# Ultimate Compressive Strength of H-Section Stub Columns Subject to Random Fitting Corrosion Damage
## 3 Results and Analyses
### Equivalent Thickness Method
#### 3.3.3 Verification of Equivalent Thickness Method  
According to the Chinese standard [26], the ultimate strength, \(F\), of axially loaded stub H-section columns can be calculated as follows:  
\[F=\varphi Af_{y}, \tag{5}\]  
\[A=\sum\rho_{i}A_{i}, \tag{6}\]  
\[\left\{ \begin{aligned} \varphi=1-a_{1}\lambda_{n}^{2}& \lambda_{n}\leq 0.215,\\ \varphi=\frac{1}{2\lambda_{n}^{2}}[&(a_{2}+a_{3} \lambda_{n}+\lambda_{n}^{2})-\sqrt{(a_{2}+a_{3}\lambda_{n}+\lambda_{n}^{2})^{ 2}-4\lambda_{n}^{2}}\;]&\lambda_{n}>0.215.\end{aligned} \right. \tag{7}\]  
where \(A\) is the cross-sectional area of a column, \(f_{y}\) is the yield strength of steel, \(\varphi\) is the stability coefficient of the column, and \(\rho_{i}\) is the effective section coefficient for a plate of the H-section; \(\lambda_{n}\) is the dimensionless slenderness ratio of the column, \(\lambda_{n}=\frac{\lambda}{\pi}\sqrt{\frac{f_{y}}{E}}\), \(\lambda\) is the slenderness ratio, \(\lambda=\frac{\mu l}{l}=\frac{\mu l}{\sqrt{l_{0}/A_{0}}}\), wherein \(\mu\) is the calculated length factor, \(i\) is the radius of gyration, and \(I_{0}\) is the moment of inertia of the section; \(a_{1}\), \(a_{2}\) and \(a_{3}\) are coefficients corresponding to the respective section categories. For an axial compressive column, the ultimate strength is addressed in the European Standard [27], as follows:  
\[F=\frac{\chi Af_{y}}{\gamma M1}, \tag{8}\]  
\[\left\{ \begin{aligned} \chi=\frac{\chi=1\;\overline{\lambda} \leq 0.2,\\ \frac{1}{\phi+\sqrt{\phi^{2}-\overline{\chi}^{2}}}}\overline{ \lambda}>0.2,\end{aligned} \right. \tag{9}\]\[\phi=0.5\Big{[}1+\alpha\big{(}\overline{\lambda}-0.2\big{)}+\overline{\lambda}^{2} \Big{]}, \tag{10}\]  
where \(\chi\) is the reduction factor for the relevant buckling mode, \(\phi\) is global initial sway imperfection, \(\gamma_{M1}\) is the local safety factor, taken as 1.0, \(\alpha\) is the defect factor, \(\lambda\) is the dimensionless slenderness ratio of the column, \(\overline{\lambda}=\sqrt{\frac{A_{y}}{N_{cr}}}\), and \(N_{cr}\) is the elastic critical force based on the gross section properties for the relevant buckling mode. Figure 15 exhibits the ultimate strength of randomly pitted columns, considering different flange and web thicknesses, based on both the Chinese and European standards. The determination of the equivalent thickness was based on the \(\sigma-\)based equivalent  
Figure 14: Ultimate strength of corroded columns based on pit depth \(\sigma-\)based equivalent thickness: (a) different flange thickness; (b) different web thickness. thickness with \(k=-1.25\). The comparison is divided into two cases: different flange thickness and different web thickness. The prediction of ultimate strength on the basis of the \(\sigma-\)based equivalent thickness did not significantly differ between the Chinese and European standards. However, as the level of pitting intensity increases, both standards tended to overestimate the ultimate strength, leading to a failure risk in the damaged members. This suggests that the current specifications had limitations when used to predict ultimate strength. In the case of columns with different flange thicknesses, as displayed in Figure 15a, the relative errors remained below 5% when the \(DOV\) was less than 9%. However, at a higher \(DOV\) of 11.8%, the relative errors reached about 11% for both the Chinese Standard and European Standard. Conversely, for columns with different web plate thicknesses, both the Chinese and European standards provided more accurate predictions, as depicted in Figure 15b. The maximum relative errors for both standards were 5.3% and 5.7% respectively, occurring at a \(DOV\) of 13.8%. Furthermore, the Chinese and European Standards were employed to verify the tested H-sections with openings presented in reference [24], using the equivalent thickness method. Figure 16 illustrates the ultimate strength of columns with different opening sizes, where \(F_{ut}\) represents the test results.