BEAMS, PURLINS AND BRACING. 5.1 General The design of beams for strength is usually governed by one of the following limit states:

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1 CHAPTER 5 BEAMS, PURLINS AND BRACING 5.1 General The design of beams for strength is usuall governed b one of the following limit states: (a) (b) (c) (d) (e) ielding of the most heavil loaded cross section in bending including local and postlocal buckling of the thin plates forming the cross-section, or elastic or inelastic buckling of the whole beam in a flexural-torsional (commonl called lateral) mode, or elastic or inelastic buckling of a length of beam in a distortional mode, or ielding and/or buckling of the web subjected to shear, or combined shear and bending, or ielding and/or buckling of the web subjected to bearing (web crippling) or combined bearing and bending. The design for (a) determines the nominal section moment capacit (M s ) given b Eq. (5.1). M s = Z e f (5.1) where Z e is the effective section modulus about a given axis computed at the ield stress (f ). Calculation of the effective section modulus at ield is described in Chapter 4 of this book. As specified in Table 1.6 of AS/NZS 4600, the capacit reduction factor (φ b ) for computing the design section moment capacit is 0.95 for sections with stiffened or partiall stiffened compression flanges and 0.90 for sections with unstiffened compression flanges. The design for (b) and (c) determines the nominal member moment capacit (M b ) given b Eq. (5.2). M b = Z c f c (5.2) M c where f c = (5.3) Z f Mc is the critical moment for lateral or distortional buckling. Zc is the effective section modulus for the extreme compression fibre computed at the critical stress (fc) and Zf is the full unreduced section modulus for the extreme compression fibre. Equation 5.2 allows for the interaction effect of local buckling on lateral or distortional buckling. The use of the effective section modulus computed at the critical stress (fc) rather than the ield stress (f) allows for the fact that the section ma not be full stressed when the critical moment is reached and hence the effective section modulus is not reduced to its value at ield. The method is called the unified approach and is described in detail in Ref For the specific case of distortional buckling where the flange locall buckles before the web, interaction buckling does not occur and the full section modulus (Zf) is used in place of the effective section modulus (Zc) as described in Clause of AS/NZS Hence Mb is simpl Mc in this case. As specified in Table 1.6 of AS/NZS 4600, the capacit reduction factor (φb) for computing the design member moment capacit is Clause of AS/NZS 4600 gives design rules for laterall unbraced and intermediatel braced beams including box, I-beams, T-beams, C- and Z-section beams when cross-sectional distortion does not occur. The basis of the design rules for lateral buckling is described in the following Section 5.2 of this book. Clause of AS/NZS 4600 gives design rules for beams which undergo distortional buckling, as shown in Fig. 1.18, rather than lateral buckling. This usuall occurs when the compression flange of a beam is laterall restrained but the flange and lip are free to rotate about the flange/web junction as shown in Fig and this is specified in Clause (a) of 76

