Accessed by BHP BILLITON on 27 Jun 2002 AS/NZS 4600 Supp1:1998 AS/NZS 4600 Supplement 1:1998 Cold-formed steel structures— Commentary (Supplement 1 to AS/NZS 4600:1996)‘Accessed by BHP BILLITON on 27 Jun 2002 ASINZS 4600 Supp1:1998 This Joint Australian/New Zealand Standard was prepared by Joint Technical Committee BD/82, Cold-formed Steel Structures, It was approved on behalf of the Council of Standards Australia on 11 September 1998 and on dehalf of the Council of Standards New Zetland on 1] September 1998, It was published on 5 November 1998, The following interests are represented on Committee BD/82: Association of Consulting Engineers Australia ‘Australian Building Codes Board ‘Australian Chamber of Commerce and Industry ‘Australian Institute of Stee! Construction Bureau of Steel Manufacturers of Australia CSIRO, Building, Construction and Engineering Institution of Professional Engineers New Zealand Metal Building Products Manufacturers Association Metal Trades Industry Association of Australia ‘New Zealand Heavy Engineering Resesreh Association Now Zealand Metal Roofing and Cladding Manufucturers Association ‘New Zealand Structural Engineering Society The University of Queensland University of Sydney Welding Technology Institute of Australia Revlew of Standards. To keep abreast of progress in industry, Joint Australian! New Zealand Standards are subject to periodic review and are kept up to date by the issue of amendments or new editions as necessary, It is important taerefore’ that Standards users ensure that they are in possession of the latest edition, and any amendments there Full details ofall Joint Standards and related publications will be found in the Standards Australia and Standards New Zealand Catalogue of Publications: this information is supplemented each month by the magazines ‘The Australian Standard” and ‘Standards New. Zealand’, wich subscribing members receive, and which give details of new publications, new editions and amendments, and of withdrawn Standards Suggestions for improvements to Joint Standards, addressed to the head office of either Standards Australia or Standards New Zealand, are welcomed. Notification of any inaccuracy or ambiguity found in a Joint Australian/New Zealand Standard should be ‘made without delay in order thal the matler may be investigated and appropriate action taken,by BHP BILLITON on 27 AS/NZS 4600 Supp1:1998 AS/NZS 4600 Supplement 1:1998 Cold-formed steel structures— Commentary (Supplement 4 to AS/NZS 4600:1996) bodes ASINZS 4600 Supple 11998, Published jointly by: Standards Australia 1 The Crescent, Homebush NSW 2140 Australia Standards New Zealand Level 10, Radio New Zealand House, 155 The Terrace, Wellington 6001 New Zealand ISBN 0 7387 2237 7‘Accessed by BHP BILLITON on 27 Jun 2002 PREFACE This Commentary was prepared by the Joint Standards Australia/ Standards New Zealand Committee BD/82, Cold-formed Stecl Structures. ‘The objective of this Commentary is to provide users with background information and guidance to AS/NZS 4600:1996. The Standard and Commentary are intended for use by design professionals with demonstrated engineering competence in their fields. In Australia, the Australian Standard for the design of cold-formed steel structural members was first issued in permissible stress format as AS 1538—1974 (Standards Australia, 1974), based mainly on the 1968 edition of the AISI Specification (AISI, 1968), but with modifications to the beam and column design curves to keep them aligned with the Australian Steel Structures Code at that time, ASCA1 (Standards Australia, 1968). It was revised and published in 1988 as AS 1538—1988 (Standards Australia, 1988) and was based mainly on the 1980 edition of the AISI Specification (AISI, 1983), but included some material from the 1986 edition of the AISI Specification (AISI, 1986). In 1996, a limit states version of the cold-formed steel structures Standard was produced by Standards Australia and Standards New Zealand, It was based mainly on the 1996 edition of the AISI Specification (AISI, 1996) but with amendments where necessary to reflect Australian/New Zealand practice. In this Commentary, AS/NZS 4600:1996 is referred as ‘the Standard’ To be consistent with the AISI Comment Appendix A are listed in alphabetical order. referenced documents provided in The clause numbers and titles used in this Commentary are the same as those in ASINZS 4600, except that they are prefixed by the letter *C’. To avoid possible confusion between the Commentary and the Standard, 2 Commentary clause is referred to as “Clause C....” in aecordance with Standards Australia/Standards New Zealand policy. (© Copyright ~ STANDARDS AUSTRALIA STANDARDS NEW ZEALAND Exeepe where the Copyright Act alow! and except where proved for teow "wo pobicwtone oF sofware prodieed Sandu Auseas or tundatds New Zealand may be repeodused, fused i a euiealsyster nym or ward by any eats Sppropricc voyaly payment. Australian requests Tor permission and ifurmavon on commercial software Yoyalcs should be diecied 19 ‘Standard without payment ofa royalty or advice to Standards Auwiralia or Stancarés New Zealand, * Incision of sopsight mitral n computer saftware pogrims i lo pemited witht roy payment povided seh progane do ied wacutely oboe by We cow ultbe propane my pement pos pee Care shouldbe taken to enue that satel wedi ro the curt edition of the Standard ad ht ts updated whenever the Sand {s'snenied or reveed Tbe mom ae of the Stand ea orca be ceary tented The use of mate in pec form jo compte: sofware progr 0 be sed commercial, wih o- without poy 1 rin commercial enacts sje othe pyanat of a ely. Ths pl tay be vred by Sandards Ausalia er Sundae Sew ead stay tae‘Accessed by BHP BILLITON on 27 Jun 2002 CONTENTS, Page INTRODUCTION 5 SECTION Cl SCOPE AND GENERAL CLI SCOPE . . 7 C12 REFERENCED DOCUMENT: 7 C13 DEFINITIONS wee cee 7 C14 NOTATION 12 CLS MATERIALS 2 C16 DESIGN REQUIREMENTS 2 CLT NON-CONFORMING SHAPES AND CONSTRUCTION 29 SECTION C2. ELEMENTS 2.1 SECTION PROPERTIES 30 (2.2. EFFECTIVE WIDTHS OF STIFFENED ELEMENTS 33 2.3. EFFECTIVE WIDTHS OF UNSTIFFENED ELEMENTS 40 2.4 EFFECTIVE WIDTHS OF UNIFORMLY COMPRESSED ELEMENTS. WITH AN EDGE STIFFENER OR ONE INTERMEDIATE STIFFENER ... 43 2.5 NED ELEMENTS WITH ONE OR MORE INTERMEDIATE STIFFENERS OR STIFF ELEMENTS WITH MORE THAN ONE INTERMEDIATE STIFFENER 44 €2.6 ARCHED COMPRESSION ELEMENTS 46 2.7 STIFFENERS 46 SECTION C3. MEMBERS 3.1 GENERAL : cee a7 3.2 MEMBERS SUBJECT TO TENSION 47 (3.3. MEMBERS SUBJECT TO BENDING 47 3.4 CONCENTRICALLY LOADED COMPRESSION MEMBERS. 65 3.5 COMBINED AXIAL LOAD AND BENDING 17 3.6 CYLINDRICAL TUBULAR MEMBERS. . 80 SECTION C4 STRUCTURAL ASSEMBLIES 4.1 BUILT-UP SECTIONS 86 4.2. MIXED SYSTEMS 86 (C43 LATERAL RESTRAINTS . . . 86 C44 WALL STUDS AND WALL STUD ASSEMBLIES 91 SECTION C5. CONNECTIONS 3.1 GENERAL 92 (3.2 WELDED CONNECTIONS, 93 5.3. BOLTED CONNECTIONS 96 C3.4 SCREWED CONNECTION wee 99) 5.5 BLIND RIVETED CONNECTIONS 103 3.6 RUPTURE ce : 104‘Accessed by BHP BILLITON on 27 Jun 2002 Page SECTION C6 TESTING C6.1_ TESTING FOR DETERMINING MATERIAL PROPERTIES 106 (6.2. TESTING FOR ASSESSMENT OR VERIFICATION 106 APPENDIX A. REFERENCED DOCUMENTS 109‘Accessed by BHP BILLITON on 27 Jun 2002 INTRODUCTION Cold-formed steel members have been used economically for building construction and other applications (Winter 1959a, 19596; Yu 1991; Hancock 1998). These types of sections are cold-formed from steel sheet, strip, plate or flat bar in roll-forming machines or by press brake or bending operations. The thicknesses of steel sheets or strip generally used for cold-formed steel structural members range from 0.4 mm to about 6.4 mm. Steel plates and bars as thick as 25 mm can be cold-formed successfully into structural shapes and their design is covered by the Standard, In general, cold-formed steel structural members can offer the following advantages for building construction (Winter, 1970; Yu, 1991): (a) Light members can be manufactured for relatively light loads or short spans, or both, (b) Unusual sectional configurations can be produced economically by cold-forming operations 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 some cases they can also provide enclosed cells for electrical and other conduits, (Panels and decks not only withstand loads normal to their surfaces, but they can also act as shear diaphragms to resist forces in their own planes if they are adequately interconnected to cach other and to supporting members, The use of cold-formed stcel members in building construction began in about the 1850s. However, in the United States such steel members were not widely used in buildings until the publication of the first edition of the American Iron and Steel Institute Specification in 1946 (AISI, 1946). This first design Standard was primarily based on the research work ed by AISI at Cornell University since 1939, It was revised subsequently by the AISI Committee in 1956, 1960, 1962, 1968, 1980 and 1986 to reflect the technical developments and the results of continuing research, In 1991, AISI published the first edition of the Load and Resistance Factor Design Specification for Cold-formed Steel Structural Members (AISI, 1991). Both allowable stress design (ASD) and load and resistance factor design (LRFD) specifications were combined into a single document in 1996, In Australia, the Australian Standard for the design of cold-formed steel structural members was first issued in permissible stress format as AS 1538—1974 (Standards Australia, 1974) based mainly on the 1968 edition of the AISI Specification (AISI, 1968) bout with modifications to the beam and column design curves to keep them aligned with the Australian Steel Structures Code at that time, ASCA (Standards Australia, 1968). It was revised and published in 1988 as AS 1538—1988 (Standards Australia, 1988) and was hased mainly on the 1980 edition of the AISI Specification (AISI, 1983) but included some material from the 1986 edition of the AISI Specification (AISI, 1986). In 1996, a joint Australian/New Zealand limit states version of the cold-formed steel structures Standard was produced by Standards Australia and Standards New Zealand, It was based mainly on the 1996 edition of the AISI Specification (AISI, 1996) but with amendments, where necessary, to reflect Australian/New Zealand prac! During the period from 1958 through to 1983, AISI published Commentaries on several editions of the AISI design specification, which were prepared by Professor George Winter of Cornell University in 1958, 1961, 1962, and 1970. In the 1983, 1986 and 1996 editions, the format used for the AISI Commentary has been changed in that the same section numbers are used in the AISI Commentary as in the AISI Specification. As for‘Accessed by BHP BILLITON on 27 Jun 2002 previous editions of the AISI Commentary, this document contains a brief presentation of the characteristics and the performance of cold-formed steel members. In addition, it provides a record of the reasoning behind and the justification for various provisions of the Standard. A cross-reference is provided between various design provisions and the published research data. This Commentary to AS/NZS 4600:1996 is based mainly on the 1996 edition of the Commentary to the AISI Specification, and has been amended, whe! necessary, to reflect the differences between the AISI Specification and AS/NZS 4600.‘Accessed by BHP BILLITON on 27 Jun 2002 STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND Australian/New Zealand Standard Cold-formed steel structures—Commentary (Supplement 1 to AS/NZS 4600:1996) SECTION Cl SCOPE AND GENERAL C11 SCOPE The cross-sectional configurations, manufacturing processes and fabrication practices of cold-formed steel structural members differ in several respects from those of hot-rolled steel shapes. For cold-formed steel sections, the forming process is performed at, or near, room temperature by the use of bending brakes, press brakes or rolleforming machines. Some of the significant differences between cold-formed sections and hot-rolled shapes are— (a) absence of the residual stresses caused by uneven cooling due to hot-rolling; (b) lack of comer fillets; (©) presence of increased yield strength with decreased proportional limit and ductility resulting from cold forming; (G) presence of cold-reducing stresses when cold-rolled steel stock has not been fully annealed; (©) prevalence of elements having large width-to-thickness ratios and, hence, subject to local buckling in compression; (0) rounded comers; and (g) stress-strain curves can be either shatp-yielding type or gradual-yielding type. ASINZS 4600 (Standards Australia/Standards New Zealand, 1996) is limited to the design of steel structural members cold-formed from carbon or low-alloy sheet, strip, plate or bar. The design is to be in accordance with the limit states design method, The Standard is applicable only to cold-formed sections not more than 25mm in thickness. Research conducted at the University of Missouri-Rolla (Yu, Liv, and McKinney, 1973b and 1974) has verified the applicability of the Standard’s provisions for such cases, In view of the fact that most of the design provisions have been developed on the experimental work subject to static loading, the Standard is intended for the design of cold-formed steel structural members to be used for load-carrying purposes in buildings. For structures other than buildings, appropriate allowances should be made for dynamic effects. The Standard docs not apply to the design of structures subject to fire or fatigue since insufficient data was available on these phenomena for cold-formed members during its preparation, C1.2 REFERENCED DOCUMENTS The Standards listed in Appendix A are subject to revision from time to time and the current issue should always be used. The currency of any Standard may be checked with Standards Australia or Standards New Zealand. C13 DEFINITIONS Many of the definitions in Clause 1.3 are self-explanatory. In New Zealand, terms used in limit state design may differ from those used in Australia. These are included in brackets. Those definitions that are not self-explanatory or that are not defined in Clause 1.3 are briefly discussed in this Clause.‘Accessed by BHP BILLITON on 27 Jun 2002 C1313 Distortional buckling—the mode of distortional buckling is included for the first time in AS/NZS 4600. Figure C1.3(4)(a) shows distortional buckling for a compression member, and Figure C1.3(b) for a flexural member. Appendix D gives equations to compute elastic distortional buckling stresses. 1.3.14 Effective design width—the effective design width is a concept that takes account of local buckling and post-buckling strength for compression elements. The effect of shear lag on short, wide flanges is also handled by using an effective design width. These matters are treated in Section 2, and the corresponding effective widths are discussed in the Commentary on that Section. 1.3.17 Flexural-torsional buckling—the 1968 edition of the AISI Specification and AS 1538—1974 pioneered methods for calculating column loads of cold-formed steel sections prone to buckle by simultaneous twisting and bending. This complex behaviour may result in lower column loads than would result from primary buckling by flexure alone (Trahair, 1993), €1.3.19 Limit state—limit states design (LSD) is a method of designing structural components such that the applicable limit state is not exceeded when the structure is subjected to all appropriate load combinations as specified in Clause 1.6.1 1.3.23. Multiple-stiffened clements—multiple-stiffened elements of two sections are shown in Figure C1.3(1). Each of the two outer sub-clements shown in Figure C1.3(1}(a) are stiffened by a web and an intermediate stiffener while the middle sub-element is stiffened by two intermediate stiffeners. The two sub-elements shown in Figure C13(1)(b) sned by a web and the attached intermediate middle stiffener. ja yp bet 26, re RP ES Neutral axis t 1d hat-section la} Multiple. stiffer 1V2b_| v2 peat oy Neutral axis Ae. [0] Multiple stiffened inverted U-section Flexural members, such as beams FIGURE C1.3(1) MULTIPLE-STIFFENED COMPRESSION ELEMENTS‘Accessed by BHP BILLITON on 27 Jun 2002 1.3.38. Stiffened or partially stiffened compression elements—stiffened compression elements of various sections are shown in Figure C1.3(2), in which sections shown in Figures C1.3(2)(a) to C1.3(2\(e) are for flexural members, and sections shown in Figures C1.3Q)(f) to C1.3(2)(i) are for compression members. Sections shown Figures C1.3(2)(a) and C1.3(2)(b) each have a web and a lip to stiffen the compressi clement, i.e. the compression flange, the ineffective portion of wi For the explanation of these ineffective portions, see Figures C1.3(2)(c) to C1.3(2)(e) show compression elemes stiffened by two webs Figures C1.3(2)(1) and C1.3(2)(h) show edge-stiffened flange elements that have a vertical element (web) and an edge stiffener (lip) to stiffen the elements while the web itself is stiffened by the flanges. Figure C1.3(2)(g) shows four compression elements stiffening each other, and Figure Cl other stiffened element. (2\(i) has each stiffened ele ont stiffened by a lip and the‘Accessed by BHP BILLITON on 27 Jun 2002 tbe /2- 2b /2- H bed ___ Neutral eabe/2--} bes. t (0) Lipped channel (b) I-beam made of two lipped channels back to back etbe/2 jo <2be/2— foby f= = Vebe i y fh —be3 iT] 2 5e2 | Neutral 1 7 os my (c) Het-section ® . fyb, 2h fyb, 2b bet Lt bey i “ge Sos] bod bea (d) Box-section (e) Inverted U-section Flexural members, such os beams (top flonge in compression) by ata”? cobe/2=14 i best ' abez (f) Lipped channel /2b—2 {2 Lata ( (¢) Box-section & » * ciber/2. —c1be1/2 citer /2 eabet/2-— b4— caber/2 caber/2—Li-t | ver | asl ite] ll bea ett |r te ' Yabo (Upped engle (h) Iesection mode of two lipped channels beck to back ‘Compression members, such os columns FIGURE C1.3(2) STIFFENED COMPRESSION ELEMENTS‘Accessed by BHP BILLITON on 27 Jun 2002 €1.3.46 Thickness—in calculating section properties, the reduction in thickness that occurs at corner bends is ignored unless the manufacturing process warrants consideration of a more accurate method (sce Clause 2.1.2.1), and the base steel thickness of the flat steel stock, exclusive of coatings, is used in all calculations for load-carrying purposes. 1.3.49 Unstiffened compression clement—unstiffened elements of various sections are shown in Figure C1.3(3), in which sections shown in Figures C1.3(3)(a) to C1.3(3)(@) are for flexural members and sections shown in Figures C1.3(3)(6) to C1.3(3)(a) are for compression members. Sections shown in Figures C1.3(3)(a) to C13(3)(e) have only a web to stiffen the compression flange clement. The legs of the section shown in Figure C1.3(3)(@) provide mutual stiffening action to cach other along their common edges, Sections showa in Figures C1.3(3)(¢) © C13(3)(g), acting as columns, have vertical stiffened elements (webs) which provide support for one edge of the unstffened flange clements. The legs of the section shown in Figure C1.3(3)(h) provide mutual stiffening action se fay] [i (Ft 2 yt Bt {a} Plain channo! (0) Plain 2-section (cl -boam made of (a) Plain angie two plain channels, back-to-back Flexural members, such as beams +2 a [ae] [ee | Py T bg/2 o ’ ote 1 | te we | f ra a Eee two plain channels back-to-back Compression members, such as columes FIGURE C1.3(3) UNSTIFFENED COMPRESSION ELEMENTS‘Accessed by BHP BILLITON on 27 Jun 2002 ranaation Rotation Rotation by | Ld) (3) Compression tb) Fiexure FIGURE ©1.3(4) DISTORTIONAL BUCKLING MODES C14 NOTATION The basis of the notation is in accordance with ISO 3898, as much as possible C15 MATERIALS, C1S.1 Structural steel 1.5.1.1 Applicable steels The Australian and New Zealand Standards are the basic source of steel designations for use with the Standard, Clause 1.5.1.1 provides a list of Australian, New Zealand and Australian/New Zealand Standards for steels that are acceptable by the Standard. The important material properties for the design of cold-formed steel members are yield stress, tensile strength and ductility, Ductility is the ability of a steel to undergo sizeable plastic or permanent strains before fracturing and is important both for structural safety and for cold forming. It is usually measured by the elongation in a 50 mm gauge length, The ratio of the tensile strength to the yield stress is also an important material property. This is an indication of strain-hardening and the ability of the material to redistribute stress, For the listed Australian and New Zealand Standards, the yield stresses of stecls range from 200 10 $50MPa and the tensile strengths vary Irom 300 to 990 MPa. The clongations are no less than 8%. Exceptions are AS 1397—GSS0 steel with a specified minimum yield stress of 550 MPa, a specified minimum tensile strength of 550 MPa, and with @ minimum elongation of 2% in a 50 mm gauge length. This low ductility steel has limits on its applicability for structural framing members and so its application without restriction is limited to steels not less than 0.9 mm thick. Nevertheless, they are being used successfully for specific applications, such as decks, panels and in steel-framed housing, as structural members. The conditions for the use of AS 1397—GSS0 steel less than 0.9 mm thick are outlined in Clause 1.5.1.5. 15.1.2 Osher steels Although the use of Australian and Australian/New Zealand Standards listed in Clause 1.5.1.1 is encouraged, other steels that satisfy the ductility requirements of Clause 1.5.1.5 may also be used in cold-formed steel structures. 1.5.1.3 Strength increase resulting from cold forming The mechanical properties of the flat steel sheet, strip, plate or bar, such as yield stress, tensile strength, and elongation may be substantially different from the properties exhibited by the cold-formed stccl jons. Figure C1.5.1.3(1) shows the inerease of yield strength and tensile strength from‘Accessed by BHP BILLITON on 27 Jun 2002 those of the virgin material at the section locations in a cold-formed steel channel section and a joist chord (Karren and Winter 1967). This difference can be attributed to cold working of the material during the cold-forming process, The influence of cold-work on mechanical properties was investigated by Chajes, Britvec, Winter, Karren, and Uribe at Comell University in the 1960s (Chajes, Britvec, and Winter, 1963; Karren, 1967; Karren and Winter, 1967; Winter and Uribe, 1968). It was found that the changes of mechanical properties due to cold-stretching are caused mainly by strain-hardening and strain-ageing, as shown in Figure C1.5.1.3(2) (Chajes, Britvec, and Winter 1963). In this Figure, Curve A represents the stress-strain curve of the virgin material. Curve B is due to unloading in the strain-hardening range, Curve C represents immediate reloading, and Curve D is the stress-strain curve of reloading after strain-ageing. It is interesting to note that the yield points of both Curves C and D are higher than the yield point of the virgin material and that the ductilities decrease after strain-hardening and strain-ageing,‘Accessed by BHP BILLITON on 27 Jun 2002 + H > E F 6 Spe ys} se fe we |e [56 |r |e 3 6 75 70| ie 65 : oy h oy we ultimate strength 7] g 490 3 60 420 g fe Fol a é z HS & G8 ~ a & 50] 3 350 4s] J Virgin yield strength 40| ABO Der SAT KL 280 —e— Yield strength ultimate strength {a} Channel section FIGURE 1.5.1.3(1) (in part) EFFECT OF COLD-WORK ON MECHANICAL PROPERTIES IN COLD-FORMED STEEL SECTIONS‘Accessed by BHP BILLITON on 27 Jun 2002 028" * o B55 é 3 50 360 Virgin yield strength set \ Virgin ultimate strength ABCD CE Cr OCH] —s— Yield strength <5 — Ultimate strength 30| (0) Joist chora FIGURE C1.5.1.3(1) (in part) EFFECT OF COLD-WORK ON MECHANICAL PROPERTIES IN COLD-FORMED STEEL SECTIONS‘Accessed by BHP BILLITON on 27 Jun 2002 increase in f, [Elongation / ageing Elongation ageing Stress Elongation Ductility after 3 ‘elongation hardening Virgin ductility FIGURE C1.5.1.3(2) EFFECT OF ELONGATION HARDENING AND ELONGATION AGEING ON STRESS-ELONGATION CHARACTERISTICS. Cornell research also revealed that the effects of cold-work on the mechanical properties of corners usually depend on the following: (a) The type of steel (b) The type of stress (compression or tension). (©) The direction of stress with respect to the direction of cold-work (transverse or longitudinal). (@) The fuf, rato (©) The inside-radius-to-thickness ratio n/t (0) The amount of cold-work Among Items (a) to (1), the £/f, and r/t ratios are the most important factors to affeet the change in mechanical properties of formed sections. Virgin material with a large f/f, ratio possesses a large potential for strain-hardening. Consequently, as the ratio increases, the effect of cold-work on the increase in the yield point of steel increases. Small insidi radius-to-thickness ratios (1/1) correspond to 2 large degree of cold-work in a corner and, therefore, for a given material, the smaller the r./¢ ratio, the larger the increase in yield point. Investigating the influence of cold-work, Karren derived the following equations for the ratio of corner yield strength to virgin yield strength (Karren, 1967) fe c1sasay fy (i wo a.= 69) -onsla—s custae) win m= oan) - 008 cuatae)‘Accessed by BHP BILLITON on 27 Jun 2002 where fre = tensile yield stress of bends fy = tensile yield stress of unformed section B. = constant = constant tensile strength of unformed section inside bend radius f= sheet thickness With regard to the full section properties, the tensile yie be approximated by using a weighted average as follows: stress of the full section may fog” fet = Cig 13.134) where fy = average design yield stress of the steel in the full section of compression members C= ratio of bend area to total cross-sectional area, For flexural members having unequal flanges, the one giving a smaller C value is considered to be the controlling flange = average tensile yield stress of bends BL, . — €1.5.1.3(5) rly" Joe ~ average tensile yield stress of flats Good agreement between the calculated and the tested stress-strain characteristics for a channel section and a joist chord section were demonstrated by Karen and Winter (Karren and Winter, 1967). In the last two decades, additional studies were made by numerous investigators. These investigations dealt with the cold-formed sections having large rit ratios and with thick materials. They also considered residual stress distribution, simplification of design methods, and other related subjects. For details, see Yu (1991). In 1962, the AISI Specification permitted the utilization of cold-work of forming on the basis of full section tests. Since 1968, the AISI Specification has allowed the use of the increased average yield point of the section (f,,) to be determined by— (A) full section teasile tests; (B) stub column tests; or (©) calculated in accordance with Equation C1.