COLUMN WEB STRENGTH IN STEEL BEAM-TO-COLUMN CONNECTIONS

Transcription

1 1524 AseE Annual and National Environmental Engineering Meeting October 18-22, 1971 St. Louis, Missouri $0.50 COLUMN WEB STRENGTH IN STEEL BEAM-TO-COLUMN CONNECTIONS W. F. Chen, A. M. ASCE and D. E. Newlin, A. M. ASCE Meeting Preprint 1524

2 This preprint has been provided for the purpose of convenient distribution of information at the Meeting. To defray, in part, the cost of printing, a meeting price of SO to all registrants has been established. The post-meeting price, when ordered from ASCE headquarters will be 50 while the supply lasts. For bulk orders (of not less than 200 copies of one preprint) please write for prices. No acceptance or endorsement by the American Society of Civil Engineers is implied; the Society is not responsible for any statement made or opinion expressed in its publications. Reprints may be made on condition that the full title, name of author, and date of preprinting by the Society are given.

3 COLUMN WEB STRENGTH IN STEEL BEAM-TO-COLUMN CONNECTIONS by W. F. Chen l and D. E. Newlin 2 Associate Members, ASCE ABSTRACT In the design of an interior beam-to-column connection, consideration must be given to column, web stiffening. The present AISC Specifications require stiffening of the compression region of column web on the basis of two formulas. The first formula defines the strength of the compression region as a function of web and flange thickness and the applied load from the beam flanges. The second formula precludes instability on the basis of the web depth-to-thickness ratio. If stability is the more critical, web stiffening is required regardless of the magnitude of the applied load. Results of previous and the present investigation indicate that both formulas are conservative. This report is a further examination of the criteria for stiffening the column web opposite the beam compression flange(s). In the experimental program this compression region is simulated in a manner allowing rapid and easy testing of specimens. A formula is developed for predicting the load carrying capacity of the compression region for sections in the range of instability. Moreover, the effects of strength and stability are combined into a single formula. Simulation tests are also made to investigate the effect of column flange thickness and less common loading condi~ tions on the strength and stability of the compression region. lassociate Professor of Civil Engineering, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pennsylvania. 2Teaching Assistant, Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylvania. i

4 1. I N T ROD U C T ION IIi. the present AISC Specification [1] there are two formulas giving the requirements for stiffening the compression region of a column web at an interior beam-to-column moment connection. (Fig. 1 illustrates this region). Formula (1.15-1) in Ref. 1 or Eq in Ref. 2 gives the strength a column web will develop in resisting the compression forces delivered by beam flanges as (1) This equation was developed from the concept that the column flange acts as a bearing plate as illustrated in Fig. 2. It distributes the load caused by the beam compression flange of thickness t, to some larger length t b b + 5k at the Hedge" of the column web. The distance from the beam flange to the edge of the column web is.k (Fig. 2). In Ref. 6 the stress distribution at the distance was developed by curve fitting of test results on steel having a yield stress of 36 ksi. Ref. 5 the formula was shown to be.conservative:.. In The application of Eq. 1 is limited by the" AISC Specifications to cases where the column web depth-to-thickness ratio, dclt, is small enough to preclude instability. The limiting ratio is defined by the formula d c T 180 I(J Y (2) -1-

5 This formula can be derived using the concept of simply supported edge conditions for the column web panel with an elastic solution for the buckling of a simply supported long plate compressed by two equal and opposite forces [5]. The test results of Ref. 5 and Ref. 6 show Eq. 1 to be conservative for all grades of steel and for all sections tested regardless of dc/t. (The test set-up is shown in Fig. 3). The present AISC Specifications do not permit consideration of any load carrying capacity in the compression region of sections with d /t ratios greater than 180/ra-. Development of c y a method of determining ultimate loads for such a condition is one of the objectives of this report. Of course, strength and stability are interrelated. Thus an additional objective will be to develop a single formula for predicting the ultimate load carrying capacity of the compression region regardless of the dcft ratio of the column section. Within the compression region, the column flange simulates a shallow continuous beam. The bending stiffness of the column flange is primarily a function of its thickness. It is the third objective of this report to investigate the contribution of the column flange as a shallow beam to the load carrying capacity of the compression region. occasiona~ly, the opposing beams of an interior beam-tocolumn moment connection will be of unequal depths. This may -2-

