Articles Benjamin W.

Schafer
DOI: 10.1002/stco.201110019

Cold-formed steel structures around the world

A review of recent advances in applications, analysis and design
The objective of this paper is to provide a brief review of recent (over approximately the last five years) advances in the application, analysis and design of cold-formed steel structures. Attention here is focused on load-bearing cold-formed steel structures; as opposed to secondary systems, curtain walls, etc. Cold-formed steel applications continue to advance in three primary categories: framing, metal buildings, and racks. Examples largely derived from the authors experiences in North America are used to illustrate the applications. The behaviour of cold-formed steel structures can be complicated due to the thin-walled nature of the sections; thus, analysis advances are required. Recent work in Generalized Beam Theory and the constrained Finite Strip Method demonstrate that, at least when it comes to thin-walled members, significant advances in structural analysis are still possible and desirable. Design of cold-formed steel structures continues to see significant improvements and refinements. Recent efforts related to the Direct Strength Method of design are highlighted, including novel extensions from the member to the system level. Finally, similar to many other areas of structural engineering, seismic engineering has motivated notable advances in applications, analysis, and design. For cold-formed steel structures these advances are reviewed to demonstrate current progress and future directions in this important area.

2.1 Framing
For many engineers, their first reaction to CFS framing is that it can only be a low-rise solution. Views of lowrise structures framed from CFS are superficially similar to timber construction, and thus the general presumption is that CFS framing will only be competitive in countries with timber framing traditions, and then only for one, or maybe two, story structures. Thus, the increasingly common use of mid-rise CFS framing in the United States, even in seismically active areas, can be a surprise for some. Fig. 1 provides an example of a six story mid-rise CFS structure constructed in the United States [8]. Many mid-rise CFS structures utilize ledger framing

1 Introduction
Today, cold-formed steel (CFS) structures enjoy widespread use in many countries and design specifications, e.g., [1] and [2] are well established, even if they are ever changing! Extensive reviews of the CFS literature are available [3], [4] and more targeted research reviews also exist: [5], [6] and Chapter 13 of [7]. However, even in the last five years significant progress has been made, particularly in analysis and design. Further, the state of the art in cold-formed steel applications, both structures and members, has not been detailed. This brief review paper provides an overview of recent advances in CFS structural applications, members, analysis, member design, system design, and seismic design. The selected
Selected and reviewed by the Scientific Commitee of the 6th European Conference on Steel and Composite Structures, 31 August to 2 September 2011, Budapest, Hungary

topics and discussions have two strong biases that must be recognized from the outset: (1) many of the applications are focused on North America, where the author resides and has the greatest interaction with the practice, and (2) the selected topics largely reflect areas where the author has been involved in one form or another (through direct research, committee work in the development of codes and specifications, or international collaborations). Given these biases, it is without a doubt that, novel applications and important research will be missed, for these shortcomings the fault is that of the author alone, and apologies are extended.

2 Structures
The three primary areas of load-bearing CFS applications are: framing, metal buildings, and racks. Each of these areas is briefly reviewed here with an emphasis on recent advances in applications, and in targeted research on these applications.

Fig. 1. Mid-rise CFS framing, adapted from [8]

Ernst & Sohn Verlag fr Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Steel Construction 4 (2011), No. 3

141

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

are typically designed as an entire system. In some cases panelized CFS framing construction is extended to metal buildings (e.g. Nunconsteel in the United States provides such a system). However, even in the last five years, interesting efforts exist: in Australia with frames relying only on stiffened sheeting [10], in Hungary [11] and Poland [12] with frames using utilizing novel built-up sections and connections, and in the UK with a long term research effort employing cassette walls for the structure [13].

2.3 Racks
CFS storage racks are remarkably efficient structures that have long used novel cross-sections and connections in their design. Although the members and connections have not changed significantly in the last five years understanding of behaviour and translating that understanding into improved designs has been very active. Significant new testing has been conducted on uprights [14], [15] upright to shelf beam connections [16], [17] and base plates [18]. Testing protocols have advanced and become formalized [19], as well as analysis protocols particularly in the use of second-order analysis [20], [21]. Contemporary concerns such as impact forces [22], [23] and progressive collapse [24] have also seen recent study. Standards organizations supporting the CFS rack industry are active, and in many instances quite progressive due to the complicated nature of rack structural performance. For example, the forthcoming Australian rack standard (AS 4084) will provide complete codified guidance on performing geometric and material nonlinear analysis on the imperfect structure (GMNIA), similar in spirit to Eurocode for shell structures.

Fig. 2. CFS typical ledger framing detail

as opposed to platform framing. In ledger framing the building is constructed story-by-story, but the floors are hung from the studs using rim track, see Fig. 2. Mid-rise CFS construction requires technical expertise on the part of the engineer/designer, and the development and support of applicable code provisions. An entire family of CFS standards specifically for framing have been developed in North America (e.g., [9]) and form the basis for the adoption of these systems in building codes. In addition, many companies working in this market are panelizers, and thus perform significant construction offsite. In North America, the pre-engineered truss industry provides a model for this form of construction; and indeed pre-engineered metal trusses are used extensively in North America today.

