Flexural Capacity of Discretely Braced C's and Z's

Transcription

1 Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold- Formed Steel Structures (1992) - 11th International Specialty Conference on Cold-Formed Steel Structures Oct 20th Flexural Capacity of Discretely Braced C's and Z's Thomas Sputo Jack Haynes Duane S. Ellifritt Follow this and additional works at: Part of the Structural Engineering Commons Recommended Citation Sputo, Thomas; Haynes, Jack; and Ellifritt, Duane S., "Flexural Capacity of Discretely Braced C's and Z's" (1992). International Specialty Conference on Cold-Formed Steel Structures This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in International Specialty Conference on Cold-Formed Steel Structures 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.

2 Eleventh International Specialty Conference on Cold Formed Steel Structures St. Louis, Missouri, U.S.A., October 20-21, 1992 FLEXURAL CAPACITY OF DISCRETELY BRACED C'S AND Z'S Duane Ellifrittl, Thomas Sput0 2, and Jack Haynes 3 INTRODUCTION The Ameri can Iron and Steel Inst itute I s Specifi cat i on for the Des i gn of Cold-Formed Steel Structural Members (1) presently requires that channel and zee flexural members, when not attached to sheathing, be braced aga inst twist and lateral translation at the quarter-points of the span (Section D3.2.2). This provision first appeared in the Second Edition of the Specification in 1956, and has been there through all succeeding editions up through the 1989 Addendum. The newest formula for lateral buckling (part (a) of C3.1.2) is a more exact procedure for calculating lateral torsional buckling of a doubly, singly, or point symmetrical section than was the earlier one (now part (b}). It is fair to ask, then, whether the requirement for quarter-point bracing is still needed. If a user wishes to space lateral braces at greater distances and accept a reduced bending capacity, why should quarter-point braces be mandated? Was the original reason for including this provision in the 1956 Specification more a serviceability consideration than strength? The purpose of this research was to find answers to these questions. BACKGROUND The primary research work that led to the requirement of quarter-point bracing in the Specification seems to have been that of Winter, Lansing and McCalley (2). They tested channels on an 11 ft.-6in. (3.5 m) simple span with lateral braces at each of the supports and two other locations which were varieu symmetrically about the beam mid-span, as shown in Figure l(a). The channels were loaded with two concentrated, symmetrically placed loads whose positions were constant for all tests. The spacing between these loads was 2 ft.-2 in. (.66 m), and the loads were never applied at a braced point. Taking the distance between supports as "L" and the distance between the braces as "a", four different ail ratios were tested: 0,.478,.652, and 1.0. The first corresponds fully braced, the second to a single mid-span brace, the third (roughly) to braces at the V4 and 0/4 positions, and the last to the completely unbraced case. Seven channel sections were tested, their depths ranging from 4 to 8 in. (102 to 203 mm), their flange widths from 2 V2 to 4 in. (63 to 102 mm) and the thicknesses from.060 to.151 in. (1.5 to 3.8 mm). Lips were about 3/4 in. (19 mm) for all sections. Professor, Department of Civil Engineering, University of Florida, Gainesville, Florida, 3261l. Consulting Engineer, Gainesville, Florida. Engineer, LoBuono, Armstrong & Associates, Tallahassee, Florida. 109