6 result in a situation where the loads applied to the compression region are eccentric (Fig. 4). Investigation of the effect of this type of eccentricity on the strength and stability of the compression region is also included in this report. 2. A N A L Y TIC A L MET HOD S A complete elastic-plastic analysis ofa beam-to-column connection using the finite element method has recently been reported by Bose [4]. Both buckling and ultimate strength solutions are obtained. The finite element approach is important to the understanding of the behavior of the connection. However, a practicing engineer is not likely to attempt the use of it in the design of steel structures. Additionally, there remain the questionable areas of boundary condition stress, residual stress, and degree of accuracy. In contrast to the very rigorous approach it is current practice to accept the results of physical experiments coupled with drastically simplified statical analyses as a basis for design rules. This is, indeed, a logical approach for practical use. It is evident, however, that, to gain the accuracy needed for more effective and efficient connection design, large amounts of experimental data would be required. The quantity of tests -3-

7 needed to cope with all of the variables affecting connection behavior makes further pursuit of this approach unattractive. A compromise between the crude and rigorous approaches, that optimizes the benefits of experimental tests in combination with certain idealized theoretical aspects of,the problem, is the essence of the approximate approach proposed herein. The problem will be tre~ted as an elastic plate with proper interpretation of boundary conditions for the inelastic range. The desired effect is that of increasing accuracy while retaining simplicity for design use. 3. D EVE LOP MEN T STRENGTH o F B U C K LIN G FORMUL'A One of the major contributions of the column flanges is to provide lateral support to the edge of the web panel. The flanges provide web edge supports because of the very high bending stiffness of the flange in the plane of the flange. The flanges provide what accounts to simple support with 36 ksi material because of the early yielding near the juncture of the web and flange. It was observed that further t4is local yielding does not spread throughout the compression panel until just prior to ultimate load when the panel begins to buckle. With the use of high strength materials this local yielding can not occur prior to ultimate load and the flanges therefore closely simulate the role of fixed end supports for the web panel. -4-

8 From observations of the test results in the present and previous tests, it appears justified to assume that the concentrated beam-flange load acts on a square panel whose dimensions are d c x d c. For this condition the critical buckling stress becomes Pcr 33,400 ocr = dct = (d It)2 c as developed in Ref. 5. (3) In Ref. 7 the buckling -load of a fixed end long plate compressed by two equal and opposite forces is twice the buckling load of the same plate when it is simply supported. It was also observed in previous tests [5] that sections made of 100 ksi yielding stress steel having dclt ratios greater than Eq. 2 did attain stresses approaching twice the critical stresses predicted by the simply supported theory. This is illustrated graphically in Fig. 5. It can, therefore, be stated that cr cr = 33,400/(d c /t)2 is a lower bound for 36 ksi material and 20 cr is an upper bound for 100 ksi material. The above conditions can be closely approximated for all grades of steel by making ocr a function of cry as follows f(5 cr p 33,400 (----y) (4) cr dct = (d It)2 6 c If th~ e~pression for Ocr in Eq. 4 is adjusted to fit the most critical test (test point marked No. 21 in Fig. 5) -5-