2 AS/NZS This mode is sometimes called Flange Distortional and is described in Section of this book. In some cases, such as for the Hollow Flange Beam and the LiteSteel beam subject to bending, distortional buckling ma involve transverse flexure of the web as shown in Fig and 3.16 and this is specified in Clause (b) of AS/NZS This mode is sometimes called Lateral Distortional and is described in Section of this book. The basic behaviour of purlins is described in Section 5.4, and design methods for purlins are described in Section 5.5. These include the R-factor design approach in Clause of AS/NZS 4600 which allows for the restraint from sheeting attached b screw-fastening to one flange. Methods for bracing beams against lateral and torsional deformation are described in Clause 4.3 of AS/NZS 4600 and are described in Section 5.6 of this book. Allowance for inelastic reserve capacit of flexural members is included as Clause of AS/NZS 4600 as an alternative to initial ielding described b Clause and specified b Eq 5.1. Inelastic reserve capacit is described in Section 5.7 of this book. The design for (d) requires computation of the nominal shear capacit (V V ) of the beam and is full described in Chapter 6 (Webs) of this book. The design for (e) requires computation of the nominal capacit for concentrated load (Rb) (bearing) and is also described in Chapter 6 (Webs) of this book. The interaction of both shear and bearing with section moment is also described in Chapter Flexural-Torsional (Lateral) Buckling Elastic Buckling of Unbraced Simpl Supported Beams The elastic buckling moment (M o ) of a simpl supported and I-beam, monosmmetric I-beam or T-beam bent about the x-axis perpendicular to the web as shown in Fig. 5.1(a) with equal and opposite end moments and of unbraced length (l) is given in Refs 5.1 and 5.2 and is equal to: M o = 2 π EI 2 GJ πδ πδ π EI w 1 2 l 2 2 GJl (5.4) where δ = ± β x l EI GJ (5.5) Lateral Buckling Mode Lateral Buckling Mode x x (a) I-section and Monosmmetric I-section bent about x-axis Lateral Buckling Mode Lateral Buckling Mode x x (b) Hat and Inverted Hat Sections bent about -axis Fig. 5.1 Lateral buckling modes and axes The value of δ is positive when the larger flange is in compression, is zero for doubl smmetric beams, and is negative when the larger flange is in tension. 77

3 Design of Cold-Formed Steel Structures (To Australian/New Zealand Standard AS/NZS 4600:2005) b Gregor J. Hancock BSc BE PhD DEng Bluescope Steel Professor of Steel Structures Dean Facult of Engineering & Information Technologies Universit of Sdne fourth edition

4 PREFACE TO THE 4 th EDITION CONTENTS Page viii CHAPTER 1 INTRODUCTION Design Standards and Specifications for Cold-Formed Steel General Histor of Australian Cold-Formed Steel Structures Standards and USA Specifications New Developments in the 2005 Edition Common Section Profiles and Applications of Cold-Formed Steel Manufacturing Processes Special Problems in the Design of Cold-Formed Sections Local Buckling and Post-local Buckling of Thin Plate Elements Propensit for Twisting Distortional Buckling Cold Work of Forming Web Crippling under Bearing Connections Corrosion Protection Inelastic Reserve Capacit Fatigue Loading Combinations Limit States Design Computer Analsis References 20 CHAPTER 2 MATERIALS AND COLD WORK OF FORMING Steel Standards Tpical Stress-Strain Curves Ductilit Effects of Cold Work on Structural Steels Corner Properties of Cold-Formed Sections Fracture Toughness Background Measurement of Critical Stress Intensit Factors Evaluation of the Critical Stress Intensit Factors for Perforated Coupon Specimens Evaluation of the Critical Stress Intensit Factors for Triple Bolted Specimens References 36 CHAPTER 3 BUCKLING MODES OF THIN-WALLED MEMBERS IN COMPRESSION AND BENDING Introduction to the Finite Strip Method Monosmmetric Column Stud Unlipped Channel Lipped Channel Lipped Channel (Fixed Ended) Purlin Section Stud Channel Section Z-Section 46 iii

5 3.4 Tubular Flange Sections Hollow Flange Beam in Bending LiteSteel Beam Section in Bending References 49 CHAPTER 4 STIFFENED AND UNSTIFFENED COMPRESSION ELEMENTS Local Buckling Postbuckling of Plate Elements in Compression Effective Width Formulae for Imperfect Elements in Pure Compression Effective Width Formulae for Imperfect Elements under Stress Gradient Stiffened Elements Unstiffened Elements Effective Width Formulae for Elements with Stiffeners Edge Stiffened Elements Intermediate Stiffened Elements with One Intermediate Stiffener Edge Stiffened Elements with Intermediate Stiffeners, and Stiffened Elements with more than One Intermediate Stiffener Uniforml Compressed Edge Stiffened Elements with Intermediate Stiffeners Examples Hat Section in Bending Hat Section in Bending with Intermediate Stiffener in Compression Flange C-Section Purlin in Bending References 75 CHAPTER 5 BEAMS, PURLINS AND BRACING General Flexural-Torsional (Lateral) Buckling Elastic Buckling of Unbraced Simpl Supported Beams Continuous Beams and Braced Simpl Supported Beams Bending Strength Design Equations Distortional Buckling Flange Distortional Buckling Lateral-Distortional Buckling Basic Behaviour of Purlins Linear Response of Channel and Z-sections Stabilit Considerations Sheeting and Connection Tpes Design Methods for Purlins No Lateral and Torsional Restraint Provided b the Sheeting Lateral Restraint but No Torsional Restraint Lateral and Torsional Restraint Bracing Inelastic Reserve Capacit Sections with Flat Elements Clindrical Tubular Members Examples Simpl Supported C-Section Purlin Distortional Buckling Stress for C-Section Continuous Lapped Z-Section Purlin Z-Section Purlin in Bending References 122 iv