2.2 Metal Buildings

In metal buildings CFS members typically only provide the secondary system: purlins, girts, sheeting, etc. Research work on these secondary systems remains active (particularly with purlins), but is not the focus here. The distinction between CFS framing and load-bearing CFS metal buildings is not perfect, but CFS metal buildings typically attempt to create clear span space in the interior, while CFS framing may not. Further CFS metal buildings use steel sheet for sheathing as opposed to plywood, gypsum board, etc. In addition, CFS metal buildings

3 Members
CFS members in common use in North America include the C (with and without lips), the Z (typically with sloping lips), and a variety of generally hat-shaped deck sections. Specialty cross-sections are also used in the CFS rack industry for both uprights and beams. All of these conventional sections have been in regular use for numerous years. In the past

five years cross-section innovation has begun to take greater advantage of manufacturing technology, and begun to seriously push the boundaries of available design methods. North America has long neglected cross-section innovation, preferring a more commodity-based approach, but this is changing as evidenced by Fig. 3. For example sections are now available in North America (Fig. 3a), though the longspan deck sections in use in many parts of Europe are still yet to be utilized here. The most significant crosssection innovations occurring in North America are associated with proprietary, pre-engineered, solutions. In particular, several truss companies in North America use novel sections with narrow webs, wide flanges, intermediate stiffeners, and return lips as chords in their trusses (Fig. 3b and c). The CFS framing industry has also introduced a variety of novel variations on typical C sections for use as studs, headers, jambs, distribution members, and even bracing. One of the most popular versions of these advanced sections uses stiffened holes in the webs of joists to provide room for services, the evolution of this idea is the creation of a hybrid between the bar joist and the CFS floor joist as exemplified by products such as that of Fig. 3d. For non load-bearing applications sections cold-formed from knurled steel have been developed (Fig. 3e) with the primary advantages coming from improved fire/thermal and acoustic performance, Any discussion of new CFS members would be remiss if it did not include the highly researched: LiteSteel Beam (Fig. 3f). By using closed tubular sections for the flanges of a channel this section is able to provide capacities more typically associated with hot-rolled, than cold-formed steel [25], [26]. However, as the researchers have shown high torsional rigidity concentrated in the flanges, while overall extremely beneficial, does lead to unique behaviour and interactions most-notably lateral-distortional [27]. The Australian CFS Specification provides the most up to date treatment of this unique CFS building product. A number of even more unique CFS cross-sections, that stretch the boundaries of what it means to rollform a section, and combine multiple

142

Steel Construction 4 (2011), No. 3

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3. Example of recently developed CFS members in use in North America; (a) TSNSigmaStud, (b) TrusSteel Dyna Truss Chord, (c) Nuconsteel NUTRUSS Chord, (d) SteelForm DeltaStud, (e) ClarkDietrich UltraSteel Stud, (f) LST Lite Steel Beam

manufacturing technologies, exist in various stages of product development. The desire to achieve even lighter, greener structures, and minimize material cost and impact will aid in bringing many of these ideas to market. The challenge remains for researchers, design methods, and design specifications/codes to keep up with these innovations and be vehicles for progress instead of impediments to new technology in CFS applications.

4 Analysis
Analysis of CFS members presents a unique challenge in civil engineering. At one end of the spectrum GMNIA analysis with shell finite elements provides a compelling multi-purpose simulation tool, even if sensitivity and knowledge of the required inputs can be a challenge [28], [29]. While at the other end of the spectrum typical CFS practice either uses no formal computational structural analysis, or when analysis is employed it is linear elastic with frame elements. Frame elements in typical use do not properly include torsional-flexural coupling in unsymmetric members (such as the CFS C-section), and are completely incapable of including cross-section deformations associated with local or distortional buckling. However, currently frame elements are the only solution that is computationally efficient enough to be used on large-scale civil systems for linear and nonlinear analysis, and under the multitude of necessary load cases. Given this situation CFS analysis has always been a vibrant area for

alternatives from conventional civil engineering analysis. Most notably, the finite strip method (particularly on the member level) has been demonstrated to provide a useful compromise between the power of shell finite elements and the needed efficiency of frame finite elements. In fact, the signature curve generated by a stability member analysis using the classical finite strip method [30] provides the organizing principles that much of the design advances of the last thirty years have been based upon. Recent advances in the finite strip method include the continuing development of open source tools [31], extensions to

general boundary conditions for stability analysis [32], the constrained Finite Strip Method (cFSM) which enables modal decomposition and identification [33] to [36], and the development of finite strip-based modal identification tools for general purpose shell finite element analysis [37]. Efforts are underway to enrich frame finite elements with cross-section finite strip analysis; however, more elegant approaches with Generalized Beam Theory (GBT) exist. GBT, which is predicated on an enriched Vlasov beam theory, is ideally suited for the needs of frame element-based civil engineering system