$.1.3(4), However, such a strength increase is limited only to relatively compact sections designed in accordance with Clause 3,3 (bending strength excluding the use of inelastic reserve capacity), Clauses 3.4, 3.5, 3.6 and 4.4 In some cases, when evaluating the effective area of the web, the effective width fector (in accordance with Clause 2.2, may be less than unity but the sum of Band b,, of Figure 2.2.3 may be such that the web is fully effective, and the cold-work of forming may be used. C15.1.4 Effect of welding Welding may affect the mechanical properties of a member, particularly in the heat-affected zone (HAZ). The designer should make allowances for this on the basis of testing‘Accessed by BHP BILLITON on 27 Jun 2002 C1S.1. Ductility The nature and importance of ductility and the ways in which this property is measured are briefly discussed in Clause C1.5.1.1 Low-carbon sheet and strip steels with specified minimum yield points from 250 MPa to 500 MPa need to meet Australian and New Zealand Standards specified minimum clongations in a 50mm gauge length of at least 8%. However, for AS 1397—GSS0, for which the specified minimum yield stress is $50 MPa, the clongation requirement is 2 on a 50mm gauge length for steels greater than or equal to 0.60 mm thick, and no elongation is specified for thinner steels. G550 steel less than 0.9 mm thick, differs from the array of stecls listed Clause 1.5.1.1 In 1968, because new steels of higher strengths were being developed, sometimes with lower elongations, the question of how much elongation is really needed in a structure was the focus of a study initiated at Corel! University. Steels that had yield strengths ranging from 310 to 690 MPa, clongations in SO mm ranging from 50 to 1.3%, and tensile-to-yield strength ratios ranging from 1.51 to 1.00 were studied (Dhalla, Errera and Winter, 1971; Dhalla and Winter, 1974a; Dhalla and Winter, 1974b). ‘The investigators developed elongation requirements for ductile steels. These measurements are more accurate but cumbersome to make. Therefore, the investigators recommended the following determination for adequately ductile steels: (a) The tensile-to-yield strength ratio should not be less than 1.08. (b) The total elongation in a $0 mm gauge length should not be less than 10%, or not less than 7% in a 200 mm gauge length, Also, the Standard limits the use of Sections 2 to 5 to adequately ductile steels. In licu of the tensile-to-yield strength limit of 1.08, the Standard permits the use of elongation requirements using the measurement technique as given by Dhalla and Winter (1974a) (Yu, 1991). Because of limited experimental verification of the structural performance of members using materials having a tensile-to-yield strength ratio less than 1.08 (Macadam et al., 1988), the Standard limits the use of this material to purlins and girts meeting the elastic design requirements of Clauses 3.3.2.3, 3.3.3.2, 3.3.3.3 and 3.3.3.4, Thus, the use of such steels in other applications (compression members, tension members, other flexural members including those whose strength is based on inclastic reserve capacity, and the like) is prohibited, However, in purlins and girts, concurrent design axial forces of relatively small magnitude are acceptable providing the requirements of Clause 1.5.1.5 of the Standard are met and N*/§R, docs not exceed 0.15. AS 1397—GS50 steel less than 0.9 mm thick does not have adequate ductility as specified in Clause 1.5.1.5(a). Its use has been limited as specified in Clause 1.5.1.5(b) to particular configurations. The limit of the design yield stress to 75% of the specified minimum yield stress, and the design tensile strength to 75% of the specified minimum tensile strength, or 450 MPa, whichever is lower, introduces a higher safety factor, but still allows low ductility steels, such as AS 1397—GSS0 less than 0.9 mm thick, to be used by the results of load tests that are permitted as an alternative to making this reduction, It is also permitted to use higher design stresses than specified in Clause 1.5.1.5(b)(i), provided it is established that material ductility docs not affect the strength, stability and serviceability of the member or structural configuration to which the member belongs. This provision is, in AS/NZS 4600 but not in the AISI 1996 specification, 1.5.1.6 Acceptance of steels Sheet and strip steels, both coated and uncoated, may be ordered to nominal or minimum thickness. If the steel is ordered to minimum thickness, all thickness tolerances are over (+) and nothing under (-). If the steel is ordered to nominal thickness, the thickness tolerances are divided equally between over and under. Therefore, in order to provide the similar material thickness between the two methods of ordering sheet and strip steel, it was decided to require that the delivered thickness of a cold-formed product be at least 95% of the design thickness. Thus, it is apparent that 2 portion of the factor of safely may be considered to cover minor negative thickness tolerances.‘Accessed by BHP BILLITON on 27 Jun 2002 Generally, thickness measurements should be made in the centre of flanges. For decking and sheeting, measurements should be made as close as practicable to the centre of the first full flat of the section, The responsibility of m mamufa sing this requirement for a cold-formed product is that of the rer of the product, not the steel producer, 1.5.1.7 Unidentified steel Clause 1.5.1.7 is carried over from AS 1538 and is not included in the AISI specification, 1.8.2 Design stresses The sirength of cold-formed steel structural members depends on the yield stress, except in those cases where elastic local buckling or overall buckling. is critical. Because the stress-strain curve of steel sheet or strip can be either sharp- yielding type (see Figure C1.5.2(1)(a)) or gradual-yielding type (see Figure C1.5.2(1)(b)), the method for determining the yield stress for sharp-yiclding steel and the yield stress for gradual-yielding steel are based on AS 1391 (Standards Australia, 1991). As shown in Figure C1.5.2@)(@), the yield stress for sharp-yielding steel is defined by the stress level of the plateau. For gradual-yielding steel, the stress-strain curve is rounded out at the “knee” and the proof stress is determined by either the non-proportional elongation method (see Figure C1,5.2@)(b)) or the total elongation method (see Figure C1.5.2(2)¢). The term yield stress used in the Standard applies to either yield stress or yield stren; The strength of members that are governed by buckling depends not only on the yield stress but also on the modulus of clasticity (EZ) and the tangent modulus (£,). The modulus of clasticity is defined by the slope of the initial straight portion of the stress-strain curve (see Figure C1.5.2(1)). The measured values of £ on the basis of the standard methods usually range from 200 to 207 GPa. A value of 200 GPa is used in the Standard for design purposes, The tangent modulus is defined by the slope of the stress-strain curve at any stress level, as shown in Figure C1.5.2(1)(b), For sharp-yielding steels, E, is equal to E up to the yield stress, but with gradually yielding steels, £, equals to £ only up to the proportional limit (J). Once the stress exceeds the proportional limit, the tangent modulus (E,) becomes progressively smaller than the initial modulus of elasticity Various buckling provisions of the Standard have been written for gradually yielding steels whose proportional limit is not lower than about 70% of the specified minimum yield point. Determination of proportional limits for information purposes can be done simply by using the offset method shown in Figure C1.5.2(2)(b) with the distance (om) equal to 0.0001 Iength/length (0.01% offset) and calling the stress (R), where mn intersects the stress-strain curve at the proportional limit Clause 1.5.2 stipulates the need for the yield stresses and tensile strengths not to exceed those given in Table 1.5.‘Accessed by BHP BILLITON on 27 Jun 2002 | f Elongation hardening ~lL Inelastic range Elastic range tate i= E Elongation Tel lal Sharp yielding > Stress (a) Elongation (el (b} Gradual yielding FIGURE €1.5.2(1) STRESS-ELONGATION CURVES OF CARBON STEEL SHEET OR STRIP RI al RI i E Elongation /'_Etongstion Elongation om = specified offset om = specified offset under load [al Yiels stress (0) Proof stress by the (cl Proof stress by the corresaonging with non-proportional total elongetion method top of knee elongation method FIGURE C1.5.2(2) STRESS-ELONGATION DIAGRAMS SHOWING METHODS OF YIELD POINT AND YIELD STRENGTH DETERMINATION‘Accessed by BHP BILLITON on 27 Jun 2002 1.5.3 Fasteners and electrodes In Clause 1.5.3 of the Standard, the relevant Australian and Australia/New Zealand Standards for steel bolts, nuts, washers, welding consumables and screws are given. ANSI/AWS D1.3 may also be used to specify welding consumables, C16 DESIGN REQUIREMENTS 1.6.1. Loads and load combinations In Australia, the load combinations are to be calculated in accordance with AS 1170.1 (1989). Dead loads and live loads are also given in AS 1170.1, wind loads are given in AS 1170.2, snow loads are given in AS 1170.3 and earthquake loads are given in AS 1170.4. In New Zealand, load combinations, dead and live loads, wind loads, snow Toads and earthquake loads are to be caleulated in accordance with NZS 4203, Recognized engineering procedures should be employed to reflect the effect of impact loads on a structure. For building design, reference may be made to AISC publications (AISC, 1989; AISC 1993) When gravity and horizontal loads produce forces of opposite sign in members, consideration should be given to the minimum gravity loads acting in combination with wind or earthquake loads. 1.6.2 Structural analyses and design €1.6.2.1 General A limit state is the condition at which the structural usefulness of a load-carrying clement or member is impaired to such an extent that it becomes unsafe for the occupants of the structure, or the element no longer performs its intended function, Typical limit states for cold-formed steel members are excessive deflection, yielding, buckling and attainment of maximum strength after local buckling, (i.e. post-buckling strength). These limit states have been established through experience in practice or in the laboratory, and they have been thoroughly investigated through analytical and experimental research. The background for the establishment of the limit states is extensively documented (Winter, 1970; Pekéz, 1986b; and Yu, 1991), and a continuing research effort provides further improvement in understanding them, The following types of limit states are specified in Clause 1.6.2: (a) ‘The limit state of the strength required to resist the extreme loads during the intended life of the structure. (b) ‘The limit state of the structure as 2 whole to prevent overturning, uplift or sliding. (c) The limit state of the ability of the structure to perform its intended function during its life These three limit states are usually referred to as the strength (ultimate) limit state, the stability limit state and the serviceability limit state, AS/NZS 4600 focuses on the limit state of strength in Clause 1.6.2.2, the limit state of stability (which in accordance with NZS 4203 is part of the ultimate limit state) in Clause 1.6.2.3 and the limit state of serviceability in Clause 1.6.2.4, €1.6.2.2 Strength [ultimate] limit state For the limit state of strength [ultimate], the general format of the limit states method is expressed as follows: SER, 1.62.20) where s design action effects (design actions) R, = design capacity‘Accessed by BHP BILLITON on 27 Jun 2002 The design action effects [design actions] (S*) may be determined by an clastic structural analysis (normally linear clastic) or a plastic structural analysis if the plastic hinges have adequate strength and ductility. Testing in accordance with Section 6 may be used in lieu of analysis to establish member strength, The design capacity (R,) can be determined as the product of the nominal capacity (strengih reduction) (,) with the capacity [strength reduction] factor, i.e. Ry = Ry, or by testing in accordance with Section 6, The principal purpose of the capacity [strength reduction] factor (p) is to compensate for uncertainties inherent in the design, fabrication, or erection of building components, as well as uncertainties in the estimation of applied loads, The nominal capacity (R,) is the strength of the clement or member for a given limit state, caleulated for nominal section properties and for minimum specified material properties in accordance with the appropriate analytical model which defines the strength. The capacity [strength reduction] factor ()) accounts for the uncertainties and variabilities inherent in Ry, and is usually less than unity The design action effects [design actions] (S*) are the forces on the cross-section (ie. bending moment, axial force, or shear force) determined from the specified nominal loads by structural analysis. The advantages of limit states design are as follows: (a) The uncertainties and the variabilities of different types of loads and capacities are different (c.g. dead load is less variable than wind load), and so these differences can be accounted for by use of multiple load factors, (©) By using the probability theory, designs can ideally achieve a more consistent reliability. Thus, limit states design provides the basis for a more rational and refined design method than is possible with the previous permissible stress desiga method. The probabilistic basis for the limit state design of cold-formed steel structures is as follows: () Probabilistic concepts Safety factors or load factors are provided against the uncertainties and variabilities that are inherent in the design process. Structural design consists of comparing nominal design action effects [design action] (S) to nominal capacities (R), but both S and R are random parameters (see Figure C1.6.2.2(1)). A limit state is violated if 2 is less than S. While the possibility of this event ever occurring is never zero, a successful design should, nevertheless, have only an acceptably small probability of exceeding the limit state. If the exact probability distributions of S and R were known, then the probability of (R — S) being less than zero could be exactly determined for any design. In general, the distributions of § and R are not known, and only the means, S,, and R,, and the standard deviations, 6, and Gy are available. Nevertheless it is possible to determi relative reliabilities’ of several designs by the scheme shown in Figure C1.6.2.2(2). The distribution curve shown is for In (R/S) and a limit state is exceeded when In (R/S) is less than or equal to zero, The area under In (R/S) being less than or equal to zero is the probability of violating the limit state, The size of this area is dependent on the distance between the origin and the mean of In (8/5). For given statistical data Ry, Sy, 6, and Oy, the area under In (R/S) is less than or equal to zero can be varied by changing the value of B (see Figure C1.6.2.2(2)), since Bo yx) is equal to In (R/S), and B is calculated as follows: 1.6.2.2)‘Accessed by BHP BILLITON on 27 Jun 2002 Vq = coefficient of variation of R oe Ry V.. = coefficient of variation of S ‘The index B is called the ‘reliability index’ and it is a relative measure of the safety of the design, When two designs are compared, the one with the larger B is more reliable. ‘The concept of the reliability index can reliabil reliabil e used for determining the relative inherent in current design and can be used in testing out the of new design formats, as given by the following example of simply supported, braced beams subjected to dead and live loading. The limit state design requirement of the Standard for such a beam is as follows: 67, , (E32 15Q)) (using AS 1170.1) €1.6.2.2Ga) 02,7 (ea 26+ 162) (using NZS 4203) 1.6.2.2) 4 = capacity [strength reduction] factor for bending 09 Z, = elastic seotion modulus based on the effective section Sy = specified yield stress {, = span length 5 = beam spacing G = dead load Q = live load The mean resistance (R,) is calculated as follows (Ravindra and Galambos, 1978) Ry 7 RP yMy Fe) 1.62.24) R, = nominal resistance R, = ZSy €1.6.2.215) Z, = clastic section modulus based on th clive section f, = yield stress of beam R, is the nominal moment predicted on the basis of the post-buckling strength of the compression flange and the wed. The mean values P., M,, and F,, and the corresponding coefficients of variation ¥,, Vy, and Vy are the statistical parameters which define the variability of the resistance.‘Accessed by BHP BILLITON on 27 Jun 2002 P,, = mean ratio of the experimentally determined moment to the predicted moment for the actual material, and cross-sectional properties of the test specimens mean ratio of the actual yield point to the minimum specified value F, = mean ratio of the actual section modulus to the specified (nominal) value The coefficient of variation of R is calculated as follows: Ve €1.6.2.2(6) The values of these data were obtained from examining the available tests on beams having different compression flanges with partially and fully effective flanges and webs, and from analysing data on yield stress values from tests and cross-sectional dimensions from many measurements. This information was developed from research (Hsio, Yu and Galambos, 1988 and 1990; Hsiao, 1989) and is given as follows: (A Py 1 Bh = 0.09 © My, = 1.10 © = 010 (BE) Fy 1.0 © % = 0.05 (G) Ry = 122R, % = 014 Probability density St [Arm 1 Besign action eltect 1S") ~ Geen ‘scrion! Capacity (A) FIGURE 1.6.2.2(1) RANDOMNESS S* AND R‘Accessed by BHP BILLITON on 27 Jun 2002 In F/S Bones Probablity of exceeding @ limit state FIGURE C1.6.2.2(2) RELIABILITY INDEX 8 ‘The mean load effect (S,) is calculated as follows: s. = (B$)iG,-2,) 1.62.27) v, = Wate! (@a¥e) €1.6.2.2(8) Gy Qu, Gq. = mean dead toad intensity Q,, = mean live load intensity V;, ~ coefficient of variation of G Y, ~ coefficient of variation of Q Load statistics were analysed in a study of the National Bureau of Standards (NBS) (Ellingwood et al., 1980), where it was shown that— G. = 1.086 Vo = 04 Qn = D Vy = 0.25 The mean live load intensity equals the code live load intensity if the tributary area is small enough so that no live load reduction is included. Substitution of the load statistics into Equations C1.6.2.2(7) and C1.6.2.2(8) ives the following: ‘je 1.6.2.2) €1.6.2.210)‘Accessed by BHP BILLITON on 27 Jun 2002 «a Sy, and Vy thus depend on the dead-to-live load ratio, Cold-formed steel beams typically have small G/Q, and for the purposes of checking the reliability of these strength limit state criteria, it will be assumed that— andso 5, = 1211 (22) a) BY, = 021 From Equations C1,6.2,2(3) and C1.6.2.2(5) the nominal resistance (R,) can be obtained for G/Q equal to 1/5 and 9 equal to 0.9 as follows: ~ 196023) 1.622111) In order to determine the reliability index (B) from Equation C1,6.2.2(2) the RJSq ratio is required by considering R,, equal to 1.22R, as follows: 122 x 194 x of §) Rae 8) _ 196 C1.6.2.2(12) 12 efe 2) Therefore, from Equation C1.6.2.2(2)— p- BU) _ 366 €1.6.2.2013) V1" + O20 If B is equal to 2.66 for beams having different compression flanges with partially and fully effective flanges, and webs designed by the Standard are compared tof for other types of cold-formed steel members, and to B for designs of various types from hot-rolled steel shapes or even for other materials, then it is possible to say that this particular cold-formed steel beam has about an average reliability (Galambos et al., 1982) Basis for limit state design of cold-formed steel structures A great deal of work has been performed for determining the values of the reliability index (B) inherent in traditional design as exemplified by the current structural design specifications such as the AISC Specification for hot-rolled steel, the AISI Specification for cold-formed steel, the ACI Code for reinforced concrete members, AS 4100 and NZS 3404 for steel structures in Australia and New Zealand, and the like. The studies for hot-rolled steel are summarized by Ravindra and Galambos (1978), where also many papers, which contain additional data, are referenced. The determination of for cold-formed steel elements or members is presented in several research reports of the University of Missouri-Rolla (Hsiao, Yu, and Galambos, 1988; Rang, Galambos and Yu, 1979a, 197%, 1979¢ and 1979d; Suporn- silaphachai, Galambos and Yu, 1979), where both the basic research data as vwell as the Bs inherent in the AISI Specification are presented in great detail The Bs calculated in the above-referenced publications were developed with slightly different load statistics than those of this Commentary, but the essential conclusions remain the same‘Accessed by BHP BILLITON on 27 Jun 2002 In Australia, the underlying philosophy behind the limit state codes and their calibration is set out in Leicester, Pham and Kleeman (1985) and Pham (1985). No detailed calibration of AS/NZS 4600 has been performed. However, calibration of the R-factor design procedures for purlins under wind uplift has been performed by Rousch and Hancock (1996a, 1996b). ‘The entire set of data for hot-rolled steel and cold-formed steel designs, as well as data for reinforced concrete, aluminium, laminated timber and masonry walls was re-analysed by Ellingwood, Galambos, MacGregor and Comell (Ellingwood et al., 1980; Galambos et al., 1982; Ellingwood et al., 1982) using updated load statistics and a more advanced level of probability analysis, which was able to incorporate probability distributions and to describe the true distributions more realistically. The details of this extensive reanalysis are presented by the investigators. Only the final conclusions from the analysis are summarized below. The values of the reliability index (B) vary considerably for the diferent kinds of loading, the different types of construction, and the different types of members within a given material design specification, In ordet to achieve more consistent reliability, it was suggested by Ellingwood et al. (1982) that the following values of 8 would provide this improved consistency while at the same time would give, on the average, essentially the same design by the limit state design method as is obtained by current design forall materials of construction. These target reliabilities (B.) for use in limit state design are given as follows: (A) For basie case (gravity load) B, . 3.0 (B) For connections B, 45 (©) For wind toad B, 25. The target reliability indices are the ones inherent in the load factors recommended in the ASCE 7-95 Load Standard (ASCE, 1995), For simply supported, braced, cold-formed steel beams with stiffened flanges, which were designed in accordance with the 1996 AISI allowable stress design method or to any previous version of that specification, it was shown that for the representative dead-to-live load ratio of 1/5, the reliability index P is equal to 2.79. Considering the fact that for other such load ratios, or for other types of members, the reliability index inherent in current cold- formed steel construction could be more or less than this value of 2.79, a somewhat lower target reliability index of B, equal to 2.5 is recommended as a lower limit for the AISI LRFD Specification. The capacity factors (6) were selected such that B, equal to 2.5 is essentially the lower bound of the actual B values for members. In order to assure that failure of a structure is not initiated in the connections, a higher target reliability index of B, equal to 3.5 is recommended for joints and fasteners. These two targets of 2°5 and 3.5 for members and connections, respectively, are somewhat lower than those recommended by the ASCE 7-95, but they are essentially the same targets as are the basis for the AISC LRED Specification (AISC, 1993). For wind loads the same ASCE target value of B, equal to 2.5 is used in the AISI LRFD Specification In the development of the AISI LRFD Specification, the following statistical data on material and cross-sectional properties were developed by Rang, Galambos and Yu (1979a and 1979b) for use in the derivation of capacity [strength reduction] factors (9:‘Accessed by BHP BILLITON on 27 Jun 2002 fly ~ E1OG; -M, = 1.00; Vy = 7, = OL Uraly ~ FOG My = 1.10; Vig = Fy ~ 0.11 Ui, = FIO My = 110; Vy = Va = 0.08 F, = 100; Fy, = 0.05 m= mean value V = coefficient of variation 5 ratio of the mean-lo-the nominal material property F = ratio of mean to nominal cross-sectional property f f fe These statistical data are based on the analysis of many samples (Rang et al., 1978) and they are representative properties of materials and cross-sections used in the industrial application of cold-formed steel structures specified minimum yield point ", = average yield point including the effect of cold-forming specified minimum tensile strength, €1.6.2.3 Stability limit state This limit state is included in the Standard although itis not included in the AISI Specification, In the New Zealand Loadings Standard, NZS 4203 (1992), itis treated as part of the ultimate limit state €1.6.2.4 Serviceability limit states Serviceability limit states are conditions under which a structure can no longer perform its intended functions. Safety and strength considerations are generally not affected by serviceability limit states, However, serviceability criteria aro essential to ensure functional performance and economy of design. Common conditions which may require serviceability limits are as follows (a) Excessive deflections or rotations which may affect the appearance or functional use of the structure. Deflections which may cause damage to non-structural elements should be considered. (b) Excessive vibrations which may cause occupant discomfort or equipment malfunctions. (©) Deterioration over time which may include corrosion or appearance considerations. When checking serviceability, the designer should consider the appropriate service loads, the response of the structure, and the reaction of building occupants. Service loads that may require consideration include static loads, snow or rain loads, temperature fluctuations, and dynamic loads from human activities, wind-induced effects, of the operation of equipment. The service loads are actual loads that act on the structure at an arbitrary point in time. Appropriate service loads for checking serviceability limit states may only be a fraction of the nominal loads. The response of the structure to service loads can normally be analysed assuming linear elastic behaviour. However, members that accumulate residual deformations under service loads may require consideration of this long-term behaviour.‘Accessed by BHP BILLITON on 27 Jun 2002 Serviceability limits depend on the function of the structure and on the perceptions of the observer. In contrast to the strength limit states, it is not possible to specify general serviceability limits that are applicable to all structures. The Standard does not contain explicit requirements; however, guidance is generally provided by the applicable building code. In the absence of specific criteria, guidelines may be found in Fisher and West (1990), Ellingwood (1989), Murray (1991), Allen and Murray (1993). Serviceability limits for domestic metal framing in Australia are given in AS 3623 (Standards Australia, 1993a) including both static and dynamic limits. For New Zealand, contact the National Association of Steel Framed Housing (NASH), New Zealand, 1.7 NON-CONFORMING SHAPES AND CONSTRUCTION Alternative shapes and construction should comply with Section 6, particularly Clause 6.2‘Accessed by BHP BILLITON on 27 Jun 2002 s ECTION C2 ELEMENTS €2.1 SECTION PROPERTIES €21.1 General In cold-formed sicel construction, individual elements of steel structural members are thin and the width-to-thickness ratios are large, when compared with hot-rolled steel shapes. These thin elements may buckle locally at a stress level lower than the yield point of steel when they are subjected to compression in flexural bending, axial compression, shear, or bearing. Figure C2.1 illustrates some local buckling patterns of certain beams and columas (Yu, 1991), Because local buckling of individual elements of cold-formed steel sections is a major design criterion, the design of such members should provide sufficient safety against failure by local instability with due consideration given to the post-buckling strength of structural components. Section 2 of the Standard contains the design requirements for width-to-thickness ratios and the design equations for determining the effective widths of stiffened compression elements, unstiffened compression clements, and clements with edge stiffeners or intermediate stiffeners. Additional provisions are made for the use of, stiffeners, flange ( it 4 ee O AY an Becton AA tty Vit ptt Ib} Columns FIGURE 2.1 LOCAL BUCKLING OF COMPRESSION ELEMENTS €2.1.2 Design procedures The appropriate use of full and effective section properties is explained in this Section. Full section properties are used for the determination of buckling moments and stresses, as specified in Clause 3.1. Clause 2.1.2.1 specifies clearly how the full section properties are to be calculated. For the more dif perty calculations such as distortional buckling, shear centre position, warping constant and monosymmetry parameters, the bends may be eliminated, The Standard has been calibrated on this assumption,‘Accessed by BHP BILLITON on 27 Jun 2002 Effective section properties are used for the determination of section and member capacities to allow for local instabilities of elements in compression, and for shear lag. Clause 2.1.2.3 specifies where the reduced widths are to be located for both stiffened and unstiffened elements, and elements under stress gradient and with edge stiffeners. These requirements are the same as the ones shown in the appropriate figures later in the Section. 