Scholars' Mine. Missouri University of Science and Technology. Ling-En Hsiao. Wei-wen Yu Missouri University of Science and Technology,

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1 Missouri Uiversity of Sciece ad Techology Scholars' Mie Ceter for Cold-Formed Steel Structures Library Wei-We Yu Ceter for Cold-Formed Steel Structures Load ad resistace factor desig of cold-formed steel load ad resistace factor desig specificatio for cold-formed steel structural members with commetary Lig-E Hsiao Wei-we Yu Missouri Uiversity of Sciece ad Techology, Theodore V. Galambos Follow this ad additioal works at: Part of the Structural Egieerig Commos Recommeded Citatio Hsiao, Lig-E; Yu, Wei-we; ad Galambos, Theodore V., "Load ad resistace factor desig of cold-formed steel load ad resistace factor desig specificatio for cold-formed steel structural members with commetary" (1989). Ceter for Cold-Formed Steel Structures Library This Report - Techical is brought to you for free ad ope access by Scholars' Mie. It has bee accepted for iclusio i Ceter for Cold-Formed Steel Structures Library by a authorized admiistrator of Scholars' Mie. This work is protected by U. S. Copyright Law. Uauthorized use icludig reproductio for redistributio requires the permissio of the copyright holder. For more iformatio, please cotact scholarsmie@mst.edu.

2 CIVIL ENGINEER:SO STUDY 89-5 STRUCTURAL SERIES Twelfth Pr0lTesa Report LOAD AND RESISTANCE FACTOR DESIGN OF COLD-FORMED STEEL LOAD AND RESISTANCE FACTOR DESIGN SPECIFICATION FOR COLD-FORMED STEEL STRUCTURAL MEMBERS WITH COMMENTARY by Lie-E Hsiao Research Assistat Uiversity or Missouri-Rolla Wei-We Yu Project Director Uiversity or Missouri-Roa Theodore V. Galambos Cosultat Uiversity or Miesota A Research Project Sposored by the America Iro ad Steel Istitute August 1989 DEPARTMENT OF CML ENGINEERING UNIVERSITY OF MISSOURI ROLLA ROLLA. MISSOURI

3 FOREWORD This progress report cotais the followig two parts: Part I: Load ad Resistace Factor Desig Specificatio for Cold-Formed Steel Structural Members (pp. i-107). Part II: Commetary o the Load ad Resistace Factor Desig Specificatio for Cold-Formed Steel Structural Members (pp ). The load ad resistace factor desig specificatio proposed herei is the revised versio of the desig recommedatios prepared i February 1988 ad submitted to America Iro ad Steel Istitute as Teth Progress Report. This documet was prepared accordig to the 1986 editio of the AISI Specificatio for the Desig of Cold-Formed Steel Structural Members. The selectios of ~ factors are discussed i the Commetary for various types of structural members ad coectios. This ivestigatio was sposored by America Iro ad Steel Istitute. The techical guidace provided by the AISI Subcommitte o Load ad Resistace Factor Desig ad the AISI Staff is gratefully ackowledged. Members of the AISI Subcommitte are: K. H. Klippstei (Chairma), R. Bjorhovde, D. S. Ellifritt, S. J. Errera, T. V. Galambos, B. Hall, D. H. Hall, R. B. Heagler, N. Iwakiw, A. L. Johso, D. L. Johso, A. C. Kuetz, A. S. Nowak, T. B. Pekoz, C. W. Pikham, R. M. Schuster, ad W. W. Yu. Former members of theaisi Task Group o LRFD icluded R. L. Cary, N. C. Lid, R. B. Matlock, W. Mueller, F. J. Phillips, D. S. Wolford ad Late Professor G. Witer. 1-1

4 Special thaks are exteded to T. V. Galambos, Cosultat of the project, T. N. Rag, B. Suporsilaphachai, B. K. Syder, L. C. Pa, ad M. K. Ravidra for their cotributios to the project. 1-2

5 PART I LOAD AND RESISTANCE FACTOR DESIGN SPECIFICATION FOR COLD-FORMED STEEL STRUCTURAL MEMBERS

6 PREFACE The AISI allowable stress desig specificatio has log bee used for the desig of cold-formed steel structural members. The Load ad Resistace Factor Desig (LRFD) Specificatio has recetly bee developed from a research project sposored by America Iro ad Steel Istitute. I this LRFD Specificatio, separate load ad resistace factors are applied to specified loads ad omial resistace to esure that the probability of reachig a limit state is acceptably small. These factors reflect the ucertaities of aalysis, desig, loadig, material properties ad fabricatio. They are derived o the basis of the first order probabilistic methodology as used for the developmet of the AISC Load ad Resistace Factor Desig Specificatio for Structural Steel Buildigs. This Specificatio cotais six chapters of the LRFD recommedatios for cold-formed steel structural members ad coectios. The backgroud iformatio for the desig criteria is discussed i the Commetary ad other related refereces. i

7 TABLE OF CONTENTS PREFACE... i TABLE OF CONTENTS " ii SYMBOLS AND DEFINITIONS vii A. GENERAL PROVISIONS I Al Limits of Applicability ad Terms '" I AI.I Scope ad Limits of Applicability AI.2 Terms... I I Al.3 Uits of Symbols ad Terms 4 A2 No-Coformig Shapes ad Costructios 4 A3 Material 4 A3. I Applicable Steels... 4 A3.2 Other Steels... S A3.3 Ductility A3.4 Delivered Miimum Thickess 8 A4 Loads... 8 A4.1 Dead Load, A4.2 Live or Sow Load A4.3 Impact Load... 8 A4.4 Wid or Earthquake Load 8 A4.S Podig... 9 AS Structural Aalysis ad Desig 9 AS.1 Desig Basis... 9 AS. 1.1 Limit State - Stregth... 9 AS.1.2 Limit State - Serviceability 10 ii

8 A Nomial Load A5.1.4 Load Factors ad Load Combiatios 11 A5.I.S Resistace Factors 12 A5.2 Yield Poit ad Stregth Icrease from Cold Work of Formig.. 15 A Yield Poit A5.2.2 Stregth Icrease from Cold Work of Formig 15 A5.3 Durability A6 Referece Documets B. ELEMENTS B1 Dimesioal Limits ad Cosideratios 21 Bl.l Flage F1at-Width-to-Thickess Cosideratios 21 Bl.2 Maximum Web Depth-to-Thickess Ratio 24 B2 Effective Widths of Stiffeed Elemets 24 B2.1 Uiformly Compressed Stiffeed Elemets 24 B2.2 Uiformly Compressed Stiffeed Elemets with Circular Holes.. 27 B2.3 Effective Widths of Webs ad Stiffeed Elemets with Stress Gradiet B3 Effective Widths of Ustiffeed Elemets 30 B3.1 Uiformly Compressed Ustiffeed Elemets 30 B3.2 Ustiffeed Elemets ad Edge Stiffeers with Stress Gradiet 31 B4 Effective Widths of Elemets with a Edge Stiffeer or Oe Itermediate Stiffeer 31 B4.1 Uiformly Compressed Elemets with a Itermediate Stiffeer. 33 B4.2 Uiformly Compressed Elemets with a Edge Stiffeer 34 BS Effective Widths of Edge Stiffeed Elemets with Itermediate iii

