# Experimental Study on Flexural Capacity of Corroded RC Slabs Reinforced with Basalt Fiber Textile
## 4 Flexural Capacity Analysis  
### Theory Assumptions  
From the test results presented in Section 3, it can be seen that the tensile reinforcement yielded when specimens reached the ultimate load, with subsequent damage to the strengthening materials. In this study, the obvious debonding phenomenon of specimens mainly occurred at the post-peak stage. This indicates that the corroded RC slabs and the strengthening layers were both satisfied with the plane section assumption. Therefore, the simplified computing model and formula based on that assumption could be obtained as shown in Figure 17 and Equation (3). \[\frac{\varepsilon_{\text{c,t}}}{\xi h_{0}}=\frac{\varepsilon_{\text{s}}}{(1- \xi)h_{0}}=\frac{\varepsilon_{\text{r}}}{\xi h_{\text{r}}} \tag{3}\]  
where \(\varepsilon_{\text{c,t}}\) denotes the compressive strain of concrete at the top of specimen compression zone, \(\varepsilon_{\text{s}}\) denotes the tensile strain of steel reinforcements, \(\varepsilon_{\text{r}}\) denotes the tensile strain of strengthening layer, \(\xi\) denotes the relative depth of compression zone, \(h_{0}\) denotes the effective height of test specimen, and \(h_{\text{r}}\) denotes the distance between the strengthening layer center and the compression zone edge. According to the load-displacement relationship of the test specimens, it can be regarded that after the tensile reinforcing bars yielded at the peak loads, the concrete compression zone was reached at the elastic-plastic stage, and the strain at the top of the compression zone varied within \(\varepsilon_{0}\leq\varepsilon_{\text{c,t}}\leq\varepsilon_{\text{cu}}\). The corresponding stress information can be obtained by using the equations suggested by [PERSON] et al. [45] as follows:  
\[\sigma_{\text{c}}=f_{\text{c}} \tag{4}\]  
\[\sigma_{\text{s}}=f_{\text{y}} \tag{5}\]  
\[\sigma_{\text{r}}=E_{\text{r}}\varepsilon_{\text{r}}=E_{\text{r}}\frac{1-\xi} {\xi h_{0}}\varepsilon_{\text{c,t}}h_{\text{r}} \tag{6}\]  
where \(\sigma_{\text{c}}\) denotes the concrete compressive stress under compressive strain \(\varepsilon_{\text{c}}\), \(f_{\text{c}}\) denotes the axial compressive strength, \(\varepsilon_{0}\) and \(\varepsilon_{\text{cu}}\) denotes the peak and ultimate compressive strain of concrete, which is generally defined as the values for 0.002 and 0.0033, respectively, \(\sigma_{\text{s}}\) denotes the tensile stress under tensile strain \(\varepsilon_{\text{s}}\), \(f_{\text{y}}\) denotes the yield strength of steel reinforcement, and \(\sigma_{\text{r}}\) and \(E_{\text{r}}\) are the tensile stress and elastic modulus of the strengthening layer, respectively. According to the calculation model (Figure 17), the mechanical equilibrium equation in the horizontal direction and the bending moment equilibrium equation around the strengthening layer center could be obtained by using the equations suggested by [PERSON] et al. [46] as follows:  
\[f_{\text{c}}b\xi h_{0}\bigg{(}1-\frac{\varepsilon_{0}}{3\varepsilon_{\text{c, t}}}\bigg{)}-f_{\text{y}}A_{\text{s}}-E_{\text{r}}\frac{1-\xi}{\xi h_{0}} \varepsilon_{\text{c,t}}h_{\text{r}}A_{\text{r}}=0 \tag{7}\]  
Figure 17: Simplified computation model for structural flexural capacity calculation. \[M_{\text{u,cal}}=f_{\text{c}}b\xi h_{0}\left(1-\frac{\varepsilon_{0}}{3\varepsilon_ {\text{c,t}}}\right)\left\{h-\zeta h_{0}\left[1-\frac{\frac{1}{12}\left(\frac{ \varepsilon_{0}}{\varepsilon_{\text{c,t}}}\right)^{2}}{1-\frac{\varepsilon_ {0}}{3\varepsilon_{\text{c,t}}}}\right]\right\}-f_{\text{y}}A_{\text{s}}a_{ \text{s}} \tag{8}\]  
where \(M_{\text{u,cal}}\) denotes the calculated flexural capacity of test specimen, \(A_{\text{s}}\) denotes the total cross-sectional area of tensile reinforcing bars, \(A_{\text{r}}\) denotes the cross-sectional area of strengthening layers, and \(a\) denotes the distance between the strengthening layer center and the centroid of steel bar cross section.