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

1 Introduction

Today, cold-formed steel (CFS) struc-tures enjoy widespread use in manycountries and design specifications,e.g., [1] and [2] are well established,even if they are ever changing! Exten-sive reviews of the CFS literature areavailable [3], [4] and more targeted re-search reviews also exist: [5], [6] andChapter 13 of [7]. However, even inthe last five years significant progresshas been made, particularly in analy-sis and design. Further, the state ofthe art in cold-formed steel applica-tions, both structures and members,has not been detailed.

This brief review paper providesan overview of recent advances inCFS structural applications, members,analysis, member design, system de-sign, and seismic design. The selectedtopics and discussions have two strongbiases that must be recognized fromthe outset: (1) many of the applicationsare focused on North America, wherethe author resides and has the great-est interaction with the practice, and

(2) the selected topics largely reflectareas where the author has been in-volved in one form or another (throughdirect research, committee work in thedevelopment of codes and specifica-tions, or international collaborations).Given these biases, it is without adoubt that, novel applications and im-portant research will be missed, forthese shortcomings the fault is that ofthe author alone, and apologies areextended.

2 Structures

The three primary areas of load-bear-ing CFS applications are: framing,metal buildings, and racks. Each ofthese areas is briefly reviewed herewith an emphasis on recent advancesin applications, and in targeted re-search on these applications.

2.1 Framing

For many engineers, their first reac-tion to CFS framing is that it can onlybe a low-rise solution. Views of low-

rise structures framed from CFS aresuperficially similar to timber construc-tion, and thus the general presump-tion is that CFS framing will only becompetitive in countries with timberframing traditions, and then only forone, or maybe two, story structures.Thus, the increasingly common use ofmid-rise CFS framing in the UnitedStates, even in seismically active ar-eas, can be a surprise for some. Fig. 1provides an example of a six storymid-rise CFS structure constructed inthe United States [8]. Many mid-riseCFS structures utilize ledger framingas opposed to platform framing. Inledger framing the building is con-structed story-by-story, but the floorsare hung from the studs using rimtrack, see Fig. 2.

Benjamin W. Schafer

Cold-formed steel structures around the worldA 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 lastfive 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 sec-ondary systems, curtain walls, etc. Cold-formed steel applications continue to advance inthree primary categories: framing, metal buildings, and racks. Examples largely derivedfrom the author’s experiences in North America are used to illustrate the applications. Thebehaviour of cold-formed steel structures can be complicated due to the thin-walled natureof the sections; thus, analysis advances are required. Recent work in Generalized BeamTheory and the constrained Finite Strip Method demonstrate that, at least when it comes tothin-walled members, significant advances in structural analysis are still possible and desir-able. Design of cold-formed steel structures continues to see significant improvements andrefinements. 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 manyother areas of structural engineering, seismic engineering has motivated notable advancesin applications, analysis, and design. For cold-formed steel structures these advances arereviewed to demonstrate current progress and future directions in this important area.

ArticlesSteel Construction 3/2011 � druckfrei � nach Korrektur druckfreiArticles-No. 8

Datum, UnterschriftDOI: 10.1002/stco.201110000

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

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

Steel Construction 4 (2011), No. 3

Mid-rise CFS construction re-quires technical expertise on the partof the engineer/designer, and the de-velopment and support of applicablecode provisions. An entire family ofCFS standards specifically for fram-ing have been developed in NorthAmerica (e.g., [9]) and form the basisfor the adoption of these systems inbuilding codes. In addition, many com-panies working in this market are pan-elizers, and thus perform significantconstruction offsite. In North America,the pre-engineered truss industry pro-vides a model for this form of con-struction; and indeed pre-engineeredmetal trusses are used extensively inNorth America today.