Fig. 4. Comparison of member stability analysis by GBT and cFSM, adapted from [38]

Steel Construction 4 (2011), No. 3

143

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

analysis. In theory, if only classical modes are contained in the model then traditional framework finite element results will be obtained. However, as cross-section deformation modes are included: local-plate, distortional, shear, transverse extension, then the frame element takes on the mechanics of a typical shell finite element but with the advantage that the deformation fields are separated and known a priori in the analysis. The cFSM approach was derived based on the mechanical assumptions underlying GBT and as [38] and Fig. 4 show, they provide similar solutions. Recent GBT research demonstrates that geometric and material nonlinear analysis on the member level [39] and GBT-based frame elements for system analysis even including local loads and load height effects are possible [40], [41]. Further GBT, and its ability to identify and isolate the participation of a given deformation mode, has been shown to provide new insights on difficult problems in CFS behaviour [42]. Tools even exist for engineers to experiment with GBT analysis on their own [43]. Nearly all of the work for a fully nonlinear GBT frame element appropriate for CFS structures is in place, and the potential impact of this advancement on the analysis of CFS systems cannot be overstated. With either shell finite element analysis or advanced models based on cFSM or GBT, GMNIA based procedures for CFS are possible. However, before they can enjoy widespread use,

it must be recognized that CFS members have significant sensitivity to geometric imperfections, residual stresses and strains, and modelling parameters [28]. Thus, characterization of the inputs to GMNIA analysis remains an important area of research for CFS members and structures. Progress has been made in statistical characterizations of manufacturing imperfections [45], and in residual stresses and strains from the roll-forming process [46], [47], but significant work remains.

5 Design: member
Member design for CFS is complicated by the existence of local, distortional, and global buckling modes. In addition, the fundamental modes may interact with one another as well as with material yielding. Of course member-system interaction through secondary bracing, or through the primary framing (e.g., second-order effects) also must be considered. The primary design philosophy used in codes and standards for CFS member design is the Effective Width Method, e.g., in [1], [2]; however the Direct Strength Method (DSM) as provided in Appendix 1 of [1] and fully reviewed in [48] has been developed as an alternative approach. DSM has been formally adopted in many countries for CFS design, e.g.: Australia, the United States, Canada, Mexico, and Brazil. Under Eurocode the Direct Strength Method is best understood as falling in the family of general methods (e.g., see [49] for more on general methods). DSM combines linear eigenvalue analysis (i.e., elastic buckling analysis) with material nonlinear analysis to provide a prediction of the strength. From the users standpoint DSM is more formalized/simplified than the Eurocode general methods in that the strength curves to connect linear eigenvalue analysis with material nonlinear analysis in local, distortional, and global buckling have already been established. Regardless, the philosophy and implementation are in essence the same. Significant new work in the development of DSM has been completed in the last five years. CFS members commonly include holes, but until recently DSM provided no guidance on this situation. Recent work provides tools for under-

GBT Pcr = 48.46 kN GBT frame element DOF: order 100 ANSYS Pcr = 48.03 kN Shell elements DOF: order 10,000

Fig. 5. GBT frame stability and comparison with shell elements, adapted from [44]

standing and modelling the impact of holes on cross-section buckling modes from plates [50] to members [51], see Fig. 6a. Using a combination of new testing [52] and nonlinear finite element collapse analysis correct implementation of the DSM strength curves was also established; this included the use of net section yielding properties and modifications in the inelastic buckling regime for distortional buckling failures [53], [54], to handle transitions like Fig. 6b. This work is currently under ballot for North American CFS design in [1]. Additional progress has been made on a general/DSM method for shear, and shear and bending interaction. Current design provisions essentially only include shear buckling of the webs, and further presume the webs are flat. The newly proposed methods treat shear buckling as a cross-section buckling mode, similar to compression and bending. The impact of the flange on the solution is explicitly considered, as is the impact of other cross-section details such as rolled-in longitudinal stiffeners [55] to [59]. Research continues to determine the proper analogs to local, distortional, and global buckling for shear; meanwhile proposals are under ballot in North America to integrate the improvements already established [60], [61]. In North America fire analysis of CFS is typically completed experimentally on a given (wall or ceiling) assemblage. However, recent work has shown that available DSM expressions can properly predict the reduced strength of members, and even the switching between controlling buckling modes that occurs due to the temperature dependence of elastic buckling and yielding properties [62] to [65]. Integration of these degraded strengths with a true fire analysis is not yet completed, but is certainly on the horizon. As implemented DSM covers beams and columns explicitly, but relies on interaction equations for beamcolumns. Such an approach is not in the spirit of the general methods or of DSM. Instead the cross-section stability: local, distortional, and global should be assessed under the actual applied loads (at least axial plus bending). Section yielding may also be determined under the actual applied

144

Steel Construction 4 (2011), No. 3

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

(a)

(b)

