# Investigating the Effect of Screw Size on the Stress Level in MERO Joint for Space Frame Structures
## 1 Introduction  
The growth of human population has led to an increasing need for large spaces without the presence of middle pillars, such as community halls, passenger terminals, factory halls, sports stadiums, and recreational and cultural centers. Space frame structures are used in order to cover large spans without columns in these spaces. The term \"space frame structure\" refers to a structural system which is created from a large number of members (modules) connected to the standard parts, creating a lightweight system with high rigidity [1]. In other words, space frame structures are a set of repetitive components including rods and nodes, through different arrangements out which various 3D shapes can be generated [2]. The term \"MERO\" is derived from Mengeringhausen Rohrbauweise, which is a German term for a tubular structure [3]. In a MERO space frame structure, which was first designed and commercially marketed by the MERO Company in 1942 in Germany, the main components include ball (MERO connector), pipe, conical piece, screw or bolt, and sleeve, as shown in Figure 1[4]. In general, the geometrical composition, applied loads, internal forces, and displacements in a space frame structure are not located in one plane. In fact, the combination of the structural geometry, applied loading, internal forces, and structural displacements are out of just one plane [2]. The main advantage of these structures is that the spherical nodes are considered as the influence line for internal forces of all members which intersect at the center of the node. Therefore, there is no eccentricity to cause bending moments for pipes which initially carry compressive and tensile axial forces [5]. The spherical node isregarded as a physical metal piece which is utilized to create stability and integrity between the members of the space structure [6]. The spherical MERO joints are made of CK45 forged steel [2]. Space frame structures using the MERO connector provide the possibility of connecting the maximum number of 18 tubular members in different directions to a single join. The MERO joint is regarded as just one of the various standard joints and includes 18 threaded holes and machining surfaces that are located at 45, 60, and 90\({}^{\circ}\) from each other [7]. Another component of the space frame structures is the pipe, mainly made of ST37 steel, which is used to resist axial tensile and compressive loads. The pipe head is welded to a conical metal piece, which allows for joining of pipes to the spherical joint. In space frame structures, the screw is a detachable element that under applied loads transfers its internal tensile force to the conical piece. These screws have high stiffness classes of 8.8 or 10.9 [6]. Owing to engineering considerations, a conical steel piece welded to the pipe is used at the intersection of the pipe to the MERO joint. In addition, the hexagonal pod (sleeve), which transfers the created internal compressive force to the ball, is used to tighten the screw to the MERO joint. A pin, which passes through the sleeve's hole and the transverse hole of the screw, leads to the simultaneous rotation of the sleeve and screw which allows tightening of the screw. Sleeves are produced in two forms of grooved and holed, and are connected to the screw through a pin [6]. The stability of these structures relies considerably on the joints between pipes. Generally, the joints of space frame structures such as any other civil engineering structure can be classified into rigid, semi-rigid, and pinned [2]. Semi-rigid joints can tolerate tensile and compressive loads, as well as bending moments [8]. Thus, all the forces and moments should be considered when simulating the performance of space frame structures which use this kind of joints. In these structures, joints play a prominent role in the total cost of construction as the joints account for almost 50% of the required materials [9], while at the same time have a substantial effect on the structural behavior of the space frame.