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3.6 DISTORTIONAL BUCKLING: ANALYTICAL METHODS FOR PREDICTING ELASTIC DISTORTIONAL BUCKLING STRESSES

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Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

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Following pioneering research in the 1940s, research into cold-formed steel intensified in the 1970s and led to numerous national European design specifications, and subsequently the preparation of Part 1-3 of Eurocode3 (EN1993-1-3) for cold-formed steel structures. Now a Euronorm, EN1993- 1-3 is fully embedded in the Eurocode framework.

This book serves as a reference text for design engineers using EN1993-1-3. It forms part of the suite of ECCS Eurocode Design Manuals prepared in recent years for other parts of EN1993 and other Eurocodes to aid the implementation of Eurocodes in European states. The book draws on the authors’ considerable experience with designing cold-formed steel structures, both as academics and practitioners, and strikes a balance between theory and practice.

Applications of cold-formed steel have broadened over the years. Cold-formed steel is now used as primary structural elements, as in steel framed residential buildings, steel storage racks, portal frames, and tubular truss and frame structures, and as secondary structural elements, as in roofing and wall systems featuring purlins, girts and corrugated steel sheeting. Additionally, integrated building systems have been developed, such as cassettes, as have stressed skin principles for designing the building envelope.

The design of cold-formed steel is perceived to be challenging by many structural engineers because the thinness of the steel leads to buckling and failure modes not found in the design of hot-rolled and fabricated steel structures. Furthermore, roll-forming techniques have developed rapidly in recent decades and spawned highly optimised cross sections featuring intermediate stiffeners and complex lip stiffeners, which are not easily designed using conventional methods. The book covers the design of structural members of complex shapes and connections as well as the design of integrated structural solutions, such as cassettes, and design using stressed skin principles. The structural behaviour and design to EN1993-1-3 are explained and numerous worked examples are included to guide or enable a cross-check for structural design engineers.

The final Chapter 8 deserves a special mention as it addresses the comprehensive range of considerations other than structural to be made in cold-formed steel construction, including thermal transmission and sound, serviceability, durability, sustainability and recyclability. Methods of design for single and multi-storey housing are explained in detail, concluding with a comprehensive worked example of a residential building.

This book presents a landmark in the development of guidelines for the structural design of cold-formed steel. It is arguably the most extensive reference available for designing cold-formed steel structures to EN1993-1-3, and will serve the structural engineering community well in adapting to the expanding range of residential and industrial applications of cold-formed steel.

The use of cold-formed steel members in building construction began in the 1850s in both the United States and Great Britain. In the 1920s and 1930s, acceptance of cold-formed steel as a construction material was still limited because there was no adequate design standard and there was limited information on material use in building codes. One of the first documented uses of cold-formed steel as a building material is the Virginia Baptist Hospital, constructed around 1925 in Lynchburg, Virginia, USA. The building structure was composed by masonry and the floors supported by cold-formed steel built-up joists of back- to- back lipped channel sections. Only some 20 years later, only, Lustron Corporation built in Albany, New York, with almost 2500 steel-framed homes, with the framing, finishes, cabinets and furniture made from cold-formed steel. These inexpensive houses were built for the veterans returning from the World War II. This was the beginning of cold-formed steel adventure in building.

In recent years, cold formed steel sections are used more and more as primary framing components. Wall stud systems in housing, trusses, building frames or pallet rack structures are some examples. As secondary structural systems they are used as purlins and side rails or floor joists, as well as in building envelops. Cassette sections in modern housing systems play simultaneously the role of primary structure and envelope. Profiled decking is widely used as basic components in composite steel-concrete slabs.

Cold-formed steel members are efficient in terms of both their stiffness and strength. Additionally, because the base steel is thin, even less than 1mm thick when high strength steel is used, the members are lightweight. The use of thinner sections and high strength steel leads to design problems for structural engineers which may not normally be encountered in routine structural steel design. Further, the shapes which can be cold-formed are often considerably more complex than hot-rolled steel shapes such as I-sections and plain channel sections. The cold-formed sections commonly have mono-symmetric or point symmetric shapes, and normally have stiffening lips on flanges and intermediate stiffeners in wide flanges and webs. Both simple and complex shapes can be formed for structural and non-structural applications.

Cold-formed steel design is dominated by two specific problems, i.e. (1) stability behaviour, which is dominant for design criteria of thin sections, and (2) connecting technology, which is specific and influences significantly the structural performance and design detailing.