6 CHAPTER 6 WEBS General Webs in Shear Shear Buckling Shear Yielding Webs in Bending Webs in Combined Bending and Shear Web Stiffeners Web Crippling (Bearing) of Open Sections Edge Loading Alone Combined Bending and Edge Loading Webs with Holes Examples Combined Bending and Shear at the End of the Lap of a Continuous Z-Section Purlin Combined Bearing and Bending of Hat Section References 139 CHAPTER 7 COMPRESSION MEMBERS General Elastic Member Buckling Flexural, Torsional and Flexural-Torsional Buckling Distortional Buckling Section Capacit in Compression Member Capacit in Compression Flexural, Torsional and Flexural-Torsional Buckling Distortional Buckling Effect of Local Buckling Monosmmetric Sections High Strength Steel Box Sections Examples Square Hollow Section Column Unlipped Channel Column Lipped Channel Column References 164 CHAPTER 8 MEMBERS IN COMBINED AXIAL LOAD AND BENDING Combined Axial Compressive Load and Bending - General Interaction Equations for Combined Axial Compressive Load and Bending Monosmmetric Sections under Combined Axial Compressive Load and Bending Sections Bent in a Plane of Smmetr Sections Bent about an Axis of Smmetr Combined Axial Tensile Load and Bending Examples Unlipped Channel Section Beam-Column Bent in Plane of Smmetr Unlipped Channel Section Beam-Column Bent about Plane of Smmetr Lipped Channel Section Beam-Column Bent in Plane of Smmetr References 180 v

7 CHAPTER 9 CONNECTIONS Introduction to Welded Connections Fusion Welds Butt Welds Fillet Welds subject to Transverse Loading Fillet Welds subject to Longitudinal Loading Combined Longitudinal and Transverse Fillet Welds Flare Welds Arc Spot Welds (Puddle Welds) Arc Seam Welds Resistance Welds Introduction to Bolted Connections Design Formulae and Failure Modes for Bolted Connections Tearout Failure of Sheet (Tpe I) Bearing Failure of Sheet (Tpe II) Net Section Tension Failure (Tpe III) Shear Failure of Bolt (Tpe IV) Screw Fasteners and Blind Rivets Rupture Examples Welded Connection Design Example Bolted Connection Design Example References 208 CHAPTER 10 DIRECT STRENGTH METHOD Introduction Elastic Buckling Solutions Strength Design Curves Local Buckling Flange-distortional buckling Overall buckling Direct Strength Equations Examples Lipped Channel Column (Direct Strength Method) Simpl Supported C-Section Beam References 218 CHAPTER 11 STEEL STORAGE RACKING Introduction Loads Methods of Structural Analsis Upright Frames - First Order Upright Frames - Second Order Beams Effects of Perforations (Slots) Section Modulus of Net Section Minimum Net Cross-Sectional Area Form Factor (Q) Member Design Rules Flexural Design Curves Column Design Curves 226 vi

8 Distortional Buckling Example References 235 SUBJECT INDEX BY SECTION 236 vii