# Investigating the Effect of Screw Size on the Stress Level in MERO Joint for Space Frame Structures
## 2 Geometry and Dimensions of MERO Double-Layer Joint
### Loading and Analysis  
In a MERO joint, the screws which are located in the base plane are always in tension, but inclined holes are loaded with a compression-tension pair force. The place, where forces are applied, is regarded as the most important subject in loading analysis. So, herein, to follow a practical loading condition, compressive loading has been applied to the conical piece while screws bear the tensile forces. Thus, in the tensile direction the effect of nuts and in the compressive loading direction the effect of details of screws can be neglected with a good approximation. Analyses in ANSYS were conducted through linear static analysis method and stress results presented in section 5 are Von Mises stresses generated in ball joints. Tensile forces are applied to threads of holes in the ball, whereas the location of the compressive loads is on the interface between the sleeve and the shear surface of the ball. The compressive-tensile force pair leads to a static equilibrium in the ball. Force values of 5 tons are applied to each point in the second layer of the joint. Figure 6 shows loading of the MERO joint in ANSYS. Loading of the system under a uni-axial 5 tons tensile force (red arrow) has been depicted in Figure 7, while Figures 8 and 9 show the system subject to application of bi-axial and simultaneous compressive-tensile loading, respectively. No-displacement constraint in point B over the conical piece, and constraint in  
Figure 5: The grid of the whole system including the MERO joint, pipe, conical piece, sleeve, and the screw. (**a**) Perspective, (**b**) Section.  
point C along z axis to avoid undesirable rotations are the applied boundary conditions. In modeling and simulations threads have not been modeled. Instead of modeling the threads over two surfaces of the screw and the hole, two cylindrical surfaces with permanent and complete connection (Bonded contact) are simulated which is an acceptable approximation in assembly collection simulations. Moreover, modeling details of threads, due to the specific geometrical nature of them, will result in point stress concentration and divergence of results to inexact values. To avoid this problem, grid of the threads region (crest and root) should be very fine. On the other hand, modeling such very find grids for threads will cause computational cost to increase significantly. Von Mises stress contours on the body of the screw under 5 tons tensile force have been illustrated in Figure 10a,b while the resultant stresses in the ball joint have been presented in Figure 11a,b. As can be observed in these figures, stress in two positions in the bolt has become critical which are beneath the screw head and the hole embedded in the screw.  
Figure 6: Applying a load to the MERO joint.  
Figure 7: Loading of the system under a uni-axial 5 tons tensile force.  
Figure 8: Loading of the system under bi-axial 5 tons tensile forces.  
Figure 10: _Cont._  
Figure 9: Loading of the system under simultaneous compressive-tensile 5 tons forces.  
Figure 11: Von [PERSON] stress contour in MERO joint ball under a 5 tons tensile force. (**a**) Perspective, (**b**) Section.  
Figure 10: [PERSON] stress contour over the body of the screw under a 5 tons tensile force. (**a**) Perspective, (**b**) Section.