2.2 Metal Buildings

In metal buildings CFS members typ-ically only provide the secondary sys-tem: purlins, girts, sheeting, etc. Re-search work on these secondary sys-tems remains active (particularly withpurlins), but is not the focus here. Thedistinction between CFS framing andload-bearing CFS metal buildings isnot perfect, but CFS metal buildingstypically attempt to create clear spanspace in the interior, while CFS fram-ing may not. Further CFS metal build-ings use steel sheet for sheathing asopposed to plywood, gypsum board,etc. In addition, CFS metal buildingsare typically designed as an entire sys-tem. In some cases panelized CFSframing construction is extended tometal buildings (e.g. Nunconsteel® inthe United States provides such a sys-

tem). However, even in the last fiveyears, interesting efforts exist: in Aus-tralia with frames relying only on stiff-ened sheeting [10], in Hungary [11] andPoland [12] with frames using utiliz-ing novel built-up sections and con-nections, and in the UK with a longterm research effort employing cas-sette walls for the structure [13].

2.3 Racks

CFS storage racks are remarkably ef-ficient structures that have long usednovel cross-sections and connectionsin their design. Although the membersand connections have not changedsignificantly in the last five years un-derstanding of behaviour and trans-lating that understanding into im-proved designs has been very active.Significant new testing has been con-ducted on uprights [14], [15] uprightto shelf beam connections [16], [17]and base plates [18]. Testing protocolshave advanced and become formal-ized [19], as well as analysis protocolsparticularly in the use of second-or-der analysis [20], [21]. Contemporaryconcerns such as impact forces [22],[23] and progressive collapse [24] havealso seen recent study. Standards or-ganizations supporting the CFS rackindustry are active, and in many in-stances quite progressive due to thecomplicated nature of rack structuralperformance. For example, the forth-coming Australian rack standard(AS 4084) will provide complete cod-ified guidance on performing geomet-ric and material nonlinear analysison the imperfect structure (GMNIA),similar in spirit to Eurocode for shellstructures.

3 Members

CFS members in common use inNorth America include the C (withand without lips), the Z (typically withsloping lips), and a variety of gener-ally “hat-shaped” deck sections. Spe-cialty cross-sections are also used inthe CFS rack industry for both up-rights and beams. All of these con-ventional sections have been in regu-lar use for numerous years. In the pastfive years cross-section innovation hasbegun to take greater advantage ofmanufacturing technology, and begunto seriously push the boundaries ofavailable design methods.

North America has long ne-glected cross-section innovation, pre-ferring a more commodity-based ap-proach, but this is changing as evi-denced by Fig. 3. For example Σsections are now available in NorthAmerica (Fig. 3a), though the long-span deck sections in use in manyparts of Europe are still yet to be uti-lized here. The most significant cross-section innovations occurring in NorthAmerica are associated with propri-etary, pre-engineered, solutions. Inparticular, several truss companies inNorth America use novel sections withnarrow webs, wide flanges, intermedi-ate stiffeners, and return lips as chordsin their trusses (Fig. 3b and c).

The CFS framing industry hasalso introduced a variety of novelvariations on typical C sections foruse as studs, headers, jambs, distribu-tion members, and even bracing. Oneof the most popular versions of theseadvanced sections uses stiffened holesin the webs of joists to provide roomfor services, the evolution of this ideais the creation of a hybrid betweenthe bar joist and the CFS floor joist asexemplified by products such as thatof Fig. 3d. For non load-bearing ap -plications sections cold-formed fromknurled steel have been developed(Fig. 3e) with the primary advantagescoming from improved fire/thermaland acoustic performance,

Any discussion of new CFS mem-bers would be remiss if it did not in-clude the highly researched: LiteSteelBeam (Fig. 3f). By using closed tubu-lar sections for the flanges of a chan-nel this section is able to provide ca-pacities more typically associated withhot-rolled, than cold-formed steel [25],[26]. However, as the researchers haveshown high torsional rigidity concen-trated in the flanges, while overall ex-tremely beneficial, does lead to uniquebehaviour and interactions most-no-tably lateral-distortional [27]. The Aus-tralian CFS Specification provides themost up to date treatment of thisunique CFS building product.

