## 4 Parametric Analysis of Side Joints
### Lateral Resistance under Load Case 1
#### 4.1.1 Arrangement Length of URSP Connectors  
As illustrated in Figure 3, \(L_{U}\) is the length of regions where URSP connectors are placed along the beam. Load-displacement results at the beam end depicted in Figure 9 are the results corresponding to the side joint with different \(L_{U}\)s and three extreme cases including the perfect interaction (nodes of the RC slab and steel beam are shared with each other), no interaction (the longitudinal stiffness of shear connectors at the interface is zero) and the bare steel beam (without an RC slab). It can be seen from Figure 9 that the ultimate resistances of the joint with perfect interaction are 8.7% and 7.7% larger than that with all studs (\(L_{U}=0\)) when subjected to a hogging and sagging moment, respectively. For the overall stiffness, the increases are 10.7% and 23%, respectively, which is consistent with the results presented in an earlier study [50]. Compared to the result with all studs (\(L_{U}=0\)), the differences corresponding to \(L_{U}\) ranging from 0.2\(L\) to 0.9\(L\) are very small and can be neglected under a hogging and sagging moment. For simplicity, only the numerical result while \(L_{U}\) is equal to 0.5\(L\) is plotted in the figures. However, compared to the result with all studs (\(L_{U}=0\)), the ultimate resistances with \(L_{U}=L\) decrease by 10.9% and 23.3% under a hogging and sagging moment, respectively, and for overall stiffness, the decreases are up to 23.0% and 38.7%. Moreover, it can be observed that the curve with \(L_{U}=L\) is very close to the results with no interaction, which demonstrates that the interfacial shear force can be effectively released by applying URSP connectors along the whole beam. Nevertheless, due to the contribution of the RC slab, the ultimate capacities corresponding to the hogging and sagging moment while the \(L_{U}=L\) are 13.7% and 6.6% higher than those of the bare steel beam. Meanwhile, the increment ratios of structural stiffness are 9.3% and 7.5%, respectively. In addition, it can be observed that obvious buckling of the bottom flange of the steel beam occurs under the hogging moment with a high strain level, resulting in a rapid reduction of the load-bearing capacity of beams with perfect \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Parameter** & **Considered Values** \\ \hline URSP length \(L_{U}\) (\(L\)) & **0** *, 0.2, 0.3, 0.4, **0.5**, 0.6, 0.7, 0.8, 0.9, 1 \\ Shear connector spacing \(d\) (mm) & **100**, 200, 300 \\ Slab thickness \(h_{c}\) (mm) & 75, **100**, 125, 150 \\ Slab width \(b\) (mm) & 1000, 1500, **2000**, 2500, 3000 \\ Steel beam height \(h_{b}\) (mm) & 300, 350, **400**, 450 \\ \hline \hline \end{tabular}  
* Bold font represents for the initial values. \(L_{U}\) is the length of regions where URSP connectors are placed along the beam, as illustrated in Figure 3.  
\end{table} 
Table 1: Design parameters for load case 1.  
interaction and all studs, as presented in Figure 9a. The occurrence of buckling can be effectively postponed due to the application of URSP connectors, which increases the ductility of the beam hinge and the whole frame structures under seismic loads. When subjected to the hogging moment, the load-strain curves of the bottom flange at the beam section where the max moment occurs are illustrated in Figure 10. As shown in Figure 10, the linear relationship between load-strain curves can be observed before the bottom flange reaches its yielding strength. With the increasing of cracks in the concrete slab and the yielding of the bottom flange, the specimen exhibits apparent nonlinear behavior. The buckling of the bottom flange occurs in several beams, as presented in Figure 9.  
For different beams, the strain distributions along the section height of the composite beam at the drift ratio of 1/50 (corresponding to the ultimate limit state) are shown in Figure 11. This figure shows that interface slip exists in the beam with all studs of a full shear connection degree.