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DIRECT STRENGTH METHOD FOR WEB CRIPPLING OFCOLD-FORMED STEEL C-SECTIONSPraveen Kumar Reddy SeelamThesis Prepared for the Degree ofMASTER OF SCIENCEUNIVERSITY OF NORTH TEXASMay 2013APPROVED:Yu Cheng, Major ProfessorHaifeng Zhang, Committee MemberPhillip R. Foster, Committee MemberSeifollah Nasrazadani, CommitteeMemberEnrique Barbieri, Chair of theDepartment of EngineeringTechnologyCostas Tsatsoulis, Dean of the Collegeof EngineeringMark Wardell, Dean of the ToulouseGraduate School
Seelam, Praveen Kumar Reddy. Direct Strength Method for Web Crippling ofCold-Formed Steel C-Sections. Master of Science (Engineering Systems-MechanicalSystems), May 2013, 68 pp., 12 tables, 21 figures, references, 16 titles.Web crippling is a form of localized buckling that occurs at points of transverseconcentrated loading or supports of thin-walled structural members. The theoreticalcomputation of web crippling strength is quite complex as it involves a large number offactors such as initial imperfections, local yielding at load application and instability ofweb. The existing design provision in North American specification for cold-formed steelC-sections (AISI S100, 2007) to calculate the web-crippling strength is based on theexperimental investigation.The objective of this research is to extend the direct strength method to the webcrippling strength of cold-formed steel C-sections.ABAQUS is used as a main tool to apply finite element analysis and is used to dothe elastic buckling analysis. The work was carried out on C-sections under interior twoflange (ITF) loading, end two flange (ETF) loading cases. Total of 128 (58 ITF, 70 ETF)sections were analyzed. Sections with various heights (3.5 in.to 6 in.) and variouslengths (21 in. to 36 in.) were considered. Data is collected from the tests conducted inlaboratory and the data from the previous researches is used, to extend the directstrength method to cold formed steel sections. Proposing a new design for both theloading cases and calculation of the resistance factors under (AISI S100, 2007)standards is done.
Copyright 2013byPraveen Kumar Reddy Seelamii
ACKNOWLEDGEMENTSI would like to express my sincere gratitude to Dr. Cheng Yu for giving me theopportunity to perform this research at University of North Texas. His guidance andunending support from initial to final level enabled me to understand the research and isgreatly appreciated.I would like to express gratitude to my professors and committee members – Dr.Seifollah Nasrazadani, and Dr. Phillip R. Foster, Dr.Haifeng Zhang, – for their supportand guidance throughout my graduate program and in completing this thesis. I thank Dr.Enrique Barbieri, Chair of the Department of Engineering Technology, for his time andsupport.I also give special thanks to NoritsuguYanagi and Guowang Yu, and mydepartment staff and fellow students whose help made this thesis possible.I want to thank my family for their unending support, devotion and dedicationwithout which any of this would have been possible.iii
TABLE OF CONTENTSPageACKNOWLEDGEMENTS . iiiLIST OF TABLES . viLIST OF FIGURES . viiLIST OF IMPORTANT SYMBOLS . viiiCHAPTER 1 FACTORS AFFECTING THE WEB CRIPPLING RESISTANCE . 11.1Section Geometry . 41.2Load Cases. 51.3Section Geometry and Web Crippling Coefficient . 61.4Bearing Length . 6CHAPTER 2 RESEARCH OBJECTIVES . 7CHAPTER 3 LITERATURE REVIEW . 93.1Existing Research . 93.2AISI Specification . 19CHAPTER 4 DIRECT STRENGTH METHOD. 234.1Introduction . 234.2Effective Width Method . 234.3Direct Strength Method . 254.4Direct Strength Methods for Beams . 264.5Direct Strength Method for Columns. 28CHAPTER 5 EXPERIMENTAL STUDY . 305.1General Introduction . 305.2Test Specimen Description . 305.3Material Properties . 305.4Test Setup and Experimental Procedure . 315.5Test Results . 32CHAPTER 6 FINITE ELEMENT ANALYSIS . 35iv
6.1Introduction . 356.2Finite Element Modeling . 356.3Interior Two Flange (ITF) Loading Case . 386.4End Two Flange (ETF) Loading Case . 38CHAPTER 7 ANALYTICAL STUDY . 447.1Calculation of Web-Crippling Strength Using AISI Specification . 447.2Direct Strength Method for Web-Crippling Equation for C-section . 447.3Calculation of Resistance Factors . 477.4Calculation of Safety Factor . 49CHAPTER 8 DESIGN EXAMPLES . 538.1Introduction . 538.2Design Method for Interior Two Flange (ETF). 548.3Design Method for End Two Flange (ETF) . 55CHAPTER 9 CONCLUSION . 58APPENDIX: DIMENSIONS, COUPON TESTS AND RESULTS OF THE C-SECTIONSOF THE PRESENT AND PAST DATA . 59REFERENCES . 67v