Special design standards have been developed to cover the specific problems of cold-formed steel structures. In the USA, the Specification for the design of cold-formed steel structural members of the American Iron and Steel Institute was first produced in 1946 and has been regularly updated based on research to the most recent 2007 edition, AISI S100-07, entitled North American Specification for Design of Cold-Formed Steel Structural Members.

In Europe, the ECCS Committee TC7 originally produced the European Recommendations for the design of light gauge steel members in 1987 (ECCS, 1987). This European document has been further developed and published in 2006 as the European Standard Eurocode 3: Design of steel structures. Part 1-3: General Rules. Supplementary rules for cold-formed thin gauge members and sheeting (EN 1993-1-3, 2006).

In Australia and New Zeeland, the last version of specification for the design of cold-formed steel structures, AS/NZS 4600, was published in December 2005, and the review of cold-formed steel design specification could be continued around the world.

The market share of cold-formed structural steelwork continues to increase in the developed world. The main reasons can be found in the improving technology of manufacture and corrosion protection which leads, in turn, to an increased competitiveness of resulting products as well as new applications. Recent studies have shown that the coating loss for galvanised steel members is sufficiently slow, and indeed slows down to effectively zero, than a design life in excess of 60 years can be guaranteed.

The range of use of cold-formed steel sections specifically as load-bearing structural components is very wide. Besides building applications, cold-formed steel elements can be met in the Automotive industry, Shipbuilding, Rail transport, in Aircraft industry, Highway engineering, Agricultural and Industry equipment, Office equipment, Chemical, Mining, Petroleum, Nuclear and Space industries.

This book is primarily concerned with the design of cold-formed steel members and structures in building construction in Europe. For this reason it is mainly focused on the EN 1993-1-3, and the related parts of EN 1993 (e.g. EN 1993-1-1, EN 1993-1-5, EN 1993-1-8, etc.).

Generally, the book contains the theoretical background and design rules for cold-formed members and connections, accompanied by design oriented flow charts and worked examples for common building application.

The book was conceived primarily as a technical support for structural engineers in design and consulting offices, but it is expected to be of interest and useful for students and staff members of structural engineering faculties, as well as, for engineers working in steelwork industry.

Chapter 1

INTRODUCTION TO COLD-FORMED STEEL DESIGN

1.1 GENERAL

Cold-formed steel products are found in all aspects of modern life. The use of these products are multiple and varied, ranging from “tin” cans to structural piling, from keyboard switches to mainframe building members. Nowadays, a multiplicity of widely different products, with a tremendous diversity of shapes, sizes, and applications are produced in steel using the cold-forming process.

The use of cold-formed steel members in building construction began about the 1850s in both the United States and Great Britain. However, such steel members were not widely used in buildings until 1940.

In recent years, it has been recognised that cold-formed steel sections can be used effectively as primary framing components. In what concerns cold-formed steel sections, after their primarily applications as purlins or side rails, the second major application in construction is in the building envelope. Options for steel cladding panels range from inexpensive profiled sheeting for industrial applications, through architectural flat panels used to achieve a prestigious look of the building. Light steel systems are widely used to support curtain wall panels. Cold-formed steel in the form of profiled decking has gained widespread acceptance over the past fifteen years as a basic component, along with concrete, in composite slabs. These are now prevalent in the multi-storey steel framed building market. Cold-formed steel members are efficient in terms of both stiffness and strength. In addition, because the steel may be even less than 1 mm thick, the members are light weight. The already impressive load carrying capabilities of cold-formed steel members will be enhanced by current work to develop composite systems, both for wall and floor structures.

The use of cold-formed steel structures is increasing throughout the world with the production of more economic steel coils particularly in coated form with zinc or aluminium/zinc coatings. These coils are subsequently formed into thin-walled sections by the cold-forming process. They are commonly called “Light gauge sections” since their thickness has been normally less than 3 mm. However, more recent developments have allowed sections up to 25 mm to be cold-formed, and open sections up to approximately 8 mm thick are becoming common in building construction. The steel used for these sections may have a yield stress ranging from 250 MPa to 550 MPa (Hancock, 1997). The higher yield stress steels are also becoming more common as steel manufacturers produce high strength steel more efficiently.

The use of thinner sections and high strength steels leads to design problems for structural engineers which may not normally be encountered in routine structural steel design. Structural instability of sections is most likely to occur as a result of the thickness of the sections, leading to reduced buckling loads (and stresses), and the use of higher strength steel typically makes the buckling stress and yield stress of the thin-walled sections approximately equal. Further, the shapes which can be cold-formed are often considerably more complex than hot-rolled steel shapes such as I-sections and unlipped channel sections. Cold-formed sections commonly have mono-symmetric or point-symmetric shapes, and normally have stiffening lips on flanges and intermediate stiffeners in wide flanges and webs. Both simple and complex shapes can be formed for structural and non-structural applications as shown in Figure 1.1. Special design standards have been developed for these sections.

