Subcommittee Reports on Cold-Formed Steel Specification, Manuais, Projetos, Pesquisas de Engenharia Civil

Baixe Subcommittee Reports on Cold-Formed Steel Specification e outras Manuais, Projetos, Pesquisas em PDF para Engenharia Civil, somente na Docsity! Missouri University of Science and Technology Scholars' Mine AISI-Specifications for the Design of Cold-Formed Steel Structural Members Wei-Wen Yu Center for Cold-Formed Steel Structures 7-2003 North American Specification for the Design of Cold-Formed Steel Structural Members, 2001 Edition, with incorporation of Errata No. 1 American Iron and Steel Institute Follow this and additional works at: http://scholarsmine.mst.edu/ccfss-aisi-spec Part of the Structural Engineering Commons This Report - Technical is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in AISI-Specifications for the Design of Cold-Formed Steel Structural Members by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. Recommended Citation American Iron and Steel Institute, "North American Specification for the Design of Cold-Formed Steel Structural Members, 2001 Edition, with incorporation of Errata No. 1" (2003). AISI-Specifications for the Design of Cold-Formed Steel Structural Members. 132. http://scholarsmine.mst.edu/ccfss-aisi-spec/132 TERRA IPEN)  North American Cold-Formed Steel Specification December 2001 3 PREFACE This is the first edition of the North American Specification for the Design of Cold-Formed Steel Structural Members; as its name implies, it is intended for use throughout Canada, Mexico, and the United States. This Specification supersedes the previous editions of the Specification for the Design of Cold-Formed Steel Structural Members published by the American Iron and Steel Institute and the previous editions of CSA Standard S136, Cold Formed Steel Structural Members, published by the Canadian Standards Association. The Specification was developed by a joint effort of the American Iron and Steel Institute’s Committee on Specifications, the Canadian Standards Association’s Technical Committee on Cold Formed Steel Structural Members (S136), and Camara Nacional de la Industria del Hierro y del Acero (CANACERO) in Mexico. This effort was coordinated through the North American Specification Committee, which was made up of three members each from the AISI Committee on Specifications, CSA’s S136 Committee, and CANACERO. Since the Specification is intended for use in Canada, Mexico, and the United States, it was necessary to develop a format that would allow for requirements particular to each country. This resulted in a main document, Chapters A through G, that is intended for use in all three countries, and three country-specific appendices (A to C). Appendix A is for use in the United States, Appendix B is for use in Canada, and Appendix C is for use in Mexico. A symbol A,B,C is used in the main document to point out that additional provisions are provided in the corresponding appendices indicated by the letters. This Specification provides an integrated treatment of Allowable Strength Design (ASD), Load and Resistance Factor Design (LRFD), and Limit States Design (LSD). This is accomplished by including the appropriate resistance factors (φ) for use with LRFD and LSD, and the appropriate factors of safety (Ω) for use with ASD. It should be noted that LSD is limited to Canada and LRFD and ASD are limited to Mexico and the United States. The Specification also contains some terminology that is defined differently in Canada, the United States, and Mexico. These differences are set out in Section A1.2, “Terms”. The Specification provides well-defined procedures for the design of load-carrying cold- formed steel members in buildings, as well as other applications provided that proper allowances are made for dynamic effects. The provisions reflect the results of continuing research to develop new and improved information on the structural behavior of cold-formed steel members. The success of these efforts is evident in the wide acceptance of the predecessor documents to this Specification. The AISI and CSA consensus committees responsible for developing these provisions provide a balanced forum, with representatives from steel producers, fabricators, users, educators, researchers, and building code regulators. They are composed of engineers with a wide range of experience and high professional standing from throughout Canada, Mexico, and the United States. AISI, CANACERO, and CSA acknowledge the continuing dedication by the members of the specifications committees and their subcommittees. The membership of these committees follows this Preface. Preface 4 December 2001 Because this is the first edition of the North American Cold-Formed Steel Specification, no attempt will be made here to list provisions that represent changes to the documents that it supersedes. Such changes are numerous and are distributed throughout. Users of the Specification are encouraged to offer comments and suggestions for improvement. American Iron and Steel Institute Canadian Standards Association Camara Nacional de la Industria del Hierro y del Acero December 2001 North American Cold-Formed Steel Specification December 2001 5 North American Specification Committee AISI CSA CANACERO R. L. Brockenbrough R. M. Schuster, Chairman M. Saldivar H. H. Chen S. R. Fox, Secretary J. L. Hernandez J. N. Nunnery T. W. J. Trestain J. Garcia AISI Committee on Specifications for the Design of Cold–Formed Steel Structural Members and its Subcommittees R. L. Brockenbrough, Chairman J. W. Larson, Vice Chairman H. H. Chen, Secretary R. Bjorhovde R. E. Brown J. K. Crews D. A. Cuoco R. Daudet E. R. diGirolamo D. S. Ellifritt S. J. Errera E. R. Estes, Jr. J. M. Fisher S. R. Fox J. Garcia M. Golovin W. B. Hall G. J. Hancock A. J. Harrold R. B. Haws J. L. Hernandez D. L. Johnson J. M. Klaiman R. A. LaBoube C. J. Lanz R. L. Madsen J. Mattingly R. R. McCluer W. R. Midgley J. A. Moses T. M. Murray J. N. Nunnery T. B. Pekoz C. W. Pinkham V. E. Sagan M. Saldivar B. W. Schafer R. M. Schuster P. A. Seaburg W. L. Shoemaker T. Sputo M. A. Thimons T. W. J. Trestain W. W. Yu Subcommittee 3 - Connections A. J. Harrold, Chairman R. Bjorhovde R. Daudet E. R. diGirolamo D. S. Ellifirtt E. R. Estes, Jr. M. Golovin W. B. Hall G. J. Hancock R. B. Haws D. L. Johnson W. E. Kile J. S. Kreiner R. A. LaBoube J. Mattingly J. N. Nunnery T. B. Pekoz C. W. Pinkham S. Rajan R. M. Schuster W. L. Shoemaker T. Sputo S. J. Thomas W. W. Yu Subcommittee 4 – Stud Design and Perforated Elements V. E. Sagan, Chairman K. Bielat R. Daudet E. R. diGirolamo E. R. Estes, Jr. P. S. Green W. T. Guiher R. A. LaBoube R. L. Madsen J. P. Matsen W. R. Midgley T. H. Miller T. B. Pekoz B. W. Schafer T. Sputo T. W. J. Trestain S. H. Walker J. Wellinghoff R. Zadeh Subcommittee 6 – Test Procedures S. R. Fox, Chairman R. E. Brown R. Daudet E. R. diGirolamo D. S. Ellifritt S. J. Errera E. R. Estes, Jr. M. Golovin W. B. Hall D. L. Johnson R. C. Kaehler W. E. Kile R. A. LaBoube W. R. Midgley T. M. Murray T. B. Pekoz C. W. Pinkham S. Rajan R. M. Schuster S. J. Thomas W. W. Yu Subcommittee 7 - Editorial C. W. Pinkham, Chairman D. A. Cuoco J. M. Fisher T. B. Pekoz P. A. Seaburg Preface 8 December 2001 R. C. Kaehler Computerized Structural Design, Inc. W. E. Kile Structuneering Inc. J. M. Klaiman ADTEK Engineers J. S. Kreiner Tiden, Lobnitz, Cooper R. A. LaBoube University of Missouri–Rolla C. J. Lanz American Institute of Steel Construction J W. Larson Bethlehem Steel Corporation M. R. Loseke Loseke Properties, Inc. R. L. Madsen Devco Engineering, Inc. M. K. Madugula University of Windsor J. P. Matsen Matsen Ford Design Associates, Inc. J. Mattingly Nicholas J. Bouras, Inc. S. McCavour McCavour Engineering Ltd. R. R. McCluer Building Officials & Code Administrators, International W. R. Midgley Midgley, Clauer and Associates T. H. Miller Oregon State University F. Morello M.I.C. Industries, Inc. J. A. Moses Unistrut Corporation T. M. Murray Virginia Polytechnic Institute J. N. Nunnery Varco–Pruden Buildings T. B. Pekoz Cornell University N. L. Perterson Steel Stud Manufacturers Association C. W. Pinkham S. B. Barnes Associates D. Polyzois University of Manitoba S. Rajan Alpine Engineering Products, Inc. V. E. Sagan Simpson Gumpertz & Heger Inc. M. Saldivar CANACERO B. W. Schafer Johns Hopkins University N. Schillaci Dofasco Inc. R. M. Schuster University of Waterloo P. A. Seaburg Southern Illinois University D. R. Sherman Consultant W. L. Shoemaker Metal Building Manufacturers Association K. S. Sivakumaran McMaster University M. Sommerstein M&H Engineering T. Sputo Sputo Engineering K. Taing VICWEST C.R. Taraschuk NRC/IRC Canadian Code Centre M. A. Thimons CENTRIA S. J. Thomas Varco-Proden Buildings T. W. J. Trestain T. W. J. Trestain Structural Engineering M. Tumkur Canadian Standards Association L. Vavek Structural Engineer E.F. Vickers Robertson Building Systems R. Vincent Le Group Canam Manac Inc. S. H. Walker Steven H. Walker J. Wellinghoff Clark Steel Framing T. Wolf MBCI L. Xu University of Waterloo W. W. Yu Consultant R. Zadeh Unimast Incorporated North American Cold-Formed Steel Specification December 2001 9 TABLE OF CONTENTS NORTH AMERICAN SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS 2001 EDITION PREFACE................................................................................................................................................3 SYMOBLS AND DEFINITIONS ..............................................................................................................15 A. GENERAL PROVISIONS .................................................................................................................33 A1 Limits of Applicability and Terms ............................................................................................. 33 A1.1 Scope and Limits of Applicability................................................................................... 33 A1.2 Terms ............................................................................................................................... 34 A1.3 Units of Symbols and Terms............................................................................................ 37 A2 Material .......................................................................................................................................... 37 A2.1 Applicable Steels ............................................................................................................... 37 A2.2 Other Steels ........................................................................................................................ 38 A2.3 Ductility .............................................................................................................................. 38 A2.4 Delivered Minimum Thickness....................................................................................... 40 A3 Loads .............................................................................................................................................. 40 A4 Allowable Strength Design ......................................................................................................... 40 A4.1 Design Basis ....................................................................................................................... 40 A4.1.1 ASD Requirements ............................................................................................. 40 A4.1.2 Load Combinations for ASD............................................................................. 41 A5 Load and Resistance Factor Design ........................................................................................... 41 A5.1 Design Basis ....................................................................................................................... 41 A5.1.1 LRFD Requirements........................................................................................... 41 A5.1.2 Load Factors and Load Combinations for LRFD ........................................... 41 A6 Limit States Design....................................................................................................................... 41 A6.1 Design Basis ....................................................................................................................... 41 A6.1.1 LSD Requirements.............................................................................................. 41 A6.1.2 Load Factors and Load Combinations for LSD.............................................. 42 A7 Yield Point and Strength Increase from Cold Work of Forming ........................................... 42 A7.1 Yield Point .......................................................................................................................... 42 A7.2 Strength Increase from Cold Work of Forming ............................................................ 42 A8 Serviceability ................................................................................................................................. 43 A9 Referenced Documents ................................................................................................................ 43 B. ELEMENTS .....................................................................................................................................45 B1 Dimensional Limits and Considerations................................................................................... 45 B1.1 Flange Flat-Width-to-Thickness Considerations .......................................................... 45 B1.2 Maximum Web Depth-to-Thickness Ratios................................................................... 46 B2 Effective Widths of Stiffened Elements ..................................................................................... 47 B2.1 Uniformly Compressed Stiffened Elements .................................................................. 47 B2.2 Uniformly Compressed Stiffened Elements with Circular Holes .............................. 49 B2.3 Webs and other Stiffened Elements under Stress Gradient ........................................ 49 B2.4 C-Section Webs with Holes under Stress Gradient ...................................................... 51 B3 Effective Widths of Unstiffened Elements ................................................................................ 52 Table of Contents 10 December 2001 B3.1 Uniformly Compressed Unstiffened Elements ............................................................. 