LIST OF TABLESPage1.AISI single web channel and C-section coefficients . 202.Test matrix for specimens under ITF loading case . 283.Test matrix for specimens under ITF loading case . 284.Experimental studies on C-sections in laboratory . 32A1.Measured test specimen dimensions, yield strengths and test loads for Csections (ITF). 58A2.Measured test specimen dimensions, yield strengths and test loads for Csections (ETF) . 59A3.Measured test specimen dimensions, yield strengths and test loads for Csections (ITF) by Hetrakul . 60A4.Measured test specimen dimensions, yield strengths and test loads for Csections (ETF) by Hetrakul . 61A5.Measured test specimen dimensions, yield strengths and test loads for Csections (ITF) by Cheng Yu . 62A6.Measured test specimen data on ITF by Cheng Yu, University of North Texas . 62A7.Measured test specimen data on ETF by Cheng Yu, University of North Texas 63A8.Measured test specimen data on ETF by Cheng Yu, University of North Texas 64vi
LIST OF ILLUSTRATIONSPage1.Loading cases . 32.Different types of cold-formed steel section . 43.Winter sections . 104.Influence of angel on sections . 125.Pattern for I-section specimens . 176.Effective section of a C-section in bending . 227.Test setup for ITF . 308.Test setup for ETF . 319.Web crippling test on cold-formed steel. 3110.Web crippling test on cold-formed steel. 3211.Assembled C-section with ITF loading case . 3512.Web crippling of the C-section at Mode 1 . 3613.Web crippling of the C-section at Mode 2 . 3614.Web crippling of the C-section at Mode 3 . 3715.Assembled C-section with two flanges ETF case . 3916.Web-crippling zone at Mode 1 ETF . 4017.Web crippling analysis of a section at Mode 2 . 4118.Web crippling analysis of a section at Mode 3 . 4119.ITF plot of data points . 4820.ETF Plot of data points . 4921.Sample C-section . 50vii
LIST OF IMPORTANT SYMBOLSCCoefficient depending on the section typeChWeb slenderness coefficientCNBearing length coefficientCRInside bend radius coefficientC.O.V.Coefficient of variationDTotal depth of the deckEYoung’s modulus of steelEOFEnd one flange loadingETFEnd two flange loadingFyYield strength of steelhFlat dimension of web measured in plane of webIOFInterior one flange loadingITFInterior two flange loadingNBearing lengthpPitch lengthPmMeanPnComputed web crippling strengthPtWeb crippling strength in the testRInside bend radiustThickness of the webVPCoefficient of variationβReliability indexviii
Angle between the plane of the web and plane of bearing surfaceΩFactor of safetyФResistance factorσStandard deviationix
CHAPTER 1FACTORS AFFECTING THE WEB CRIPPLING RESISTANCECold-formed steel is used in buildings, automobiles, equipment and officefurniture, storage racks, highway products, and bridges, etc. The use of cold-formedsteel in the modern construction keeps on increasing due to its high durability, strength,light weight and excellent material consistency. Cold-formed steel members are usuallythin members with large width-to-thickness ratios, easy of prefabrication and massproduction. In construction industry cold-formed steel products can be classified intothree categories: members, panels and fabricated assemblies. Typical cold-formed steelmembers such as studs, tracks, purlins, girts and angles are mainly used for carryingloads while panels and decks constitute useful surfaces such as floors, roofs and walls,in addition to resisting in-plane and out-of-plane surface loads. Usual shapes such asC‐sections, Z-sections, angles, hat sections, I-sections, T‐sections and tubularmembers of cold‐formed sections are generally used in structural framing. Width-tothickness ratios of cold-formed steel sections are relatively high compared to hot-rolledsteel sections. This property of the cold-formed steel sections causes local buckling atstress levels lower than the actual yield stress of the steel. However, it is theredistribution of the stresses that allows the member to continue to carry loads afterlocal buckling. The ability of the section to carry loads after local buckling is called postbuckling behavior. Basically these failure modes can be identified as shear failure, webcrippling, bending failure and failures resulting from the interaction of two or more of theabove mentioned failure modes (Harrison and Bailey, 2003). Among these failure1
modes, the web crippling is a significant failure mode that may be experienced by beammembers under concentrated loads or reaction forces.Cold-formed steel members generally have large slenderness ratios, their websmay cripple due to high local intensity of load or reaction (Wing and Pian, 1946). Webcrippling is defined as a local failure in the web (shear resisting) element(s) of a sectiondue to a concentrated load as per (AISI S100, 2007). Web crippling is a complexproblem for theoretical analysis because it is highly dependent on the load positioning,the section geometry, support conditions, and other member cross-section parameters.The investigation of web crippling behavior of cold-formed steel members startedat Cornell University in the year 1939, under the direction of George Winter. The firstAmerican Iron and Steel Institute design specification was published in 1940s, while thefirst codes for cold steel design in Canada were issued in 1963. It was 1970s when thefirst European cold formed steel codes were published.Web crippling may occur in various loading cases; these loading conditions aredefined based on the position of the load or reaction applied and depending on whetherthe web is loaded through a single flange or both flanges. Four basic loading conditionsare defined by AISI specifications for a web crippling, namely end-one-flange (EOF)loading, interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF) asshown in figure 1.2