9 the resulting equation p cr 4100 t 3 10 y d c (5) will be conservative for all grades of steel and for all dc/t ratios. Comparision of Eq. 5 with test results is shown in Fig. 6 using nominal values of yield stress. A good agreement is observed. 4 D EVE LOP MEN T' OFT H E I N T ERA C T ION FOR M U L A Fig. 7 is a non-dimensional comparison of test results and the AISC There are a design formulas for strength and stability. number of observationa that may be made. First, when the dc/t ratio exceeds the values (180/;a;) the specification implies that the section must be stiffened regardless of the magnitude of the applied load. Some specimens obviously have a load capacity that is even greater than required. Second, the test data seems too scattered to permit an accurate prediction of the ultimate load capacity. It is evident that the strength formulation does not describe what really occurs in the column compression region of a beam-tocolumn connection. If, on the other hand, one assumes that the compression region of the column is effectively a square web panel with -6-

10 _ _ ~~~---- dimensions d c x dc' the data is considerably less scattered (Fig. 8). In Fig. a this interaction between strength and stability can be conservatively described by the straight line in the form: (J 3/2 P = (1.75 cry) dct - ( lao ) d~ (6) It was found that Eq. 6 is in good agreement with results of all tests except on those specimens made of 100 ksi material. For these specimens the axis intersection points in Fig. 8 would have to be at least 2.2 or 2.3. If the constant 1.75 was adjusted so that it was a function of the yield stress, this would accomplish the desirable effect of shifting the interaction line upward for higher strength steel. Changing 1.75 to 1.75(;0-/136) gives y an unconservative prediction for 50 ksi materials. Changing 1.75 to 1.70 (to/ t3'6) provides the desirable effect. The y interaction equation takes the form: (JZ5/4 cr- 3/2 P = ( 1.44) d t - (-tao-) a 2 c c which reduces to, for example (7) p 61 d t a 2 for cr 36 ksi c c y P 92 d t d 2 for a 50 ksi c c y P 128 d t d 2 for cry 65 ksi c c and P 220 d t d 2 for cr 100 ksi c c y (7a) (7b) (70) (7d) -7-

11 When the formula is solved for t it takes the form: t d 2 c ;a; C l 125 d c to:; A f (8) this can be similarly reduced to, for example where C l stress and A f d C A t c l f 51 + l.7d for cry = 36 ksi (8a) c is tne ratio of beam yield stress to column yield is the area of the beam flange delivering the concentrated load, P. Thus, C l A f = P/cr y Then t becomes the required web thickness in the column compression zone regardless of de/t. The predicted ultimate loads from Egs. 5 and 7 for recent Lehigh University tests are tabulated on Table land comparatively plotted against test values in Fig. 9. Fig. 9 shows that the interaction equation (7) is as accurate as the stability equation (5) and for 100 ksi material the interaction equation (7) provides better accuracy than the stability equation (5). In the range where the stability equation is not applicable, i.e. dc/t < l80/~, the interaction equation (7) is compared with AISC predictions in Fig. 9. Where the stability formula is applicable, AISC makes no prediction. -8-

12 5. DES C RIP T ION a F S PEe I A L T EST S 5.1 TEST PROGRAM -Fifteen tests were performed to explore web behavior as influenced by various types of loading conditions and column flange variations. Figure 3 gives a schematic of the web crippling test set-up. The first series of tests simulated the compression zone of a column loaded by moments from two opposing beams of unequal depth. This is illustrated schematically in Fig. 4. To observe the effect of increased column flange thickness, tests were performed on specimens with and without COver plates. These plates were I inch thick, 20 inches long, and slightly wider than the specimen flanges (to permit fillet welding all around). In a separate test series the role of the column flange as a continuous stiffening beam was studied. The column flanges were slotted from the outside edges to the web on both sides of the load points. The ends of the cuts near the web were pre-drilled to avoid sharp notches. On one test the distance along the column between the slots was equivalent to t f + 5k. On another specimen the distance was d - 2 t where f t is the flange thickness and d is the specimen depth (see f Fig. 12). -9-