52 B3.2 Unstiffened Elements and Edge Stiffeners under Stress Gradient............................. 52 B4 Effective Widths of Elements with One Intermediate Stiffener or an Edge Stiffener......... 53 B4.1 Uniformly Compressed Elements with One Intermediate Stiffener.......................... 53 B4.2 Uniformly Compressed Elements with an Edge Stiffener........................................... 54 B5 Effective Widths of Stiffened Elements with Multiple Intermediate Stiffeners or Edge Stiffened Elements with Intermediate Stiffeners...................................................................... 56 B5.1 Effective Widths of Uniformly Compressed Stiffened Elements with Multiple Intermediate Stiffeners ..................................................................................................... 56 B5.1.1 Specific Case: ‘n’ Identical Stiffeners, Equally Spaced .................................. 57 B5.1.2 General Case: Arbitrary Stiffener Size, Location and Number.................... 57 B5.2 Edge Stiffened Elements with Intermediate Stiffeners ................................................ 59 C. MEMBERS .....................................................................................................................................60 C1 Properties of Sections................................................................................................................... 60 C2 Tension Members ......................................................................................................................... 60 C3 Flexural Members......................................................................................................................... 60 C3.1 Bending ............................................................................................................................... 60 C3.1.1 Nominal Section Strength [Resistance] ........................................................... 60 C3.1.2 Lateral-Torsional Buckling Strength [Resistance].......................................... 62 C3.1.2.1 Lateral-Torsional Buckling Strength [Resistance] of Open Cross Section Members............................................................................... 62 C3.1.2.2 Lateral-Torsional Buckling Strength [Resistance] of Closed Box Members ............................................................................................ 65 C3.1.3 Beams Having One Flange Through-Fastened to Deck or Sheathing......... 65 C3.1.4 Beams Having One Flange Fastened to a Standing Seam Roof System ..... 67 C3.1.5 Strength [Resistance] of Standing Seam Roof Panel Systems ...................... 67 C3.2 Shear ............................................................................................................................... 68 C3.2.1 Shear Strength [Resistance] of Webs without Holes ..................................... 68 C3.2.2 Shear Strength [Resistance] of C-Section Webs with Holes ......................... 69 C3.3 Combined Bending and Shear......................................................................................... 69 C3.3.1 ASD Method........................................................................................................ 69 C3.3.2 LRFD and LSD Methods.................................................................................... 70 C3.4 Web Crippling ................................................................................................................... 71 C3.4.1 Web Crippling Strength [Resistance] of Webs without Holes ..................... 71 C3.4.2 Web Crippling Strength [Resistance] of C-Section Webs with Holes ......... 74 C3.5 Combined Bending and Web Crippling ........................................................................ 75 C3.5.1 ASD Method........................................................................................................ 75 C3.5.2 LRFD and LSD Methods.................................................................................... 77 C3.6 Stiffeners ............................................................................................................................. 79 C3.6.1 Transverse Stiffeners.......................................................................................... 79 C3.6.2 Shear Stiffeners ................................................................................................... 80 C3.6.3 Non-Conforming Stiffeners............................................................................... 80 C4 Concentrically Loaded Compression Members....................................................................... 81 C4.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling............................. 81 C4.2 Doubly- or Singly-Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling .............................................................................................................................. 82 North American Cold-Formed Steel Specification December 2001 13 A5.1.2 Load Factors and Load Combinations for LRFD .......................................... A4 A9a Referenced Documents ............................................................................................................... A4 C2 Tension Members ........................................................................................................................ A4 C3.1.4 Beams Having One Flange Fastened to a Standing Seam Roof System .... A5 E2a Welded Connections ................................................................................................................... A5 E3a Bolted Connections...................................................................................................................... A6 E3.1 Shear, Spacing and Edge Distance................................................................................. A7 E3.2 Fracture in Net Section (Shear Lag) ............................................................................... A8 E3.4 Shear and Tension in Bolts.............................................................................................. A9 E4.3.2 Connection Shear Limited by End Distance................................................ A14 E5 Rupture ....................................................................................................................................... A14 E5.1 Shear Rupture ................................................................................................................. A14 E5.2 Tension Rupture ............................................................................................................. A14 E5.3 Block Shear Rupture ...................................................................................................... A14 PREFACE TO APPENDIX B: ................................................................................................................ B2 APPENDIX B: PROVISIONS APPLICABLE TO CANADA...................................................................... B3 A1.2a Terms ...............................................................................................................................B3 A2.1a Applicable Steels ...............................................................................................................B3 A2.2 Other Steels ........................................................................................................................B3 A2.2.1 Other Structural Quality Steels.........................................................................B3 A2.2.2 Other Steels..........................................................................................................B3 A2.4a Delivered Minimum Thickness.......................................................................................B3 A3 Loads ..............................................................................................................................................B4 A3.1 Specified Loads..................................................................................................................B4 A3.2 Temperature Effects ..........................................................................................................B5 A6.1.2 Load Factors and Load Combinations for LSD..............................................B5 A6.1.2.1 Load Factors (α) ................................................................................B5 A6.1.2.2 Load Combination Factor (ψ) .........................................................B5 A6.1.2.3 Importance Factor (γ) .......................................................................B5 A9a Reference Documents ..................................................................................................................B6 C2 Tension Members .........................................................................................................................B6 C2.1 Yielding of Gross Section .................................................................................................B6 C2.2 Fracture of Net Section .....................................................................................................B6 C3.1.4 Beams Having One Flange Fastened to a Standing Seam Roof System .....B7 D3a Lateral Bracing ..............................................................................................................................B7 D3.1a Symmetrical Beams and Columns ..................................................................................B7 D3.1.1 Discrete Bracing ..................................................................................................B8 D3.1.2 Bracing by Deck, Slab, or Sheathing ................................................................B8 D3.2a C-Section and Z-Section Beams.......................................................................................B8 D3.2.3 Discrete Bracing ..................................................................................................B8 D3.2.4 One Flange Braced by Deck, Slab, or Sheathing ............................................B8 D3.2.5 Both Flanges Braced by Deck, Slab, or Sheathing..........................................B9 E2a Welded Connections ....................................................................................................................B9 E2.2a Arc Spot Welds ..................................................................................................................B9 E2.3a Arc Seam Welds.................................................................................................................B9 E3a Bolted Connections.....................................................................................................................B10 Table of Contents 14 December 2001 E3.1 Shear, Spacing and Edge Distance................................................................................B10 E3.2 Fracture in Net Section (Shear Lag) ..............................................................................B10 E3.3a Bearing .............................................................................................................................B11 E3.4 Shear and Tension in Bolts.............................................................................................B11 E4.3.2 Connection Shear Limited by End Distance.................................................B12 E5 Rupture ........................................................................................................................................B12 APPENDIX C: PROVISIONS APPLICABLE TO MEXICO....................................................................... C3 A1.1a Country Specific Scope and Limits of Applicability ................................................... C3 A2.2 Other Steels ....................................................................................................................... C3 A3 Loads ............................................................................................................................................. C3 A3.1 Nominal Loads ................................................................................................................. C3 A4.1.2 Load Combinations for ASD............................................................................ C3 A5.1.2 Load Factors and Load Combinations for LRFD .......................................... C4 A9a Referenced Documents ............................................................................................................... C4 C2 Tension Members ........................................................................................................................ C5 C3.1.4 Beams Having One Flange Fastened to a Standing Seam Roof System .... C5 E2a Welded Connections ................................................................................................................... C5 E3a Bolted Connections..................................................................................................................... C6 E3.1 Shear, Spacing and Edge Distance................................................................................. C7 E3.2 Fracture in Net Section (Shear Lag) ............................................................................... C8 E3.4 Shear and Tension in Bolts.............................................................................................. C9 E4.3.2 Connection Shear Limited by End Distance................................................ C13 E5 Rupture ....................................................................................................................................... C13 E5.1 Shear Rupture ................................................................................................................. C13 E5.2 Tension Rupture ............................................................................................................. C13 E5.3 Block Shear Rupture ...................................................................................................... C13 North American Cold-Formed Steel Specification SYMBOLS AND DEFINITIONS Symbol Definition Section December 2001 15 A Full unreduced cross-sectional area of member C3.1.2.1, C4.2, C4.6, C5.2.1, C5.2.2, C6.2, D4.1 A Area of directly connected elements or gross area E2.7 Ab b1t + As, for transverse stiffeners at interior support and C3.6.1 under concentrated load, and b2t + As, for transverse stiffeners at end support Ab Gross cross-sectional area of bolt E3.4 Ac 18t2 + As, for transverse stiffeners at interior support C3.6.1 and under concentrated load, and 10t2 + As, for transverse stiffeners at end support Ao Reduced area due to local buckling C6.2 Ae Effective area at stress Fn C3.6.1, C4, C4.2, C5.2.1, C5.2.2, C6.2, D4, D4.1 Ae Effective net area E2.7, E3.2 Ag Gross area of element including stiffeners B5.1 Ag Gross area of section C2, E2.7, E3.2 Agt Gross area subject to tension E5.3 Agv Gross area subject to shear E5.3 Ant Net area subject to tension E5.3 Anv Net area subject to shear E5.3 An Net area of cross section C2, E3.2 As Reduced cross sectional area of edge or intermediate B4, B4.1, B4.2 stiffener As Cross-sectional area of transverse stiffener C3.6.1 As Gross area of stiffener B5.1 A′s Effective area of stiffener B4, B4.1, B4.2 Ast Gross area of shear stiffener C3.6.2 At Net tensile area G4 Aw Area of web C3.2.1 Awn Net web area E5.1 a Shear panel length of unreinforced web element, or C3.2.1, C3.6.2 distance between transverse stiffeners of reinforced web elements a Intermediate fastener or spot weld spacing C4.5 a Fastener distance from outside web edge C4.6 Symbols and Definitions SYMBOLS AND DEFINITIONS Symbol Definition Section 18 December 2001 d Visible diameter of outer surface of arc spot weld E2.2.1, E2.2.2 d Diameter of bolt E3a, E3.2, E3.3.1, E3.3.2, E3.4 da Average diameter of arc spot weld at mid-thickness E2.2.1, E2.2.2 of t da Average width of seam weld E2.3 db Nominal diameter (body or shank diameter) G4 de Effective diameter of fused area E2.2, E2.2.1, E2.2.2 de Effective width of arc seam weld at fused surfaces E2.3 dh Diameter of standard hole B2.2, E3a, E3.1, E3.2, E5.1 d0 Depth of web hole B2.4, C3.2.2, C3.4.2 ds Reduced effective width of stiffener B4, B4.2 d′s Effective width of stiffener calculated according to B3.1 B4, B4.2 dwx Screw head or washer diameter E4.4 dw Larger value of screw head or washer diameter E4, E4.4, E4.4.2 E Modulus of elasticity of steel, 29,500 ksi (203,000 MPa, A2.3.2, B1.1, B2.1, B4, B5.1, or 2,070,000 kg/cm2) C3.1.1, C3.1.2.1, C3.1.2.2, C3.2.1, C3.5.1, C3.5.2, C3.6.1, C3.6.2, C4.1, C4.6, C5.2.1, C5.2.2, C6, C6.1, C6.2, D1.2, D4.1, E2.2.1 E Live load due to earthquake A3.1, A6.1.2 Eo Initial column imperfection; a measure of initial D4.1 twist of stud from initial, ideal, unbuckled shape E1 Term used to compute shear strain in wallboard D4.1 E′ Inelastic modulus of elasticity D4.1 e Distance measured in line of force from E3.1, E3.1a center of a standard hole to nearest edge of an adjacent hole or to end of connected part toward which force is directed e Distance measured in line of force from center E4.3.2 of a standard hole to nearest end of connected part emin Minimum allowable distance measured in line of E2.2.1, E2.2.2 force from centerline of a weld to nearest edge North American Cold-Formed Steel Specification SYMBOLS AND DEFINITIONS Symbol Definition Section December 2001 19 of an adjacent weld or to end of connected part toward which the force is directed ey Yield strain = Fy/E C3.1.1 F Fabrication factor F1.1 F Nominal tensile or shear strength E3.4 FSR Design stress range G3 FTH Threshold fatigue stress range G1, G3, G4 Fc Critical buckling stress B2.1, C3.1.2.1, C6.1 Fcr Plate elastic buckling stress B2.1, B5.1 Fe Elastic buckling stress C3.1.2.1, C3.1.2.2, C4, C4.1, C4.2, C4.3, C4.4, C6.2, D4.1 Fm Mean value of fabrication factor C3.1.5, F1.1 Fn Nominal buckling stress B2.1, C4, C5.2.1, C5.2.2, C6.2, D4, D4.1 Fn Nominal strength of bolts E3.4 Fnt Nominal tensile strength of bolts E3.4 Fnv Nominal shear strength of bolts E3.4 F′nt Nominal tensile strength for bolts subject to combination E3.4 of shear and tension Fsy Yield point as specified in Section A2.1, A2.2 or A2.3.2 A1.2, A2.3.2, E2.2.1, E3.1 Ft Nominal tensile stress in flat sheet E3.2 Fu Tensile strength as specified in Section A2.1, A2.2 A2.3.2, C2, E2.2.1, E2.2.2, E2.3, or A2.3.2 E2.4, E2.5, E2.7, E3.1, E3.2, E3.3.1, E3.3.2, E4.3.2, E5.1, E5.3 Fuv Tensile strength of virgin steel specified by Section A2 A7.2 or established in accordance with Section F3.3 Fwy Yield point for design of transverse stiffeners C3.6.1 Fxx Tensile strength of electrode classification E2.1, E2.2.1, E2.2.2, E2.3, E2.4, E2.5 Fu1 Tensile strength of member in contact with screw head E4, E4.3.1, E4.4.2 Fu2 Tensile strength of member not in contact with screw E4, E4.3.1, E4.4.1 head Symbols and Definitions SYMBOLS AND DEFINITIONS Symbol Definition Section 20 December 2001 Fv Nominal shear stress E3.2.1 Fy Yield point used for design, not to exceed specified A1.2, A2.3.2, A7.1, A7.2, yield point or established in accordance with Section F3, B2.1, C2, C3.1.1, C3.1.2.1, or as increased for cold work of forming in Section C3.1.2.2, C3.1.3, C3.2.1, A7.2 or as reduced for low ductility steels in Section C3.1.4, C3.4.1, C3.5.1, C3.5.2, C3.6.1, C3.6.2, C4, C4.2, C5.1.1, C5.1.2, C5.2.1, C5.2.2, C6, C6.1, C6.2, D1.2, D4.1, E2.1, E2.2.2, E5.2, G1 Fya Average yield point of section A7.2 Fyc Tensile yield point of corners A7.2 Fyf Weighted average tensile yield point of flat portions A7.2, F3.2 Fys Yield point of stiffener steel C3.6.1 Fyv Tensile yield point of virgin steel specified by Section A7.2 A2 or established in accordance with Section F3.3 f Stress in compression element computed on B2.1, B2.2, B2.4, B3.1, B3.2, basis of effective design width B4, B4.1, B4.2, B5.1, B5.1.1, B5.1.2, B5.2 fav Average computed stress in full unreduced flange B1.1 width fc Stress at service load in cover plate or sheet D1.2 fd Computed compressive stress in element being B2.1, B2.2, B3.1, B4.1, B4.2, considered. Calculations are based on effective B5.1.1, B5.1.2, B5.2 section at load for which deflections are determined. fd1, fd2 Computed stresses f1 and f2 as shown in Figure B2.3-1. B2.3 Calculations are based on effective section at load for which serviceability is determined. fd3 Computed stress f3 in edge stiffener, as shown in Figure B3.2 B4-2. Calculations are based on effective section at load for which serviceability is determined. fv Computed shear stress on a bolt E3.4 f1, f2 Web stresses defined by Figure B2.3-1 B2.3, B2.4 North American Cold-Formed Steel Specification SYMBOLS AND DEFINITIONS Symbol Definition Section December 2001 23 Lx Unbraced length of compression member for bending C3.1.2.1, C5.2.1, C5.2.2 about x-axis Ly Unbraced length of compression member for bending C3.1.2.1, C3.1.2.2, C5.2.1, about y-axis C5.2.2 Lu Limit of unbraced length by which lateral-torsional C3.1.2.2 buckling is not be considered Mmax, Absolute value of moments in unbraced segment, C3.1.2.1 MA, MB, used for determining Cb MC Mm Mean value of material factor C3.1.5, F1.1 Mn Nominal flexural strength [resistance] B2.1, C3.1, C3.1.1, C3.1.2.1, C3.1.2.2, C3.1.3, C3.1.4, C3.3.1, C3.3.2, C6.1 M Required allowable flexural strength, ASD C3.3.1, C3.5.1 Mnx, Nominal flexural strengths [resistances] about C5.1.1, C5.1.2, C5.2.1, Mny centroidal axes determined in accordance with C5.2.2, D4.3 Section C3 Mnxo, Nominal flexural strengths [resistances] about C3.3.1, C3.3.2, C3.5.1, C3.5.2, Mnyo centroidal axes determined in accordance with D4.2, D4.3 Section C3.1 excluding provisions of Section C3.1.2 Mno Nominal yield moment for nested Z-sections C3.5.1, C3.5.2 Mnxt, Nominal flexural strengths [resistances] about C5.1.1, C5.1.2 Mnyt centroidal axes determined using gross, unreduced cross-section properties Mf Factored moment C3.3.2 Mfx, Moments due to factored loads with respect to C4, C5.1.2, C5.2.2 Mfy centroidal axes Mx, Required allowable flexural strength with respect to C4, C5.1.1, C5.2.1 My centroidal axes for ASD Symbols and Definitions SYMBOLS AND DEFINITIONS Symbol Definition Section 24 December 2001 Mu Required flexural strength for LRFD C3.3.2, C3.5.2 Mux, Required flexural strength with respect to C4, C5.1.2, C5.2.2 Muy centroidal axes for LRFD M Required flexural strength [factored moment] C3.3.2, C3.5.2 xM , Required flexural strengths [factored moments] C4, C5.1.2 yM My Moment causing maximum strain ey B2.1, C3.1.2 M1 Smaller end moment C3.1.2.1, C5.2.1, C5.2.2 M2 Larger end moment C3.1.2.1, C5.2.1, C5.2.2 m Degrees of freedom F1.1 m Term for determining tensile yield point of corners A7.2 m Distance from shear center of one C-section to D1.1, D3.2.2 mid-plane of web mf Modification factor for type of bearing connection E3.3.1 N Actual length of bearing C3.4.1, C3.4.2, C3.5.1, C3.5.2 N Number of stress range fluctuations in design life G3 n Coefficient B4.1, B4.2 n Number of stiffeners B5.1, B5.1.1, B5.1.2 n Number of holes E5.1 n Number of tests F1.1 n Number of anchors in test assembly with same C3.1.5 tributary area (for anchor failure), or number of panels with identical spans and loading to failed span (for non-anchor failure) n Number of threads per inch G4 nb Number of bolt holes E3.2 np Number of parallel purlin lines D3.2.1 P Required allowable strength for concentrated load C3.5.1 reaction in presence of bending moment for ASD P Required allowable strength (nominal force) transmitted E2.2.1 North American Cold-Formed Steel Specification SYMBOLS AND DEFINITIONS Symbol Definition Section December 2001 25 by weld for ASD P Required allowable compressive axial strength for ASD A2.3.1, C5.2.1 P Professional factor F1.1 P Pitch (mm per thread for SI units and cm per thread G4 for MKS units) PEx, Elastic buckling strengths [resistances] C5.2.1, C5.2.2 PEy Pf Axial force due to factored loads A2.3.1, C5.2.2 Pf Concentrated load or reaction due to factored loads C3.5.2 Pf Factored shear force transmitted by welding E2.2.1 PL Force to be resisted by intermediate beam brace D3.2.1, D3.2.2 Pm Mean value of the tested-to-predicted load ratios F1.1 Pn Nominal web crippling strength [resistance] C3.4.1, C3.5.1, C3.5.2 Pn Nominal axial strength [resistance] of member A2.3.1, C4, C4.6, C5.2.1, C5.2.2, C6.2, D4.1, D4.3 Pn Nominal axial strength [resistance] of transverse stiffener C3.6.1 Pn Nominal strength [resistance] of connection component E2.1, E2.2.1, E2.2.2, E2.3, E2.4, E2.5, E2.6, E3.1, E3.2, E3.4 Pn Nominal bearing strength [resistance] E3.3.1, E3.3.2 Pn Nominal tensile strength of welded member E2.7 Pno Nominal axial strength [resistance] of member C5.2.1, C5.2.2 determined in accordance with Section C4 with Fn = Fy Pnot Nominal pull-out strength [resistance] per screw E4, E4.4.1, E4.4.3 Pnov Nominal pull-over strength [resistance] per screw E4, E4.4.2, E4.4.3 Pns Nominal shear strength [resistance] per screw E4, E4.2, E4.3.1, E4.3.2, E4.3.3 Pnt Nominal tension strength [resistance] per screw E4, E4.4.3 Ps Concentrated load or reaction D1.1 Pss Nominal shear strength [resistance] of screw as E4, E4.3.3 reported by manufacturer or determined by independent laboratory testing Symbols and Definitions SYMBOLS AND DEFINITIONS Symbol Definition Section 28 December 2001 smax Maximum permissible longitudinal spacing of welds or D1.1 other connectors joining two C-sections to form an I-section T Required allowable tensile axial strength for ASD C5.1.1 T Load due to contraction or expansion caused by A3.1, A3.1, A6.1.2, A6.1.2.2 temperature changes Tf Tension due to factored loads C5.1.2 Tn Nominal tensile strength [resistance] C2, C5.1.1, C5.1.2 Ts Design strength [factored resistance] of connection in D1.1 tension Tu Required tensile axial strength for LRFD C5.1.2 T Required tensile axial strength [factored tensile force] C5.1.2 with respect to centroid t Base steel thickness of any element or section A1.2, A2.3.2, A2.4, A7.2, B1.1, B1.2, B2.1, B2.2, B2.4, B4, B4.1, B4.2, B5.1, B5.1.1, B5.1.2, B5.2, C3.1.1, C3.2.1, C3.2.2, C3.4.1, C3.4.2, C3.5.1, C3.5.2, C3.6.1, C3.6.2, C4.6, C6, C6.1, C6.2, D1.2, D3.2.1, D4, D4.1, E3.3.1, E3.3.2, E4.3.2 t Thickness of coped web E5.1 t Total thickness of two welded sheets E2.2.1, E2.2.2, E2.3 t Thickness of thinnest connected part E2.4, E2.5, E2.6, E3.1, E3.2, E3.3.2 t1, t2 Based thicknesses connected with fillet weld E2.4 t1 Thickness of member in contact with screw head E4, E4.3.1, E4.4.2 t2 Thickness of member not in contact with screw head E4, E4.3.1 tc Lesser of depth of penetration and t2 E4, E4.4.1 te Effective throat dimension of groove weld E2.1 ti Thickness of uncompressed glass fiber blanket insulation C3.1.3 ts Thickness of stiffener C3.6.1 tw Effective throat of weld E2.4, E2.5 North American Cold-Formed Steel Specification SYMBOLS AND DEFINITIONS Symbol Definition Section December 2001 29 U Reduction coefficient E2.7, E3.2 V Required allowable shear strength for ASD C3.3.1 VF Coefficient of variation of fabrication factor C3.1.5, F1.1 VM Coefficient of variation of material factor C3.1.5, F1.1 Vf Shear force due to factored loads for LSD C3.3.2 Vn Nominal shear strength [resistance] C3.2.1, C3.3.1, C3.3.2, C3.6.2, E5.1 VP Coefficient of variation of tested-to-predicted load C3.1.5, F1.1 ratios VQ Coefficient of variation of load effect C3.1.5, F1.1 Vu Required shear strength for LRFD C3.3.2 V Required shear strength [factored shear] C3.3.2 W Design load supported by all purlin lines being D3.2.1 restrained W Live load due to wind A3.1, A6.1.2, A6.1.2.2 w Flat width of element exclusive of radii A2.3.2, B1.1, B2.1, B2.2, B3.1, B4, B4.1, B4.2, C3.1.1, C3.6.1, D1.2 w Flat width of beam flange which contacts bearing C3.5.1, C3.5.2 plate w Flat width of narrowest unstiffened compression D1.2 element tributary to connections wf Width of flange projection beyond web for I-beams B1.1 and similar sections; or half distance between webs for box- or U-type sections w1 Leg of weld E2.4, E2.5 w2 Leg of weld E2.4, E2.5 x Distance from concentrated load to brace D3.2.2 x Non-dimensional fastener location C4.6 x Nearest distance between web hole and edge of bearing C3.4.2 xo Distance from shear center to centroid along principal C3.1.2.1, C4.2, D4.1 x-axis x Distance from shear plane to centroid of cross section E2.7, E3.2 Symbols and Definitions SYMBOLS AND DEFINITIONS Symbol Definition Section 30 December 2001 Y Yield point of web steel divided by yield point of C3.6.2 stiffener steel α Coefficient for purlin directions D3.2.1 α Coefficient for conversion of units C4.6, E3.3.2, G3 α Load factor A1.2a αD Dead load factor A6.1.2, A6.1.2.1 αE Load factor of live load due to earthquake A6.1.2, A6.1.2.1 αL Live load factor A6.1.2, A6.1.2.1 αT Load factor due to contraction or expansion caused by A6.1.2, A6.1.2.1 temperature changes αW Wind load factor