Frames with unique global and local imperfection in the shape of the elastic buckling mode (Part 1)

The principles and applications of the procedure using the equivalent unique global and local imperfection hinit,m (x) in the shape of the elastic buckling mode given in EN1993-1-1:2005, 5.3.2(11) and EN1999-1-1:2005 are presented here. The maximum amplitude of such an imperfection is determined from the fundamental requirement: the buckling resistance of the frame structure with axially loaded members only should be equal to the flexural buckling resistance of the equivalent member. The buckling resistance of such a frame is determined by the resistance of its critical cross-section m with allowance for second-order effects.
In this paper basic formulas defining the equivalent unique global and local imperfection are established and other formulas useful for easier calculations in practical cases are shown too. Numerical examples provide guidance on the proper application of the procedure presented. The verification of the buckling resistance for the continuous frame in a numerical example shows good agreement with other methods from EN 1993-1-1:2005, 5.2.2(3) with application of imperfections according to EN 1993-1-1:2005, 5.3.2(3). Full agreement with the method 5.2.2(3)c) of EN 1993-1-1:2005 is always reached for individual uniform members with constant axial force along their whole length.