# Ultimate Compressive Strength of H-Section Stub Columns Subject to Random Fitting Corrosion Damage
## 3 Results and Analyses
### Ultimate Strength Assessment  
This section aims to examine the ultimate strength assessment of randomly pitted columns. Three types of sections of H7.5 \(\times\) 7.5, H11.5 \(\times\) 7.5 and H11.5 \(\times\) 9.5 were considered. The first two sections were designed to clarify the influence of flange thickness under the constant web thickness of 7.5 mm. The latter two sections were used to explore the impact of web thickness under the constant flange thickness of 11.5 mm. Stochastic simulations were employed to generate numerous numerical models of columns with random pitting corrosion, thoroughly considering the random nature of size, shape and distribution of corrosion pits. The ultimate strength of damaged columns was evaluated, and the results were further used to verify the existing standards for predicting the ultimate strength of plated structures. In addition to the ultimate strength obtained from nonlinear finite element (FE) analyses, results from both the Chinese and European Standards were considered, based on the equivalent thickness determined by Equation (4). Figure 17 presents the results of the stochastic simulations alongside the current standards. Specifically, Figure 17a-c display, respectively, the results for columns with three types of sections, consolidated in Figure 17d. Figure 17: Ultimate strength of columns with random pitting corrosion: (**a**) H7.5 \(\times\) 7.5; (**b**) H11.5 \(\times\) 7.5; (**c**) H11.5 \(\times\) 9.5; and (**d**) collected data. There are limitations in the current standards to predict the ultimate strength of randomly pitted columns based on the equivalent thickness, as depicted in Figure 17. The standards demonstrated better predictions for columns with relatively thinner plate thickness. From Figure 17a-c, a point of intersection between the results of stochastic simulations and standards is observed at a certain \(DOV\) for each section, indicating a correlation with column section size. For the H7.5 \(\times\) 7.5, H11.5 \(\times\) 7.5 and H11.5 \(\times\) 9.5 sections, these \(DOV\) values were 7.8%, 6.5% and 5.9%, respectively. Interestingly, this trend suggests that as the plate element of the column became thicker, the corresponding \(DOV\) value decreased, signifying a decline in range of application of the current standards. Specifically, compared to the H11.5 \(\times\) 7.5, the increase in the flange thickness of the H7.5 \(\times\) 7.5 decreased the upper range of application from \(DOV\) 7.8% to 6.5%. Similarly, increasing the web thickness of the H11.5 \(\times\) 9.5 further reduced the range to 5.9%. Overall, both the current standards consistently exhibited a conservative prediction of the ultimate strength of randomly pitted columns within their range of application, with a similar prediction accuracy. Furthermore, a regression analysis was conducted to derive an exponential function based on the stochastic simulation results of each type of section, as presented in Figure 17 a-c. The observed function exhibited a similar trend under different sizes of columns. Hence, these findings, along with the results obtained from the existing empirical formula, are synthetically illustrated in Figure 17d. The CCS Specification [28] utilizes an adjustment coefficient to account for the impact of random pitting corrosion on the ultimate strength of plates under uniaxial longitudinal compression, as follows:  
\[\frac{F_{u}}{F_{u0}}=1-54.716 DOV^{3}+14.804 DOV^{2}-3.298 DOV,\ DOV\leq 10\%. \tag{11}\]  
Moreover, the first author proposed a power function, based on a set of stochastic simulations, to predict the ultimate strength of unstiffened plates affected by random pitting damage [25], defined as  
\[\frac{F_{u}}{F_{u0}}=1-0.04749(DOV\times 100)^{0.6459}. \tag{12}\]  
It should be emphasized that the prediction provided by Equation (13) represents the mean value of the ultimate strength of unstiffened plates with random pitting corrosion damage, which follows a normal distribution in the size.