Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient

Significance 

Cold-formed steel members are made from structural quality sheet steel that are formed into C-sections and other shapes by roll forming the steel through a series of dies. For such open sections, distortional buckling is a potential failure mode, where an entire stiffened compression flange becomes unstable. Analytical methods for predicting this complex behavior have been developed for compression members and even extended for flexural members with the aim being to provide more rigorous treatments for distortional buckling strength prediction. Numerous studies on this failure mode have been undertaken using varying techniques. For instance, the generalized beam theory (GBT) has been used to investigate the limiting slenderness of hat, C-sections and Z-sections. In essence, the American Iron and Steel Institute (AISI) specification for the design of cold-formed steel structural members supports two methods of predicting the elastic distortional buckling stresses of stiffened flanges: numerical and analytical. Technically, AISI provides analytical solutions that permit the direct (although complex) calculation of distortional buckling stress predictions. Channels, hat sections, and many custom shapes have been used for members where bending occurs about the axis perpendicular to the flange, which may also be subject to distortional buckling if the flange stiffener is in compression.

The strength of cold-formed steel beams with stiffened flanges may be controlled by distortional buckling. However, channel sections are commonly used where bending occurs about the minor axis with flanges under a stress gradient, such that the edges that are in compression and the flanges may experience distortional buckling. Current design specifications do not explicitly address this failure mode, which could lead to unsafe designs. To be specific, there lacks a direct hand solution for these minor axis bending cases in design specifications may result in oversight by the engineer of this potential distortional buckling failure mode. To address this, RSG Software Incorporation President: Robert S. Glauz, developed new analytical method for the prediction of elastic distortional buckling stresses for flanges under a stress gradient, with verification against numerical solutions permitted by the AISI specification. His work is currently published in the Journal of Structural Engineering.

His objective was to develop this method as an extension to the current AISI provisions for flanges under uniform compression. He developed an approach that was verified for simple lip stiffeners, intermediates stiffeners, complex stiffeners, and perforated webs. A wide range of geometric proportions were evaluated to cover a broad application. Comparisons were made to finite-strip solutions with reliable results.

The author reported on an analytical approach was consistent with other AISI distortional buckling provisions, permitting a clean implementation for bending about the axis perpendicular to the flange. Also, the author reviewed current AISI equations for distortional buckling of flexural members bending about the axis perpendicular to the web.

In summary, an analytical method was developed to accurately predict the elastic distortional buckling stress. This was meant to address the current inadequacies in design specifications; i.e. they do not explicitly address the buckling mode, which could result in unsafe designs. In a statement to Advances in Engineering, Engineer Glauz explained that his approach was consistent with the design method used for flanges under uniform compression in the AISI specification for the design of cold-formed steel members. This consistency facilitates a straightforward incorporation into the design specification.

Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient - Advances in Engineering
Figure 1. Distortional buckling of flanges under major and minor axis bending
Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient - Advances in Engineering
Figure 2. Flange under stress gradient
Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient - Advances in Engineering
Figure 3. Influence of web depth for a typical flange
Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient - Advances in Engineering
Figure 4. Complex stiffener examples analyzed

About the author

Bob Glauz is President and Owner of RSG Software, Inc., and the author of the CFS® software used internationally for cold-formed steel design. He is a Professional Engineer with a Master’s degree in Civil Engineering. Bob is a member of the American Iron and Steel Institute (AISI) Committee on Specifications and chair of the AISI subcommittee on member design. He is also a member of the Structural Stability Research Council (SSRC) and a member of the SSRC task group on stability of steel members.

Reference

Robert S. Glauz. Distortional Buckling of Cold-Formed Steel Flanges under Stress Gradient. Journal of Structural Engineering: Volume 146 Issue 9.

Go To Journal of Structural Engineering

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