A number of even more uniqueCFS cross-sections, that stretch theboundaries of what it means to roll-form a section, and combine multiplemanufacturing technologies, exist invarious stages of product development.The desire to achieve even lighter,greener structures, and minimize ma-terial cost and impact will aid in bring-

Fig. 2. CFS typical ledger framing detail

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3Steel Construction 4 (2011), No. 3

ing many of these ideas to market. Thechallenge remains for researchers, de-sign methods, and design specifica-tions/codes to keep up with these in-novations and be vehicles for progressinstead of impediments to new tech-nology in CFS applications.

4 Analysis

Analysis of CFS members presents aunique challenge in civil engineering.At one end of the spectrum GMNIAanalysis with shell finite elementsprovides a compelling multi-purposesimulation tool, even if sensitivityand knowledge of the required inputscan be a challenge [28], [29]. While atthe other end of the spectrum typicalCFS practice either uses no formalcomputational structural analysis, orwhen analysis is employed it is linearelastic with frame elements. Frame el-ements in typical use do not properlyinclude torsional-flexural coupling inunsymmetric members (such as theCFS C-section), and are completelyincapable of including cross-sectiondeformations associated with local ordistortional buckling. However, cur-rently frame elements are the only so-lution that is computationally efficientenough to be used on large-scale civilsystems for linear and nonlinear analy-sis, and under the multitude of neces-sary load cases.

Given this situation CFS analy-sis has always been a vibrant area foralternatives from conventional civilengineering analysis. Most notably, thefinite strip method (particularly on themember level) has been demonstratedto provide a useful compromise be-tween the power of shell finite ele-

ments and the needed efficiency offrame finite elements. In fact, the sig-nature curve generated by a stabilitymember analysis using the classical finite strip method [30] provides theorganizing principles that much ofthe design advances of the last thirtyyears have been based upon. Recentadvances in the finite strip method in-clude the continuing development ofopen source tools [31], extensions togeneral boundary conditions for sta-bility analysis [32], the constrained Fi-nite Strip Method (cFSM) which en-ables modal decomposition and iden-tification [33] to [36], and the develop-ment of finite strip-based modal iden-tification tools for general purpose

shell finite element analysis [37]. Ef-forts are underway to enrich frame fi-nite elements with cross-section finitestrip analysis; however, more elegantapproaches with Generalized BeamTheory (GBT) exist.

GBT, which is predicated on anenriched Vlasov beam theory, is ide-ally suited for the needs of frame ele-ment-based civil engineering systemanalysis. In theory, if only classicalmodes are contained in the modelthen traditional framework finite ele-ment results will be obtained. How-ever, as cross-section deformationmodes are included: local-plate, dis-tortional, shear, transverse extension,then the frame element takes on the

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

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

(a) (b) (c) (d) (e) (f)

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

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mechanics of a typical shell finite ele-ment – but with the advantage thatthe deformation fields are separatedand known a priori in the analysis. ThecFSM approach was derived basedon the mechanical assumptions un-derlying GBT and as [38] and Fig. 4show, they provide similar solutions.Recent GBT research demonstratesthat geometric and material nonlin-ear analysis on the member level [39]and GBT-based frame elements forsystem analysis even including localloads and load height effects are pos-sible [40], [41]. Further GBT, and itsability to identify and isolate the par-ticipation of a given deformationmode, has been shown to providenew insights on difficult problems inCFS behaviour [42]. Tools even existfor engineers to experiment with GBTanalysis on their own [43]. Nearly allof the work for a fully nonlinear GBTframe element appropriate for CFSstructures is in place, and the poten-tial impact of this advancement onthe analysis of CFS systems cannotbe overstated.

