# Biegeknicken und Biegedrillknicken von Stäben und Stabsystemen auf einheitlicher Grundlage

- Flexural buckling and lateral torsional buckling of members and frames on a common basis

Naumes, Johannes Caspar; Feldmann, Markus (Thesis advisor)

*Aachen : Shaker (2010)*

Dissertation / PhD Thesis

Zugl.: Aachen, Techn. Hochsch., Diss., 2009

Abstract

Eurocode 3 Part 1-1 gives design rules for flexural and lateral torsional buckling of structural members and frames treating both failure modes as different stability phenomena, so that for the assessment of these phenomena two different reduction curves chi.c and chi.LT are applied. While the flexural buckling curve chi.c is based on a mechanical model, with an equivalent geometric imperfection that fulfils the reliability requirements of EN 1990 - Annex D, the lateral torsional buckling curve chi.LT is the result of "estimations" which are based on FE-calculation with certain assumptions leaving the application open by opening notes for National choices in the National Annexes. This paper introduces a solution for an European harmonisation of these design rules. The solution is a general buckling curve chi.LT.GM, applicable to both flexural and lateral torsional buckling and also to mixed phenomena based on a mechanical background model. It gives for the specific case of flexural buckling the same results as the European column buckling curve chi.c. For deriving the general buckling curve in a first step the general validity of the column buckling curve for the case of non-uniform columns with any kind of loading and boundary conditions is proved. It constitutes the cross-sectional verification at the relevant location x.d. On the basis of this definition the "standardised European lateral-torsional buckling curve" chi.LT.GM is derived, which considers the relevant location x.d and the torsional rigidity of the cross-section within one formula. In a further step the method is extended to allow for an easy and transparent calculation for combinations of in-plane and out-of-plane loads. The additional lateral and torsional bending effects are expressed in terms of series of Eigenmodes including the basic Eigenmode, which already has been used to define the initial equivalent imperfection. The convergence could be optimised in such a way, that a good approximation is given on the basis of the first Eigenmode only. For practical use a general method for the determination of the relevant design location x.d for any kind of axial force, bending-moment and torsional-moment distribution is given. Thus the present work gives a consistent and general solution with respect to the definition of the initial equivalent geometrical imperfection for the use of any assessment method and the particular procedure for assessing different type of stability phenomena of structural members and frames by using buckling curves. The proposed procedure is compared to the alternative methods given in EN 1993 1-1 and its reliability is proved by the evaluation of test-results. Finally the calculation procedure is demonstrated with selected design examples.

### Identifier

- ISBN: 978-3-8322-8754-2
- URN: urn:nbn:de:hbz:82-opus-30356
- RWTH PUBLICATIONS: RWTH-CONV-112651