Interior one-flange (IOF)End one-flange (EOF)End two-flange (ETF)Interior two-flange (ITF)Figure 1: Loading cases.The web crippling strength of cold-formed steel sections is a function of number ofvariables such as section type, cross sectional parameters, bearing length, etc. Designequations in the specifications have been empirical formulas developed by curve fittingof experimental data. AISI S100, (2007) has a unified design expression with differentcoefficients for different section and loading types, AISI (1996) has different designexpressions for different types of sections and loading cases, the Canadian Standard(S136-94) has one in unified design expression in with different coefficients for differentsection types and loading. In both of the standards the web crippling calculations are3
based on unfastened specimens and are limited to the use of decks with certaingeometric parameters.1.1 Section GeometryThe following are the important factors which affect the web crippling of a coldformed steel C-section. (Baher and Beshara, 2000).Web crippling is affected by the degree of restraint of the web against rotation. Eachsection has different behavior characteristics. There are many geometric shapes, thefollowing being the most common in the construction building industry. I –sections C-sections Z-sections Single hat sections Multi-web sections (decks)Figure 2: Different types of cold-formed steel sections.The following parameters have an impact on the Web crippling resistance.4
Yield strength of steel (Fy) Web thickness (t) Inside bend radius(r) Web height (h) Angle between plane of web and plane of bearing surface (Θ)1.2 Load CasesThe location of the load along the length of a cold-formed steel member significantlyaffects its web crippling capacity, hence it is important to know where and how aconcentrated load is applied on a member (Beshara and M.Schuster 2003). Thefollowing are the combination of concentrated loads that can be classified by these fourload cases. Interior one-flange (IOF) End one-flange (EOF) End two-flange (ETF) Interior two-flange (ITF)One-flange loading refers to a web crippling case where the crippled web section issubjected to a concentrated load being applied to just one flange. Two-flange loadingrefers to a web crippling case where the crippled web section is subjected to aconcentrated load being applied to both the top and bottom flanges simultaneously. TheIOF case is characterized by a concentrated load applied to one flange, either top orbottom, located anywhere within the span of the member. A concentrated load applied5
to one flange, but located at the end of the member is the EOF case (James A. Wallace,2003).Two loads are applied in opposite directions to opposite flanges, and are appliedwithin 1.5 times the height of the member from each other, and then two-flange loadingoccurs. If the loads are separated by a distance greater than 1.5 times the height thentwo separate one-flange loadings are said to occur. Similar to IOF and EOF cases, theITF and ETF cases refer to a two-flange loading located somewhere within the spanand a two-flange loading located at the end of the span.1.2.1 Section Geometry and Web crippling CoefficientsCold-formed steel allows a large variety of section geometries that can befabricated with relative ease and economy. As the section geometry changes theresistance of the section also changes. It varies from C-section to Z-section, I-sectionetc.1.3 Bearing LengthThe length over which the load is distributed also has an influence on the webcrippling resistance, the longer the bearing plate width, the larger the web cripplingresistance; it also depends on the type of material used for the bearing plate.6
CHAPTER 2RESEARCH OBJECTIVESThe main objective of this research is to extend the direct strength method to beapplicable to the web crippling strength of cold-formed C-sections subjected to end twoflanges (ETF) and interior two flanges (ITF) loading.The present direct strength method is used to design the cold-form steel columnsand beams. For beams a graphvs.is drawn with all the data points and acurve is fitted with the points.Where My is yield strengthMcr is elastic critical bucklingMtest is the test data.This research work used the same idea and plotvs.,graph and plot thedata and try to fix a curve and generate a curve equation based on the direct strengthmethod.Pny is yield strength which isWhere Fy is the yield strength of C-section.Pcrw is elastic web crippling load which can be found using finite element analysis(ABAQUS software).Pnw is the nominal web crippling strength from the tests.7
