Local Buckling Tests On Cold-Formed Steel Beams
Local Buckling Tests on Cold-Formed Steel BeamsCheng Yu1 and Benjamin W. Schafer2Abstract: C and Z sections are two of the most common cold-formed steel shapes in use today. Accurate prediction of the bendingperformance of these sections is important for reliable and efficient cold-formed steel structures. Recent analytical work has highlighteddiscontinuities and inconsistencies in the American Iron and Steel Institute 共AISI兲 and Canadian Standards Association 共S136兲 designprovisions for stiffened elements under a stress gradient 共i.e., the web of C or Z sections兲. New methods have been proposed for design,and an interim method has been adopted in the North American Specification 共NAS兲. However, existing tests on C and Z sections do notprovide a definitive evaluation of the design expressions, due primarily to incomplete restriction of the distortional buckling mode.Described in this paper is a series of flexural tests with details selected specifically to insure that local buckling is free to form, butdistortional buckling and lateral-torsional buckling are restricted. The members selected for the tests provide systematic variation in theweb slenderness (h/t) while varying other relevant nondimensional parameters 共i.e., h/b, b/t, d/t, d/b). Initial analysis of the completedtesting indicates that overall test-to-predicted ratios for AISI, S136, NAS, and the direct strength method are all adequate, but systematicdifferences are observed.DOI: 兲CE Database subject headings: Thin-wall structures; Steel beams; Buckling; Cold-formed steel.IntroductionThe determination of the ultimate bending capacity of coldformed steel C and Z sections is complicated by yielding and thepotential for local, distortional, and lateral-torsional buckling ofthe section, as shown in Fig. 1. Local buckling is particularlyprevalent and is characterized by the relatively short-wavelengthbuckling of individual plate elements. Distortional buckling involves both translation and rotation at the compression flange/lipfold line of the member. The wavelength of distortional bucklingis generally intermediate between that of local buckling andlateral-torsional buckling. Lateral-torsional buckling occurs whenthe cross section buckles without distortion.In the process of developing the new North American Specification for the Design of Cold-Formed Steel Structural Members共NAS 2001兲 and harmonizing the existing American Iron andSteel Institute 共AISI兲 共1996兲 and Canadian S136 共1994兲 methods,one of the significant differences observed between the specifications was the calculation of the web effective width. The S136method systematically employed more conservative expressionsfor the web effective width. Evaluation of existing data lead to theconclusion that web/flange interaction 共driven by h/b) was ofprimary importance 共Schafer and Trestain 2002兲. Interim ruleswere adopted for NAS 共2001兲 which use AISI 共1996兲 when h/b 4 and S136 共1994兲 when h/b 4. However, at that time, it wasfelt that the issue was not fully resolved, as existing data did notdistinguish between local and distortional buckling failures andwas not considered to be generally representative of industrypractice. Therefore, new testing and evaluation, as reported in thispaper, was initiated and completed.Existing tests on C and Z sections 共see summaries by Elhouarand Murray 1985; Schafer and Peköz 1999兲 generally focus onthe performance of the compression flange and do not providedefinitive evaluations of the design expressions for the web dueto: incomplete restriction of the distortional mode, arrangement ofthe specimens 共back to back versus toe to toe兲, and a general lackof information on bracing details. Further, when compared withindustry practice, existing data are not representative of commonly used sections. A series of new flexural tests focused on therole of web slenderness in local buckling failures of C and Zsections is reported in this paper. Bracing has been carefully considered in these tests to insure that distortional buckling and1Graduate Research Assistant, 306 Latrobe Hall, Johns Hopkins Univ.,Baltimore, MD 21218. E-mail: cheng.yu@jhu.edu2Assistant Professor, 203 Latrobe Hall, Johns Hopkins Univ.,Baltimore, MD 21218. E-mail: schafer@jhu.eduNote. Associate Editor: Mark D. Bowman. Discussion open until May1, 2004. Separate discussions must be submitted for individual papers. Toextend the closing date by one month, a written request must be filed withthe ASCE Managing Editor. The manuscript for this paper was submittedfor review and possible publication on March 29, 2002; approved onMarch 6, 2003. This paper is part of the Journal of Structural Engineering, Vol. 129, No. 12, December 1, 2003. ASCE, ISSN 0733-9445/2003/12-1596 –1606/ 18.00.1596 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / DECEMBER 2003Fig. 1. Buckling modes of a cold-formed steel beam