Fig. 6. Modeling and design method development for members with holes, adapted from [54], (a) stability analysis with and without holes, (b) transition from distortional buckling to net section failure as hole size increases

loads. Preliminary work [66] demonstrates that extension of DSM in this manner is possible and desirable in many cases provides significant improvements over current design. One shortcoming of DSM, as implemented, is that the buckling mode interactions that are considered are not cross-section dependent. So, for example a lipped channel with intermediate stiffeners in the flange and web has been experimentally shown to have meaningful distortional-global interactions [67], [68], but DSM only includes local-global interaction and assumes distortional buckling modes do not interact with other modes. This assumption was validated for lipped channels [7], but intense interest ex-

ists in explaining and determining the best way to handle these interactions in the future [42], [69] to [72]. One approach may be to evolve DSM further, recently the author explored the use of the strain energy distribution of the cross-section buckling modes as a means to determine an effective thickness in the cross-section [73]. In addition, work towards true nonlinear analysis (GMNIA analysis in Eurocode parlance) may be the best final direction for CFS member design. Indeed, recent efforts lead by Rasmussens research [17], [18], [22], [23] and codified in the Australian CFS rack standards (AS 4084) provide a pioneering example of such an approach in CFS member design.

6 Design: walls and systems

Many innovations in CFS involve systems, as opposed to isolated members. Thus, design methods need to evolve towards incorporating system analysis. This trend is most prevalent in seismic design, see Section 7, but is also important in basic CFS systems such as walls and roofs. For example, a multi-year effort to develop axial capacity design provisions for CFS studs braced only by external sheathing was recently completed [74] to [76]. As Fig. 7 indicates, even for a wall with nominally identical studs, the sheathing plays a crucial role in the strength, stiffness, ductility, and observed limit state. The research in [77] provided

(c)

(a)

(b)

(d)

Fig. 7. Performance of CFS sheathed walls in compression, adapted from [75], (a) P- response of full scale walls in compression, (b) OSB-Bare Failure (flex-tors), (c) OSB-Gyp failure (local), (d) OSB-OSB failure (local)

Steel Construction 4 (2011), No. 3

145

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

the key step for integrating the system behaviour into the DSM method of design, namely, if the stud-to-sheathing fastener stiffness and sheathing diaphragm stiffness are tested or calculated these may be integrated into the cross-section stability analysis (as spring restraints) and thus provide member local, distortional, and global buckling loads that reflect the systemlevel bracing behaviour. This was completed and the conventional DSM expressions used for strength prediction are shown to agree well with tests [74] when the elastic buckling loads were suitably updated to include the system-level bracing. As another example of the evolution of system-level design the DSM methodology was also extended to the design of continuous roof purlins, where the entire multi-span beam and all its possible limit states are treated together for the stability analysis and for the strength prediction, instead of reducing down to the cross-section as in traditional design [78]. System-level analysis methods like these hold particular promise for predicting efficiencies in repetitively framed structures such as those commonly used in CFS framing.

7 Design: seismic
Seismic engineering and design is an area of high research activity throughout structural engineering, and CFS is no different. In North America CFS seismic design is not codified in one standard, forcing engineers to work across multiple standards to achieve their designs. Nonlinear time history analysis, which forms the computational engine for modern seismic design philosophies such as performance-based design, must be grossly simplified for CFS structures due to limitations in modelling (as discussed in Section 4). System-level seismic design of CFS is still in its infancy, currently the governing philosophy is to drive all energy dissipation into pre-identified discrete elements, such as prescriptively designed shearwalls. The primary lateral force resisting system in CFS framing is the shearwall, and testing on this system continues worldwide, with recent (in the last five years) contributions from Italy on wood sheathed walls [79],

from Canada on strap-braced walls [80], from Canada and the United States on steel sheet shearwalls [81], [82], from China on corrugated steel sheet shearwalls [83], and from the United States on wood sheathed walls with pins [84] and adhesives [85]. Research on the translation of CFS shearwall test data into seismic design also continues worldwide [86] to [89]. In North America, all CFS shearwall design criteria have recently been brought together into a single design specification [9]. In the broader seismic engineering community significant research effort has been expended in developing systems that concentrate inelastic energy dissipation into replaceable fuse elements. This concept has been recently extended to CFS shearwalls by Japanese researchers with a remarkably innovative system that integrates a ductile fuse into the holddown [90]. As demonstrated experimentally, the resulting shearwall system has stable loops in cyclic testing, with little if any degradation. Analytical modelling indicates an energy dissipating performance that is far and above what is available today in CFS shearwalls. As an alternative to shearwalls a novel seismic system using hot-rolled steel tube columns bolted to CFS beams was successfully developed and approved for use in seismic design in the United States [91], [92]. The systems original use was for mezzanine structures in industrial buildings, but in the United States the system has spawned commercial framing products for the residential market (e.g., BlueSky FrameTM). Current CFS seismic research projects that the author is aware of as being underway, but not yet represented fully in the literature, include cyclic tests on CFS members, shake table tests on multi-story shear walls, diaphragms, and even full-scale buildings. The authors recent work in CFS seismic design is summarized in [93]; clearly, much work remains.

