## 3 Results and Discussion
### Comparison between the Experimental and Calculated Results  
The maximum load did not increase as the tensile capacity by the longitudinal strands of the carbon grid-reinforced specimens increased (Figure 15). Particularly, in the case of specimens reinforced with the cross-laminate structured carbon grids, the maximum load did not increase in proportion to the tensile capacity by the longitudinal strands because all specimens reached the maximum load by mortar crushing. As shown in Table 7, the strains of the longitudinal strands under the maximum load ranged from 38 to 82% of the tensile strain. Particularly, the longitudinal strands of the cross-laminate structured carbon grids exhibited a smaller strain than the longitudinal strands of the biaxial warp-knitted structured carbon grids. On the other hand, the maximum load tended to be higher in the specimens reinforced with small cross-sectional areas and spacings of the longitudinal strands but high tensile strength compared with the specimens reinforced with large cross-sectional areas and spacings of the longitudinal strands but low tensile strength. Figure 14: Idealized load and mid-span deflection relationship. Figure 15: Relationship between carbon grid tensile force and maximum load. Figure 16 presents the crack and flexural strength ratio of experimental and calculation results, considering the tensile force by the longitudinal strands. The crack strength ratio ranged from 0.77 to 1.35, and the flexural strength ratio ranged from 0.71 to 1.33. The maximum load was generally higher than the flexural capacity. Particularly, in the case of specimens reinforced with the biaxial warp-knitted structured carbon grids with a relatively low tensile capacity, the maximum load was more than 1.0 times higher than the flexural capacity. In the case of specimen G2, which exhibited a poor bond between the carbon grid and mortar, the maximum load was 1.3 times higher than the flexural capacity, indicating that the flexural capacity was conservatively evaluated. Flexural stiffness is usually calculated using the moment of inertia related to the section states: the gross moment of inertia, \(I_{g}\), for the uncracked section and effective moment of inertia, \(I_{e}\), for the cracked section. It is known that in the case of TRC members, the effective moment of inertia becomes lower compared with that of RC members because of the different material properties of FRP reinforcement. Therefore, researchers [7; 25] proposed the formation of an effective moment of inertia which modified [PERSON]'s equation for RC members [26] based on experimental results using glass fiber-reinforced plastic (GFRP) bars, as presented in Equation (1). \[I_{e}\frac{I_{cr}}{1-\left(\frac{M_{cr}}{M_{a}}\right)^{2}\left[1-\frac{I_{ cr}}{I_{g}}\right]} \tag{1}\]  
where, \(I_{cr}\) is the cracked transformed moment of inertia (mm\({}^{4}\)) of the following Equation (2), \(M_{cr}\) is the cracking moment (Nimm), and \(M_{a}\) is the maximum load moment for the deflection calculation (Nmm). \[I_{cr}\ =\ \frac{bd^{3}}{3}k^{3}+nA_{CFRP}d^{2}(1-k)^{2} \tag{2}\]  
where, \(b\) is the width (mm), \(d\) is the effective depth (mm), \(n\) is the elastic modulus ratio of the carbon grid and concrete, \(A_{CFRP}\) is the longitudinal strand area (mm\({}^{2}\)), and \(k\) is the normalized neutral axis depth of the cracked section. In all specimens, the calculated stiffness of the cracked sections using \(I_{e}\) in Equation (1) was revealed to be 1.5 times higher than the stiffness of the crack formation stage from the experimental results (Table 9 and Figure 17). Here, the calculated crack and flexural moments in Table 4 were used for \(M_{cr}\) and \(M_{a}\), respectively. Meanwhile, the calculation (Table 9) showed that \(I_{e}\) and \(I_{cr}\) were similar, and the calculated stiffness of the cracked  
Figure 16: Strength ratio of experimental and calculation results according to carbon grid tensile force: (**a**) crack; and (**b**) flexural strengths.