Space frame structures satisfy the ever-increasing requirements of societies for providing a variety of structural forms and architectural spaces with special characteristics, such as aesthetic and free-form features, population-wise capacities, and structural performance, among others. Structural behavior of these systems largely depend on the type of joints and their components which are to be considered appropriately in design and analysis. Screws comprise one of the key components of joints in these structures and play a pivotal role in the total cost of the structure, as well as the maximum stress level created in joints. The present study aims to evaluate the effect of screw size on the maximum stress generated in three MERO double-layer ball joints with diameters of 98, 110, and 132 mm as a sample numerical analysis case to pinpoint this fact. Numerical simulations were conducted using ANSYS workbench software. Based on the results, in order to achieve the maximum factor of safety (FOS), the minimum stress, and keeping the total construction cost optimal, it is recommended to use M16, M20, and M24 screws for the ball joints of diameters 98, 110, and 132 mm, respectively.