Thursday, 14 May 2020

Restrained or unrestrained purlins?

Design of non-symmetric cold-formed open sections require special attention. Producer catalogues quote effective cross-section properties, but they can lead to a misleading estimation of the resistance of such sections. For example in case of a Z section, the quoted Wy,eff value in the local coordinate system is calculated based on a stress distribution resulting from the additional assumption, that the section is fully restrained against lateral displacement and rotation. If this is not sufficiently provided, the section will most probably be subject to biaxial bending, requiring therefore effective cross-section properties in both principal axes of the cross-section. For such application, the usual catalogue values are not applicable.

Let us consider the following singly supported purlin with Z section loaded on the top of its web.

The figures below show the normal stress distribution of the cross-section at mid-span for the restrained and unrestrained cases respectively. The first case is the default Eurocode assumption valid in case of fully effective lateral and torsional restraint only. 

The difference is well visible. As it can be seen the stress distributions on the flanges are significantly different, in the unrestrained case even the stress changes sign making the edge stiffeners compressed at the tension flange and tensioned at the compressed flange.

The following figures show the different effective cross-sections from the two different stress distributions and the table shows the resulted effective section moduli.

It can be seen there are considerable differences between the effective properties using the two different assumptions for the stress distribution.

ConSteel can consider the true restraining effect provided by any connected sheeting and determine the all effective cross-section properties for the actual stress distribution from biaxial bending with torsion and warping and perform design calculations according to EN 1993-1-3.

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