# Shear Tests of Deep Hollow Core Slabs Strengthened by Core-Filling
## 4 Review of the Code Provisions and Recommendation
### Modified Shear Strength Equation for the PHCS with Filled Cores  
For shear strengthening of the PHCS, the top flange of the PHCS unit should be cut lengthwise and opened to fill the hollow cores with concrete. The test results showed that when the entire hollow core is filled with concrete, the interface between the web of the PHCS unit at the edge of the section and the filled core is damaged, as shown in the upper right corner of Figure 11a, which makes it difficult to provide effective shear resistance to the external shear force. Therefore, in this study, the section of the PHCS with filled cores was idealized, as shown in the lower right corner of Figure 11a, and only the part corresponding to the area marked with oblique lines was assumed to exert effective shear resistance. In addition, the contribution of shear reinforcement (\(V_{s}\)) was ignored because the helix reinforcement placed in the filled cores did not contribute to shear resistance mechanism. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Test Results**} & \multicolumn{2}{c}{**ACI 318-14**} & \multicolumn{2}{c}{**CSA-A23.3**} & \multicolumn{2}{c}{**BS EN 1168**} \\ \cline{2-7}  & **kN** & **kN** & **Ratio \({}^{*}\)** & **kN** & **Ratio \({}^{*}\)** & **kN** & **Ratio \({}^{*}\)** \\ \hline NR-0/4 (1) & 351.0 & \begin{tabular}{c} 159.1 \\ (318.2 **) \\ \end{tabular} & 2.21 (1.10) & 269.0 & 1.30 & 397.7 & 0.88 \\ NR-0/4 (2) & 331.0 & \begin{tabular}{c} 159.1 \\ (318.2 **) \\ \end{tabular} & 2.08 (1.04) & 269.0 & 1.23 & 397.7 & 0.83 \\ NR-2/4 (1) & 472.0 & \begin{tabular}{c} 271.6 \\ (430.6 **) \\ \end{tabular} & 1.74 (1.10) & 386.6 & 1.22 & 562.7 & 0.84 \\ NR-2/4 (2) & 451.2 & \begin{tabular}{c} 271.6 \\ (430.6 **) \\ \end{tabular} & 1.66 (1.05) & 386.6 & 1.17 & 562.7 & 0.80 \\ NR-4/4 (1) & 426.9 & \begin{tabular}{c} 384.0 \\ (543.1 **) \\ \end{tabular} & 1.11 (0.79) & 504.2 & 0.85 & 727.8 & 0.59 \\ NR-4/4 (2) & 422.3 & \begin{tabular}{c} 384.0 \\ (543.1 **) \\ \end{tabular} & 1.10 (0.78) & 504.2 & 0.84 & 727.8 & 0.58 \\ LR-2/4 (1) & 444.7 & \begin{tabular}{c} 363.6 \\ (522.7 **) \\ \end{tabular} & 1.22 (0.85) & 539.3 & 0.82 & 645.5 & 0.69 \\ LR-2/4 (2) & 428.7 & \begin{tabular}{c} 363.6 \\ (522.7 **) \\ \end{tabular} & 1.18 (0.82) & 539.3 & 0.79 & 645.5 & 0.66 \\ HR-2/4 (1) & 436.6 & \
\begin{tabular}{c} 478.6 \\ (637.7 **) \\ \end{tabular} & 0.91 (0.69) & 725.4 & 0.60 & 749.0 & 0.58 \\ HR-2/4 (2) & 446.1 &
\begin{tabular}{c} 478.6 \\ (637.7 **) \\ \end{tabular} & 0.93 (0.70) & 725.4 & 0.61 & 749.0 & 0.60 \\ Average & - & 1.41 (0.89) & - & 0.94 & - & 0.71 \\ STD & - & 0.47 (0.16) & - & 0.26 & - & 0.12 \\ COV & - & 0.33 (0.18) & - & 0.28 & - & 0.17 \\ \hline \hline \end{tabular} \({}^{*}\)\(V_{n,tot}/V_{n,tot.}\). \({}^{**}\) The shear strength without considering additional reduction factor (0.5) for the PHCS with height greater than 315 mm.  
\end{table} 
Table 5: Comparison of test and calculation results. As shown in Tables 1 and 5, the shear strength equation presented in the ACI 318-14 code has a simple form, but was found to provide very approximate predictions of the shear strengths of the NR-0/4 and NR-2/4 specimens when the additional shear reduction factor (0.5) was not taken into account. Therefore, this study modifies the shear strength equation of ACI 318 to fit the PHCS with filled cores, as follows:  
\[V_{c}=0.17k_{c}\sqrt{f_{c,core}}b_{c}l_{c}+k_{pc}\Big{(}0.29\sqrt{f_{c,pc}}+0.3f _{pc}\Big{)}b_{w}d_{p}, \tag{2}\]  
where, \(k_{c}\) is the ratio of the number of filled cores \(\big{(}n_{c,full}\big{)}\) to the number of entire hollow cores (\(n_{c,tot}\)), \(f_{c,core}\) and \(f_{c,pc}\) are the concrete compressive strength of filled core and the PHCS unit, respectively, \(f_{pc}\) is the compressive stress of concrete at the centroid of the section due to effective prestress, \(b_{c}\) and \(h_{c}\) are the width and height of filled cores, respectively, \(b_{w}\) is the web width of the PHCS unit, and \(d_{p}\) is the depth of the prestressing strand.