3 110 On the basis of these tests, a simple theory was developed that summed stresses at the corner of flange and web, calculating stress by vertical loading only, then adding the stress due to a lateral force of Pel2h acting on a section made up of the compression flange, lip, and Y4 of the web. (h is the channel depth, e the distance from the shear center to the centerline of the web, and P the vertical load.) This simplified approach agreed with the test results within 5-6%. The theoretical results for various parameters have been plotted in Figure l(b). It can be seen that, up to about ail of 0.5, there is only about a 10% variation from the fully braced case. The authors have said, "It would seem therefore, that within the limits of our test evidence, a theoretical overstress of about 15% can be disregarded in practical design. The problem is, then, merely to locate braces such that no more than this overstress will occur." Further in the paper, they state, "for a great variety of practical loading schemes-it is never necessary to provide more than four braces between supports in order to limit the overstress to 10% [of the yield stress]. If 15% overstress is accepted for practical design, as was previously suggested on the basis of Figure 10 [Figure l(b) in this report], similar calculations show that three braces equally spaced between supports will satisfy this requirement for most practical loadings." On the other hand, it is also stated in this paper, "It is seen that for the smaller of the two spacings of braces, [ail = 0.47S] ultimate loads for all practical purposes are the same as for continuous bracing." This quote is repeated by Dr. Yu in hi s book on page 247 (3). It seems to contradi ct the earlier quotes citing the need for "three braces equally spaced between supports." And it should be noted that the case of 114-point bracing was never actually tested. No zee sections were included in these tests either. TEST PROGRAM In the research conducted by the writers (4), typical channel and zee sections were tested in flexure with various types of bracing. The bracing conditions were: continuous bracing, quarter-point, third-point, mid-point and no bracing at all. All tests were performed on IS-foot (6 m) simple span purlin sections suppl ied by Pascoe Steel Buildings. The dimensions of the sections tested are shown in Table 1. The test set-up and loading mechanism is shown in Figure 2. It should be emphasized that the quarter-point brace requirement in the AISI Specification applies Qllly when the member is not attached to deck or sheathing. Therefore, the load was applied as two concentrated loads rather than a uniform load. In the first series of tests (Groups I through IV), the load point was not a braced point. A second series of tests (Groups V and VI) was run with the loads applied at a braced point. Two beams were tested simultaneous 1 y for each brac i ng cond it ion. Channels were positioned back-to-back; zees were placed with the bottom flange facing inward. The bracing consisted of 1 x 1 in. (25 x 25 mm) angles connecting the two members; the pair was not braced to any external support, but served to brace each other.

4 111 TEST RESULTS A total of 23 tests were done, the results of which are listed in Table 2. Various types of failure can be seen in Figures 3 through 8. None of the tests failed by classic lateral buckling, but by distortional buckling of the compression flange. Classical lateral-torsional buckling, that is, bifurcation buckling, does not occur in channels or zees, because lateral deflection begins with the first load. The term "lateral-torsional buckling" needs to be replaced with some definition more characteristic of such behavior. For this paper, the term "translation-rotation failure" will be used to mean large rotations and lateral deflections leading either to an inelastic failure at the flange-web junction, or excessive deformations. When an unsymmetrical section like a channel or zee is loaded in a plane parallel to the web, its natural tendency is to deflect laterally and twist in such a way as to relieve the compression on the stiffening lip. Near a braced point, this tendency to translate and twist is restrained, leading to a large compress i on stress on the 1 i p, with eventual 1 i P buckl i ng 1 eadi ng to fl ange buckl ing. This may occur at a load less than that predicted by the "lateral buckling" equations of C Such a failure mode could be called "flexuraldistortional buckling" to differentiate it from lateral-torsional buckling and distortional buckling under pure compression. It is not predicted by any procedure currently in the AISI Specs. With this definition in mind, it can be said that the only tests to exhibit "translation-rotation failure" were those that were totally unbraced. All the rest failed by lateral-distortional buckling. COMPUTER PROGRAM According to the AISI Specification, the nominal moment capacity is M n = Sf e where Se is the effective section modulus at some stress level f. This means that the flexural capacity of a slender section is a function of the stress at the buckling load times the effective section modulus calcylated at the buckling stress. The problem is a complicated one because the effective section changes with every change in unbraced length. The authors have written a computer program to take the drudgery out of these calculations. A typical moment vs. unbraced 1 ength curve is shown in Fi gure 9. Note that at some unbraced length, the section becomes fully effective. Such curves were developed for the six test groups and are shown in Figures 10 through 15 with the test values superimposed.

