## Nomenclature  
\(\alpha\) is the imperfection factor related to the flexural buckling curve (Tables 6.1 and 6.2 of EN 1993-1-1 [1]; Tables 3.2 and 6.6 in EN 1999-1-1 [2]). \(\alpha_{LT}\) is the imperfection factor for lateral torsional buckling related to buckling curve (Tables 6.3, 6.4 and 6.5 in EN 1993-1-1 [1]; 6.3.2.2 in EN 1999-1-1 [2]). \(\alpha_{cr}\) is the minimum load amplifier for the axial force configuration in members to reach the elastic critical buckling load (5.2.1(3) in [1]; 5.2.1(3) in [2]). \(\alpha_{all}\) is the amplifier for the load of members to reach the characteristic resistance of the critical cross-section (6.3.4(2) in [1], where more the convenient symbol \(\alpha_{all,k}\) is used; [2] does not know such quantity and symbol). \(\alpha_{b}\) is the load amplifier of members to reach the ultimate buckling load (see Equations (12) and (16); the symbol is not used in [1; 2]). \(\gamma_{M0}\) is the partial safety factor for the resistance of cross-section whatever the class is (6.1 in [1]; [2] does not know such quantity and symbol). \(\gamma_{M1}\) is the partial safety factor for the resistance of members to instability assessed by member checks (6.1 in [1] and 6.1.3; Table 6.1 in [2]). \(\chi\) is the reduction factor for the relevant buckling curve (6.3.1.2 in [1]; 6.3.1.2 in [2]). \(\overline{\lambda}\) is the relative slenderness (6.3.1.2 in [1]; 6.3.1.2 in [2]). \(\overline{\lambda}_{0}\) is the plateau length of buckling curves (for steel [1]: 0.2; for the aluminum alloy [2]: 0.1 for buckling class A and 0.0 for buckling class B). \(\overline{\lambda}_{LT}\) is the relative slenderness for lateral torsional buckling (6.3.2.2 and 6.3.2 in [1]; 6.3.2.2 in [2]). \(\overline{\lambda}_{TF}\) is the relative slenderness for torsional flexural buckling. \(\overline{\lambda}_{LT,0}\) is the plateau length of lateral torsional buckling curves. \(\beta\) is the correction factor for lateral torsional buckling curves (6.3.2.3 in [1]; [2] does not know such quantity and symbol). \(\eta_{0}\) is the amplitude of UGLI imperfection. \(\left\{\eta_{init}\right\}\) is UGLI imperfection in the shape of elastic critical buckling mode. \(\left\{\eta_{\alpha r}\right\}\) is the shape of elastic critical buckling mode. \(\eta_{\alpha r,r}\) is the displacement of the buckling shape component perpendicular to axis y along the x axis. \(\eta_{\alpha r,r\beta}\) is the displacement of the buckling shape component perpendicular to axis z along the x axis. \(\eta_{\alpha r,0x}\) is the torsional rotation of the buckling shape component about shear center axis along the x axis. \(A\) is the cross-sectional area. \(E\) is the modulus of elasticity (210,000 MPa for steel [1]; 70,000 MPa for aluminum alloy [2]). \(\phi_{0,k}\) is the design (characteristic) value of the initial imperfection amplitude of the equivalent member used in the calculation of UGLI imperfection amplitude. It is given in 5.3.2(11) [1; 2] or in 7.3.6(1) [4] or in 7.3.2(11) in [5]. The indices \(d\) and \(k\) are sometimes omitted. \(e_{0}\) is the local bow imperfection given in Table 5.1[1; 2] or in 7.3.3.1(1)[4] or in 7.3.2(3)b)[5]. It is used when performing second order analysis including member imperfections related to flexural buckling. It is not used in UGLI imperfech method and must not be commuted with the above amplitude. \(l_{y}\), \(l_{z}\) are the second moments of area with respect to the y, z axes. \(l_{w}\) is the warping constant. \(N_{cr}\) is the elastic critical force of the relevant buckling mode based on the gross cross-section properties. \(N_{Ed}\) is the design value of normal force. \(N_{\text{Rk}}\) is the characteristic resistance of normal force in the critical section (depending on Class 1, 2 and 3 cross-section). \(M_{\text{Rk}}\) is the characteristic resistance of bending moment in the critical section (depending on Class 1, 2 and 3 cross-section). \(W_{z}\) is the section modulus about z axis (depending on Class 1, 2 and 3 cross-section).