13 5.2 TEST PROCEDURES The test set-up permits rapid testing of specimens. It is basically the same one used by Graham et al [6], and is shown in Figs. 2 and 3. Essentially a simulation test, a short length of column is placed horizontally between the loading platens of a testing machine and is then compressed at the top and bottom faces of the column. The bar is tackwelded to the column flange to simulate a beam flange framing into it at that point. The specimens were tested in the 800 kip mechanical machine at Fritz Laboratory. The instrumentation consisted of dial gages to monitor the deflection in the direction of the applied load and another dial gage to monitor the lateral deflection of the column web. This lateral deflection indicated the stability of the column web. 6. RES U L T S Table 1 summarizes the measured properties of all test specimens not only those described in the previous sections (WIO to W-21) but also including the tests reporte~ in Ref. 5 (W-3 to W-9). Table 1 also summarizes the test results and the theoretical predictions. 6.1 ECCENTRIC LOAD TESTS (Simulation Beams of Unequal Depth) Fig. 10 shows the load-vertical deflection diagram (p-~ curves) for three specimens (Test 1, Test 2, and control test) -10-

14 with three different eccentricities (10 in., 5 in., and O). From the curves it is seen that the ultimate load is essentially unaffected by the eccentric load condition. Eccentric load has the effect of adding an additional amount of stiffness to the web. Design based on the assumption of equal depth beam condition (zero eccentricity) will be conservative. 6.2 INCREASED FLANGE THICKNESS Fig. 11 shows the load-deflection diagram (p-a curves) for two such tests, one for a plain beam with no cover plate, and the other for the same section with 1 inch cover plate. Referring to the plain beam test, it is seen that from no load to approximately half of ultimate load the curve is almost linear, and the upper half of the curve to ultimate load is at a lesser slope indicating the occurence of some yielding and redistribution of stresses from the increasing load. The maximum design load, as determined by the quantity (t b + 5k)tcr y, shown in Fig. 11 by the horizontal line is reached soon after the' occurence of some yielding on the load deflection curve with considerable reserve capacity remaining. The addition of the one inch cover plate made a significant difference. The p-a curve is essentially linear all the way to ultimate load indicating no occurence of significant yielding. The load corresponding to (t b + 5k)to y formula (one inch cover pla~e is included in k dimension) leaves only 4.8% of ultimate -11~

15 load as reserve capacity as compared to 43% in the WID x 29 control shape without cover plate. For tests of the W12 x 27 shape these figures are 4.8% and 33% respectively. Although the flange thickness is tripled, the ultimate load in increased only by a factor of SLOTTED FLANGE TEST Fig. 12 shows the load-deflection diagram for three such tests, one for a control test with no flanges slotted, and the other two for the same shape with the flanges slotted and the distance along the column between the slots being d-2 t f and tf+sk respectively. From the curves it is seen that the ultimate load is decreased only slightly by slotting the flanges. Slotting the flanges has the effect of adding a small amount of stiffness to the co1umb web during the early stages of loading but weaking the web stiffness when the column web is significantly yielded. Specimens at the end of the test are shown in Fig DEFORMATION CAPACITY When the column web has the requisite strength the desired rotation capacity of the connection is supplied jointly by the column web and the end portions of the beam. In Ref. 3 it is developed that the required rotation at the ends of a fixed ended beam uniformly loaded along its length, so that it will be able to form a mechanism, is Mp~/6EI. In the practical case of a Wl6 x 36 beam spanning 24 feet the required rotation is calculated ~n Ref. 3 to be 7.2 x 10-3 radians. If this -12-

16 deformation was to be absorbed entirely by an interior column web, the required compression deformation would be 2 x 8 x (7.2 x 10-3 ) or about 0.12 inches. All the tests reported herein the specimens can develop the required deformation. 8. SUMMARY AND R E COM MEN D A T ION S 8 1 PARAMETERS It has been' shown that the parameters most pertinent to the strength and stability of the column compression zone in a beam-to-column connection are four fold. They are web thickness, t, column depth, dc' yield stress, cry' and the role of the column flanges as supports for the web panel. The column flanges vary in their support effect from a lower bound of simple edge supports for structural carbon steels to an upper bound of fixed edge supports for high strength steels. 8.2 FORMULAS The formulas developed or under consideration in this study are summarized below. Strength governs when t d c vcr; > --raod I(J. Stability governs when t < c 180y -13-

