# Investigating the Effect of Screw Size on the Stress Level in MERO Joint for Space Frame Structures
## 4 Conclusions  
In this research paper, a brief introduction and literature review on the space frame structures using MERO ball joints, their importance, applications, materials, geometries, dimensions, and their potentials and capabilities were presented. The key role of joints in space frame structures, their modeling and dynamic behavior, flexibility of the joint in simulations and their effect on the stability and integrity of the whole structure was discussed briefly by referring to the research conducted in literature. Keeping the significance of joints in mind and focusing on the screw size and its corresponding effect on the maximum stress levels created in the ball joints, factor of safety (FOS) and the final weight and cost of the space frame, analyses were conducted in ANSYS finite element (FE) software by considering screw sizes of M12 to M33, and ball joints of diameters 98, 110, and 132 mm under tensile and compressive loads of 4 and 5 tons. Analysis results demonstrated that under the considered loading conditions, smaller ball joints will experience higher stress levels, and, thus, stronger materials should be applied for them. Furthermore, the parabolic behavior of the stress diagram proved that an optimal screw size can be recommended for each size of the MERO double-layer ball joint, for which the minimum stress level will be generated in the joint. Maximum stress level created in the ball joint for three sizes of 98, 110, and 132 mm for each of screws M12, M16, and M20 was evaluated. For screw M20 there is a sharp reduction in stress level in the ball joint from 98 to 110 mm while increasing the ball diameter more than 110 mm for this screw or the ball diameter from 98 to 132 mm for other screws does not have a significant reduction trend. So, application of screw M20 for ball joints of diameter less than 100 mm or more than 1100 mm is not recommended to keep a trade-off between the optimal stress level and the final cost of the structure. Regarding the FOS, it was observed that its value is improved by the increase in the ball diameter and has a roughly linear and reverse relationship with the amount of the applied load. Results showed that screw M12 is not appropriate for loads more than 4 tons as it will result to an FOS of less than 1. Finally, based on the obtained simulation results of the present study, it is recommended to apply the screw M16 for the ball joint of diameter 98 mm, M20 for the ball joint of diameter 110 mm, and M24 screw for the ball joint with diameter of 132 mm to simultaneously obtain the optimal values of stress level generated in the ball joint, FOS, and cost of the structure. Therefore, results of this study show that for analysis and design of space frame systems using MERO joint, a wise selection of the screw size for each appropriate MERO ball joint size for the considered structural configuration of the system in every architectural form can be adopted to obtain the best possible results in terms of the structural responses of the system and construction cost. Moreover, according to the observed stress concentrations under applied loads under the screw head and in the location of the embedded hole in the screw below general recommendations can be drawn:  
* As far as it is possible, it is recommended to avoid embedding a hole in the body of the screw or another mechanism is utilized for rotation and bolt tightening, like press-fitting of the pin in the hole, to prohibit stress concentration in the screw. * A fillet is created under the screw head to decrease the stress concentration in this location. * In case of a fillet generation under the screw head as mentioned above, in the corresponding location over the internal surface of conical piece hole, an appropriate level is created to assure a complete contact between the lower surface of the screw head and the internal surface of the conical piece hole and stress concentration is decreased, simultaneously. Conceptualization, Y.D. and A.M.; methodology, A.M.; validation, Y.D.