9 Stiffeers or Stiffeed Elemets with More Tha Oe Itermediate Stiffeer B6 Stiffeers 37 B6.1 Trasverse Stiffeers 37 B6.2 Shear Stiffeers 38 B6.3 No-Coformig Stiffeers 39 C. MEMBERS C1 Properties of Sectios 40 C2 Tesio Members 40 C3 Flexural Members 40 C3.1 Stregth for Bedig Oly 40 C3.1.1 Nomial Sectio Stregth 41 C3.1.2 Lateral Bucklig Stregth 43 C3.1.3 Beams Havig Oe Flage Through-Fasteed to Deck or Sheathig 47 C3.2 Stregth for Shear Oly : 48 C3.3 Stregth for Combied Bedig ad Shear 50 C3.4 Web Cripplig Stregth 50 C3.5 Combied Bedig~ad Web Cripplig Stregth 54 C4 Cocetrically Loaded Compressio Members 55 C4.1 Sectios Not Subject to Torsioal or Torsioal-Flexural Bucklig C4.2 Doubly- or Sigly-Symmetric Sectios Subject to Torsioal or Torsioal-Flexural Bucklig 58 C4.3 Nosymmetric Sectios 58 C5 Combied Axial Load ad Bedig 58 iv

10 C6 Cylidrical Tubular Members 60 C6.1 Bedig C6.2 Compressio C6.3 Combied Bedig ad Compressio 62 D. STRUCTURAL ASSEMBLIES D1 Built-Up Sectios 63 D1.1 I-Sectios Composed of Two Chaels 63 Dl.2 Spacig of Coectios i Compressio Elemets 65 D2 Mixed Systems 66 D3 Lateral Bracig 66 D3.1 Symmetrical Beams ad Colums 66 D3.2 Chael-Sectio ad Z-Sectio Beams 66 D3.2.1 Achorage of Bracig for Roof Systems Uder Gravity Load With Top Flage Coected to Sheathig 67 D3.2.2 Neither Flage Coected to Sheathig 69 D3.3 Laterally Ubraced Box Beams 71 D4 Wall Studs ad Wall Stud Assemblies 71 D4.1 Wall Studs i Compressio 72 D4.2 Wall Studs i Bedig 76 D4.3 Wall Studs with Combied Axial Load ad Bedig 76 E. CONNECTIONS AND JOINTS E1 Geeral Provisios E2 Welded Coectios E2.1 Groove Welds i Butt Joits 78 E2.2 Arc Spot Welds " 79 E2.3 Arc Seam Welds 84 v

11 E2.4 Fillet Welds 85 E2.5 Flare Groove Welds 87 E2.6 Resistace Welds 89 E3 Bolted Coectios 89 E3.1 Spacig ad Edge Distace 91 E3.2 Tesio i Coected Part 93 E3.3 Bearig 94 E3.4 Shear ad Tesio i Bolts 95 E4 Shear Rupture E5 Coectios to Other Materials 98 E5.1 Bearig 98 E5.2 Tesio 99 E5.3 Shear F. TESTS FOR SPECIAL CASES 100 Fl Tests for Determiig Structural Performace 100 F2 Tests for Cofirmig Structural Performace 105 F3 Tests for Determiig Mechaical Properties 105 F3.1 Full Sectio 105 F3.2 Flat Elemets of Formed Sectios 106 F3.3 Virgi Steel 107 vi

12 SYMBOLS AND DEFINITIONS Symbol Defiitio Sectio A Full ureduced cross-sectioal area of the member C , C , C4, C6.2, D4.1 b 1 t+a s ' for trasverse stiffeers at iterior B6.1 support ad uder cocetrated load, ad b 2 t+a s ' for trasverse stiffeers at ed support A e A A s A' s A st Gross cross-sectioal area of bolt 18t 2 +A, for trasverse stiffeers at iterior s support ad uder cocetrated load, ad 10t 2 +A, s for trasverse stiffeers at ed support Effective area at the stress F Net area of cross sectio Cross-sectioal area of trasverse stiffeers Effective area of stiffeer Gross area of shear stiffeer E3.4 B6.1 C4, C6.2 C2, E3.2 B4, B4. 1, B4.2, B6.1 B4, B4.1, B4.2 B6.2 A w Net web area E4 Al Bearig area E5.I A 2 Full cross sectioal area of cocrete support E5.1 a Shear pael legth of the ureiforced web elemet. B6.2, C3.2, For a reiforced web elemet, the distace betwee D3.2 a trasverse stiffeers Legth of bracig iterval D3.2 vii

13 Symbol Defiitio Sectio B B c b b d Stud spacig Term for determiig the tesile yield poit of corers Effective desig width of compressio elemet Effective width for deflectio calculatio D4.I A5.2.I B2.I, B2.2, B2.3, B3.I, B3.2, B4.1, B4.2, B5, D3.2.I B2.I, B2.2 b e Effective desig width of sub-elemet or elemet b See Fig. B4.1 o C For flexural members, ratio of the total corer AI.2, B2.3, BS B4, B4.I, B5 A5.2.2 cross-sectioal area of the cotrollig flage to the full cross-sectioal area of the cotrollig flage C b Bedig coefficiet depedet o momet gradiet C3.1.2 C Ed momet coefficiet i iteractio formula C5 m C Coefficiet for lateral bracig of C- ad Z-sectio D3.2.I ms C Ed momet coefficiet i iteractio formula C5 mx C Ed momet coefficiet i iteractio formula C5 my C p Correctio factor Fl C Coefficiet for lateral torsioal bucklig C3.1.2 s C TF Ed momet coefficiet i iteractio formula C3.1.2 C th Coefficiet for lateral bracig of C- ad Z-sectio D3.2.1 viii