A6.1.2, A.6.1.2.1 l/αx, Magnification factors C5.2.1, C5.2.2 l/αy β Coefficient B5.1.1, B5.1.2, C4.2, D4.1 βo Target reliability index C3.1.5, F1.1 δ, δi, Coefficients B5.1.1, B5.1.2 γ, γi, ω, ωi γ Actual shear strain in sheathing D4.1 γ Permissible shear strain of sheathing D4.1 γ Importance factor A1.2a, A6.1.2, A6.1.2.3 γi Load factor F1.1 θ Angle between web and bearing surface >45° but no C3.4.1 more than 90° θ Angle between vertical and plane of web of Z-section, D3.2.1 degrees θ Angle between an element and its edge stiffener B4, B4.2 North American Cold-Formed Steel Specification December 2001 33 NORTH AMERICAN SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS A. GENERAL PROVISIONS A1 Limits of Applicability and Terms A1.1 Scope and Limits of Applicability This Specification shall apply to the design of structural members cold- formed to shape from carbon or low-alloy steel sheet, strip, plate or bar not more than one in. (25.4 mm) in thickness and used for load-carrying purposes in buildings. It shall be permitted to be used for structures other than buildings provided appropriate allowances are made for dynamic effects. This Specification includes Symbols and Definitions, Chapters A through G, and Appendices A through C which shall apply as follows: • Appendix A shall apply only in the United States, • Appendix B shall apply only in Canada, and • Appendix C shall apply only in Mexico This Specification includes design provisions for Allowable Strength Design (ASD), Load and Resistance Factor Design (LRFD) and Limit States Design (LSD). These design methods shall apply as follows: • The use of ASD and LRFD shall be limited to the United States and Mexico, and • The use of LSD shall be limited to, and is mandatory in Canada The nominal strength [nominal resistance] and stiffness of cold-formed steel elements, members, assemblies, connections, and details shall be determined in accordance with the provisions in Chapters B through G and Appendices A through C of the Specification. Where the composition or configuration of such components is such that calculation of strength [resistance] and/or stiffness cannot be made in accordance with those provisions, structural performance shall be established from either of the following: (a) Determine design strength [factored resistance] or stiffness by tests, undertaken and evaluated in accordance with Chapter F. (b) Determine design strength [factored resistance] or stiffness by rational engineering analysis based on appropriate theory, related testing if data is available, and engineering judgment. Specifically, the design strength [factored resistance] shall be determined from the calculated nominal strength [resistance] by applying the following factors of safety or resistance factors: Members USA and Mexico Canada Ω (ASD) φ (LRFD) φ(LSD) 2.00 0.80 0.75 Connections USA and Mexico Canada Ω (ASD) φ (LRFD) φ(LSD) 2.50 0.65 0.60 A,C Chapter A, General Provisions 34 December 2001 Note: * Bracketed terms are equivalent terms that apply particularly to LSD. ** Symbol A,C is used to point out that additional provisions are provided in the appendices as indicated by the letters. A1.2 Terms Where the following terms appear in this Specification they shall have the meaning herein indicated: General Terms Cold-Formed Steel Structural Members. Shapes manufactured by press-braking blanks sheared from sheets, cut lengths of coils or plates, or by roll forming cold- or hot-rolled coils or sheets; both forming operations being performed at ambient room temperature, that is, without manifest addition of heat such as would be required for hot forming. Confirmatory Test. Test made, when desired, on members, connections, and assemblies designed according to the provisions of Chapters A through G of this Specification or its specific references, in order to compare actual versus calculated performance. Cross-Sectional Area: Effective Area. Effective area, Ae, calculated using the effective widths of component elements in accordance with Chapter B. It can be a gross area or a net area, as applicable, if the effective widths of all component elements, determined in accordance with Chapter B, are equal to the actual flat widths. Full, Unreduced Area. Full, unreduced area, A, calculated without reducing the widths of component elements to their effective widths. It can be an unreduced gross area or an unreduced net area, as applicable. Gross Area. Gross area, Ag, without deductions for holes, openings, and cutouts. Net Area. Net area, An, equal to gross area less the area of holes, openings, and cutouts. Distortional Buckling. A mode of buckling involving change in cross-sectional shape, excluding local buckling. Doubly Symmetric Section. A section symmetric about two orthogonal axes through its centroid. Effective Design Width. Flat width of an element reduced for design purposes, also known simply as the effective width. Flange of a Section in Bending. Flat width of flange including any intermediate stiffeners plus adjoining corners. Flat Width. Width of an element exclusive of corners measured along its plane. Flat-Width-to-Thickness Ratio (Flat Width Ratio). Flat width of an element measured along its plane, divided by its thickness. North American Cold-Formed Steel Specification December 2001 35 Girt. Horizontal structural member which supports wall panel and is subjected to principally bending under applied loads. Local Buckling. Buckling of elements only within a section, where the line junctions between elements remain straight and angles between elements do not change. Master Coil. One continuous, weld-free coil as produced by a hot mill, cold mill, metallic coating line or paint line and identifiable by unique coil number. This coil may be cut into smaller coils or slit into narrower coils; however, all of these smaller and/or narrower finished coils could be said to have come from the same master coil if they are traceable to the original master coil number. Multiple-Stiffened Element. Element stiffened between webs, or between a web and a stiffened edge, by means of intermediate stiffeners parallel to the direction of stress. Performance Test. Test made on structural members, connections, and assemblies whose performance cannot be determined by the provisions of Chapters A through G of this Specification or its specific references. Point-Symmetric Section. Section symmetrical about a point (centroid) such as a Z-section having equal flanges. Purlin. Horizontal structural member which supports roof deck and is subjected to principally bending under applied loads. Rational Engineering Analysis. Analysis based on theory that is appropriate for the situation, any available test data that is relevant, and sound engineering judgment. Singly-Symmetric Section. Section symmetric about only one axis through its centroid. Specified Minimum Yield Point. Lower limit of yield point in a test specified to qualify a lot of steel for use in a cold-formed steel structural member designed at that yield point. Stiffened or Partially Stiffened Compression Elements. Flat compression element (i.e., a plane compression flange of a flexural member or a plane web or flange of a compression member) of which both edges parallel to the direction of stress are stiffened either by a web, flange, stiffening lip, intermediate stiffener, or the like. SS. ASTM designation for certain sheet steels intended for structural applications. Stress. Stress as used in this Specification means force per unit area. Sub-Element of a Multiple Stiffened Element. Portion of a multiple stiffened element between adjacent intermediate stiffeners, between web and intermediate stiffener, or between edge and intermediate stiffener. Tensile Strength: Maximum stress reached in a tension test. Thickness. The thickness, t, of any element or section shall be the base steel thickness, exclusive of coatings. Torsional-Flexural Buckling. Buckling mode in which compression members bend and twist simultaneously without change in cross sectional shape. Unstiffened Compression Elements. Flat compression element stiffened at only one edge parallel to the direction of stress. Chapter A, General Provisions 38 December 2001 ASTM A606, Steel, Sheet and Strip, High Strength, Low Alloy, Hot-Rolled and Cold-Rolled, with Improved Atmospheric Corrosion Resistance ASTM A653/A653M (SS Grades 33 (230), 37 (255), 40 (275), and 50 (340) Class 1 and Class 3; HSLAS Types A and B, Grades 40 (275), 50 (340), 60 (410), 70 (480) and 80 (550)), Steel Sheet, Zinc-Coated (Galvanized) or Zinc-Iron Alloy-Coated (Galvannealed) by the Hot-Dip Process ASTM A792/A792M (Grades 33 (230), 37 (255), 40 (275), and 50 Class 1 (340 Class 1)), Steel Sheet, 55% Aluminum-Zinc Alloy-Coated by the Hot-Dip Process ASTM A847, Cold-Formed Welded and Seamless High Strength, Low Alloy Structural Tubing with Improved Atmospheric Corrosion Resistance ASTM A875/A875M (SS Grades 33 (230), 37 (255), 40 (275), and 50 (340) Class 1 and Class 3; HSLAS Types A and B, Grades 50 (340), 60 (410), 70 (480), and 80 (550)), Steel Sheet, Zinc-5% Aluminum Alloy-Coated by the Hot- Dip Process ASTM A1003/A1003M, Steel Sheet, Carbon, Metallic- and Nonmetallic- Coated for Cold-Formed Framing Members ASTM A1008/A1008M (SS Grades 25 (170), 30 (205), 33 (230) Types 1 and 2, and 40 (275) Types 1 and 2; HSLAS Classes 1 and 2, Grades 45 (310), 50 (340), 55 (380), 60 (410), 65 (450), and 70 (480); HSLAS-F Grades 50 (340), 60 (410), 70 (480), and 80 (550)), Steel, Sheet, Cold-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-Strength Low-Alloy with Improved Formability ASTM A1011/A1011M (SS Grades 30 (205), 33 (230), 36 (250) Types 1 and 2, 40 (275), 45 (310), 50 (340), and 55 (380); HSLAS Classes 1 and 2, Grades 45 (310), 50 (340), 55 (380), 60 (410), 65 (450), and 70 (480); HSLAS-F Grades 50 (340), 60 (410), 70 (480), and 80(550)), Steel, Sheet and Strip, Hot-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-Strength Low- Alloy with Improved Formability A2.2 Other Steels The provisions of this section are given in Section A2.2 of the Appendices. A2.3 Ductility Steels not listed in Section A2.1 and used for structural members and connections in accordance with Section A2.2 shall comply with one of the following ductility requirements: A2.3.1 The ratio of tensile strength to yield point shall not be less than 1.08, and the total elongation shall not be less than 10 percent for a two- inch (50 mm) gage length or 7 percent for an eight-inch (200 mm) gage length standard specimen tested in accordance with ASTM A370. If these requirements cannot be met, the following criteria shall be satisfied: (1) local elongation in a 1/2 in. (12.7 mm) gage length across the fracture shall not be less than 20 percent, (2) uniform elongation outside the fracture shall not be less than 3 percent. When material ductility is B A,B,C North American Cold-Formed Steel Specification December 2001 39 determined on the basis of the local and uniform elongation criteria, the use of such material is restricted to the design of purlins and girts in accordance with Sections C3.1.1(a), C3.1.2, C3.1.3, and C3.1.4. For purlins and girts subject to combined axial load and bending moment (Section C5), n c P PΩ shall not exceed 0.15 for ASD, nc u P P φ shall not exceed 0.15 for LRFD and nc f P P φ shall not exceed 0.15 for LSD. A2.3.2 Steels conforming to ASTM A653/A653M SS Grade 80 (550), A1008/A1008M SS Grade 80 (550), A792/A792M Grade 80 (550), A875/A875M SS Grade 80 (550) and other steels which do not meet the provisions of Section A2.3.1 shall be permitted for multiple-web configurations such as roofing, siding and floor decking provided that: (1) the yield point, Fy, used for determining nominal strength [resistance] in Chapters B, C, and D is taken as 75 percent of the specified minimum yield point or 60 ksi (410 MPa or 4220 kg/cm2), whichever is less, and (2) the tensile strength, Fu, used for determining nominal strength [resistance] in Chapter E is taken as 75 percent of the specified minimum tensile strength or 62 ksi (427 MPa or 4360 kg/cm2), whichever is less. Alternatively, the suitability of such steels for any multi-web configuration shall be demonstrated by load tests according to the provisions of Section F1. Design strengths [factored resistances] based on these tests shall not exceed the design strengths [factored resistances] calculated according to Chapters B through G, using the specified minimum yield point, Fy, and the specified minimum tensile strength, Fu. Exception: For multiple-web configurations, a reduced yield point, RbFy, shall be permitted for determining the nominal flexural strength [moment resistance] in Section C3.1.1(a), for which the reduction factor, Rb, shall be determined as follows: (a) Stiffened and Partially Stiffened Compression Flanges For w/t ≤ 0.067E/Fy Rb = 1.0 For 0.067E/Fy < w/t < 0.974E/Fy Rb =1-0.26[wFy/(tE) – 0.067]0.4 (Eq. A2.3.2-1) For 0.974E/Fy ≤ w/t ≤ 500 Rb = 0.75 (b) Unstiffened Compression Flanges For w/t ≤0.0173E/Fy Rb = 1.0 For 0.0173E/Fy < w/t ≤ 60 Chapter A, General Provisions 40 December 2001 Rb = )tE/(wF6.0079.1 y− (Eq. A2.3.2-2) where E = Modulus of elasticity Fy = Yield point as specified in Section A7.1 ≤ 80 ksi (550 MPa, or 5620 kg/cm2) t = Thickness of section w = Flat width of compression flange The above Exception does not apply to the use of steel deck for composite slabs, for which the steel deck acts as the tensile reinforcement of the slab. A2.4 Delivered Minimum Thickness The uncoated minimum steel thickness of the cold-formed product as delivered to the job site shall not at any location be less than 95 percent of the thickness, t, used in its design; however, lesser thicknesses shall be permitted at bends, such as corners, due to cold-forming effects. A3 Loads Loads and load combinations shall be as stipulated by the applicable country specific provisions, Section A3 of Appendix A, B, or C. A4 Allowable Strength Design A4.1 Design Basis Design under this Section of the Specification shall be based on Allowable Strength Design (ASD) principles. All provisions of this Specification, except for those in Sections A5 and A6 and in Chapters C and F designated for LRFD and LSD, shall apply. A4.1.1 ASD Requirements A design satisfies the requirements of this Specification when the allowable strength of each structural component equals or exceeds the required allowable strength, determined on the basis of the nominal loads, for all applicable load combinations. The design shall be performed in accordance with Equation (A4.1.1-1): R ≤ Rn /Ω (Eq. A4.1.1-1) where R = Required allowable strength Rn = Nominal strength specified in Chapters B through G Ω = Factor of safety specified in Chapters B through G Rn/Ω = Allowable design strength B A,B,C North American Cold-Formed Steel Specification December 2001 43 Fyc = BcFyv/(R/t)m, tensile yield point of corners. This equation (Eq. A7.2-2) is applicable only when Fuv/Fyv ≥ 1.2, R/t ≤ 7, and the included angle ≤ 120o Bc = 3.69 (Fuv/Fyv) - 0.819 (Fuv/Fyv)2 - 1.79 (Eq. A7.2-3) m = 0.192 (Fuv/Fyv) - 0.068 (Eq. A7.2-4) R = Inside bend radius Fyv = Tensile yield point of virgin steel specified by Section A2 or established in accordance with Section F3.3 Fuv = Tensile strength of virgin steel specified by Section A2 or established in accordance with Section F3.3 (b) For axially loaded tension members the yield point of the steel shall be determined by either method (1) or method (3) prescribed in paragraph (a) of this Section. (c) The effect of any welding on mechanical properties of a member shall be determined on the basis of tests of full section specimens containing within the gage length, such welding as the manufacturer intends to use. Any necessary allowance for such effect shall be made in the structural use of the member. A8 Serviceability A structure shall be designed to perform its required functions during its expected life. Serviceability limits shall be chosen based on the intended function of the structure, and shall be evaluated using realistic loads and load combinations. A9 Referenced Documents The following documents are referenced in this Specification. Refer to Section A9a of Appendix A, B, or C for documents applicable to the corresponding country. 