# Finite Element Analysis of Proposed Self-Locking Joint for Modular Steel Structures
## 5 Parametric Study on the Proposed Connection  
The seismic performance of a building is highly affected by the strength and stiffness of the column beam joint. In current codes [32; 33], a joint may be classified as rigid, nominally pinned, or semi-rigid according to its rotational stiffness capacity. For a bolted connection, the surface conditions of connecting plates and pretension force applied to the bolts influence the initial stiffness of the connection. However, the size of the section affects the rotation capacity of a joint. As for the proposed connection, it is involved a dual bolted and plug-in connection. Therefore, it is essential to know the factors that can affect the proposed connection's performance under lateral load and as well as under axial tensile load. A parametric study presented here is divided into two parts representing by 10 FE models of various combination parameters as indicates in Table 5. There are four different parameters evaluated in this parametric study namely as spring pin and bolt, bolt pretensioned load, thickness of beam and coefficient of friction. In the first part (Cp2 and Cp3), the effect of the spring pin and bolt at the outer face of the column was evaluated. Boundary conditions for this setup were selected as pinned support at the bottom of the lower column and the ends of beams. The beams were allowed to rotate in the loading direction only while an axial tension load was applied on the top upper column [24]. While in the second part (Cp1, Cp4, Cp5, Cp6, Cp7, Cp8, and Cp9), the moment-rotation curve under lateral load was computed by changing different parameters. (i) Bolt pretension load: The bolt pretension load is applied with different ranges of snug tightening. The applied bolt load was calculated according to Equation (13) obtained from Eurocode 3 [32]. \[F_{pcd}=0.7f_{ub}*A_{s}/\gamma_{M7} \tag{13}\]  
where \(F_{pcd}\) is designed to preload force, \(f_{ub}\) is the ultimate tensile strength of the bolt, \(A_{s}\) is the tensile stress area of the bolt, and \(\gamma_{M7}\) is taken as 1.1. (ii) Thickness of beams: Another parameter considered is the thickness of beams which were selected from a range of joints to satisfy the condition of \"strong column--weak beam\" joint to the condition of \"weak column-strong beam\" joint, this range was selected to know the seismic behavior of proposed connection in both conditions. (iii) Coefficient of friction \(\mu\). The coefficient of friction was modified from 0.19 to 0.23 and then 0.27 between all contact surfaces in the model, i.e., plates to the column, SHS sidewalls, and bolt surfaces. These values reflect varying forms of surface treatment, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parts** & **Steel Grade** & \begin{tabular}{c} **Elastic** \\ **Modulus** \\ **(Gpa)** \\ \end{tabular} & \begin{tabular}{c} **Yield Strength** \\ **(Mpa)** \\ \end{tabular} & \begin{tabular}{c} **Ultimate** \\ **Strength (Mpa)** \\ \end{tabular} & \begin{tabular}{c} **Elongation (\%)** \\ **(v)** \\ \end{tabular} & \begin{tabular}{c} **Poisson Ratio** \\ **(v)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Beam and \\ column \\ Component of \\ connectors \\ \end{tabular} & \begin{tabular}{c} Q345B \\ U20452 (45\#) \\ \end{tabular} & 195.8 & 393.8 & 523.5 & 33.8 & 0.3 \\ \hline \
\begin{tabular}{c} Beam and \\ column \\ Component of \\ connectors \\ \end{tabular} & U20452 (45\#) & 193.3 & 441.3 & 553.7 & 30.6 & 0.3 \\ \hline
\begin{tabular}{c} Bolt \\ \end{tabular} & 8.8 & 210 & 640 & 880 & 12 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical properties of materials [18].