In the USA, the Specification for the design of cold-formed steel structural members of the American Iron and Steel Institute was first produced in 1946 and has been regularly updated based on research to the most recent 2007 edition (AISI, 1996, 1999, 2001, 2004, 2007). The first edition of the unified North American Specification (AISI, 2001) was prepared and issued in 2001, followed by Supplement 2004: Appendix 1, Design of Cold-Formed Steel Structural Members Using Direct Strength Method (AISI, 2004). It is applicable to the United States, Canada and Mexico for the design of cold-formed steel structural members. In 2007, the second edition of the North American Specification for the Design of Cold- Formed Steel Structural Members was issued (AISI, 2007). The document was prepared on the basis of the 2001 edition of the Specification, the Supplement 2004 to the 2001 Specification, and subsequent developments. The new and revised provisions provide up-to-date information for the design of cold-formed steel structural members, connections, assemblies, and systems.

Figure 1.1 – Collection of cold-formed steel sections shapes: a) sections for cold-formed steel structural members; b) profiled sheets

In Australia and New Zeeland, a revised limit states design standard AS/NZS4600 for the design of cold-formed steel structures was published in December 2005 (AS/NZS 4600:2005).

The market share of cold-formed structural steelwork continues to increase in the developed world. The reasons for this include the improving technology of manufacture and corrosion protection which leads, in turn, to the increase competitiveness of resulting products as well as new applications. Recent studies have shown that the coating loss for galvanised steel members is sufficiently slow, and indeed slows down to effectively zero, that a design life in excess of 60 years can be guaranteed.

The range of use of cold-formed steel sections specifically as load-bearing structural components is very wide, encompassing residential, office and industrial buildings, the automobile industry, shipbuilding, rail transport, the aircraft industry, highway engineering, agricultural and industry equipment, office equipment, chemical, mining, petroleum, nuclear and space industries.

This book is primarily concerned with the design of cold-formed steel members and structures in building construction in Europe and for this reason it is based on the European Design Code EN1993-1-3 (CEN, 2006a).

1.2 COLD-FORMED STEEL SECTIONS

1.2.1 Types of cold-formed steel sections

Cold-formed members and profiled sheets are steel products made from coated or uncoated hot-rolled or cold-rolled flat strips or coils. Within the permitted range of tolerances, they have constant or variable cross section.

– Individual structural framing members;

– Panels and decks.

Individual structural members (bar members) obtained from so called “long products” include:

– single open sections, shown in Figure 1.2a;

– open built-up sections (Figure 1.2b);

– closed built-up sections (Figure 1.2c).

Usually, the depth of cold-formed sections for bar members ranges from 50 – 70 mm to 350 – 400 mm, with thickness from about 0.5 mm to 6 mm. Figure 1.3 shows, as an example, some series of lipped channel and “sigma” sections (www.kingspanstructural.com/multibeam/ – Multibeam products).

Panels and decks are made from profiled sheets and linear trays (cassettes) as shown in Figure 1.4. The depth of panels usually ranges from 20 to 200 mm, while thickness is from 0.4 to 1.5 mm.

Figure 1.5 shows examples of Rannila corrugated sheets for roofing, wall cladding systems and load-bearing deck panels.

In order to increase the stiffness of both cold-formed steel sections and sheeting, edge and intermediate stiffeners are used (Figure 1.6); they can be easily identified in examples from Figures 1.3 and 1.5.

In general, cold-formed steel sections provide the following advantages in building construction (Yu, 2000):

- As compared with thicker hot-rolled shapes, cold-formed steel members can be manufactured for relatively light loads and/or short spans;

- Nestable sections can be produced, allowing for compact packaging and shipping;

- Unusual sectional configurations can be produced economically by cold-forming operations (see Figure 1.1), and consequently favourable strength-to-weight ratios can be obtained;

- Load-carrying panels and decks can provide useful surfaces for floor, roof, and wall construction, and in other cases they can also provide enclosed cells for electrical and other conduits;

- Load-carrying panels and decks not only withstand loads normal to their surfaces, but they can also act as shear diaphragms to resist force in their own planes if they are adequately interconnected to each other and to supporting members.

Compared with other materials such timber and concrete, the following qualities can be realised for cold-formed steel structural members.

