professor ben schafer's thin-walled structures research group - johns hopkins university


Computational Modeling of Cold-Formed Steel


Computational modeling of cold-formed steel, that is modeling cold-formed steel members and systems to and through collapse is a central focus of the thin-walled structures research group. This brief page does not provide a complete summary of the breadth of efforts in this area but does provide a 2008 paper and presentation that present a reasonably up to date summary of current efforts.


Excerpts from "Computational Modeling of Cold-Formed Steel" CIMS 2008 (paper) (presentation)


Note, the paper was revised and improved and published as a journal article in Thin-walled Structures currently (In Press) August 2010. (doi:10.1016/j.tws.2010.04.008)



The objective of this paper is to summarize recent research and experiences with computational modeling of cold-formed steel conducted within the author’s research group at Johns Hopkins University. 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,

  • boundary conditions,

  • element choice,

  • element discretization, and

  • solution controls

in collapse modeling of cold-formed steel. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.


1 Introduction

Modeling cold-formed steel, particularly through collapse, presents a strongly nonlinear problem with both material and geometric nonlinearity. However, meaningful modeling requires more than a good nonlinear solution scheme and a robust element. Successful modeling requires in-depth understanding of the model inputs and their sensitivities, as well the limitations and strengths of the modeling tools themselves. This paper presents a brief introduction to the tools and current issues surrounding computational modeling in cold-formed steel, an introduction which is strongly biased by the research experiences within the author’s research group. Thus, this paper does not attempt to provide a comprehensive survey of the computational modeling literature – my apologies to the many excellent researchers who contribute to this area and do not find themselves mentioned herein.


2 Elastic buckling analysis

2.1 Tools

Computational modeling of the elastic buckling of cold-formed steel members is an important step in understanding the behavior (and even designing) cold-formed steel members. Three tools are in regular use in the author’s research group for elastic buckling analysis: CUTWP [1], CUFSM [2], and ABAQUS [3]. The former two are freely available, open source programs distributed by the author, while the latter is a well known general purpose commercial finite element package. CUTWP provides global member stability solutions using expressions based on classical beam theory and Vlasov warping torsion [4]. CUTWP sees regular use in our efforts because it: (i) uses the same mechanics employed in codes and standards; (ii) readily allows for different global effective length factors (KxLx, KyLy, KtLt); and (iii) has been modified to read CUFSM input files. CUFSM, which provides an implementation of the semi-analytical finite strip method (FSM), appropriate for cold-formed steel members with (locally) pinned boundary conditions (see [5] for another example), is the workhorse of the authors research group. Basic understanding begins with interpretation of the CUFSM buckling analysis of a given member. ABAQUS, is a well known general purpose finite element method (FEM) package; for the purposes of this paper only models built from shell elements are considered for discussion.



Links to full paper and conference presentation


Schafer, B.W. (2008). "Computational Modeling of Cold-Formed Steel." Proceedings of Coupled Instabilities in Metal Structures, Sydney, Australia (paper) (presentation)



List of references on computational modeling of cold-formed steel


The paper concludes with a number of recent references of interest in this area, these references are provided here for those interested:


[1] Sarawit, A., CUTWP: Cornell University Thin-walled Section Properties. p. December 2006.

[2] Schafer, B.W. and S. Adany. Buckling analysis of cold-formed steel members using CUFSM: Conventional and constrained finite strip methods. in Eighteenth International Specialty Conference on Cold-Formed Steel Structures. 2006. Orlando, FL, United States: University of Missouri-Rolla, Rolla, MO, 65409-1060, United States.

[3] Simulia, ABAQUS. 2008.

[4] Timoshenko, S., Theory of elastic stability. 2d ed. Engineering societies monographs;. 1961, New York: McGraw-Hill. 541 p. illus. 24 cm.

[5] Papangelis, J.P. and G.J. Hancock, Computer analysis of thin-walled structural members. Computers and Structures, 1995. 56(1): p. 157-176.

[6] Silvestre, N. and D. Camotim, First-order generalised beam theory for arbitrary orthotropic materials. Thin-Walled Structures, 2002. 40(9): p. 755-789.

[7] Silvestre, N. and D. Camotim, Second-order generalised beam theory for arbitrary orthotropic materials. Thin-Walled Structures, 2002. 40(9): p. 791-820.

[8] Adany, S. and B.W. Schafer, A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method. Journal of Constructional Steel Research, 2008. 64(1): p. 12-29.

[9] Ádány, S., et al., GBT and cFSM: Two modal approaches to the buckling analysis of unbranched thin-walled members. International Journal of Advanced Steel Construction, 2008 (Accepted).

[10] Bradford, M.A. and M. Azhari, Buckling of plates with different end conditions using the finite strip method. Computers and Structures, 1995. 56(1): p. 75-83.

[11] Ádány, S., A. Joó, and B.W. Schafer, Approximate identification of the buckling modes of thin-walled columns by using the modal base functions of the constrained finite strip method, in International Colloquium on Stability and Ductility of Steel Structures, D. Camotim, N. Silvestre, and P.B. Dinis, Editors. 2006: Lisbon, Portugal. p. 197-204.

[12] Ádány, S., Flexural buckling of thin-walled columns: discussion on the definition and calculation, in International Colloquium on Stability and Ductility of Steel Structures, D. Camotim, N. Silvestre, and P.B. Dinis, Editors. 2006, IST Press: Lisbon, Portugal. p. 249-258.

[13] Schafer, B.W., Cold-formed steel behavior and design : analytical and numerical modeling of elements and members with longitudinal stiffeners. 1997, Cornell University. p. xxiv, 454 leaves.

[14] Moen, C.D., Schafer, B.W., Direct Strength Design for Cold-Formed Steel Members With Perforations, Progress Report No. 1. 2006, American Iron and Steel Institute.

[15] Dawson, R.G. and A.C. Walker, Post- buckling of geometrically imperfect plates. 1972. 98(ST1): p. 75-94.

[16] Gardner, L. and D.A. Nethercot, Numerical modeling of stainless steel structural components - A consistent approach. Journal of Structural Engineering, 2004. 130(10): p. 1586-1601.

[17] Ashraf, M., L. Gardner, and D.A. Nethercot, Finite element modelling of structural stainless steel cross-sections. Thin-Walled Structures, 2007. 44(10): p. 1048-1062.

[18] Borges Dinis, P., D. Camotim, and N. Silvestre, FEM-based analysis of the local-plate/distortional mode interaction in cold-formed steel lipped channel columns. Computers and Structures, 2007. 85(19-20): p. 1461-1474.

[19] Schafer, B.W. and T. Pekoz, Computational modeling of cold-formed steel: Characterizing geometric imperfections and residual stresses. Journal of Constructional Steel Research, 1998. 47(3): p. 193-210.

[20] Moen, C. and B.W. Schafer, A general prediction method for residual stresses and strains in cold-formed steel members, in Fifth International Conference on Coupled Instabilities in Metal Structures. 2008: Sydney, Australia.

[21] Dinis, P.B. and D. Camotim. On the use of shell finite element analysis to assess the local buckling and post-buckling behaviour of cold-formed steel thin-walled members. in Third European Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering. 2006. Lisbon, Portugal.


last updated 08/16/10