## 4 Calculation for Axial Compressive Bearing Capacity
### Steel Plate Resistance
#### 4.1.3 Effect of Local Buckling on Bearing Capacity  
The critical local buckling stresses of specimen HGW-1 and HGW-3 were calculated using Equation (11), and the stress of specimen HGW-2 was calculated using Equation (19). The calculated values are shown in Table 3. For specimen HGW-1, the calculated buckling stress is smaller than the yield stress, but the buckling of the steel plate in the test is later than the steel yield, mainly because the concrete plays a role in the inhibition of the out-of-plane deformation of the steel plate. Until the concrete reaches the ultimate compressive strain at the ultimate load, the concrete inhibition effect on the steel plate decreases rapidly, and the buckling of the steel plate takes place immediately. For specimen HGW-2, owing to the concrete inhibition effect on the steel plate, the actual local buckling stress is far higher than the calculated buckling stress, which was originally larger than the yield stress, so the test buckling stress value does not appear in Table 3. Therefore, since the buckling is later than the yield for specimens HGW-1 and HGW-2, the effect of local buckling on the bearing capacity is unthinkable in the calculation of the axial compressive bearing capacity.  
For specimen HGW-3, the calculated buckling stress is in good agreement with the test buckling stress shown in Table 3, and both buckling stresses are less than the yield stress, which means that local buckling occurs earlier than the yield of the steel plate. Due to uniform compression, the steel plate bends slightly after buckling, and the deflection in the central section is greater than that at the two edges, and the flexural shortening in the central section outweighs that at the two edges, which means that the stress redistribution occurs with greater stress at the two edges, and less stress in the central section. After local buckling of the steel plate occurs, the stress in the central section no longer increases, and the stress at the two edges continues to increase, until the yielding of the steel plate. So, the evaluation criterion for whether the steel plate reaches the ultimate load, is whether the plate edge yields or not. As shown in Figure 11, the plate stresses in the range of approximately \(b_{e}/2\) at the two edges, only reach yield strength \(f_{y}\), when the effective width is introduced, in order to present an effective action of the steel plate at the ultimate load. According to [PERSON] [12], the ratio of the effective width to width b, can be calculated by the following equation:  
\[\frac{b_{e}}{b}=\sqrt{\frac{\sigma_{\sigma}}{f_{y}}}\Bigg{[}1-0.22\sqrt{\frac {\sigma_{\sigma}}{f_{y}}}\Bigg{]} \tag{20}\]  
where \(b_{e}\) is the effective width, \(b\) is the actual width, and \(\sigma_{u}\) is the average stress in the limit state.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specimen No.**} & **Calculated Buckling** & **Test Buckling** & **Yield Stress** & \\  & **Stress (N/mm\({}^{2}\))** & **Stress (N/mm\({}^{2}\))** & **(N/mm\({}^{2}\))** & **\(\eta\)** \\ \hline HGW-1 & 133 & 333 & 333 & - \\ HGW-2 & 689 & - & 333 & - \\ HGW-3 & 302 & 311 & 376 & 0.719 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Buckling stress of specimens.  
The buckling influence coefficient of the steel plate \(\eta\) is defined as the ratio of effective width \(b_{e}\) to width \(b\), and is introduced to the axial compressive bearing capacity formula of the steel plate.  
\[N_{\mathrm{s}}=b_{e}t_{1}f_{y}=\eta bt_{1}f_{y} \tag{21}\]  
For specimen HGW-3, the calculated \(\eta\) value is 0.719, shown in Table 3.