1. American Society of Mechanical Engineers, ASME B46.1-85, “Surface Texture, Surface Roughness, Waviness, and Lay”, American Society of Mechanical Engineers, 1828 L Street, NW, Washington, DC 20036. 2. American Society for Testing and Materials (ASTM), 100 Barr Harbor Drive, West Conshohocken, Pennsylvania 19428-2959: ASTM A36/A36M-00a, Carbon Structural Steel ASTM A194/A194M-00b, Carbon and Alloy Steel Nuts for Bolts for High- Pressure and High-Temperature Service ASTM A242/A242M-00a, High-Strength Low-Alloy Structural Steel ASTM A283/A283M-00, Low and Intermediate Tensile Strength Carbon Steel Plates ASTM A307-00, Carbon Steel Bolts and Studs, 60,000 PSI Tensile Strength ASTM A325-00, Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength ASTM A325M-00, High Strength Bolts for Structural Steel Joints [Metric] A,B,C Chapter A, General Provisions 44 December 2001 ASTM A354-00a, Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners ASTM A370-97a, Standard Test Methods and Definitions for Mechanical Testing of Steel Products ASTM A449-00, Quenched and Tempered Steel Bolts and Studs ASTM A490-00, Heat-Treated Steel Structural Bolts, 150ksi Minimum Tensile Strength ASTM A490M-00, High Strength Steel Bolts, Classes 10.9 and 10.9.3, for Structural Steel Joints [Metric] ASTM A500-99, Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes ASTM A529/A529M-00, High-Strength Carbon-Manganese Steel of Structural Quality ASTM A563-00, Carbon and Alloy Steel Nuts ASTM A563M-00, Carbon and Alloy Steel Nuts [Metric] ASTM A572/A572M-00a, High-Strength Low-Alloy Columbium- Vanadium Structural Steel ASTM A588/A588M-00a, High-Strength Low-Alloy Structural Steel with 50 ksi [345 MPa] Minimum Yield Point to 4 in. [100 mm] Thick ASTM A606-98, Steel, Sheet and Strip, High-Strength, Low-Alloy, Hot- Rolled and Cold-Rolled, with Improved Atmospheric Corrosion Resistance ASTM A653/A653M-00, Steel Sheet, Zinc-Coated (Galvanized) or Zinc- Iron Alloy-Coated (Galvannealed) by the Hot-Dip Process ASTM A792/A792M-99, Steel Sheet, 55% Aluminum-Zinc Alloy-Coated by the Hot-Dip Process ASTM A847-99a, Cold-Formed Welded and Seamless High Strength, Low Alloy Structural Tubing with Improved Atmospheric Corrosion Resistance ASTM A875/A875M-99, Steel Sheet, Zinc-5% Aluminum Alloy-Coated by the Hot-Dip Process ASTM A1003/A1003M-00, Steel Sheet, Carbon, Metallic- and Nonmetallic-Coated for Cold-Formed Framing Members ASTM A1008/A1008M-00, Steel, Sheet, Cold-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-Strength Low-Alloy with Improved Formability ASTM A1011/A1011M-00, Steel, Sheet and Strip, Hot-Rolled, Carbon, Structural, High-Strength Low-Alloy and High-Strength Low-Alloy with Improved Formability ASTM F436-00, Hardened Steel Washers ASTM F436M-00, Hardened Steel Washers [Metric] ASTM F844-00, Washers, Steel, Plain (Flat), Unhardened for General Use ASTM F959-99a, Compressible Washer-Type Direct Tension Indicators for Use with Structural Fasteners ASTM F959M-99a, Compressible Washer-Type Direct Tension Indicators for Use with Structural Fasteners [Metric] North American Cold-Formed Steel Specification December 2001 45 B. ELEMENTS B1 Dimensional Limits and Considerations B1.1 Flange Flat-Width-to-Thickness Considerations (a) Maximum Flat-Width-to-Thickness Ratios Maximum allowable overall flat-width-to-thickness ratios, w/t, disregarding intermediate stiffeners and taking as t, the actual thickness of the element, shall be as follows: (1) Stiffened compression element having one longitudinal edge connected to a web or flange element, the other stiffened by: Simple lip 60 Any other kind of stiffener i) when Is < Ia 60 ii) when Is ≥ Ia 90 where Is = Actual moment of inertia of full stiffener about its own centroidal axis parallel to element to be stiffened Ia = Adequate moment of inertia of stiffener, so that each component element will behave as a stiffened element. (2) Stiffened compression element with both longitudinal edges connected to other stiffened elements 500 (3) Unstiffened compression element 60 It shall be noted that unstiffened compression elements that have w/t ratios exceeding approximately 30 and stiffened compression elements that have w/t ratios exceeding approximately 250 are likely to develop noticeable deformation at the full design strength [factored resistance], without affecting the ability of the member to develop the required strength [factored strength]. Stiffened elements having w/t ratios larger than 500 can be used with adequate design strength [factored resistance] to sustain the required loads; however, substantial deformations of such elements usually will invalidate the design equations of this Specification. (b) Flange Curling Where the flange of a flexural member is unusually wide and it is desired to limit the maximum amount of curling or movement of the flange toward the neutral axis, the following equation applies to compression and tension flanges, either stiffened or unstiffened: wf = 4 fav )d/c100(f/tdE061.0 (Eq. B1.1-1) Chapter B, Elements 48 December 2001 For compression members, f is taken equal to Fn as determined in Section C4 or D4.1 as applicable. E = Modulus of elasticity k = Plate buckling coefficient = 4 for stiffened elements supported by a web on each longitudinal edge. Values for different types of elements are given in the applicable sections. (b) Serviceability Determination The effective width, bd, used in determining serviceability shall be calculated from the following equations: bd= w when λ ≤ 0.673 (Eq. B2.1-6) bd= ρw when λ > 0.673 (Eq. B2.1-7) where w = Flat width ρ = Reduction factor determined by either of the following two procedures: (1) Procedure I. A low estimate of the effective width can be obtained from Eqs. B2.1-3 and B2.1-4 except that fd is substituted for f, where fd is the computed compressive stress in the element being considered. (2) Procedure II. For stiffened elements supported by a web on each longitudinal edge, an improved estimate of the effective width can be obtained by calculating ρ as follows: ρ = 1 when λ ≤ 0.673 (Eq. B2.1-8) ρ = (1.358 - 0.461/λ )/λ when 0.673 < λ < λc (Eq. B2.1-9) ρ = (0.41 + 0.59 dy f/F - 0.22/λ)/λ when λ ≥ λc (Eq. B2.1-10) ρ shall not exceed 1.0 for all cases. where λc = 0.256 + 0.328 (w/t) E/Fy (Eq. B2.1-11) and λ is as defined by Eq. B2.1-4, except that fd is substituted for f.
   /                  Figure B2.1-1 Stiffened Elements North American Cold-Formed Steel Specification December 2001 49 B2.2 Uniformly Compressed Stiffened Elements with Circular Holes (a) Strength Determination The effective width, b, shall be determined as follows: for 0.50 ≥ w dh ≥ 0, and t w ≤ 70 and the distance between centers of holes ≥ 0.50w and ≥3dh, b = w - dh when λ ≤ 0.673 (Eq. B2.2-1) b = λ     − λ − w )d8.0()22.0( 1w h when λ > 0.673 (Eq. B2.2-2) b shall not exceed w - dh where w = Flat width dh = Diameter of holes λ is as defined in Section B2.1. (b) Serviceability Determination The effective width, bd, used in determining serviceability shall be equal to b calculated in accordance with Procedure I of Section B2.1(b), except that fd is substituted for f, where fd is the computed compressive stress in the element being considered. B2.3 Webs and other Stiffened Elements under Stress Gradient The following notation is used in this section: b1 = Effective width, dimension defined in Figure B2.3-1 b2 = Effective width, dimension defined in Figure B2.3-1 be = Effective width b determined in accordance with Section B2.1 with f1 substituted for f and with k determined as given in this section bo = Out-to-out width of the compression flange as defined in Figure B2.3-2 f1, f2 = Stresses shown in Figure B2.3-1 calculated on the basis of effective section. Where f1 and f2 are both compression, f1 ≥ f2 ho = Out-to-out depth of web as defined in Figure B2.3-2 k = Plate buckling coefficient ψ = |f2/f1| (absolute value) (Eq. B2.3-1) (a) Strength Determination (i) For webs under stress gradient (f1 in compression and f2 in tension as shown in Figure B2.3-1) k = 4 + 2(1 + ψ)3 + 2(1 + ψ) (Eq. B2.3-2) Chapter B, Elements 50 December 2001 For ho/bo ≤ 4 b1 = be/(3 + ψ) (Eq. B2.3-3) b2 = be/2 when ψ > 0.236 (Eq. B2.3-4) b2 = be – b1 when ψ ≤ 0.236 (Eq. B2.3-5) In addition, b1 + b2 shall not exceed the compression portion of the web calculated on the basis of effective section. For ho/bo > 4 b1 = be/(3 + ψ) (Eq. B2.3-6) b2 = be/(1 + ψ) – b1 (Eq. B2.3-7) (ii) For other stiffened elements under stress gradient (f1 and f2 in compression as shown in Figure B2.3-1)
                                             !"          Figure B2.3-1 Webs and other Stiffened Elements under Stress Gradient North American Cold-Formed Steel Specification December 2001 53 B4 Effective Widths of Elements with One Intermediate Stiffener or an Edge Stiffener The following notation is used in this section. S = f/E28.1 (Eq. B4-1) k = Plate buckling coefficient bo = Dimension defined in Figure B4-1 d, w, D = Dimensions defined in Figure B4-2 ds = Reduced effective width of stiffener as specified in this section. ds, calculated according to Section B4.2, is to be used in computing overall effective section properties (see Figure B4-2) d′s = Effective width of stiffener calculated according to Section B3.2 (see Figure B4-2) As = Reduced area of stiffener as specified in this section. As is to be used in computing overall effective section properties. The centroid of the stiffener is to be considered located at the centroid of the full area of the stiffener. Ia = Adequate moment of inertia of stiffener, so that each component element will behave as a stiffened element. Is, A′s = Moment of inertia of full section of stiffener about its own centroidal axis parallel to element to be stiffened, and effective area of stiffener, respectively. For edge stiffeners, the round corner between stiffener and element to be stiffened shall not be considered as a part of the stiffener. For the stiffener shown in Figure B4-2: Is = (d3t sin2θ)/12 (Eq. B4-2) A′s = d′st (Eq. B4-3) B4.1 Uniformly Compressed Elements with One Intermediate Stiffener (a) Strength Determination For bo/t ≤ S Ia = 0 (no intermediate stiffener required) b = w (Eq. B4.1-1) As = A′s (Eq. B4.1-2) For bo/t > S As = A′s(RI) (Eq. B4.1-3) n = 3 1 S12 t/b 583.0 o ≥    − (Eq. B4.1-4) k = 3(RI)n + 1 (Eq. B4.1-5) RI = Is/Ia ≤ 1 (Eq. B4.1-6) Chapter B, Elements 54 December 2001 where i) For S < bo/t < 3S Ia =     − 50 S t/b 50t o4 (Eq. B4.1-7) ii) For bo/t ≥ 3S Ia =     − 285 S t/b 128t o4 (Eq. B4.1-8) The effective width, b, is calculated in accordance with Section B2.1(a). (b) Serviceability Determination The effective width, bd, used in determining serviceability shall be calculated as in Section B4.1(a), except that fd is substituted for f. B4.2 Uniformly Compressed Elements with an Edge Stiffener (a) Strength Determination For w/t ≤ 0.328S: Ia = 0 (no edge stiffener needed) b = w (Eq. B4.2-1) b1 = b2 = w/2 (see Fig. B4-2) (Eq. B4.2-2) ds = d′s for simple lip stiffener (Eq. B4.2-3) As = A′s for other stiffener shapes (Eq. B4.2-4) For w/t > 0.328S b1 = b/2 (RI) (see Fig. B4-2) (Eq. B4.2-5) b2 = b – b1 (see Fig. B4-2) (Eq. B4.2-6) ds = d′s (RI) for simple lip stiffener (Eq. B4.2-7) As = A′s (RI) for other stiffener shapes (Eq. B4.2-8)                           
Figure B4-1 Elements with One Intermediate Stiffener North American Cold-Formed Steel Specification December 2001 55 where S = Term defined in Eq. B4-1. (RI) = Is/Ia≤ 1 (Eq. B4.2-9) Ia =     +≤    − 5 S t/w115t328.0 S t/wt399 4 3 4 (Eq. B4.2-10) n = 3 1 S4 t/w582.0 ≥    − (Eq. B4.2-11) The effective width, b, shall be calculated in accordance with Section B2.1 with k as given in Table B4.2. Table B4.2 Determination of Plate Buckling Coefficient k Simple Lip Edge Stiffener (140° ≥ θ ≥ 40°) D/w ≤ 0.25 0.25 < D/w ≤ 0.8 Other Edge Stiffener Shapes 443.0)R(57.3 nI ≤+ 443.0)R)( w D582.4( nI ≤+− 443.0)R(57.3 n I ≤+
θ #  #$    =  %     & '  (  )%    
"    '   *+, = -     
"      + Figure B4-2 Elements with Simple Lip Edge Stiffener Chapter B, Elements 58 December 2001 kd =     ωδ+β ωγ+β+ ∑ ∑ = = n 1i ii 2 n 1i ii 22 21 2)1( (Eq. B5.1.2-2) β = yF658.0 2 c      λ (Eq. B5.1.2-3) If Lbr < βbo then Lbr/bo shall be permitted to be substituted for β to account for increased capacity due to bracing. 3 o isp i tb )I(92.10 =γ (Eq. B5.1.2-4) ) b c (sin o i2 i π=ω (Eq. B5.1.2-5) tb )A( o is i =δ (Eq. B5.1.2-6) (b) Serviceability Determination The effective width, bd, used in determining serviceability shall be calculated as in Section B5.1.2(a), except that fd shall be substituted for f, where fd is the computed compressive stress in the element being considered based on the effective section at the load for which serviceability is determined.
