# Mechanics of Screw Joints Solved as Beams Placed in a Tangential Elastic Foundation
## 3 Material and Methods  
To solve the problem of pulling screws out of fasteners (see the previous text) it is advisable:  
1. To prepare test samples for woodwork screw joints in the laboratory.
2. To determine experimentally the dependence of pulling force \(\mathrm{F}=N=f(u,\,\dots)\) in the laboratory (i.e., the pull-out test).
3. To determine the appropriate shapes of the reaction force \(\mathrm{q}_{N}\) (i.e., to design a physical model of the tangential foundation) based on the evaluation of the experiment (laboratory measurements, regression methods, etc.).
4. To solve differential Equation (3) based on the knowledge of the reaction force \(\mathrm{q}_{N}\), i.e., to acquire the axial displacement \(u\).
5. To compare the obtained results with experiments and to evaluate proposed models of the tangential foundation, including the correctness of theory and use.
6. To check dependencies on other materials such as bone (i.e., \"similar\" applications in biomechanics, traumatology and orthopaedics).
7. To conduct a discussion, draw conclusions and suggest future possible applications and other possible solutions.  
The screws examined in this publication are made of two types of material, namely 1.4441 stainless steel (AISI 316L) and Ti6 Al4V titanium alloy. The basic mechanical properties of these materials are given in Table 1 (see references [36; 37; 40]). Hence, screws are considered to be isotropic, homogeneous materials and biocompatible from a human perspective.  
The screws are made using either a conventional machining method or metal powder 3D printing technology where machining is the finishing process (see [34; 35; 37; 38; 39]). However, the screw production technology is not dealt with in this article because the main objective is to verify the material models of the tangential elastic foundation. Since the screws are stiffer than wood (i.e., the screws have a greater modulus of elasticity than wood), the screw production technology does not have a significant impact on the results of the pull-out tests (see [13; 24; 37]).  
Two types of screws, HB 6.5 (full cross-section) and HB 7 (cannulated cross-section, i.e., hollow cross-section profile), are used for both computational and experimental measurements. Both screws have thread length \(\mathrm{L}_{2}=0.09\) m. The manufacturer of these screws is the Czech company MEDIN a.s. For more details, see Table 2 and the web page of MEDIN a.s. [20].  
Thus, the tangential foundation simply replaces the effect of wood-screwed parts (i.e., simplifies mechanical contact), and this has a major impact on the practicality of the entire proposed model. Then, assuming that the functional dependency of \(\mathrm{q}_{N}\) is correctly determined, the model can be used for generally anisotropic and non-homogeneous and dry or moist materials, which is undoubtedly the case for wood. Therefore, the tangential foundation offers the possibility of significant and highly effective simplification in conventional timber structure calculations.  
Wood is hygroscopic but \"dry\" wood of _Picea abies_ was chosen for the first verification.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Modulus of**} & \multirow{2}{*}{**Yield Limit [MPa]**} & \multirow{2}{*}{**Fracture Limit [MPa]**} \\  & **Elasticity \(E\) [Pa]** & & \\ \hline
1.4441 & \(2.1\times 10^{11}\) & 892 & 977 \\ \hline Ti6 Al4V & \(1.06\times 10^{11}\) & 919 & 1034 \\ \hline \end{tabular}
\end{table}
Table 1: Basic material information on the applied screws.