## 3 Results  
To control the accuracy of the equations obtained and the developed methodology, the first step was to solve the test problem in elastic formulation with subsequent comparison in the LIRA-SAPR software package [30]. The solution was carried out with the following initial data: \(D=0.3\) m, \(\delta=2\) mm, \(E_{b}=3\times 10^{4}\) MPa, \(E_{s}=2\times 10^{5}\) MPa, \(F=100\) kN, \(e=D/2\), \(\
u_{s}=0.3\), \(\
u_{b}=0.2\). By virtue of symmetry, half of the cross-section was considered. The LIRA-SAPR software package solved the problem in the three-dimensional formulation, volumetric prismatic FE modeled concrete, and the steel shell was modeled by flat shell FE. To exclude local effects at the point of application of the force, the plate of high rigidity was installed at the upper end of the column. The calculation scheme is shown in Figure 4.  
The resulting mosaics of stresses \(\sigma_{z}\), \(\sigma_{x}\), \(\sigma_{y}\) are shown in Figures 5-7. A comparison of the maximum stress values in LIRA-SAPR and MATLAB is given in Table 1.  
Figure 6: Mosaic of stresses \(\sigma_{x}\) (MPa): (**a**) MATLAB; (**b**) LIRA-SAPR. Figure 7: Mosaic of stresses \(\sigma_{y}\) (MPa): (**a**) MATLAB; (**b**) LIRA-SAPR. Also, the developed methodology and software was tested on experimental data presented in the works of [PERSON] and [PERSON] [31; 32; 33]. The comparison with the experimental data for two series of columns with an outer diameter of the concrete core of 159 and 219 mm and wall thickness of 6 and 8 mm, can be introduced respectively. Table 2 presents the experimental values of the ultimate loads \(N_{u,\mathrm{exp}}\), the theoretical values \(N_{u,theor}\) were obtained, as well as the values of the ultimate loads \(N_{u,bs}\), calculated without taking into account the lateral compression of the core. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\sigma_{z}\), **MPa** & \(\sigma_{x}\), **MPa** & \(\sigma_{y}\), **MPa** \\ \hline MATLAB & 5.23 & 0.125 & 0.0659 \\ LIRA-SAPR & 5.2 & 0.123 & 0.0639 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of maximum stresses in LIRA-SAPR and MATLAB. Figure 8: Mosaic of stresses \(\sigma_{y}\) (MPa) for the finer FE mesh in MATLAB. For all specimens, the modulus of elasticity of steel was taken equal to \(E_{s}\) = 2 \(\times\) 10\({}^{5}\) MPa and the yield strength was assumed to be \(R_{y}\) = 400 MPa. For the samples 1-3, the initial modulus of elasticity of concrete \(E_{b0}\) and tensile strength \(R_{bt}\) were taken \(E_{b0}\) = 3 \(\times\) 10\({}^{4}\) MPa and \(R_{bt}\) = 1.8 MPa. For the samples 4-6: \(E_{b0}\) = 3.7 \(\times\) 10\({}^{4}\) MPa and \(R_{bt}\) = 2.25 MPa. From Table 2, it can be seen that the agreement of the results is quite good; the greatest deviation of the ultimate loads theoretical values from the experimental ones is  
\[\delta=\frac{\left|N_{u,\text{exp}}-N_{u,\text{theor}}\right|}{N_{u,\text{exp }}}\cdot 100\%=\frac{\left|1412-1430\right|}{1412}\cdot 100\%=1.3\%. \tag{42}\]  
Figures 9 and 10 show the theoretical graphs of changes in stresses \(\sigma_{s\theta}\) at \(y\) = -\(R\) (at the point with the lowest absolute value of the compressive stresses \(\sigma_{s\Sigma}\)) and \(y\) = \(R\) (where the highest compressive stresses along \(z\) occur) depending on the load for columns 1-3 in Table 2.  
From the presented graphs, it can be seen that--with an increase in eccentricity--the stresses \(\sigma_{s\theta}\) decrease, which also indicates a reduction in the stresses of the lateral compression of concrete. This explains the fact that the area of effective operation of CFST columns is small eccentricities of the longitudinal force.