 
  Figure B5.1-1 Plate Widths and Stiffener Locations Centroid t Centroid t 0.5b
0.5b
Figure B5.1-2 Effective Width Locations North American Cold-Formed Steel Specification December 2001 59 B5.2 Edge Stiffened Elements with Intermediate Stiffeners (a) Strength Determination The effective width, be, shall be determined as follows: If bo/t ≤ 0.328S, the element is fully effective and no local buckling reduction is required. If bo/t > 0.328S, then the plate buckling coefficient, k, shall be determined from the provisions of Section B4.2, but with bo replacing w in all expressions. If k calculated from Section B4.2 is less than 4.0 (k < 4), the intermediate stiffener(s) shall be ignored and the provisions of Section B4.2 be followed for calculation of the effective width. If k calculated from Section B4.2 is equal to 4.0 (k = 4), the effective width of the edge stiffened element shall be calculated from the provisions of Section B5.1, with the following exception: R calculated from equations B5.1-7 and B5.1-8 must be less than or equal to 1. where bo = Total flat width of edge stiffened element Other variables are defined in Section B4 and B5.1. (b) Serviceability Determination The effective width, bd, used in determining serviceability shall be calculated as in Section B5.2(a), except that fd shall be substituted for f and f1, where fd is the computed compressive stress in the element being considered. Chapter C, Members 60 December 2001 C. MEMBERS C1 Properties of Sections Properties of sections (cross-sectional area, moment of inertia, section modulus, radius of gyration, etc.) shall be determined in accordance with conventional methods of structural design. Properties shall be based on the full cross section of the members (or net sections where the use of net section is applicable) except where the use of a reduced cross section, or effective design width, is required. C2 Tension Members The provisions of this section are given in Section C2 of the Appendices. C3 Flexural Members C3.1 Bending The nominal flexural strength [moment resistance], Mn, shall be the smallest of the values calculated according to Sections C3.1.1, C3.1.2, C3.1.3, C3.1.4, and C3.1.5, where applicable. The provisions of this Section do not consider torsional effects, such as those resulting from loads that do not pass through the shear center of the cross section. See Section D3 for the design of lateral bracing required to restrain lateral bending or twisting. C3.1.1 Nominal Section Strength [Resistance] The nominal flexural strength [moment resistance], Mn, shall be calculated either on the basis of initiation of yielding in the effective section (Procedure I) or on the basis of the inelastic reserve capacity (Procedure II) as applicable. For sections with stiffened or partially stiffened compression flanges: USA and Mexico Canada Ωb(ASD) φb(LRFD) φb(LSD) 1.67 0.95 0.90 For sections with unstiffened compression flanges: USA and Mexico Canada Ωb(ASD) φb(LRFD) φb(LSD) 1.67 0.90 0.90 (a) Procedure I - Based on Initiation of Yielding Effective yield moment based on section strength [resistance], Mn, shall be determined as follows: Mn = SeFy (Eq. C3.1.1-1) A,B,C North American Cold-Formed Steel Specification December 2001 63 (a) For singly-, doubly-, and point-symmetric sections: Fe = teyS AorbC f σσ for bending about the symmetry axis. (Eq. C3.1.2.1-5) For singly-symmetric sections, x-axis is the axis of symmetry oriented such that the shear center has a negative x-coordinate. For point-symmetric sections, use 0.5 Fe. X-axis of Z-sections is the centroidal axis perpendicular to the web. Alternatively, Fe can be calculated using the equation given in (b) for doubly-symmetric I-sections, singly-symmetric C-sections, or point- symmetric Z-sections. For singly-symmetric sections bending about the centroidal axis perpendicular to the axis of symmetry: Fe = ( )    σσ σ ext 2 o 2 s fTF exs /r+jC+j SC AC (Eq. C3.1.2.1-6) Cs = +1 for moment causing compression on shear center side of centroid Cs = -1 for moment causing tension on shear center side of centroid σex = ( )2xxx 2 /rLK Eπ (Eq. C3.1.2.1-7) σey = ( )2yyy 2 /rLK Eπ (Eq. C3.1.2.1-8) σt = ( )         π 2 tt w 2 2 o LK EC +GJ Ar 1 (Eq. C3.1.2.1-9) A = Full unreduced cross-sectional area Sf = Elastic section modulus of full unreduced section relative to extreme compression fiber Cb = CBAmax max 3M+4M+3M+2.5M 12.5M (Eq. C3.1.2.1-10) where: Mmax = Absolute value of maximum moment in unbraced segment MA = Absolute value of moment at quarter point of unbraced segment MB = Absolute value of moment at centerline of unbraced segment MC = Absolute value of moment at three-quarter point of unbraced segment Cb is permitted to be conservatively taken as unity for all cases. For cantilevers or overhangs where the free end is unbraced, Cb shall be taken as unity. Chapter C, Members 64 December 2001 E = Modulus of elasticity CTF = 0.6 - 0.4 (M1/M2) (Eq. C3.1.2.1-11) where M1 is the smaller and M2 the larger bending moment at the ends of the unbraced length in the plane of bending, and where M1/M2, the ratio of end moments, is positive when M1 and M2 have the same sign (reverse curvature bending) and negative when they are of opposite sign (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, CTF shall be taken as unity. ro = Polar radius of gyration of cross section about shear center = 2o 2 y 2 x x+r+r (Eq. C3.1.2.1-12) rx, ry = Radii of gyration of cross section about centroidal principal axes G = Shear modulus Kx, Ky, Kt = Effective length factors for bending about x- and y-axes, and for twisting Lx, Ly, Lt = Unbraced length of member for bending about x- and y- axes, and for twisting xo = Distance from shear center to centroid along principal x- axis, taken as negative J = Saint-Venant torsion constant of cross section Cw = Torsional warping constant of cross section j = o 2 A 3 Ay x-dAxy+dAx 2I 1     ∫∫ (Eq. C3.1.2.1-13) (b) For I-sections, singly-symmetric C-sections, or Z-sections bent about the centroidal axis perpendicular to the web (x-axis), the following equations are permitted to be used in lieu of (a) to calculate Fe: Fe = 2 yyf yc 2 b )L(KS EdIC π (Eq. C3.1.2.1-14) = 2 yyf yc 2 b )L(K2S EdIC π for point-symmetric Z-sections (Eq. C3.1.2.1-15) where d = Depth of section Iyc = Moment of inertia of compression portion of section about centroidal axis of entire section parallel to web, using full unreduced section Other terms are defined in (a). for doubly-symmetric I-sections and singly-symmetric C-sections North American Cold-Formed Steel Specification December 2001 65 C3.1.2.2 Lateral-Torsional Buckling Strength [Resistance] of Closed Box Members For closed box members, the nominal flexural strength [moment resistance], Mn, shall be determined as follows: If the laterally unbraced length of the member is less than or equal to Lu, the nominal flexural strength [moment resistance] shall be determined by using Section C3.1.1. where Lu = y fy b EGJI SF 0.36C π (Eq. C3.1.2.2-1) If the laterally unbraced length of a member is larger than Lu, the nominal flexural strength [moment resistance] shall be determined in accordance with C3.1.2.1, where the critical lateral buckling stress, Fe, is calculated as follows: Fe = yEGJI fSLK bC yy π (Eq. C3.1.2.2-2) where Iy = Moment of inertia of full unreduced section about centroidal axis parallel to web J = Torsional constant of box section Other variables are defined in Section C3.1.2.1. C3.1.3 Beams Having One Flange Through-Fastened to Deck or Sheathing This section does not apply to a continuous beam for the region between inflection points adjacent to a support, or to a cantilever beam. The nominal flexural strength [moment resistance], Mn, of a C- or Z-section loaded in a plane parallel to the web, with the tension flange attached to deck or sheathing and with the compression flange laterally unbraced shall be calculated as follows: Mn = RSeFy (Eq. C3.1.3-1) USA and Mexico Canada Ωb(ASD) φb(LRFD) φb(LSD) 1.67 0.90 0.90 where R is obtained from Table C3.1.3-1 for simple span C- or Z- sections, and R = 0.60 for continuous span C-sections = 0.70 for continuous span Z-sections Se and Fy are defined in Section C3.1.1. The reduction factor, R, shall be limited to roof and wall systems meeting the following conditions: (1) Member depth less than 11.5 in. (292 mm) (2) Member flanges shall have edge stiffeners (3) 60 ≤ depth/thickness ≤ 170 Chapter C, Members 68 December 2001 C3.2 Shear C3.2.1 Shear Strength [Resistance] of Webs without Holes The nominal shear strength [resistance], Vn, shall be calculated as follows: Vn = AwFv (Eq. C3.2.1-1) (a) For h/t ≤ yv F/Ek Fv = 0.60Fy (Eq. C3.2.1-2) (b) For ≤< t/hF/Ek yv 1.51 yv F/Ek Fv = ( )th FEk60.0 yv (Eq. C3.2.1-3) (c) For h/t > 1.51 yv F/Ek Fv = ( )22 v 2 th)1(12 Ek µ− π = 0.904 Ekv/(h/t)2 (Eq. C3.2.1-4) where Aw = Area of web element = ht E = Modulus of elasticity of steel Fv = Nominal shear stress Vn = Nominal shear strength [resistance] t = Web thickness h = Depth of flat portion of web measured along plane of web µ = Poisson’s ratio = 0.3 kv = Shear buckling coefficient determined as follows: 1. For unreinforced webs, kv = 5.34 2. For webs with transverse stiffeners satisfying the requirements of Section C3.6 when a/h ≤ 1.0 ( )2v ha 34.500.4k += (Eq. C3.2.1-5) when a/h > 1.0 ( )2v ha 00.434.5k += (Eq. C3.2.1-6) where a = Shear panel length of unreinforced web element = Clear distance between transverse stiffeners of reinforced web elements. For a web consisting of two or more sheets, each sheet shall be USA and Mexico Canada Ωv(ASD) φv(LRFD) φv(LSD) 1.60 0.95 0.80 North American Cold-Formed Steel Specification December 2001 69 considered as a separate element carrying its share of the shear force. C3.2.2 Shear Strength [Resistance] of C-Section Webs with Holes These provisions shall be applicable within the following limits: (1) d0/h ≤ 0.7 (2) h/t ≤ 200 (3) Holes centered at mid-depth of web (4) Clear distance between holes ≥ 18 in. (457 mm) (5) Non-circular holes, corner radii ≥ 2t (6) Non-circular holes, d0 ≤ 2.5 in. (64 mm) and b ≤ 4.5 in. (114 mm) (7) Circular holes, diameter ≤ 6 in. (152 mm) (8) d0 > 9/16 in. (14 mm) The nominal shear strength [resistance], Vn, determined by Section C3.2.1 shall be multiplied by qs: When c/t yfyb EGSF0.36Cπ 54 qs = 1.0 (Eq. C3.2.2-1) When 5 ≤ c/t < 54 qs = c/(54t) (Eq. C3.2.2-2) where c = h/2 - d0/2.83 for circular holes (Eq. C3.2.2-3) = h/2 - d0/2 for non-circular holes (Eq. C3.2.2-4) d0 = Depth of web hole b = Length of web hole h = Depth of flat portion of web measured along plane of web C3.3 Combined Bending and Shear C3.3.1 ASD Method For beams subjected to combined bending and shear, the required allowable flexural strength, M, and required allowable shear strength, V, shall not exceed Mn/Ωb and Vn/Ωv, respectively. For beams with unreinforced webs, the required allowable flexural strength, M, and required allowable shear strength, V, shall also satisfy the following interaction equation: 0.1 V V M M 2 n v 2 nxo b ≤    Ω +    Ω (Eq. C3.3.1-1) For beams with transverse web stiffeners, when ΩbM/Mnxo > 0.5 and ΩvV/Vn > 0.7, M and V shall also satisfy the following interaction equation: 3.1 V V M M 6.0 n v nxo b ≤    Ω +    Ω (Eq. C3.3.1-2) Chapter C, Members 70 December 2001 where: Ωb = Factor of safety for bending (See Section C3.1.1) Ωv = Factor of safety for shear (See Section C3.2) Mn = Nominal flexural strength when bending alone is considered Mnxo= Nominal flexural strength about centroidal x-axis determined in accordance with Section C3.1.1 Vn = Nominal shear strength when shear alone is considered C3.3.2 LRFD and LSD Methods For beams subjected to combined bending and shear, the required flexural strength [factored moment], ,M and the required shear strength [factored shear], ,V shall not exceed φbMn and φvVn, respectively. For beams with unreinforced webs, the required flexural strength [factored moment], ,M and the required shear strength [factored shear], ,V shall also satisfy the following interaction equation: 0.1 V V M M 2 nv 2 nxob ≤    φ +    φ (Eq. C3.3.2-1) For beams with transverse web stiffeners, when M /(φbMnxo) > 0.5 and V /(φvVn) > 0.7, M and V shall also satisfy the following interaction equation: 3.1 V V M M6.0 nvnxob ≤    φ +    φ (Eq. C3.3.2-2) where: φb = Resistance factor for bending (See Section C3.1.1) φv = Resistance factor for shear (See Section C3.2) Mn = Nominal flexural strength [moment resistance] when bending alone is considered Mnxo = Nominal flexural strength [moment resistance] about centroidal x-axis determined in accordance with Section C3.1.1 M = Required flexural strength [factored moment] M = Mu (LRFD) M = Mf (LSD) Vn =Nominal shear strength [resistance] when shear alone is considered V = Required shear strength [factored shear] V = Vu (LRFD) V = Vf (LSD) North American Cold-Formed Steel Specification December 2001 73 Note: (1) The above coefficients apply when h/t ≤ 200, N/t ≤ 210, N/h ≤ 2.0 and θ = 90°. (2) For interior two-flange loading or reaction of members having flanges fastened to the support, the distance from the edge of bearing to the end of the member shall be extended at least 2.5h. For unfastened cases, the distance from the edge of bearing to the end of the member shall be extended at least 1.5h. TABLE C3.4.1-3 SINGLE WEB Z-SECTIONS USA and Mexico Support and Flange Conditions Load Cases C CR CN Ch ASD Ωw LRFD φw Canada LSD φw Limits End 4 0.14 0.35 0.02 1.75 0.85 0.75 R/t ≤ 9 One-Flange Loading or Reaction Interior 13 0.23 0.14 0.01 1.65 0.90 0.80 R/t ≤ 5 End 9 0.05 0.16 0.052 1.75 0.85 0.75 R/t ≤ 12 Fastened to Support Stiffened or Partially Stiffened Flanges Two-Flange Loading or