- High strength and stiffness;

- Ability to provide long spans, up to 12 m (Rhodes, 1991);

- Ease of prefabrication and mass production;

- Fast and easy erection and installation;

- Substantial elimination of delays due to weather;

- More accurate detailing;

- Non-shrinking and non-creeping at ambient temperatures;

- Formwork unnecessary;

- Termite-proof and rot-proof;

- Economy in transportation and handling;

- Non-combustibility;

- Recyclable material.

The combination of the above-mentioned advantages can result in cost saving in construction.

1.2.2 Manufacturing

Cold-formed members are normally manufactured by one of two processes. These are:

- Folding and press braking.

Roll forming consists of feeding a continuous steel strip through a series of opposing rolls to progressively deform the steel plastically to form the desired shape. Each pair of rolls produces a fixed amount of deformation in a sequence of type shown in Figure 1.7a. Each pair of opposing rolls is called a stage as shown in Figure 1.7. In general, the more complex the cross sectional shape, the greater the number of stages required. In the case of cold-formed rectangular hollow sections, the rolls initially form the section into a circular section and a weld is applied between the opposing edges of the strip before final rolling (called sizing) into a square or rectangular shape.

Figures 1.8 (a and b) shows two industrial roll forming lines for long products profiles and sheeting, respectively.

A significant limitation of roll forming is the time taken to change rolls for a different size sections. Consequently, adjustable rolls are often used which allows a rapid change to a different section width or depth.

Folding is the simplest process, in which specimens of short lengths, and of simple geometry are produced from a sheet of material by folding a series of bends (see Figure 1.9). This process has very limited application.

Press braking is more widely used, and a greater variety of cross sectional forms can be produced by this process. Here a section is formed from a length of strip by pressing the strip between shaped dies to form the profile shape (see Figure 1.10). Usually each bend is formed separately. The set up of a typical brake press is illustrated in Figure 1.11. This process also has limitations on the profiled geometry which can be formed and, often more importantly, on the lengths of sections which can be produced. Press braking is normally restricted to sections of length less than 5 m although press brakes capable of producing 8 m long members are in use in industry.

Roll forming is usually used to produce sections where very large quantities of a given shape are required. The initial tooling costs are high but the subsequent labour cost is low. Brake pressing is normally used for low volume production where a variety of shapes are required and the roll forming costs cannot be justified.

1.2.3 Some peculiar characteristics of cold-formed steel sections

Compared to hot-rolled steel sections, the manufacturing technology of cold-formed steel sections induces some peculiar characteristics. First of all, cold-forming leads to a modification of the stress-strain curve of the steel. With respect to the virgin material, cold-rolling provides an increase of the yield strength and, sometimes, of the ultimate strength that is important in the corners and still appreciable in the flanges, while press braking leave these characteristics nearly unchanged in the flanges. Obviously, such effects do not appear in case of hot-rolled sections, as shown in Table 1.1 (Rondal, 1988).

Table 1.1 – Influence of manufacturing process on the basic strengths of hot and cold-formed profiles

The increase of the yield strength is due to strain hardening and depends on the type of steel used for cold rolling. On the contrary, the increase of the ultimate strength is related to strain aging, that is accompanied by a decrease of the ductility and depends on the metallurgical properties of the material.

Design codes provide formulas to evaluate the increase of yield strength of cold-formed steel sections, compared to that of the basic material.

Hot-rolled profiles are affected by residual stresses, which result from air cooling after hot-rolling. These stresses are mostly of membrane type, they depend on the shape of sections and have a significant influence on the buckling strength. Therefore, residual stresses are the main factor which causes the design of hot-rolled sections to use different buckling curves in European design codes (CEN, 2005a).

In the case of cold-formed sections the residual stresses are mainly of flexural type, as Figure 1.12 demonstrates, and their influence on the buckling strength is less important than membrane residual stresses as Table 1.2 shows (Bivolaru, 1993).

Figure 1.12 – Evidence of flexural residual stresses in a lipped channel cold-formed steel section (Bivolaru, 1993)

On the other hand, cold rolling produce different residual stresses in the section when compared with press braking, as shown in Table 1.2, so the section strength may be different in cases where buckling and yielding interact (Rondal, 1988).

Experimental evidence shows more complex actual distributions of residual stresses. Figure 1.13 (a to c) presents the distribution of measured residual stress for a cold-formed steel angle, channel and lipped channel (Rondal et al, 1994).

The European buckling curves have been calibrated using test results on hot formed (rolled and welded) steel sections, obtained during a large experimental program in Europe in the 1960’s (Sfintesco, 1970). These curves are based on the well-known Ayrton-Perry formula, in which the imperfection factor α was correspondingly calibrated (Rondal & Maquoi, 1979).

