Verification of flexural buckling according to Eurocode 3 part 1‐1 using bow imperfections

Abstract

The resistance of compression members may be calculated by the design buckling resistance based on the reduction factor χ, which depends on the slenderness, or by the cross‐section resistance based on internal forces according to a second‐order analysis taking into account equivalent initial bow imperfections as well. The second way is especially advantageous in the case of axial forces and bending. Values for equivalent initial bow imperfections are given in codes such as Eurocode 3 [5] or DIN 18800 [4]. For comparison, initial bow imperfections are derived here from the buckling curves for compression members with different cross‐sections, buckling directions and steel grades based on different types of cross‐sectional interaction. The results are discussed and commented with regard to the design of compression members. Furthermore, investigations are carried out for cases of axial compression and bending moments My or Mz. Data available from ultimate load calculations are used for comparison. The consequences for the assumed design verification according to second‐order theory are discussed and a proposal is presented.

Additional investigations concerning initial bow imperfections for flexural buckling according to Eurocode 3 Part 1‐1

“…3 shows that values η ul > 1.0 represent results on the unsafe side. c) In [6] it already is proposed and in [5] it is confirmed that for axial compression and flexural buckling about axis y-y, a linear plastic interaction should be used. Axial compression and flexural buckling about axis y-y a) Based on the interaction formula according to EN 1993-1-1, sec.…”

“…6.9.2.1 or the interaction formula according to the proposal by Kindmann/Stroetmann [6], some results around 1.05 occur if only the test series i), ii) or iii) are taken into account: for series i), max η = 1.032; for series ii), max η = 1.050; and for series iii), max η = 1.044. linear plastic N test ultimate load according to the tests mentioned before Eq.…”

“…All investigations in the past [6] were carried out for yield strength f y = 235, 355 or 460 N/mm 2 . Therefore, additional ultimate load FEM calculations were carried out here similar to those which were discussed in [6], taking into account initial bow imperfections L/1000, residual stresses according to the 1976 ECCS manual as explained in [7] as well as plasticizing within the cross-section and along the member length.…”

“…6.3.1), or a cross sectional verification according EN 1993-1-1, sec. In [4] and [6], considerations are taken into account how to improve the values of Table 5.1 of EC3:2009 [3], especially regarding members subjected to axial compression and bending moments of external loads. Here, bending moments according to second order theory must be calculated, where initial bow imperfections e 0 according to EN 1993-1-1, sec.…”

“…6.2. Concerning the result of [6], a proposal for an amendment was already accepted in Working Group 1 of EN 1993-1-1 [5]. 5.3 must be taken into account.…”