important structural domains and continues to expand into new areas, such as mid-rise construction. Coldformed steel members have definitively evolved to include numerous optimized shapes beyond the conventional cross-sections. Analysis advances in the Finite Strip Method and Generalized Beam Theory provide unique capabilities for modal decomposition and identification of thin-walled members, but important work still remains to provide efficient tools that can be readily integrated with conventional structural analysis. Member design has advanced significantly due to the flexibility afforded by the direct integration of computational cross-section stability in the Direct Strength Method. New tools for system design are aiming to duplicate that success for cold-formed steel systems. Finally, a rich array of work is underway in coldformed steel seismic design. Taken in total recent advances in cold-formed steel structures indicate that significant potential continues to exist for this versatile thin-walled building material.

Acknowledgments
This paper came about through discussions with Laszlo Dunai, and I would like to thank him for the opportunity to provide this review. I would also like to thank the members and staff of the American Iron and Steel Institute Committee on Specifications and Committee on Framing Standards, many of the big picture viewpoints shared in this review were developed though my participation in those committees. I would also like to thank Dinar Camotim who provided me with the insight and parallels between the Direct Strength Method and Eurocode general methods; however any misinterpretations of Eurocode still remain my own. I would also like to thank the numerous collaborators and students who informed the research that is so briefly summarized here. Finally, I would again like to apologize for those in the cold-formed steel research community who are not detailed herein; due to the topics I have chosen, a lack of space, and most importantly my own ignorance, I am sure I have missed important contributions, for this I am truly sorry.

8 Conclusions
This paper provides a review of the state-of-the-art in cold-formed steel structural applications, members, analysis, and design. Cold-formed steel enjoys widespread use in a number of

146

Steel Construction 4 (2011), No. 3

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

References
[1] AISI, North American Specification for the Design of Cold-Formed Steel Structural Members. American Iron and Steel Institute, Washington, D.C., 2007. [2] ECCS, Eurocode 3 Design of Steel Sructures, Part 1-3: General rules Supplementary rules for cold formed thin gauge members and sheeting. Vol. EN 1993-1-3, No., 2006. [3] Yu, W.-W., LaBoube, R. A.: ColdFormed Steel Design. John Wiley & Sons, Inc.: Hoboken. p. 1 online resource (515 p.), 2010. [4] Hancock, G. J., Murray, T. M., Ellifritt, D. S.: Cold-formed steel structures to the AISI specification. Civil and environmental engineering. New York: M. Dekker. xiii, 398 p., 2001. [5] Hancock, G. J.: Cold-formed steel structures. Journal of Constructional Steel Research, Vol. 59, No. 4, pp. 473487, 2003. [6] Rondal, J.: Cold formed steel members and structures: General Report. Journal of Constructional Steel Research, Vol. 55, No. 13, pp. 155158, 2000. [7] Ziemian, R. D.: Guide to stability design criteria for metal structures. 6th ed., Hoboken, N. J.: John Wiley & Sons. xli, 1078 p., 2010. [8] SFA (2010) Park 4200 Condominium, Dallas, TX. Steel Success Stories, 2. 2010. [9] AISI, North American Standard for Cold-Formed Steel Framing Lateral Design. American Iron and Steel Institute: Washington, D.C., 2007. [10] Darcy, G., Mahendran, M.: Development of a new cold-formed steel building system. Advances in Structural Engineering, Vol. 11, No. 6, pp. 661677, 2008. [11] Dunai, L., Jakab, G.: Stability behaviour and design of non-conventional cold-formed steel structures. International Journal of Structural Stability and Dynamics, Vol. In Press, No., 2011. [12] Dubina, D., Stratan, A., Nagy, Z.: Full Scale tests on cold-formed steel pitched-roof portal frames with bolted joints. Advanced Steel Construction, Vol. 5, No. 2, pp. 175194, 2009. [13] Davies, J. M.: Light gauge steel cassette wall construction theory and practice. Journal of Constructional Steel Research, Vol. 62, No. 11, pp. 10771086, 2006. [14] Casafont, M. et al.: An experimental investigation of distortional buckling of steel storage rack columns. ThinWalled Structures, Vol. 49, No. 8, pp. 933946, 2011.