17 Strength Ultimate Load Form Strength Design Form _._--- p = (t b + 5k)tcr y C l A f AISC t ~ t b +5k (Eqs.1&2) Stability Stability P = 0 Stiffener Required Strength & Stability cr 5/4 cr 3/2 P = (~) dct - (~) d; Strength & Stability d~ ~ C 1 A f t < -----""---:----~ to d y 0 r--~--~~~---~--~-~~-~-~~--_~_.~~~_~~_~ ~_;...~~~~ Interaction (Eqs. 7&8) Strength Stability 4100 t 3,,;-ap = y d c Stability d > 4100 t 3 o - C l A f ~ combination of AISC and Buckling Formula (Eqs.2&5) The present AISC formulas are conservative. This has been shown previously and is reconfirmed in this report. The AISC formulas are perhaps incomplete in that they offer no estimate of the load carrying capacity of the compression zone when dc/t exceeds lbo/va;. The stability formula given by Eq. 5 can predict the load carrying capacity of the column web accurately when dolt exceeds l80/~. The interaction formula given by Eq. 7 has the advantage of being a conservative fit to pertinent test data. Another -14-

18 advantage is that it makes possible a one-step analysis of the compression zone of a connection to determine whether or not a stiffener is required. 9. ACKNOWLEDGEMENTS The work is a part of the general investigation on T1Beam-to-Column Connections," sponsored by American Iron and Steel Institute and Welding Research Council (WRC) at the Fritz Engineering Laboratory, Lehigh University. Technical advice for the project is provided by the WRC Task Group on Beam-to-Column Connections, of which J. A. Gilligan is chairman. The writers are especially thankful to'messrs. W. E. Edwards, A. N. Sherbourne, G. C. Driscoll, and members of the WRC Task Group for their comments, to Messrs. J. A. Gilligan, T. R. Higgins, and L. S. Beedle for their review of the manuscript, to G. L. Smith for conducting tests and reduction of data, to P. A. Raudenbush for her help in typing the manuscript, and to J. Gera for preparing the drawings. -15-

19 10. REF ERE NeE S 1. AISC SPECIFICATION FOR THE DESIGN FABRICATION, AND ERECTION OF STRUCTURAL STEEL FOR BUILDINGS, American Institute of Steel Construction, February ASCE and WRC PLASTIC DESIGN IN STEELS - A GUIDE AND COMMENTARY, The Welding Research Council and the American Society of Civil Engineers, ASCE Manuals and Reports on Engineering Practice No. 41, second edition, Beedle" L. S. PLASTIC DESIGN OF STEEL FRAMES, John Wiley and Sons, New York, Chen, W~ F. and Oppenheim, I. J. WEB BUCKLING STRENGTH OF BEAM-TO-COLUMN CONNECTIONS, Fritz Engineering Laboratory Report No , Lehigh University, Bethlehem, Pennsylvania, September Graham, J. D., Sherbourne, A. N., Khabbas, R. N., and Jensen, C. D. WELDED INTERIOR BEAM-TO-COLUMN CONNECTIONS, AISC Publication, Fritz Engineering Laboratory Report No , Also, Bulletin No. 63, WELDING RESEARCH COUNCIL, New York, August Timoshenko, S. P. and Gere, J. M. THEORY OF ELASTIC STABILITY, 2nd edition, Mcgraw-Hill, New York, Bose, Somesh K. ANALYSIS AND DESIGN OF COLUMN WEBS IN STEEL BEAM-TO COLUMN CONNECTIONS, Ph.D. Dissertation, Department of Civil Engineering, University of Waterloo, Canada, March

20 11. NOT A T ION area of one flange (of the beam framing in); ratio of the beam yield stress to the column yield stress; column web depth between column k-lines or between toes of fillets; depth of beam; distance from outer face of flange to web toe of fillet, Fig. 2i p concentrated load; thickness of the beam flange; column web thickness; cr normal stressi yield stress in ksi; vertical displacement, Fig

