Consistent approach of equivalent geometric imperfections for the stability cases flexural and lateral torsional buckling considering steel grades up to S 700


The equivalent geometric imperfection method can easily be applied within the framework of a computer-based analysis of steel structures using the state-of-the-art computational tools. Internal forces are computed according to 2nd order theory considering the effects of equivalent geometric imperfections. These internal forces are used for a cross-section verification. The equivalent imperfections take into account, among other things, the effects of geometrical imperfections, residual stresses as well as stiffness degradation and load-redistribution due to partial yielding of the structural members.

The framework for the structural analysis provided in prEN 1993-1-1:2018 facilitates the application of the equivalent geometric imperfection method for flexural and lateral-torsional buckling verification.

In the context of the revision of EN 1993-1-1: 2010, Lindner et. al. recommended to critically reflect the existing approaches for equivalent geometric imperfections. The cause and background of this discussion were among other things: (i) the equivalent bow imperfections were specified for a member that is subjected only to a compression force. For flexural buckling, however, the extended yielding range and stiffness reduction due to additional bending moments should be taken into account. In case of lateral torsional buckling the divergent stability behavior between a member subjected to uniform compression and latter case ought to be considered. (ii) As part of the further development of EN 1993-1-1, structural steels with steel grades up to S700 are considered.

The method using equivalent geometric imperfections is directly connected with the used cross section interaction. Therefore, the discussion concerning the decisive cross section interaction is part of the further development of EN 1993-1-1. The partial internal forces method can be determined in case of all stability cases and considers the transition of compact and slender members. Therefore, the present study concerning equivalent geometric imperfections is based on the partial internal forces method and includes steel grades up to S 700. Initial bow imperfections for doubly symmetric I-/H- cross sections subjected to lateral torsional buckling have been determined based on a numerical simulation study. For simplification, the bow imperfections have been proposed to be independent of the steel grade and bending moment distribution for design purposes. A comparative study has shown that the proposed bow imperfections lead to suitable design results compared to numerically determined member capacities. The proposal forms a consistent approach for the structural design of compact and slender steel members.


Winkler, R., & Knobloch, M. (2019). Effect of the steel grade on equivalent geometric imperfections for lateral torsional buckling. In F. Wald & M. Jandera (Hrsg.), Stability and ductility of steel structures 2019: proceedings of the International Colloquia on Stability and Ductility of Steel Structures, Prague, Czech Republic, September 11-13, 2019 (S. 1283–1291).

Winkler, R., & Knobloch, M. (2018). Geometrische Ersatzimperfektionen zur Anwendung des Teilschnittgrößenverfahrens für Biegeknicken um die schwache Querschnittsachse. Stahlbau87(4), 308–322.

Winkler, R., Niebuhr, M., Knobloch, M., & Kindmann, R. (2017). Geometrische Ersatzimperfektionen für Biegeknicken um die starke Querschnittsachse unter Berücksichtigung des Teilschnittgrößenverfahrens: Herrn Univ.‐Prof. Dr.‐Ing. Rolf Kindmann zur Vollendung seines 70. Lebensjahrs gewidmet. Stahlbau86(11), 961–971.

Winkler, R., Reddel, J., & Knobloch, M. (2017). Geometrische Ersatzimperfektionen stabförmiger Bauteile unter Normalkraft, Biegung und Torsion. Stahlbau86(8), 716–728.

Contact person

Dr. Rebekka Winkler