis for practical engineering applications.