# Effect of Corrosion on the Hysteretic Behavior of Steel Reinforcing Bars and Corroded RC Columns
## 3 Experimental Results and Discussion
### Stress-Strain Behavior of Steel Reinforcing Bars under Dynamic Loading
As previously stated, the localized corrosion of steel by means of pitting is characterized by a particular non-uniformity in the sense of the length and perimeter of the material, resulting in the fluctuating of the residual active area for each specimen. As a result, the modelling of the corroded steel in the case of pitting corrosion took into consideration the most unfavorable cases from the tested specimens. The modelling of the non-linear behavior of the steel adopted the hysteretic model of steel as defined in the OpenSees analysis code [44] and the proposed tension and compression envelope curves of corroded rebars is shown in Figure 12. For this purpose, the points \(\mathrm{P_{1}}^{+},\mathrm{P_{2}}^{+},\mathrm{P_{3}}^{+},\mathrm{P_{1}}^{-}, \mathrm{P_{2}}^{-},\mathrm{P_{3}}^{-}\) were defined to establish the hysteretic model for each case (Table 4). The abovementioned points were determined by the envelope curves of the experimental tests. As presented in the previous section of the experimental results, the compressive load bearing capacity of steel bars was significantly affected due to the buckling phenomena related to the wide stirrups spacing (\(\Phi\)8/240 mm). More precisely, in non-corroded conditions the maximum recorded compressive stress was approximately equal to 400 MPa, while rapid degradation was observed as the imposed deformations increased. In corroded conditions, the reduction in the cross-section led to strong and weak bending axes along the steel bar resulting in degrading buckling resistance of corroded bars, which is reflected by the points \(\mathrm{P_{1}}^{-},\mathrm{P_{2}}^{-}\) and \(\mathrm{P_{3}}^{-}\). Figure 11: Differences of the failure mechanism due to pitting corrosion: (**a**) overall view of steel reinforcing bars; (**b**) focus on the failure area of corroded steel bars in contrast to the non-corroded bar (as shown in red cycles). Figure 12: Proposed characteristic points of hysteretic curves in tension and compression. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multirow{2}{*}{**Point**} & \multicolumn{2}{c}{**Non-Corroded Steel**} & \multicolumn{2}{c}{**Steel with**} & \multicolumn{2}{c}{**Steel with**} \\  & & & & **Uniform Corrosion** & & **Pitting Corrosion** \\  & & **E** & \(\sigma\) & \(\varepsilon\) & \(\sigma\) & \(\varepsilon\) & \(\varepsilon\) & \(\Sigma\) \\ \hline \multirow{4}{*}{Anion branch} & \(1\) & \(0.005\) & \(535\) & \(0.0042\) & \(400\) & \(0.0038\) & \(333\) \\  & \(2\) & \(0.018\) & \(575\) & \(0.0148\) & \(428\) & \(0.0059\) & \(352\) \\  & \(3\) & \(0.045\) & \(140\) & \(0.03\) & \(202\) & \(0.018\) & \(115\) \\  & \(1^{\prime}\) & \(-0.004\) & \(-455\) & \(-0.0033\) & \(-345\) & \(-0.0028\) & \(-300\) \\ \cline{1-1}  & \(2^{\prime}\) & \(-0.0165\) & \(-170\) & \(-0.01\) & \(-200\) & \(-0.0083\) & \(-185\) \\ \cline{1-1}  & \(3^{\prime}\) & \(-0.04\) & \(-55\) & \(-0.03\) & \(-100\) & \(-0.03\) & \(-90\) \\ \hline \end{tabular}
\end{table} 
Table 4: Coordinates for the extracted envelope curves of hysteretic models of steel reinforcing bars in non-corroded (Figure 13), uniform corrosion (Figure 14) and pitting corrosion conditions (Figure 15). Figure 13: Hysteretic curve for non-corroded steel reinforcement. The uniaxial Hysteretic material model in the OpenSees is a generic hysteric model that can be used to model the stress-strain behavior of a material or force-displacement behavior of a structural component. The backbone curves in tension and compression can be defined by three points. Figures 13-15 represent the envelope of the hysteretic models for each case of the tested conditions, namely (i) non-corroded (reference) conditions, (ii) uniform corrosion for 9.5% mass loss corresponding to a residual cross-section equal to 181.9 mm\({}^{2}\) and (iii) pitting corrosion, for a theoretical mass loss of 11.7% and mean reduced cross-section equal to 177.7 mm\({}^{2}\).