Consistency of Imperfections in Steel Eurocodes

The second-order theory was used to analyze the flexural buckling of an individual member simply supported on both member ends, with a uniform double symmetric cross-section under a uniform axial force in an elastic state. The purpose was to show the influence of four different amplitudes of initial imperfections on the shape of the elastic buckling mode ηcrx used in the current EN 1993-1-1 and its new draft, prEN 1993-1-1. Three methods were followed for the analysis: the equivalent member (EM) method, the unique global and local initial (UGLI) imperfection method, and second-order theory with the initial imperfection having an initial local bow imperfection e0. For the relevant quantities, simple formulae were derived and their distribution was drawn on diagrams to represent their graphical interpretations for the first time ever. The formulae and diagrams were valid for the ultimate limit state, which means NEd=Nb,Rd. The influence of four different amplitude values was evaluated: (a) e0,k, proposed for the UGLI imperfection method in the draft EN 1993-1-1; (b) the initial local bow imperfection e0, utilized in the current EN 1993-1-1; (c) the other one employed in its draft; and (d) e0,d, used in the UGLI imperfection method in the current EN 1993-1-1, the current EN 1999-1-1, and the draft prEN 1999-1-1. The main conclusion was that e0,k must not be used in the draft EN 1993-1-1. The UGLI imperfection method was also applied to the column fixed at one end and simply supported at the other end. This example showed the geometrical interpretation of relevant amplitudes. The historical development of the UGLI imperfection method is also presented. All the relations are illustrated in two numerical examples, and the geometrical interpretations of formulae were used in the diagrams. The partial results were verified by the independent computer programs FE-STAB and IQ 100.