## 5 Probabilistic Flexural Strength Model of RC Slab Members
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Study** & **Basic Random Variables** & **Bias Factor** & **Cov** & **PDF** & **Ref.** \\ \hline \multirow{4}{*}{[PERSON] et al. [1]} & \(f_{ck}\) (20.7, 27.6, 34.5 MPa) & 0.92, 0.85, 0.81 & 0.18, 0.18, 0.15 & Normal & [20] \\  & \(f_{y}\) (420 MPa) & 1.13 & 0.10 & Beta & [21] \\  & Effective depth, bottom rebar & \(-\)3.30 mm \({}^{*}\) & SD = 8.89 mm & Normal & [22,23] \\  & Effective depth, upper rebar & \(-\)10.16 mm \({}^{*}\) & SD = 12.70 mm & Normal & [22,23] \\  & Experimental strength biasness & 1.01 & 0.046 & Normal & [24] \\ \hline \multirow{4}{*}{[PERSON] et al. [4]} & \(f_{ck}\) (20.7–41.3 MPa) & 1.35–1.12 & 0.10 & Normal & - \\  & \(f_{y}\) (420 MPa) & 1.15 & 0.05 & Normal & - \\  & Area of rebar, \(A_{s}\) & 1.00 & 0.02 & Normal & - \\  & Effective depth of slab, & 0.92 & 0.12 & Normal & [1] \\  & cast-in-place & & & & \\  & Experimental strength biasness & 1.02 & 0.06 & Normal & [1] \\ \hline \multirow{4}{*}{[PERSON] et al. [5]} & \(f_{ck}\) (20.7–44.8 MPa) & 1.31–1.14 & 0.17–0.12 & Normal & - \\  & \(f_{y}\) (420 MPa) & 1.13 & 0.03 & Normal & - \\  & Area of rebar, \(A_{s}\) & 1.00 & 0.02 & Normal & - \\  & Effective depth of slab, & 0.92 & 0.12 & Normal & [1] \\  & \(\text{cas-in-place}\) & & & & \\  & Experimental strength biasness & 1.02 & 0.06 & Normal & [1] \\ \hline \multirow{4}{*}{[PERSON] et al. [7]} & \(f_{ck}\) (25 MPa) & 1.35 & 0.18 & Normal & [1,4,12] \\  & \(f_{y}\) (450 MPa) & 1.22 & 0.05 & LN & - \\  & Area of rebar, \(A_{s}\) & 1.00 & 0.01 & Normal & [1,4,12] \\  & Effective depth of beam & 0.99 & 0.04 & Normal & [1,4,12] \\  & Width of beam & 1.10 & 0.04 & Normal & [1,4,12] \\  & Experimental strength biasness & 1.02 & 0.06 & Normal & [1,4,12] \\ \hline \multirow{4}{*}{Present study (Positive moment strength)} & \(f_{ck}\) (27 MPa) & 1.13 & 0.222 & Normal & - \\  & \(f_{y}\) (400 MPa) & 1.17 & 0.043 & Normal & - \\  & \(\lambda_{t}\) (slab thickness biasness) & 1.004 & 0.032 & Normal & - \\  & \(c_{s1}\)(cover depth of bottom rebar) & 1.19 & 0.065 & Normal & - \\  & \(c_{s2}\)(cover depth of upper rebar) & 0.98 \({}^{**}\) & 0.068 \({}^{***}\) & LN & - \\  & Experimental strength biasness & 1.15 & 0.043 & Normal & - \\ \hline \hline \end{tabular}  
*—median; material partial safety factors are included.  
\end{table} 
Table 8: Statistical parameters of flexural resistances in previous studies. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Study** & **Structural Type** & **Bias Factor** & **Cov** \\ \hline [PERSON] et al. [1] & One-way RC slab; 127 mm-thick & 1.21 & 0.15 \\ [PERSON] et al. [4] & RC slab cast-in-place & 1.08 & 0.15 \\ [PERSON] et al. [5] & One-way RC slab; 102–203 mm-thick & 1.06 & 0.15 \\ [PERSON] et al. [7] & RC beam; 500–850 mm-thick & 1.65 \({}^{***}\) & - \\ Present study & One-way RC slab; 300–500 mm-thick & 1.38 & 0.08 \\ \hline \hline \end{tabular}  
*—median; material partial safety factors are included.  
\end{table} 
Table 7: Probabilistic models of basic random variables in previous studies. In [PERSON] et al. [6], the material partial factors were included in the nominal resistance to be divided and the higher bias factor was evaluated. The main reason for this result is that the mean value of the experimental strength biasness was higher than that of other studies [1; 4; 6; 1], as mentioned in Section 4.2. The mean biasness of \(f_{y}\) based on the Korean industrial data was slightly higher than those in other studies, except for that of [PERSON] et al. [6]. However, the cov values of the basic design variables were slightly smaller than others, because the probabilistic models of the basic design variables adopted in this study were based on the critical regions--either the lower tail region or the upper tail region. Therefore, the cov of the resistance model results in a smaller cov. To verify the simulation procedure proposed in this study, the simulation procedure was performed with the basic random variable models recommended in [PERSON] et al.