Reaction Interior 24 0.07 0.07 0.04 1.85 0.80 0.70 R/t ≤ 12 End 5 0.09 0.02 0.001 1.80 0.85 0.75 One-Flange Loading or Reaction Interior 13 0.23 0.14 0.01 1.65 0.90 0.80 R/t ≤ 5 End 13 0.32 0.05 0.04 1.65 0.90 0.80 Stiffened or Partially Stiffened Flanges Two-Flange Loading or Reaction Interior 24 0.52 0.15 0.001 1.90 0.80 0.65 R/t ≤ 3 End 4 0.40 0.60 0.03 1.80 0.85 0.70 R/t ≤ 2 One-Flange Loading or Reaction Interior 13 0.32 0.10 0.01 1.80 0.85 0.70 R/t ≤ 1 End 2 0.11 0.37 0.01 2.00 0.75 0.65 Unfastened Unstiffened Flanges Two-Flange Loading or Reaction Interior 13 0.47 0.25 0.04 1.90 0.80 0.65 R/t ≤ 1 Note: (1) The above coefficients apply when h/t ≤ 200, N/t ≤ 210, N/h ≤ 2.0 and θ = 90°. (2) For interior two-flange loading or reaction of members having flanges fastened to the support, the distance from the edge of bearing to the end of the member shall be extended at least 2.5h. For unfastened cases, the distance from the edge of bearing to the end of the member shall be extended at least 1.5h. Chapter C, Members 74 December 2001 TABLE C3.4.1-4 SINGLE HAT SECTIONS USA and Mexico Support Conditions Load Cases C CR CN Ch ASD Ωw LRFD φw Canada LSD φw Limits End 4 0.25 0.68 0.04 2.00 0.75 0.65 R/t ≤ 5 One-Flange Loading or Reaction Interior 17 0.13 0.13 0.04 1.90 0.80 0.70 R/t ≤ 10 End 9 0.10 0.07 0.03 1.75 0.85 0.75 Fastened to Support Two-Flange Loading or Reaction Interior 10 0.14 0.22 0.02 1.80 0.85 0.75 R/t ≤ 10 End 4 0.25 0.68 0.04 2.00 0.75 0.65 R/t ≤ 4 Unfastened One-Flange Loading or Reaction Interior 17 0.13 0.13 0.04 1.70 0.90 0.75 R/t ≤ 4 Note: The above coefficients apply when h/t ≤ 200, N/t ≤ 200, N/h ≤ 2 and θ = 90°. TABLE C3.4.1-5 MULTI-WEB DECK SECTIONS USA and Mexico Support Conditions Load Cases C CR CN Ch ASD Ωw LRFD φw Canada LSD φw Limits End 3 0.08 0.70 0.055 2.25 0.65 0.55 R/t ≤ 7 One-Flange Loading or Reaction Interior 8 0.10 0.17 0.004 1.75 0.85 0.75 R/t ≤ 10 End 9 0.12 0.14 0.040 1.80 0.85 0.70 Fastened to Support Two-Flange Loading or Reaction Interior 10 0.11 0.21 0.020 1.75 0.85 0.75 R/t ≤ 10 End 3 0.08 0.70 0.055 2.25 0.65 0.55 One-Flange Loading or Reaction Interior 8 0.10 0.17 0.004 1.75 0.85 0.75 R/t ≤ 7 End 6 0.16 0.15 0.050 1.65 0.90 0.80 Unfastened Two-Flange Loading or Reaction Interior 17 0.10 0.10 0.046 1.65 0.90 0.80 R/t ≤ 5 Notes: (1) The above coefficients apply when h/t ≤ 200, N/t ≤ 210, N/h ≤ 3. (2) 45° ≤ θ ≤ 90° C3.4.2 Web Crippling Strength [Resistance] of C-Section Webs with Holes When a web hole is within the bearing length, a bearing stiffener shall be used. For beam webs with holes, the web crippling strength [resistance] shall be computed by using Section C3.4.1 multiplied by the reduction factor, Rc, given in this section. North American Cold-Formed Steel Specification December 2001 75 These provisions shall be applicable within the following limits: (1) d0/h ≤ 0.7 (2) h/t ≤ 200 (3) Hole centered at mid-depth of web (4) Clear distance between holes ≥ 18 in. (457 mm) (5) Distance between end of member and edge of hole ≥ d (6) Non-circular holes, corner radii ≥ 2t (7) Non-circular holes, d0 ≤ 2.5 in. (64 mm) and b ≤ 4.5 in. (114 mm) (8) Circular holes, diameters ≤ 6 in. (152 mm) (9) d0 > 9/16 in. (14 mm) For end-one flange reaction (Equation C3.4.1-1 with Table C3.4.1-2) when a web hole is not within the bearing length: Rc = 0.1hx083.0hd325.001.1 0 ≤+− (Eq. C3.4.2-1) N ≥ 1 in. (25 mm) For interior-one flange reaction (Equation C3.4.1-1 with Table C3.4.1-2) when any portion of a web hole is not within the bearing length: Rc = 0.1hx053.0hd047.090.0 0 ≤+− (Eq. C3.4.2-2) N ≥ 3 in. (76 mm) where b = Length of web hole d = Depth of cross section d0 = Depth of web hole h = Depth of flat portion of web measured along plane of web x = Nearest distance between web hole and edge of bearing N = Bearing length C3.5 Combined Bending and Web Crippling C3.5.1 ASD Method Unreinforced flat webs of shapes subjected to a combination of bending and concentrated load or reaction shall be designed to meet the following requirements: (a) For shapes having single unreinforced webs: 5.1 M M P P2.1 nxo b n w ≤    Ω +    Ω (Eq. C3.5.1-1) Exception: At the interior supports of continuous spans, the above equation is not applicable to deck or beams with two or more single webs, provided the compression edges of adjacent webs are laterally supported in the negative moment region by continuous or intermittently connected flange elements, rigid cladding, or lateral bracing, and the spacing between adjacent webs does not exceed 10 in. (254 mm). (b) For shapes having multiple unreinforced webs such as I-sections made of two C-sections connected back-to-back, or similar sections which provide Chapter C, Members 78 December 2001 P = Pu (LRFD) P = Pf (LSD) Pn = Nominal strength [resistance] for concentrated load or reaction in absence of bending moment determined in accordance with Section C3.4 M = Required flexural strength [factored moment] at, or immediately adjacent to, the point of application of the concentrated load or reaction P M = Mu (LRFD) M = Mf (LSD) Mnxo= Nominal flexural strength [moment resistance] about centroidal x-axis determined in accordance with Section C3.1.1 w = Flat width of beam flange which contacts bearing plate t = Thickness of web or flange λ = Slenderness factor given by Section B2.1 (c) For two nested Z-shapes φ≤+ 65.1 P P85.0 M M nno (Eq. C3.5.2-3) In addition, the moment, ,M and the concentrated load or reaction, ,P shall satisfy M ≤ φbMno, and P ≤ φwPn. where M = Required flexural strength [factored moment] at section under consideration M = Mu (LRFD) M = Mf (LSD) Mno= Nominal flexural strength for nested Z-sections, i.e., sum of two sections evaluated individually, determined in accordance with Section C3.1.1 P = Required strength for concentrated load or reaction [factored concentrated load or reaction] in presence of bending moment P = Pu (LRFD) P = Pf (LSD) Pn = Nominal web crippling strength [resistance] assuming single web interior one-flange loading for nested Z-sections, i.e., sum of two webs evaluated individually φ = 0.90 (LRFD) = 0.80 (LSD) The above equation is valid for shapes that meet the following limits: h/t ≤ 150 N/t ≤ 140 North American Cold-Formed Steel Specification December 2001 79 Fy ≤ 70 ksi (480 MPa or 4910 kg/cm2) R/t ≤ 5.5 The following conditions shall also be satisfied: (1) The ends of each section shall be connected to the other section by a minimum of two 1/2 in. (12.7 mm) diameter A307 bolts through the web. (2) The combined section shall be connected to the support by a minimum of two 1/2 in. (12.7 mm) diameter A307 bolts through the flanges. (3) The webs of the two sections shall be in contact. (4) The ratio of the thicker to the thinner part shall not exceed 1.3. C3.6 Stiffeners C3.6.1 Transverse Stiffeners Transverse stiffeners attached to beam webs at points of concentrated loads or reactions, shall be designed as compression members. Concentrated loads or reactions shall be applied directly into the stiffeners, or each stiffener shall be fitted accurately to the flat portion of the flange to provide direct load bearing into the end of the stiffener. Means for shear transfer between the stiffener and the web shall be provided according to Chapter E. For concentrated loads or reactions the nominal strength [resistance] equals Pn, where Pn is the smaller value given by (a) and (b) as follows: (a) Pn = FwyAc (Eq. C3.6.1-1) (b) Pn = Nominal axial strength [resistance] evaluated according to Section C4(a), with Ae replaced by Ab USA and Mexico Canada Ωc(ASD) φc(LRFD) φc(LSD) 2.00 0.85 0.80 where Ac = 18t2 + As, for transverse stiffeners at interior support and under (Eq. C3.6.1-2) concentrated load Ac = 10t2 + As, for transverse stiffeners at end support (Eq. C3.6.1-3) Fwy = Lower value of Fy for beam web, or Fys for stiffener section Ab = b1t + As, for transverse stiffeners at interior support and under (Eq. C3.6.1-4) concentrated load Ab = b2t + As, for transverse stiffeners at end support (Eq. C3.6.1-5) As = Cross sectional area of transverse stiffeners b1 = 25t [0.0024(Lst/t) + 0.72] ≤ 25t (Eq. C3.6.1-6) b2 = 12t [0.0044(Lst/t) + 0.83] ≤ 12t (Eq. C3.6.1-7) Lst = Length of transverse stiffener t = Base thickness of beam web Chapter C, Members 80 December 2001 The w/ts ratio for the stiffened and unstiffened elements of transverse stiffeners shall not exceed 1.28 ysF/E and 0.42 ysF/E , respectively, where Fys is the yield point, and ts is the thickness of the stiffener steel. C3.6.2 Shear Stiffeners Where shear stiffeners are required, the spacing shall be based on the nominal shear strength [resistance],Vn, permitted by Section C3.2, and the ratio a/h shall not exceed [260/(h/t)]2 nor 3.0. The actual moment of inertia, Is, of a pair of attached shear stiffeners, or of a single shear stiffener, with reference to an axis in the plane of the web, shall have a minimum value of Ismin =5ht3[h/a - 0.7(a/h)] ≥ (h/50)4 (Eq. C3.6.2-1) The gross area of shear stiffeners shall not be less than YDht )h/a(1)h/a( )h/a( h a 2 C1 A 2 2 v st           ++ − − = (Eq. C3.6.2-2) where Cv = 2 y v )t/h(F Ek53.1 when Cv ≤ 0.8 (Eq. C3.6.2-3) Cv = y v F Ek t/h 11.1 when Cv > 0.8 (Eq. C3.6.2-4) kv = ( )2h/a 34.500.4 + when a/h ≤ 1.0 (Eq. C3.6.2-5) kv = ( )2h/a 00.434.5 + when a/h > 1.0 (Eq. C3.6.2-6) a = Distance between transverse stiffeners Y = steel stiffener of point Yield steel web of point Yield D = 1.0 for stiffeners furnished in pairs D = 1.8 for single-angle stiffeners D = 2.4 for single-plate stiffeners t and h are as defined in Section B1.2 C3.6.3 Non-Conforming Stiffeners The design strength [factored resistance] of members with transverse stiffeners that do not meet the requirements of Section C3.6.1 or C3.6.2, such as stamped or rolled-in transverse stiffeners, shall be determined by tests in accordance with Chapter F or rational engineering analysis in accordance with A1.1(b). North American Cold-Formed Steel Specification December 2001 83 minor principal axis of the section. C4.4 Nonsymmetric Sections For shapes whose cross sections do not have any symmetry, either about an axis or about a point, Fe shall be determined by rational analysis. Alternatively, compression members composed of such shapes shall be permitted to be tested in accordance with Chapter F. C4.5 Built-Up Members For compression members composed of two sections in contact, the nominal axial strength [compressive resistance] shall be determined in accordance with Section C4(a) subject to the following modification. If the buckling mode involves relative deformations that produce shear forces in the connectors between individual shapes, KL/r is replaced by (KL/r)m determined as follows: 2 i 2 om r a r KL r KL     +    =     (Eq. C4.5-1) where: (KL/r)o = Overall slenderness ratio of entire section about built-up member axis a = Intermediate fastener or spot weld spacing ri = Minimum radius of gyration of full unreduced cross-sectional area of an individual shape in a built-up member Other symbols are defined in C4.1. In addition, the fastener strength [resistance] and spacing shall satisfy the following: (1) The intermediate fastener or spot weld spacing, a, shall be limited such that a/ri does not exceed one half the governing slenderness ratio of the built-up member. (2) The ends of a built-up compression member shall be connected by a weld having a length not less than the maximum width of the member or by connectors spaced longitudinally not more than 4 diameters apart for a distance equal to 1.5 times the maximum width of the member. (3) Each discrete connector shall be capable of transmitting a longitudinal shear force of 2.5% of the total force (unfactored force for ASD and factored force for LRFD and LSD) in the built-up member. C4.6 Compression Members Having One Flange Through-Fastened to Deck or Sheathing These provisions are applicable to C- or Z-sections concentrically loaded along their longitudinal axis, with only one flange attached to deck or sheathing with through fasteners. The nominal axial strength [resistance] of simple span or continuous C- Chapter C, Members 84 December 2001 or Z-sections shall be calculated as follows: (a) For weak axis nominal strength [resistance] Pn = C1C2C3AE/29500 kips (Newtons) (Eq. C4.6-1) USA and Mexico Canada Ω(ASD) φ(LRFD) φ(LSD) 1.80 0.85 0.80 where: C1 = (0.79x + 0.54) (Eq. C4.6-2) C2 = (1.17αt + 0.93) (Eq. C4.6-3) C3 = α(2.5b - 1.63d) + 22.8 (Eq. C4.6-4) For Z-sections: x = The fastener distance from the outside web edge divided by the flange width, as shown in Figure C4.6. For C-sections: x = the flange width minus the fastener distance from the outside web edge divided by the flange width, as shown in Figure C4.6. t = C- or Z-section thickness b = C- or Z-section flange width d = C- or Z-section depth A = Full unreduced cross-sectional area of C- or Z-section E = Modulus of elasticity of steel = 29,500 ksi for U.S. customary units = 203,000 MPa for SI units = 2,070,000 kg/cm2 for MKS units α = Coefficient for conversion of units = 1 when t, b, and d are in inches = 0.0394 when t, b, and d are in mm = 0.394 when t, b, and d are in cm Eq. C4.6-1 shall be limited to roof and wall systems meeting the following conditions: (1) t ≤ 0.125 in. (3.22 mm) (2) 6 in. (152mm) ≤ d ≤ 12 in. (305 mm) (3) Flanges are edge stiffened compression elements (4) 70 ≤ d/t ≤ 170 (5) 2.8 ≤ d/b ≤ 5 (6) 16 ≤ flange flat width / t ≤ 50 (7) Both flanges are prevented from moving laterally at the supports (8) Steel roof or steel wall panels with fasteners spaced 12 in. (305 mm) on center or less and having a minimum rotational lateral stiffness of 0.0015 k/in./in. (10,300 N/m/m) (fastener at mid-flange width for stiffness