Figure 1.13 – Measured residual stress in cold-formed steel sections: a) cold-rolled angle; b) cold-rolled C profile; c) press braked U profile (Rondal et al, 1994)

Due to the fact the mechanical properties of cold-formed sections – e.g. cold-forming effect and residual stresses – are different to those of hot-rolled ones, different buckling curves should be justified (Dubina, 1996). Nowadays both numerical and experimental approaches are available to calibrate appropriate α factors for cold-formed sections (Dubina, 2001) but, for the sake of simplicity of the design process, the same buckling curves as for hot formed sections are still used (CEN, 2005a and CEN, 2006a).

1.3 PECULIAR PROBLEMS OF COLD-FORMED STEEL DESIGN

The use of thin-walled sections and cold-forming manufacturing effects can results in special design problems not normally encountered when tick hot-rolled sections are used. A brief summary of some special problems in cold-formed steel design are reviewed in the following (Dubina, 2005).

1.3.1 Buckling strength of cold-formed steel members

Steel sections may be subject to one of four generic types of buckling, namely local, global, distortional and shear. Local buckling is particularly prevalent in cold-formed steel sections and is characterised by the relatively short wavelength buckling of individual plate element. The term “global buckling” embraces Euler (flexural) and flexural-torsional buckling of columns and lateral-torsional buckling of beams. It is sometimes termed “rigid-body” buckling because any given cross section moves as a rigid body without any distortion of the cross section. Distortional buckling, as the term suggests, is buckling which takes place as a consequence of distortion of the cross section. In cold-formed sections, it is characterised by relative movement of the fold-lines. The wavelength of distortional buckling is generally intermediate between that of local buckling and global buckling.

It is a consequence of the increasing complexity of section shapes that local buckling calculation are becoming more complicated and that distortional buckling takes on increasing importance.

Local and distortional buckling can be considered as “sectional” modes, and they can interact with each other as well as with global buckling (Dubina, 1996). Figure 1.14 shows single and interactive (coupled) buckling modes for a lipped channel section in compression. The results have been obtained using an elastic eigen-buckling FEM analysis.

For given geometrical properties of member cross section, the different buckling modes depend by the buckling length, as shown in Figure 1.15 (Hancock, 2001).

The curves shown in Figure 1.15 have been obtained using an elastic Finite Strip (FS) software, analysing and describing the change of buckling strength versus buckle half-wavelength.

Figure 1.14 – Buckling modes for a lipped channel in compression Single modes: a) local (L); b) distortional (D); c) flexural (F); d) flexural-torsional (FT); Coupled (interactive) modes: e) L + D; f) F + L; g) F + D; h) FT + L; i) FT + D; j) F + FT (Dubina, 2002)

A first minimum (Point A) occurs in the curve at a half-wavelength of 65 mm and represents local buckling in the mode shown. The local mode consists mainly of deformation of the web element without movement of the line junction between the flange and lip stiffener. A second minimum also occurs at a point B at a half-wavelength of 280 mm in the mode shown. This mode is the distortional buckling mode since movement of the line junction between the flange and lip stiffener occurs without a rigid body rotation or translation of the cross section. In some papers, this mode is called a local-torsional mode. The distortional buckling stress at point B is slightly higher than the local buckling stress at point A, so that when a long length fully braced section is subjected to compression, it is likely to undergo local buckling in preference to distortional buckling. The section buckles in a flexural or flexural-torsional buckling mode at long wavelengths, such as at points C, D and E. For this particular section, flexural-torsional buckling occurs at half-wavelengths up to approximately 1800 mm beyond which flexural buckling occurs.

Figure 1.15 – Buckling strength versus half-wavelength for a lipped channel in compression (Hancock, 2001)

The dashed line in Figure 1.15, added to the original figure, qualitatively shows the pattern of all modes or coupled mode.

The effect of interaction between sectional and global buckling modes results in increasing sensitivity to imperfections, leading to the erosion of the theoretical buckling strength (see hachured zones in Figure 1.15). In fact, due to the inherent presence of imperfection, buckling mode interaction always occurs in case of thin-walled members.

Figure 1.16 shows the difference in behaviour of a thick-walled slender bar in compression (Figure 1.16a), and a thin-walled bar (Figure 1.16b); they are assumed, theoretically, to have the same value of their gross areas. Both cases of an ideal perfect bar and a geometric imperfect bar are presented.