[15] Roure, F. et al.: Stub column tests for racking design: Experimental testing, FE analysis and EC3. Thin-Walled Structures, Vol. 49, No. 1, pp. 167184, 2011. [16] Filiatrault, A. et al.: Experimental stiffness of pallet-type steel storage rack tier drop connectors. Practice Periodical on Structural Design and Construction, Vol. 12, No. 4, pp. 210215, 2007. [17] Gilbert, B. P., Rasmussen, K. J. R.: Bolted moment connections in drivein and drive-through steel storage racks. Journal of Constructional Steel Research, Vol. 66, No. 6, pp. 755766, 2010. [18] Gilbert, B. P., Rasmussen, K. J. R.: Determination of the base plate stiffness and strength of steel storage racks. Journal of Constructional Steel Research, Vol. 67, No. 6, pp. 10311041, 2011. [19] Baldassino, N., Zandonini, R.: Design by testing of industrial racks. Advanced Steel Construction, Vol. 7, No. 1 SPEC. ISSUE, pp. 2747, 2011. [20] Pekoz, T., Karakaplan, A., Koo, A.: Frame analysis and design of industrial cold-formed steel racks. 2010. [21] Sarawit, A. T., Pekoz, T.: Notional load method for industrial steel storage racks. Thin-Walled Structures, Vol. 44, No. 12, pp. 12801286, 2006. [22] Gilbert, B. P., Rasmussen, K. J. R.: Impact tests and parametric impact studies on drive-in steel storage racks. Engineering Structures, Vol. 33, No. 5, pp. 14101422, 2011. [23] Gilbert, B. P., Rasmussen, K. J. R.: Determination of accidental forklift truck impact forces on drive-in steel rack structures. Engineering Structures, Vol. 33, No. 5, pp. 14031409, 2011. [24] Ng, A. L. Y., Beale, R. G., Godley, M. H. R.: Methods of restraining progressive collapse in rack structures. Engineering Structures, Vol. 31, No. 7, pp. 14601468, 2009. [25] Anapayan, T., Mahendran, M., Mahaarachchi, D.: Section moment capacity tests of LiteSteel beams. ThinWalled Structures, Vol. 49, No. 4, pp. 502512, 2011. [26] Keerthan, P., Mahendran, M.: New design rules for the shear strength of LiteSteel beams. Journal of Constructional Steel Research, Vol. 67, No. 6, pp. 10501063, 2011. [27] Anapayan, T., Mahendran, M., Mahaarachchi, D.: Lateral distortional buckling tests of a new hollow flange channel beam. Thin-Walled Structures, Vol. 49, No. 1, pp. 1325, 2011. [28] Schafer, B. W., Li, Z., Moen, C. D.: Computational modeling of cold-formed steel. Thin-Walled Structures, Vol. 48, No. 1011, pp. 752762, 2010.

[29] Yu, C., Schafer, B. W.: Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method. Journal of Constructional Steel Research, Vol. 63, No. 5, pp. 581590, 2007. [30] Hancock, G. J.: Local, distortional and lateral buckling of I-beams. ASCE J Struct Div, Vol. 104, No. 11, pp. 17871798, 1978. [31] Schafer, B. W., Adany, S.: Buckling analysis of cold-formed steel members using CUFSM: Conventional and constrained finite strip methods, 2006. [32] Li, Z., Schafer, B. W.: Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: Conventional and constrained finite strip methods, 2010. [33] Adany, S., Schafer, B. W.: Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation. Thin-Walled Structures, Vol. 44, No. 5, pp. 563584, 2006. [34] Adany, S., Schafer, B. W.: Buckling mode decomposition of single-branched open cross-section members via finite strip method: Application and examples. Thin-Walled Structures, Vol. 44, No. 5, pp. 585600, 2006. [35] Adany, S., Schafer, B. W.: A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method. Journal of Constructional Steel Research, Vol. 64, No. 1, pp. 1229, 2008. [36] Li, Z. et al.: Impact of basis, orthogonalization, and normalization on the constrained Finite Strip Method for stability solutions of open thin-walled members. Thin-Walled Structures, No. [37] Adany, S., Joo, A. L., Schafer, B. W.: Buckling mode identification of thinwalled members by using cFSM base functions. Thin-Walled Structures, Vol. 48, No. 1011, pp. 806817, 2010. [38] Adany, S. et al.: GBT and cFSM: Two modal approaches to the buckling analysis of unbranched thin-walled members. Advanced Steel Construction, Vol. 5, No. 2, pp. 195223, 2009. [39] Goncalves, R., Dinis, P. B., Camotim, D.: GBT formulation to analyse the first-order and buckling behaviour of thin-walled members with arbitrary cross-sections. Thin-Walled Structures, Vol. 47, No. 5, pp. 583600, 2009. [40] Camotim, D., Basaglia, C., Silvestre, N.: GBT buckling analysis of thinwalled steel frames: A state-of-the-art report. Thin-Walled Structures, Vol. 48, No. 1011, pp. 726743, 2010. [41] Goncalves, R., Camotim, D.: Generalised beam theory-based finite elements