14 Symbol Defiitio Sectio C tr Coefficiet for lateral bracig of C- ad Z-sectio D3.2.1 C v C w C y Co C 1 Shear stiffeer coefficiet Torsioal warpig costat of the cross-sectio Compressio strai factor Iitial colum imperfectio. Term used to compute shear strai i wall board B6.2 C C D4.1 B4, B4.1, D4.2 C 2 Coefficiet as defied i Fig. B4.2 B4, B4.2 c f D D D D D o d d d d d a Amout of curlig Outside diameter of cylidrical tube Overall depth of lip Shear stiffeer coefficiet Nomial dead load Iitial colum imperfectio Depth of sectio Width of arc seam weld Visible diameter of outer surface of arc spot weld Diameter of bolt Average diameter of the arc spot weld at mid-thickess of t B1.1b C6.1, C6.2, D4.2 B1. 1, B4, D1. 1 B6.2 AS D4.1 Bl.lb, B4, C3.1.1, Dl.l, D3.2.1, D4.1 E2.3 E2.2 E3, E3.1, E3.2 E2.2 ix

15 Symbol Defiitio Sectio d a d e d e d h d s d' s d wc Average width of seam weld Effective diameter of fused area Effective width of arc seam weld at fused surfaces Diameter of stadard hole Reduced effective width of stiffeer Actual effective width of stiffeer Coped web depth E2.3 E2.2 E2, E2.3 B2.2, E3.1, E4 B4, B4.2 B4, B4.2 E4 E Modulus of elasticility of steel (29.5 x 10 3 ksi) B1. Ib, B2.1, E E o E' e. m1. Nomial earthquake load Iitial colum imperfectio; a measure of the iitial twist of the stud from the iitial, ideal, ubuckled locatio Term used to compute shear strai i wallboard Ielastic modulus of elasticility Miimum allowable distace measured i the lie of force from the ceterlie of a weld to the earest edge of a adjacet weld or to the ed of the coected part toward which the force is directed B6.1, C , C3.2, C4, C4.1, C5, C6.1, D1. 2, D4.1, D4.2, E2.2 A D4.1 D4.1 D4.1 E2.2 x

16 Symbol Defiitio Sectio e. The distace e measured i the lie of force from ml. E3.1 e y F e F m F F v F' t the ceterlie of a stadard hole to the earest edge of a adjacet hole or to the ed of the coected part toward which the force is directed Yield strai = F IE y Elastic bucklig stress Mea value of the fabricatio factor Nomial bucklig stress Nomial tesile stregth of bolts Nomial shear stregth of bolts Nomial tesile stregth for bolts subject to combiatio of shear ad tesio C C4, C4.1, C4.2, C4.3, C6.2, D4.1 Fl C4, C6.2 E3.4 E3.4 E3.4 F Yield poit as specified i Sectios A3.1 or A3.2 sy A3.1, A3.2, A3.3.2, E2.2, E3.1, E3.2 F u Tesile stregth as specified i Sectios A3.1 or A3.1, A3.2, A3.2, or as reduced for low ductility steel A3.3, A3.3.2, E2.2, E2.3, E2.4, E2.5, E3. I, E3.2, E3.3, E4 xi

17 Symbol Defiitio Sectio F uv F wy Tesile stregth of virgi steel specified by Sectio A3 or established i accordace with Sectio F3.3 Yield poit for desig of trasverse stiffeers A3, AS.5.2, EZ.2, F3.3 B6.1 F xx Stregth level desigatio i AWS electrode EZ.2, E2.3, classificatio E2.4, E2.5 F Y Yield poit used for desig, ot to exceed the A1.2, A3.3, specified yield poit or established i accordace A5.2.1, A5.2.2, with Sectio F3, or as icreased for cold work of BZ. 1, B5, B6. 1, formig i Sectio A5.Z.2 or as reduced for low ductility steels i Sectio A3.3.2 C2, C3.1, C3.Z, C4, C6.1, C6.2, F ya F yc F yf F ys F yv f Average yield poit of sectio Tesile yield poit of corers Weighted average tesile yield poit of the flat portios Yield poit of stiffeer steel Tesile yield poit of virgi steel specified by Sectio A3 or established i accordace with Sectio F3.3 Stress i the compressio elemet computed o the basis of the effective desig width D1.2, D4.2, E2 A5.2.1, E5.1 A5.2.1 A5.2.1, F3.2 B6.1 A3, A5.2.2, F3.3 BZ.l, B2.2, B3. 2, B4, B4. 1 xii

18 Symbol Defiitio Sectio f av Average computed stress i the full, ureduced flage width B1.1b f' Specified compressio stress of cocrete E5.1 c f d Computed compressive stress i the elemet beig B2.1, B2.2, cosidered. Calculatios are based o the effective sectio at the load for which deflectios are B3.1, B4.1, B4.2 determied f d1,f d2 Computed stresses f 1 ad f Z as show i Fig. BZ.3 BZ.3-1. Calculatios are based o the effective sectio at the load for which deflectios are determied Computed stress f 3 i edge stiffeer, as show B3.2 i Fig. B4-Z. Calculatios are based o the effective sectio at the load for which deflectios are determied f v Computed shear stress o a bolt E4 Web stresses defied by Fig. BZ.3-1 Edge stiffeer stress defied by Fig. B4.2 B2.3 B3.2 Shear modulus for steel C3.I.l, D4.1 G' g Ielastic shear modulus Vertical distace betwee two rows of coectios earest to the top ad bottom flages D4.1 DI. 1 xiii

19 Symbol Defiitio Sectio h Depth of flat portio of web measured alog the plae of web B1.2, B6.2, C3.2, C3.4 I a Adequate momet of iertia of. stiffeer so that B1.1, B4, B4.1, each compoet elemet will behave as a stiffeed B4.2 elemet Momet of iertia of the full ureduced sectio C5 about the bedig axis I s Actual momet of iertia of the full stiffeer B1.1, B4, B4.1, about its ow cetroidal axis parallel to the B4.2, B5 elemet to be stiffeed Momet of iertia of the full area of the multiple B5 stiffeed elemet, icludig the itermediate stiffeers, about its ow cetroidal axis parallel to the elemet to be stiffeed I, I Momet of iertia of full sectio about pricipal x y axes D1.1, D3.2.2 I xy I yc J j Product of iertia of full sectio about major ad mior cetroidal axes Momet of iertia of the compressio portio of a sectio about the gravity axis of the etire sectio about the y-axis St. Veat torsio costat Sectio property for torsioal-flexural bucklig D3.2.2, D4.1 C C C xiv

20 Symbol Defiitio Sectio K K' K b K t K x K y k k v L Effective legth factor A costat Effective legth factor i the plae of bedig Effective legth factor for torsio Effective legth factor for bedig about x-axis Effective legth factor for bedig about y-axis Plate bucklig coefficiet Shear bucklig coefficiet Full spa for simple beams, distace betwee iflectio poits for cotiuous beams, twice the legth of catilever beams C3.1.2, C4, C4.1, CS D3.2.2 C5 C C C B2.1, B2.3, B3.1, B3.2, B4, B4.1, B4.2 B6.2, C3.2 B1. Ic, D3.2.I L Legth of seam weld ot icludig the circular eds E2.3 L Legth of fillet weld E2.4, E2.S L Ubraced legth of member C3.1.2, C4. I, D1.I L L r Nomial live load Nomial roof live load Legth of trasverse stiffeer Ubraced legth of compressio member for torsiq Ubraced legth of compressio member for bedig about x-axis AS AS B6.I C C xv

