Slenderness-based design for sigma sections subjected to interior one flange loading

Abstract

Due to their thin-walled nature and complex geometry, cold-formed steel purlins are prone to a variety of instabilities. Sigma purlins are a family of cold-formed steel members with folding-lines along their webs. The non-straight geometry of their web is beneficial in terms of reducing the susceptibility of the web to local buckling, however, it increases their susceptibility to web crippling when the purlins are subjected to concentrated transverse loads and hence it may reduce their overall moment resistance. This paper reports a series of experiments on sigma purlins under the interiorone-flange (IOF) loading condition. Two different section geometries and three different bearing plate widths were examined. To investigate further the effect of web geometry on the IOF web crippling strength of sigma sections, an FE model was developed and validated against the reported test results. Following successful replication of the experimental observations, a comprehensive parametric study was performed, and several sigma sections covering a wide range of crosssectional geometries and slenderness were numerically modelled. Finally, a slenderness-based (or direct strength) design approach previously developed for the web crippling design of channel and hat sections is extended to sigma sections.

A Slenderness-Based Method for Web Crippling Design of Aluminum Tubular Sections

“…Same trend was observed in past studies on other cross-sections and materials (Duarte and Silvestre 2013, Bock and Real 2014and Almatrafi et al 2021. To obtain the plastic load Rw,pl, the graphical method proposed by Dos Santos et al ( 2018) was used which assumes that the plastic load is attained when the slope of the load-deflection curve is 1% of the initial stiffness.…”

“…Same approach was also used in Bock and Real (2014) and Almatrafi et al (2021). Coefficients kF were therefore derived herein by using multilinear regression analysis considering relevant geometrical variables and are given by Eqs.…”

“…( 24) which is similar to the model employed by EN 1999EN -1-1 (2000 to predict plastic loads in the provision dealing with concentrated transverse forces which is based on plastic line theory. It is worth pointing out that this model does not contain the internal radius r and that other models for plastic loads are available for cross-sections with rounded corners and materials such as cold formed channels (Duarte and Silvestre 2013), stainless steel hat sections (Bock and Real 2014), cold-formed sigma sections (Almatrafi et al 2021), cold-formed SHS and RHS (Zhao and Hancock 1995) and cold-formed lipped channels (Nguyen et al 2020). In Eq.…”

“…Figure 17 also shows available curves for cold formed (CF) channels (Duarte and Silvestre 2013) and cold-formed sigma sections (Almatrafi et al 2021) as well as stainless steel hat sections (Bock and Real 2014). Note that other χ(λ) curves with similar coefficients are also available in Nguyen et al (2020) for cold-formed lipped channels but have not been added in Figure 17 for simplicity.…”

“…The result of the parametric study were used to derive a new slenderness based method for web crippling design employing strength curves which is the same approach used for the treatment of other buckling instabilities such as local, overall buckling and patch loading. Past studies have proved that slenderness based approaches are possible for web crippling design and provide more reliable predictions (Duarte and Silvestre 2013, Bock and Real 2014, Almatrafi et al 2021, Zhao and Hancock 1995, Nguyen et al 2017and Nguyen et al 2020.…”