2, €2.1.3.1 Maximum flat-width-to-thickness ratios Clause 2.1.3.1. of the Standard contains limitations on permissible flat-width-to-thickness ratios of compression flanges. To some extent, these limitations are arbitrary. They do, however, reflect 2 long-time experience and are intended to define practical ranges of application (Winter, 1970). Dimensional limits The limitation to a maximum bit of 60 for compression flanges having one longitudinal edge connected to a web and the other edge stiffened by a simple lip is based on the fact that if the 6 ratio of such a flange exceeds 60, a simple lip with a relatively large depth would be required to stiffen the flange (Winter, 1970). The local instability of the lip would necessitate a reduction of the bending capacity to prevent premature buckling of the stiffening lip, The limitation to 6/¢ equal to 90 for compression flanges with any other kind of stiffeners indicates that thinner flanges with large bit ratios are quite flexible and liable to be damaged in transport, handling and erection. The same is true for the limitation to bit equal to 500 for stiffened compression elements with both longitudinal edges connected to other stiffened clements and for the limitation to b/t equal to 60 for unstiffencd compression clemeats. The Note specifically states that wider flanges are not unsafe, but that when the dif ratio of unstiffened flanges exceeds 30 and the b/t ratio of stiffened flanges exceeds 250, they are likely to develop noticeable deformation at the full design strength, without affecting the ability of the member to develop the required strength. In both cases the maximum bit is set at twice that ratio at which first noticeable deformations are likely to appear, based on observations of such members under tests. These upper limits will generally keep such deformations to reasonable limits, In cases where the limits are exceeded, tests in accordance with Section 6 are required €2.1.3.2 Flange curling In beams that have unusually wide and thin but stable flanges, i.e. primarily tension flanges with large bit ratios, there is a tendency for these flanges to curl under bending. That is, the portions of these flanges most remote from the wed (cdges of I-beams, centre portions of flanges of box or hat beams) tend to deflect toward the neutral axis, An approximate, analytical treatment of this problem is given by Winter (1948b). Equation 2.1.3.2 of the Standard permits one to compute the maximum permissible flange width (b,) for a given amount of flange curling (c). It should be noted that Clause 2.1.3.2 does not stipulate the amount of curling, which can bbe regarded as tolerable, bul an amount of curling in the order of 5% of the depth of the section is not excessive under usual conditions. In general, flange curling is not a eritical factor to govern the flange width. However, when the appearance of the section is important, the out-of-plane distortion should be closely controlled in practice. Recently, research on flange curling of profiled steel decks was completed by Bernard, Bridge and Hancock (1996). A number of alternative curling models were developed for profiled steel decks. €2.1.3.3 Shear lag effects (short spans supporting concentrated loads) For beams usual shapes, the normal stresses are induced in the flanges through shear stresses transferred from the web to the flange. These shear stresses produce shear strains in the flange which, for ordinary dimensions, have negligible effects. However, if flanges are unusually wide (relative to their length) these shear strains have the effect that the normal bending stresses in the flanges decrease with increasing distance from the web, This phenomenon is known as shear lag. It results in a non-uniform stress distribution across‘Accessed by BHP BILLITON on 27 Jun 2002 the width of the flange, similar to that in stiffened compression elements (see Clause C2.2), though for entirely different reasons. The simplest way of accounting for this stress variation in design is to replace the non-uniformly stressed flange of actual width (b,) by one of reduced, effective width subject to uniform stress (Winter, 1970), Theoretical analyses by various investigators have arrived at results which differ numerically (Roark, 1965). The provisions of Clause 2.1.3.3 are based on the analysis and supporting experimental evidence obiained by detailed stress measurements on clevs beams (Winter, 1940), In fact, the values of effective widths in Table 2.1.2 are taken directly from Curve A of Figure 4 of Winter (1940). It should be noted that, in accordance with Clause 2.1.3.3, the use of a reduced width for stable, wide flanges is required only for concentrated load, as shown in Figure C2.1.3.3. For uniform load, it can be seen from Curve B of Figure C2.1.3.3 that the width reduction due to shear lag for any practicable large width-span ratio is so small as to be effectively negligible. The phenomenon of shear lag is of considerable consequence in naval architecture and aircraft design. However, in cold-formed steel construction it is infrequent that beams are so wide as to require significant reductions in accordance with Clause 2.1.3.3 {For uniform oad 3| * \ 8 pot ee a AlS\ ang AS/NZS 4809 ale oe < cesign evtera $15 o7| For concentrated load by FIGURE 2.1.3.3 ANALYTICAL CURVES FOR DETERMINING EFFECTIVE WIDTH OF FLANGE OF SHORT SPAN BEAMS. €2.1.3.4 Maximum web depth-to-thickness ratio Prior 10 1980, the maximum web depth-to-thickness ratio (d,/t,) was limited to— (a) 150 for cold-formed steel members with unreinforced webs; and (6) 200 for members that are provided with adequate means of transmitting concentrated loads or reactions into the web, or both. Based on the studies conducted at the University of Missouri-Rolla in the 1970s (LaBoube and Yu, 1978a, 1978, and 1982; Hetrakul and Yu, 1978 and 1980; Nguyen and Yu, 1978a and 1978b), the maximum dy/t, ratios were increased to— (200 for unreinforeed webs; i) 260 for webs using bearing stiffeners; and Gi) 300 for webs using bearing and intermediate stiffeners in the 1980 edition of the AISI Specification.‘Accessed by BHP BILLITON on 27 Jun 2002 These dj/t, limitations are the same as those used in the AISC Specification (AISC, 1989) for plate girders and are retained in the 1996 edition of the AISI Specification and ASINZS 4600. Because the definition for d, was changed in the 1986 edition of the AISI Specification from the ‘clear distance between flanges’ to the ‘depth of flat portion’ measured along the plane of web, the prescribed maximum dy, ratio may appear to be more liberal. An unpublished study by LaBoube concluded that the present definition for , had negligible influence on the web strength. 2.2. EFFECTIVE WIDTHS OF STIFFENED ELEMENTS It is well known that the structural behaviour and the load-carrying capacity of a stiffened compression element, such as the compression flange of a hat section, depend on the b/t ratio and the supporting condition along both longitudinal edges. If the b/¢ ratio is small, the stress in the mpression flange can reach the yield stress of steel and the strength of the compression element is governed by yielding. For the compression flange with large bir ratios, local buckling (see Figure C2.2(1)) will occur at the following clastic critical buckling stress (ha fy > tee c22 zit-v4(2) ly where k ~ plate buckling coefficient (see Table C22) 4 for stiffened compression elements supported by a web on each longitudinal case FE ~ modulus of lestcity of sel Vv = Poisson's ratio = 0.3 for stel inthe clastic range fat width ofthe compression element 1 ~ thickness ofthe compression element When the clastic critical buckling stress calculated using Equation C2.2(1) exceeds the proportional limit of the steel, the compression element will buckle in the inelastic range (Yu, 1991),Accessed by BHP BILLITON on 27 Jun 2002 TABLE C22 VALUES OF PLATE BUCKLING COEFFICIENTS : Vat of for cose Boundary condition Type ofa | Yauco ® El. J Compression | 40 © Compression | 6 © FEbs. ss| ‘Compression 0.425 EES cree © Compression lan xa © Er. 4 Compresion sao © sss shear su ores ® Fined “Fixe ster so Fixed ® = sss K Bending ne Exe Fixed Fixed Bending aus Fixed‘Accessed by BHP BILLITON on 27 Jun 2002 FIGURE C2.2(1) LOCAL BUCKLING OF STIFFENED COMPRESSION FLANGE OF HAT-SHAPED BEAM Unlike one-dimensional structural members such as columns, stiffened compression clements will nat collapse when the buckling stress is reached. An additional load can be carried by the element after buckling by means of a redistribution of stress. This phenomenon is known as post-buckling strength of the compression elements and is most pronounced for stiffened compression elements with large 5/t ratios. The mechanism of the post-buckling action of compression elements is discussed by Winter in earlier editions of the AISI Commentary (Winter, 1970), Imagine, for the sake of simplicity, a square plate uniformly compressed in one direction, with the unloaded edges simply supported. Since it is difficult to visualize th performance of such two-dimensional elements, the plate will be replaced by a model, which is shown in Figure C2.2(2), The model consists of a grid of longitudinal and transverse bars in which the material of the actual plate is thought to be concentrated, Since the plate is uniformly compressed, each of the longitudinal struts represents a column loaded by N/S where N is the total axial force on the plate, As the force is gradually increased, the compression stress in each of these struts will reach the critical column buckling value and all five struts will tend to buckle simultaneously. If these struts were simple columns, unsupported except at the ends, they would simultaneously collapse through unrestrained, increasing horizontal deflection. It is evident, however, that this cannot occur in the grid model of the plate, Indeed, as soon as the longitudinal struts start deflecting at their buckling stress, the transverse bars that are connected to them should stretch like ties in order to accommodate the imposed deflection, Like any structural material, they resist stretch and, thereby, have a restraining effect on the deflections of the longitudinal struts. The tension forces in the horizontal bars of the grid model correspond to the so-called membrane stresses in a real plate. These stresses, just as in the grid model, come into play as soon as the compression stresses begin to cause buckling waves. They consist mostly of transverse tension, but also of some shear stresses, and they counteract increasing wave deflections, i.e. they tend to stabilize the plate against further buckling under the applied increasing longitudinal compression. Hence, the resulting behaviour of the model is as follows: (a) There is no collapse by unrestrained deflections as in unsupported columns, (b) The various struts will deflect unequal amounts, those nearest the supported edges being held almost straight by the ties, those nearest the centre being able to deflect most.‘Accessed by BHP BILLITON on 27 Jun 2002 FIGURE €2.2(2) POST-BUCKLING STRENGTH MODEL In consequence of Item (a), the model will not collapse and fail when its buckling stress (see Equation C2.2(1)) is reached, in contrast to columns it will merely develop slight deflections but will continue to carry increasing load. In consequence of Item (b), the struts (strips of the plate) closest to the centre, which deflect most, ‘get away from the load’, and hardly participate in carrying any further load increases. These centre s may, in fact, even transfer part of their pre-buckling load to their neighbours. The struts (or sirips) closest to the edges, held straight by the ties, continue to resist increasing load with hardly any increasing deflection. For the plate, this means that the hitherto uniformly distributed compression stress re-distributes itself in a manner shown in Figure C2.2(3), the stresses being largest at the edges and smallest in the centre. With additional increase in load this non-uniformity increases further, as also shown in Figure C2.2(3). The plate fails, ic. refuses to carry any further load increases, only when the most highly stressed strips, near the supported edges, begin to yield, ie. when the compression stress (fay) reaches the yield stress (f). This post-buckling strength of plates was discovered experimentally approximate theory of it was first given by Th. v. Karman in 1932 (Bleich, 1952). It has been used in aircraft design ever since. A graphic illustration of the phenomenon of post-buckling strength can be found in the series of photographs shown in Figure 7 of Winter (1959b). 1928, and an The model shown in Figure C2.2(2) demonstrates the behaviour of a compression element supported along both longitudinal edges, as docs the flange shown in Figure C2.2(1). In fact, such elements buckle into approximately square waves. In order to utilize the post-buckling strength of the stiffened compression element for design purposes, the AISI Specification has used the effective design width approach to determine the sectional properties, and since 1946 and AS/NZS 4600 has adopted this effective width approach, In Clause 2.2 of the Standard, design equations for calculating the effective widths are provided for the following three cases: (Uniformly compressed stiffened elements‘Accessed by BHP BILLITON on 27 Jun 2002 Gi) Uniformly compressed stiffened elements with circular holes. Gil) Webs and stiffened elements with a stress gradient The background information on various design requirements is discussed in the subsequent sections herein, 2.2.1 Uniformly compressed stiffened elements €2.2.1.2 Effective width for capacity calculations In the ‘effective design width’ approach, instead of considering the non-uniform distribution of stress over the entire width of the plate (6) it is assumed that the total load is carried by a fictitious effective width (2,) subject to a uniformly distributed stress equal to the edge stress (/,,,) a8 shown in Figure C2.2G). The width (b,) is selected so that the area under the curve of the actual non-uniform stress distribution is equal to the sum of the two parts of the equivalent rectangular shaded arca with a total width (6,) and an intensity of stress equal to the edge SHESS (Fp) Imex bev? 0/2 FIGURE C2.2(3) STRESS DISTRIBUTION IN STIFFENED COMPRESSION ELEMENTS Based on the concept of “effective width’ introduced by von Karman et al. (von Karman, Sechler and Donnell, 1932) and the extensive investigation on light-gauge, cold-formed steel sections at Cornell University, the following equation was developed by Winter in 1946 for determining the effective width (6,) for stiffened compression elements simply supported along both longitudinal edges: =| Ein - oars) | 2.21.21) ow 0) Fa Equation C2.2.1.2(1) can be written in terms of the ratio fy ify, a8 follows: a. | fal te fee | fal) gas |e 221120) > re ° { z| °‘Accessed by BHP BILLITON on 27 Jun 2002 During the period from 1946 to 1968, the AISI design provision for the determination of the effective design width was based on Equation C2.2.1.2(1). A long-time accumulated experience has indicated that the following more realistic equation may be used for the determination of the effective width (b,) (Winter, 1970): (1) [Z In = 041s Ne 2.2.1.2) The correlation between the test data on stiffened compression elements and Equation C2.2.1.2(3) is illustrated by Yu (1991). It should be noted that Equation C2.2.1.2(3) may also be rewritten in terms of the fulfuu ratio as follows: fy 022 | 2.21.24) Tow fa} ‘Therefore, the effective width (b) can be determined as follows: b= pb 2.2.1.5) where effective width factor €2.2.1.2(6) In Equation C2.2.1.3(6), 4 is a slenderness ratio and is calculated as follows: n2 (i - v4 (3) ) 7 (exe) 22.1.2) 1,052) (b) | Foe -( 2 (= VENNUNE Figure C2.2(4) shows the relationship between ¢ and A. It can be seen that if A is less than or equal to 0.673, is equal to 1.0.‘Accessed by BHP BILLITON on 27 Jun 2002 10 oa] oa| o7| as| o.s| oak Equation €2.2.1316) gat 0222/01 osk ok REDUCTION FACTOR 6) oak a ost 23486 78 SLENDERNESS RATIO (A) FIGURE C2.2(4) REDUCTION FACTOR (¢) VERSUS SLENDERNESS FACTOR (2) Based on Equations C2.2.1.2(5) to C2.2.1.2(7) and the unified approach proposed by Pekiz (1986b and 1986c), the 1986 edition of the AISI Specification adopted the non-dimensional format in Clause 2.2 for determining the effective design width (b,) for uniformly, compressed stiffened elements. The same design equations are used in the 1996 edition of the AISI Specification and in the Standard. Tm the Standard, fyy, in. Equation C2.2.1.2(7) is taken as /*, the design compression element calculated on the basis of the effective design width €2.2.1.3 Effective width for deflection calculations The effective design width equations for load capacity determination discussed in Clause C2.2.1.2 can also be used to obtain a conservative effective width (b,4) for deflection calculation. It is included in Clause 2.2.1.3 of the Standard as Procedure | s in the For stiffened compression elements supported by a web on cach longitudinal edge, a study conducted by Weng and Pek6z (1986) indicated that Equations 2.2.1.2(3) to 2.2.1.2(6) of the Standard can yield a more accurate estimate of the effective width (b,,) for deflection analysis. These equations are given in Procedure II of the Standard for additional design information. The design engineer has the option of using one of the two procedures for determining the effective width to be used for deflection calculations, 2.2.2 Uniformly compressed stiffened elements with circular holes In cold-formed stee] structural members, holes are sometimes provided in webs or flanges, or both, of ‘beams and columns for duet work, piping and other construction purposes. The presence of such holes may result in a reduction of the strength of individual component elements and the overall strength and stiffness of the members depending on the size, shape arrangement of holes, the geometric configuration of the cross-section, and the mechanical properties of the material The exact analysis and the design of steel sections having perforations are complex, particularly when the shapes and the arrangement of holes are unusual, The limited design provisions included in Clause 2.2.2 of the Standard for uniformly compressed stiffened elements with circular holes are based on a study conducted by Ortiz-Colberg and Pekéz at Comell University (Ortiz-Colberg and Pek6z, 1981). For additional information on the structural behaviour of perforated elements, see Yu and Davis (1973a) and Yu (1991).‘Accessed by BHP BILLITON on 27 Jun 2002 €2.2.3. Stiffened elements with stress gradient When a beam is subjected to bending moment, the compression portion of the web may buckle duc to the compressive stress caused by bending. The theoretical critical buckling stress for a flat rectangular plate under pure bending can be calculated using Equation C2,2(1), except that the depth-to- thickness ratio (d,/t,) is substituted for the width-to-thickness ratio (6/1) and the plate buckling coefficient (f) is equal to 23.9 for simple supports as given in Table C2.2, In AS 1538— 1988, the design of cold-formed steel beam webs was based on the full web depth with the permissible bending stress (F,,) specified in the Standard. In order to unify the design methods for web elements and compression flanges, the ‘effective desiga depth’ approach was adopted in the 1986 edition of the AISI Specification on the basis of the studies made by Pek6z (1986b), Cohen and Pekiz (1987). This is a different approach as compared with the past practice of using a full area of the web element in conjunction with a reduced stress to account for local buckling and post-buckling strength (LaBoube and Yu, 1982; Yu, 1985). The effective design depth approach is used in the Standard, €2.3. EFFECTIVE WIDTHS OF UNSTIFFENED ELEMENTS Similar to stiffened compression elements, the stress in the unstiffened compression elements can reach t! yield stress of stecl if the bit ratio is small. Because the unstiffened clement has one longitudinal edge supported by the web and the other edge is free, the limiting width-to- thickness ratio of unstiffened elements is much less than that for stiffened elements When the bit ratio of the unstiffened element is large, local buckling (see Figure C2.3(1)) will occur at the elastie critical stress calculated using Equation C2.2(1) with a value of k equal to 0.43. This buckling coefficient is given in Table C2.2 for Case (c). For the intermediate range of b/t ratios, the unstiffened clement will buckle in the inclastie range. Figure C2.3(2) shows the relationship between the maximum stress for unstiffened compression elements and the bit ratio, in which Line A is the yield point of steel, Line B represents the inclastic buckling stress, Curves C and D illustrate the clastic buckling stress, The equations for Curves A,B,C and D have been developed from previous experimental and analytical investigations and used for determining the allowable design stresses in the AISI Specification up to 1986 and AS 1538—1974 (Winter, 1970; Yu, 1991; Hancock, 1998). Also shown in Figure C2.3(2) is Curve E, which represents the maximum stress on the basis of the post-buckling strength of the unstiffened element. The correlation between the test data on unstiffened clements and the predicted maximum stresses is shown in Figure C2.3(3) (Yu, 1991). FIGURE €2.3(1) LOCAL BUCKLING OF UNSTIFFENED COMPRESSION FLANGE‘Accessed by BHP BILLITON on 27 Jun 2002 Stress reel, 378/J%, Inelastic buckling Yielding Elastic buckling a2 j-Based on post—buckling strength 103030 -40—CSS FIGURE C2.3(2) MAXIMUM STRESS FOR UNSTIFFENED ‘COMPRESSION ELEMENTS Inelastic Elastic Yielding | bucking buckling 10 08 Q H oO 1 i © Local buckling stress Fale stress | Failure st | i i i i 700 [200 300 [soo 500 600 166 378 FIGURE C2.3(3) CORRELATION BETWEEN TEST DATA AND PREDICTED MAXIMUM STRESS.‘Accessed by BHP BILLITON on 27 Jun 2002 Prior to 1986 (AISI) and 1988 (AS 1538), it had been a general practice to design cold-formed stee] members with unstiffened flanges by using the permissible stress design approach. The effective width equation was not used in earlier editions of the AISI Specification and AS 1538—1974 due to lack of extensive experimental verification and the concem for excessive out-of-plane distortions under service loads. In the 1970s, the applicability of the effective width concept to unstiffened elements under uniform compression was studied in detail by Kalyanaraman, Pek6z, and Winter at Cornell University (Kalyanaraman, Pekéz, and Winter, 1977; Kalyanaraman and Pekéz, 1978). The evaluation of the test data using & equal to 0.43 was presented and summarized by Pekéz in the AISI report (Pekéz, 1986b), which indicates that Equation C2.2.1.2(6), developed for stiffened compression elements, gives a conservative lower bound to the test results of unstiffened compression elements. In addition to the strength determination, the same study also investigated the out-of-plane deformations in uunstiffened elements, The results of theoretical calculations and the test results on the sections having unstiffened elements with bit equal to 60 were presented by Pekéz. in the same report. It was found that the maximum amplitude of the out-of-plane deformation at failure can be twice the thickness as the b/t ratio approaches 60. However, the deformations are significantly less under the service loads. Based on the above reasons and justifications, the effective design width approach was adopted for the first time in Section B3 of the 1986 AISI Specification and AS 1538—1988 for the design of cold-formed steel members having unstiffened compression elements. €2.3.1 Uniformly compressed unstiffened elements The effective widths (6) of uniformly compressed unstiffened elements can be determined in accordance with Clause 2.2.1.2 of the Standard with the exception that the plate buckling coefficient (&) is taken as 0.43, This is a theoretical value for long plates. See Case (c) given in Table €2.2, For deflection determination, the effective widths of uniformly compressed unstiffened elements can only be determined in accordance with Procedure! of Clause 2.2.1.3 of the Standard, because Procedure II was developed for stiffened compression elements only. 2.3.2. Unstiffened elements and edge stiffeners with stress gradient In concentrically loaded compression members and in flexural members where the uunstiffened compression element is parallel to the neutral axis, the stress distribution is uniform prior to local buckling. However, when edge stiffeners of the beam section are tured in or out, the compressive stress in the edge stiffener is not uniform but varies in proportion to the distance from the neutral axis. There is a very limited amount of information on the behaviour of unstiffened compression elements with a stress gradient. Cornell research on the b stiffeners for flexural members has demonstrated that by using Winter's equation (Equation C2.2.1.3(4)) with a k equal to 0.43, good correlation is achieved between the tested and calculated capacity (Pekiz, 1986b). The same trend is also true for deflection determination, Therefore, in Clause 2.3.2 of the Standard, unstiffened elements and edge stiffeners with stress gradient are treated as uniformly compressed elements for the calculation of effective widths with stress (f*) to be the maximum compression stress in the element, The Standard allows two additional alternative procedures to those specified in the AISI Specification, Firstly, the plate buckling coefficient (k) for each flat element may be determined from a rational clastic buckling analysis of the whole section as a plate assemblage subjected to the longitudinal stress distribution in the section prior to buckling. This could be achieved using a finite strip buckling analysis such as that described by Papangelis and Hancock (1995). The second alternative approach allowed in the Standard is given in Appendix F, This Appendix is based on Eurocode 3, Part 1.3, (1996) where buckling coefficients and effective widths of unstiffened elements under stress gradient are given in Table 4.2. The‘Accessed by BHP BILLITON on 27 Jun 2002 use of this Table is assumed not to be iterative so that the stresses /*, and /*, used to calculate the buckling coefficient (k) and effective width (B,) ate based on the stresses on the full (gross) section. This approach is a higher tier in the Standard and further research is required to fully validate its applicability for a range of sections. 