With either shell finite elementanalysis or advanced models based oncFSM or GBT, GMNIA based proce-dures for CFS are possible. However,before they can enjoy widespread use,it must be recognized that CFS mem-bers have significant sensitivity to geo-metric imperfections, residual stressesand strains, and modelling parame-ters [28]. Thus, characterization of theinputs to GMNIA analysis remains animportant area of research for CFSmembers and structures. Progress has

4 Steel Construction 4 (2011), No. 3

been made in statistical characteriza-tions of manufacturing imperfections[45], and in residual stresses and strainsfrom the roll-forming process [46], [47],but significant work remains.

5 Design: member

Member design for CFS is compli-cated by the existence of local, distor-tional, and global buckling modes. Inaddition, the fundamental modesmay interact with one another as wellas with material yielding. Of coursemember-system interaction throughsecondary bracing, or through theprimary framing (e.g., second-ordereffects) also must be considered. Theprimary design philosophy used incodes and standards for CFS memberdesign is the Effective Width Method,e.g., in [1], [2]; however the DirectStrength Method (DSM) as providedin Appendix 1 of [1] and fully re-viewed in [48] has been developed asan alternative approach.

DSM has been formally adoptedin many countries for CFS design, e.g.:Australia, the United States, Canada,Mexico, and Brazil. Under Eurocodethe Direct Strength Method is bestunderstood as falling in the family of“general methods” (e.g., see [49] formore on “general methods”). DSMcombines linear eigenvalue analysis(i.e., elastic buckling analysis) withmaterial nonlinear analysis to providea prediction of the strength. From theusers standpoint DSM is more for-malized/simplified than the Eurocodegeneral methods in that the strengthcurves to connect linear eigenvalueanalysis with material nonlinear analy-sis in local, distortional, and globalbuckling have already been estab-lished. Regardless, the philosophy andimplementation are in essence thesame. Significant new work in the de-velopment of DSM has been com-pleted in the last five years.

CFS members commonly includeholes, but until recently DSM pro-vided no guidance on this situation.Recent work provides tools for under-standing and modelling the impact ofholes on cross-section buckling modesfrom plates [50] to members [51], seeFig. 6a. Using a combination of newtesting [52] and nonlinear finite ele-ment collapse analysis correct imple-mentation of the DSM strength curveswas also established; this included

the use of net section yielding proper-ties and modifications in the inelasticbuckling regime for distortional buck-ling failures [53], [54], to handle tran-sitions like Fig. 6b. This work is cur-rently under ballot for North Ameri-can CFS design in [1].

Additional progress has beenmade on a general/DSM method forshear, and shear and bending interac-tion. Current design provisions essen-tially only include shear buckling ofthe webs, and further presume thewebs are flat. The newly proposedmethods treat shear buckling as across-section buckling mode, similarto compression and bending. The im-pact of the flange on the solution isexplicitly considered, as is the impactof other cross-section details such asrolled-in longitudinal stiffeners [55] to[59]. Research continues to determinethe proper analogs to local, distor-tional, and global buckling for shear;meanwhile proposals are under bal-lot in North America to integrate theimprovements already established [60],[61].

In North America fire analysis ofCFS is typically completed experimen-tally on a given (wall or ceiling) as-semblage. However, recent work hasshown that available DSM expres-sions can properly predict the reducedstrength of members, and even theswitching between controlling buck-ling modes that occurs due to thetemperature dependence of elasticbuckling and yielding properties [62]to [65]. Integration of these degradedstrengths with a true fire analysis isnot yet completed, but is certainly onthe horizon.

As implemented DSM coversbeams and columns explicitly, but re-lies on interaction equations for beam-columns. Such an approach is not inthe spirit of the general methods or ofDSM. Instead the cross-section sta -bility: local, distortional, and globalshould be assessed under the actualapplied loads (at least axial plus bend-ing). Section yielding may also be de-termined under the actual appliedloads. Preliminary work [66] demon-strates that extension of DSM in thismanner is possible and desirable – inmany cases provides significant im-provements over current design.

