## 4 Statistical Analysis on Database of Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Investigator**} & \multirow{2}{*}{**Quantity**} & \multicolumn{2}{c}{**Interface**} & \(A_{cv}\) & \(f_{c}^{\prime}\) **for Weaker** & \(\rho_{v}f_{y}\) **(MPa)** \\ \cline{3-6}  & & **Location** & **Surface** & **(mm\({}^{2}\))** & **(MPa)** & **(MPa)** \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [4]} & \multirow{3}{*}{32} & \multirow{3}{*}{C-type} & Smooth & \multirow{3}{*}{17–34} & \multirow{3}{*}{0.2–3.2} \\  & & & Intermediated & & & \\  & & Rough & \(\sim\)121,935 & & & \\  & & & Keyed & & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [5]} & \multirow{3}{*}{16} & \multirow{3}{*}{C-type} & \multirow{3}{*}{Rough} & 89,832 & \multirow{3}{*}{20–48} & \multirow{3}{*}{0.4–7.7} \\  & & & & & \(\sim\)359,328 & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [7]} & \multirow{3}{*}{6} & \multirow{3}{*}{C-type} & \multirow{3}{*}{Rough} & 152,903 & \multirow{3}{*}{50–78} & \multirow{3}{*}{1.0–2.1} \\ \cline{1-1} \cline{5-5} \cline{5-  
Table 6 shows the distribution characteristics of the strength ratios of the flexural tests. The beam specimens were first divided into two groups of rough and smooth surfaces, and then the rough surface was classified into Case 1 (horizontal shear transfer) and Case 2 (shear friction) categories. Figure 9 shows the distribution of strength ratios for the Case 1 category with respect to the concrete compressive strength and the clamping stress. Furthermore, Figure 10 shows the distribution of the strength ratios for the Case 2 category. The distribution of the strength ratios for specimens with a smooth surface presented in Figure 11 shows large values for the strength ratios of all design codes. These results are probably due to conservative evaluation of the resistance of the smooth interface by adhesion and shear friction. Figure 8: Comparison of tested and calculated interface shear strength for push-off test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Interface**} & \multirow{2}{*}{**Statistics**} & \multicolumn{4}{c}{**Experimental-to-Nominal Shear Strength Ratio**} \\ \cline{3-6}  & & **ACI** & **PCI** & **AASHTO** & **MC 2010** \\ \hline \multirow{6}{*}{All beam specimens} & Average & 2.30 & 1.54 & 1.77 & 3.42 \\ \cline{2-6}  & Maximum & 7.15 & 3.91 & 5.24 & 16.64 \\ \cline{2-6}  & Minimum & 0.53 & 0.49 & 0.41 & 0.67 \\ \cline{2-6}  & STD & 0.19 & 0.72 & 0.82 & 2.80 \\ \cline{2-6}  & COV (\%) & 52.0 & 46.6 & 46.3 & 81.8 \\ \hline \multirow{6}{*}{\begin{tabular}{c} Case 1: \\ Horizontal shear \\ transfer \\ (\(\rho_{o}f_{y}54 frictionaafaceR\)\(S\)\(<\) 3.5 MPa) \\ \end{tabular} } & Average & 1.90 & 1.87 & 1.71 & 2.85 \\ \cline{2-6}  & Maximum & 2.98 & 3.91 & 2.96 & 6.19 \\ \cline{2-6}  & Minimum & 0.84 & 0.81 & 0.78 & 1.40 \\ \cline{2-6}  & STD & 0.56 & 0.80 & 0.59 & 1.26 \\ \cline{2-6}  & COV (\%) & 29.4 & 42.7 & 34.7 & 44.2 \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} Case 2: \\ Shear friction \\ (\(\rho_{o}f_{y}54 frictionaafaceR\)\(S\)\(>\) 3.5 MPa) \\ \end{tabular} } & Average & 1.22 & 1.02 & 0.93 & 1.35 \\ \cline{2-6}  & Maximum & 2.03 & 1.63 & 1.63 & 1.99 \\ \cline{2-6}  & Minimum & 0.53 & 0.49 & 0.41 & 0.67 \\ \cline{2-6}  & STD & 0.48 & 0.39 & 0.38 & 0.47 \\ \cline{2-6}  & COV (\%) & 39.4 & 37.9 & 40.7 & 34.8 \\ \hline \multirow{6}{*}{
\begin{tabular}{c} Interface with smooth surface \\ \end{tabular} } & Average & 4.86 & 1.38 & 2.32 & 5.31 \\ \cline{2-6}  & Maximum & 16.38 & 3.08 & 5.24 & 16.64 \\ \cline{2-6}  & Minimum & 2.09 & 0.82 & 1.43 & 2.38 \\ \cline{2-6}  & STD & 3.43 & 0.50 & 0.85 & 3.77 \\ \cline{2-6}  & COV (\%) & 70.5 & 36.1 & 36.4 & 71.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical analysis between design provisions and database from beam specimens. Figure 9: Tested-to-calculated shear strength ratios for beam tests with Case 1 category (roughened surface).