21 Symbol Defiitio Sectio L y M c M e M m M Ubraced legth of compressio member for bedig about y-axis Critical momet Elastic critical momet Mea value of the material factor Nomial flexural stregth C C C FI C3.1, C3.1.I, C3.1. 2, C6.I M M Nomial flexural stregths about the cetroidal C5 x' y axes determied i accordace with Sectio C3 M u M ux M uy m N Required flexural stregth Required flexural stregth about x-axis Required flexural stregth about y-axis Momet causig a maximum strai e y Smaller ed momet Larger ed momet Distace from the shear ceter of oe chael to the mid-plae of its web Actual legth of bearig Number of holes Number of tests Number of parallel purli lies Force to be resisted by itermediate beam brace Mea value of the tested-to-predicted load ratios C3.3, C3.5 C5 CS B2.1, C3.I C3.1.2, C5 C , C5 D3.2.2, D1.I D3.6 E4 FI D3.2.I C5 D3.2.I FI xvi

22 Symbol Defiitio Sectio P P P o P u Q q r Nomial axial stregth of member Nomial stregth of coectio compoet Nomial axial stregth of member determied i accordace with Sectio C4 for L = 0 Required axial stregth Desig shear rigidity for sheathig o both sides of the wall assembly Load effect Uiformly distributed factored load i the plae of the web Desig shear rigidity for sheathig per ich of stud spacig Factor used to determie desig shear rigidity Reductio factor Coefficiet Iside bed radius Nomial roof rai load Nomial resistace Average value of all test results Radius of gyratio of full, ureduced cross sectio C4, C6.2 E2, E2.2, E2.3, E2.4, E2.5 CS CS D4.1 Fl Dl.l D4.1 D4.1 C C4, C6.2 AS.2.1, C3.4 AS Fl Fl C3.1.1, C4, C4.1 xvii

23 Symbol Defiitio Sectio r r cy Force trasmitted by the bolt or bolts at the sectio cosidered, divided by the tesio force i the member at that sectio Radius of gyratio of oe chael about its cetroidal axis parallel to web Radius of gyratio of I-sectio about the axis perpedicular to the directio i which bucklig would occur for the give coditios of ed support ad itermediate bracig E3.2 D1.1 D1.1 r Polar radius of gyratio of cross sectio about the C3.1.1, C4.2, o shear ceter r, r Radius of gyratio of cross sectio about x y s cetroidal pricipal axes 1. 28JE/ f D4.1 C B4, B4.1 S c S e Elastic sectio modulus of the effective sectio calculated at a stress Me/Sf i the extreme fiber Elastic sectio modulus of the effective sectio calculated with extreme compressio or tesio C3.1.1, C3.1.2, C4 C S fiber at F y Elastic sectio modulus of full, ureduced sectio for the extreme compressio fiber Nomial sow load C , C , C6.1 AS xviii

24 Symbol Defiitio Sectio smax s s s T T s Maximum permissible logitudial spacig of welds or other coectors joiig two chaels to form a I-sectio Fasteer spacig Spacig i lie of stress of welds, rivets, or bolts coectig a compressio coverplate or sheet to a o-itegral stiffeer or other elemet Weld spacig Nomial tesile stregth Desig stregth of coectio i tesio D1. 1 D1. 2, D4. 1 E3.2 D1. 1 C2 D1.1 t Base steel thickess of ay elemet or sectio A1.2, A3.4, A , B1. 1, B1.1b, B1.2, B2. 1, B4, B4. 1, B4. 2, B5, B6. 1, C3.1.1, C3.2, C3.4, C4, C6.1, t t s t w Thickess of the thiest coected part Equivalet thickess of a multiple-stiffeed elemet Effective throat of weld C6.2, D1.2, E2.4, E2.5 E3.1, E4 B5, B6.1 E2.4, E2.5 xix

25 Symbol Defiitio Sectio V F V M V Coefficiet of variatio of the fabricatio factor Coefficiet of variatio of the material factor Nomial shear stregth Fl Fl 86.2, C3.2, C3.3 V p Coefficiet of variatio of the tested-to-predicted F1 load ratios Coefficiet of variatio of the load effect Required shear stregth Factored load supported by all purli lies beig Fl C3.3 D3.2.1 W w restraied Nomial wid load Flat width of elemet exclusive of radii AS A1.2, B1.1, B2.1, B2.2, B3.1, B4, B4.1, B4.2, B5, C3.1.1, C4, D1.2 Width of flage projectio beyod the web or half B1.1c the distace betwee webs for box- or U-type sectios Projectio of flages from iside face of web Leg o weld Leg o weld 81. 1b, D xx

26 Symbol Defiitio Sectio x x o Y Distace from cocetrated load to brace Distace from shear ceter to cetroid alog the pricipal x-axis Yield poit of web steel divided by yield poit of stiffeer steel D3.2 C3.1.1, C4.2, D4.1 B6.2 1/0, Magificatio factors x C5 1/0 y ~ Coefficiet ~o Target reliability idex C4.2, D4.1 Fl y V Actual shear strai i the sheathig Permissible shear strai of the sheathig D4.1 D4.1 y. 1 Load factor e Agle betwee web ad bearig surface > 45 0 but o Fl C3.4 more tha 90 0 e Agle betwee the vertical ad the plae of the web D3.2.1 of the Z-sectio, degrees cr p ;..., ;... c Stress related to shear strai i sheathig Theoretical elastic bucklig stress Torsioal bucklig stress Reductio factor Slederess factors D4.1 D4.1 C3.1.1, C4.2, D4.1 B2.1 B2.1, C3.S.2 B2.3 xxi

27 Symbol Defiitio Sectio Resistace factor A , E2, E2.1, E2.2, E2.3, E2.4, E2.5, E2.6, E3.1, E3.2, E3.3, E3.4, E4, Fl Resistace factor for bedig stregth A , C3, C , C , C3.1.3, C3.3, C3.5, C5, C6.1, C6.3, D4.2, D4.3 Resistace factor for cocetrically loaded compressio member A3.3.1, A5.1.5, B6.1, C4, C5, C6.2, C6.3, D4.1, D4.3 4>c Resistace factor for bearig stregth 4>t Resistace factor for tesio member 4>v Resistace factor for shear stregth Resistace factor for web cripplig stregth E5.1 C2 B6.2, C3.2, C3.3 C3.4, C3.5 xxii

