# Ultimate Compressive Strength of H-Section Stub Columns Subject to Random Fitting Corrosion Damage
## 4 Discussion
The difference between the average cross-section and the minimum cross-section became more and more significant for the higher \(DOV\), as shown in Figure 19. This meant that in the case of serious pitting corrosion, the overestimation in predicting the ultimate strength based on the average thickness may become more excessive. In fact, for the double-flange corrosion in Figure 19a, at the \(DOV\) 4.8%, the area loss ratios of the average and minimum cross-sections were 3.8% and 9.6%, respectively. At the \(DOV\) 13.8%, the area loss ratios of two types of cross-sections were 10.8% and 17.9%, respectively. For double-flange combined corrosion in Figure 19b, at the \(DOV\) 4.8%, the area loss ratios of the average and minimum cross-sections were 4.8% and 11.8%, respectively. At the \(DOV\) 13.8%, the area loss rates of two types of cross-sections were 13.8% and 20.9%, respectively. In addition, it seems difficult to determine the minimum cross-section under random pitting corrosion damage due to variation in pitting features in the size, shape and location. Figure 19a shows that in the case of the double-flange corrosion, a larger residual cross-section occurred at the \(DOV\) 11.8% despite its higher level of pitting damage compared with the \(DOV\) 8.8%. This influenced the strength reduction concurrently with a significant variation in the strength of randomly pitted structures [25]. Local buckling may occur in the flange and web of H-section columns if the width-to-thickness ratio of a plate is \(h_{0}/l_{w}>33\varepsilon_{k}\) for the web, and \(b_{f}/t_{f}>9\varepsilon_{k}/\alpha\) for the flanges (where \(\varepsilon_{k}=\sqrt{235/f_{y}}\) and \(\alpha=0.5\)) in line with the European Standard [27]. Based on the equivalent thickness determined by Equation (4), the width-to-thickness ratios of all the randomly pitted columns were checked. It was found that the resistance of local buckling was good enough for the web of the columns, but the thinner flanges may not meet the local buckling criteria due to pitting corrosion. For example, in the column with a flange thickness of 7.5 mm (H7.5 \(\times\) 7.5\(-\)DF + W\(-\)13.8%), the limitation of local buckling in the intact column  
Figure 19: Comparison between the average and minimum cross-sectional area of a corroded column (H11.5 \(\times\) 7.5): (a) double-flange corrosion; (b) double-flange combined corrosion. was \(b_{f}/t_{f}=9\epsilon_{k}/\alpha=14.0\), while the width-to-thickness ratio of the pitted column was actually 14.8, signifying that the local buckling took place in the damaged column. Figure 20 illustrates the load-displacement curves of the column obtained from the models with random pitting corrosion and the equivalent thickness. The ultimate load of the random pitting model was \(F_{u}=1061\) kN, which was larger than that of the equivalent thickness model, \(F_{w}=1021\) kN. There was no significant disparity in the load-displacement behavior of the two types of models before the ultimate state. However, at the post-collapse stage, the random pitting model showed a significantly better resistance to axial deformation. The outstand flange of an H-section column can be treated as a rectangular plate with three sides supported and one side free. The local buckling stress, \(\sigma_{cr}\), can be decided by  
\[\sigma_{cr}=\left(0.425+\frac{b^{2}}{a^{2}}\right)\frac{\pi^{2}t^{2}E}{12(1- \
u^{2})b^{2}}. \tag{13}\]  
where \(a\) is the length of the H-section column, \(b\) is the length of the outstand flange, \(b_{f}\), and \(t\) is the thickness of the flange, \(t_{f}\). Combining Equation (4) with Equation (13), the elastic buckling load (\(F_{cr}=A_{e}\sigma_{cr}\), \(A_{e}\) is the cross-sectional area in terms of the \(\sigma-\)based equivalent thickness) can be determined to be 1006 kN.