# Delaying the Occurrence of Bar Buckling in RC Columns Confined with SRG Jacketing
## 4 Analysis of the Axial and Lateral Response Due to SRG Confinement
### Axial Response Indices  
The average confining pressure exerted by the SRG-jacketing system when applied to RC members is obtained as the average lateral stress developing in the two principal directions of the cross section. Similar to the FRP jacketing [8; 23; 29], the average confining pressure is  
\[\sigma_{lat}=\frac{1}{2}\left(\underbrace{\alpha^{SRG}\rho_{\rm v}^{SRG}E_{f} \epsilon_{jeff}}_{SRG\ confinement}+\underbrace{\alpha^{st}\rho_{\rm v}^{st}f ^{st}}_{strirup\ confinement}\right) \tag{1}\]  
The first and second part of Equation (1) correspond to the contribution of the SRG jacket and stirrups, respectively. Term E\({}_{\rm f}\) is the modulus of elasticity of steel cord (i.e., 190 GPa), and \(\epsilon_{\rm eff}\) is the effective tensile strain the jacket develops. The volumetric ratios \(\rho_{\rm v}\)\({}^{\rm i}\) of the transverse reinforcements are as follows: for the SRG \(\rho_{\rm v}\)\({}^{\rm SRG}\) = 2 nt\({}_{\rm g}\) (b + h)/(bh) where n is the number of layers and t\({}_{\rm s}\) is the equivalent layer thickness per unit width (see Section 2.2) and b, h are the cross section sides (i.e., here b = h = 200 mm); for stirrups \(\rho_{\rm v}\)\({}^{\rm st}\) = \(A_{\rm st}\) (b\({}_{\rm o}\) + h\({}_{\rm o}\))/(b\({}_{\rm o}\)h\({}_{\rm o}\)s) where A\({}_{\rm st}\) is their total sectional area (i.e., here 2 \(\times\)\(\pi\)\(\times\)\(\delta^{2}\)/4 = 56.5 mm\({}^{2}\)) and b\({}_{\rm o}\), h\({}_{\rm o}\) the confined core dimensions [i.e., here b\({}_{\rm o}\) = h\({}_{\rm o}\) = 200 - 2 \(\times\) (c + D\({}_{\rm st}\)) = 148 mm]. The term \(\alpha^{\rm i}\) is the confinement effectiveness factor of the transverse reinforcement; for the SRG jacket \(\alpha^{\rm SRG}\) = 0.63 as it is defined by Equation (A1) in Appendix A[23]. The term \(\alpha^{\rm st}\) defined according to EC8-Part I [30] is calculated equal to 0.07, 0.16, 0.19 for the \(\mathcal{Q}\)6/150, \(\mathcal{Q}\)6/75 and \(\mathcal{Q}\)6/50 stirrups respectively. The confined concrete strength f\({}_{\rm cc}\) and the corresponding strain \(\epsilon_{\rm cc}\) are calculated from the confinement model of [PERSON] et al. [31] as follows (f\({}_{\rm o}\) is the unconfined concrete strength):  
\[f_{cc}=f_{o}+3\sigma_{lat} \tag{2}\]  
\[\epsilon_{cc}=0.002\bigg{(}1+15\frac{\sigma_{lat}}{f_{o}}\bigg{)} \tag{3}\]  
The failure strain of confined concrete, \(\epsilon_{\rm ccu}\), corresponding to a compression strength reduction in excess of 15% is obtained from [23]:  
\[\epsilon_{ccu}=0.0035+0.075\bigg{(}\frac{2\sigma_{lat}}{f_{c}}-0.1\bigg{)} \geq 0.0035 \tag{4}\]  
Equations (1) and (2) are used to predict the deformation indices measured during the testing procedure. From Equation (2), lateral pressure \(\sigma_{\rm lat}\) is estimated by using f\({}_{\rm cc}\) values from column (1) of Table 3 and f\({}_{\rm o}\) = 29 MPa. The term \(\sigma_{\rm lat}\)/f\({}_{\rm o}\) shown in column (4) of Table 3 represents a measure of the confining pressure magnitude provided by the SRG jacket as per the unconfined concrete strength; it ranges from 3% for low SRG stiffness (i.e., one layer 4 cords/in) to 17% for increased SRG stiffness (i.e., 2 layers of 12 cords/in). The \(\epsilon_{\rm cc}\)P and \(\epsilon_{\rm ccu}\)P values (i.e., the superscript p indicates the predicted values using Equation (3,4)) are compared with the experimental values \(\epsilon_{\rm cc}\) and \(\epsilon_{\rm ccu}\) (see columns (2) and (3) in Table 3), respectively. The \(\varepsilon_{\rm cc}\)P/\(\varepsilon_{\rm cc}\) and \(\varepsilon_{\rm ccu}\)P/\(\varepsilon_{\rm ccu}\) ratios (columns (5) and (6) in Table 3, respectively) indicate that Equation (3) is conservative, and Equation (4) is less conservative with an exception of columns L2C, which show a larger difference between experimental values \(\varepsilon_{\rm cc}\) and \(\varepsilon_{\rm ccu}\). Given the lateral pressure \(\sigma_{\rm lat}\), the effective strain of the SRG jacket \(\varepsilon_{\rm jeff}\) is estimated using Equation (1) (see column (7) of Table 3).