## 3 Validation of Presented Procedure
The utilization at the buckling load level is shown in Figure 17. The buckling resistance \(\mathrm{\underline{\mathrm{\underline{\mathrm{\alpha_{b=1.189\) was calculated according to authors' procedure and checked with GMNIA value \(\mathrm{\underline{\mathrm{\alpha_{b=1.24\) (Figure 15).\)\) \begin{tabular}{tabular}{}  
\end{tabular} {tabular}{}  
_In Example 5, GMNIA was performed by the authors (Figure 15) using the Open System for Earthquake Engineering Simulation (OPENSEES) software taking into account a geometrical imperfection with the shape of the buckling mode and amplitude of L/500 (\(L_{cr}\)/1000), also considering the residual stresses of a hot-rolled cross-section._  
_In Example 5, the maximum moment \(M_{max}(x=0\ m)\) can be obtained from Equation (26), which serves to verify the value \(M_{max}(x=0\ m)=101.731\ \mathrm{kN}m\) given in Figure 15:_  
\[ \begin{array}{l}M_{\max}\ =\ \frac{F_{EH}\cdot\eta_{min}^{x-15}}{\left(1- \frac{1}{\alpha_{cr}}\right)}+\frac{F_{EH}\cdot\eta_{min}^{x-10}}{\left(1- \frac{1}{\alpha_{cr}}\right)}+\frac{F_{EH}\cdot\eta_{min}^{x-5}}{\left(1- \frac{1}{\alpha_{cr}}\right)}=\\ =\frac{101/1000}{\left(1-\frac{1}{131}\right)}(95+0.41\cdot 225+0.095\cdot 550) \approx 101.731\ \mathrm{kN}\cdot\mathrm{m}\end{array}  \tag{26}\]  
Figure 17: Example 5: UGLI imperfection \(\eta_{init}\), bending moment \(M\), shear force \(V\), and utilization factor \(U_{N+M}=1.0\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Iteration** & \(\alpha_{ult}\) & \(\widetilde{A}\) & \(X\) & \(\alpha_{b}\) & \(x_{cr,i}\) & \(\frac{\eta_{i,i}}{\eta_{0}}\) \\ \hline
1 & 3.0523 & 1.5139 & 0.3372 & 1.0292 & 0.0 & 2.0485 \\ \hline
2 & 9.5979 & 2.6845 & 0.1224 & 1.1749 & 10 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Example 5: key values for each iteration. _If the value of the force of \(F_{Ed,2}=225\) kN (Figure 14) changes, the values of UGLI imperfection amplitude and the critical section position \(x_{cr}\) are given in Table 6. There is no problem to find the location of the critical section \(x_{cr}\). From Table 6, it can be concluded that UGLI imperfection amplitude has the step change when the critical section position changes from \(x_{cr}=10\) to \(5\) m. It changes from \(\eta_{0}=101\) to \(145\) mm for steel grade S355._  
_In Table 7, the buckling resistance \(\alpha_{b}\) calculated according to the authors' procedure is checked with the GMNIA value for steel grades 235, 275 and 355._  
_In [PERSON]'s work [24], where for UGLI imperfection the incorrect name EUGLI is used, the critical section \(x_{cr}\) could not be found using the utilization factor matrix due to numerical issues. According to the procedure proposed in this work, the critical section \(x_{cr}\) is possible to find. It may be concluded that [PERSON]'s method has no obstacles._  
**Example 6. **_[PERSON] solved in [30] by equivalent member method given in [2] the member made of aluminum alloy EN AW-6005A-T6, buckling class A, with a yield strength \(f_{0}=215\) MPa, ultimate strength \(f_{u}=260\) MPa and \(\gamma_{M1}=1.1\). He also took into account welds located in the fixed end and in the place where a member changes his cross-section._  
_We took from example 6.11 [30] only the geometry \(L=5\) m and loading. The purpose was to show that also in example 6.11 [30], which is similar to Example 6, the presented procedure may obtain desired results without problems. Our member (Figure 18) is made of the aluminum alloy EN AW-6061-T6, buckling class A, \(E=70\),000 MPa, \(f_{0}=240\) MPa, \(f_{u}=260\) MPa (Table 3.2b [2]), \(\gamma_{M1}=1.1\). The section properties of EP (extruded profile) are \(A_{1}=38.8\) cm\({}^{2}\), \(I_{1}=1673\) cm\({}^{4}\), \(W_{1}=220\) cm\({}^{3}\) and \(A_{2}=91\) cm\({}^{2}\), \(I_{2}=8091\) cm\({}^{4}\), \(W_{2}=736\) cm\({}^{3}\)._