## 5 Compressive Resistance of SDC Sandwich Wall
### Theoretical Method
To get conservative prediction results, only the equivalent compressive resistance of steel sheets and sleeves are considered and the N\({}_{\text{rein}}\) can be calculated by:  
\[\text{N}_{\text{rein}}=\text{N}_{\text{sheet}}+\text{N}_{\text{ sleeve}}=\text{f}_{y,3}\text{A}_{\text{sheet}}+\text{f}_{y,4}\text{A}_{\text{ sleeve}} \tag{21}\]  
\[\text{A}_{\text{sheet}}=\text{n}\frac{\pi\text{n}_{\text{sheet}}^{2}\text{t}_ {\text{sheet}}}{\text{S}} \tag{22}\]  
\[\text{A}_{\text{sleeve}}=2\text{n}\frac{\pi\big{(}\text{r}_{\text{sleeve},2}^{ 2}-\text{r}_{\text{sleeve},1}^{2}\big{)}\big{(}\text{t}-2\text{t}_{\text{sp}}- 2\text{t}_{\text{sheet}}\big{)}}{\text{S}} \tag{23}\]  
where A\({}_{\text{sheet}}\) and A\({}_{\text{sleeve}}\) denote the equivalent cross-sectional area of the steel sheet and sleeve; r\({}_{\text{sheet}}\) and t\({}_{\text{sheet}}\) denote the radius and thickness of the steel sheet; and r\({}_{\text{sleeve},1}\) and r\({}_{\text{sleeve},2}\) denote the inner and outer radius of the sleeve  
(4)  
The compressive resistance of steel plates can be calculated by adding the resistance of steel face plate and steel side plate:  
\[\text{N}_{\text{s}}=\sigma_{\text{cr}}\text{A}_{\text{surf}}+\text{f}_{y,2} \text{A}_{\text{side}} \tag{24}\]  
According to the suggestion of [PERSON] [48], the yield stress of steel face plate can be calculated as follows:  
\[\mathrm{N_{rub}}\ =\ \sigma_{\mathrm{rub}}\mathrm{A_{rub}}\ =\ \mathrm{E_{ rub}}\varepsilon_{\mathrm{rub}}\mathrm{A_{rub}}\]0  
where E\({}_{\text{s}}\) denotes the elastic modulus of the steel; u denotes the effective length coefficient, and its value can be determined as 0.7 for safety reserves. To demonstrate Equation (25) and investigate the effect of the plate slenderness ratio on buckling performance of SCS wall, buckling analysis and ultimate stress state analysis was carried out by [PERSON] [45] and the following formula was proposed to compute the buckling stress of steel face plates:  
\[\sigma_{\text{cr}}=\left\{ \begin{array}{cc}\text{f}_{y},&\text{s}/\text{t }_{\text{s}}\leq\pi\sqrt{\text{E}_{\text{s}}/(5.88\text{f}_{y})}\\ \frac{\pi^{2}\text{E}_{\text{s}}}{5.88(\text{f}_{\text{s}}/\text{t}_{\text{s} })},&\text{s}/\text{t}_{\text{s}}>\pi\sqrt{\text{E}_{\text{s}}/(5.88\text{f} _{y})}\end{array} \right. \tag{26}\]  
As can be seen in FE model, although the boundary conditions of steel face plates in SCS wall and SDC wall are not the same due to inner rubber layer and steel sheets, the local buckling modes of the steel face plates in these two types of composite walls are similar: The steel face plates are restrained and forced by inner concrete core and steel sheets, which can be seen as rigid media, to form away from the concrete [36]. Thus, Equation (26) can be utilized for calculating the buckling stress of steel face plates. (5)  
The compressive resistance of concrete core can be calculated as follows:  
\[\text{N}_{\text{c}}=\alpha_{\text{c}}\text{f}_{\text{c}}\text{A}_{\text{c}} \tag{27}\]  
where \(\alpha_{\text{c}}\) denotes the reduction factor of concrete considering the weakening effect caused by the ratio of the thickness of steel plates to the spacing of binding bars and rubber layer;  
In the case of the SCS wall, \(\alpha_{\text{c}}\) can be determined by the \(\beta\) and \(\beta_{2}\), expressed as Equation (15); However, in terms of the SDC wall, the confinement on concrete provided by external steel plates is modest due to the rubber layer sandwiched between them, which means that \(\beta_{2}\) can be removed. Instead, lateral cracksin the concrete core expand more easily because of the lack of restraint of bilateral steel plates, which leads to reduced compressive resistance of composite walls. This reduction is determined by the relationship of thicknesses of rubber layer, steel face plates, and concrete core. According to the numerical results, \(\mathrm{t_{r}}\) and \(\mathrm{t_{sp}}\) are more influential towards the reduction than \(\mathrm{t_{c}}\).