# Mechanics of Screw Joints Solved as Beams Placed in a Tangential Elastic Foundation
## 8 Conclusions  
The problem of the solution of beams placed on an elastic foundation is very extensive and of great importance in the theoretical and practical field of science and technology. Typical applications are predominantly in bending tasks. However, this article focuses on new, original and highly efficient tension/pressure load applications.  
A new model of a tangential foundation has been proposed (i.e., the differential equation and its solution) which is applicable to a beam (screw) drilled (placed) in this type of the foundation and subjected to tension/pressure. Properties of this foundation were investigated analytically (compilation and solution of a differential equation including boundary conditions), experimental execution of pull-out tests and finding a suitable simple and sufficiently accurate regression \(N=\frac{\text{F}_{\text{E}}}{2^{n}}\left[1-\cos(\frac{\pi}{u_{\text{E}}}\frac{ u}{\text{F}_{\text{E}}})\right]^{m}\) of the dependence of normal forces \(N\) on elongation (displacement) \(u\) of the screw.  
The scope of application of the new tangential elastic foundation is up to the limit failure state of the screw joint (i.e., either screw breakage or the screw pulling out of the fastener).  
HB 6.5 and HB 7 screws made of stainless steel 1.4441 (AISI 316L) and titanium alloy Ti6 Al4V were chosen as testing tasks. These screws were made using conventional machining methods and also by 3D printing with machining as a finishing operation.  
Dry spruce wood and human/bovine cadaveric bones were chosen as the fasteners.  
A certain variability of the technological procedure of placing (screwing) the screw was selected (the size of the pre-drilled holes (0.0032 m; 0.0055 m) for the thread, the use of the screw taps in the bones according to the surgical procedures in orthopaedics and traumatology).  
From the above, it is clear that the newly designed tangential foundation model can be used for anisotropic/orthotropic or isotropic materials and it depends on the knowledge of the course of pull-out tests of screws in the fasteners.  
In all test cases, a high consensus with the experiment (pull-out tests) was achieved, and the proposed tangential elastic foundation model is suitable for both technical and biomechanical applications.  
Uniaxial pull-out tests afford an accurate method of comparing and evaluating screw joints. Our acquired results (dependencies, limit states \(\langle u_{\text{E}};\,\text{F}_{\text{E}}\rangle\), regressions, etc.) are in good agreements with other references. For example, see [10; 16; 24; 25; 27].  
There are also other possible directions of development in theoretical and application areas, such as biomechanics (i.e., applications in traumatology and orthopaedics, see [12; 13; 14; 15; 17; 19; 24; 26; 28; 29; 30], etc.), wooden structures (see [1; 2; 6; 8]), plastics and probabilistic reliability assessment of screw joints (see [3; 6; 29; 31; 32; 33], etc).  
**Author Contributions:** Conceptualization: [PERSON] and S.M.; Investigation: [PERSON], [PERSON] and L.P.; Formal analysis: J.K., K.P.D. and R.M.; Methodology: J.F. and K.F.; Resources: A.T.; Supervision: [PERSON], [PERSON] and L.B.; Validation: [PERSON], [PERSON] and [PERSON]; Writing--review & editing: [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This article was supported by Czech project SP2021/66 and by projects CZ.02.1.01/0.0/17_049/0008407 and CZ.02.1.01/0.0/0.0/17_049/0008441 within the Operational Programme Research, Development and Education financed by the European Union and from the state budget of the Czech Republic.  
**Data Availability Statement:** Not available.  
**Conflicts of Interest:** The authors declare no conflict of interest.