5 112 EVALUATION OF TEST RESULTS ill beams except the un braced ones failed by flexural-distortional buckling of the compression flange, which is not predicted by Section C Note that the flexural-distortional failure mode usually occurs at a lower load than that predicted by the lateral buckling equations currently in the AISI Specification. See Figure 12 for example. The two points falling below the theoretical curve are those at 4 V2' (1.5 ml and 6' (2 ml, or quarter-point and third-point bracing, respectively. The results of ll tests are shown in one non-dimensionalized plot in Figure 16. For quarter and third-point bracing, six of the eight tests failed at less than the predicted lateral buckling load. For mid-point bracing, six of the seven tests exceeded the predicted and for the totally un braced case, ll tests exceeded the predicted. This leads to the startling conclusion that the 1956 quarter-point bracing requirement not only is not needed, it may actually be harmful. It may give the designer a false sense of confidence by predicting a load that cannot be achieved. There is currently no provision in the AISI Specifications that deals with flexural-distortional buckling. As was noted earlier, there has been some feeling that the quarter-point bracing requirement was put in the spec to limit deflections and rotations. In test Groups V and VI, the loads were applied at braced points. In some tests, only the top flange was laterally braced and in other tests, both flanges were braced. Rotations, vertical and horizontal deflections were measured in these tests. The results are shown in Table 3. For example, look at the 14-gage channel with third-point loading. When completely unbraced, the channel rotated 50 degrees at mid-span! With thirdpoint bracing of the top flange only, this was cut to 18 degrees. By bracing the bottom flange as well, a further reduction to 3 degrees was achieved. These values were at failure loads; at service loads these same three numbers were 18, 6, and 1 degrees. A close scrutiny of this table will indicate that one brace at mid-span holds deflections and rotations to well within acceptable limits. CONCLUSIONS From this study, the authors conclude that the requirement for the quarterpoint bracing of channels and zees not attached to deck or sheathing is not needed. It is recommended, however, that a mid-span brace be used to control lateral deflections and rotations at service loads. At the same time, it should be noted that the present lateral buckling equations in the 1989 AISI Specification for predicting the capacity of such members may be unconservative for cases where lateral braces are spaced closer than mid-point.

6 113 REFERENCES 1. American Iron and "Steel Institute, Specification for the Design of Cold Formed Structural Steel Members," 1989 Addendum. 2. Winter, G., Lansing, W., and McCalley, R., "Performance of Laterally Loaded Channel Beams," Reprinted in "Four Papers on the Performance of Thin-Walled Stee 1 Structures," Repri nt No. 33, Cornell Uni vers i ty Engi neeri ng Experiment Station, November 1, 1950, Ithaca, New York. 3. Yu, W., "Cold-Formed Steel Design," John Wiley & Sons, Inc., 2nd Edition, Ell i fri tt, D., Sputo, T., and Haynes, J., "Fl exura 1 Strength and Defl ect ions of Discretely Braced Cold Formed Steel Channel and Zee Sections," University of Florida Research Report No , August, 1991.

7 114 Table 1. Properties of Test Specimens Group Section Thickness* Depth Fl ange Lip Yield in. (mm) in. (mm) in. (mm) in. (mm) Strength ksi (mpa) I C.0723(1.8) 8.15 (207) 3.39(86).868(22) 63.6(438) II C.0954(2.4) 8.24(209) 3.44(87).827(21) 60.4 (417) III Z.0574(1.5) 8.25(210) 2.32(59).758(19) 65.9(455) IV Z.0869(2.2) 8.25(210) 2.38(61).742(19) 60.0(414) V C.0728(1.8) 8.12(206) 3.18(81) (27) 60.0(414) VI Z.0590 (1. 5) 8.31(211) 2.28(58).776(20) 62.0(428) *without paint

8 115 Table 2. Test Results N n Nt/N N n n N/N n Failure Group Test #* Nt Other Other ail C b = 1 C b = 1 Modes** C b I C14U % 1.00 A C14M % 89% 0.50 B C14T % 0.33 C C14Q % 0.25 C C14F % 0.00 C I I C12U % 1.00 A C12M % 105% 0.50 B III Z16U % 1.00 A Zl6M % 87% 0.50 B Zl6T % 0.33 D Z16Q % 0.25 C Zl6F % 0.00 E IV Z13U % 1.00 A V C14TU % A C14TT % 0.33 C C14TB % 0.33 C C14MT % 93% 0.50 C C14MB % 91% 0.50 C VI Zl6TU % A Z16TT % 0.33 E Zl6TB % 0.33 B Zl6MT % 64% 0.50 B Zl6MB % 98% 0.50 B * Test Designation: Nt = Failure moment from test, in -k N n = Nominal Calculated Moment, in -k C 14 U (AISI, Sec. C3.1.2a) Section Bracing ~ Condition C or Z U = Un braced T = Third-point F = Fully braced ** Modes: Gage M = Mid-point Q = Quarter point TU = Third-point loading, unbraced TT = Third-point loading, top flange, braced TB = Third-point loading, top and bottom flanges braced MT = Mid-point loading, top flange braced MB = Mid-point loading, top and bottom flange braced. A = Web buckled at midspan B = Flange buckled at midspan C = Stiffener/flange/web buckled at load point D = Web buckled in midspan - stiffeners buckled in end spans E = Stiffener buckled in midspan C b