Steel Construction 4 (2011), No. 3

147

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

for elastoplastic thin-walled metal members. Thin-Walled Structures. [42] Silvestre, N., Camotim, D.: Localplate and distortional postbuckling behavior of cold-formed steel lipped channel columns with intermediate stiffeners. Journal of Structural Engineering, Vol. 132, No. 4, pp. 529540, 2006. [43] Bebiano, R., Silvestre, N., Camotim, D.: GBTUL A code for the buckling analysis of cold-formed steel members, 2008. [44] Basiglia, C., Camotim, D.: On the Incorporation of Load Application Effects in the GBT Buckling Analysis of Thin-Walled Steel Beams and Frames, in Annual Stability Conference. Structural Stability Resarch Council: Pittsburgh, PA. p. 20, 2011. [45] Zeinoddini, V. M., Schafer, B. W.: Global Imperfections and Dimensional Variations in Cold-Formed Steel Members. International Journal of Structural Stability and Dynamics, World Scientific, Vol. In Press, No., 2011. [46] Moen, C. D., Igusa, T., Schafer, B. W.: Prediction of residual stresses and strains in cold-formed steel members. Thin-Walled Structures, Vol. 46, No. 11, pp. 12741289, 2008. [47] Quach, W. M., Teng, J. G., Chung, K. F.: Finite element predictions of residual stresses in press-braked thinwalled steel sections. Engineering Structures, Vol. 28, No. 11, pp. 16091619, 2006. [48] Schafer, B. W.: Review: The Direct Strength Method of cold-formed steel member design. Journal of Constructional Steel Research, Vol. 64, No. 78, pp. 766778, 2008. [49] Greiner, R., Lindner, J.: Interaction formulae for members subjected to bending and axial compression in EUROCODE 3 the Method 2 approach. Journal of Constructional Steel Research, Vol. 62, No. 8, pp. 757770, 2006. [50] Moen, C. D., Schafer, B. W.: Elastic buckling of thin plates with holes in compression or bending. Thin-Walled Structures, Vol. 47, No. 12, pp. 15971607, 2009. [51] Moen, C. D., Schafer, B. W.: Elastic buckling of cold-formed steel columns and beams with holes. Engineering Structures, Vol. 31, No. 12, pp. 28122824, 2009. [52] Moen, C. D., Schafer, B. W.: Experiments on cold-formed steel columns with holes. Thin-Walled Structures, Vol. 46, No. 10, pp. 11641182, 2008. [53] Moen, C. D., Schafer. B. W.: Extending direct strength design to cold-formed steel beams with holes, 2010. [54] Moen, C. D., Schafer, B. W.: Direct strength method for design of coldformed steel columns with holes. Jour-

nal of Structural Engineering, Vol. 137, No. 5, pp. 559570, 2011. [55] Pham, C. H., Hancock, SG. J.: Hear buckling of thin-walled channel sections. Journal of Constructional Steel Research, Vol. 65, No. 3, pp. 578585, 2009. [56] Pham, C. H., Hancock, G. J.: Numerical simulation of high strength cold-formed purlins in combined bending and shear. Journal of Constructional Steel Research, Vol. 66, No. 10, pp. 12051217, 2010. [57] Pham, C. H., Hancock, G. J.: Experimental investigation of high strength cold-formed-sections in combined bending and shear. Journal of Structural Engineering, Vol. 136, No. 7, pp. 866878, 2010. [58] Bebiano, R., Silvestre, N., Camotim, D.: GBT formulation to analyze the buckling behavior of thin-walled members subjected to non-uniform bending. International Journal of Structural Stability and Dynamics, Vol. 7, No. 1, pp. 2354, 2007. [59] Naik, R. T., Moen, C. D.: Elastic buckling studies of thin plates and coldformed steel members in shear, 2010. [60] Pham, C. H., Hancock, G. J.: Direct strength design of cold-formed purlins. Journal of Structural Engineering, Vol. 135, No. 3, pp. 229238, 2009. [61] Pham, C. H., Hancock, G. J.: Direct strength design of cold-formed C-sections for shear, 2010. [62] Alves, M. C., Batista, E. M., Camotim, D.: Buckling, post-buckling and ultimate strength of cold-formed steel lipped channel members underfire condition, 2007. [63] Chen, J., Young, B.: Cold-formed steel lipped channel columns at elevated temperatures. Engineering Structures, Vol. 29, No. 10, pp. 24452456, 2007. [64] Chen, J., Young, B.: Design of high strength steel columns at elevated temperatures. Journal of Constructional Steel Research, Vol. 64, No. 6, pp. 689703, 2008. [65] Landesmann, A., Camotim. D.: Distortional failure and design of coldformed steel lipped channel columns under fire conditions, 2010. [66] Shifferaw, Y., Schafer, B. W.: Towards a direct strength method for cold-formed steel beam-columns, 2010. [67] Yap, D. C. Y., Hancock, G. J.: Experimental study of complex high-strength cold-formed cross-shaped steel section. Journal of Structural Engineering, Vol. 134, No. 8, pp. 13221333, 2008. [68] Yap, D. C. Y., Hancock, G. J.: Experimental study of high-strength coldformed stiffened-web C-sections in compression. Journal of Structural Engineering, Vol. 137, No. 2, pp. 162172, 2011.