28 LOAD AND RESISTANCE FACTOR DESIGN SPECIFICATION FOR COLD-FORMED STEEL STRUCTURAL MEMBERS A. GENERAL PROVISIONS Al Limits of Applicability ad Terms AI.I Scope ad Limits of Applicability This Load ad Resistace Factor Desig Specificatio is iteed as a alterate to the Specificatio for the Desig of Cold-Formed Steel Structural Members of the America Iro ad Steel Istitute. This specificatio shall apply to the desig of structural members cold-formed to shape from carbo or low-alloy steel sheet, strip, plate or bar ot more tha oe ich i thickess ad used for load-carryig purposes i buildigs. It may also be used for structures other tha buildigs provided appropriate allowaces are made for thermal ad/or dyam'ic effects. AI.2 Terms Where the followig terms appear i this Specificatio they shall have the meaig herei idicated: (a) Stiffeed or Partially Stiffeed Compressio Elemets. A stiffeed or partially stiffeed compressio elemet is a flat compressio elemet (i.e., a plae compressio flage of a flexural member or a plae web or flage of a compressio member) of which both edges parallel to the directio of stress are stiffeed by a web, flage, stiffeig lip, itermediate stiffeer, or the like. 1

29 (b) Ustiffeed Compressio Elemets. A ustiffeed compressio elemet is a flat compressio elemet which is stiffeed at oly oe edge parallel to the directio of stress. (c) Multiple-Stiffeed Elemets. A multiple-stiffeed elemet is a elemet that is stiffeed betwee webs, or betwee a web ad a stiffeed edge, by meas of itermediate stiffeers which are parallel to the directio of stress. A sub-elemet is the portio betwee adjacet stiffeers or betwee web ad itermediate stiffeer or betwee edge ad itermediate stiffeer. (d) Flat-Width-to-Thickess Ratio. The flat width of a elemet measured alog its plae, divided by its thickess. (e) Effective Desig Width. Where the flat width of a elemet is reduced for desig purposes, the reduced desig width is termed the effective width or effective desig width. (f) Thickess. The thickess, t, of ay elemet or sectio shall be the base steel thickess, exclusive of coatigs. (g) Torsioal-Flexural Bucklig. Torsioal-flexural bucklig is a mode of bucklig i which compressio members ca bed ad twist simultaeously. (h) Poit-Symmetric Sectio. A poit-symmetric sectio is a sectio symmetrical about a poit (cetroid) such as a Z-sectio havig equal flages. (i) Yield Poit. Yield poit, F or F,as used i this Specificay sy tio shall mea yield poit or yield stregth. (j) Stress. Stress as used i this Specificatio meas force per uit area. 2

30 (k) Cofirmatory Test. A cofirmatory test is a test made, whe desired, o members, coectios, ad assemblies desiged accordig to the provisios of Sectios A through E of this Specificatio or its specific refereces, i order to compare actual versus calculated performace. (1) Performace Test. A performace test is a test made o structural members, coectios, ad assemblies whose performace caot be determirled by the provisios of Sectios A through E of this Specificatio or its specific refereces. (m) Virgi Steel. Virgi steel refers to steel as received from the steel producer or warehouse before beig cold worked as a result of fabrieatig operatios. () Virgi Steel Properties. Virgi steel properties refer to mechaical properties of virgi steel such as yield poit, tesile stregth, ad elogatio. (0) Specified Miimum Yield Poit. The specified miimum yield poit is the lower limit of yield poit which must be equalled or exceeded i a specificatio test to qualify a lot of steel for use i a cold-formed steel structural member desiged at that yield poit. (p) Cold-Formed Steel Structural Members. Cold-formed steel structural members are shapes which are maufactured by press-brakig blaks sheared from sheets, cut legths of coils or plates, or by roll formig coldor hot-rolled coils or sheets; both formig operatios beig performed at ambiet room temperature, that is, without maifest additio of heat such as would be required.for hot formig. (q) LRFD (Load ad Resistace Factor Desig). A method of proportioig structural compoets (members, coectors, coectig elemets ad

31 assemblages) such that o applicable limit s tate is exceeded whe the structure is subjected to all appropriate load combiatios. (r) Desig Stregth. Factored resistace or stregth (force, momet, as appropriate), ~R, provided by the structural compoet. (s) Required Stregth. Load effect (fotce, momet, as appropriate) actig o the structural compoet determied by structural aalysis from the factored loads (usig most appropriate critical load combiatios). AI.3 Uits of Symbols ad Terms The Specificatio is writte so that ay compatible system of uits may be used except where explicitly stated otherwise i the text of these provisios. A2 No-Coformig Shapes ad Costructio The provisios of the Specificatio are ot iteded to prevet the use of alterate shapes or costructios ot specifically prescribed herei. Such alterates shall meet the provisios of Sectio F of the Specificatio ad be approved by the appropriate buildig code authority. A3 Material A3.1 Applicable Steels This Specificatio requires the use of steel of structural quality as defied i geeral by the provisios of the followig specificatios of the America Society for Testig ad Materials: ASTM A36/A36M-84a, Structural Steel ASTM A242/A242M-85, High-Stregth Low-Alloy Structural Steel 4

32 ASTM A441M-85, High-Stregth Low-Alloy Structural Magaese Vaadium Steel ASTM A446/A446M-85 (Grades A, B, C, D, & F) Steel, Sheet, Zic-Coated (Galvaized) by the Hot-Dip Process, Structural (Physical) Quality ASTM A500-84, Cold-Formed Welded ad Seamless Carbo Steel Structural Tubig i Rouds ad Shapes ASTM A529/A529M-85, Structural Steel with 42 ksi Miimum Yield Poit (1/2 i. Maximum Thickess) ASTM A570/A570M-85 Steel, Sheet ad Strip, Carbo, Hot-Rolled, Structural Quality ASTM A572/A572M-85, High-Stregth Low-Alloy Columbium-Vaadium Steels of Structural Quality ASTM A588/A588M-85, High-Stregth Low-Alloy Structural Steel with 50 ksi Miimum Yield Poit to 4 i. Thick ASTM A Steel, Sheet ad Strip, High Stregth, Low Alloy, Hot-Rolled ad Cold-Rolled, with Improved Atmospheric Corrosio Resistace ASTM A Steel Sheet ad Strip, High Stregth, Low Alloy, Columbium or Vaadium, or both, Hot-Rolled ad Cold-Rolled ASTM A (Grades A, B, C, & D) Steel, Sheet, Carbo, Cold-Rolled, Structural Quality ASTM A (Grades 50 ad 60) Sheet Steel ad Strip, High-Stregth, Low-Alloy, Hot-Rolled, with Improved Formability ASTM A792-85a (Grades 33, 37, 40 & 50) Steel Sheet, Alumium-Zic Alloy-Coated by the Hot-Dip Process, Geeral Requiremets A3.2 Other Steels 5