2.4 EFFECTIVE WIDTHS OF UNIFORMLY COMPRESSED ELEMENTS WITH AN EDGE STIFFENER OR ONE INTERMEDIATE STIFFENER For cold-formed steel beams such as hat, box or inverted U-type sections shown in Figures C1,3.2(c), (d) and (e) the compression flange is supported along both longitudinal edges by webs. In this, case, if the webs are properly designed, they provide adequate stiffening for the compression elements by preventing their longitudinal edges from out-of displacements. On the other hand, in many cases, only one longitudinal edge is stiffened by the web, while the other edge is supported by an edge stiffener. In most cases, the edge stiffener takes the form of a simple lip, such as in the channel and [-section as shown in Figures C1.3.2(a) and (b) The structural efficiency of a stiffened element always exceeds that of an unstiffened the same bit ratio by a sizeable margin, except for low bit ratios, for which the compression element is fully effective. When stiffened elements with large bit ratios are used, the material is not employed economically in as much as an increasing proportion of the width of the compression element becomes ineffective. On the other hand, in many applications of cold-formed stec] construction, such as panels and decks, maximum coverage is desired and, therefore, large d/t ratios are called for. For large b/t ratios, structural economy can be improved by providing intermediate stiffeners between webs. Such intermediate stiffeners provide optimum stiffening if they do not participate the wave-like distortion of the compression element, in which case they break up the wave pattern so that the two strips to each side of intermediate stiffener distort independently of each other, each in a pattern similar to that shown for a simple, stiffened element in Figure C2.2(1). Compression clements furnished with such intermediate stiffeners are designated as ‘multiple-stiffened segments’ element As far as the design provisions are concerned, the 1980 and earlier editions of the AISI Specification and AS 1538—1988 included the requirements for the minimum second moment of area of stiffeners to provide sufficient rigidity. When the size of the actual stiffener does not satisfy the required second moment of area, the load-carrying capacity of the beam has to be determined either on the basis of a flat element disregarding the stiffener or through tests. n 1986, the AISI Specification included the revised provisions in Clause 2.4 for etermining the effective widths of elements with an edge stiffener or one intermediate stiffener on the basis of Pekbz's research findings in regard to stiffeners (Pekéz, 1986b). These design provisions were based on both critical local buckling and ultimate strength criteria recognizing the interaction of plate elements, Also, for the first time, the design provisions could be used for analysing partially stiffened and adequately stiffened compression clements using different sizes of stiffeners. These provisions are included in Clause 2.4 of the Standard, 2.4.2. Elements with an intermediate stiffener The buckling behaviour of rectangular plates with central stiffeners is discussed by Bulson (1969). For the design of cold-formed steel beams using intermediate stiffencrs, the 1980 AISI Specification and AS 1538—1988 contained provisions for the minimum required second moment of area, which was based on the assumption that an intermediate stiffener needed to be twice as rigid as an edge stiffener. Subscquent research conducted by Desmond, Pekiz, and Winter (1981b) has developed expressions for evaluating the required stiffener rigidity based upon the geomerty of the contiguous flat elements.‘Accessed by BHP BILLITON on 27 Jun 2002 In view of the fact that for some cases the design requirements for intermediate stiffeners included in the 1980 Specification could be unduly conservative (Pckéz, 1986b), the AISI design provisions were revised in 1986 according to Pekiz’s research findings (Pekéz, 1986b and 1986c). In this method, the buckling coefficient for determining the effective width of sub-elements and the reduced area of the stiffener are to be calculated by using the ratio 1//,, In the foregoing expression, /, is the actual stiffener second moment of arca and J, is the adequate second moment of area of the stiffener determined from the applicable equations. 2.4.3 Elements an edge stiffener An edge stiffener is used to provide a continuous support along a longitudinal edge of the compression flange to improve the buckling stress. Even though in most cases, the edge sliffener takes the form of a simple lip, other types of edge stiffeners can also be used for cold-formed steel members. In order to provide necessary support for the compression element, the edge stiffener must possess sufficient rigidity. Otherwise it may buckle perpendicular 10 the plane of the element to be stiffened, Both theoretical and experimental studies on the local stability of compression flanges stiffened by edge stiffeners have been carried out in the past. The design requirements included in Clause 2.4.3 of the Standard are based on the investigations on adequately stiffened and partially stiffened elements conducted by Desmond, Pekiz and Winter (1981a), with the additional research work by Pek6z and Cohen (Pek6z, 1986b). Thes design provisions were developed on the basis of the critical buckling criterion and the ultimate strength criterion, Clause 2.4.3 recognizes that the necessary stiffener rigidity depends upon the slenderness (bit) of the plate element being stiffened. Thus, Cases I, I] and III each contains different definitions for an adequate stiffener second moment of area, The interaction of the plate elements, as well as the degree of edge support, full or partial is compensated for in the expressions for k, d,, and A, (Pekiz, 1986b). In the 1996 edition of the AISI Specification (AISI, 1996) and AS/NZS 4600, the design equations for buckling coefficient were changed for further clarity. In Case II, the equation for k, equal to 5.25 — 5 (d,/b) $4.0 is applicable only for simple lip stiffeners decause the term d;/b is meaningless for other types of edge stiffeners. It should be noted that the provisions in this section were based on research dealing only with simple lip stiffeners and extension to other types of stiffeners was purely intuitive, The requirement of 140° 6 > 40° for the applicability of these provisions was also decided on an intuitive basis. Test data to verify the accuracy of the simple lip stiffener design was collected from a number of sources, both university and industry. These tests showed good correlation with the equations in Clause 2.4.3. However, proprietary testing conducted in 1989 revealed that lip lengths with a dit ratio of greater than 14 gave unconservative results. A review of the original research data showed a lack of data for simple stiffening lips with d/t ratios greater than 14. Therefore, pending further research, an upper limit of 14 is, recommended C25 EFFECTIVE WIDTHS OF EDGE-STIFFENED ELEMENTS WITH ONE OR MORE INTERMEDIATE STIFFENERS OR STIFFENED ELEMENTS WITH MORE THAN ONE INTERMEDIATE STIFFENER As discussed in Clause C2.4, the current design provisions for the effective widths of elements with an edge stiffener or one intermediate stiffener were based on the results of previous Comell research. Because there has been insufficient research to further our understanding of the behaviour of rmultiple-stiffened elements, the 1996 edition of the AISI Specification and AS/NZS 4600 have retained Equation 2.5(1) from previous editions of the Specification (AISI, 1986; 1991) and AS 1538 (1988) for evaluating the minimum required rigidity (I, 4) of an‘Accessed by BHP BILLITON on 27 Jun 2002 intermediate stiffener for multiple-stiffened elements, If the actual second moment of area of the full intermediate stiffener (/,) docs not satisfy the minimum requirement Equation 2.5(1), the intermediate stiffener is disregarded for the determination of the effective width of stiffened elements. The problem involved in the determination of the load-carrying capacities of members having such inadequately stiffened compression clements is complex because the buckling wave tends to spread across the intermediate stiffener rather than being limited to individual waves occurring on both sides of the stiffener. Once such a spreading wave occuts, the stiffened compression element is hardly etter than an clement without intermediate stiffeners. For this reason, the sectional properties of members having inadequately stiffened compression flanges are determined on the basis of flat elements disregarding the intermediate stiffeners. The same is true for cedge-stiffened clements with intermediate stiffeners, In addition, Clause 2.5(a) stipulates that if the spacing of intermediate stiffeners between two webs is such that for the sub-clement between stiffeners b, < b, only two intermediate stiffeners adjacent to web elements shall be counted as effective. Additional stiffeners would have two or more sub-elements between themselves and the nearest shear-transmitting clement (ie. web) and, hence, could be ineffective. Clause 2.5(b) applies the same reasoning to intermediate stiffeners between a web and an edge stiffener. If intermediate stiffeners are spaced so closely that the sub-elements are fully effective, i.e. b, equal to , no plate buckling of the sub-elements will occur. Therefore, the entire assembly of sub-elements and intermediate stiffeners between webs behaves like a single compression clement whose rigidity is given by the second moment of area (J,,) of the full area of the multiple-stiffened clement, including stiffeners. Although the effective width calculations are based upon an equivalent element having width (5,) and thickness (f,), the actual thickness should be used when calculating section modulus. With regard to the effective design width, results of tests of cold-formed steel sections having intermediate stiffeners showed that the effective design width of a sub-clement of the multiple-stiffened compression elements is less than that of a single-stiffened element with the same bie ratio, This is true, particularly if the B/t ratio of the sub-element exceeds about 60. This phenomenon is due to the fact that, in beam sections, the normal stresses in the flanges result from shear stresses between web and flange. The web generates the normal stresses by means of the shear stress, which transfers to the flange. The more remote portions of the flange obtain their normal stress through shcar from those close to the web, For this reason there is a difference between webs and intermediate stiffeners. Th latter is not a shear-resisting element and does not generate normal stresses through shear. Any normal stress in the intermediate stiffener should be transferred to it from the web or webs through the flange portions. As long as the sub-element between web and stiffener is flat or is only very slightly buckled, this stress transfer proceeds in an unaffected manner. In this case, the stress in the stiffener equals that at the web, and the sub-clement is as fictive as a regular single-stiffened clement with the same bit ratio. However, for sub-elements having larger 6/¢ ratios, the slight buckling waves of the sub-element interfere with complete shear transfer and create a ‘shear lag’ problem which results in a stress distribution as shown in Figure C2.5. For multiple-stiffened compression clements or wide stiffened clements with edge stiffeners, the effective widths of sub-elements and the effective areas of stiffeners are calculated using Equations 2.5(3) to 2.5(6) of Clause 2.5.‘Accessed by BHP BILLITON on 27 Jun 2002 q Maximum ‘stress FIGURE ©2.5 STRESS DISTRIBUTION IN COMPRESSION FLANGE WITH INTERMEDIATE STIFFENERS €2.6 ARCHED COMPRESSION ELEMENTS An arched compression element is shown in Figure 1.3(d) and defined in Clause 1.3.3 of the Standard. This provision was carried forward from AS 1538— 1988, 2.7 2.7.1 Transverse stiffeners Design requirements for attached transverse stiffeners and for shear stiffeners were added in the 1980 AISI Specification and were unchanged in the 1986 Specification and were also given in AS 1538 (1988). The same design equations are retained in the 1996 AISI Specification and the Standard. The nominal strength equation given in Item (a) of Clause 2.7.1 of the Standard serves to prevent end crushing of the transverse stiffeners, while the nominal strength equation given in Item (b) of Clause 2.7.1 is to prevent columa-type buckling of the web-stiffeners, The equations for calculating the effective areas (4,, and 4,,) and the effective widths (b, and b,) were adopted from Nguyen and Yu (1978a) with minor modifications. NERS The available experimental data on cold-formed steel transverse stiffeners were evaluated by Hsiao, Yu and Galambos (1988). A total of 61 tests was examined. The capacity factor of 0.85 used was selected on the basis of the statistical data, €2.7.2 Shear stiffeners The requirements for shear stiffeners included in Clause 2.7.2 of the Standard were primarily adopted from the AISC Specification (1978). The equations for calculating the minimum required second moment of area (Equation 2.7.2(1)) and the minimum required gross area (Equation 2.7.2(2)) of intermediate stiffeners are based on the studies summarized by Nguyen and Yu In Equation 2.7.2(1), the minimum value of (d\/50)" was sclected from the AISC Specification (AISC, 1978), The available experimental data on the shear strength of beam webs with shear stiffeners were calibrated by Hsiao, Yu and Galambos (1988). The statistical data used for determining the capacity factor were summarized in the AISI Design Manual (AISI, 1991). Based on these data, the safety index was found to be 4.10 for ¢ equal to 0.90. €2.7.3._ Non-conforming stiffeners Tests on rolled-in transverse stiffeners covered in Clause 2.7.3 of the Standard were not conducted in the experimental program reported by Neuyen and Yu (1978a), Lacking reliable information, the design capacities of members are to be determined by tests in accordance with Section 6 of the Standard,‘Accessed by BHP BILLITON on 27 Jun 2002 SECTION C3 MEMBERS INTRODUCTION Section 3 provides the design requirements for the following: (a) Tension members, (b) Flexural members. (©) Concentrically loaded compression members. () Combined axial load and bending (e) Cylindrical tubular members. To simplify the use of the Standard, all design provisions for a given specific member type have been assembled in a particular Section within the Standard. In general, a common nominal strength equation is provided in the Standard for a given limit state with ‘a required capacity [strength reduction] factor (9) for limit states design, 3.1 GENERAL The geometric properties of a member (ic. area, second moment of area, section modulus, radius of gyration and the like) are evaluated using conventional methods of structural design, These properties are based upon either full cross-section dimensions, effective widths or net section, as applicable. For the design of tension members, the net section is employed when calculating the nominal tensile strength of the axially loaded tension members, For flexural members and axially loaded compression members, both full and effective dimensions are used to calculate sectional properties. The full dimensions are used when calculating the buckling load or moment, while the effective dimensions are used to calculate the section and member capacities. For deflection calculation, the effective dimension should be determined for the compressive stress in the element corresponding to the service load. Pekéz (1986a and 1986b) discusses this concept in more detail C3.2. MEMBERS SUBJECT TO TENSION There is very limited amount of data regarding the capacity of cold-formed steel tension members. The provisions in Clause 3.2 of the Standard are the same as those in Clauses 7.2 and 7.3 of AS 4100/NZS 3404. The Commentary to AS 4100 (AS 4100 Supp 1—1990) or to NZS 3404 (NZS 3404:Part 2:1997) should, therefore, be referred to for the explanation of Clause 3.2, 3.3. MEMBERS SUBJECT TO BENDING For the design of cold- Aexural members, consideration should be given to the following: med. steel (a) Bending strength and deflection. (b) Shear strength of webs and combined bending and shear. (c) Web crippling strength and combined bending and web crippling. (4) Bracing requirements, For some cases, special consideration should also be given to shear lag and flange curling due to the use of thin material. The design provisions for Items (a), (b) and (c) are provided in Clause 3.3 of the Standard, while the requirements for lateral bracing are specified in Clause 4.3. The treatments for flange curling and shear lag were discussed in Clauses €2.1.3.2 and C2.1.3.3, respectively.‘Accessed by BHP BILLITON on 27 Jun 2002 €3.3.1. Bending moment Bending strengths of flexural members are differentiated according to whether or not the member is laterally braced or the compression flange is torsionally braced, If such members are laterally supported, then they are proportioned in accordance with the nominal section moment capacity (see Clause 3.3.2 of the Standard), If they are laterally unbraced, then the limit state is lateral buckling (see Clause 3.3.3.2 of the Standard) or lateral-distortional buckling (see Clause 3.3.3.3(b) of the Standard). If the compression flange is torsionally unbraced but the member is laterally braced, then the limit state may be flange distortional buckling (see Clause 3.3.3.3(a) of the Standard). For channel or Z-sections with the tension flange attached to deck or sheeting and with the compression flange laterally unbraced, the bending capscity is less than that of a fully braced member but greater than that of an unbraced member (see Clause 3.3.3.4 of the Standard). The governing nominal bending capacity is the smallest of the values determined from the applicable conditions, €3.3.2. Nominal section moment capacity Clause 3.3.2 of the Standard includes two design procedures for calculating the nominal section moment capacity. The first procedure in Clause 3.3.2.2 of the Standard is based on initiation of yielding and the second procedure in Clause 3.3.2.3 of the Standard is based on inelastic reserve capacity. €3,3.2.2 Based on initiation of yielding In Clause 3.3.2.2 of the Standard, the nominal section moment capacity (IM,) is the effective yield moment determined on the basis of the effective areas of Manges and the beam webs. The effective width of the compression flange and the effective depth of the webs can be calculated from the design equations given in Section 2 of the Standard. Similar to the design of hot-rolled steel shapes, the yield moment of a cold-formed steel at which an outer fibre (tension, compression, or both) first attains the yield point of the stecl. This is the maximum bending capacity to be used in elastic design, Figure C3.3.2.2 shows several types of stress distributions for yield moment based on different locations of the neutral axis. For balanced sections (sce Figure C3.3.2,2(a)), the outer fibres in the compression and tension flanges reach the yield point at the same time. However, if the neutral axis is eccentrically located, as shown in Figures C3.3.2.2(6) and (c), the initial yielding takes place in the tension flange for Case (b) and in the compression flange for Case (e) Accordingly, the nominal section strength for initiation of yielding is calculated using Equation C3.3.2.2 as follows: M, c where Z, = elastic section modulus of the effective section calculated with the extreme compression or tension £ J, = design yield stress For coldeformed steel design, Z, is usually calculated by using one of the following: (a) If the neutral axis is closer to the tension than to the compression flange, the maximum stress occurs in the compression flange and, therefore, the plate slendemess ratio (4) and the effective width of the compression flange are determined using the B/t ratio and f* equal to f,. This procedure is also applicable to those beams for which the neutral axis is located at the mid-depth of the section. (b) If the neutral axis is closer to the compression than to the tension flange, the maximum stress of f, occurs in the tension flange. The stress in the compression flange depends on the location of the neutral axis, which is determined by the effective arca of the section. The latter cannot be determined unless the compressive stress is known. A closed-form solution of this type of design is possible but would be a very tedious and complex procedure. It is therefore customary to determine the sectional properties of the section by iteration.‘Accessed by BHP BILLITON on 27 Jun 2002 For determining the design section moment capacity (9M), slightly different capacity factors are used for the sections with stiffened or pattially stiffened compression flanges and the sections with unstiffened compression flanges. These @, values were derived from the test results and a dead-to-live load ratio of 1/5. They provide B values ranging from 2.53 to 4.05 (AISI, 1991; Hsiao, Yu and Galambos, 1988) fy, ‘ y, he a 4 outra Nbutcal Noutra Jk 4 wes /| 4 4 In (a) Balances sections He ty Hs ly ay AR Neutra fueuteas Novica 4 (oI 4 tb] Neutral axis close to compression flange 4 fy, he ye i SL Les, 3M, Mya, = absolute value of maximum moment in the unbraced segment M, = absolute value of moment at quarter point of unbraced segment M, = absolute value of moment at centerline of unbraced segment M, — = absolute value of moment at three-quarter point of unbraced segment Equation C3.3.3.2(5) was derived by Kirby and Nethercot (1979) and can be used for various shapes of moment diagrams within the unbraced length under consideration (equivalent to segment in AS 4100 and in NZS 3404). It gives accurate solutions for fixed-end beams and moment diagrams that are not straight lines. Equation C3.3.3.2(5) is, the same as that being used in the AISC LRED Specification (AISC, 1993). Based on the clastic critical buckling stress of an I-section calculated using Equation C3,3.3.2(4), the simplified elastic buckling moment for lateral buckling of point symmetric Z-sections can be determined using Equation C3.3.3.2(6) c. Equation 3.3.3.2(16) in the Standard), which is simply detived by factoring Equation C3.3.3.2(4) by % to allow for the inclined principal axes of the Z-section, as follows: 2 Bal, M,~ = €3.3.3.2(6) ai Equation C3.3.3.2(2) applies only to elastic buckling of cold-formed steel beams when the calculated theoretical buckling stress is less than or equal to the proportional limit, When the calculated stress exceeds the proportional limit, the beam behaviour will be governed by inelastic buckling. The inelastic buckling stress can be calculated using Equation C3.3.3.2(7) (Yu, 1991) as follows: €3.3.3.2(8) the moment causing initial yield at the entrance compression fi section and equals Z,f, The elastic and inelastic buckling moments for lateral buckling strength are shown in Figure C3.3.3.2(1) (Yu, 1991). As specified in Clause 3.3.3.2(a) of the Standard, buckling. is considered to be elastic up to a moment equal to 0.56 M,. The inelastic region is defined by a Johnson parabola from 0.56 M, to (10/9) M, at an unsupported length of zero. The (10/9) factor is based on the partial plastification of the section in bending (Galambos, 1963). A flat pleteau is created by limiting the maximum moment to M, which enables the calculation of the maximum unsupported length for which there is no moment reduction due to lateral instability. This maximum unsupported length can be calculated by setting M, equal to the Johnson parabola. This inelastic lateral buckling curve for singly-, doubly- and point-symmeiric sections has been confirmed by research in beam columns (Pekdz and Sumer, 1992) and wall studs (Kian and Pekéz, 1994) the full‘Accessed by BHP BILLITON on 27 Jun 2002 FIGURE C3.3.3.2(1) ELASTIC AND INELASTIC CRITICAL MOMENTS. FOR LATERAL BUCKLING STRENGTH In the Standard, the design equations from AS 1538—1988 were converted to limit states format and included in Clause 3.3.3.2(b) of the Standard. In particular, the strength Equations 3.3.3.2(17), 3.3.3.2(18) and 3.3.3.2(19) in the Standard were derived directly from Clause 3.3.2 of AS 1538 with stresses (F, My and #,) replaced by equivalent moments (M,, M, and M,), and with the factor of safety of 1.67 removed, The above discussion deals only with the lateral buckling strength of locally stable beams. For locally unstable beams, the interaction of the local buckling of compression elements and the overall lateral buckling of beams may result in a reduction of the lateral buckling strength of the member. The effect of local buckling on critical moment is considered in Clause 3.3.3.2 of the Standard, in which the nominal member moment capacity is determined as follows: (Z.) ) €3.3.3.29) 4) MoM.) where M, = clastic or inelastic critical moment, whichever is applicable Z, = elastic section modulus of the effective section calculated at a stress M,Z, in the extreme compression fibre clastic section modulus of the full unreduced section for the extreme compression fibre In Equation C3.3.3.2(9), the ratio buckling strength of beams, represents the effect of local buckling on lateral Using the above nominal member moment capacity with a capacity factor of 6, equal to 0.90, values of B vary from 2.4 to 3.8. Lateral buckling problems discussed above deal with the type of lateral buckling of T-beams, channels and Z-shaped sections for which the entire cross-section rotates and deflects in the lateral direction. This is not the case for U-shaped beams and the combined sheet-stiffener sections shown in Figure C3.3,3.2(2). For this case, when the section is loaded in such 2 manner that the flanges of stiffeners are in compression, the tension flange of the beam remains straight and does not displace laterally; only the compression flange tends to buckle separately in the lateral direction, accompanied by out-of-plane bending of the web, as shown in Figure C3.3.3.2(3), unless adequate bracing is provides‘Accessed by BHP BILLITON on 27 Jun 2002 The precise analysis of the lateral buckling of U-shaped beams is rather complex. The compression flange and the compression portion of the web act not only like a column on an clastic foundation, but the problem is also complicated by the weakening influence of the torsional action of the flange. For this reason, the design procedure outlined in Chapter C of Supplementary Information of the AISI Design Manual for determining the allowable design strength for laterally unbraced compression flanges is based on the considerable simplification of an analysis presented by Douty (1962). In 1964, Haussler presented rigorous methods for determining the strength of elastically stabilized beams (Haussler, 1964). In his methods, Haussler also treated the unbraced compression flange as a column on an clastic foundation and maintained more rigour in his development, A comparison of Haussler’s method with Douty’s simplified method indicates that the latter may provide a smaller critical stress. An additional study of laterally unbraced compression flanges was recently made at Comell University (Serrette and Pek6z, 1992, 1994 and 1995) and an analytical procedure was developed for determining the distortional buckling strength of the standing seam roof panel. C4 LST _~ 1] [ 1, fot _l [4 FIGURE C3.3.3.2(2) COMBINED SHEET-STIFFENER SECTIONS FIGURE ©3.3.3.2(3) LATERAL BUCKLING OF U-SHAPED BEAM €3.3.3.3 Members subject to distortional buckling Recent research conducted by Ellifritt, Sputo and Haynes (1992) has indicated that when the unbraced length is defined as the spacing between intermediate