21 Tab'Ie 1 SECTION PROPERTIES AND PREDICTED CRITICAL LOADS,. Inter- Measured Dimensionst AISC Buckling action cr cr P p. y P Tests y d cr cr cr Test (Nom.) Measured c t P k Eqs.I,2 Eqs.S,2 Eq. 7 ult No. Section ksi ksi in. in. in. kips kips kips kips I J-I CD I W-3* WID x S ,0 20S W-4* W12 x 4S , W-S* W12 x W-6* WID x W-7* WI0 'x S 'ISS 215 W-8* W 8 x S W-9* W12 x W-I0** HID x W-12 W12 x W-1S W12 x W-17 WIO x W-20 W12 x '64 W-21 W12 x *Reported in Ref. 5 **Welded Section td c ' t, and d (depth) were actually measured and k was computed from the expressions (d - d c )/2

22 ( \ I L ""'-Compression Region t. Fig. 1 Schematic of Typical Interior Beam-To-Co1umn Moment Connection p prtb l/ 2.5:1 (Jytttttttt --i to- tb + 5k Uy t t t t t t..j1iiii' Fig. 2 Simulation of the Compression Region -19-

23 + e- Eccentricity Fig. 4 Schematic- of'eccentricity Problem SOOk Me'chine Fig. 3 Test Set-up -2-0-

24 ksi o 50 ksi D 36 ksi Clamped Support u= 66,800 (de/t)2 80 a KSI Simple,Support p 33,400 (j=-=-~det (d e /t)2 40 o 20 delt 40 Fig. 5. Comparison of Theory Developed in Ref. 5. Using Tests of Specimens with daft Ratio Greater than or Close to l80/;cr; -21-

25 12 crer _ 4100 Iffy - (d e /t)2 p = de t :p;; []l ksi ksi D 36 ksi a delt Fig. 6 Comparison of Stability Formula with Tests of Specimens with d It Ratio Greater than or Close to 180/~ c y -22-

26 cr Uy ($) DO 21 CJ 1.5 D D AISC Eq P (j =(tb +5k) t DO (\J ksi I Safe 0 50 ksi 0.5 l() Region - 0 ct 36 ksi (de) = 180 I.LJ u C/) t a loy « (dc/f) (de/t )0 Fig. 7 comparison of Test Results with AISC Formulas _.._---~

27 [] (j P I (Jy = = (de /t)2 dct (jy. (del t)o (j (jy [] 0 0 D ksi 0 50 ksi [] 36 ksi Eq. 0 o JI7 D 6/ 12 ~I o Fig. 8 Comparison of Test Results with Interaction Formula. Ref. 6 Points not Numbered (dc/t)a = 180/rcr; -24-

28 TEST P ult KIPS Test No _ ~ l.2.:::::o:i )41., 100 DAise,Eqs. I,2 20~ Stability, Eq~. 2,5 o Interaction, Eq. 7 o PREDICTION Per' KIPS Fig. 9 composite Comparison of maximum Test Load, with Maximum Pr'edicted Load,as. Determined by th-e Various Formulas -25-

29 P KIPS Test I Test Control Test R Control Test Test I Test 2 WI2 x ksi o ~, INCH Fig. 10 Eccentric Loading Results -26-

30 , ",, c--c-----c--c----_ P KIPS With Cover Plate Control Test (Plain Beam) 60 p III =2000/0 P 40 WID x29 20 P Actual Test P Control Test o ~,INGH Fig. 11 Contribution of Increased Flange Thickness, t -27-

31 P KIPS Control Test P P tf, = WI2x45 J: P Control 40 Test 20 stotted Flange Test o A,INCH Fig

32 a) Side View Slotted Flange Test b) Top View, Width = d' Fig. 13 Slotted Flange Specimen After Test -29-