determination) as determined by the AISI test procedure (9) C- and Z-sections having a minimum yield point of 33 ksi (230 MPa or 2320 kg/cm2) (10) Span length not exceeding 33 feet (10 m) North American Cold-Formed Steel Specification December 2001 85 (b) For strong axis nominal strength [resistance], the equations contained in Sections C4 and C4.1 of the Specification shall be used. Note: Further information on the test procedure should be obtained from "Rotational- Lateral Stiffness Test Method for Beam-to-Panel Assemblies", AISI Cold-Formed Steel Design Manual, Part VIII. C5 Combined Axial Load and Bending C5.1 Combined Tensile Axial Load and Bending C5.1.1 ASD Method The required allowable strengths T, Mx, and My shall satisfy the following interaction equations: 0.1 T T M M M M n t nyt yb nxt xb ≤ Ω + Ω + Ω (Eq. C5.1.1-1) and 0.1 T T M M M M n t ny yb nx xb ≤ Ω − Ω + Ω (Eq. C5.1.1-2) where T = Required allowable tensile axial strength Mx, My = Required allowable flexural strengths with respect to centroidal axes of section Tn = Nominal tensile axial strength determined in accordance with Section C2 Mnx, Mny = Nominal flexural strengths about centroidal axes determined in accordance with Section C3.1 Mnxt, Mnyt = SftFy Sft = Section modulus of full unreduced section relative to extreme tension fiber about appropriate axis For Z-Section x = b a (Eq. C4.6-5) For C-Section x= b ab − (Eq. C4.6-6) Figure C4.6 Definition of x a b Chapter C, Members 88 December 2001 Ix = Moment of inertia of full unreduced cross section about x-axis Iy = Moment of inertia of full unreduced cross section about y-axis Lx = Unbraced length for bending about x-axis Ly = Unbraced length for bending about y-axis Kx = Effective length factor for buckling about x-axis Ky = Effective length factor for buckling about y-axis Cmx, Cmy = Coefficients whose values shall be determined as follows: 1. For compression members in frames subject to joint translation (sidesway) Cm = 0.85 2. For restrained compression members in frames braced against joint translation and not subject to transverse loading between their supports in the plane of bending Cm = 0.6 - 0.4 (M1/M2) (Eq. C5.2.1-8) where M1/M2 is the ratio of the smaller to the larger moment at the ends of that portion of the member under consideration which is unbraced in the plane of bending. M1/M2 is positive when the member is bent in reverse curvature and negative when it is bent in single curvature 3. For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between their supports, the value of Cm shall be permitted to be determined by rational analysis. However, in lieu of such analysis, the following values shall be permitted to be used: (a) for members whose ends are restrained, Cm = 0.85 (b) for members whose ends are unrestrained, Cm = 1.0 C5.2.2 LRFD and LSD Methods The required strengths [factored axial force and moment] ,P xM , and yM shall satisfy the following interaction equations. In addition, each individual ratio in Eqs. C5.2.2-1 to C5.2.2-3 shall not exceed unity. 1.0≤ αΜφ Μ + αΜφ + φ ynyb ymy xnxb xmx nc CMC P P (Eq. C5.2.2-1) 1.0≤ Μφ Μ + Μφ Μ+ φ nyb y nxb x nocP P (Eq. C5.2.2-2) North American Cold-Formed Steel Specification December 2001 89 When P /φcPn ≤ 0.15, the following equation shall be permitted to be used in lieu of the above two equations: 1.0≤ Μφ Μ + Μφ + φ nyb y nxb x nc M P P (Eq. C5.2.2-3) where P = Required compressive axial strength [factored compressive force] P = Pu (LRFD) P = Pf (LSD) xM , yM = Required flexural strengths [factored moments] with respect to centroidal axes of effective section determined for required compressive axial strength [factored axial force] alone. For singly-symmetric unstiffened angle sections with unreduced effective area, yM shall be permitted to be taken as the required flexural strength [factored moment] only. For other angle sections or singly-symmetric unstiffened angles for which the effective area (Ae) at stress Fy is less than the full unreduced cross-sectional area (A), yM , shall be taken either as the required flexural strength [factored moment] or the required flexural strength [factored moment] plus ( P )L/1000, whichever results in a lower permissible value of P . xM = Mux, yM = Muy (LRFD) xM = Mfx, yM = Mfy (LSD) Pn = Nominal axial strength [axial resistance] determined in accordance with Section C4 and C6 Pno = Nominal axial strength [axial resistance] determined in accordance with Section C4 and C6, with Fn = Fy Mnx, Mny = Nominal flexural strengths [moment resistances] about centroidal axes determined in accordance with Section C3.1 αx = ExP P1 − (Eq. C5.2.2-4) αy = EyP P1 − (Eq. C5.2.2-5) PEx = 2 xx x 2 )LK( EIπ (Eq. C5.2.2-6) Chapter C, Members 90 December 2001 PEy = 2 yy y 2 )LK( EIπ (Eq. C5.2.2-7) φb = For bending strength [resistance] (Section C3.1.1), φb = 0.90 or 0.95 (LRFD) and 0.90 (LSD). For laterally unbraced beams (Section C3.1.2), φb = 0.90 (LRFD and LSD) φc = 0.85 (LRFD) = 0.80 (LSD) Ix = Moment of inertia of full unreduced cross section about x-axis Iy = Moment of inertia of full unreduced cross section about y-axis Lx = Unbraced length for bending about x-axis Ly = Unbraced length for bending about y-axis Kx = Effective length factor for buckling about x-axis Ky = Effective length factor for buckling about y-axis Cmx, Cmy = Coefficients whose values shall be determined as follows: 1. For compression members in frames subject to joint translation (sidesway) Cm = 0.85 2. For restrained compression members in frames braced against joint translation and not subject to transverse loading between their supports in the plane of bending Cm = 0.6 - 0.4 (M1/M2) (Eq. C5.2.2-8) where M1/M2 is the ratio of the smaller to the larger moment at the ends of that portion of the member under consideration which is unbraced in the plane of bending. M1/M2 is positive when the member is bent in reverse curvature and negative when it is bent in single curvature. 3. For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between their supports, the value of Cm shall be permitted to be determined by rational analysis. However, in lieu of such analysis, the following values shall be permitted to be used: (a) for members whose ends are restrained, Cm = 0.85, (b) for members whose ends are unrestrained, Cm = 1.0 North American Cold-Formed Steel Specification December 2001 93 D. STRUCTURAL ASSEMBLIES D1 Built-Up Sections D1.1 I-Sections Composed of Two C-Sections (a) For compression members: Refer to Section C4.5. (b) For flexural members: The maximum permissible longitudinal spacing of welds or other connectors, smax, joining two C-sections to form an I-section shall be: smax = L / 6 ≤ mq gT2 s (Eq. D1.1-1) where L = Span of beam Ts = Design strength [factored resistance] of connection in tension (Chapter E) g = Vertical distance between two rows of connections nearest to top and bottom flanges q = Design load on beam for spacing of connectors (Use nominal loads for ASD, factored loads for LRFD and LSD. For methods of determination, see below) m = Distance from shear center of one C-section to mid-plane of web. The load, q, is obtained by dividing the concentrated loads or reactions by the length of bearing. For beams designed for a uniformly distributed load, q shall be taken equal to three times the uniformly distributed load, based on nominal loads for ASD, factored loads for LRFD and LSD. If the length of bearing of a concentrated load or reaction is smaller than the weld spacing, s, the required design strength [factored resistance] of the welds or connections closest to the load or reaction is Ts = Psm/2g (Eq. D1.1-2) where Ps is a concentrated load or reaction based on nominal loads for ASD, factored loads for LRFD and LSD. The allowable maximum spacing of connections, smax, depends upon the intensity of the load directly at the connection. Therefore, if uniform spacing of connections is used over the whole length of the beam, it shall be determined at the point of maximum local load intensity. In cases where this procedure would result in uneconomically close spacing, either one of the following methods shall be permitted to be adopted: (a) the connection spacing may be varied along the beam according to the variation of the load intensity; or (b) reinforcing cover plates may be welded to the flanges at points where concentrated loads occur. The design shear strength of the connections joining these plates to the flanges shall then be used for Ts, and g shall be taken as the depth of the beam. Chapter D, Structural Assemblies 94 December 2001 D1.2 Spacing of Connections in Compression Elements The spacing, s, in the line of stress, of welds, rivets, or bolts connecting a cover plate, sheet, or a non-integral stiffener in compression to another element shall not exceed: (a) that which is required to transmit the shear between the connected parts on the basis of the design strength [factored resistance] per connection specified elsewhere herein; nor (b) 1.16t cf/E , where t is the thickness of the cover plate or sheet, and fc is the stress at nominal load [specified load] in the cover plate or sheet; nor (c) three times the flat width, w, of the narrowest unstiffened compression element tributary to the connections, but need not be less than 1.11t yF/E if w/t < 0.50 yF/E , or 1.33t yF/E if w/t ≥ 0.50 yF/E , unless closer spacing is required by (a) or (b) above. In the case of intermittent fillet welds parallel to the direction of stress, the spacing shall be taken as the clear distance between welds, plus 1/2 in. (12.7 mm). In all other cases, the spacing shall be taken as the center-to-center distance between connections. Exception: The requirements of this Section do not apply to cover sheets which act only as sheathing material and are not considered as load- carrying elements. D2 Mixed Systems The design of members in mixed systems using cold-formed steel components in conjunction with other materials shall conform to this Specification and the applicable specification of the other material. D3 Lateral Bracing Braces shall be designed to restrain lateral bending or twisting of a loaded beam or column, and to avoid local crippling at the points of attachment. D3.1 Symmetrical Beams and Columns Braces and bracing systems, including connections, shall be designed considering strength and stiffness requirements. D3.2 C-Section and Z-Section Beams The following provisions for bracing to restrain twisting of C-sections and Z-sections used as beams loaded in the plane of the web, apply only when (a) the top flange is connected to deck or sheathing material in such a manner as to effectively restrain lateral deflection of the connected flange, or (b) neither flange is so connected. When both flanges are so connected, no further bracing is required. When the Specification does not provide an explicit method for design, further information should be obtained from the Commentary. B B B North American Cold-Formed Steel Specification December 2001 95 D3.2.1 Anchorage of Bracing for Roof Systems Under Gravity Load With Top Flange Connected to Sheathing For C-sections and Z-sections designed according to Section C3.1.1, and having deck or sheathing fastened to the top flanges (through fastened or standing seam systems), provisions shall be made to restrain the flanges so that the maximum top flange lateral displacements with respect to the purlin reaction points do not exceed the span length divided by 360. If the top flanges of all purlins face in the same direction, anchorage of the restraint shall satisfy the requirements of Sections D3.2.1(a) and D3.2.1(b). If the top flanges of adjacent lines of purlins face in opposite directions, a restraint system shall be provided to resist the down-slope component of the total gravity load. Anchored braces need to be connected to only one line of purlins in each purlin bay of each roof slope if provision is made to transmit forces from other purlin lines through the roof deck and its fastening system. Anchored braces shall be as close as possible to the flange which is connected to the deck or sheathing. Anchored braces shall be provided for each purlin bay. For bracing arrangements other than those covered in Sections D3.2.1(a) and D3.2.1(b), tests in accordance with Chapter F shall be performed so that the type and/or spacing of braces selected are such that the test strength [resistance] of the purlin assembly is equal to or greater than its nominal flexural strength [moment resistance], instead of that required by Chapter F. (a) C-Sections For roof systems using C-sections for purlins with all compression flanges facing in the same direction, a system possessing restraint force, PL, in addition to resisting other loading, shall be provided: PL = (0.05αcosθ - sinθ)W (Eq. D.3.2.1-1) where W = Total vertical load (nominal load for ASD, factored load for LRFD and LSD) supported by all purlin lines being restrained. Where more than one brace is used at a purlin line, the restraint force PL shall be divided equally between all braces. α = +1 for purlin facing upward direction, and -1 for purlin facing down slope direction. θ = Angle between vertical and plane of web of C-section, degrees. A positive value for the force, PL, means that restraint is required to prevent movement of the purlin flanges in the upward roof slope direction, and a negative value means that restraint is required to prevent movement of purlin flanges in the downward slope direction. (b) Z-Sections For roof systems having four to twenty Z-purlin lines with all top flanges facing in the direction of the upward roof slope, and with restraint braces at the purlin supports, midspan or one-third points,