## 4 Statistical Analysis on Database of Experimental Results
Figures 9 and 11 show that safety-side estimation can be made if a strength reduction factor of 0.75 is used when calculating the horizontal shear strength for cases of a smooth interface or composite beam in the Case 1 category. However, Figure 10 shows unsafe cases in which the horizontal shear strength for Case 2 category was overestimated regardless of concrete compressive strength and clamping stress. This phenomenon is related to the interface location as a design variable that affects the horizontal shear strength of the composite beam. However, the current design codes do not take into account this variable, so it is necessary to quantify such an adverse effect. Table 7 shows the strength ratios for beam specimens with rough surface connecting to the category divisions of Case 1 and Case 2. It shows statistical indices relating with the distribution of the strength ratio with respect to the interface location. Figures 12 and 13 show the distribution of the strength ratios for a total of 63 beam specimens according to the concrete compressive strength and the clamping stress by classifying them into T-type interface and C-type interface, respectively. As a result, the C-type interface shows a minimum strength ratio of 0.78 to 1.56 and an average value of 1.67 to 2.75 according to the design codes. On the other hand, the strength ratio for T-type interface indicates  
Figure 11: Tested-to-calculated shear strength ratios for beam tests with smooth surface. Figure 10: Tested-to-calculated shear strength ratios for beam tests with Case 2 category (roughened surface). a minimum value of 0.41-0.67 and an average value of 0.77-1.15 in accordance with the design codes. For composite beams with T-type interface, the horizontal shear strength increased as the compressive strength of concrete increased, but decreased as the clamping stress increased. It was confirmed that the current code equation tends to overestimate the interface shear strength for composite beams, with T-type interface having a clamping stress of 4 MPa or more, as shown in Figure 12b. However, MC 2010 gives a relatively safe estimation of the horizontal shear strength for specimens with T-type interface in case of Case 2 category. It is considered that MC 2010 specifies the friction factor of 0.7 to reflect the contribution of shear friction by shear connector. On the other hand, ACI code with a friction factor of 1.0 produced a minimum strength ratio of 0.53. However, if a friction factor of 0.7 is applied for ACI prediction for T-type interface in shear friction design category, all strength ratios can rise above a strength reduction factor of 0.75. Therefore, it is recommended that the friction factor of 0.7 is used in order to reflect the deterioration of horizontal shear performance for T-type interface. \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{4}{*}{T-type with rough surface} & Average & 0.99 & 0.81 & 0.77 & 1.15 \\ \cline{2-6}  & Maximum & 1.58 & 1.27 & 1.29 & 1.89 \\ \cline{2-6}  & Minimum & 0.53 & 0.49 & 0.41 & 0.67 \\ \cline{2-6}  & STD & 0.34 & 0.25 & 0.28 & 0.40 \\ \cline{2-6}  & COV (\%) & 34.0 & 31.1 & 36.5 & 34.6 \\ \hline \multirow{4}{*}{C-type with rough surface} & Average & 1.89 & 1.84 & 1.67 & 2.75 \\ \cline{2-6}  & Maximum & 2.98 & 3.91 & 2.96 & 6.19 \\ \cline{2-6}  & Minimum & 0.84 & 0.81 & 0.78 & 1.56 \\ \cline{2-6}  & STD & 0.53 & 0.76 & 0.57 & 1.23 \\ \cline{2-6}  & COV (\%) & 28.1 & 41.4 & 34.3 & 44.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical analysis of design provisions depending on the interface location. Figure 12: T-type interface with roughened surface for beam specimens.