# A Component-Based Model for Novel Modular Connections with Inbuild Component
## 4 Validation
### Global Connections  
The global simplified finite element model of novel modular connections was shown in Figure 43. It consists of two simplified intramodule connection models and a beam element to represent the intermodule connection. The mechanical properties of intermodule connection should cover all the bending deformation between the upper and lower intramodule connections, such as upper and lower columns, the inbuild component, side plates and the beam-end plate. However, for the novel modular connections, it was obvious that the inbuild component was the main part to transfer the bending moment. Therefore, the cross-section characteristics of the beam can be determined according to the inbuild component dimension. The length of intramodule connection \(l_{p}\) was the distance between the geometric centerline of floor beams and ceiling beams. In this paper, the twin beams were in direct contact, hence the \(l_{p}\) was half of the total height of the ceiling and the floor beams. The intermodule beam was rigidly connected with the upper and lower intramodule connections to simulate the fixing effect of the long-split bolts. In the simplified model, equal vertical displacement was applied to the ends of the floor and ceiling beams simultaneously to ensure that the loading condition was equivalent to that of the refined model in the finite element parameter analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Joint No.**} & \multicolumn{3}{c}{**Initial Stiffness (kNm/rad)**} & \multicolumn{3}{c}{**Ultimate Bending Moment (kNm)**} \\ \cline{2-7}  & **Simplified** & **FEM** & **Error** & **Simplified** & **FEM** & **Error** \\ \hline B250 & 13,180 & 12,438 & +5.9\% & 111 & 115 & \(-\)3.5\% \\ B225 & 10,029 & 9860 & +1.71\% & 105 & 99 & 6.1\% \\ B200 & 7896 & 7650 & +3.2\% & 90 & 84 & 7.1\% \\ B250-P & 13,937 & 13,518 & +3.1\% & 119 & 123 & \(-\)3.3\% \\ B225-P & 10,714 & 10,734 & \(-\)0.19\% & 107 & 104 & 2.9\% \\ B200-P & 8362 & 8318 & +0.53\% & 91 & 87 & 4.6\% \\ B250-P & 14,796 & 14,603 & \(-\)1.3\% & 157 & 167 & \(-\)6.0\% \\ B225-P & 11,316 & 11,606 & \(-\)2.5\% & 128 & 146 & \(-\)12.3\% \\ B200-P & 8849 & 9022 & \(-\)1.9\% & 113 & 125 & 9.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The comparison between simplified and finite element model. Figure 42: Moment-rotation curves of intramodule connections: (**a**) Under positive bending moment without inbuild component; (**b**) Under positive bending moment with inbuild component; (**c**) Under negative bending moment with inbuild component; (**d**) Under negative bending moment with inbuild component and take construction errors into consideration. According to the research results of intramodule connection, a slip stage would appear in the moment-rotation curves when there was construction allowable error. This result was obtained when the geometric centerline of the inbuild component coincides perfectly with that of the side column. However, in the process of the global modular connection deformation, it was difficult to determine the exact relative position between the inbuild component with the upper and lower columns. Therefore, the conservative estimation method as shown in Figure 44 was used to calculate the moment-rotation curve when the allowable error of construction was considered in global modular connections. Thus, the initial stiffness and ultimate bearing capacity of the global modular connections can be obtained, which are summarized in Table 4. When the construction error was \(1\) mm, the predicted initial stiffness of the simplified finite element model was \(2.12\%\) higher than that of the refined finite element model. The predicted initial stiffness of the other models was lower than that of the refined finite element model, and the error of F225C200 model was slightly more than \(10\%\). The average error of the simplified finite element model about initial stiffness was \(3.9\%\).