braces, the equations used in Clause 3.3.3.2 of the Standard may be conservative for cases where one mid-span brace is used, but may be lunconservative where more than one intermediate brace is used,‘Accessed by BHP BILLITON on 27 Jun 2002 The above-mentioned research (Ellifritt, Sputo, and Haynes, 1992) and the recent study of Kavanagh and Ellifritt (1993 and 1994) have shown that a discretely braced beam, not attached to deck and shecting, may fail cither by lateral-torsional buckling betwes braces, or by distortional buekling at or near the braced point. The distortional buckling strength of C-sections and Z-sections has recently been studied extensively at the University of Sydney by Lau and Hancock (1987); Hancock, Kwon and Bernard (1994); and Hancock (1997). Two types of distortional buckling are specified in Clause 3.3.3.3 of the Standard. These are flange distortional buckling, which involves rotation of a flange and lip about the flange/web junction of a C-section or (ion, as shown in Figure C3.3.3.3(a), and lateral-distortional buckling, which involves transverse bending of a vertical web as shown in Figure C3.3.3.3(b). The flange-distortional mode is specified in Clause 3.3.3.3(a) of the Standard. The elastic distortional buckling stress (f..) can be based on a rational clastic buckling analysis, such as that given in Paragraph D3 of Appendix D of the Standard, which is based on Hancock (1997). ‘The equation for critical moment (M,) is developed in Hancock, Kwon and Bernard (1994), and is further supported by testing (Hancock, Rogers and Schuster (1996). Flange distortional buckling is most likely to occur in the unshected compression ‘anges of purlins under wind uplift when the purlins are braced to prevent twisting and lateral buckling, The lateral-distortional mode is specified in Clause 3.3.3.3(b) of the Standard. It is most likely to occur in beams, such as the hollow flange beam shown in Figure C3.3.3.3(b), where the high torsional rigidity of the tubular compression flange prevents it from twisting during lateral displacement. Equations for the elastic distortional buckling stress are given in Pi and Trahair (1997). The equation for critical moment (M,) is based on the Johnston parabola (Galambos, 1988) and, at this stage, has not been supported by testing. Compression flange: (a) Flange distortional (b} Lateral cistortional FIGURE 3.3.3.3 FLEXURAL DISTORTIONAL BUCKLING MODES. €3.3.3.4 Beams having one flange through-fastened to sheeting For beams having the tension flange attached to deck or sheeting and the compression flange unbraced, e.g. a roof purlin or wall girt subjected to outward wind pressure, the bending capacity is less than a fully braced member, but greater than an unbraced member. This partial restraint is function of the rotational stiffness provided by the panel-to-purlin connection, Th Standard contains factors that represent the reduction in capacity from a fully braced condition. The factors in the AISI Specification (1996) are based on experimental results‘Accessed by BHP BILLITON on 27 Jun 2002 obtained for both simple and continuous span purlins (Pek6z and Soroushian, 1981 and 1982; LaBoube, 1986; Haussler and Pahers, 1973; LaBoube, et al., 1988; Haussler, 1988). In the Standard the R factors were calibrated by Johnston and Hancock (1994), based on testing in the vacuum test rig at the University of Sydney (Hancock, Celeban and Healy (1993). As indicated by LaBoube (1986), the rotational stiffness of the panel-to-purlin connection is primarily @ function of the member thickness, shect thickness, fastener type and fastener location. For compressed glass fibre blanket insulation of initial thicknesses of zero to six inches (152 mm), the rotational stiffness is not measurably affected (LaBoube, 1986). To ensure adequate rotational stiffness of the roof and wall systems designed in accordance with the Standard, Clause 3.3.3.4 of the Standard explicitly states the acceptable panel and fastener types. In Australia, cleats were used in the vacuum rig tests, and these are specified clearly in Clause 3.3.3.4 of the Standard, Also in Australia, no insulation was used between the purlin and sheeting, Continuous beam tests were made in Australia on three equal spans under both wind uplift and downwards loading and the R values were calculated from the failure loads assuming a bending moment distribution based on double the second moment of area in the lapped regions, The provisions of Clause 3.3.3.4 of the Standard apply to beams for which the tension flange is attached to sheeting by screw fasteners and the compression flange is unbraced or has bridging which effectively prevents lateral and torsional deformation at support points In the case of simply supported purlins without bridging, considerable twisting of the purlins occurred which caused the screw heads to pull through the sheeting when load-spreading (cyclone) washers were not used. The AISI R-factor values are considerably lower than those in the Standard and can be used in the case when load-spreading (cyclone) washers are not used ‘The Refactor method cannot be used with clip fasteners of any form including sliding clips unless testing validates the restraint provided by the clips is adequate to prevent torsional deformation and allow the R factors in Clause 3.3.3.4 to be used, For the limit states method, the use of the reduced nominal member moment capacity with a capacity factor of @, equal to 0.90, Equation 3.3.3.4 of the Standard provides B values varying from 2.5 to 2.7, which are satisfactory for the target value of 2.5. This analysis was based on the load combination of (J¥,~ 0.86) (Rousch and Hancock (1996, 1996b)), 3.3.4. Shear The shear strength of beam webs is governed by either yielding or buckling, depending on the dy/f ratio and the mechanical properties of steel. For beam webs having small dy/t ratios, the nominal shear capacity is governed by shear yielding and can be calculated as follows - OSTIf dt, 3.3.4) where arca of the beam web computed by dt, yield point of steel in shear, which ean be caleulated by f/V3‘Accessed by BHP BILLITON on 27 Jun 2002 For beam webs having large d/, ratios, the nominal shear capacity is governed by elastic shear buckling and can be calculated as follows: 2 EA, Vi Ay, 7 — 3.3.42) ay * where t,, = critical shear buckling stress in the elastic range k, ~ shear buckling coefficient E_ = modulus of elasticity v= Poisson’s ratio dy = web depth 1, = web thickness By using v equal to 0.3, the shear strength (V,) can be calculated as follows: 2 V, = 0.905 Bk, 7 33.403) For beam webs having moderate dy/¢ ratios, the nominal shear strength is based on inelastic shear buckling and can be calculated as follows: V, = 0640, JR FE 33.404) ‘The provisions in the Standard ate applicable for the design of webs of beams and decks either with or without transverse web stiffeners The nominal strength equations of Clause 3.3.4 of the Standard are similar to the nominal shear strength equations given in the AISI LRED Specification (AISI, 1991). The acceptance of these nominal strength cquations for cold-formed steel sections was considered in the study summarized by LaBoube and Yu (1978a). Previous editions of the ASD Specification (AISI, 1986) and AS 1538—1988 employed three different factors of safety when evaluating the permissible shear strength of an unreinforced web because it was intended to use the same permissible values for the AISI and AISC specifications (i.e. 1.44 for yielding, 1.67 for inelastic buckling and 1.71 for elastic buckling). For the limit states design method in the Standard, the 4, factors used in Clause 3.3.4 of the Standard were derived from the condition that the nominal capacities for the limit states design method and the permissible stress method in AS 1538—1988. are the same, because the appropriate test data on shear were not available (IIsiao, Yu and Galambos, 1988a; AISI, 1991). €3.3.8 Combined bending and shear For cantilever beams and continuous beam: high bending stresses often combine with high shear stresses at the supports. Such beam webs should be safeguarded against buckling due to the combination of bending and shear stresses, For disjointed flat rectangular plates, the critical combination of bending and shear stresses can be approximated by the following equation (Bleich, 1952) €3.3.5(1)‘Accessed by BHP BILLITON on 27 Jun 2002 where A, = actual compressive bending stress fi, = theoretical buckling stress in pure bending, + = actual shear stress tq = theoretical buckling stress in pure shear Equation C3.3.5(1) was found to be conservative for beam webs with adequate transverse stiffeners, for which a diagonal tension field action can be developed. Based on the studies made by LaBoube and Yu (1978a), the following equation was developed for beam webs with transverse stiffeners satisfying the requirements of Clause 2.7 of the Standard * =13 €3.3.5(2) Equation C3.3.5(2) was added to the AISI Specification in 1980 and to AS 1538 in 1988. The correlations between Equation C3.3,5(2) and the test resulls of beam webs having a diagonal tension field action are shown in Figure C3.3.5. For the limit states design method, the Equation in Clause 3.3.5 of the Standard for combined bending and shear are based on Equation C3.3.5(1) and Equation C3.3.5(2) by using the nominal section moment capacity and nominal shear capacity. 12 ° 104 Bee ~ de Equation C3,3.5(2) 08 ° a Equotion C3.3.5(4}~ c 7 6 ou Se i20 Lg \ oe 4-150 04 4 rf = 4 =200 0.2 ol 02 04 06 08 fy I max. [NOTE: Solid symbols represent tes: specimens without additional sheets on top and bottom flanges. FIGURE 3.3.5 INTERACTION DIAGRAM FOR ¢/¢ pax, AND f/f,‘Accessed by BHP BILLITON on 27 Jun 2002 €3.3.6 Bearing For cold-formed steel beams, transverse and shear stiffeners are not frequently used. The webs of beams may cripple due to the high local intensity of the load or reaction. Figure C3.3.6(1) shows the types of failure caused by web crippling of unreinforeed single webs (see Figure C3.3.6(1){a)) and of I-beams (see Figure C3.3.6(1)(). FIGURE C3.3.6(1) WEB CRIPPLING OF COLD-FORMED STEEL BEAMS In the past, the buckling problem of separate flat rectangular plates and web crippling behaviour of cold-formed steel beam webs under locally distributed edge forces have been. studied by numerous investigators (Yu, 1991) and it was found that the theoretical analysis of web crippling for cold-formed stecl flexural members is rather complicated because it involves the following: (a) Non-uniform stress distribution under the applied load and adjacent portions of the web, (b) Elastic and inelastic stability of the web element, (©) Local yielding in the immediate region of load application. (Bending produced by rie load (or reaction) when it is applied on the bearing. ange at a distance beyond the curved transition of the web. (c) Initial out-of-plane imperfection of plate clements, (©) Various edge restraints provided by beam flanges and interaction between flange and web elements. (g) _ Inclined webs for decks and panels. For these reasons, the present AISI design provisions for web crippling and the ASINZS 4600 design provisions for bearing are based on the extensive experimental investigations conducted at Cornell University by Winter and Pian (Winter and Pian, 1946), and by Zetlin (Zetlin, 1955) in the 1940s and 1950s, and at the University of Missouri-Rolla by Hetrakul and Yu (Hetrakul and Yu, 1978). In these experimental investigations, the web crippling tests were carried out under the following four loading conditions for beams having single unreinforced webs and I-beams: (@ End one-flange (EOF) loading. flange (IOF) loading. Gii) End two-flange (BTF) loading Interior (iv) Interior two-flange (ITF) loading, All loading conditions are shown in Figure C3.3.6(2). In Figures (a) and (b), the distances between bearing plates were kept to no less than 1.5 times the web depth in order to avoid the two-flange loading action.‘Accessed by BHP BILLITON on 27 Jun 2002 Che isee £ Region of Ragion of failure failure (a) EOF loading (0) 10F loading 4 4 * (c) ETF loading (9) ITF loasing FIGURE C3.3.6(2) LOADING CONDITIONS FOR WEB CRIPPLING TESTS Clause 3.3.6 of the Standard provides design equations to determine the web crippling strength of flexural members having flat single webs (channels, Z-sections, hat sections, tubular members, roof deck, floor deck and the like) and I-beams (made of two channels connected back to back, by welding two angles to a channel, or by connecting three channels). Different design equations are used for various loading conditions, as shown in Figure C3.3.6(3), and Tables 3.3.6(1) and 3.3.6(2) in the Standard, These design equations are based on experimental evidence (Winter, 1970; Hetrakul and Yu, 1978) and the assumed distributions of loads or reactions into the web as shown in Figure C3.3.6(4), The assumed distributions of loads or reactions into the web, as shown in Figure C3.3.6(4), are independent of the flexural response of the beam. Due to flexure, the point of bearing will vary relative to the plane of bearing resulting in non-uniform bearing load distribution into the web. The value of R, will vary because of a transition from the interior one-flange loading (sce Figure C3.3.6(4)(b)) to the end one-flange loading condition (see Figure C3.3.6(4)(a)). ‘These discrete conditions represent the experimental basis on which the design provisions were founded (Winter, 1970; Hetrakul and Yu, 1978). From Tables 3.2.6(1) and 3.3.6(2) in the Standard, it can be scen that the nominal capacity for concentrated load or reaction of cold-formed steel beams depends on the ratios of diltg, Ito Filly, the web thickness (1(¢,)), the yield stress (_f), and the web inclination angle (8). With regard to the limit states design approach, the use of , equal to 0.75 for single unreinforced webs and @, equal to 0.80 for I-sections provide values of safety index ranging from 2.4 to 3.8 Recent research indicated that a Z-seetion having its end support flange bolted to the section's supporting member through two 12.7 mm diameter bolts will experience an increase in end-one-flange web crippling capacity (Bhakta, LaBoube and Yu, 1992; Cain, LaBoube and Yu, 1995). The increase in load-carrying capacity was shown to range from 27 to $5% for the sections under the limitations prescribed in the Standard. A lower ‘bound value of 30% increase is permitted in Clause 3.3.6 of the StandardAccessed by BHP BILLITON on 27 Jun 2002 21505 ese Interior one-flange End one-flange tossing loading {a} One interior and one end one-flange loacing Interior two-tlange Interior two-tlange loading loading | I< 150 LH «150; Jf < asa, <1805 End one-tlange Interior two-tlange End two-tlange loading loading toaving (b} Three interior two-tlange, one ené one-tlange and one end two-tlange loading End one-tlange End two-tlange loading loading Interior one-tlange Th = or [Teel {ec} One interior one Loe Fl n9®, one ond one-tlange and one and two-flange loading FIGURE C3.3.6(3) APPLICATION OF DESIGN EQUATIONS GIVEN IN TABLES 3.3.6(1) AND 3.3.6(2) OF THE STANDARD‘Accessed by BHP BILLITON on 27 Jun 2002 (a) End one-tlange loading co bisa, Disa, (b} Interior one-tlenge loading | <18d,4 besa, I 184, (6) Interior two-tlange loading + FIGURE C3.3.6(4) ASSUMED DISTRIBUTION OF REACTION OR LOAD‘Accessed by BHP BILLITON on 27 Jun 2002 €3.3.7 Combined bending and bearing Clause 33.7 of the Standard contains interactions for the combination of bending and bearing. Clauses 3.3.7(a) and 3.3.7(b) of the Standard are based on the studies conducted at the University of Missouri-Rolla for the effect of bending on the reduction of web crippling loads with the applicable capacity factors used for bending and bearing (Hetrakul and Yu, 1978 and 1980; Yu, 1981 and 1991). Figures C3.3.7(1) and C3.3.7(2) show the correlations between the interactions and test results. For embossed webs, bearing should be determined by tests in accordance with Section 6 of the Standard, The exception included in Clause 3.3.7 of the Standard for single unreinforced applies to the interior supports of continuous spans using decks and beams, as shown in Figure C3.3.7(3). Results of continuous beam tests of steel decks (Yu, 1981) and several independent studies by manufacturers indicate that, for these types of members, the post-buckling behaviour of webs at interior supports differs from the type of failure mode occurring under concentrated loads on single span beams. This post-buckling strength enables the member to redistribute the moments in continuous spans. For this reason, the interaction in Clause 3.3.7(2) of the Stondard is not applicable to the interection between bending and the reaction at interior supports of continuous spans. This exception applies only to the members shown in Figure C3.3.7(3) and similar situations explicitly described in Clause 3.3.7 of the Standard. The exception should be interpreted to mean that the effects of combined bending and bearing need not be checked for determining load-carrying capacity. Furthermore, the positive bending resistance of the beam should be at least 90% of the negative bending resistance in order to ensure the safety specified by Clause 3.3.7 of the Standard. Using this procedure, serviceability loads may— (a) produce slight deformations in the beam over the support; (b) increase the actual compressive bending stresses over the support to as high as 0.8 f3 and (©) result in additional bending deflection of up to 22% due to elastic moment redistribution, If load-carrying capacity is not the primary design concern because of the above behaviour, the designer is urged to ignore the exception in Clause 3.3.7(a) of the Standard With regard to Clause 3.3.7(b) of the Standard, previous tests indicate that when the dy/ty ratio of an I-beam web does not exceed 233/\/,J£ and when 10.673, the bending moment has little or no effect on the web crippling load (Yu, 1991). For this reason, the permissible reaction or concentrated load can be determined by the equations given in Clause 3.3.6 of the Standard without reduction for the presence of bending, In the development of the limit states equations, a total of $51 tests were calibrated for combined bending and bearing. Based on $, equal to 0.75 for single unreinforced webs and 6,, equal to 0.80 for L-sections, the values of safety index vary from 2.5 to 3.3,‘Accessed by BHP BILLITON on 27 Jun 2002 12 10} o8| 2 O48 oy, ity of Mi °, oe 25 jg score wives cae, SR eS renee a eg L 009208 FIGURE ©3.3.7(1) GRAPHIC PRESENTATION FOR WEB CRIPPLING AND COMBINED. WEB CRIPPLING AND SENDING FOR SINGLE UNREINFORCED WEBS 10) o| os oa 02> University of Missouri-Rolla data| 4 Cornell University data L L L 0092 04 06 08 10 Frost Ae FIGURE C3.3.7(2) INTERACTION BETWEEN WEB CRIPPLING AND BENDING FOR IBEAMS HAVING UNREINFORCED WEBS‘Accessed by BHP BILLITON on 27 Jun 2002 JS \n J ln TF (al Decks Deck or cladging r T L La (0) Beams Deck, cladding X + <250 mm FIGURE €3.3.7(3) SECTIONS USED FOR EXCEPTION OF CLAUSE 3.3.7(a) OF THE STANDARD €3.4 CONCENTRICALLY LOADED COMPRESSION MEMBERS Depending on the configuration of the cross-section, thickness of material, unbraced length, and end restraint, axially loaded compression members should be designed for the following ultimate limit state conditions: (a) Yielding It is well known that a very short, compact column under an axial load may fail by yielding. The yield load is determined by the following equation: Nw Ads c3.4() where A, = gross area of the column f, = yield stress of steel (b) Overall column buckling (flexural buckling, torsional buckling or flexural-torsional buckling) (i) Flexural buckling of columns (A) Elastic buckling stress A slender, axially loaded column may fail by overall flexural buckling if the cross-section of the column is a doubly-symmetric shape, closed shape (square or rectangular tube), cylindrical shape, or point-symmetric shape. For singly-symmetric shapes, flexural buckling is one of the possible failure modes. Wall studs connected with sheeting material can also fail by flexural buckling. ‘The clastic critical buckling load for a long column can be determined by the following Euler formula: ~ eH «a? N, loc 3.42)‘Accessed by BHP BILLITON on 27 Jun 2002 (B) where = column buckling load in the elastic range modulus of elasticity ‘ond moment of area = effective length factor 1 =unbraced length Accordingly, the elastic column buckling stress can be caleulated as follows: fy) Noe 3.403) oem c where 1 = radius gyration of the fll erose-sction Lr = the effective slenderness ratio Inelastic. buckling stress When the clastic column buckling stress calculated using Equation C3.4(3) exceeds the proportional limit (f), the column will buckle in the inelastic range, Prior to 1996, th following cquation was used in the AISI Specification for calculating the inelastic column buckling stress: (4 Godt "ht ~ ©3.4(4) xis] It should be noted that because Equation C3.4(4) is based on the assumption that f, is equal to fy, itis applicable only for (f,), greater than or equal to 72 By using 2, as the column slenderness parameter instead of the snderness ratio (//r), Equation C3.4(4) can be rewritten as follows: 3.4(5) fh - | AK 3.46 \Ge 18 Ke) Accordingly, Equation C3.4(5) is applicable only for %, Tess than or equal to y2 In AS 15381988, the Perry curve (Ayston and Perry (1986)) was used to define the column strength since geometric imperfections were included in the column design philosophy used in Australia. The Perry curve gives a lower column strength than Equation 3.4(5) in the Standard due to the inclusion of imperfections.‘Accessed by BHP BILLITON on 27 Jun 2002 ) ) Design compressive axial force for locally stable columns It the individual components of compression members have small bit rati ‘ocal buckling will not occur before the compressive stress reaches the column buckling stress and the yield stress of steel. Therefore, the ‘nominal axial strength can be determined as follows: N 7 Ay Vocdicnt 3.4(7) where N. = nominal member capacity of the member in compression A, = gross area of the column Gram = column buckling stress (clastic or inclastie as appropriate) Design compressive axial force for locally unstable columns For cold-formed steel compression members with large b/t ratios, local ‘buckling of individual component plates may occur before the applied load reaches the nominal axial strength determined by Equation C3.4(7). The interaction effect of the local and overall column buckling may result in a reduction of the overall columa strength. From 1946 through 1986, the effect of local buckling on column. strength was considered "in the AISI Specification and AS 1538—1988 by using a form factor (Q) in the determination of the permissible stress for the design of axially loaded compression members (Winter, 1970; Yu, 1991). Even though the Q-factor method was used successfully for the design of cold-formed steel compression members, research work conducted at Comell University and other institutions has shown that this method is capable of improvement. On the basis of the test results and analytical studies of DeWolf, Pekiz, Winter, and Mulligan (DeWolf, Pekéz and Winter, 1974; Mulligan and Pekiz, 1984) and Pek62's development of a unified approach for the design of cold-formed steel members (Pek6z, 1986b), the Q-factor ‘method was eliminated in the 1986 edition of the AISI Specification Im order to reflect the effect of local buckling on the reduction of column strength, the nominal axial strength is determined by the critical column buckling stress and the effective area (A,) instead of the full sectional area. For a more in depth discussion of the background for these provisions, see Pekéz (1986b). Therefore, the nominal member capacity of cold-formed steel compression members can be determined by the following equation: NT Adit ©3.4(8) where (/,)eq1 i8 the column buckling stress (clastic or inclastic as appropriate). An exception for Equation C3.4(7) is for C-shapes and Z-shapes, and single-angle sections with unstiffened flanges. For these cases, the nominal axial strength is also limited by the following capacity, which is determined by the local buckling stress of the unstiffened element and the area of the full cross-section as follows: y ~ ABED 257 \ 1) 63.419)‘Accessed by BHP BILLITON on 27 Jun 2002 Equation C3.4(9) was included in Section C4(b) of the 1986 edition of the AISI Specification when the unified design approach was adopted. A recent study conducted by Rasmussen at the University of Sydney (Rasmussen, 1994) indicated that the design provisions of, Section C4(b) of the 1986 AISI Specification lead to unnecessarily and excessively conservative results. This conclusion was based on the analytical studies carefully validated against test results as reported by Rasmussen and Hancock (1992). Consequently, Section C4(b) of the AISI Specification (Equation C-C4(9)) was deleted in 1996 and is not included in the Standard. In the AISI Specification, the design equations for calculating the critical stress have been changed from those given by Equations C3.4(3) and C3.4(4) to those used in the AISC LRFD Specification (AISC, 1993), As given in Clause 3.4.1 of the Standard, these design regulations are as follows: For 4.21.5: f, = (0.658 |p, 3.410) For 2.91.5: f, » [2877 3.41) where s f= critical stress which depends on the value of Re VFI (ioe = clastic flexural buckling stress calculated using Equation C3.4(3), Consequently, the equation for determining the nominal axial strength can be written as follows: Nom Ahy 3.4(12) which is Equation 3.4.2(2) of the Standard with f equal 19 UG), The reasons for changing the design equations from Equation C3.4(4) to Equation C3.4(10) for inelastic buckling stress. and from Equation C3.4(3) to Equation C3.4(11) for elastic buckling stress are as follows: (1) The revised column design equations (Equations C3.4(10) and C3.4(11) were shown to be more accurate by Pekéz and Sumer (1992), In this study, 299 test results on columns and beam-columns were evaluated. The test specimens included members with component elements in the post-local buckling range as well as those that were locally stable. The test specimens included members subject to flexural buckling as well as flexural- torsional buckling. (2) Because the revised column design equations represent the maximum strength with due consideration given to initial erookedness and can provide a better fit to test results, the required factor of safety can be reduced. In addition, the revised equations enable the usc of a single capacity factor for all i, values even though the nominal member capacity of columns decreases as the slenderness increases because of initial out-of- straightness,‘Accessed by BHP BILLITON on 27 Jun 2002 The design provisions included in the AISI Specification (AISI, 1986), the AISI-LRFD Specification (AISI, 1991), the combined ASDILRFD Specification (AISI, 1996) and the Standard are shown in Figure C3.4()) AISI-1986 and 1991 Equation C3.4(4) Equation C3.4(103 {Equation 63.4(3 AISI-1996 and AS/NZS 4600: 1996: Equation C3.4(1 ogh fer 7, 06 fy fn os fy o2b 00 05 1 15 2 de FIGURE C3.4(1) COMPARISON BETWEEN THE CRITICAL BUCKLING STRESS. © EQUATIONS. Effective length factor (k) The effective length factor (K) accounts for the influence of restraint against rotation and translation at the ends of a colamn on its load-carrying capacity. For the simplest case, a column with both ends hinged and braced against lateral translation, buckling occurs in a single half-wave and the effective length (1. is equal to ki being the length of this half-wave, is equal to the actual physical length of the column (see Figure C3.4(2)); correspondingly, for this case, k is cqual to 1. This situation is approached if @ given compression member is part of a structure that is