Figure 1.16 – Behaviour of (a) slender thick-walled and (b) thin-walled compression bar

Looking at the behaviour of a thick-walled bar it can be seen that it begins to depart from the elastic curve at point B when the first fibre reaches the yield stress, N_el, and it reaches its maximum (ultimate) load capacity, N_u, at point C; after which the load drops gradually and the curve approaches the theoretical rigid-plastic curve asymptotically. The elastic theory is able to define the deflections and stresses up to the point of first yield and the load at which first yield occurs. The position of the rigid-plastic curve determines the absolute limit of the load carrying capacity, above which the structure cannot support the load and remain in a state of equilibrium. It intersects the elastic line as if to say “thus far and no further” (Murray, 1985).

In case of a thin-walled bar, sectional buckling, e.g. local or distortional buckling, may occur prior to the initiation of plastification. Sectional buckling is characterised by the stable post-critical path and the bar does not fail as a result of this, but significantly lose stiffness. Yielding starts at the corners of cross section prior to failure of the bar, when sectional buckling mode changes into a local plastic mechanism quasi-simultaneously with the occurrence of global buckling (Dubina, 2000). Figure 1.17, obtained by advanced FEM simulation, clearly shows the failure mechanism of a lipped channel bar in compression (Ungureanu & Dubina, 2004).

Figure 1.17 – Failure mode of a lipped channel in compression (Ungureanu & Dubina, 2004)

Figure 1.18 shows the comparison between the buckling curves of a lipped channel member in compression, calculated according to EN1993-1-3 (CEN, 2006a), considering the fully effective cross section (i.e. no local buckling effect) and the reduced (effective) cross section (i.e. when local buckling occurs and interacts with global buckling).

However the effectiveness of thin-walled sections, expressed in terms of load carrying capacity and buckling strength of compression walls of beam and columns can be improved considerably by the use of edge stiffeners or intermediate stiffeners (see Figure 1.6).

1.3.2 Torsional rigidity

Cold-formed sections are normally thin and consequently they have low torsional stiffness. Many of the sections produced by cold-forming are mono-symmetric and their shear centres are eccentric from their centroids as shown in Figure 1.19a. Since the shear centre of a thin-walled beam is the axis through which it must be loaded to produce flexural deformation without twisting, then any eccentricity of the load from this axis will generally produce considerable torsional deformations in a thin-walled beam as shown in Figure 1.19a. Consequently, thin-walled beams usually require torsional restraints either at intervals or continuously along the length to prevent torsional deformations. Often, this is the case for beams such as Z- and C- purlins which may undergo flexural-torsional buckling because of their low torsional stiffness, if not properly braced.

In addition, for columns axially loaded along their centroid axis, the eccentricity of the load from the shear centre axis may cause buckling in the flexural-torsional mode as shown in Figure 1.19b at a lower load than the flexural buckling mode also shown in Figure 1.19b. Hence the checking for the flexural-torsional mode of buckling is necessary for such mono-symmetric columns.

Figure 1.19 – Torsional deformations: a) eccentrically loaded lipped channel beam; b) axially loaded lipped channel column

1.3.3 Web crippling

Web crippling at points of concentrated load and supports can be a critical problem in cold-formed steel structural members and sheeting for several reasons. These are:

- in cold-formed steel design, it is often not practical to provide load bearing and end bearing stiffeners. This is always the case in continuous sheeting and decking spanning several support points;

- the depth-to-thickness ratios of the webs of cold-formed members are usually larger than for hot-rolled structural members;

- in many cases, the webs are inclined rather than vertical;

- the intermediate element between the flange, onto which the load is applied, and the web of a cold-formed member usually consists of a bend of finite radius. Hence the load is applied eccentrically from the web.

Special provisions are included in design codes to guard against failure by web crippling.

1.3.4 Ductility and plastic design

Due to sectional buckling mainly (cold-formed sections are of class 4 or class 3, at the most), but also due to the effect of cold-forming by strain hardening, cold-formed steel sections possess low ductility and are not generally allowed for plastic design. The previous discussion related to Figure 1.16b revealed the low inelastic capacity reserve for these sections, after yielding initiated. However, for members in bending, design codes allow to use the inelastic capacity reserve in the part of the cross section working in tension.

Because of their reduced ductility, cold-formed steel sections cannot dissipate energy in seismic resistant structures. However, cold-formed sections can be used in seismic resistant structures because there are structural benefits to be derived from their reduced weight, but only elastic design is allowed and no reduction of the shear seismic force is possible. Hence, in seismic design, a reduction factor q = 1 has to be assumed as stated in EN1998-1 (CEN, 2004).

