Keywords: plates, compression, post-buckling, failure, strength, initial imperfection.

This paper discusses the behaviour of first-generation sheeting close to the intermediate supports, loaded by the combination of a bending moment and a concentrated load. The current design code predicts the failure separately for both load conditions which are finally combined; several procedures should be used which are not based directly on the failure modes that occur. Therefore, the ultimate failure model was developed [1] using the Marguerre's equations [2] to determine the post-buckling behaviour of the initially imperfect plate loaded by the compressive stress. Marguerre equations are too tedious to use as a design rule and they are only able to predict failure by first membrane yield, as is also done in Eurocode3. Extended research has shown that first yield is not always a good prediction of the ultimate load [3]. In this paper the plate failure criteria, based on the theory of elasticity, will be used for the failure model of the sheeting. These failure criteria are easier to use and provide additional insight in the plate failure behaviour. Experiments are used to compare both analytical solutions and the Eurocode3 procedure, and conclusions and recommendations are given.

Based on the finite element numerical simulations two different failure modes and the theory of the fictitious elastic strains at failure have been defined. The method presented will predict the fictitious strain at failure which corresponds to the elasto-plastic failure load. It can be seen that for plates failing by edge failure, the use of this method results in a much improved strength prediction. Because it also gives very good results for plates failing by centre yielding, the calculation presented can than be used for strength predictions of all plates.

The failure model of the plate is extended to a failure model of the real sheet-section. First, the calculation of the web-crippling stiffness is needed which can be used to predict the out-of-plane deformation of the plate centre. Next, the force in the compressed flange should be determined. For the initial imperfection and the concentrated force, the failure of the part of the compressed flange can be predicted.

Both analytical methods and the current European design rules of Eurocode3 were compared using the experiments reported in the literature. It is shown, that the ultimate failure model using the theory of elasticity performs equally well as Eurocode3 for all aspects; however it provides more insight because it is fully based on analytical models. The fictitious strain method is a better alternative for Marguerre's equations, especially comparing the attained errors in predictions and also because the fictitious strain method's equations are easier to use.

Simplifications for the method presented can still be found, but first a study on plates with other geometries, loading and boundary conditions is needed. The extension of the finite element parameter study for small and high slenderness ratios and for larger initial imperfections is recommended.

1

H. Hofmeyer, J.G.M. Kerstens, H.H. Snijder, M.C.M. Bakker, "New prediction model for failure of steel sheeting subject to concentrated load (Web crippling and bending moment)", Thin-Walled Structures, 39(9), 773-796, 2001. doi:10.1016/S0263-8231(01)00032-5

2

N.W. Murray, "Introduction to the theory of thin-walled structures", Oxford engineering science series 13, Clarendon Press, Oxford, United Kingdom, 1985.

3

M.C.M. Bakker, M. Rosmanit, H. Hofmeyer, "Prediction of the elasto-plastic post-buckling strength of uniformly compressed plates from the fictitious elastic strain at failure", Thin-Walled Structures, 47(1), 1-13, 2009. doi:10.1016/j.tws.2008.04.004

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