# Mechanics of Screw Joints Solved as Beams Placed in a Tangential Elastic Foundation
## 1 Introduction  
Screw joints of various types and designs are very common in general technical practice. These are, e.g., removable/permanent joints of wood or other materials (wooden structures, plastics, furniture, construction, automotive industry, etc. ), dowel joints, thread-forming/self-tapping/self-drilling screws, foundation screws, ground screws, shrink rings, etc. (see Figure 1a-c and references [1; 2; 3; 4; 5; 6; 7; 8; 9]). Screw joints are actually a variation of a bolted joint (see [5; 10; 11]). Important applications of screws are also found in surgery and in the treatment of complicated fractures and deformities of humans/animals in traumatology/orthopaedics (external and internal fixations in osteeosyntheses, etc.) (see Figure 1c and, for example, references [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]). It is also surprising that screw joints even occur naturally in some biological tissues, e.g., coxa-trochanteral joints on the legs of the weevil _Trigonopterus oblongus_. The hips of weeevils do not consist of the usual hinges, but of \"unknown\" joints based on a screw-and-nut system. This \"unusual\" biological screw thread is about half a millimeter in size (see references [22; 23]). Pull-out tests of screw joints are carried out mostly in orthopaedics/traumatology applications (see [16; 24; 25; 26; 27; 28]). Orthopaedic/traumatology surgery often involves the use of bone screws to stabilize fractures via fixation techniques. Measured or calculated pull-out strength is commonly used to measure screw fixation strength and for the reliability assessment of screw fixation. However, \"similar\" applications are found in wooden structures (see [1; 4]). For the above reasons, it is advisable to deal with the screw joint mechanics. Therefore, this article deals with new and original material models of screw joints with a focus on the interaction between the screw and the material, including the evaluation of limit states. The purpose is to find the characteristics of a tangential elastic foundation that should simplify the solved task of mechanics. Hence, theory, the derivation of analytical linear/non-linear solutions and first experiments are exposed and evaluated. Unlike common, simplified orientation design procedures (see [1; 2; 3; 5; 6; 11] and others) and calculations using the finite element method (FEM) (see [7; 10; 12; 29; 30] and others), a new approach to solving the problems of screw joints is proposed, applied and experimentally verified in this article. This new approach is based on the application of the proposed tangential elastic foundation as a sufficiently accurate and effective solution to the interaction between the screw and the material to be joined. The results and procedures are valid for the axial tensile stress of the screw joints in the elastic and elasto-plastic areas, including the limit states of pulling the screw out of the material or the screw breakage. Depending on the technical need and severity of the problem, it is possible to choose the proposed shape of the linear/non-linear model, including its analytical solution. Thus, in some cases, the use of new tangential foundation models eliminates the need for sophisticated/time-consuming FEM modeling, and it also offers various simplifications and acceleration of the calculation, or a rapid probability stochastic approach to the solution, for example, using the Monte Carlo method, SBRA method and others (see, e.g., [6; 12; 29; 31; 32; 33]). These may lead to improving the production of screws (i.e., machining and 3D printing technologies, material properties, etc.) (for example, see [20; 34; 35; 36; 37; 38; 39; 40]). Therefore, there is an alternative simplification of the calculation of the tangential elastic foundation applications, which is the subject of our article. Verification of the models  
Figure 1: Common applications and design of engineering screw joints.