# A Component-Based Model for Novel Modular Connections with Inbuild Component
## 3 Component-Based Model
### Characteristics of Components
#### 3.2.2 Converged Section Component  
The dimension of \"L\" type intramodule connection was shown in Figure 34. The converged section components were marked as red dashed lines which are located at the column corresponding to the top and bottom flanges of the beam. For the sake of easy description, the component near the column end was named \"II\" and the other side was named \"I\". The moment direction from \"II\" to \"I\" was defined as positive. The deformation mode of the converged section component was shown in Figure 35; \(\Delta_{A}\) represents the vertical deformation caused by bending of the main column surface, and \(\Delta_{B}\) represents the vertical deformation caused by tension or compression of the column side wall. The total displacement \(\Delta_{i}\) of the converged section component can be obtained with \(\Delta_{A}\) plus \(\Delta_{B}\). According to the previous parameter analysis and the research in RHS joints [31] area, the main factors affecting the mechanical properties of the converged section component include the height (\(h_{c}\)) and thickness (\(t_{c}\)) of the column, the thickness of the beam end plate (\(t_{p}\)), the length of the loading area (beam flange width (\(w\))). Moreover, one of the main features of intramodule connection is that the joint panel is very close to the column open end. It will lead to the distance (d) between the converged section model and the column end becoming an important influencing parameter. Based on the above reasons, this paper used the fitting method to obtained the force-displacement relationship of the converged section component. The reference finite element model was shown in Figure 36. The length of the model was six times the height. The model was meshed by the \"S4\" shell element in Abaqus. The material properties are the same as the refined finite element model in Section 2.3. It was found that the force-displacement relationship of the converged section component can be expressed as  
\[F_{b}=P_{1}\ \times\Delta_{i}/(P_{2}+\Delta_{i}) \tag{5}\]  
Figure 34: Dimensions and geometric construction of intramodule connection. Figure 35: Deformation model of converged section component. \(P_{1}\) and \(P_{2}\) are the shape parameters. As \(\Delta_{i}\) approaches infinity, \(F_{b}\) is equal to \(P_{1}\). As \(\Delta_{i}\) is equal to 0, the slope of the functions is \(P_{1}\)/\(P_{2}\). It illustrates that \(P_{1}\) and \(P_{2}\) reflect the initial stiffness and ultimate strength of the converged section component to a certain extent. Therefore, studying the influence of various factors on the mechanical properties of the component section area is equivalent to studying that of various factors on \(P_{1}\) and \(P_{2}\). The relationship between (\(P_{1}\), \(P_{2}\)) and (\(h_{c}\), \(t_{c}\)) was first studied. Using the control variable method, the thickness of the beam end plate (\(t_{p}\)) was set as 0, and the width of the beam flange (w) was equal to the height of the ring region \(h_{c}\). Finite element modeling was carried out for square columns with a height of 100 mm to 500 mm in Appendix 1 of \"Cold formed Hollow Steel for Structure\" [28], and 79 groups of numerical models were built. The force-displacement curves of 79 models were fitted according to the rules of (5), and 79 groups of (\(P_{1}\), \(P_{2}\)) were obtained. Constructing \(f_{1}(h_{c},t_{c})\) and \(g_{1}(h_{c},t_{c})\) represents the relation between \(P_{1}\) and \(P_{2}\) with (\(h_{c}\), \(t_{c}\)), respectively.