[69] Borges Dinis, P., Camotim, D.: Local/distortional mode interaction in cold-formed steel lipped channel beams. Thin-Walled Structures, Vol. 48, No. 1011, pp. 771785, 2010. [70] Borges Dinis, P., Camotim, D., Silvestre, N.: FEM-based analysis of the local-plate/distortional mode interaction in cold-formed steel lipped channel columns. Computers and Structures, Vol. 85, No. 1920, pp. 14611474, 2007. [71] Dinis, P. B., Camotim, D.: Post-buckling behaviour and strength of coldformed steel lipped channel columns experiencing distortional/global interaction. Computers and Structures, Vol. 89, No. 34, pp. 422434, 2011. [72] Silvestre, N., Camotim, D., Dinis, P. B.: Direct strength prediction of lipped channel columns experiencing localplate/distortional interaction. Advanced Steel Construction, Vol. 5, No. 1, pp. 4971, 2009. [73] Seif, M., Schafer, B. W.: Towards a strain energy based strength prediction for locally slender structural steel columns, in Annual Stability Conference. Structural Stability Research Council: Pittsburgh, PA. p. 14, 2011. [74] Vieira Jr, L. C. M., Schafer, B. W.: Behavior and design of axially compressed sheathed wall studs, 2010. [75] Vieira Jr, L. C. M., Schafer, B. W.: Full-scale testing of sheathed coldformed steel wall stud systems in axial compression, 2010. [76] Vieira Jr, L. C. M., Shifferaw, Y., Schafer, B. W.: Experiments on sheathed cold-formed steel studs in compression. Journal of Constructional Steel Research. [77] Vieira Jr, L. C. M., Schafer, B. W.: Lateral Stiffness and Strength of Sheathing Braced Cold-Formed Steel Stud Walls. Engineering Structures, Vol. Submitted, No., 2011. [78] Basaglia, C., Camotim D.: On the direct strength design of continuous cold-formed steel beams, 2010. [79] Landolfo, R., Fiorino, L., Della Corte, G.: Seismic behavior of sheathed coldformed structures: Physical tests. Journal of Structural Engineering, Vol. 132, No. 4, pp. 570581, 2006. [80] Al-Kharat, M., Rogers, C. A.: Inelastic performance of cold-formed steel strap braced walls. Journal of Constructional Steel Research, Vol. 63, No. 4, pp. 460474, 2007. [81] Rogers, C. A. et al.: Development of seismic design provisions for steel sheet sheathed shear walls, 2011. [82] Yu, C.: Shear resistance of coldformed steel framed shear walls with 0.686 mm, 0.762 mm, and 0.838 mm steel sheet sheathing. Engineering Struc-

148

Steel Construction 4 (2011), No. 3

B. W. Schafer Cold-formed steel structures around the world A review of recent advances in applications, analysis and design

tures, Vol. 32, No. 6, pp. 15221529, 2010. [83] Li, Y. et al.: Shear behaviors of lightgauge composite walls under monotonic and cyclic loading, 2010. [84] Serrette, R., Nolan, D. P.: Reversed cyclic performance of shear walls with wood panels attached to cold-formed steel with pins. Journal of Structural Engineering, Vol. 135, No. 8, pp. 959967, 2009. [85] Serrette, R. et al.: Cold-formed steel frame shear walls utilizing structural adhesives. Journal of Structural Engineering, Vol. 132, No. 4, pp. 591599, 2006. [86] Serrette, R.: Seismic design strength of cold-formed steel-framed shear walls. Journal of Structural Engineering, Vol. 136, No. 9, pp. 11231130, 2010. [87] Dubina, D.: Behavior and performance of cold-formed steel-framed houses under seismic action. Journal of

Constructional Steel Research, Vol. 64, No. 78, pp. 896913, 2008. [88] Fiorino, L., Iuorio, O., Landolfo, R.: Sheathed cold-formed steel housing: A seismic design procedure. ThinWalled Structures, Vol. 47, No. 89, pp. 919930, 2009. [89] Xu, L., Martinez, J.: Strength and stiffness determination of shear wall panels in cold-formed steel framing. Thin-Walled Structures, Vol. 44, No. 10, pp. 10841095, 2007. [90] Ozaki, F. et al.: Innovative damage control systems using replaceable energy dissipating steel fuses for coldformed steel structures, 2010. [91] Sato, A., Uang, C. M.: Seismic performance factors for cold-formed steel special bolted moment frames. Journal of Structural Engineering, Vol. 136, No. 8, pp. 961967, 2010. [92] Uang, C. M. et al.: Cyclic testing and modeling of cold-formed steel special bolted moment frame connections. Jour-

nal of Structural Engineering, Vol. 136, No. 8, pp. 953960, 2010. [93] Schafer, B. W., CFS-NEES: Advancing Cold-Formed Steel Earthquake Engineering. [cited 2011 June 21]; CFSNEES Project Page]. Available from: http://www.ce.jhu.edu/cfsnees/. 2011. Keywords: cold-formed steel; constrained Finite Strip Method; Direct Strength Method; review

Author:
Prof. Benjamin W. Schafer Johns Hopkins University, Dept. of Civil Engineering, USA schafer@jhu.edu

Steel Construction 4 (2011), No. 3

149