Table 1. Measured GeometryStudyNo.1Test labelSpecimen共mm兲bc共mm兲dc共mm兲 c共deg兲bt共mm兲dt共mm兲 t共deg兲r hc共mm兲r dc共mm兲r ht共mm兲r 1W6C054-2E1W4C054-1E2W3.62C054-1E2WtNote: Typical specimen label is Z(or C)xxx-x. For example, 8.5Z073-1 means the specimen is 216 mm 共8.5 in.兲 high for the web, Z section, 1.85 mm共0.073 in.兲 thick and the beam number is 1 共used to distinguish with other specimens with same dimensions兲. Typical test label is Z(or C)xxx-xExW.For example, test 8.5Z073-1E2W means the two paired specimens are 8.5Z073-1 at the east side and 8.5Z073-2 at the west side.JOURNAL OF STRUCTURAL ENGINEERING ASCE / DECEMBER 2003 / 1597
Fig. 2. Definitions of specimen dimensions for Z and CFig. 4. Overall view of test setuplateral-torsional buckling do not influence the interpretation ofresults. The test results can be used for the evaluation of existingand proposed methods for strength prediction of webs in localbuckling. In addition, these tests can form the basis for laterevaluations in which restrictions on the distortional mode are relieved.The mean dimensions, as determined from the three sets ofmeasurements within the constant moment region, are given inTable 1.Testing DetailsLocal Buckling TestsSpecimen SelectionThe AISI 共1996兲 specification calculates the effective width ofwebs as a function of the web slenderness (h/t) alone. The proposed tests are designed to provide systematic variation in webslenderness (h/t) while also varying the other nondimensionalparameters that govern the problem such as flange slenderness(b/t), edge stiffener slenderness (d/t), and relevant interactions,such as the web height to flange width (h/b) ratio. The focus ofthe testing is on the web, therefore significant variation in stiffener length to flange width ratio (d/b) is not investigated.The selected specimens are summarized in Table 1. The use ofindustry standard sections dictates the manner in which the webslenderness (h/t) can be varied. For the Z sections, the specimensvary in t while holding h, b, and d approximately constant 共studies1 and 2 in Table 1兲. However, the wide variety of C specimenscommonly produced to the Steel Stud Manufacturers AssociationStandards allows both independent h and t variations to be examined for C sections 共studies 3 and 4 in Table 1兲.The dimensions of the specimens were recorded at midlengthand middistance between the center and loading points, for a totalof three measurement locations for each specimen. The definitions of specimen dimensions for Z and C are shown in Fig. 2.The basic testing setup is illustrated in Figs. 3– 6. The 4.9 m 共16ft兲 span length, four-point bending test, consists of a pair of 5.5 m共18 ft兲 long C or Z specimens in parallel loaded at the 1/3 points.The members are oriented in an opposed fashion, such that inplane rotation of the C or Z leads to tension in the panel, and thusprovides additional restriction against distortional buckling of thecompression flange. Small angles, 32 32 1.45 mm (1 1/4 1 1/4 0.057 in.), are attached to the tension flanges every 305mm 共12 in.兲 and a through-fastened panel 关 t 0.48 mm 共0.019in.兲, 32 mm 共1 1/4 in.兲 high rib兴 is attached to the compressionflanges. Hot-rolled tube sections, 254 191 152 6 mm(10 7 1/2 6 1/4 in.), bolt the pair of C or Z sections togetherat the load points and the supports, and insure that shear and webcrippling problems are avoided at these locations. When testingthe Z’s, the hot-rolled angles detailed at the end plates 共Fig. 4兲connect to the tube and the purlin to remove any crippling orrolling at the supports. The C’s use a similar detail, but the connection is to the inside of the tube.The loading system employs an 89 kN 共20 kip兲 MTS actuator,which has a maximum 152 mm 共6 in.兲 stroke. The test was performed in displacement control at a rate of 0.0381 mm/s 共0.0015in./s兲. An MTS 407 controller and load cell monitored the forceand insured the desired displacement control was met. Meanwhile, deflections for one specimen at the 1/3 points were measured using two linear variable differential transformers 共LVDTs兲.Fig. 3. Elevation view of overall test arrangement for four point bending test1598 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / DECEMBER 2003
