## 5 Conclusions  
During this study, the effects of the number of rivets, number of rivet rows, rivet arrangement, and the rivet row spacing on the lap joint strength were first investigated with the peak load used as the evaluation index. Since changing the rivet spacing or the edge distance leads to changes in the plate width, the effects of the rivet spacing and the edge distance on the lap joint strength were also studied while using the line load density as the evaluation index. Finally, a spring-mass model was developed. The study produced four primary conclusions:  
1. The primary failure forms in riveted lap joints are rivet shear damage and plate fracture. The failure form follows the \"strength competition\" principle. When the total rivet strength is less than the remaining strength of the plate, rivet shear damage  
Figure 23: Comparisons between theoretical and simulated curves: (**a**) 8-5-22222-8-20-12 (**b**) 8-5-22222-12-20-12 (**c**) 8-5-22222-12-16-12 (**d**) 8-5-22222-12-24-12.  
occurs. At this point, the peak load is linearly related to the number of rivets. When the total rivet strength is greater than the remaining strength of the plate, the plate then fractures. In this case, the fracture area is primarily related to the rivet arrangement. When each row contains the same number of rivets, fracture occurs at the load end. When the number of rivets varies between rows, fracture occurs on the side with more rivets.
2. When there are more than two rivet rows, more rivets should be placed in the middle, and fewer rivets should be placed on both sides. There is no significant difference between the lap strengths of the staggered and parallel arrangements.
3. For a certain edge distance and row spacing arrangement, the rivet spacing is the primary factor that affects the mechanical properties of a lap joint. When the rivet spacing is less than 5d, the lap joint strength increases with increases in the rivet spacing. When the rivet spacing is greater than 5d, the lap joint strength does not change significantly. For a certain rivet spacing and row spacing arrangement, the edge distance is the primary factor that affects the mechanical properties of the lap joint. When the edge distance is less than 3d, the lap strength increases with increases in the edge distance; however, when the edge distance is greater than 3d, the lap strength does not change significantly. For a certain rivet spacing and edge distance arrangement, the effect of the row spacing on the lap strength is limited. Further analysis shows that the lap length has a limited effect on the lap strength.
4. A spring-mass model was developed. The model explains that the presence of a bypass load leads to significantly higher stresses around the riveted holes at the ends of a lap joint than at the intermediate locations. In addition, the force-displacement curves corresponding to different rivet spacing, edge distance, and row spacing can be calculated by the model, which reduces the test costs of studying the rivet arrangement method.  
K.R.: Conceptualization, K.R. and H.H.; data curation, W.X.; methodology, H.Q.; project administration, K.R. and W.X.; software, K.R.; supervision, H.Q. and H.H.; validation, K.R. and H.H.; writing--original draft, W.X. and H.H.; writing--review and editing, K.R. and H.H. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data will be made available on request.  
The authors declare no conflict of interest.