Tests are being conducted on unstiffened fastened end-two flange (ETF) loadingand interior-two flange loading cases, data is collected. Pnw, the nominal web cripplingstrength from tests partial data collected as a part of the literature review from previousresearchers as well as the data from the tests conducted in the laboratory at Universityof North Texas are used to plot the graph similar to the one shown, predict the webcrippling strength for cold-formed steel C-sections.The study included on Web crippling failure testing (which is a compression test)of the different dimensional sections on an Instron machine, and finite element analysisusing ABAQUS software for all the sections including available from the previousresearch data base.Applying the buckling mode analysis of the section and changing the length ofsection until influence of the web-crippling strength is felt. Calculating the values of Pt,Pny, and Pcrw for every loading case and recording them is done. Once the data isrecorded applying DSM for the available data and developing a new equation is done.Plottingvs.graph using Matlab and developing a new equation fromthe graph obtained is done. Calculation of resistance factors as close as (AISI S100,2007) is achieved, mean and standard deviation is also calculated.8
CHAPTER 3LITERATURE REVIEW3.1 Existing ResearchThe purpose of this chapter is to provide the background about the existinganalytical and experimental studies of the web crippling strength of web plates.Numerous research reports and publications were reviewed in the initial phase of thisstudy. A brief review of the history of analytical and experimental studies is presented,as well as the present North American design criteria for determining the Web cripplingstrength at last.The study of web crippling behavior of cold-formed steel flexural members started in1940s (Winter and Pian, 1946). Most of the research work that has been done on thisarea is based on experimental studies and the results have been used to develop thedesign formulae for calculation of web crippling strength. There have been some studiescarried out on the theoretical analysis of web crippling behavior despite the fact that it isextremely complicated because it involves the following factors. Non-uniform stress distribution under the applied load Elastic and inelastic behavior of the web element Local yielding in the immediate region of load application Bending produced by eccentric load when it is applied on the bearing flanges at adistance beyond the curved transition of the web Initial out-of-plane imperfection of plate elements Various edge restraints provided by beam flanges and interaction betweenflanges and web elements9
Research on web crippling strength of cold-formed steel members was startedin1939 at Cornell University by Winter and Pian (1946) and they carried out webcrippling tests on I-sections and developed the following web crippling equations for Isections.For end-one flange (EOF) loading case:Pult For interior-one flange loading case:Pult WherePult ultimate web crippling load per webFy yield strength of steelh clear distance between flanges measured in the plane of the webN bearing length to thickness ratiot thickness of webThe range of parameters of these tests was, 30 h/t 175, 7 n/t 77 and 30ksi Fy 39 ksi.10
a) double webb) single webFigure 3: Winter sections (Winter and Pian 1946).Many tests were conducted at Cornell University on cold-formed beams during1950s on single unreinforced webs (hat and u-sections).It was concluded from thesestudies that the web crippling resistance of cold-formed steel members is a function ofh/t, R/t, N/t and Fy.The following equations were derived for cold-formed steel sections withunreinforced webs by Macdonald at Cornell University in 1953 (Macdonald andHeiyantuduwa, 2003).i)For end reactions and for concentrated loads on outer ends of cantilevers:For R/t 1Pult For 1 R/t 4(Pult) 1 ii)(Pult)For reactions at interior supports or for concentrated loads :For R\t 111
Pult For 1 R\t 4(Pult) 1 (Pult)WhereP ultimate computed web crippling load per webFy yield strengtht thickness of the webk Fy(ksi) /33 ;Fy(N/mm2) /228N bearing length of loadh flat dimension of web measured in plane of webH web slenderness ratio, h / tR inside bend radiusBaehre (1975) tested unreinforced multi web hat sections under interior oneflange loading at the Royal Institute of Technology, Sweden, found the web inclination,θ, shown in figure 4 to be an important factor that influences web-crippling strength anddeveloped the following relationship for the ultimate load at intermediate supports(Baehre,1975):12
Figure 4: Influence of angle on sections.Pult Where:Pult computed ultimate web crippling load per webFy yield strengtht thickness of the webh clear distance between flanges measured in the plane of the webH web slenderness ratio, h / tk Fy(ksi) /49.3N bearing length of loadR inside bend radiusθ angle between the plane of the web and plane of bearing surfaceThe ranges of parameters in this study were:h/ t 170R / t 1050 θ 90 13