braced in such @ ‘manner that no lateral translation (sidesway) of one end of the column relative to the other can occur. This is so for columns or studs in a structure with diagonal bracing, diaphragm bracing, shear-wall construction or any other provision that prevents _ horizontal displacement of the upper relative to the lower column ends, In these situations, itis safe and only slightly, if at all, conservative to take & equal to 1‘Accessed by BHP BILLITON on 27 Jun 2002 Nw FIGURE C3.4(2) OVERALL COLUMN BUCKLING If translation is prevented and abutting members (including foundations) at one or both ends of the member are rigidly connected to the column in a manner that provides substantial restraint against rotation, k values smaller than 1 are sometimes justified. Table C3.4 gives the theoretical k values for six idealized conditions in which joint rotation and translation are either fully realized or non-existent Table C3.4 also includes the & values recommended by the Structural Stability Research Council for design use (Galambos, 1988), In trusses, the intersection of members provides rotational restraint to the compression members at service loads. As the collapse load is approached, the member stresses approach the yield stress, which greatly reduces the restraint they can provide. For this reason, the k value is usually taken as unity regardless of whether they are welded, bolted, or connected by screws. However, when sheeting is attached directly to the top flange of @ continuous compression chord, recent research (Harper, LaBoube and Yu, 1995) has shown that the & values may be taken as 0.75 (AISI, 1995). On the other hand, when no lateral bracing against sidesway is present, such as in the portal frame shown in Figure C3.4G3), the structure depends on its own bending stiffness for lateral stability. In this case, if buckling of the columns were to occur, it invariably takes place by the sidesway motion shown, This occurs at a lower load than the columns would be able to carry if they were braced against sidesway and the figure shows that the half-wave length into which the columns buckle is longer than the actual column length. Hence, in this case, & is larger than I and its value can be read from the graph shown in Figure C3.4(4) (Winter, et al. 1948a and 1970). Since column bases are rarely either actually hinged or completely fixed, k values between the two curves should be estimated depending on actual base fixity.Accessed by BHP BILLITON on 27 Jun 2002 EFFECTIVE L NGTH TABLE C: FACTORS (k) FOR CONCENTRICALI COMPRESSION MEMBERS @ o © @ © © Buckled shape of column i shown by dashed line Theoretical & value 05 07 10 Lo 20 20 Revommended F value when ideal conditions exe | 0.65 | 0.80 12 Lo 2.10 20 approximated End contition code Rotation fixed, translation fixed Rotation free, translation fixed Rotation fixed, trazsation fee Rotation free, ransation free FIGURE €3.4(3) | 7 wt -| r | LATERALLY UNBRACED PORTAL FRAM:‘Accessed by BHP BILLITON on 27 Jun 2002 50 40 | Hinged 30 base W seam WA cotumn 20 Fixed 10} \ base 7+ FIGURE C3.4(4) EFFECTIVE LENGTH FACTOR (k) IN LATERALLY UNBRACED. Gi) PORTAL FRAMES Figure C3.4(4) can also serve as a guide for estimating & for other simple situations. For multi-bay or multi-storey frames, of both, simple alignment charts for determining k are given in the AISC Commentaries (AISC, 1989; 1993). For additional information oa frame stability and second order effects, see SSRC Guide 10 Stability Design Criteria for Metal Structures (Galambos, 1988) or the Commentaries to AS 4100—1998 or NZS 3404:1997. The Australian Standard AS 4100—1998 and NZS 3404:1997 give graphs for determining effective length factors for sway and non-sway frames. If roof or floor slabs, anchored to shear walls or vertical plane bracing systems, are counted upon to provide lateral support for individual columns in a building system, their stiffness should be considered when functioning as horizontal diaphragms (Winter, 1958). Torsional buckling of columns As pointed out at the beginning of this Clause, purely torsional buckling, i.e, failure by sudden twist without concurrent bending, is also possible for certain thin-walled open shapes. These are all point-aymmetric shapes in which the shear ceatre and centroid coincide, such as doubly-symmetric I-shapes, anti-symmetric Z-shapes and such unusual sections as cruciforms, swastikas, and the like, Under concentric load, torsional buckling of such shapes very rarely governs design. This is so because such members of realistic slendemess will buckle fAlexurally or by a combination of flexural and local buckling at loads smaller than those which would produce torsional buckling. However, for relatively short members of this type, catefully dimensioned to minimize local buckling, such torsional buckling cannot be completely ruled out. If such buckling is clastic, it occurs at the critical stress (f,,) calculated as follows (Winter, 1970): 3.4(13)‘Accessed by BHP BILLITON on 27 Jun 2002 Equation C3.4(13) is the same as Equation 3.3.3.2(12) in the Standard— G = shear modulus J = St. Venant torsion constant of the cross-section A. = full cross-sectional area 4, = polar radius of gyration of the cross-section about the shear centre 1, = torsional warping constant of the cross-section 1, ~ effective length for twisting For inelastic buckling, the critical torsional buckling stress can also be calculated using Equations C3.4(10) and C3.4(11) and using f,, instead of f,. (iii) Flexural-torsional buckling of columns Concentrically loaded columns can buckle in the flexural buckling mode by bending about one of the principal axes; or in the torsional buckling mode by twisting about the shear centre; or in the flexural-torsional buckling mode by simultaneous bending and twisting. For singly-symmetric shapes such as channels, hat sections, angles, T-seetions, and I-sections with unequal flanges, for which the shear centre and centroid do not coincide, flexural-torsional buckling is one of the possible buckling modes as shown in Figure C3.4(5). Non-symmetric sections will always buckle in the flexural-torsional mode. Centrois a) I FIGURE C3.4(5) TORSIONAL-FLEXURAL BUCKLING OF A CHANNEL IN AXIAL, COMPRESSION It should be emphasized that one needs to design for flexural-torsional buckling only when it is physically possible for such buekling to occur. This, means that if a member is so connected to other parts of the structure, such as wall sheeting, that it can only bend but cannot twist, it needs to be designed for flexural buckling only. This may hold for the entire member or for individual parts. For instance, a channel member in a wall or the chord of a roof truss is easily connected to girts or purlins in a manner that prevents‘Accessed by BHP BILLITON on 27 Jun 2002 twisting at these connection points. In this case, flexural-torsional buckling needs to be checked only for the unbraced lengths between such connections. Likewise, a doubly-symmetrie compression member can be made up by connecting two spaced channels at intervals by batten plates, In this case, each channel constitutes an ‘intermittently fastened component of a built-up shape’. Here, the entire member, being doubly-symmetric, is not subject to flexural-torsional buckling so that this mode needs to be checked only for the individual component channels between batten connections (Winter, 1970), The governing elastic flexural-torsional buckling load can be calculated using the following equation (Chajes and Winter, 1965; Chajes, Fang and Winter, 1966; Yu, 1991); 3.44) If both sides of this equation are divided by the cross-sectional area (4), one obtains the equation for the clastic, flexural-torsional buckling stress (f,.) as follows: fox * Sou) 4B fon Soy 1 ; fos” 5p Vix * Sa) ~ c3.ac15) In Equation C3.4(15) as in all provisions which deal with flexural-torsional buckling, the x-axis is the axis of symmetry: f= #'E/(lgir,) is the flexural (Buler) buckling stress about the x-axis, fis the {orsional buckling stress (see Equation C3.4(13)) and B = 1 (xr) It is worth noting that the flexural-trsional buckling stress is always lower than the Buler stress (f,) for flexural buckling about the symmetry axis, Hence, for these singly-symmetric sections, flexural buckling can only oceur, if at all, about the y-axis which is the principal axis perpendicular to the axis of symmetry For inclastic buckling, the critical flexural-torsional buckling stress can also be calculated by using Equations C3,14(10) and C3.14(11), An inspection of Equation C3.14(15) will show that in order to calculate B and fo. it is necessary to determine x, equal to the distance between the shear centre and centroid, J equal to the St. Venant torsion constant and /, equal to the warping constant, in addition to several other, more familiar cross- sectional properties. Because of these complexities, the calculation of the flexuralstorsional buckling stress cannot be made as simply as that for flexural buckling. Equations for these properties are given in Paragraph El of Appendix E of the Standard Any singly-symmetric shape can buckle either flexurally about the y-axis or flexurally-torsionally, depending on its detailed dimensions, For instance, @ channel stud with narrow flanges and wide web will generally buckle flexurally about the y-axis (axis parallel to web); in contrast, a channel stud with wide flanges and a narrow web will generally fail in flexural-torsional buckling‘Accessed by BHP BILLITON on 27 Jun 2002 The above discussion refers to members subject to fMexural-torsional buckling, but made up of elements whose bt ratios are small enough so that no local buckling will occur. For shapes that are sufficiently thin, ic. with bit ratios sufficiently large, local buckling can combine with’ flexural- torsional buckling similar to the combination of local with flexural buckling, For this case, the effect of local buckling on the flexural-torsional buckling strength can also be handled by using the effective arca (4,) determined the stress (f) for Mlexural-torsional buckling. (©) Local buckling of individual elements (See Item (b)(i(D).) (@ Distortional buckling (See Clause C3.4.6.) 3.4.2 Sections not subject to torsional or flexural-torsional buckling If concentrically loaded compression members can buckle in the flexural buckling mode by bending about one of the principal axes, the nominal flexural buckling strength of the column should be determined in accordance with Clause 3.4.1 of the Standard. The clastic Mexural buckling stress is calculated using Equation 3.4.2 of the Standard, which is the same as Equation C3.4(3). This provision is applicable to doubly-symmetric sections, closed cross-sections and any other sections not subject to torsional or flexural-torsional buckling, €3.4.3. Doubly- or _ singly-symmetric sections flexural-torsional buckling As discussed in Clause C the possible buckling modes for doubly- and point-symmetric sections. For singly- symmetric sections, flexural-torsional buckling is one of the possible buckling modes, The other possible buckling mode is flexural buckling by bending about the y-axis (ie. assuming x-axis is the axis of symmetry). subject to torsional or 4, torsional buckling is one of For torsional buckling, the elastic buckling stress can be calculated using Equation C3.4(13). For flexural-torsional buckling, Equation C3.4(15) can be used to calculate the elastic buckling stress. The following simplified equation for elastic flexural torsional buckling stress is an alternative permitted by the Standard. Soa tox 3416 Tou > Sos “9 Equation C3.4(16) is based on the following relationship given by Pekox and Winter (1969a). 3.417) 3.418) teh Soc Sow 3.4.4 Point-symmetric sections Point-symmetric sections either buckle flexurally or torsionally, and so the lower buckling load is chosen. €3.4.5 Non-symmetric sections For non-symmetric open shapes, the analysis for flexural-torsional buckling becomes extremely tedious unless its need is sufficiently frequent to warrant computerization, For one thing, instead of the quadratic equations, a cubic equation has to be solved. For another, the calculation of the required section properties, particularly /,, becomes quite complex. Clause 3.4.5 of the Standard specifi that calculation in accordance with this Clause shall be used or tests in accordance with Section 6 shall be made when dealing with non-symmetric open shapes.‘Accessed by BHP BILLITON on 27 Jun 2002 3.4.6 Singly-symmetrie sections subject to distortional buckling Some singly-symmetric sections such as the storage rack columns shown in Figure C3.4.6 are particulary sensitive to distortional buckling in the modes shown. Distortional buckling in this mode was investigated in detail by Hancock (1985) mainly for sections used in steel storage racks, by Lau and Hancock (1987, 19882, 1988b, 1990) and by Kwon and Hancock (19928, 1992) for high-strength’ stecl channel 'scetions with intermediate stiffeners, The elastic distortional buckling stress (f,) can be based on a rational elastic buckling analysis such as that given in Papangelis and Hancock (1995), or in Paragraphs DI and D2 of Appendix D of the Standard, which are based on Lau and Hancock (1987). The equation for the critical stress (f,) is developed in Hancock, Kwon and Bernard (1994). It is normally not necessary to” check simple lipped channels in accordance with Clause 3.4.6, because they are adequately designed by Clause 2.4.3 of the Standard for the distortional mode. FIGURE 3.4.6 DISTORTIONAL BUCKLING MODES OF SINGLY SYMMETRIC COMPRESSION MEMBERS 3.4.7 Columns with one flange through-fastened to sheeting For axially loaded C-sections or Z-sections having one flange attached to deck or sheeting, and the other flange unbraced, e.g. a roof purlin or wall girt subjected to wind or seismic-generated compression forces, the axial load capacity is less than a fully braced member, but greater than an unbraced member. The partial restraint relative to weak axis buckling is a function of the rotational stiffness provided by the panel-to-purlin connection. Equation 3.4.7 in the Standard is used to calculate the weak axis capacity. This Equation is not valid for sections attached to standing seam or clip-fastened roofs. The Equation was developed by Glaser, Kachler and Fisher (1994) and is also based on the work contained in the reports of Hatch, Easterling and Murray (1990) and Simaan (1973), A limitation on the maximum yield point of the C-section or Z-section is not given in the Standard since Equation 3.4.7 of the Standard is based on elastic buckling criteria. A limitation on minimum length is not contained in the Standard because Equation 3.4.7 is conservative for spans less than 4.5 m. As indicated in Clause 3.4.7 of the Standard, the strong axis axial load capacity is determined assuming that the weak axis of the strut is braced, and so Clauses 3.5.1 and 3.5.2 of the Standard should be used ‘The controlling axial capacity (weak or strong axis) is suitable for use in the combined axial load and bending equations in Clause 3.5 of the Standard (latch, Easterling, and Murray, 1990).‘Accessed by BHP BILLITON on 27 Jun 2002 €3.5_ COMBINED AXIAL LOAD AND BENDING In the 1996 edition of the AISI Specification, the design provisions for combined axial load and bending were expanded to include expressions for the design of members subject to combined tensile axial load and bending, These additional expressions are also included in the Standard, C351 Combined axial compressive load and bending Cold-formed steel members under a combination of compressive axial load and bending are usually referred to as ‘beam-columns. The bending may result from eccentric loading, transverse loads or applied. moments. Such members are often found in framed structures, trusses and exterior wall studs. For the design of such members, interactions have been developed for locally stable and unstable beam-columns on the basis of thorough comparisons with rigorous theory and verified by the available test results (Pekiz, 1986a; Pek6z and Sumer, 1992), The structural behaviour of beam-columns depends on the shape and dimensions of the cross-section, the location of the applied eccentric load, the column length, the end restraint and the condition of bracing, When a beam-column is subject to an axial load (N*) and end moments (M*) as shown in Figure C3.5.1, the combined axial and bending stress in compression is calculated using the following equation, as long as the member remains straight: Nt ~-N Mw 35.11 Lrg a hth where f* = combined stress in compression ff = axial compressive stress J = bending stress in compression N* = applied axial load A = cross-sectional area M* = applied bending moment Z = clastic section modulus It should be noted that in the design of such a beam: the combined stress should be limited to a certain stres ths OR, FOF* If the left-hand term in Equation C3.5.1(2) is multiplied by the area (4) in the numerator and demoninator, and the right-hand term is multiplied by the section modulus in the ‘numerator and denominator, then Equation (2) becomes— olumn by using the limiting stress (F), that is— 10 €3.5.12) Net 5103) VM s10 3.5.16, OM, ° where N* = applied axial load = a‘Accessed by BHP BILLITON on 27 Jun 2002 1, = axial section capacity =AF M* ~ applied moment =ZR M, = bending section capacity a If the axial section capacity is reduced by the capacity factor (0,) for compression and the bending section capacity is reduced by the capacity factor ($,) for bending, then Equation C3.5.1(3) becomes— v 7 aN,” OM, ~ 10 35.104) Equation C3.5.1(4) is well-known, and has been adopted in some specifications and Standards for the design of beam-columns. It can be used with reasonable accuracy for short members and members subjected to a relative small axial load. It should be realized that in practical applications, when end moments are applied to the member, it will be bent as shown in Figure C3.5.1(b) due to the applied moment (M*), the secondary ‘moment resulting from the applied axial load (N*) and the deflection (5) of the member. ‘The maximum bending moment at mid-length (point C) can be calculated as follows Mig €3.5.165) a, whore May. maximum bending moment at midlength M* = applied end moments «, amplification factor The amplification factor (0,) may be ealeulated as follows: Ny 5 -1-¥ 35.16 «, x 6) where NV, = elastic column buckling load (Buler load) = wie, If the maximum bending moment (M",,,,.) is used to replace M*, the following equation can be obtained from Equation C3.5.14) and Equation C3.5.1(6) as follows: NM oN, <10 3.5.10) Moa, For members that can buckle under axial compression, as described in Clause C3.4, N, is replaced by N. and for members that can buckle laterally or distortionally, as described in Clause C3.3, M, is replaced by M,, so that— ue we ON, OyMye, = 10 C3.5.1(8)‘Accessed by BHP BILLITON on 27 Jun 2002 It has been found that Equation C3.5.1(8), developed for a member subjected to an axial compressive load and equal end moments, can be used with reasonable accuracy for braced members with unrestrained ends subjected to an axial load and a uniformly distributed transverse load, However, it could be conservative for compression members in unbraced frames (with sidesway), and for members bent in reverse curvature. For this reason, the Equation C3.5.1(8) should be further modified by a coefficient (C,) as given in Equation C3,5.1(9) to account for the effect of end moments — GM" ON Oia Equation C3.5.1(9) forms the basis of Clause 3.5.1(a) of the Standard, = 10 35.10) In Equation €3.5.1(9), C, can be determined for one of the three cases specified in Clause 3.5.1 of the Standard. It can be calculated using Equation C3.5.1(10) for restrained compression members braced against joint translation and not subject to transverse Ioading (Case ii) as follows: os - 04 {2} (Ms) €3.5.1(10) where MyM, is the ratio of the smaller to the larger end moments. For Case (iii), C, may be approximated by using the value given in the AISC Commentaries for the applicable condition of transverse loading and end restraint (AISC, 1989 and 1993), When the maximum moment occurs at braced points, Equation C3.5.1(11) Gc. Clause 3.5.1(b) of the Standard) should be used to check the member at the braced ends as follows, + ON, OyMy Furthermore, for the condition of small axial load, the influence of C,/at, is usually small and may be neglected. Therefore, when N*/9.N, $0.15, Equation C3.5.1(4) may be used for the design of beam-columns. €3.5.1(11) If a second-order clastic analysis is performed in accordance with Appendix E of AS 4100—1998 or NZS 3404:1997, then it is appropriate to use the second-order elastic moments in place of the first order elastic moments (M*) in Equation C3.5.1(9), and the value of C,/a, may be taken as 1.0 since the effect of non-uniform moment and the moment amplification are now included in the determination of the second order moments, €3.5.2 Combined axial tensile load and bending The design criteria included in Clause 3.5.2 of the Standard are new requirements. These provisions apply to concurrent bending and tensile axial load. If bending can occur without the presence of tensile axial oad, the member should also conform to the provisions of Clause 3.3 of the Standard, Care should be taken not to overestimate the tensile load, as this would be unconservative. Clause 3.5.2(a) of the Standard provides a design criterion to prevent failure of the compression flange. Clause 3.5.2(b) of the Standard provides a design criterion to prevent yielding of the tension flange of a member under combined tensile axial load and bending,‘Accessed by BHP BILLITON on 27 Jun 2002 ta) (o) FIGURE 03.5.1 BEAM-COLUMN SUBJECTED TO AXIAL LOADS AND END MOMENTS 3.6 CYLINDRICAL TUBULAR MEMBERS Thin-walled cylindrical tubular members are economic sections for compression and torsional members because of their large ratio of radius of gyration to area, of having the same radius of gyration in all directions and their large torsional rigidity. Like other cold-formed steel compression members, cylindrical tubes should be designed to provide adequate safety not only against overall column buckling but also against local buckling. It is well known that the classical theory of local buckling of longitudinally compressed cylinders overestimates the actual buckiing strength and that inevitable imperfections and residual stresses reduce the actual strength of compressed tubes radically below their theoretical value. For this reason, 1! design provisions for local buckling have been based largely on test results. Considering the post-buckling behaviour (local buckling stress) of the axially compressed cylinder and the important effect of the initial imperfection, the design provisions included in the Standard were originally based on Plantema’s graphic representation and the additional results of cylindrical shell tests made by Wilson and Newmark at the University of Illinois (Winter, 1970). From the tests of compressed tubes, Plantema found that the ratio ff, depends on the parameter (£if,) (UD) in which t is the wall thickness, D is the mean diameter of the tubes and fo, is the ultimate stress or collapse stress. As shown in Figure C3.6(1), Line | corresponds to the collapse stress below the proportional limit, Line 2 corresponds to the collapse stress between the proportional limit and the yield point, and Line 3 represents the collapse stress occurring at the yield point. In the range of Line 3, local buckling will not occur before yielding. In ranges 1 and 2, local buckling occurs before the yield point is reached. The cylindrical tubes should be designed to safeguard egainst local buckling, Based on a conservative approach, the Standard specifies that when the d,/f ratio is smaller than or equal to 0.112Eif,, the tubular member should be designed for yielding, This provision is based on point 4,, for which (B/f,) (t/d,) is equal to 8.93 When 0.1126/f, < d/t < 0.4412/f,, the design of tubular members is based on the inelastic local buckling criteria, For the purpose of developing a design equation for inelastic buckling, point B, was selected to represent the proportional limit, For point B,, the maximum stress of cylindrical tubes can be calculated as follows: (F) la}- 227 3.6(1)‘Accessed by BHP BILLITON on 27 Jun 2002 fo \ (4 5 #2 - 00x F[ 3.62) h 4) (de) When dit 2 0.441 Bf, the following equation represents Line 1 for the elastic local buckling stress fon (£ (2) Fa ~ o529(4|(4) 3.603) hy Vel\4, ce Inelastic bucking, Yielding bucking rm) i © ; ' ors uation 3.62) os ' | | | Equation c3.610) | | | | = OMA E/H) For dp/t = 0.412 EM, / For te iy 227 @93 0 3 4 6 8m z FIGURE C3.6(1) CRITICAL STRESS OF CYLINDRICAL TUBES FOR LOCAL BUCKLING The correlation between the available test data and Equations C3.6(1) and C: shown in Figure C3.6(2) 6.3) is It should be noted that the design provisions of Clause 3.6 of the Standard are applicable only for members having a ratio of outside diameter-to-wall thickness (d,/f) not greater than 0.441 EVf, because the design of extremely thin tubes will be governed by clastic local buckling resulting in an uneconomical design, In addition, cylindrical tubular members with unusually large d,/t ratios are very sensitive to geometric imperfections.‘Accessed by BHP BILLITON on 27 Jun 2002 oa ° “eatin cei § Sena gmat, ° L L L L 14 FIGURE 3.6(2) CORRELATION BETWEEN TEST DATA AND CRITERIA FOR LOCAL BUCKLING OF CYLINDRICAL TUBES UNDER AXIAL COMPRESSION €3.6.2. Bending For non-slender cylinders in bending, the initiation of yielding does rot represent a failure condition as is generally assumed for axial loading. Failure is at the plastic moment capacity which is at least 1.29 times the moment at first yielding. In addition, the conditions for inelastic local buckling are not as severe as in axial compression due to the stress gradient. Equations 3.6.2(1), 3.6.2(2) and 3.6.2(3) in the Standard are based upon the work reported. by Sherman (1985) and an assumed minimum shape factor of 1.25. This slight reduction in the inelastic range has been made to limit the maximum bending stress to 0.75/,. a value typically used for solid sections in bending for the permissible stress method. The reduction also brings the criteria closer to a lower bound for inclastic local buckling. A small range of elastic local buckling has been included so that the upper d,/t limi 0.44 1LBif, is the same as for axial compression. All three equations in Clause 3.6.2 of the Standard for determining the nominal flexural strength of cylindrical tubular members are shown in Figure C3.6.2. These equations have been used in the AISI Specification since 1986 and are retained in the 1996 Specificatio: and the Standard. The capacity factor ($,) is the same as that used in Clause 3.3.2 of the Standard for sectional bending strength.‘Accessed by BHP BILLITON on 27 Jun 2002 14 Equation 3.6.2(1) g/t = O.AME/, agit = OS19E/t, g/t = OEM, FIGURE (3.6.2 NOMINAL FLEXURAL STRENGTH OF CYLINDRICAL TUBULAR MEMBERS. €3.6.3. Compression When cylindrical tubes are used as concentrically loaded compression members, the nominal axial strength is determined by the same equation as given in Clause 3.4 of the Standard, except that— (a) the nominal buckling stress (f,.) is determined only for flexural buckling; and (b) the effective area (4,) is calculated as follows: €3.6.3(1) €3.6.3(2) 3.6.33) where A is the area of the unreduced cross-section. The capacity factor (},) is the same as that used in Clause 3.4 of the Standard for compression members, Equation C3.6.3(3) is used for calculating the reduced area due to local buckling. It is derived from Equation C3.6(2) for inelastic local buckling stress (Yu, 1991), €3.6.4 Combined bending and compression The interactions given in Clause 3.5 of the Standard can also be used for the design of cylindrical tubular members when these members are subject to combined bending and compression.