# Shear Tests of Deep Hollow Core Slabs Strengthened by Core-Filling
## 1 Introduction
Investigating the shear strengthening effect of the core-filling method is very important because it has been widely applied as a shear strengthening method of PHCSs in construction fields due to its simple working process ([PERSON] and [PERSON], 2018; [PERSON], 2019). Table 1 shows the shear strength equations for reinforced concrete (RC) and prestressed concrete (PSC) members specified in the current design codes ([PERSON] et al., 2019; [PERSON], 2019; [PERSON], 2019). In practice, the shear contribution of concrete (\(V_{c}\)) of the PHCS with core-filling concrete is often simply calculated as \(V_{PHCS}+V_{core}\), but in that case, the \(V_{c}\) could be overestimated. [PERSON] and [PERSON] (2018) conducted web-shear tests on 400 mm thick PHCS strengthened by the core-filling method, and analyzed the web-shear strength equation presented in ACI 318-05 ([PERSON] and [PERSON], 2018). Note that there is no provision for the additional strength reduction factor (0.5) in ACI 318-05. Based on their test results, [PERSON] and [PERSON] reported that when calculating the web-shear strength of PHCS with filled cores, the shear contribution of the filled cores should be reduced by as much as 50% \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(V_{core}\)(kN) & \(V_{PHCS}\)(kN) & \(V_{s}\)(kN) \\ \hline ACI 318 & \(V_{core}=0.17\sqrt{f_{c}}b_{c}d\) & * \(V_{PHCS}=\big{(}0.29\sqrt{f_{c}}+0.3f_{pc}\big{)}b_{w}d_{p}\) & \(V_{s}=\frac{A_{s}f_{cd}}{s}\) \\ \hline \multirow{3}{*}{CSA-A23.4} & \(V_{c}=\beta\sqrt{f_{c}}b_{w}d_{v},d_{v}=\max(0.72h,0.9d)\) & \multirow{3}{*}{\(V_{s}=\frac{A_{s}f_{cd}}{s}\cot\theta\)} \\  & Simplified method & & General method & \(\theta=35^{\circ}\) \\  & \(\beta=0.18\sigma\frac{230}{(1000+d_{v})}\) & \(\beta=\frac{0.40\cdot 1300}{(1+1500\epsilon_{x})\cdot(1000+\epsilon_{x})}\) & & \\ \hline \multirow{2}{*}{BS EN 1168} & \multirow{2}{*}{\(V_{core}=\frac{2}{3}b_{c}d_{c}d_{c}\)} & \multirow{2}{*}{\(V_{PHCS}=\frac{lh_{p}}{S}\sqrt{\left(f_{cd}\right)^{2}+f_{pc}f_{cd}}\)} & \multirow{2}{*}{\(V_{s}=\frac{A_{s}f_{cd}}{s}\cot\theta\)} \\  & & & \(1.0\leq\cot\theta<2.5\) \\ \hline \hline \end{tabular}  
* Note: \(V_{PHCS}\) should be reduced by half for the PHCS with the height (\(h\)) larger than 315 mm. Notations: \(A_{t}\): sectional area of shear reinforcement, \(b_{v}\): web width of filled cores, \(b_{w}\): web width of PHCS unit, \(d\): effective depth of filled core, \(d_{v}\): depth from extreme compression fiber to the center of prestressing strands, \(f_{c}\): actual compressive strength of concrete, \(f_{dd}\): tensile strength of concrete, \(f_{pc}\): compressive stress of concrete at the centroid of section due to effective prestress, \(f_{\psi}\): yield strength of shear reinforcement, \(h\): height of PHCS unit, \(h_{c}\): height of filled core, \(I\): moment of inertia of PHCS unit, \(S\): first moment of area of PHCS unit, \(s\): spacing between stirrupps, \(s_{xx}\): crack spacing parameter, \(\epsilon_{x}\): longitudinal strain of concrete at the mid-depth of section.  
\end{table} 
Table 1: Code equations for estimating shear strength of reinforced concrete (RC) and prestressed concrete (PSC) members. of the shear strength calculated using a code equation, in order to obtain accurate analysis results. That is, it turned out that the filled cores made a partial contribution to the shear strength of the member but failed to achieve 100% of their shear capacity in the test. On the other hand, [PERSON] et al. [25] performed shear tests of PHCSs applied in a slim floor system, in which two specimens were reinforced with core-filling concrete. In their tests, however, the shear strengths of the PHCSs did not increase by the core-filling concrete. As mentioned above, previous researchers reported different test results on the shear strength of PHCS with filled cores, which is considered to be because of a very different bond condition, often poor, between the PHCS unit and filled cores. Thus, it is very hard to estimate the shear strengthening effect of the core-filling method.