1.3.5 Connections

Conventional methods for connections used in steel construction, such as bolting and arc-welding are available for cold-formed steel sections but are generally less appropriate because of the wall thinness, and special techniques more suited to thin materials are often employed. Long-standing methods for connecting two thin elements are blind rivets and self drilling, self tapping screws. Fired pins are often used to connect thin materials to a ticker supporting member. More recently, press-joining or clinching technologies (Predeschi et al, 1997) have been developed, which require no additional components and cause no damage to the galvanising or other metallic coating. This technology has been adopted from the automotive industry and is successfully used in building construction. “Rosette” system is another innovative connecting technology (Makelainen & Kesti, 1999), applicable to cold-formed steel structures.

1.3.6 Design assisted by testing

Cold-forming technology makes available production of unusual sectional configurations (see Figure 1.1). However, from the point of view of structural design, the analysis and design of such unusual members may be very complex. Structural systems formed by different cold-formed sections connected to each other (like purlins and sheeting, for instance) can also lead to complex design situations, not entirely covered by design code procedures. Of course, numerical FEM analysis is always available, but for many practical situations, modelling can be very complicate. For such complex design problems, modern design codes permit the use of testing procedures to evaluate structural performances. Testing can be used either to replace design by calculation or combined with calculation. Only officially accredited laboratories, by competent authorities, are allowed to perform such tests and to delivery relevant certificates.

1.3.7 Design standards

Extensive research and product development in the past has led to national design specifications for cold-formed steel sections and structures in many countries. On the following, a summary review of main design specifications is presented.

1.3.7.1 North American Cold-formed Steel Specification, 2001 Edition (AISI, 2001) and 2007 Edition (AISI, 2007)

The first edition of the unified North American Specification was prepared and issued in 2001, together with commentaries. It is applicable to the United States, Canada and Mexico for the design of cold-formed steel structural members.

This edition of the Specification was developed on the basis of the 1996 AISI Specification with the 1999 Supplement (AISI, 1999) and the 1994 Canadian Standard (CSA, 1994), which is based on Limit State Design (LSD), like in Europe and Australia.

Since the Specification is intended for use in Canada, Mexico and the United States, it was necessary to develop a format that would facilitate the allowance of unique requirements in each country. This resulted in a format that contained a basic document, Chapters A through G, intended for use in all three countries, and three country specific appendices, Appendix A – United States, Appendix B – Canada, and Appendix C – Mexico.

Three design methods are recognized: ASD – now termed Allowable Strength Design, LRFD – Load and Resistance Factor Design, and LSD – Limit States Design. The use of ASD and LRFD is limited to the US and Mexico; LSD is limited to Canada. LRFD and LSD are essentially the same except for differences in nomenclature, load factors, load combinations, and target reliability indexes. Equivalent LSD terminology is shown in brackets throughout the Specification.

A new design method for cold-formed steel members – the Direct Strength Method – has been developed by Schafer (2006) and adopted in 2004 as Appendix 1 of the North American Specification for the Design of Cold-Formed Steel Structural Members (AISI, 2004).

The second edition of the unified North American Specification for the Design of Cold-Formed Steel Members (AISI S100-07) was issued by American Iron and Steel Institute in 2007, together with Commentary on North American Specification for the Design of Cold-Formed Steel Members (AISI S100-07-C).

Also the 2007 editions of the AISI standards for cold-formed steel framing have been approved. It should be noted that the words “North American” are now in the titles of many of these standards. This was done to emphasize that these documents are intended for adoption throughout North America and use not just in the United States. In all such documents, provisions applicable to Canada were added. This work by the AISI Committee on Framing Standards includes the revision of six current standards and the issuing of two new standards, as follows:

- AISI S200-07: North American Standard for Cold-Formed Steel Framing – General Provisions;

- AISI S211-07: North American Standard for Cold-Formed Steel Framing – Wall Stud Design;

- AISI S212-07: North American Standard for Cold-Formed Steel Framing – Header Design;

- AISI S213-07: North American Standard for Cold-Formed Steel Framing – Lateral Design;

- AISI S214-07: North American Standard for Cold-Formed Steel Framing – Truss Design;

- AISI S230-07: Standard for Cold-Formed Steel Framing – Prescriptive Method for One and Two Family Dwellings;

- AISI S201-07: North American Standard for Cold-Formed Steel Framing – Product Data;

- AISI S210-07: North American Standard for Cold-Formed Steel Framing – Floor and Roof System Design.