Fig. 8. Lowest buckling mode predicted by finite element model forsingle screw fastener configuration 共note center panels removed forvisual clarity only, the dots indicate fastener locations兲Fig. 5. Support configurationFig. 9. Lowest buckling mode predicted by finite element model forpaired screw fastener configuration 共note center panels removed forvisual clarity only, the dots indicate fastener locations兲Fig. 6. Loading point configurationFig. 7. Plan view of fastener locations for panel-to-purlin connectionLater, for the 254 mm 共10 in.兲 C and 292 mm 共11.5 in.兲 Z beams,the 2 LVDTs were replaced by four position transducers. For alimited number of tests, strain gauges were placed at midspan, onthe lip, and the top of the web, at the same vertical cross sectionheight, to monitor the longitudinal strain.After initial testing, the details were improved to insure purebending was maintained, and to restrict distortional and lateraltorsional buckling. The arrangement of rollers at the supports wasmodified to more closely model a pin-roller configuration 共Fig. 5兲.Additional web stiffening bars were added to the I beams at thesupports and load points. Machined, quarter-round aluminumblocks were placed as guides for the rollers at the loading points共Fig. 6兲. Thin Teflon sheets were added at the load points andsupport points to limit unwanted friction and help insure that theboundary conditions were predictable 共Figs. 5 and 6兲.Fig. 10. Selected standard panel-to-purlin and panel-to-panelfastener configurationPanel-to-Purlin Fastener ConfigurationA series of tests on the 216 mm 共8.5 in.兲 deep Z’s with t 1.85 mm 共0.073 in.兲 and t 1.50 mm 共0.059 in.兲 was conductedin order to determine the appropriate panel-to-purlin fastener detail for restricting the distortional mode. Investigated fastener locations are depicted in Fig. 7. Initial testing using single panelto-purlin fasteners placed through the center of the purlin flangeand spaced at 305 mm 共12 in.兲 on center 共test 8.5Z073-6E5W,panel type A兲 failed at a capacity of 89% of the AISI 共1996兲prediction and visually appeared to suffer from deformations consistent with distortional buckling. Elastic finite element analysis,JOURNAL OF STRUCTURAL ENGINEERING ASCE / DECEMBER 2003 / 1599
Table 2. Summary of Tension Test ResultsSpecimenFig. 11. Dimensions of tensile couponFig. 8, using the commercial finite element package ABAQUS共HKS 2001兲 confirmed that the lowest elastic buckling mode forthis fastener detail was distortional buckling. Additional analysis共Fig. 9兲 indicated that a pair of fasteners placed on either side ofthe raised ribs 共panel type C兲 would force local buckling to be thelowest mode. Testing of 8.5Z073-4E3W confirmed this prediction and paired fasteners as shown in Fig. 10 provided a capacity10% greater than single fasteners and 98% of the AISI 共1996兲prediction. Further, testing (8.5Z059-2E1W) with additionalpaired fasteners in the center of the pans 共Fig. 7, panel type D兲 didnot improve the results over type C 共compare with test8.5Z059-4E3W). Additionally, the modeling indicates that thepaired fasteners do not change the local buckling mode; thus, itcan be safely assumed that panel type C restricts distortionalbuckling without artificially increasing the local bucklingstrength.The selected standard panel-to-purlin fastener detail 共paneltype C兲 for this study is a pair of screws placed 38 mm 共1.5 in.兲for C section, 64 mm 共2.5 in.兲 for Z section, apart and spaced 203mm 共8 in.兲 away from a second pair in the pan of the deck, asshown in Fig. 10. The paired fastener configuration is only maintained inside the constant moment region of the test. In the shearspan, one screw is used instead of one pair, at the same locationas that of the constant moment region.Tension TestsTension tests were carried out following ‘‘ASTM E8-00 StandardTest Methods for Tension Testing of Metallic Material’’ 共ASTM2000兲. The dimensions of a typical tensile coupon are shown inFig. 