‘Accessed by BHP BILLITON on 27 Jun 2002 s STION C4 STRUCTURAL ASSEMBLIES C41 BUILT-UP SECTIONS C4.1.1 L-sections composed of two channels [-sections made by connecting two channels back to back are often used as either compression of flexural members. Cases (b) and (h) of Figure C1.3.2 and Cases (c) and (g) of Figure C1.3.3 show several built-up sections, as follows: (a) Compression members For the I-sections to be used as compression members, the longitudinal spacing of connectors should not exceed the value of s,,,, calculated using Equation 4.1.1(1) of the Standard. This prevents flexural buckling of the individual channels about the axis parallel to the web at a load smaller than that at which the entire I-section would buckle. This provision is based on the requirement that the slendemness ratio of an individual channel between connectors (Spux/Ps)) should not be greater than one-half of the pertinent slenderess ratio (li) of the entire I-seetion (Winter, 1970; Yu, 1991) and follows for one of the connectors becoming loose or ineffective. mn though Clause 4.1.1 of the Standard refers only to L-sections, ation 4.1.1(1) of the Standard can also be used for determining the maximum, spacing of welds for box-shaped compression members made by connecting two channels tip to tip. In this case, r, is the smaller of the two radii of gyration of the box-shaped section. (b) Flexural members For the L-sections to be used as flexural members, the longitudinal spacing of connectors is limited by Equation 4.1.1(2) of the Standard. The first requirement is an arbitrarily selected limit to prevent any possible excessive distortion of the top flange between connectors. The second is based the strength and arrangement of connectors and the intensity of the load acting on the beam (Yu, 1991). The maximum spacing of connectors required by Equation 4.1.1(2) of the Standard is based on the fact that the shear centre of the channel is neither coincident with nor located in the plane of the web; and that when a load (Q) is applied in the plane of the web, it produces a twisting moment (Om) about its shear centre, as shown in Figure C4.1.1(1). The tensile force of the top connector (N*) can then be calculated from the equality of the twisting moment (Qm) and the resisting moment (N*s,), as follows: Qm = N's, C41.) 4.1.12) Considering that q is the intensity of the load and that » is the spacing of connectors as shown in Figure C4.1.1(2), the applied load (Q) is equal to gs/2, The maximum spacing (jx) used in the Standard can easily be obtained by substituting the value of Q into Equation C4.1.1(2). The determination of the load intensity (q) is based upon the type of loading applied to the beam. In addition to the required strength of connections, the spacing of connectors should not bbe So great as to cause excessive distortion between connectors by separation along the top flange. In view of the fact that channels are connected back to back and are continuously in contact along the bottom flange, a maximum spacing of 1/3 may be used, Considering the possibility that one connection may be defective, a maximum spacing of Soom, equal to 1/6 i also required in Equation 4.1.1(2) of the Standard‘Accessed by BHP BILLITON on 27 Jun 2002 FIGURE C4.1.1(1) TENSILE FORCE DEVELOPED IN THE TOP CONNECTOR FOR CHANNEL FIGURE C4.1.1(2) SPACING OF CONNECTORS C4.1.2 Cover plates, sheets or non-integral stiffeners in compression When compression elements are joined to other parts of built-up members by intermittent connections, these connectors should be closely spaced to develop the required strength of the connected element, Figure C4.1.2 shows a box-shaped beam made by connecting a flat sheet to an inverted hat section. If the connectors are appropriately placed, this flat sheet will act as a stiffened compression element with a width (6) equal to the distance between rows of connectors, and the sectional properties can be calculated accordingly. This is the intent of the provisions in Clause 4.1.2 of the Standard. Clause 4.1.2(a) of the Standard requires that the necessary shear strength be provided by the same standard structural design procedure that is used in calculating flange connections in bolted or welded plate girders or similar structures. Clause 4.1.2(b) of the Standard ensures that the part of the flat sheet between two adjacent connectors will not buckle as a column (see Figure C4.1,2) at a stress less than 1.67f,, where f, is the stress at service load in the connected compression element (Winter, 1970; Yu, 1991). The AISI requirement is based on the following Euler equation for column buckling: €4.1.2(1)‘Accessed by BHP BILLITON on 27 Jun 2002 by substituting o,, equal to 1.67 f, J, equal {0 0.65 and r equal 10 #1yT2. This provision is conservative because the length is taken as the centre distance instead of the clear distance between connectors, and the effective length (J) is taken as 0.68 instead of 0.55, which is a theoretical value for a column with fixed end support. Clause 4.1.2(c) of the Standard ensures satisfactory spacing to make a row of connectors act as @ continuous line of stiffening for the flat sheet under most conditions (Winter, 1970; Yu, 1991), FIGURE (4.1.2 SPACING OF CONNECTORS IN COMPOSITE SECTION C4.2 MIXED SYSTEMS When cold-formed steel members are used in conjunction with other construction materials, the design requirements of the other material standards should be satisfied 4.3. LATERAL RESTRAINTS Bracing design requirements were expanded in the 1986 Specification to include a general statement regarding bracing for symmetrical ‘beams and columns and specific requirements for the design of roof systems subjected to gravity load. These requirements are retained with some revisions of Clause 4.3.3.4 of the Standard for the required number of braces. 4.3.2. Symmetrical beams and columns There are_no simple, generally accepted techniques for determining the required strength and stiffness for discrete braces in steel construction. Winter (1960) offered @ partial solution and others have extended this knowledge (Haussler, 1964; Haussler and Pahers, 1973; Lutz and Fisher, 1985; Salmon and Johnson, 1990; Yura, 1993; SSRC, 1993). The design engineer is encouraged to seek out the stated references to obtain guidance for the design of a brace or brace system. In the Standard, the provisions of AS 4100—1998 or NZS 3404:1997 are used for Clause 4.3.2 of the Standard. Reference should be made to Clause C543 of the Commentary to AS 4100, or to Clause C5.4.3 of the Commentary to NZS 3404:1997. The latter is augmented by the guidance given in HERA Report RA—92. 4.3.3 Channel and Z-section beams Channel and Z-sections used as beams to support transverse loads applied in the plane of the web may twist and deflect laterally unless adequate lateral supports are provided. Clauses 4.3.3.2 and 4.3.3.3 of the Standard deal with the bracing requirements when one flange of the beam is connected to deck or sheeting material, Clause 4.3.3.4 of the Standard covers the requirements for spacing and design of braces, when neither flange of the beam is connected to sheeting or is connected to sheeting with concealed fasteners €4.3.3.2 One flange connected to sheeting and subjected to wind uplift Clause 4.3.3.2 of the Standard permits the bracing not to be connected to a stiff member but be capable of preventing torsional deformation of the beam at the point of attachment, if the cleat and screw-fastening requirements of Clause 3.3.3.4, Items (ix) to (xiv), of the Standard‘Accessed by BHP BILLITON on 27 Jun 2002 are satisfied. This provision is based on testing at the University of Sydney (Hancock, Celeban and Healy (1993)) of typical Australian purlin-sheeting systems with screw- fastened sheeting, cleats and side lep fasteners. €4.3.3.3 Bracing for roof systems under gravity load The provisions of Clause 4.3.3.3 of the Standard are based on USA research where cleats are nof used at support point The design rules for Z-purlin-supported roof systems are based on a first order, elastic stiffness model (Murray and Elhouar, 1985). For the design of lateral bracing, Equations 4.3.3.3(1) to 4.3.3.3(6) of the Standard can be used to determine the restraint forces for single-span and multiple-span systems with braces at various locations. These design equations are written in terms of the cross-sectional dimensions of the purlin, umber of purlin lines, number of spans, span length for multiple-span systems, and the total load applied to the system. The accuracy of these design equations was verified by Murray and Elhouar using their experimental results of six prototype and 33 quarter-scale tests, €4.3.3.4 Neither flange connected to sheeting or connected to sheeting with concealed fasteners Where neither flange is connected to sheeting or where the flange is connected to sheeting with concealed fasteners, the following should be considered: (a) Bracing of channel beams If channels are used singly as beams, rather than being paired to form L-sections, they should evidently be braced at intervals so as to prevent them from rotating in the manner shown in Figure C4.3.3.4(1). Figure C4.3.3.4(2), for simplicity, shows two channels braced at intervals against each other. The situation is evidently much the same as in the composite I-section shown in Figure C4.1.1(2), except that the role of the connectors is now played by the braces. The difference is that the two channels are not in contact and that the spacing of braces is generally considerably larger than the connector spacing. Ia consequence, each channel may actually rotate very slightly between braces and this, will cause some additional stresses which superpose on the usual, simple bending stresses, Bracing should be so arranged that— (i) these additional stresses are small enough so that they will not reduce the load-carrying capacity of the channel (as compared to what it would be in the continuously braced condition); and i) rotations should be kept small enough to be a degrees) eptable (of the order of 1 to 2 In order to develop information on which to base appropriate bracing provisions, different channel shapes were tested at Cornell University (Winter, 1970). Each of these was tested with full, continuous bracing, without any bracing, and with intermediate bracing at two different spacings. In addition to this experimental work, an approximate method of analysis was developed and checked against the test results. A condensed account of this is given by Winter, Lansing and McCalley (1949). The reference indicates that the requirements are satisfied for most distributions of beam load if between supports not less than three equidistant braces are placed (ie. at quarter-points of the span or closer). The exception is the where a large part of the total load of the beam is concentrated over a short portion of the span. In this case, an additional brace is to be placed at such a load. Correspondingly, previous editions of the AIST Specification (AIST, 1986; AIST, 991) provided that the distance between braces shall not be greater than one- quarter of the span. It also defined the conditions under which an additional brace shall be placed at a load concentration. For such braces to be effective, it is not only necessary that their spacing be appropriately limited. In addition, their strength should suffice to provide the force required to prevent the channel from rotating. It is, therefore, necessary also to determine the forces that will act in braces, such as those forces shown in‘Accessed by BHP BILLITON on 27 Jun 2002 b) © Figure C4.3,3.4(3), These forces are found if one considers that the action of a load applied in the plane of the web (which causes a torque (Qm)) is equivalent to that same load when applied at the shear centre (where it causes no torque) plus two forces N* equal to Omid which, together, produce the same torque Om. As shown in Figure C4.3.3.4(4) and shown in some detail by Winter, Lansing and MeCalley (1949b), cach half of the channel can then be regarded as a continuous beam loaded by the horizontal forces and supported at the brace points, The horizontal brace force is then, simply, the appropriate reaction of this continuous beam. The provisions of Clause 4.3.3.4 of the Standard represent a simple and conservative approximation for determining these reactions. These reactions are equal to the force N*y, Which the brace is required to resist at each flange. Bracing of Z-section beams Most Z-sections are anti-symmetrical about the vertical and horizontal centroidal axes, i.e. they are point-symmetrical, In view of this, the centroid and the shear centre coincide and are located at the midpoint of the web. A load applied in the plane of the web has, then, no lever arm about the shear centre (m equal to 0) and does not tend to produce the kind of rotation a similar load would produce on a channel, However, in Z-sections, the principal axes are oblique to the web (sce Figure C4.3.3.4(5)). A load applied in the plane of the web, resolved in the direction of the two axes, produces deflections in each of them. By projecting these deflections onto the horizontal and vertical planes, it is found that a Z-beam loaded vertically in the plane of the web deflects not only vertically but also horizontally. If such deflection is permitted to occur, then the loads, moving sideways with the beam, are no longer in the same plane with the reactions at the ends. In consequence, the loads produce a twisting moment about the line connecting the reactions. In this manner, it is seen that a Z-beam, unbraced between ends and loaded in the plane of the web, deflects laterally and also twists. Not only are these deformations likely to interfere with a proper functioning of the beam, but the additional stresses caused by them produce failure at a load considerably lower than when the same beam is used fully braced, In order to develop information on which to base appropriate bracing provisions, tests were carried out on three different Z-shapes at Cornell University, unbraced as well as with variously spaced intermediate braces. In addition, an approximate method of analysis was developed and checked against the test results, An account of this was given by Zetlin and Winter (1955). Briefly, it shows that intermittently braced Z-beams can be analysed in much the seme way as intermittently braced channels. It is merely necessary, at the point of each actual vertical load (Q), to apply a fictitious horizontal load N* equal to O(yy/l). One can then calculate the vertical and horizontal deflections, and the corresponding stresses, in conventional ways by utilizing the centroidal axes x’ and y’ (rather than x and y, as shown in Figure C4,3,3.4(5)) except that certain modified section properties have to be used, Jn this manner, it has been shown that as to the location of braces, the same provisions that apply to channels also apply to Z-beams, Likewise, the forces in the braces are again obtained as the reactions of continuous beams horizontally loaded by fictitious loads "5, Spacing of braces During the period from 1956 through 1996, the AIST Specification required that braces be attached both to the top and bottom flanges of the beam, at the ends and at intervals not greater than one-quarter of the span length, in such a manner as to prevent tipping at the ends and lateral deflection of either flange in either direction at intermediate braces. The lateral buckling equations provided in Clause 3.3.3.2 of the Standard can be used to predict the moment capacity of the member. Recently, beam tests conducted by Ellifritt, Sputo and Haynes (1992) have shown that for typical sections, a mid-span brace may reduce service load horizontal deflections and rotations by as much as 80% when‘Accessed by BHP BILLITON on 27 Jun 2002 compared to 2 completely unbraced beam, However, the restraining effect of braces may change the failure mode from lateral-torsional buckling to distortional buckling of the flange and lip at brace point. The natural tendency of the member under vertical load is to twist and translate in such a manner as to relieve the compression on the lip. When such movement is restrained by intermediate braces, the compression on the stiffening lip is not relieved, and may increase. In this case, distortional buckling may oceur at loads lower than that predicted by the lateral buckling equations given in Clause 3.3.3.2 of the Standard. Hence, equations for distortional buckling were included in Clause 3.3.3.3 of the Standard, The Standard permits omission of discrete braces when all loads and reactions on a beam are transmitted through members that frame into the section in such a manner as to effectively restrain the member against torsional rotation and lateral displacement. The inclusion of purlins with sheeting connected with concealed fasteners in Clause 4.3.3.4 of the Standard is based on testing at the University of Sydney (Hancock, Celeban and Healy (1994) where concealed fastened sheeting was found not to provide adequate lateral restraint due to shear slippage between the sheets. FIGURE ©4.3.3.4(1) ROTATION OF CHANNEL BEAMS FIGURE C4.3.3.4(2) TWO CHANNELS BRACED AT INTERVALS AGAINST EACH OTHER‘Accessed by BHP BILLITON on 27 Jun 2002 wee om. aT]. y AL | a Om wey FIGURE C4.3.3.4(3) LATERAL FORCES APPLIED TO CHANNEL FIGURE C4.3.3.4(4) HALF OF CHANNEL TREATED AS A CONTINUOUS BEAM LOADED BY HORIZONTAL FORCES. FIGURE ©4.3.3.4(5) PRINCIPAL AXES OF Z-SECTION‘Accessed by BHP BILLITON on 27 Jun 2002 4.4 WALL STUDS AND WALL rUD ASSEMBLIES It is well known that column strength can be increased considerably by using adequate bracing, even though the bracing is relatively flexible. This is particularly true for those sections generally used as load-bearing wall studs which have large /,/I, ratios Cold-formed channels or box-type studs are generally used in walls with their webs placed perpendicular to the wali surface. The walls may be made of different materials, such as fibre board, pulp board, plywood or gypsum board. If the wall material is strong enough and there is adequate attachment provided between wall material and studs for lateral support of the studs, then the wall material can contribute to the structural economy by increasing the useable strength of the studs substantially. In order to determine the necessary requirements for adequate lateral support of the wall studs, theoretical and experimental investigations were conducted in the 1940s by Green, Winter, and Cuykendall (1947). The study included 102 tests on studs and 24 tests on a variety of wall material. Based on the findings of this earlier investigation, specific AISI provisions were developed for the design of wall studs. In the 1970s, the structural behaviour of columns braced by steel diaphragms was @ special subject investigated at Cornell University and other institutions. The renewed investigation of wall-braced studs has indicated that the bracing provided for studs by steel panels is of the shear diaphragm type rather than the linear type that was considered in the 1947 study. Simaan (1973) and Simaan and Pekoz (1976), which are summarized by Yu (1991), contain procedures for calculating the strength of Channel and Z-section wall studs that are braced by sheeting materials. The bracing action is due to both the shear rigidity and the rotational restraint supplied by the sheeting material. The treatment by Simaan (1973) and Simaan and PekSz (1976) is quite general and includes the case of studs braced on one as well as on both flanges. In Australia, it is not common to account for sheeting in the design of wall studs. Hence, intermediate braces such as noggins (dwangs) are used, Design is then performed in accordance with Section 3 of the Standard with appropriate effective lengths about the x, y and 2 axes, In New Zealand, bracing gypsum board is commonly used in conjunction with the means of attachment so that stud flange restraint is provided. For assemblies, this bracing gypsum board can be used with tension strap bracing to provide adequate bracing without dwangs.‘Accessed by BHP BILLITON on 27 Jun 2002 s ECTION CS CONNECTIONS ERAL Welds, bolts, screws, rivets and other special devices such as clinching, nailing and structural adhesives are generally used for cold-formed steel connections (Brockenbrough, 1995). The 1996 edition of the AISI Specification contains provisions in Chapter E for welded connections, bolted connections and screw connections. The Standard includes the same provisions in Section S and also blind-riveted connections. Design rules for clinching are not given at this stage, since clinches are proprietary devices for which information on strength of connections should be obtained from tests carried out by or for the user. The provisions in Section 6 of the Standard are to be used in these tests, The plans or specifications, or both, are to contain information and design requirement data for the detailing of cach connection, if each connection is not detailed on 1 engineering design drawings. For stocl thickness less than 0.75 mm, the design value of the connection will generally be that determined by the material thickness, However, for heavier steels, the shear or tension value of the fastener (dependent on size) will usually govern. The fastener strength in both shear and tension, should be 1.25 times that of the connection. ‘The design capacity for a connection can be determined as follows: (a) Use the equations given in Clause 5.2 for welds, Clause for boll Clauses $.4.2 and 5.4.3 for serews, and Clause 5.5.2 for rivets, where the calculated nominal capacity is factored by the capacity [strength reduction] factor (@) given in Table 1.6 of the Standard. (b) Determine the design capacity [strength] of @ single-point connection by test as follows: 5.2 where oR, = design capacity [strength] by (est of a single-point connection R = target test loads for the member of units to be tested. k = variability factor given in Table 6.2.2 of the Standard fe = minimum tensile strength of the connected material given in Table 1,5 of the Standard = average value of the tensile strength from the sample tested Consideration should be given to the durability of the connections and these should be designed to functionally perform during the expected life of the structure, Compatibility is important when dissimilar metals are combined or when fasteners are exposed to other than dry internal environments. Fuente The ratio {foresee eset) Adjusts the test loads to allow for the fact that the material from which the specimens ate made may be of higher strength than the minimum specified.‘Accessed by BHP BILLITON on 27 Jun 2002 C5.2. WELDED CONNECTIONS Welds used for cold-formed steel construction may be classified as are welds and resistance welds. Arc welding is used for connecting cold- formed steel members to each other as well as connecting such members to heavy, bot- rolled steel framing (such as floor panels to beams of the steel frame), It is used in butt welds, fillet welds, are spot welds (puddle welds), arc seam welds and flare welds. The design provisions contained in the Standard for are welds are based primarily on experimental evidence obtained from an extensive test program conducted at Cornell University. The results of this program are reported by Pekbz and McGuire (1979) and summarized by Yu (1991). All possible failure modes are covered in the present provisions, whereas the earlier provisions mainly dealt with shear fai For most of the connection tests reported by Pekéz and McGuire (1979), the onset of yielding was either poorly defined or followed closely by ultimate failure. Therefore, in the provisions of Section 5 of the Standard, rupture rather than yielding is used as a more reliable criterion of failure. In addition, the Cornell research has provided the experimental basis for the AWS Structural Welding Code for Sheet Steel (AWS, 1989). In most cases, the provisions of the AWS code are in agreement with Section $ of the Standard. The welded connection tests, which served as the basis of the provisions given in Clause 5.2 of the Standard, were conducted on sections with single and double sheets. The largest total sheet thickness of the cover plates was approximately 3.81 mm, However, within the Standard, the validity of the equations is limited to welded connections which the thickness of the thinnest connected part is 3 mm (2.5 mm for fillet welds) or less. For welds in thicker material, the provisions of AS 4100 or NZS 3404 should be used. These limitations were based on testing by Zhao and Hancock (199Sa, 1995b). The terms used in Section 5 of the Standard agree with the standard nomenclature given in the AWS Welding Code for Sheet Steel (AWS, 1992). 8.2.2. Butt welds The design equations for determining nominal capacity for butt welds are taken from the AISC LRFD Specification (AISC, 1993) where the effective throat thickness (t,) is replaced by its equivalent, the design throat thickness (1), as specified in AS/NZS 1554.1:1995, €8.2.3 Fillet welds For fillet welds on the lap joint specimens tested in the Comell research (Pekiz and McGuire, 1979), the dimension of the leg on the sheet edge generally was equal to the sheet thickness; the other leg often was two or three times longer. In connections of this type, the fillet weld throat commonly is larger than the throat of a conventional fillet weld of the same size. Usually, ultimate failure of fillet welded joints has been found to occur by the tearing of the plate adjacent to the weld (see Figure C5.2.3). Im most cases, the higher strength of the weld material prevents weld shear failure; therefore, the provisions of the standard section arc based on shect tearing. For sections thicker than 2.5 mm, the provisions of AS 4100 and NZS 3404, as appropriate, should be used. This limit is based on the research of Zhao and Hancock (199Sa, 199Sb) C524 Are spot welds (puddle welds) Arc spot welds (puddle welds) used for connecting thin shects are similar to plug welds used for relatively thicker plates. The difference between plug welds and are spot welds is that the former are made with prepunched holes, but for the latter no prepunched holes are required. Instead, a hole is burned in the top sheet by the arc and then filled with weld metal to fuse it to the bottom, sheet or a framing member.