One shortcoming of DSM, as im-plemented, is that the buckling modeinteractions that are considered are

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

Fig. 5. GBT frame stability and com-parison with shell elements, adaptedfrom [44]

GBT

Pcr = 48.46 kN

GBT frame element

DOF: order 100

ANSYS

Pcr = 48.03 kN

Shell elements

DOF: order 10,000

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not cross-section dependent. So, forexample a lipped channel with inter-mediate stiffeners in the flange andweb has been experimentally shownto have meaningful distortional-globalinteractions [67], [68], but DSM onlyincludes local-global interaction andassumes distortional buckling modesdo not interact with other modes. Thisassumption was validated for lippedchannels [7], but intense interest ex-ists in explaining and determining thebest way to handle these interactionsin the future [42], [69] to [72]. One ap-proach may be to evolve DSM fur-ther, recently the author explored theuse of the strain energy distributionof the cross-section buckling modesas a means to determine an effective

thickness in the cross-section [73]. Inaddition, work towards true nonlin-ear analysis (GMNIA analysis in Euro -code parlance) may be the best finaldirection for CFS member design. In-deed, recent efforts lead by Rasmus -sen’s research [17], [18], [22], [23] andcodified in the Australian CFS rackstandards (AS 4084) provide a pio-neering example of such an approachin CFS member design.

6 Design: walls and systems

Many innovations in CFS involve sys-tems, as opposed to isolated mem-bers. Thus, design methods need toevolve towards incorporating systemanalysis. This trend is most prevalent

in seismic design, see Section 7, but isalso important in basic CFS systemssuch as walls and roofs. For example,a multi-year effort to develop axial ca-pacity design provisions for CFS studsbraced only by external sheathing wasrecently completed [74] to [76]. AsFig. 7 indicates, even for a wall withnominally identical studs, the sheath-ing plays a crucial role in the strength,stiffness, ductility, and observed limitstate. The research in [77] providedthe key step for integrating the systembehaviour into the DSM method ofdesign, namely, if the stud-to-sheath-ing fastener stiffness and sheathingdiaphragm stiffness are tested or cal-culated these may be integrated intothe cross-section stability analysis (as

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

Fig. 6. Modeling and design method development for members with holes, adapted from [54], (a) stability analysis with andwithout holes, (b) transition from distortional buckling to net section failure as hole size increases

(a) (b)

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

(a) (b)

(c)

(d)

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spring restraints) and thus providemember local, distortional, and globalbuckling loads that reflect the system-level bracing behaviour. This was com-pleted and the conventional DSM ex-pressions used for strength predictionare shown to agree well with tests[74] when the elastic buckling loadswere suitably updated to include thesystem-level bracing.

As another example of the evolu-tion of system-level design the DSMmethodology was also extended tothe design of continuous roof purlins,where the entire multi-span beam andall its possible limit states are treatedtogether for the stability analysis andfor the strength prediction, instead ofreducing down to the cross-section asin traditional design [78]. System-levelanalysis methods like these hold par-ticular promise for predicting efficien-cies in repetitively framed structuressuch as those commonly used in CFSframing.

7 Design: seismic

Seismic engineering and design is anarea of high research activity through-out structural engineering, and CFS isno different. In North America CFSseismic design is not codified in onestandard, forcing engineers to workacross multiple standards to achievetheir designs. Nonlinear time historyanalysis, which forms the computa-tional engine for modern seismic de-sign philosophies such as performance-based design, must be grossly simpli-fied for CFS structures due to limita-tions in modelling (as discussed inSection 4). System-level seismic de-sign of CFS is still in its infancy, cur-rently the governing philosophy is todrive all energy dissipation into pre-identified discrete elements, such asprescriptively designed shearwalls.

