# Finite Element Analysis of Proposed Self-Locking Joint for Modular Steel Structures
## 6 Conclusions  
This study proposed a self-locking connection to address the issues related to fixing intermodular connections between modules. This connection consists of adapters, center plate, a flat spring and long bolts. The proposed connection uses a flat spring mechanism and does not require extra workspace between modules. Finite element analysis was performed on the proposed connection design for modular steel building using ABAQUS software. The aim of the numerical study was to know the stress distribution among different connection components and to the understand the failure mode of structural members considering various parameters. The parametric study was conducted by varying beam thickness, bolt pretension force and friction coefficient \(\upmu\). The conclusions derived from the analysis are set below:  
1. The proposed connection was able to maintain 80% of Mu at a drift ratio of 0.04 radian, hence meeting the criteria of ductility; therefore, it can be categorized as special moment frame (SMF) according to AISC. The initial stiffness ratio was leftover between the boundaries of the rigid connection and pinned connection; for that reason, the proposed connection can be characterized as a semi-rigid connection according to Eurocode 3. 2. The spring pin and outer bolt significantly mitigated the separation between column and connection under axial tension load. The proposed connection contributed sufficiently to carrying the bending moment produced at the joint; the upper and lower adapter has taken a load from the respective column by bearing action, which causes shear stress on the walls of the adapter. 3. Load carrying capacity and initial rotational stiffness of joint increased with an increase in thickness of floor and ceiling beams. Bolt pretension force was up to 20% of ultimate strength of the bolt shown, increasing moment carrying capacity of the joint, \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Joint ID** & \(M_{pcb}\) **(\(\delta\)Nm)** & \(M_{pcb}\) **(\(\delta\)Nm)** & \(M_{pi}\) **(\(\delta\)Nm)** & \(M_{s(\delta\)Nm)} & \(M_{s(\delta\)Nm)} & \(M_{b(\delta\)Nm)} & \(\Theta_{a}\) & \(\Theta_{y}\) & \(\Delta_{d}\) & \(M_{b(\delta\)Nm)} \\ \hline Cp1 & 86.68 & 107.1 & 193.7 & 287 & 181 & 276 & 0.055 & 0.020 & 2.75 & 0.96 \\ Cp4 & 155.6 & 171.7 & 327.3 & 327 & 218 & 306 & 0.060 & 0.020 & 3 & 0.93 \\ Cp5 & 129.6 & 129.6 & 259.2 & 312 & 172.8 & 293 & 0.064 & 0.018 & 3.5 & 0.93 \\ Cp6 & 86.68 & 107.1 & 193.7 & 273 & 182 & 266 & 0.060 & 0.020 & 3 & 0.97 \\ Cp7 & 86.68 & 107.1 & 193.7 & 273 & 182 & 273 & 0.058 & 0.021 & 2.76 & 1.0 \\ Cp8 & 86.68 & 107.1 & 193.7 & 284 & 189.3 & 272 & 0.059 & 0.021 & 2.80 & 0.95 \\ Cp9 & 86.68 & 107.1 & 193.7 & 288 & 192 & 274 & 0.056 & 0.02 & 2.80 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ductility and strength characteristics for all FE models. further increasing the pretension force, and resulting in a decreased moment capacity of the joint. Conceptualization, G.N. ; methodology, G.N. and N.A.S. ; software, G.N. ; validation, G.N., N.A.S. and N.A.B. ; formal analysis, G.N. and N.A.S. ; investigation, I.A.K., N.A.B. and N.A.M.N. ; resources, G.N. and N.A.S. ; data curation, G.N. and N.A.S. ; writing--original draft preparation, G.N. and N.A.S. ; writing--review and editing, I.A.K., N.A.B. and N.A.M.N. ; visualization, G.N. and N.A.S. ; supervision, N.A.S., I.A.K. and N.A.B. ; project administration, N.A.S. ; funding acquisition, N.A.S. All authors have read and agreed to the published version of the manuscript. This research was funded by Fundamental Research Grant Scheme, Ministry of Higher Education Malaysia (grant number: FRGS/1/2018/TK01/UPM/02/9). Not applicable. The data used to support the findings of this study are available from the corresponding author upon request. The authors would like to thank the sponsor of this research which funded using Fundamental Research Grant Scheme (FRGS), Ministry of Higher Education of Malaysia with Grant number: FRGS/1/2018/TK01/UPM/02/9.