## 4 Flexural Capacity Prediction of SCS Slabs  
Yield-line theory is a method to evaluate the flexural capacity of SCS sandwich slabs. Figure 21 shows a schematic view of the fracture pattern of yield lines in a four edge simply supported slab subjected to a concentrated patch load based on the virtual work principle, the flexural capacity can be calculated using the relation proposed by [PERSON] and [PERSON] [24]. \[F_{p}=8m_{pl}\left(\frac{L_{s}}{L-c}-0.172\right) \tag{2}\]  
where \(m_{pl}\) is the plastic moment capacity per unit length along the yield-line, \(c\) is the side length of the loading area, \(L_{s}\) is the dimension of the slab specimens, which here is 1200 mm; \(L\) is the span between the supports. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specimen** & **i (\%)** \\ \hline SCSNWC & 4.17 \\ SCSLWC & 8.13 \\ SCSSLWC & 9.78 \\ J-hook NWC [24] & 13.6 \\ J-hook LWC [24] & 9.20 \\ J-hook SLWC [24] & 10.3 \\ Stud bolt NWC [29] & 6.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: ductility of specimens. The plastic moment resistance of a fully composite SCS sandwich section can be determined by assuming a rectangular plastic stress block of depth \(x_{c}\) for the concrete and the tension and compression stress blocks for the face plates, as shown in Figure 22. The concrete beneath the plastic neutral axis (PNA) is assumed to be cracked. The forces in the steel plates depending on the material yield strength and shear strength of the connectors in resisting interfacial shear stresses between the steel plate and the concrete core. It is also assumed that sufficient shear connectors are provided to prevent local buckling of the compression steel plate [24; 29; 42]. Since the steel plates are of equal thickness and strength in this particular study, it is assumed \(t_{c}=t_{t}=t\) in Figure 22. The steel plates in SCS sandwich can be treated as the reinforcement in reinforce concrete. The SCS sandwich slab will deflect extensively and wide cracks are developed in the final loading [8]. After yielding of tension steel plate, the cracking of the concrete will continue to rise towards the compression steel plate. In this case, the strain at the bottom plate is enormous compared to the top steel plate [24]. The moment capacity of the slab is reached when the neutral axis moves near to the lower surface of the compression plate (i.e., \(x_{c}\approx 0\)), and the bottom plate is fully yielded. Therefore, in the case of \(t_{t}=t_{c}=t\), the moment of resistance of the sandwich section becomes [24]:  
\[M_{pl}=N_{t}(h_{c}+t) \tag{3}\]  
For a fully composite member, \(N_{t}=\sigma_{y}bt_{t}\), in which \(\sigma_{y}\) is the yield strength of the steel plate. In this case, it is assumed that the number of shear connectors is sufficient for a fully composite action. Therefore, Equation (3) becomes [24]:  
\[M_{pl}=\sigma_{y}bt_{t}(h_{c}+t) \tag{4}\]  
Figure 21: Formation of the yield-line mechanism of SCS slab under concentrated patch load. Figure 22: Force distribution in the section at the fully plastic stage. In order to achieve a fully composite member, the total number of shear connectors should be \(n_{s}=\sigma_{y}bt_{t}/P_{R}\) in which \(P_{R}\) is the interlayer shear strength of CSC connectors. If full composite cannot be achieved, the member should be designed for partially composite and the moment resistance has to be reduced correspondingly. For partially composite beam,  
\[N_{t}=n_{p}P_{R} \tag{5}\]  
in which \(n_{p}\) is the actual number of connectors provided between the points of zero and maximum moment. Additionally, \(P_{R}\) for each end of connectors can be obtained by push-out test.