1.3.7.2 Australian/New Zealand Standard – AS/NZS 4600, 2005 Edition (AS/NZS, 2005)

The Australian/New Zealand Standard is very similar to the AISI Specification since Section 1-5 correspond with Sections A to E of the AISI Specification. However, AS/NZS4600 only permits design by the limit states method (LSD), and not by the allowable stress method (ASD). In addition, because of the use of higher strength steels, additional provisions have been included for distortional buckling.

- Use of high strength G550 cold-reduced steels less than 0.9mm thick for structural members (in addition to sheeting).

- Distortional buckling of both flexural and compression members.

- Blind rivets connections.

- Testing provisions.

The Direct Strength Method was included in the 2005 edition of the Australian/New Zealand Standard for cold-formed steel structures (AS/NZS4600:2005).

The 4^th edition of Design of cold-formed steel structures (to AS/NZS4600:2005) by Hancock (2007), explains the basis of the design rules of AS/NZS 4600:2005 and deals with the large number of changes made to the standard since the 1996 version.

1.3.7.3 Eurocode 3 – Design of Steel Structures, Part 1.3 – General Rules, Supplementary Rules for Cold-formed Thin Gauge Members and Sheeting

EN1993-1-3 (CEN, 2006a) represents the unified European Code for cold-formed steel design, and contains specific provisions for structural applications using cold-formed steel products made from coated or uncoated thin gauge hot or cold-rolled sheet and strip. It is intended to be used for the design of buildings or civil engineering works in conjunction with EN1993-1-1 (CEN, 2005a) and EN1993-1-5 (CEN, 2006b). EN1993-1-3 permits only design by the limit states method (LSD).

The code provisions are limited to steel in the thickness range 1.0 – 8.0 mm for members, and 0.5 – 4.0 mm for sheeting. Thicker material may also be used provided the load-bearing capacity is determined by testing. Member design provisions in EN1993-1-3 are not dissimilar from the AISI Specification, even though the notations and format of formulas are different, but generally include more advanced design provisions. In some areas such as plane elements in compression and with edge or intermediate stiffeners, the EN1993-1-3 design provisions are considerably more complex. Also, compared with the AISI S100-07 (2007) and AS/NZS4600 (2005) design codes, distortional buckling design is less explicitly presented in this code.

EN1993-1-3 includes in Chapter 10 design criteria for the following particular applications:

- Beams restrained by sheeting;

- Linear trays restrained by sheeting;

- Stressed skin design;

- Perforated sheeting.

The design provisions for these particular applications are often complex but may be useful for design engineers since they include detailed methodologies not available in other standards or specifications.

As application support of this code, the European Convention for Constructional Steel Work, ECCS, published in 2008 “Worked examples according to EN1993-1-3” (ECCS, 2008b). Previously, in 2000, ECCS also edited worked examples on the same topic (ECCS, 2000).

In 1995 the European Convention for Constructional Steelwork – ECCS published the European Recommendations for the Application of Metal Sheeting acting as a Diaphragm (ECCS, 1995).

1.3.8 Fire resistance

Due to the small values of section factor (i.e. the ratio of the heated volume to the cross sectional area of the member) the fire resistance of unprotected cold-formed steel sections is reduced. For the same reason fire protection with intumescent coating is not efficient.

Sprayed cementations or gypsum based coatings, while very efficient for other applications are, generally, not usable for galvanised cold-formed steel sections. However, cold-formed steel sections can be employed as beams concealed behind a suspended ceiling. In load bearing applications, fire resistance periods of 30 minutes can usually be achieved by one layer of “special” fire resistant plasterboard, and 60 minutes by two layers of this plasterboard, which possesses low shrinkage and high integrity properties in fire. Planar protection to floors and walls provides adequate fire resistance to enclosed sections, which retain a significant proportion of their strength, even at temperatures of 500 °C.

In light gauge steel framing, the board covering of walls and floors can protect the steel against fire for up to 120 minutes, depending on the board material and the number of boards. The choice of insulation material, mineral wool or rock wool is also crucial to fire strength.

Box protection of individual cold-formed steel sections used as beams and columns is provided in much the same way as with hot-rolled sections.

Non-load bearing members require less fire protection, as they only have to satisfy the “insulation” criterion in fire conditions. Ordinary plasterboard may be used in such cases.

1.3.9 Corrosion

The main factor governing the corrosion resistance of cold-formed steel sections is the type and thickness of the protective treatment applied to the steel rather than the base metal thickness. Cold-formed steel has the advantage that the protective coatings can be applied to the strip during manufacture and before roll forming. Consequently, galvanised strip can be passed through the rolls and requires no further treatment.