33 The listig i Sectio A3.1 does ot exclude the use of steel up to ad icludig oe ich i thickess ordered or produced to other tha the listed specificatios provided such steel coforms to the chemical ad mechaical requiremets of oe of the listed specificatios or other published specificatio which establishes its properties ad suitability, ad provided it is subjected by either the producer or the purchaser to aalyses, tests ad other cotrols to the extet ad i the maer prescribed by oe of the listed specificatios ad Sectio A3.3. A3.3 Ductility Steels ot listed i Sectio A3.1 ad used for structural members ad coectios shall comply with oe of the followig ductility requiremets: A3.3.1 The ratio of tesile stregth to yield poit shall ot be less tha 1.08, ad the total elogatio shall ot be less tha 10 percet for a two-ich gage legth or 7 percet for a eight-ich gage legth stadard specime tested i accordace with ASTM A If these requiremets caot be met, the followig criteria shall be satisfied: (1) local elogatio i a 1/2 ich gage legth across the fracture shall ot be less tha 20%, (2) uiform elogatio outside the fracture shall ot be less thu... 3%". Whe material ductility is determied o the basis of the local ad *Further iformatio o the test procedures should be obtaied from the Commetary. 6

34 uiform elogatio criteria, the us~ ** desig of purlis ad girts of such material is restricted to the i accordace with Sectios C3.I.l(a), C3.l.2, ad C For purlis ad girts subject to combied axial load ad bedig momet (Sectio C5), P / P shall ot exceed u c A3.3.2 Steels coformig to ASTM A446 Grade E ad A611 Grade E ad other steels which do ot meet the provisios of Sectio A3.3.l may be used for particular cofiguratios provided (1) the yield stregth, F, used for dey sig i Chapters B, C ad D is take as 75 percet of the specified miimum yield poit or 60 ksi, whichever is less ad (2) the tesile stregth, F, u used for desig i Chapter E is take as 75 perget of the specified miimum tesile stress or 62 ksi, whichever is less. Alteratively, the suitability of such steels for the cofiguratio shall be demostrated by load tests i accordace with Sectio Fl. Desig stregths based o these tests shall ot exceed the stregths calculated accordig to Chapters B through E, usig the specified miimum yield poit, F sy ' for F y ad the specified miimum tesile stregth, F. u Desig stregths based o existig use shall ot exceed the stregths calculated accordig to Chapters B through E, usig the specified miimum yield poit, F sy ' for F y ad the specified miimum tesile stregth, F. u **Horizotal structural members which support roof deck or pael coverig ad applied loads pricipally by bedig. 7

35 A3.4 Delivered Miimum Thickess The ucoated miimum steel thickess of the cold-formed product as delivered to the job site shall ot at ay locatio be less tha 95 percet of the thickess, t, used i its desig; however, thickesses may be less at beds, such as corers, due to cold-formig effects. A4 Loads A4.1 Dead Load The dead load to be assumed i desig shall cosist of the weight of steelwork ad all material permaetly fasteed thereto or supported thereby. A4.2 Live or Sow Load The live or sow load shall be that stipulated by the applicable code or specificatio uder which the structure is beig desiged or that dictated by the coditios ivolved. A4.3 Impact Load For structures carryig live loads which iduce impact, the assumed live load shall be icreased sufficietly to provide for impact. A4.4 Wid or Earthquake Load Wid or earthquake load shall be that stipulated by the applicable code or specificatio uder which the structure is beig desiged or that dictated by the coditios ivolved. 8

36 A4.5 Podig Uless a roof surface is provided with sufficiet slope toward poits of free draiage or adequate idividual drais to prevet the a~cum~latio of raiwater, the roof system shall be ivestigated by ratioal aalysis to assure stability uder podig coditios. AS Structural Aalysis ad Desig AS.1 Desig Basis This Specificatio is based o the Load ad Resistace Factor Desig cocept. Load ad Resistace Factor Desig is a method of proportioig cold-formed steel structural compoets (i.e., members, coectors ad coectios) such that ay applicable limit state is ot exceeded whe the structure is subjected to ay appropriate load combiatios. Two types of limit states are to be cosidered: 1) the limit state of the stregth required to resist the extreme loads durig the "iteded life of the structure, ad 2) the limit state of the ability of the structure to perform its iteed fuctio durig its life. These limit states will be called the Limit State of Stregth ad the Limit State of Serviceability, respectively, i these criteria. A5.1.1 Limit State - Stregth The desig is satisfactory whe the required stregths, as determied from the assiged omial loads which are multiplied by appropriate load factors, are smaller tha or equal to the desig stregth of each structural compoet. 9

37 factor ad R The desig stregth is equal to cpr, where cp is a resistace is the omial stregth determied accordig to the formulas give i Chapter C for members, i Chapter D for structural assemblies ad i Chapter E for coectios. Values of resistace factors cp are give i Sectio AS.I.S for the appropriate limit states goverig member ad coectio stregth. AS.l.2 Limit State - Serviceability Serviceability is satisfactory if a omial structural respose (e.g. live load deflectio) due to the applicable omial loads is less tha or equal to the appropriate acceptable or allowable value of this respose. AS.I.3 Nomial Loads The omial loads shall be the miimum desig loads stipulated by the applicable code uder which the structure is desiged or dictated by the coditios ivolved. I the absece of a code, the loads ad load combiatios shall be those stipulated i the America Natioal Stadard, Miimum Desig Loads for Buildigs ad Other Structures, ANSI AS8.1. For desig purposes, the loads stipulated by the applicable code shall be take as omial loads. 10

38 A5.1.4 Load Factors ad Load Combiatios* The structure ad its compoets must be desiged for the appropriate most critical load combiatio. The followig load combiatios of the factored omial loads shall be used i the computatio of the required stregths: D + L D + 1.6L + 0.5(L or S or R r ) r D + (1.4 L or 1.6 S or 1.6 R r ) + (0.5 L or 0.8 W ) r D W L + 0.5(L or S or R ) r r D E + (0.5 L or 0.2 S ) D - (1. 3 W or 1.5 E ) where D = omial dead load E = omial earthquake load L = omial live load L = omial roof live load r R = omial roof rai load r S = omial sow load W = omial wid load (Exceptio: For wid load o idividual purlis, girts, wall paels ad roof decks, multiply the load factor for W by 0.9) * For roof ad floor costructio, recommeded load combiatios for dead load, weight of wet cocrete, ad costructio load icludig equipmet, workme ad formworkare give i Sectio A5.l of the Commetary. 11