9 116 Table 3 Measured Deflections and Rotations Un braced Top Fl ange Top & Bottom Braced Flange Braced C14 Third Point Loading 4' 6' 9' 4' 6' 9' 4' 6' 9' Ult imate Moment k-in Rotation degrees H. Defl. in V. Defl. in ** Service Moment k-in Rotation degrees H. Defl. in V. Defl. in C14 Mi d Poi nt Loading Ultimate Moment k-in Rotation degrees H. Defl. in V. Defl. in ** Service Moment k-in Rotation degrees H. Defl. in V. Defl. in Z16 Third Point Loading Ultimate Moment k- i n Rotation degrees H. Defl. in V. Defl. in ** Service Moment k-in Rotation degrees H. Defl. -j n V. Defl. in Z16 Mid Point Loading Ult-jmate Moment k-in Rotation degrees H. Defl. in V. Defl. in ** Service Moment k-in Rotation degrees H. Defl in V_ Defl. in ln mm ft.30 m ** Factor of Safety is assumed to be 1.67

10 117 p p 1.2 r ~-- r--..,.--,.8 Mer - M'j." A.2 ~----~ ~~-- +- ~ o.4,e 1.0 Figure 1. (L L Influence of Brace Locations on Moment Capacity (Winter, Lansing & McCalley, 1949)

11 6 I-' I-' 00 Non-Friction Bearing '" \ S prea d er ~ --Actuator \\ Beam "'" _ Load Ce 11 Intermediate ~ Jk Braces ~. I I ~ I I---Load Beam :.J _.J _ ~ I r:i "// //,,, Test Purl ins / I 3:Z I I 7///// 6' - 6 (2.0 m) 5' - 0 {1. 5 ml 6' - 6 (2.0 m) 18' - 0 (5.5 m) Figure 2 - Test Assembly

12 119 Figure 3 Translation Rotation Failure of 18 ft. (6 m) Unbraced Zee. Note rotation gages. Figure 4 Flexural-Distortional Buckling of Channel at Mid-Span Brace

13 120 Figure 5 Flexural-Distortional Buckling of Zee Flange Near Middle of 6 ft (2 m) Un braced Length Figure 6 Flexural-Distortional Buckling of Channel Near Mid-Span Brace

14 121 Z\8T P:2.~5 2lDsov 8 MARC.H cr I Figure 7 Flexural-Distortional Buckling of lee Near Center of 6 ft (2 m) Unbraced Length 18MB P=2.52 " Figure 8 Flexural-Distortional Buckling at lee Near Braced Point

15 122 c e +' u Q) V) 4- e >, +'.~ U ~ Q. ~ U +' C Q) E e :;: o Unbraced Length Figure 9 Typical Moment vs. Un braced Length Curve for Channel or Zee Using Section C3.1.2 (a) and Showing Influence of Effective Section

16 100 r '-... C b to >--' I>:l ~ C 14 GROUP I Mn kip-in 160~* Unbraced Length ft Theorv vs. Exoerimental Figure 10

17 ... t-:l >I>- C 12 GROUP II Mn kip-in Ir C b o LI ~ ~ L J L L L L ~ ~ o Unbraced Length ft Theory vs. Experimental Fi gure 11

18 C b' I ~ 0 Unbraced Length ft >-' l\:) 01 Z 16 GROUP III Mn kip-in I *~ 60 f- 40 I ~ Theorv vs. Experimental Figure 12

19 * t-o en Z 13 GROUP IV Mn kip-in q, Theory vs. Experimental Unbraced Length ft Figure

20 f-' ~ -l C 14 GROUP V Mn kip-in r 60 TOP FLANGE ONLY 0 BOTH FLANGES X UNBRACED ~ Theorv vs~xderimentaj Unbraced Length ft Figure 14

21 20... rx:> "" Z 16 GROUP VI Mn kip-in TOP FLANGE ONLY D BOTH FLANGES x UNBRACED 60 D D 40 Cb x o o Unbraced Length ft Theory vs. Experimental Figure 15

22 ALL GROUPS

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