# Experimental Study of High-Strength Concrete-Steel Plate Composite Shear Walls
## 4 Design Models for RCPSSW
### Flexural Strength Model  
The strain gauges were attached on the bottom part of the embedded steel plate in flexure specimens, as shown in Figure 4b. Figure 19a presents the measured strain distribution along the wall depth at the peak point. It is observed that the strain distribution keeps close to a linear fashion when the specimen reaches the peak lateral load capacity. Under such circumstance, the design flexure strength model is established based on the plain section assumption and the form refers to the bearing capacity equations of eccentrically-compressed members in Chinese Code for Design of Composite Structures [50], as represented in Figure 19b and given in Equation (8):  
\[\left\{ \begin{array}{c}N\leq N_{\text{c}}+f_{\text{a}}^{\prime}A_{\text{a}}^ {\prime}+f_{\text{y}}^{\prime}A_{\text{s}}^{\prime}-\sigma_{\text{a}}A_{\text {a}}-\sigma_{\text{s}}A_{\text{s}}+N_{\text{sw}}+N_{\text{pw}}\\ N\Big{(}\sigma_{0}+\frac{h}{2}-a\Big{)}\leq M_{\text{c}}+f_{\text{a}}^{\prime }A_{\text{a}}^{\prime}(h_{0}-a_{\text{a}}^{\prime})+f_{\text{y}}^{\prime}A_{ \text{s}}^{\prime}(h_{0}-a_{\text{s}}^{\prime})+M_{\text{sw}}+M_{\text{pw}} \\ M=Ne_{0}\\ V_{f}=\frac{M}{H}\end{array} \right. \tag{8}\]  
where \(M\) and \(N\) are the design moment and axial force values; \(V_{f}\) is the design shear strength; \(e_{0}\) is the eccentricity of the axial compression force; \(H\) is the shear wall height; \(h\) is the depth of wall section; \(a\) is the distance from the extreme tension fiber to centroid of resultant tensile force in tensile I-shape steels and steel reinforcement; \(h_{0}\) is the effective depth of wall section; \(f_{\text{a}}^{\prime}\) and \(f_{\text{y}}^{\prime}\) are the yield strength of compressive I-shape steels and steel reinforcement; \(A_{\text{a}}^{\prime}\) and \(A_{\text{y}}^{\prime}\) are the areas of compressive I-shape steels and steel reinforcement; \(\sigma_{\text{a}}\) and \(\sigma_{\text{s}}\) are stresses of tensile I-shape steels and steel reinforcement; \(A_{\text{a}}\) and \(A_{\text{s}}\) are areas of tensile I-shape steels and steel reinforcement; and, \(a_{\text{a}}^{\prime}\) and \(a_{\text{s}}^{\prime}\) are distances from the extreme compression fiber to centroid of resultant compressive force in tensile I-shape steels and steel reinforcement. \(M_{\text{c}}\), \(M_{\text{sw}}\), and \(M_{\text{pw}}\) are the design moment values provided by concrete section, longitudinal steel reinforcement distributed in the wall web, and embedded steel plate, and \(N_{c}\), \(N_{\text{sw}}\), and \(N_{pw}\) are the design axial force values that are provided by those three components concrete section, which can be determined by Equations (9)-(12):  
Figure 18: Shear Strength Capacities of RCSPSW Specimens Provided by Different Components. when \(x\geq h_{\text{f}}^{\prime}\)  
\[\left\{ \begin{array}{l}N_{\text{c}}=\alpha_{1}f_{\text{c}}\Big{[}\xi b_{\text{ w}}h_{0}+(b_{\text{f}}^{\prime}-b_{\text{w}})h_{\text{f}}^{\prime}\Big{]}\\ M_{\text{c}}\leq\alpha_{1}f_{\text{c}}\Big{[}\xi(1-0.5\xi)b_{w}h_{0}^{2}+(b_{ \text{f}}^{\prime}-b_{\text{w}})h_{\text{f}}^{\prime}(h_{0}-0.5h_{\text{f}}^{ \prime})\Big{]}\end{array} \right. \tag{9}\]  
when \(x<h_{\text{f}}^{\prime}\)  
\[\left\{ \begin{array}{l}N_{\text{c}}=\alpha_{1}f_{\text{c}}\xi b_{\text{f}}^ {\prime}h_{0}\\ M_{\text{c}}\leq\alpha_{1}f_{\text{c}}\xi(1-0.5\xi)b_{\text{f}}^{\prime}h_{0} ^{2}\end{array} \right. \tag{10}\]  
when \(x\leq\beta_{1}h_{0}\)  
\[\left\{ \begin{array}{l}N_{\text{sw}}=(1+\frac{x-\beta_{1}h_{0}}{0.5\beta_{1 }h_{\text{sw}}})f_{\text{gw}}A_{\text{sw}}\\ N_{\text{pw}}=(1+\frac{x-\beta_{1}h_{0}}{0.5\beta_{1}h_{\text{pw}}})f_{\text{ pw}}A_{\text{pw}}\\ M_{\text{sw}}=[0.5-(\frac{x-\beta_{1}h_{0}}{\beta_{1}h_{\text{sw}}})^{2}]f_{ \text{gw}}A_{\text{sw}}h_{\text{sw}}\\ M_{\text{pw}}=[0.5-(\frac{x-\beta_{1}h_{0}}{\beta_{1}h_{\text{pw}}})^{2}]f_{ \text{pw}}A_{\text{pw}}h_{\text{pw}}\end{array} \right. \tag{11}\]  
when \(x>\beta_{1}h_{0}\)  
\[\left\{