39 Exceptio: The load factor for L i combiatios (3), (4), ad (5) shall equal to 1.0 for garages, areas occupied as places of public assembly, ad all areas where the live load is greater tha 100 psf. Whe the structural effects of F, H, P or T are sigificat, they shall be cosidered i desig as the followig factored loads: 1.3F, 1.6H, 1.2P, ad 1.2T, where F = loads due to fluids with well-defied pressures ad maximum heights H = loads due to the weight ad lateral pressure of soil ad water i soil P = loads, forces, ad effects due to podig T = self-straiig forces ad effects arisig from cotractio or expasio resultig from temperature chages, shrikage, moisture chages, creep i compoet materials, movemet due to differetial settlemet, or combiatios thereof. AS.1.S Resistace Factors The resistace factors to be used for determiig the desig stregths, follows: q,r, of structural members ad coectios shall be take as 12

40 Type of Stregth Resistace Factor, m (a) Stiffeers Trasverse stiffeers Shear stiffeers* (b) Cc) Tesio members o.95 Flexural members Bedig stregth For sectios with stiffeed or partially stiffeed compressio flages For sectios with ustiffeed compressio flages Laterally ubraced beams o.90 Beams havig oe flage through-fasteed to deck or sheathig (C- or Z-sectios) Web desig... Shear stregth" o.90 Web cripplig For sigle ureiforced webs For I-sectios O.80 Cd) (e) Cocetrically loaded compressio members Combied axial load ad bedig c for compressio b for bedig Usig Sectio C Usig Sectio C *Whe hit s JEk vif y, =

41 (f) Cylidrical tubular members Bedig stregth Axial compressio o.85 (g) Wall studs ad wall stud assemblies Wall studs i compressio Wall studs i bedig For sectios with stiffeed or partially stiffeed compressio flages For sectios with ustiffeed compressio flages (h) Welded coectios Groove welds Tesio or compressio Shear (welds) Shear (base metal) Arc spot welds Welds Coected part o.so-o.60 Miimum edge distace Arc seam welds Welds Coected part Fillet welds Logitudial loadig (coected part) s-0.60 Trasverse loadig (coected part) Welds---~ ~ Flare groove welds Trasverse loadig (coected part)

42 Logitudial loadig (coected part) o.55 Welds Resistace welds (i) Bolted coectios Miimum spacig ad edge distace Tesio stregth o et sectio With washers Double shear coectio Sigle shear cortectio Without washers Bearig stregth See Tables E3.3-1 ad E Shear stregth of bolts Tesile stregth of bolts (j) (k) Shear rupture Coectios to other materials (Bearig) ~ A5.2 Yield Poit ad Stregth Icrease from Cold Work of Formig A5.2.1 Yield Poit The yield poit used i desig, F, shall ot exceed the specified y miimum yield poit, or as established i accordace with Chapter F, or as icreased for cold work of formig i Sectio A5.2.2 or as reduced for low ductility steels i Sectio A A5.2.2 Stregth Icrease from Cold Work of Formig 15

43 Stregth icrease from cold work of formig may be obtaied by ~ubst~tutig F for F, where F is the average yield poit of the full ya y ya sectio. Such icrease shall be limited to Sectio C3.1 (excludig Sectio C3.1.I(b» C4, CS, C6 ad D4. The limitatios ad methods for determiig F ya are as follows: (a) For axially loaded compressio members ad flexural members whose proportios are ~:uch that the quatity p is uity as determied accordig to Sectio B2 for each of the compoet elemets of the sectio, the desig yield stress, F,of the steel shall be deterya mied o the basis of oe of the followig methods: (1) full sectio tesile tests (see paragraph (a) of Sectio F3.I) (2) stub colum tests (see paragraph (b) of Sectio F3.1) (3) computed as follows: F = CF +(I-C)F f ya yc y where (Eq. AS.2.2-1) F ya = Average yield poit of the steel i the full sectio of compressio members or full flage sectios of flexural members C = For compressio members, ratio of the total corer cross-sectioal area to the total cross-sectioal area of the full sectio; for flexural members, ratio of the total corer cross-sectioal area of the cotrollig flage to the full cross-sectioal area of the cotrollig flage F yf = Weighted average tesile yield poit of the flat portios established i accordace with Sectio F3.2 16

44 or virgi yield poit if tests are ot made F = B F I(R/t)m, tesile yield poit of corers. This yc c yv formula is applicable oly whe F IF ~ 1.2, R/t ~ 7, uv yv ad miimum icluded agle ~ (Eq. A ) B = 3.69(F IF )-O.819(F IF ) (Eq. A ) c uv yv uv yv m = 0.192(F IF ) uv yv (Eq. AS.2.2-4) R = Iside bed radius F = Tesile yield poit of virgi steel* specified by Sectio yv A3 or established i accordace with Sectio F3.3 * F = Tesile stregth of virgi steel specified by Sectio uv A3 or established i accordace with Sectio F3.3 (b) For axially loaded tesio members the yield poit of the steel shall be determied by either method (1) or method (3) prescribed i paragraph (a) of this Sectio. (c) The effect of ay weldig o mechaical properties of a member shall be determied o the basis of tests of full sectio specimes cotaiig withi the gage legth, such weldig as the maufacturer iteds to use. Ay ecessary allowace for such effect shall be made i the structural use of the member. *Virgi steel refers to the coditio (i.e. coiled or straight) of the steel prior to the cold-formig operatio. 17

45 A5.3 Durability A structure shall be desiged to perform its required fuctios durig its expected life for durability cosideratio. A6 Referece Documets This Specificatio recogizes other published ad latest approved specificatios ad mauals, whe applicable, for use i desigs cotemplated herei, as follows: 1. America Natioal Stadards Istitute, ANSI A , "Miimum Desig Loads i Buildigs ad Other Structures," America Natioal Stadards Istitute, Ic., (ANSI), 1430 Broadway, New York, New York Applicable stadards of the America Society for Testig ad Materials, (ASTM), 1916 Race Street, Philadelphia, Pesylvaia America Istitute of Steel Costructio, "Allowable Stress Desig Specificatio for Structural Steel Buildigs with a Chapter o Plastic Desig," America Istitute of Steel Costructio, (AISC), 400 North Michiga Aveue, Chicago, Illiois 60611, Jue 1, America Weldig Society, AWS D , "Structural Weldig Code-Sheet Steel," America Weldig Society, (AWS), 550 N. W. Lejeue Road, Miami, Florida Research Coucil o Structural Coectios, "Allowable Stress Desig Specificatio for Structural Joits Usig ASTM A325 or A490 Bolts," 18

