Keywords: imperfection sensitivity factor, buckling, concrete shells.

Depending on their geometry, material and boundary conditions, shells can experience a reduction in the buckling load. Several approximate methods may be used to determine the instability in concrete shells, in particular the one exposed in the recommendations of the International Association for Shell and Spatial Structures (IASS) [1]. In the latter there are some curves reflecting the influence of the initial geometric imperfections in the buckling load for simple geometries (spheres and the cylinders).

In recent decades, different revisions of the recommendations have been published, however new curves for geometries with more complexity are not available.

In this study, a method based on that used in [2,3] is implemented to determine the imperfection sensitivity factor in the case of shells with geometries such as a spherical dome, barrel vault, and double-curvature ruled surface (hyperbolic paraboloid and hyperbolic rotational surface) [4].

The geometric imperfection sensitivity factor is the relationship of the upper critical load with respect to the buckling critical load for linear homogeneous material. The calculation of this factor is often difficult. Some cases appear in the technical literature, such as spheres and cylinders. In the absence of further information about the geometry, the IASS recommends using the safest case (a sphere under radial pressure and an axially compressed cylinder). However, in most cases this approach is too conservative. Thus, it may be useful to study new geometries to obtain a better approach to their structural behaviour with imperfection.

The curves for several geometrical models of single and double curvature are presented in this study. Previously, validation of the method is performed by obtaining the curves corresponding to spheres and cylinders and by comparing them with the curves of the IASS recommendations.

One of the main conclusions is that the recommendation to quantify the influence of geometric imperfection in shells whose behaviour is not known with certainty, by means of the curves for spheres and axially compressed cylinders, may be too conservative.

1

IASS Working Group No. 5, "Recommendations for reinforced concrete shells and folded plates", IASS, Madrid, Spain, 1979.

2

L. Kollár, E. Dulácska, "Buckling of shells for engineers", Wiley, Chichester, United Kingdom, 1984.

3

E. Dulácska, L. Kollár, "Design procedure for the buckling analysis of reinforced concrete shells", Thin-Walled Structures, 23(1-4), 313-321, 1995. doi:10.1016/0263-8231(95)00019-A

4

J.P. Tovar, "Influence of initial geometrical imperfections in the buckling of concrete shells", BEng thesis, UPCT, Cartagena, Spain, 2009. (in Spanish)

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