The primary lateral force resist-ing system in CFS framing is theshearwall, and testing on this systemcontinues worldwide, with recent (inthe last five years) contributions fromItaly on wood sheathed walls [79],from Canada on strap-braced walls[80], from Canada and the UnitedStates on steel sheet shearwalls [81],[82], from China on corrugated steelsheet shearwalls [83], and from theUnited States on wood sheathed wallswith pins [84] and adhesives [85]. Re-search on the translation of CFS

6 Steel Construction 4 (2011), No. 3

shearwall test data into seismic de-sign also continues worldwide [86] to[89]. In North America, all CFS shear-wall design criteria have recently beenbrought together into a single designspecification [9].

In the broader seismic engineer-ing community significant researcheffort has been expended in develop-ing systems that concentrate inelasticenergy dissipation into replaceable“fuse” elements. This concept hasbeen recently extended to CFS shear-walls by Japanese researchers with aremarkably innovative system that in-tegrates a ductile fuse into the hold-down [90]. As demonstrated experi-mentally, the resulting shearwall sys-tem has stable loops in cyclic testing,with little if any degradation. Analyti-cal modelling indicates an energy dis-sipating performance that is far andabove what is available today in CFSshearwalls.

As an alternative to shearwalls anovel seismic system using hot-rolledsteel tube columns bolted to CFSbeams was successfully developed andapproved for use in seismic design inthe United States [91], [92]. The sys-tem’s original use was for mezzaninestructures in industrial buildings, butin the United States the system hasspawned commercial framing prod-ucts for the residential market (e.g.,BlueSky FrameTM).

Current CFS seismic researchprojects that the author is aware of asbeing underway, but not yet repre-sented fully in the literature, includecyclic tests on CFS members, shaketable tests on multi-story shear walls,diaphragms, and even full-scale build-ings. The author’s recent work in CFSseismic design is summarized in [93];clearly, much work remains.

8 Conclusions

This paper provides a review of thestate-of-the-art in cold-formed steelstructural applications, members,analysis, and design. Cold-formed steelenjoys widespread use in a number ofimportant structural domains andcontinues to expand into new areas,such as mid-rise construction. Cold-formed steel members have definitive -ly evolved to include numerous opti-mized shapes beyond the conventionalcross-sections. Analysis advances inthe Finite Strip Method and General-

ized Beam Theory provide unique ca-pabilities for modal decompositionand identification of thin-walled mem-bers, but important work still remainsto provide efficient tools that can bereadily integrated with conventionalstructural analysis. Member designhas advanced significantly due to theflexibility afforded by the direct inte-gration of computational cross-sectionstability in the Direct Strength Me -thod. New tools for system design areaiming to duplicate that success forcold-formed steel systems. Finally, arich array of work is underway in cold-formed steel seismic design. Taken intotal recent advances in cold-formedsteel structures indicate that signifi-cant potential continues to exist forthis versatile thin-walled building ma-terial.

Acknowledgments

This paper came about through dis-cussions with Laszlo Dunai, and Iwould like to thank him for the op-portunity to provide this review. Iwould also like to thank the membersand staff of the American Iron andSteel Institute Committee on Specifi-cations and Committee on FramingStandards, many of the big pictureviewpoints shared in this review weredeveloped though my participation inthose committees. I would also like tothank Dinar Camotim who providedme with the insight and parallels be-tween the Direct Strength Methodand Eurocode “general methods”;however any misinterpretations ofEurocode still remain my own. Iwould also like to thank the numer-ous collaborators and students whoinformed the research that is sobriefly summarized here. Finally, Iwould again like to apologize forthose in the cold-formed steel re-search community who are not de-tailed herein; due to the topics I havechosen, a lack of space, and most im-portantly my own ignorance, I amsure I have missed important contri-butions, for this I am truly sorry.

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Keywords: cold-formed steel, constrainedFinite Strip Method, Direct StrengthMethod, review

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

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

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