An experimental study was carried out by Hetrakul and Yu at the University ofMissouri at Rolla (UMR) in the year 1973. Based on the Cornell test data and the testsconducted at UMR, modified web crippling design equations were proposed by Hetrakuland Yu (1978).For interior one flange loading (IOF) (for stiffened and unstiffened flanges)i.Pult If N\t 60, thenii.may be increased toFor end one flange loading, EOFFor stiffened flanges:Pult If N\t 60, thenmay be increased toFor unstiffened flanges:PultIf N\t 60, theniii.may be increased toFor interior two flange loading, ITF(for stiffened and unstiffened flanges)Pult iv. For exterior two flanges loading, ETF (for stiffened and unstiffened flanges)14
Pult Where:Pult computed ultimate computed Web crippling load per webFy yield strength of steelt thickness of the webk Fy(ksi) /33C1 (1.22-0.22k)C2 (1.06-0.06R/t)C3 (1.33-0.33k)C4 (1.15-0.15k)h clear distance between flanges measured in the plane of the webH web slenderness ratio, h / tN bearing length of loadR inside bend radiusThe ranges of parameters in this study were:θ 90 33 Fy 54 ksi45 h / t 2581 R / t 311 N / t 14015
As the modified Web crippling equations based on Cornell and UMR test datawere limited by vertical webs, and by small R/t and N/t ratios, the suitability of theseequations was not certain for every cross section.Wing (1981) carried out an extensive study on Web crippling and thecombination of Web crippling and bending of multi-web cold-formed sections at theUniversity of Waterloo. All of the members were fastened to the support locations andnew Web crippling equations were derived for all loading cases except for the one endflange loading case (Wing, 1981).Interior one flange loading case IOF:Pw 16.6t2 Fy (Sinθ) (1-0.000985H)ii) Interior two flange loading, ITFPw 18t2 Fy (Sinθ) (1-0.00139H)iii). End two flange loading, ITFPw 10.9t2 Fy (Sinθ) (1-0.0020H)Where:Pw computed ultimate computed Web crippling load per webFy yield strength of steelt thickness of the webk Fy(ksi) /33h clear distance between flanges measured in the plane of the webH web slenderness ratio, h / t16
N bearing length of loadR inside bend radiusθ angle between the plane of the web and plane of bearing surfaceThe ranges of parameters in Wing’s study were:h/ t 200R / t 10Studnicka conducted an extensive experimental study on Web cripplingresistance of multi-web cold-formed steel sections at Czech Technical University,Prague, Czechoslovakia. By using Canadian 1984 (S136-94) expressions for interiorloading conditions satisfactory conformity was obtained (Studnicka, J. 1990).The effect of the flange restraint was investigated in an experimental study byBhakta, LaBoube and Yu (1992). Z-sections, multi-web roof and floor deck sections,channel sections and I-sections were tested under end one flange and interior oneflange loading. When the flanges were fastened to the support locations, there was anaverage increase of 37% in the Web crippling resistance of long span roof decks whilethe increase in Web crippling resistance of floor decks was around 20% under oneflange loading. On the other hand, there was almost no increase in Web cripplingstrength of channel and I-sections when they are subjected to either end one flange orinterior one flange loading. The Web crippling strength of Z-sections fastened tosupports was increased 30% under end one flange loading and 3% under interior oneflange loading (Bhakta, LaBoube and Yu 1992).17
Figure 5: Pattern for I-section specimens (LaBoube and Yu 1992).Parabakaran in the year 1993 did a statistically based study on Web crippling ofcold-formed steel members at the University of Waterloo. The available experimentaldata in the literature were used to derive one unified expression to calculate webcrippling capacity of cold-formed steel sections (Parabakaran.K, 1993).Pn Ct2 Fy (Sinθ)Where:Pn nominal computed ultimate computed Web crippling load or reaction per webFy yield strength of steelt thickness of the webC coefficient from tablesθ angle between the plane of the web and plane of bearing surfaceCR inside bend radius coefficientCN bearing length coefficientCh web slenderness coefficientR inside bend radiusN bearing length of load18
h clear distance between flanges measured in the plane of the webThe range of Parameters studies by PrabakaranFor I-sections and sections having single webs:h/ t 200N / t 200R / t 4N / h 1For multi-web sections:h/ t 200N / t 200R / t 10N/h 2Cain, LaBoube and Yu (1995) conducted an experimental study on Z-sectionsunder end one flange loading and I-sections under interior one fl
Cold-formed steel is used in buildings, automobiles, equipment and office furniture, storage racks, highway products, and bridges, etc. The use of cold-formed steel in the modern construction keeps on increasing due to its high durability, strength, light weight and excellent material consistency. Cold