46 Research Coucil o Structural Coectios, (RCSC), America Istitute of Steel Costructio (AISC), 400 North Michiga Aveue, Chicago, Illiois 60611, November 13, Metal BUildig Maufacturers Associatio, "Low Rise Buildig Systems Maual," Metal BUildig Maufacturers Associatio (MBMA), 1230 Keith Buildig, Clevelad, Ohio Steel Deck Istitute, "Desig Maual for Composite Decks, Formed Decks, ad Roof Decks," Steel Deck Istitute, Ic., P. O. Box 9506, Cato, Ohio 44711, Steel Joist Istitute, "Stadard Specificatios Load Tables ad Weight Tables for Steel Joists ad Joist Girders," Steel Joist Istitute, (SJI), Suite A, th Aveue North, Myrtle Beach, South Carolia 29577, Rack Maufacturers Istitute, "Specificatio for the Desig, Testig ad Utilizatio of Idustrial Steel Storage Racks," Rack Maufacturers Istitute, (RMI), 8720 Red Oak Boulevard, Suite 201, Charlotte, North Carolia 28210, America Iro ad Steel Istitute, "Stailess Steel Cold-Formed Structural Desig Maual," 1974 Editio, America Iro ad Steel Istitute, (AISI), th Street, N. W., Washigto, D. C America Society of Civil Egieers, "ASCE Stadard, Specificatio for the Desig ad Costructio of Composite Slabs," America Society 19

47 of Civil Egieers, CASCE), 345 East 47th Street, New York, New York 10017, October, America Iro ad Steel Istitute, "Tetative Criteria for Structural Applicatios of Steel Tubig ad Pipe," America Iro ad Steel Istitute, CAISI), th Street, N. W., Washigto, D. C , August America Istitute of Steel Costructio, "Load ad Resistace Factor Desig Specificatio for Structural Steel BUildigs", America Istitute of Steel Costructio, CAISC), 400 North Michiga Aveue, Chicago, Illiois 60611, September 1,

48 B. ELEMENTS Bl Dimesioal Limits ad Cosideratios Bl.l Flage Flat-Width-to-Thickess Cosideratios (a) Maximum Flat-Width-to-Thickess Ratios Maximum allowable overall flat-width-to-thickess ratios, wit, disregardig itermediate stiffeers ad takig as t the actual thickess of the elemet, shall be as follows: (1) Stiffeed compressio elemet havig oe logitudial edge coected to a web or flage elemet, the other stiffeed by: Simple lip 60 Ay other kid of stiffeer havig I > I ad Dlw < 0.8 s a accordig to Sectio B (2) Stiffeed compressio elemet with both logitudial edges coected to other stiffeed elemets 500 (3) Ustiffeed compressio elemet ad elemets with a edge stiffeer havig I < I ad D/w ~ 0.8 accordig s a to Sectio B Note: Ustiffeed compressio elemets that have wit ratios exceedig approximately 30 ad stiffeed compressio elemets that have wit ratios exceedig approximately 250 are likely to develop 21

49 oticeable deformatio at the full desig stregth, without affectig the ability of the member to carry required stregth. Stiffeed elemets havig wit ratios larger tha 500 ca be used with adequate desig stregth to sustai the required loads, however, substatial deformatios of such elemets usually will ivalidate the desig formulas of this Specificatio. (b) Flage Curlig Where the flage of a flexural member is uusually wide ad it is desired to limit the maximum amout of curlig or movemet of the flage toward the eutral axis, the followig formula applies to the compressio ad tesio flages, either stiffeed or ustiffeed: =JO.061tdE/f av 4J(lOocf/d) (Eq. Bl.lb-l) where w f = Width of flage projectig beyod the web; or half of the distace betwee webs for the box- or V-type beams t d c f = Flage thickess = Depth of beam * = Amout of curlig f = Average stress i the full, ureduced flage width. (Where av members are desiged by the effective desig width procedure, the average stress equals the maximum stress multiplied by the ratio of the effective desig width to the actual width.) *The amout of curlig that ca be tolerated will vary with differet kids of sectios ad must be established by the desiger. Amout of curlig i the order of 5 percet of the depth of the sectio is usually ot cosidered excessive. 22

50 (c) Shear Lag Effects - Uusually Short Spas Supportig Cocetrated Loads Where the spa of the beam is less tha 30w (w as defied below) f f ad it carries oe cocetrated load, or several loads spaced farther apart tha 2w, the effective desig width of ay flage, whether i f tesio or compressio, shall be limited to the followig: TABLE B1.1(c) SHORT, WIDE FLANGES MAXIMUM ALLOWABLE RATIO OF EFFECTIVE DESIGN WIDTH TO ACTUAL WIDTH L/w f Ratio L/w f Ratio " where L = Full spa for simple beams; or the distace betwee iflectio poits for cotiuous beams; or twice the legth of catilever beams. W f = Width of flage projectio beyod the web for I-beam ad similar sectios or half the distace betwee webs of box- or U-type sectios. 23

51 For flages of I-beams ad similar sectios stiffeed by lips at the outer edges, w f shall be take &s the sum of the flage projectio beyod the web plus the depth of the lip. Bl.2 Maximum Web Depth-to-Thickess Ratio The ratio, hit, of the webs of flexural members shall ot exceed the followig limitatios: (a) (b) For ureiforced webs: (hit) = 200 max For webs which are provided with trasverse stiffeers satisfyig the requiremets of Sectio B6.1: (1) (2) Whe usig bearig stiffeers oly, (hit) = 260 max Whe usig bearig stiffeers ad itermediate stiffeers, I the above, (h/t)max = 300 h = Depth of flat portio of web measured alog the plae of web t = Web thickess Where a web cosists of two or more sheets, the hit ratio shall be computed for the idividual sheets. B2 Effective Widths of Stiffeed Elemets B2.I Uiformly Compressed Stiffeed Elemets (a) Load Capacity Determiatio The effective widths, b, of uiformly compressed elemets shall be determied-from the followig formulas: b = w whe A ~ CEq. B2.1-I) b = pw whe A > (Eq. B2. 1-2) 24

52 where w = Flat width as show i Figure B2.1-1 p = (1-0.22/1'1)11. A is a slederess factor determied as follows: A = (1.052IJk)(w/t)(Jf/E) CEq. (Eq. B2.1-3) B2.1-4) t = Thickess of the uiformly compressed stiffeed elemets where f for load capacity determiatio is as follows: For flexural members: (1) If Procedure I of Sectio C3.1.1 is used, f=f if the iitial y yieldig is i compressio i the elemet cosidered. If the iitial yieldig is ot i compressio i the elemet cosidered, the the stress f shall be determied for the elemet cosidered o the basis of the effective sectio at M y (momet causig iitial yield). /' w Actual Elemet I) I I mrllll=========urrrrr--' ~i.~ ~--.l'ir I b/2 b/2 I I Effective Elemet ad Stress o Effective Elemets I Figure B2.1-1 Stiffeed Elemets with Uiform Compressio 25