## 4 Parametric Analysis of Side Joints
### Cracking and Deflection under Load Case 2  
When subjected to the vertical uniform pressure, the frame structure can be simplified to the side joint, as shown in Figure 3b. In order to study the performance of the composite frame under vertical loads, the crack performance of the concrete slab and the deflection of the whole beam are analyzed. The arrangement lengths of URSP connectors in the composite beam range from 0-0.5\(L\), while the entire length of the beam in this side joint is 0.5\(L\). Concrete stress distributions in the concrete slab of Stud and URSP-0.5\(L\) are shown in Figure 17. It is observed that the concrete stress decreases and the crack-opening-area reduces due to the presence of URSP connectors. For different arrangement lengths of URSP connectors, the variation of concrete stress, rebar stresses and the deflection at the loading point with the increase of loading displacement are illustrated in Figure 18. The location where the concrete and rebar stress investigated in the FE model is in the middle of the section, where the max moment occurs near the slab-to-column surface. Figure 16: Load-displacement curves with different steel beam heights \(h_{\mathrm{s}}\). (**a**) Hogging moment; (**b**) sagging moment. Figure 17: Concrete tensile stress distributions in the concrete slab subjected to vertical loads. (**a**) Concrete stress in the Stud model; (**b**) concrete stress in the URSP-0.5\(L\) model. It can be seen from Figure 18a that the maximum concrete stress in the models with URSP connectors lags behind that in the model with only studs. Moreover, the concrete stress corresponding to the same load will decrease with the increment of the arrangement length of URSP connectors. In other words, compared with the model with only studs, the cracking of the RC slab with URSP connectors is postponed. It can be seen from Figure 18b that the rebar stress in the FE model with URSP connector is less than that of the model with only studs under the same uniformly distributed load. In addition, it can be observed in Figure 18c that under the same load, the deflection at the loading point of models with URSP connectors is larger than that of the model with only studs, and the deflection increases with the arrangement length growth of the URSP connectors. In this case, the cracking load is defined as the value of the uniform pressure when the concrete stress reaches the peak. It can be seen from Figure 18 that the cracking load increases at most by 18% when the length of the region with URSP connectors is 0.5\(L\). Compared with studs applied in composite frame beam only, for each arrangement length of URSP connectors \(L_{\text{{U}}}\) applied in the composite frame, the amplification factor of the cracking load \(R_{F}\) is defined as  
\[R_{F}=\frac{F_{URSP}}{F_{Stud}} \tag{6}\]  
where \(F_{URSP}\) and \(F_{Stud}\) are the cracking loads of the composite frame beam while using URSP connectors and studs, respectively. In the serviceability limit states, the stiffness amplification coefficient is an important factor which can be used to calculate the deflection of the composite beam and is inversely proportional to the deflection. It can be found in Figure 18c that the stiffness amplification coefficient decreases when the URSP connectors are arranged in the composite frame beam. In addition, it decreases to a greater extent with the increment of arrangement length \(L_{\text{{U}}}\) of the URSP connectors. The ratio of the stiffness amplification coefficient \(R_{I}\) is defined as  
\[R_{I}=\frac{\alpha_{URSP}}{\alpha_{Stud}}=\frac{\delta_{URSP}}{\delta_{Stud}} \tag{7}\]  
Figure 18: Results of models subjected to vertical loads. (**a**) Concrete stress; (**b**) rebar stress; (**c**) deflection. where \(\alpha_{URSP}\) and \(\alpha_{Stud}\) are the stiffness amplification coefficients of the composite frame beam when using URSP connectors and studs, respectively.