# Flexural and Shear Performance of Prestressed Composite Slabs with Inverted Multi-Ribs
## 4 Analysis of Flexural Behavior and Shear Strength
### Estimation of Shear Strength  
Table 3 shows code equations for estimating the shear strength presented in ACI 318-14 [11], which were applied to evaluate the shear performance of the JAS. As mentioned earlier, shear reinforcement placed in the US series specimens without cast-in-place concrete did not contribute effectively to the shear resistance of the member. Therefore, only the contribution of the concrete (\(V_{cw}\)) was taken into account in estimating the shear strength of the PC unit members, without regard for the contribution of the shear reinforcement (\(V_{s}\)). Meanwhile, the compressive strengths of the PC unit and cast-in-place concrete are different in composite members, and ACI 318-14 [11] specifies that it is allowable to use the material properties of the elements that result in the most critical value of shear strength (\(V_{n}\)). However, in this case, it tends to be very conservative in evaluating the shear strength of the member. In addition, if the web shear strength equation for prestressed concrete members (\(V_{cw}\)) is applied to get the web shear strength of JAS members, it causes the fallacy that prestress is effective in all cross-sections including the cast-in-place concrete, while prestress force is introduced only to the PC unit in the JAS. Consequently, this approach provides an unsafe estimation on the shear strength of JAS members. For this reason, a way to estimate the shear strength by considering the entire composite PC slab to be reinforced concrete (RC) in order to achieve the safe side design has often been applied in practice [12]. In this study, the shear strength (\(V_{n}\)) of the composite member was estimated by three methods (labeled Methods 1, 2, 3), as shown in Figure 9. Note that the area indicated in red is where the shear strength is estimated by regarding the composite member to be PSC, whereas the area indicated in blue is where the shear strength is estimated by regarding it as being RC. Method 1 is a method for calculating the shear contribution (\(V_{cw}\)) by defining the distance from the compression edge of the composite member to the center of the strands layer as \(d_{p}\), and estimating the shear strength by considering the remaining part as RC. On the other hand, Method 2 estimates \(V_{cw}\) by considering the distance from the top of the PC unit rib to the center of the strands layer as \(d_{p}\). Method 3 estimates the shear strength by regarding the cross-section as being RC. According to the test results, the stirrup effectively contributed to the shear resistance mechanism in the composite member. Therefore, the contribution of the shear reinforcement (\(V_{s}\)) was taken into consideration in the estimation of the shear strength. However, since the critical shear crack angle (\(\beta\)) observed in the test specimens was distributed in the range from \(58^{\circ}\) to \(62^{\circ}\), \(\beta\) was applied at \(60^{\circ}\) in the estimation of \(V_{s}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Term** & **Equations** \\ \hline Shear strength of reinforced concrete (\(V_{c}\)) & \(V_{c}=0.17\sqrt{f_{c}^{\prime}}b_{w}d_{s}\) \\ \hline Web shear strength of prestressed concrete (\(V_{cw}\)) & \(V_{cw}=\left(0.29\sqrt{f_{c}^{\prime}}+0.3f_{pc}\right)b_{w}d_{p}\), where \(f_{pc}=\frac{f_{c}A_{p}}{A_{p}}\) \\ \hline Shear contribution of stirrups (\(V_{s}\)) & \(V_{s}=\frac{A_{c}f_{v}d_{s}}{s_{v}}(\sin\alpha\cot\beta+\cos\alpha)\) \\ \hline \hline \end{tabular}  
* Notations: \(b_{w}\): web width, \(d_{s}\): effective depth of tension reinforcement, \(d_{p}\): effective depth of prestressing strands, \(f_{c}\): compressive strength of concrete, \(f_{sc}\): effective prestress, \(A_{p}\): sectional area of prestressed member, \(A_{p}\): sectional area of prestressing strands, \(A_{p}\): sectional area of the stirrup, \(f_{v}\): yield strength of the stirrup, \(s_{v}\): spacing of stirrups, \(\alpha\): inclined angle of the stirrup, \(\beta\): angle of critical shear crack.  
\end{table}