The objective of this paper is to provide an overview of computational modeling, both elastic buckling and nonlinear collapse analysis, for cold-formed steel members. Recent research and experiences with computational modeling of cold-formed steel members conducted within the first author's research group at Johns Hopkins University are the focus of the presented work. This admittedly biased view of computational modeling focuses primarily on the use of the semi-analytical finite strip method and collapse modeling using shell finite elements. Issues addressed include how to fully compare finite strip and finite element solutions, and the importance of imperfections, residual stresses, material modeling, boundary conditions, element choice, element discretization, and solution controls in collapse modeling of cold-formed steel. Examples are provided to demonstrate the expected range of sensitivity in cold-formed steel collapse modeling. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.

Computational modeling of cold-formed steel

The paper describes the new developments in the Australian/New Zealand standard AS/NZS 4600. The developments are based mainly on research in Australia and the USA. They include new rules for high strength steel, the new Direct Strength Method of design as an alternative to the Effective Width Method and many other detailed changes including design of unstiffened compression elements under stress gradient. The standard is based mainly on the North American Specification published in 2001 with a 2004 Supplement but with special rules for high strength steels as produced in Australia including rules for distortional buckling and welding of high strength steel.

Development of the 2005 Edition of the Australian/New Zealand Standard for Cold-Formed Steel Structures AS/NZS 4600

In-plane stability of arches

A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method

This paper provides the first detailed presentation of the derivation for a newly proposed method which can be used for the decomposition of the stability buckling modes of a single-branched, open cross-section, thin-walled member into pure buckling modes. Thin-walled members are generally thought to have three pure buckling modes (or types): global, distortional, and local. However, in an analysis the member may have hundreds or even thousands of buckling modes, as general purpose models employing shell or plate elements in a finite element or finite strip model require large numbers of degrees of freedom, and result in large numbers of buckling modes. Decomposition of these numerous buckling modes into the three buckling types is typically done by visual inspection of the mode shapes, an arbitrary and inefficient process at best. Classification into the buckling types is important, not only for better understanding the behavior of thin-walled members, but also for design, as the different buckling types have different post-buckling and collapse responses. The recently developed generalized beam theory provides an alternative method from general purpose finite element and finite strip analyses that includes a means to focus on buckling modes which are consistent with the commonly understood buckling types. In this paper, the fundamental mechanical assumptions of the generalized beam theory are identified and then used to constrain a general purpose finite strip analysis to specific buckling types, in this case global and distortional buckling. The constrained finite strip model provides a means to perform both modal identification relevant to the buckling types, and model reduction as the number of degrees of freedom required in the problem can be reduced extensively. Application and examples of the derivation presented here are provided in a companion paper.

Buckling mode decomposition of single-branched open cross-section members via finite strip method : Derivation

Computer analysis of thin-walled structural members

A flexural torsional buckling theory for circular arches of doubly symmetric cross section is developed. Non linear expressions for the axial and shear strains are derived and these are substituted into the second variation of the total potential to obtain the buckling equation. Closed form solutions are obtained for simply supported arches subjected to equal and opposite end moments (uniform bending), and to uniformly distributed radial loads (uniform compression), and for circular rings subjected to uniformly distributed radial loads. The results are compared with previous solutions (a).

Flexural-torsional buckling of arches

Flexural torsional buckling tests on circular aluminium arches of doubly symmetric i section are described. The arches were fabricated by bending straight specimens to the required radius of curvature in a rolling machine. Calculations of the resulting residual stresses indicate that these have little effect on lateral buckling. Simply supported arches subjected to central concentrated point loads were tested in the normal and inverted attitudes. The test results are compared with previous theoretical solutions (a).

Flexural torsional buckling tests on arches

Elastic flexural–torsional buckling of structures by computer

A flexural‐torsional buckling theory is developed for arches of monosymmetric cross section. Nonlinear strain‐displacement relations are derived for the axial and shear strains, and these are substituted into the second variation of the total potential to obtain the buckling equation. Closed form solutions are obtained for arches subjected to equal and opposite end moments and for arches and rings subjected to a uniformly distributed radial load. The solutions are compared with previous theoretical results.

J.P. Papangelis

Papers

Computer analysis of thin-walled structural members

Flexural-torsional buckling of arches

Flexural torsional buckling tests on arches

Elastic flexural–torsional buckling of structures by computer

Flexural torsional buckling of monosymmetric arches