Keywords: cold-formed purlin, full-scale test, ultimate behaviour, finite element model, buckling analysis, imperfections, non-linear analysis, advanced design.

This paper presents the numerical modelling and analysis of steel cold-formed purlins with the aim to introduce an advanced design method. In the typical roofs of steel industrial type buildings cold-formed purlins, as secondary structures, are applied to support the load-bearing elements of the cladding system. The main characteristic of the behaviour of the typically used C-, Z- or -profiles is coming from the coupled plate and distortional local buckling and lateral torsional global buckling modes. These phenomena are highly influenced by the structural arrangements of the purlin and cladding system [1]. The lateral and torsional supporting effect of the cladding to the purlin is influenced by several structural parameters what can be hardly considered without experimental studies. In the existing design codes significant simplifications and limitations are used to follow this effect.

The standard design methods are studied and a new advanced methodology is under development in the frame of an ongoing research at the Department of Structural Engineering, Budapest University of Technology and Economics. It is proved that the purlin design method of Eurocode 3 [2] is conservative and benefits can be gained by improving the analysis model [3]. To support the development of the new design method the ultimate behaviour of a special purlin-cladding system is studied by a full-scale experimental program [4]. In the tests the ultimate behaviour of different purlin-cladding arrangements is determined. The obtained failure modes are mainly related to the distortional buckling phenomenon. In this paper the test results are used as experimental background of the finite element model development, what is the bases of the improved design tool.

The sophisticated finite element model is developed with the requirements to follow the complex behaviour of the complicated structural arrangements due to the interaction phenomena. The aim of the model on the other hand to be efficient enough to serve not just research but practical design purposes, too. The model is worked out in Ansys FE program with the help of the newly developed Matlab software, called Purlin-FED. The Purlin-FED program is able to build automatically the model, to control the solution and to evaluate the results, in the function of varying parameters as cross section, span, overlap length, bridge system, and anti- sag bars. This program provides with the opportunity to apply the FE program in the background of the design procedure.

By the application of Purlin-FED finite element models are built and analysed in parallel with the experimental tests. The model verifications are carried out by the results of linear, buckling and non-linear analyses. The comparison is done by the displacement and stress distribution in the linear range of loading, and by the features of the ultimate behaviour -– buckling shapes, combined failure modes -– for higher load intensity. As a conclusion of the obtained results it is stated that the developed numerical model can follow the behaviour of Z-purlins and can be integrated into the design method.

1

Chung K.F., Quinton D.St., "Structural Performance of Modern Roofs with Thick Over-purlin Insulation - Experimental Investigation", Journal of Constructional Steel Research, 40(1), 17-38, 1996. doi:10.1016/S0143-974X(96)00036-3

2

ENV 1993-1-3, Eurocode 3: Design of steel structures. Part 1-3: General rules; Supplementary rules for cold-formed thin gauge members and sheeting, 1996.

3

Joó A.L., Ádány S., Dunai L., "On the Eurocode 3 Design Method of Cold- formed Z-purlins", in "Proceeding of 3rd European Conference on Steel Structures", Coimbra, Portugal, 2002 (accepted for publication).

4

Kachichian M., Dunai L., Macdonald R., Werner F., "Full-scale site Testing of Cold-formed Z-purlins", in "Proc. of the Int. Coll. on Stability and Ductility of Steel Structures", Budapest, Hungary, 2002 (accepted for publication).

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