## 6 Conclusions
### The Influence of the Statistical Determinacy of the Structural Element  
The case study represents a numerical but especially analytical analysis, which is a different kind of approach for stability analysis. It assumes linking two theories, namely Cavalieri's principle and elastic buckling theory, in order to perform a comprehensive stability analysis in the elastic domain to increase the elastic buckling load for the beam-type element, through geometric modelling of the cross-section for the beam-type elements, with specific boundary conditions.  
The case study ranges from statically determinate to statically indeterminate structural elements, concerning the imposed kinematic boundary conditions. In the case of statically indeterminate structural assemblies, it is not possible to establish a unique numerical value for the stress ratios of the elements, due to the fact that modifying the axial stiffness of an element influences the stress redistribution in the whole structure. In the case of statically determined structural assemblies, it is possible to compute a unique value for the unitary efforts in the structural elements. The case study has proven that in the case of statically determinate structural elements have achieved the highest increase of the critical buckling load. The final result in therm of the achieved increase rates is presented in Figure 25.  
A very important result is highlighted in Figure 25 for the beam-type element with elastic supports. The elastic support connections modify significantly the behavior of the structural element under axial loads and influence excessively the critical buckling load. In the case of constant cross-sections increasing the area of the cross-section is not a rational solution and a favorable failure condition is practically impossible to achieve. Modelling a variable cross-section beam-type element is a practical solution to increase the critical buckling load above the value of the resistance of the cross-section subjected to uniform compression. A correct modelling of the shape of the beam-type element, through the moment of inertia, may point to a considerable increase of the critical buckling load, up to 1725% in the present case as against the constant cross-section, with respect to [PERSON]'s principle. A very important aspect is that by imposing elastic support connections instead of ideal ones the critical buckling load is influenced and a significant decrease is observed, up to at least 55% in the studied case. This remark is very important for structural engineers when they establish the geometric and inertial characteristics of a structural element subjected to considerable axial load.  
A certain fact is that statically determinate structures have lack of structural redundancy, but the state of stress and strain can be easily controlled through the whole elastic behavior domain of the beam-type element. By adopting beam-type elements with variable cross-sections it is possible to fix significant numerical values for the length of the elements, with respect to the secondary effects of the rigid joints.  
Based on the presented aspects the adopted beam-type elements with variable cross-sections are recommended in the case of high-span planar or spatial trusses. The mentioned structural assemblies must be statically determinate, made up of a minimum number of elements, with significant length, and using high-quality materials.