‘Accessed by BHP BILLITON on 27 Jun 2002 Sheet tear {a} Transverse filet (o} Longitudinal titer sheet tear sheet tear FIGURE 05.2.3 FILLET WELD FAILURE MODES 2 Shear and C8.24.3 Tearout The Cornell tests (Pekéz and McGuire, 1979) ied the following modes of failure for are spot welds: (a) Shear failure of welds in the fused area. (b) Tearing of the sheet along the contour of the weld with the tearing spreading the sheet at the leading edge of the weld, (c) Sheet tearing combined with buckling near the trailing edge of the weld. (@) Shearing of the sheet behind the weld, Items (a), (b) and (¢) are included in Clause $.2.4.2 of the Standard and Item (d) is included in Clause 5.2.4.3. It should be noted that many failures, particularly those of the plate tearing type, may be preceded or accompanied by considerable inelastic out-of-plane deformation of the type indicated in Figure C5.2.4.2. This form of bebaviour is similar to that observed in wide, pin-connected plates. Such behaviour should be avoided by closer spacing of welds, When arc spot welds are used to connect two sheets to a framing member as shown in Figure 5.2.4(1)(b), consideration should also be given to the possible shear failure between thin sheets. The thickness limitation of 3 mm is due to the range of the test program that served as the basis of these provisions and the need to match with AS 4100 and NZS 3404. On sheets below 0.711 mm thick, weld washers are required to avoid excessive burning of the sheets and, therefore, inferior quality welds. FIGURE C5,2.4.2 OUT-OF-PLANE DISTORTION OF WELDED CONNECTION‘Accessed by BHP BILLITON on 27 Jun 2002 €5.2.4.4 Tension For tensile capacity of are spot welds, the design provisions in the Standard are based on the tests reported by Fung (1978) and the study made by Albrecht (1988). The provisions are limited to shect failure with restrictive limitations on material properties and sheet thickness. These design criteria were revised in the 1996 AISI Specification because the recent tests conducted at the University of Missouri-Rolla (LaBoube and Yu, 1991 and 1993) have shown that two potential limit states may occur. The most common failure mode is that of sheet tearing around the perimeter of the weld. This failure condition was found to be influenced by the sheet thickness, the average weld diameter and the material tensile strength. In some cases, it was found that tensile failure of the weld can occur. The strength of the weld was determined to be a function of cross-section of the fused area and tensile strength of the weld material. Tests (LaBoube and Yu, 1991 and 1993) have also shown that when reinforced by a weld washer, thin sheet weld connections can achieve the design strength calculated using Equations F2.2.2-2 and B2.2.2-3 of the 1996 AISI Specification and using the thickness of the thinner shcet. The provisions in the 1996 AISI Specification have not been included in the Standard at this stage. The equations given in the Standard were derived from the tests for which the applied tension load imposed 2 concentric load on the weld, as would be the case, for example, for the interior welds on a roof system subjected to wind uplift. Welds on the perimeter of a roof or floor system would experience an eccentric tensile loading due to wind uplift Tests have shown that as much as a 50% reduction in nominal connection strength could occur because of the eccentric load application (LaBoube and Yu, 1991 and 1993), Eccentric conditions may also occur at connection laps shown in Figure C5.2.4.4 Ata lap connection between two deck sections as shown in Figure C5.2.4.4, the length of the unstiffened flange and the extent of the encroachment of the weld into the unstiffened flange have a measurable influence on the strength of the welded connection (LaBoube and Yu, 1991). The 1996 AISI Specification recognizes the reduced capacity of this connection detail by imposing a 30% reduction on the calculated nominal strength, ‘This requirement is not stated explicitly in the Standard but should be considered in accordance with Clause 5.2.4.4 of the Standard Interior weld subjected Exterior weld subjected a \ Beam FIGURE (5.2.4.4 INTERIOR WELD, EXTERIOR WELD AND LAP CONNECTION 8.2.5 Are seam welds The gencral behaviour of arc seam welds is similar to that of are spot welds. No simple shear failures of are seam welds were observed in the Cornell tests (Pek6z and McGuire, 1979). Therefore, Equation $.2.5.2(1) in the Standard, whieh accounts for shear failure of welds, is adopted from the AWS welding provisions for sheet steel (AWS, 1992) Equation 5.2.5.2(2) in the Standard is intended to prevent failure by a combination of tensile tearing plus shearing of the cover plates.‘Accessed by BHP BILLITON on 27 Jun 2002 €5.2.6 Flare welds The primary mode of failure in cold-formed steel sections welded by flare welds, loaded transversely or longitudinally, also was found to be sheet tearing. along the contour of the weld (sce Figure C5.2.6). The provisions of Clause 5.2.6 of the Standard ate intended to prevent shear tear failure, For sections thicker than 3mm, the provisions of AS 4100 and NZS 3404, as appropriate, should be used to check weld failure. Sheet tear Sheet tear (a) Trans (b} Longituainat sheet tear sheet tear FIGURE 5.2.6 FLARE GROOVE WELD FAILURE MODES €5.2.7 Resistance welds The values of the nominal shear capacities given in Table 5.2.7 of the Standard for outside sheets of 3.20 mm or less in thickness are based on ‘Recommended Practice for Resistance Welding Coated Low-Carbon Steels’, AWS C13-70, (Table 2.1 — Spot Welding Galvanized Low-Carbon Steel). The values of the nominal shear capacities in Table 5.2.7 of the Standard for outside sheets thicker than 3.20 mm are based on “Recommended Practices for Resistance Welding’, AWS C1.1-66, (Table 1.3 ~ Pulsation Welding Low-Carbon Steel) and apply to pulsetion welding as well as spot welding. They are applicable for all structural grades of low-carbon steel, uncoated or galvanized with 275 gramsim® of sheet, or less, and are based on values selected from Table 2.1 of AWS CI.3-70 and from Table 1.3 of AWS C1.1-66. Values for intermediate thicknesses may be obtained by straight-line interpolation. The above values may also be applied to medium carbon and low-alloy steels. Spot welds in such steels give somewhat higher shear strengths than those upon which the above values are based; however, they may require special welding conditions. In all cases, welding is to be performed in accordance with AWS C1.3-70 and AWS Cl.1-66 (AWS, 1966 and 1970), CS.3_ BOLTED CONNECTIONS The structural bebaviour of bolted connections in cold-formed steel construction is somewhat different from that in hot-rolled heavy construction, mainly because of the thinness of the connected parts. Prior to 1980, the provisions included in the AISI Specification and AS 1538—1974 for the design of bolted connections were developed on the basis of the Cornell tests (Winter, 1956a, 1956b). These provisions were updated in 1980 (1988 in Australia) to reflect the results of additional research performed in the United States (Yu, 1982) and to provide a better coordination with the specifications of the Research Council on Structural Connections (RCSC, 1980) and the AISC (1978). In AS 15381988, design provisions for the maximum size of bolt holes were added The Standard gives spe: differ for Australia and New provisions for oversized and slotted holes. These provisions ‘land, and are based on accepted practice in each country,‘Accessed by BHP BILLITON on 27 Jun 2002 The oversize and slotted holes described in Clauses 5.3.1(a) and (b) of the Standard for Australia were used in the vacuum rig testing of purlins at the University of Sydney (Hancock, Celeban and Healy (1993), The following provisions are taken into consideration: (a) Scope Previous studies and practical experiences have indicated that the structural behaviour of bolted connections used for joining relatively thick cold-formed steel members is similar to that for connecting hot-rolled shapes and built-up members. The criteria specified in Clause 5.3 of the Standard are applicable only to cold- formed steel members or elements less than 3 mm in thickness, For materials greater than or equal to 3 mm, reference is made to AS 4100 or NZS 3404, as appropriate. Because of a lack of appropriate test data and the use of numerous. surface conditions, the Standard does not provide design criteria for slip-critical (also called friction-type) connections, When such connections are used with cold-formed members where the thickness of the thinnest connected part is less than 3 mm, it is recommended that tests be conducted to confirm their design capacity. The test data should verify that the specified design capacity for the connection provides a safety against initial slip at least equal to that implied by the AS 4100 and NZS 3404 provisions. In addition, the reliability when calculating the ultimate capacity should be greater than or cqual to that implied by the Standard for bearing-type connections. These provisions apply only when there are no gaps between plies. The designer should recognize that the connection of a rectangular tubular member by means of bolt(s) through such members may have less strength than if no gap existed Structural performance of connections containing unavoidable gaps between plies requires tests in accordance with Section 6. (b) Materials Clause 1.5.3.1 of the Standard deseribes the different types of fasteners that are normally used for cold-formed steel construction. During recent years, other types of fasteners, with or without special washers, have been widely used as connectors in steel structures using cold-formed steel members. The design of these fasteners should be determined by tests in accordance with Section 6 of the Standard, (©) Bolt installation Bolted connections in cold-formed stcel structures use either mild- or high-strength steel bolts, and are designed as a bearing-type connection. Bolt pretensioning is not required for attaining the design capacity because the ultimate strength of a bolted connection is independent of the level of bolt preload. It may be required to provide twist restraint to supporting members; however, installation should ensure that the bolted assembly will not come apart during service. For examples where this applies, sce Clause 5.4.2 of NZS 3404. Experience has shown that bolts installed do not loosen or back off, if tightened to a snug tight condition under normal building conditions and are not subject to vibration or fatigue. Bolts in slip-critical connections should be tightened in a manner that assures the development of the fastener tension forces required by the Research Council on Structural Connections (1985 and 1988) for the particular size and type of bolts. Turn-of-nut rotations specified in Section 15 of AS 4100 or NZS 3404 may not be applicable because such rotations are based on larger grip lengths than are encountered in usual cold-formed construction, Reduced tum-of-nut values would have to be established for the actual combination of grip and bolt. A similar test program (RCSC, 1985 and 1988) could establish @ cut-off value for calibrated wrenches.‘Accessed by BHP BILLITON on 27 Jun 2002 () Hole sizes Im Table $.3.1 of the Standard, the maximum size of holes for bolts having diameters not less than 12 mm is based on Table 1 of the Research Council fon Structural Connections (1985 and 1988), except that for the oversized hole diameter, a slightly larger hole diameter is permitted. For bolts having diameters less than 12 mm, the diameter of a standard hole is the diameter of bolt plus 1 mm. Short-slotted holes are usually treated in the same manner as oversized holes. Washers or backup plates should be used over oversized or short-slotted holes in an outer ply unless suitable performance is demonstrated by (ests. ‘The inclusion of the design information in Table 5.3.1 of the Standard for oversized and slotted holes is because such holes are sometimes used in Australian practice to mect dimensional tolerances during erection. However, when using oversized holes care should be exercised by the designer to ensure that excessive deformation due to slip will not occur at working loads. Excessive deformations, which can occur in the direction of the slots, may be prevented by requiring bolt pretensioning, as specified in Clause 5.4.2 of NZS 3404 for restraint provision. €53.2 Tearout The provisions for minimum spacing and edge distance were revised in the 1980 Specification and AS 1538—1988 to include additional design requirements for bolted connections with standard, oversized and slotted holes. The minimum edge distance of cach individual connected part (cq,,) is determined by using the tensile strength of steel (f,) and the thickness of connected part. In accordance with the different ranges of the {//, ratio, two different capacity factors are used for determining the required minimum edge distance. These design provisions are based on the following ‘basic equation established from the test results Me oa 5.3.2 it where = the required minimum edge distance to prevent shear failure of the connected part force transmitted by one bolt {= thickness of the thinnest connected part. For design purposes, 2 capacity factor of 0.70 was used for fyf, greater than or equal to 1,08, and 0.60 for steel with {Jf less than 1.08, in accordance with the degree of correlation between Equation C5.3.2 and the test data. As a result, whenever ff is less than or equal to 1.08, the requirement is the same as the AISC specification In addition, several requirements were added to the AISI Specification in 1980 and AS 1538—1988 concerning the following (a) The minimum distance between centres of holes, as required for installation of bolts (b) The clear distance between edges of two adjacent holes, (©) The minimum distance between the edge of the hole and the end of the member. The same design provisions were retained in the 1986 AISI Specification and are also used in the Standard, except that the limiting f/f, ratio has been reduced from 1.15 to 1.08 for consistency with Clause 1.5.1.5 of the Standard. The test data used for the development of Equation 5.3.2 of the Standard are documented by Winter (1956a and 1956b) and Yu (1982, 1985, and 1991),‘Accessed by BHP BILLITON on 27 Jun 2002 5.3.3 Net section tension In the Standard, the nominal tensile capacity (Nj) on the nnet section of connected parts is based on the loads determined in accordance with Clauses 3.2 and 5.3.3 of the Standard, whichever is smaller. In the use of the equations provided in Clause 5.3.3 of the Standard, the following design features should be noted: (a) The provisions are applicable only to the thinnest connected part less than 3 mm in thickness, For materials thicker than 3 mm, the design tensile force is determined in accordance with AS 4100 or NZS 3404, as applicable, (b) The nominal tensile strength (WV) on the net section of a connected member is determined by the tensile strength of the connected part (,) and the ratios r, and 5, (©) Different equations are used for bolted connections with and without washers (Chong and Matlock, 1974) (@) The tensile capacity on the net section of a connected member is based on the type of joint, either a single shear lap joint or a double shear butt joint. 5.3.4 Bearing The available test data has shown that the bearing strength of bolted connections depends on the following: (a) The tensile strength and thickness of the connected parts. (b) _Ioints with single shear or double shear conditions, (©) The ff, ratio. () The use of washers (Winter, 19562 and 1956b; Yu, 1982 and 1991; Chong and Matlock, 1974), The nominal bearing capacities between the connected parts for different conditions are given in Tables 5.3.4.1 and 5.3.4.2 of the Standard. The capacity factors are provided in the tables for different types of joints and f/f, ratios. It should be noted that in the 1996 edition of the AISI Specification and tho Standard, the limiting value of f/f, used in Tables 5.3.4.1 and 5.3.4.2 of the Standard was changed from 1.15 to 1.08 in order to be consistent with Clause 1.5.1.5 of the Standard. €5.3.8 Bolts The provisions for bolts in shear, tension and combined shear and tension are the same as those for AS 4100 or NZS 3404. Reference should be made to Clause C9.3.2 of the Commentaries to these Standards. 5.4 SCREWED CONNECTIONS. €5.4.1 General The Standard covers cases where the loads applied to the connection are cither predominantly shear or normal teasion (head pull). It is not intended to cover cases where the connection will experience moments, combined loading or significant secondary forces such as prying. For these cases, testing in accordance with Section 6 of the Standard should be used. Testing can also be used where more accurate shear and normal tension capacities are required. Testing is particularly useful where— (a) the thickness of cold-formed high strength G550 steel sections is less than 0.90 mm; and (b) the ff, ratios are 1.0 for 0.40 mm BMT to 1.08 for 0.90 mm BMT. It is recommended that at least two screws should be used to connect individual components. This provides redundancy against poor installation and limits lap shear connection and distortion of flat unformed members, such as straps. The screws should be installed in accordance with the manufacturer's recommendations. Fine-threaded screws perform better in thick material, where several threads will engage. Conversely, coarse-threaded serews usually perform better in thin materials, especially where the material thickness fits neaily between two threads‘Accessed by BHP BILLITON on 27 Jun 2002 For connections of steels with low ductility, e.g, Grade 550 less than 0.9 mm thick, the tensile strength (f,) used in Equations 5.4,2.3(1) to 5.4.32) of the Standard should be taken as the lesser of 75% of the specified minimum tensile strength or 450 MPa as specified in Clause 1.5.1.5 of the Standard. This reduction in f, does not apply if the design capacity is determined by test in accordance with Clause 6.2 of the Standard. It is intonded that this reduction will provide a safety factor to prevent tensile failure. To ensure ductility, it is considered preferable to provide some yielding at the connection, although section buckling should occur before connection failure. Lighter sections usually produce a more flexible structure which, although strong, can be subject to cyclic flexing. due to e.g. wind forces, which a heavier structure would absorb and resist without flexing, The Standard applies only to screws with nominal diameters between 3 mm and 7 mm, This reflects the range of screws used in the tests on which the predictive equations have been based. Table C5.4.1 gives the nominal diameter of screws between 3 mm and 7 mm. TABLE C5.4.1 NOMINAL DIAMETER FOR COMMON SIZE SCREWS | Nominal diameter (Ay Size designation mom (see Figure €5.4(1) Nas 32 No. 6 38 No.7 38 No. § 42 No. 10 58 No. 12 54 No. 63 ~— 4 fi FIGURE C5.4(1) NOMINAL DIAMETER FOR SCREWS 5.4.2 Serewed connections in shear To ensure equal distribution of forces between the screws in a connection, it is important to limit the maximum spacing between the screws. This is particularly important for the outermost screws. The AISI Specification gives no guidance on this, but the European Recommendations (ECCS 1983) specifies the following, when the applied force is parallel to the rows of screws: (a) Where the distance between the outermost serews is less than 15d, the force may be distributed uniformly over the screws. (b) Where the distance between the outermost screws is 65d, the force in the connection should be limited to 75% of the sum of the design strengths of the serewed fastenings, (©) For distances between 15d, and 65d, linear interpolation should be used. Screwed connections loaded in shear can fail in one mode or in a combination of several modes, These modes are serew shear, edge tearing, tilting and subsequent pull-out of the screw, and bearing of the joined materials.‘Accessed by BHP BILLITON on 27 Jun 2002 Tilting of the screw followed by threads tearing out of the lower sheet reduces the connection shear capacity from that of the typical connection bearing strength (see Figure C5.4.2.3(1)). The provisions in Clause 5.4.2.3 of the Standard focus on the tilting and bearing failure modes, Two cases ate given depending on the ratio of thicknesses of the connected members. Normally, the head of the screw will be in contact with the thinner material as shown in Figure C5.4.2.3(2), However, when both members are of the same thickness, or when the thicker member is in contact with the screw head, tilting is also to be considered, as shown in Figure C5.4.2.3(3). It is necessary to determine the lower bearing capacity of the two members, based on the product of their respective thicknesses and tensile strengths, Equation 5.4.2.311) 2 FIGURE 5.4.2.3() COMPARISON OF TILTING AND 4 siting ¥ bearing 2 bearing 2Thayhy oF 27 ted hye FIGURE C5.4.2.3(2) DESIGN EQUATIONS FOR t/t, 2 2.5 h titing Vy = 42UPa”2 hy oF + bearing Mp = 27h obhy oF ” bearing Wy = 27d he FIGURE €5.4.2.9(3) DESIGN EQUATIONS FOR t/t, < 1.0,‘Accessed by BHP BILLITON on 27 Jun 2002 5.4.2.4 Screws in shear To prevent the connection failing in a brittle manner, the design shear capacity of the screw itself should be 1.25 times the design capacity due to tilting and bearing. In general, the shear capacity of the screw itself will be approximately 0.6 times the axial tensile strength of the screw. The shear values given by the manufacturer are not relevant where f, is less than or equal to 1.6 mm, where ¢, is the thickness of the material not in contact with the head of the C5.4.3 Screwed connections in tension CS.4.3.1 Pullout and pull-over (pull-through) Clause 5.4.3.1 of the Standard applies to static loading conditions. For pull-over (pull-through) behaviour, the tensile strength may be affected by repeated loading, such as cyclonic wind conditions in Australia and high wind areas in New Zealand, such as wind regions 1, V and VII specified in NZS 4203. The AISI Specification gives no guidance on this, while the Eurocode recommends using a cyclic loading factor of 0.5 for the calculated static design capacily. Alternatively, testing to cyclic loading in accordance with AS 4040.3 may be considered, The thickness of the washer, including where it is integrated into the head of the screw, raceds to be at least 1.3 mm or formed to an equivalent strength to withstand the bending forces with little or no deformation. Washers having diameters larger than 12.5 mm can bbe used, However, in this case the value of d, used in Equation 5.4,3(2) of the Standard is limited to 12.5 mm maximum. Alternatively, tests in accordance with Section 6 of the Standard may be considered if the full design capacity of larger washers is desired, Design capacities for connections where the members are not in contact at the point of fastening, such as crest fixing of cladding, have not been included as the design capacity of the connection is dependent on the type of profile used (Mahendran 1994), For non-cyelonic areas of Australia and protected inland areas of New Zealand, and for the design of crest-fixed profile sheeting using No. 14 screws and 0.35-0.48 mm GSS0 steel without washers, the nominal pulleover (pull-through) capacity (N,,) can be approximated as follows: vow 7 Bak Ta 5.43.1 where k, = | for static loads (non-cyelonic areas) k, = 0.54 for corrugated sheeting 0.89 for wide pan trapezoidal sheeting 0.79 for narrow pan trapezoidal sheeting 1, = thickness of the s! in contact with the serew head fa = tensile strength of the sheet in contact with the screw head For nonedrilling screws, the diameter of the hole of the member in contact with the screw hhead should not exceed that recommended in AS B194, The minimum withdrawal axial force for screws specified in AS 3566 is not relevant where f, is less than 1,6 mm, where thickness of the material not in contact with the head of the screw. .3.2 Screws in tension To prevent the connections failing in a brittle manner, the tensile design capacity [strength] of the screw should be 1.25 times the design capacity due to pull-out and pull-over (pull-through). The maximum tensile capacities [strengths] of self-drilling screws, as specified in AS 3566, are given in Table C5.4.3.2. The values given in Table C5.4.3.2 are for the screws only and not the connection. The thickness and grade of steel will generally determine the design value of the connection,‘Accessed by BHP BILLITON on 27 Jun 2002 TABLE CS. MINIMUM AXIAL TENSILE CAPACITY [STRENGTH] OF SELE-DRILLING SCREWS ‘Maximum axial tense capacity [strength Size designation ky Type ASD “Type BSD Type CSD No.6 235 435 533 Nef 635 635 a6 Ne 10 7.50 B60 oor Ne. 12 1134 18 lead Noi 1495 16.15 15.90 The values given in Table C5.4.3.2 are not the design tensile capacity [strengta] of the screw connecting plies of thin gauge steel. The screw types are described in AS 3566. €S.5. BLIND RIVETED CONNECTIONS Clause 5.5 of the Standard is based on Eurocode 3, Part 1.3 (Toma et al. 1993) in which only shear is covered, At least two rivets should be used to connect individual components, This provides redundancy against poor installation and limits lap shear connection and distortion of flat unformed members, such as straps. The rivets should be installed in accordance with the manufacturer's recommendations, Where sheets of different thicknesses are joined, it is recommended that the preformed head be placed against the thinnest sheet To limit distortion and ensure equal distribution of forces, the maximum spacing between rivets should be limited to 20 times the nominal diameter of the rivets, For connections of steels with low ductility, e.g. Grade 550 less than 0.9 mm thick, the tensile strength (f,) used in Equations 5.5.2.3(1) to 5.5.2.3(5) of the Standard should be taken as the lesser of 75% of the specified minimum tensile strength or 450 MPa, whichever is the lesser, as specified in Clause 1.5.1.5 of the Standard. This reduction in does not apply if the design capacity is determined by test in accordance with Clause 6. of the Standard. €5.5.2.4 Rivets in shear To prevent the connection failing in a brittle manner, the design shear capacity of the rivet itself should be 1.25 times the shear capacity due to tilting and bearing. The minimum shear and axial tensile capacities [strengths] of blind rivets, as specified in the Industrial Fasteners Institute Standard F114 (IFI 1988), are given in Table C5.5.2.4 The values given in Table C5.5,2.4 are nof the design shear or tensile capacity [strength] of the rivet connecting plies of thin gauge material, Similar design considerations that are required for serews are required for blind rivets, Blind rivets are manufactured in various shapes, sizes and materials but are all subject to pull-over failure in tension because the head of the rivet is much smaller than a screw head. The practical size for rivets used for structural purposes is, therefore, limited to 4.0 mm, 4.8 mm and 6.3 mm. To provide the shear and tension capacities quoted by the mamufacturer, it is essential to use the correct size drill (4.1 mm, 4,9 mm and 6.4 mm) and the correct length of rivet for the materials being fastened. It is usual to use more rivels than screws because the rivet head is not normally washered and consequently lesser values are obtained with rivets. Their spacing should be greater than 3d, and less than 20d, to minimize distortion. Galvanized steel rivets are plated only and are not considered durable except in a protected environment,‘Accessed by BHP BILLITON on 27 Jun 2002 TABLE 5.5.2.4 MINIMUM SHEAR AND AXIAL TENSILE CAPACITY [STRENGTH] OF BREAK MANDREL BLIND RIVETS Nominas | Nominal Minimum shear capacity ‘Minimum axial tensile capacity @iameter | 4 hee [strength] [strength diameter os) a) om | om [ar] [™ [ss [a] | | ss w fo [oo pa | os poe fim [a pam | oe «ep [oe [es [op [= los pas | ss os [a7 [32 [ «0 | oa oe [eae | sza | ose | om where AI = eluminium alloy, 5154, $056, 4 with carbon sts! mandrel St = low carbon steel with carbon stel mandrel M_ = nickel-copper alloy (Mone!) with carbon steel mandrel S/S = 300 sores stainless stes! with carbon or steinless steel mandrel 8.6 RUPTURE 5.6.1 Shear rupture Connection tests conducted by Birkemoe and Gilmor (1978) have shown that on coped beams a tearing failure mode as shown in Figure C5.6.1(1) can occur along the perimeter of the holes. The provisions in Clause 5.6.1 of the Standard for shear rupture are adopted from the AISC Specification (AISC, 1978). These provisions are considered to yield conservative estimate of the rupture capacity at the coped end of a beam by neglecting the contribution of the tensile area, For additional design information on tension rupture strength and block shear rupture strength of connections (see Figures C5.6.1(1) and C5.6.1(2)), refer to the AISC Specifications (ATSC, 1989 and 1993). “ Failure by tearing out of shade Failure by tearing portion out of shaded Q pertion srea./ }Htensie Tonsilo area iW FIGURE C5.6.1(1) FAILURE MODES FOR BLOCK SHEAR RUPTURE