## 3 Results and Discussion
### Flexural Behaviors of Specimens with Carbon Grids
#### 3.2.2 Behavior of Crack Formation and Stabilization Stages  
Table 7 summarizes the stiffness of the pre-cracking, crack formation, and crack stabilization stages, and Figure 11 illustrates the stiffness of the crack formation and stabilization stages. The stiffness of the pre-cracking stage indicates the stiffness between the beginning of the experiment and the initiation of crack formation. The stiffness of the crack formation stage represents the stiffness between the initiation of crack formation and the point at which cracks stop occurring continuously. The stiffness of the crack stabilization stage indicates the stiffness between the point at which cracks stop occurring continuously and the peak. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Crack Formation**} & \multicolumn{2}{c}{**Peak**} \\ \cline{2-5}  & **Load (kN)** & \
\begin{tabular}{c} **Deflection of** \\ **Mid-Span (mm)** \\ \end{tabular} & **Load (kN)** &
\begin{tabular}{c} **Deflection of** \\ **Mid-Span (mm)** \\ \end{tabular} \\ \hline G1 & 1.61 & 0.37 & 10.92 & 28.52 \\ G2 & 2.25 & 0.36 & 12.69 & 31.82 \\ G3 & 1.85 & 0.36 & 9.10 & 31.77 \\ J1 & 1.47 & 0.32 & 10.05 & 30.71 \\ J2 & 1.95 & 2.24 & 12.30 & 27.18 \\ J3 & 1.51 & 0.52 & 8.97 & 34.60 \\ J4 & 1.28 & 0.24 & 8.94 & 30.03 \\ J5 & 1.10 & 1.27 & 11.58 & 20.24 \\ J6 & 1.92 & 1.57 & 15.33 & 20.10 \\ RC & 1.00 & 1.18 & 14.73 & 14.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Test results. Figure 10: Relationship between the load and mid-span deflection for specimens considering grid longitudinal spacing. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{4}{c}{**Stiffness (N/mm\({}^{\text{2}}\))**} \\ \cline{2-6}  & **Pre-Cracking (1)** & **Crack Formation (2)** & **Crack Stabilization (3)** & **(2)/(1)** & **(3)/(1)** \\ \hline G1 & 4296 & 325 & 334 & 8\% & 8\% \\ \hline G2 & 6257 & 233 & 346 & 4\% & 6\% \\ \hline G3 & 5149 & 193 & 242 & 4\% & 5\% \\ \hline J1 & 4568 & 245 & 287 & 5\% & 6\% \\ \hline J2 & 1146 & - & 415 & - & 53\% \\ \hline J3 & 2908 & 170 & 232 & 6\% & 8\% \\ \hline J4 & 5465 & 268 & 255 & 5\% & 5\% \\ \hline J5 & 1158 & - & 553 & - & 48\% \\ \hline J6 & 1918 & - & 817 & - & 89\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Stiffness of the specimens at pre-cracking, crack formation, and crack stabilization stages. Figure 11: Stiffness in the crack formation and stabilization stages for the specimens: (**a**) G1; (**b**) G2; (**c**) G3; (**d**) J1; (**e**) J3; (**f**) J4; (**g**) J2; (**h**) J5; and (**i**) J6. The stiffness of the crack formation and stabilization stages of the carbon grid-reinforced specimens ranged from 4 to 8% and 5 to 8% of the pre-cracking stiffness, respectively, indicating that the stiffness of the specimens was rapidly reduced by cracking, and the stiffness hardly recovered even after the stabilization of crack formation. Figure 11g-i indicate that among the specimens reinforced with the cross-laminate structured carbon grids, specimens J5 and J6 with the largest cross-sectional areas of the longitudinal strands and specimen J2 with a small strand spacing immediately exhibited the behavior of the crack stabilization stage without the crack formation, unlike the behavior observed in other specimens; in the case of these three specimens, the load significantly increased, and the mid-span deflection increased only marginally because of cracking. The stiffer carbon grids with larger cross-sectional areas or smaller spacing of the strands used in specimens J5, J6, and J2 might affect the behavior of crack formation stage. The elastic modulus of the biaxial warp-knitted structured carbon grids was more than twice as high as that of the cross-laminate structured carbon grids.