# Experimental Study of High-Strength Concrete-Steel Plate Composite Shear Walls
## 4 Design Models for RCPSSW  
### Shear Strength Model  
The form of the shear strength equation refers to the design model that was suggested by Chinese Code for Design of Composite Structures [50], given as:  
\[V=V_{\mathrm{c}}+V_{\mathrm{s}}+V_{\mathrm{a}}+V_{\mathrm{P}} \tag{4}\]  
where the shear strength, \(V\), is contributed by four components: concrete shear-resisting component, \(V_{\mathrm{c}}\), horizontal reinforcement shear-resisting component, \(V_{\mathrm{s}}\), boundary steel profiles shear-resisting component, \(V_{\mathrm{a}}\), and embedded steel plate shear-resisting component, \(V_{\mathrm{P}}\). Equation (5) provides the expressions for different shear strength components. \[\left\{ \begin{array}{l}V_{\mathrm{c}}=0.67f_{\mathrm{t}}b_{\mathrm{w}}l_{0} +0.2N\frac{A_{\mathrm{w}}}{A}\\ V_{\mathrm{s}}=f_{\mathrm{b}}\frac{A_{\mathrm{b}}}{A}h\\ V_{\mathrm{a}}=\frac{0.3}{A}f_{\mathrm{a}}A_{\mathrm{a}}\\ V_{\mathrm{P}}=\frac{0.6}{\lambda-0.5}f_{\mathrm{P}}A_{\mathrm{P}}\end{array} \right. \tag{5}\]  
where \(f_{\mathrm{t}}\) is concrete tensile strength; \(b_{\mathrm{w}}\) is the web width; \(h_{\mathrm{w}}\) is the web depth; \(h\) and \(h_{0}\) are the depth and effective depth of the shear wall section; \(A_{\mathrm{w}}\) and \(A\) represent the area of concrete web and entire section, respectively; \(N\) indicates the axial compressive load, \(N\leq 0.2f_{\mathrm{c}}b_{\mathrm{w}}l_{\mathrm{w}}\); \(f_{\mathrm{y}\mathrm{b}}\), \(f_{a}\), and \(f_{\mathrm{P}}\) mean the yield strength of transverse web reinforcement, boundary I-shape steel profiles, and embedded \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen Batch** & **Specimen No.** & **Hysteresis Loop Area (kN\(\cdot\)mm)** & **EVD Coefficient** \\ \hline \multirow{4}{*}{Shear Specimens} & RCSW 1-1 & 3518 & 0.123 \\ \cline{2-4}  & RCSW 1-2 & 3513 & 0.109 \\ \cline{2-4}  & RCPSPSW 1-1 & 11600 & 0.129 \\ \cline{2-4}  & RCPSPSW 1-2 & 11949 & 0.156 \\ \cline{2-4}  & RCPSSW 1-3 & 10604 & 0.157 \\ \hline \multirow{4}{*}{Flexure Specimens} & RCSW 2-1 & 12064 & 0.212 \\ \cline{2-4}  & RCSW 2-2 & 10395 & 0.184 \\ \cline{2-4}  & RCSW 2-3 & 11790 & 0.189 \\ \cline{2-4}  & RCPSSW 2-1 & 18044 & 0.202 \\ \cline{2-4}  & RCPSSW 2-2 & 13442 & 0.207 \\ \cline{2-4}  & RCPSSW 2-3 & 11001 & 0.177 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Equivalent Viscous Damping (EVD) Coefficients of All Specimens. steel plate; \(A_{\text{yh}}\), \(A_{\text{a}}\), and \(A_{\text{p}}\) denote the area of those three components; \(s\) is the spacing of transverse reinforcement; and, \(\lambda\) is the aspect ratio. Table 6 summarizes shear strength capacities that were measured from the quasi-static cyclic load test and calculated by shear strength models. Note that the measured characteristic concrete strength values were used in the calculation. It is seen from Table 6 that design models provide 10-15 percent conservative shear strength capacity values for RCSW specimens as compared to the test results. In terms of RCSPSW specimens, shear strength capacities that are estimated by design models are very close to the average experimental data, but 5-10 percent lower shear strength values were observed in the positive direction. A correction factor, \(k_{\text{s}}\), for design models is taken as 0.9 to determine the shear strength capacity in order to achieve a reasonable degree of conservatism. Figure 15(a) presents the comparison of design strength capacities and experimental results for the shear specimens. Dash red line shows the design values determined by the modified design model with the correction factor. It is evident that the modified design shear capacities are generally larger than the test values in both positive and negative directions, and a reasonable degree of conservatism (approximate 10-20 percent) is obtained by using the shear correction factor.