## 3 Analysis of Factors Affecting Flexural Performance of Reinforced Beams
### Effect of FRP Grid Generator on Flexural Performance of Reinforced Beams  
To investigate the effect of FRP grid geometry on the flexural performance of the reinforced beams, BG-L-PCM is used as the reference beam, and the rest of the parameters remain unchanged. Controlling the total meridional cross-sectional area \(A_{f}\) = 135 mm\({}^{2}\) and the total cross-sectional area in the warp direction \(A_{f}\) = 1.260 mm\({}^{2}\), the grid spacing and single limb width are adjusted, respectively, and the thickness of all grids is 3 mm. Two different grid spacings are added; its warp and welt direction spacing are 50 \(\times\) 100 and 100 \(\times\) 50 mm, respectively, as shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Beam ID**} & \multicolumn{4}{c}{**FRP Grid**} & \multirow{2}{*}{**Yield**} & \multirow{2}{*}{**Ultimate**} & \multirow{2}{*}{**Load (kN)**} & \multirow{2}{*}{**Ultimate Load**} & \multirow{2}{*}{**Diffection**} & \multirow{2}{*}{**Value (mm)**} & **FRP Grid** & **Failure** \\  & & & & & & & & \\ \cline{2-7}  & **Blackic** & **Tensile** & **Load (kN)** & **Load (kN)** & **Increase Rate (\%)** & **Value (mm)** & **Strain** & **Mode** \\ \hline B3O50-50 & 17.4 & 455.6 & 164.4 & 211.8 & 51.5 & 21.14 & 0.0163 & D + FR \\ C3O50-50 & 41 & 492 & 174.7 & 214.9 & 53.7 & 11.65 & 0.0073 & D \\ G3O50-50 & 21 & 501 & 165.2 & 216.9 & 55.2 & 18.57 & 0.0203 & D + FR \\ \hline \hline \end{tabular}
\end{table}
Table 5: Effect of FRP grid material types on reinforced beams.  
Figure 9: Effects of FRP grid material types on load–midspan deflection curve.  
In this subsection, a total of three reinforced beams with different geometries are subjected to finite element analysis, and the load-midspan deflection curves of the reinforced beams are obtained, as shown in Figure 11. The characteristic loads, midspan deflection values, and damage modes are shown in Table 5. As can be seen from Figure 11, the simulated beams show a clear three-stage variation, and the curves of the three beams match well in the first two stages. In the third stage, it is found that the deflection values corresponding to the ultimate load of beams B3O50-100 are the greatest, those of beams B3O100-50 are the second greatest, and those of beams B3O50-50 are the lowest. From Table 6, it can be seen that when the warp spacing of the FRP grid was increased from 50 mm to 100 mm, the ultimate load of beam B3O50-100 decreased by 0.2 kN compared to that of beam B3O50-50, but the deflection increased by 3.79 mm. When the latitudinal spacing of the FRP grid was increased from 50 mm to 100 mm, the ultimate load of beam B3O100-50 compared to that of beam B3O50-50 increased by 2.5 kN. Two damage modes occurred in the simulated beams: the FRP grid was pulled off after the composite layer peeling damage occurred in beam B3O50-50, and the concrete crushing damage occurred in the compression zone between beam B3O50-100 and beam B3O100-50. This indicates that when the grid spacing is increased, the bonding area between the FRP grid and the PCM increases, the composite layer has better integrity, and the flexural reinforcement effect is somewhat improved.  
Figure 11: Effects of grid geometry on load–midspan deflection curve.  
Figure 10: The geometry of the FRP grid.  
Calculation Formula of Flexural Bearing Capacity of RC Beams Strengthened with FRP Grid and PCM Composite  
From the numerical simulation results of FRP grid-PCM-composite-reinforced concrete beams in Section 3, it can be seen that the simulated beams have a total of three damage modes: (1) concrete crushing damage in the compression zone; (2) FRP grid pulling damage; (3) FRP grid-PCM composite layer peeling damage. The research on the flexural capacity of the first two damage modes is more systematic and comprehensive, but the research on the flexural capacity of the third damage mode is less systematic and comprehensive, so research on the calculation model of the bending capacity of composite layer peeling will be carried out in this section.