Keywords: buckling, arch, perfect, imperfect, dynamic relaxation.

This paper reports on the buckling behaviour of two pin ended circular steel slender arches under pressure loading analyzed by a non-linear adapted dynamic relaxation (DR) method. Structural designers prefer slender arches for a number of reasons such as ease of construction and reduced foundation cost. Slender arches buckle under relatively low loads. Establishing under which conditions and under which geometry the arch remains stable is therefore an essential design question. A concise literature review is given of analytical work in this field. Both Timoshenko et al. [1] and Simitses et al. [2] have analytically defined buckling loads for circular pinned arches under radial loading without taking into account axial deformations. These deformations lower under certain conditions the buckling load, their effects can be accounted for in non-linear analysis methods such as finite element analysis or DR. DR is the preferred method in this study as it features in a large framework that investigates the beneficial influence of pre-stressed systems (such as membranes) on arch buckling behaviour.

A realistic case study, modelled on the arches in the light weight roof of the Gottleib Daimler Stadium, Germany [3], is introduced. This study demonstrates five distinct buckling behaviours in function of the arch height: (1) asymmetric arch buckling with increased post buckling load bearing capacity, (2) asymmetric arch buckling with decreased post buckling load bearing capacity, (3) symmetric arch buckling with horizontal displacement of the top, (4)symmetric arch buckling without horizontal top displacement and (5) no buckling but bending. These results were also found by Pi et al. [4]. The buckling loads and the pre- and post-buckling deformations obtained by the DR method are compared to published analytical results. The analytical buckling loads are higher than the non-linear obtained and are thus unsafe.

The influence of second order effects caused by arch imperfections is studied. Arch imperfections are due to geometrical imperfections, initial stresses, eccentricity of applied load and strain hardening. EC3 [5,6] defines a method to represent all these imperfections in one single initial geometrical imperfection that is added to the initial shape of the perfect arch, in a non-linear analysis such as DR. The DR analyses show that the influence of the imperfections on the magnitude of the buckling pressure depends on the arch height and the buckling behaviour. In general high arches are less influenced by imperfections. Arches that buckle in an asymmetric manner are largely influenced by imperfections. Conclusions are drawn about the validity of the numerical and analytical approach to circular slender arch buckling.

1

S.P. Timoshenko, J.M. Gere, "Theory of Elastic Stability", Second Edition, Mc Graw Hill book Company Ltd., New York, 1961.

2

G.J. Simitses, "An introduction to the elastic stability of structures", New Jersey, 1976.

3

K. Ishii, "Membrane Designs and Structures in the World", Shinkenchiku-sha Co. Ltd., Tokyo, p. 88-91, 1999.

4

Y.L. Pi, N.S. Trahair, "Non-linear buckling and post-buckling of elastic arches", Engineering Structures, p. 571-579, 1998. doi:10.1016/S0141-0296(97)00067-9

5

CEN Comite Europeen de Normalisation, "EN 1993-1-1: Berekening van staalconstructies, algemene regels en regels voor gebouwen", Brussel, Maart 2005.

6

CEN Comite Europeen de Normalisation, "EN 1993-2: Berekening van staalconstructies, Stalen bruggen", Brussel, December 2004.

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