# Experimental Study of High-Strength Concrete-Steel Plate Composite Shear Walls
## 4 Design Models for RCPSSW
### Shear Strength Model
According to Equation (5), the shear strength capacities contributed by reinforced concrete (\(V_{\text{c}}+V_{\text{s}}\)), I-shape steel profiles (\(V_{\text{a}}\)), and the steel plate (\(V_{\text{p}}\)) were quantified and are summarized in Table 7. It is seen that the embedded steel plate takes up approximately 50 percent of the design shear strength capacity. For comparisons, shear strength provided values by each component in the cyclic test were inferred from strain gauge readings. Figure 16(a) shows the strain gauge arrangement in boundary I-shape steel profiles and the embedded steel plate. Shear strength that was provided \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen No.**} & \multicolumn{2}{c}{**Experimental Results (kN)**} & \multirow{2}{*}{
\begin{tabular}{c} **Design Model** \\ **Results (kN)** \\ \end{tabular} } & \multicolumn{2}{c}{**Differences**} \\ \cline{2-3} \cline{5-8}  & **Positive** & **Negative** & **Average** & & **Positive** & **Negative** & **Average** \\ \hline RCSW 1-1 & 604 & 606 & 605 & \multirow{2}{*}{512} & 15\% & 16\% & 15\% \\ \cline{1-1} \cline{5-8} RCSW 1-2 & 522 & 617 & 570 & & 2\% & 17\% & 9\% \\ \hline RCSPSW 1-1 & 1070 & 1301 & 1186 & 1199 & \(-\)12\% & 8\% & \(-\)2\% \\ \hline RCSPSW 1-2 & 1156 & 1242 & 1199 & \multirow{2}{*}{1213} & \(-\)5\% & 2\% & \(-\)1\% \\ \cline{1-1} \cline{5-8} RCSPSW 1-3 & 1117 & 1318 & 1218 & & \(-\)9\% & 8\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of Experimental and Design Strength Capacities for Shear Specimens. Figure 16: Comparisons of Design Strength Capacities and Experimental Results for Shear Specimens and Flexure Specimens. by boundary I-shape steel profiles was calculated based on strain values of SG16-SG19 by following Equation (6). \[V_{\text{a}}=\frac{W_{\text{a}}E_{\text{a}}\big{|}\frac{\varepsilon\text{SG16}+ \varepsilon\text{SG17}}{2}-\frac{\varepsilon\text{SG18}+\varepsilon\text{SG19}}{ 2}\big{|}/2}{H} \tag{6}\]  
where \(E_{\text{a}}\) is measured Young's Modulus of I-shape steels; \(W_{\text{a}}\) is the section modulus; and, \(H\) is the height of shear specimens. Strain rosettes were attached on the embedded steel plate. Strain values of _SG7_, _SG8_, and _SG9_ are recorded and used to infer principle stress state and horizontal shear stress state and further determine the shear strength by using Equation (7). \[\left\{ \begin{array}{l}\left\{\begin{array}{l}\sigma_{1}\\ \sigma_{2}\end{array}\right\}=\frac{E\left(\varepsilon_{\text{0}}+\varepsilon _{\text{0}\text{0}}\right)}{2(1-\
u)}\pm\frac{\sqrt{E}_{\text{P}}}{2(1+\
u)} \sqrt{\left(\varepsilon_{\text{0}^{0}}-\varepsilon_{\text{450}}\right)^{2}+ \left(\varepsilon_{\text{450}}-\varepsilon_{\text{900}}\right)^{2}}\\ V_{\text{P}}=A_{\text{s}}\tau_{\text{yx}}\end{array} \right. \tag{7}\]  
where \(\varepsilon_{\text{0}}\), \(\varepsilon_{\text{450}}\), and \(\varepsilon_{\text{900}}\) represent strain rosette readings; \(E_{\text{P}}\) is the Young's Modulus of steel plate; \(\
u\) is the Poisson's ratio; \(A_{\text{s}}\) is the area of steel plate; and, \(\tau_{\text{yx}}\) is the horizontal stress. Note that the shear strength of steel plate is considered to be unchanged after yielding, and shear-resisting component of reinforced concrete is taken as the lateral load strength of RCSW specimens under the same axial compression ratios. Figure 18 shows the shear-resisting strength that was contributed by different components in the cyclic load test. The blue line, red line, and green line show the capacity trend of reinforced concrete, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen No.** & \multicolumn{4}{c}{**Shear Strength Capacities (kN)**} \\ \cline{2-5}  & **Reinforced Concrete** & **I-Shape Steels** & **Steel Plate** & **Total** \\ \hline RCPSSW 1-1 & 515 (43\%) & 116 (10\%) & 568 (47\%) & 1199 \\ \hline RCPSSW 1-2 & 529 (44\%) & 116 (10\%) & 568 (46\%) & 1213 \\ \hline RCPSSW 1-3 & 529 (44\%) & 116 (10\%) & 568 (46\%) & 1213 \\ \hline \hline \end{tabular}
\end{table}