Keywords: purlin, sheeting, lateral restraint, rotational restraint, non-linear analyses, FEM.

This paper deals with cold-formed steel continuous purlins. In the construction of steel roofs for industrial buildings, cold-formed steel purlins with Z, C and cross-sections are often used in combination with corrugated metal sheeting. The upper flange of the purlin is connected to the sheeting by self-drilling or self-tapping screw fasteners applied either at crests or at troughs - the lower flange is free. The attached sheeting provides lateral and rotational restraints to the purlins. The lateral restraint is usually considered as rigid, but the rotational restraint of the connection between the purlin and the sheeting is always flexible.

The restraining effect provided by the roof sheeting increases the strength of the attached purlins and influences their design. In the articles of Peköz and Soroushian [1], Tomà and Wittemann [2], and Sokol [3] cold-formed purlins are analysed by taking the restraining effect of the sheeting into consideration for simply supported purlins. From these research papers, it is clear that the restraining effect plays an important role in reducing the stresses in purlins and in increasing their buckling strength. Analysing the failure behaviour of multi-span purlins, which are more common in steel roofs, by including the restraining effect is vital to attain an optimal design. In this regard, LaBoube et al. [4] and Hancock et al. [5,6] performed experimental tests on continuous purlins under uplift and gravity loads. An analytical approach for the design of cold-formed continuous purlins is also presented in Eurocode 3, part 1.3 [7].

However, numerical modelling of continuous purlins leads to a better understanding of the failure behaviour and paves a way to perform parametric studies. As the rotational restraint is always flexible when compared with the lateral restraint in most purlin-sheeting systems, studying its influence on the failure load of continuous purlins for a practical range of the rotational restraint values is more appropriate for design.

In order to emphasise the above aspect, continuous purlins are analysed by using the finite element method in this article. A non-linear finite element model to analyse the failure behaviour of continuous purlins is presented in which the modified Riks-algorithm is employed. The model is implemented by using ABAQUS. The restraining effect of the roof sheeting is included in the model by attaching translational and rotational springs to the upper flange of the purlin. The model is validated by using experimental test results and found to be in good agreement.

The influence of the rotational restraint on the failure load is studied by using the validated model and the following conclusions are drawn. In most purlins under gravity and uplift, the rotational restraint increases the failure load of continuous purlins by 5-20% when compared to the failure load with no rotational restraint. However, in some purlins under uplift, the failure load decreases with increase of the rotational restraint. The reason for this decrease is due to the fact that yielding starts earlier with increase of the rotational restraint. This study emphasises the need for a design methodology to estimate the rotational restraint which is applicable to most practical conditions as the existing design rules to estimate the rotational restraint between purlin-sheeting systems have limitations or are based on experimental tests.

1

T. Peköz and P. Soroushian, "Behaviour of C and Z-purlins under Wind Uplift", Sixth International Specialty Conference on Cold-formed Steel Structures, St. Louis, Missouri, USA, 1982.

2

T. Tomà and K. Wittemann, "Design of Cold-formed Purlins and Rails Restrained by Sheeting", Journal of Constructional Steel Research, 31, 149-168, 1994. doi:10.1016/0143-974X(94)90008-6

3

L. Sokol, "Stability of Cold-Formed Purlins Braced by Steel Sheeting", Thin-Walled Structures, 25(4), 247-268, 1996. doi:10.1016/0263-8231(95)00056-9

4

R.A. LaBoube, M. Golovin, D.J. Montague, D.C. Perry and L.L. Wilson, "Behaviour of Continuous Span Purlin Systems", Ninth International Specialty Conference on Cold-formed Steel Structures, St. Louis, Missouri, USA, 1988.

5

G.J. Hancock, M. Celeban, C. Healy, P.N. Georgiou and N.L. Ings, "Tests of Purlins with Screw Fastened Sheeting under Wind Uplift", Tenth International Speciality Conference on Cold-formed Steel Structures, St. Louis, Missouri, USA, 1990.

6

G.J. Hancock, M. Celeban and C. Healy, "Tests of Continuous Purlins under Downwards Loading", Eleventh International Speciality Conference on Cold-formed Steel Structures, St. Louis, Missouri, USA, 1992.

7

Eurocode 3, "Design of Steel Structures Part 1-3., General Rules for Cold-Formed Thin Gauge Members and Sheeting", CEN, European Committee for Standardization, 2003.

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