11 and the test results are given in Table 2. Three tensilecoupons were taken from the end of each specimen: one from theweb flat, one from the compression flange flat, and one from thetension flange flat, average results are given in Table 2. A screwdriven ATS 900, with a maximum capacity of 44.5 kN 共10 kips兲was used for the loading. An MTS 634.11E-54 extensometer wasemployed to monitor the deformation. Strain gauges were installed on selected tensile coupons at the center, and on bothsides, to verify the modulus of elasticity, E. Two methods foryield strength determination were employed: 共1兲 0.2% offsetmethod for the continuous yielding materials 关Fig. 12共a兲兴; and 共2兲autographic diagram method for the materials exhibiting discontinuous yielding 关Fig. 12共b兲兴.The yield stress ( f y ) can vary greatly across the test series.The large variation in f y complicates comparisons across the testdatabase, but it is important to recognize this variation, as f y forthe Z’s varied from 365 to 475 MPa 共53 to 69 ksi兲 and for the C’sfrom 220 to 413 MPa 共32 to 60 ksi兲. An E of 203 MPa 共29,500ksi兲 is assumed for all of the members. This is supported bylimited testing on 1.5 mm 共0.059 in.兲 and 2.08 mm 共0.082 in.兲tensile specimens from the Z’s, which had an average measured Eof 201 MPa 共29,200 ksi兲.Experimental ResultsA summary of the local buckling test results is given in Table 3.Included for each test are the elastic buckling moments (M cr) 912C068-512C068-412C068-310C068-210C068-11600 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / DECEMBER 2003t 共mm兲f y 共MPa兲f u 共MPa兲f u / f y ratio 33132171167
Fig. 12. Typical stress–strain curve of tension testdetermined by the finite strip method using CUFSM 共Schafer2001兲 and ratios of test-to-predicted capacities for various designmethods.Strain gauges were placed at midspan, on the lip and the top ofthe web, at the same vertical cross section height, on nine Cmembers 共footnote c in Table 3兲, to monitor the longitudinalstrain. Typical output from the gauges is given in Fig. 13. In theinitial elastic range, the gauges read nearly identical and agreewith the simple beam theory predictions, indicating that the testing arrangement is achieving the desired loading about the geometric axis and no twisting is developing in the section. At anintermediate load level, before buckling deformations were visible, strain on either the lip or web began to reverse. In most, butnot all, the strain on the lip began to reverse prior to the web.Once buckling initiates the strain distribution varies around theprofile and along the length, and it becomes difficult to providedefinitive conclusions from the limited strain data.The actuator load–displacement response is given in Figs. 14 –17. Little nonlinear response is observed prior to formation of thefailure mechanism. The specimens which have a tested capacity ator near the yield moment (M test /M y 1, see Table 3兲 exhibit themost nonlinear deformation prior to failure; while the more slender specimens have essentially elastic response prior to formationof a sudden failure mechanism.As shown in Figs. 14 –17 failure of the weaker specimen ofthe pair results in a signif
formed steel C and Z sections is complicated by yielding and the potential for local, distortional, and lateral-torsional buckling of the section, as shown in Fig. 1. Local buckling is particularly prevalent and is characterized by the relatively short-wavelength buckling of individual plate
DIC is used to capture buckling and post-buckling behavior of large composite panel subjected to compressive loads DIC is ideal for capturing buckling modes & resulting out-of-plane displacements Provides very useful insight in the transition regime from local skin buckling to global buckling of panel
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individual studs. Global buckling can occur in one of three modes: flexural buckling, torsional buckling, or flexural-torsional buckling. Section B1.7 of AISI S211-07 Standard "North American Standard for Cold-Formed Steel Framing-Wall Stud Design" provides guidance for the calculations of the design strength of built-up stud members.
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DNA Genes to Proteins Kathleen Hill Lab Tour WSC 333. 2 The human genome is a multi-volume instruction manual The GENOME is a multi-volume instruction manual Each CHROMOSOME is a volume of text Genes are a chapter of text in the volume The text is written in a chemical language that has a four letter alphabet A,C,G,T NUCLEOTIDES Our instruction manual can be read in our DNA .
