## 4 FE Analysis and Result
### Comparison of Analysis Results and Experimental Values  
As shown in Figure 17, the number of studs was changed to eight for comparison of the FE analysis results, which were obtained using the 1/4 model, at the same load as the actual experiment results. In addition, the FE analysis results were compared by overlapping the starting displacement of each model by the initial slip amount, taking into account the initial slip (\(\delta_{initial}\)) caused by the load stabilization in the initial elastic region experiments. For model S1, the analysis values of the yield strength and initial stiffness were slightly higher than the experimental values, which is thought to have occurred because the effect of the weld bead was counted larger than it should be. For model S2, it can be seen that the stiffness of the stud bolt was manifested after an initial slip of up to 1 mm occurred at low loads due to the tolerance between the diameters of the hole in the upper flange of the H beam and stud bolt. The amount of load resistance at an initial slip of less than 1 mm can be considered to be caused by the friction effect resulting from the bolt load. For model S3-20, all the analysis results match the experimental results well, except that the ultimate load in the analysis was larger than the experimental value. In the actual experimental results, models S3 and S4 both have higher initial stiffnesses and ultimate loads when the Y-shape is 45\({}^{\circ}\) than when it is 20\({}^{\circ}\). It can be seen that in both 45\({}^{\circ}\) models, the stiffness that resists initial slip becomes larger than that in the 20\({}^{\circ}\) models due to the wedge effect caused by the bolt load. Table 7 shows the compressive and tensile failure modes of the concrete slab and the von Mises stress of the shear connectors in each model. In models S1-S3, it can be seen that shear fracturing occurred due to the concentration of stress at the same locations at which the studs fractured in the experiments. However, in model S4, considerable yielding occurred due to shear in the Y-shape location, but the actual experiments differed in that failure occurred due to the tensile fracturing of the nut fastening part. Because the material damage and failure options were not used on the stud bolts in the FE analysis, the amount of stress continually increased until the end of the analysis, and it is impossible to know where the actual fracturing began. However, considering that the equivalent stress increased greatly above and below the Y-shaped expansion in the analysis results, it is thought that the actual fracturing first occurred due to the concentration of stress caused by notches and the reduction in the cross-sectional area in the lower part in which the threads were located. Model S4 has a cross-section that is integrated via the Y-shape, and its shear \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**FE Model**} & \multirow{2}{*}{**Interactions** (**Master-Slave Surface**)} & \multicolumn{4}{c}{**Contact Properties**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**Tangent Behavior**} & \multicolumn{2}{c}{**Normal Behavior**} \\ \cline{3-6}  & & **Friction** & **Friction** & **Pressure-** & **Separation After** \\  & & **Formulation** & **Coefficient** & **Overclosure** & **Contact** \\ \hline \multirow{2}{*}{**S1**} & Stud-Conc & Penalty & 0.30 & \multirow{2}{*}{Hard} & \multirow{2}{*}{Allow} \\  & HBeam-Conc & Penalty & 0.14 & & \\ \hline \multirow{2}{*}{**S2-S4**} & Hbeam–Nut/Stud–Nut & Penalty & 0.30 & \multirow{2}{*}{Hard} & \multirow{2}{*}{Allow} \\  & HBeam–Conc/Stud–Conc & Penalty & 0.14 & & \\ \cline{1-1}  & Emb.nut–Conc/Hbeam–stud & Penalty & 0.14 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Contact properties for each interactions of analytical models. resistance cross-section is larger than those of the other models; therefore, it was able to resist a high ultimate load.