Web buckling strength of beam-to-column connections, September 1970 (74-1) PB / AS

Transcription

1 Lehigh University Lehigh Preserve Fritz Laboratory Reports Civil and Environmental Engineering 1970 Web bukling strength of beam-to-olumn onnetions, September 1970 (74-1) PB / AS W. F. Chen I. J. Oppenheim Follow this and additional works at: Reommended Citation Chen, W. F. and Oppenheim, I. J., "Web bukling strength of beam-to-olumn onnetions, September 1970 (74-1) PB /AS" (1970). Fritz Laboratory Reports. Paper This Tehnial Report is brought to you for free and open aess by the Civil and Environmental Engineering at Lehigh Preserve. It has been aepted for inlusion in Fritz Laboratory Reports by an authorized administrator of Lehigh Preserve. For more information, please ontat

2 3.1 LEHIGH U I ER Beam-to-Column Connetions E ell T T F l by w. F. Chen I. J. Oppenheim September 1970 Fritz Engineering Laboratory Report No~

3 Beam-to-Column Connetions WEB BUCKLING STRENGTH OF BEAM-TO-COLUMN CONNECTIONS by w. F. Chen and I. J. Oppenheim Department of Civil Engineering Fritz Engineering Laboratory Lehigh University Bethlehem, Pennsylvania September 1970 Fritz Engineering r,aboratory Report No

4 TABLE OF CONTENTS Page ABSTRACT l' 1. INTRODUCTION 1-1 Purpose 1-2 Previous Work THEORETICAL ANALYSIS 4 3. DESCRIPTION OF TESTS 3-1 Test Program 3-2 Test Proedures RESULTS 4-1 Load-Defletion Behavior 4-2 Yield Pattern 4-3 Analysis 4-4 Deformation Capa,ity 8 : SUMMARY AND CONC'LUSIONS 6. ACKNOWLEDGEMENTS 12. i3 7.. REFERENCES 14 8 NOMENCLATURE TABLES AND FIGURES 16-32

5 WEB BUCKLING STRENGTH OF BEAM-TO-COLUMN CONNCETIONS' by w. F. Chen 1 and I J h 2.. Qppen elm ABSTRACT In the design of an interior b~arn~to-olumn onnetion, onsideration must be given to olumn web stiffening. Stiffening may be required to inrease the olumn web shear apaity or stiffen the "olumn web opposite the beam ompression or tension flange. This report is an examination of the riteria for stiffening the olumn web opposite the beam ompression flange(s). This ompression region is simulated in a manner allowing rapid and easy testing of speimens. The two most important variables in the study are the yield strength and the web depth-to-web thikness ratioo It is found that the formulas given in the present AISC "Speifiation are onservative, espeially for strutural arbon steels. lassistant Professor of Civil Engineering, Fritz Engineering,Laboratory, Lehigh University, Bethlehem, Pennsylvania. 2Graduate Student, Fritz William College, Cambridge University, England. Formerly Teahing Assistant, : Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylvania. '

6 INTRODUCTION 1.1 Purpose In the present AISC Speifiation (February, 1969 [I]) there are two formulas governing the require~ ments for stiffening the ompression region of an interior beam-to-olumn onnetione Formula (1.15~1) (or ASCE Manual No. 41, Eq. 8.21, Ref. 2) gives the strength a olumn web wil~ develop in resisting the ompression fores delivered by beam flanges. It has the form (see Fig. 1 and Nomenlature) (1) The appliation of this formula is limited to ases where the olumn web depth-to-thikness ratio is small enough to prelued instability. The limiting ratio is desribed by Formula (1.15-2)* ra:' d Y w < 180 (2) The seond formula, and the instability effet, have not been ompletely examined. The purpose of this report is to study this effet, inluding its appliation to olumns of high-strength steel. A series of tests were performed to aomplish this. * d Some printings of the Speifiation have w < Wlli.l1 is an error. It should be as given here. ~ ȳ.

7 Previous.Work A program of researh undertaken at Lehigh University in the late 1950's is the basis for many of the urrent design provisions for beam-olumn onnetions [l]~ I~ that work the strength of the ompression region was studied but not its stability. Further~ore, all the speimens were of steel with a 36 ksi yield point. Their simulation of the ompression region of the olumn web as shown in Fig. 1 is the one used in this urrent study. The stress distribution over a width of t b + 5k is based on a urve fit to an elasti solution by Parkes. This is desribed in the appendix to the Fritz Lab. report of Graham et al [3].

8 THEORETICAL ANALYSIS In the simulated onnetion test (Fig. 1), the major ontribution of the flanges to the load-arrying apaity of the web panel may be desribed by two types of ation. The first of these is that the flanges at as bearing plates to spread the onentrated beam flange fore over some large area suh as the value (t b + 5k) used in developing Eq. 1. The seond is that the flanges serve to provide simply supported edge onditions for the web panel, beause of the very high bending stiffness of the flange in the plane of the flange. There is an elasti solution 'reported in Ref. 4 for the bukling of a simply supported long plate ompressed by two equal and opposite fores. If the slenderness ratio is taken to be the web depth between k lines, d, divided by the web thikness, w, the bukling load of the web panel is, in the usual notation p r 47TD = ---r (3 ) where D = 2 12(1-v ) (4 ). From observations of the test results in the present tests, it appears that, far more than in the elasti range, the plasti behavior of the web plate is primarily a loal matter and does not depend too muh upon geometry and loading of the entire olumn. Therefore, it appears reasonably justified to assume that the onentrated load ats only aross an effetive width, and this width

9 forms a squar~ panel, de by de. Thus the ritial buklitig stress beomes Or = p r d w = 'IT E 1 (d /w) 2 (5 ) valid for a r < a y (6) Using the typial set of values for steels: E = 29,000 ksi and v = 0.3, Eq. 5 redues to a r = 33,400 (d /w)2 (7) valid for ( 8) d w < 183 -ray This limiting value of d /w omes very lose to providing us with the formula found in the AISC Speifiations (See Eq. 2) d w = 180 (9) TO y Using Eq. 9, Eq. 7 an be redued to the nondimensional form a r --'- = (J y 1 d /w 2 (10) (d /w) a Comparison with Test Results will be disussed later.

10 DESCRIPTION OF TESTS 3.1 Test Program Nine tests were p~rformed making use of available material. The first two were not fully instrumerlted. The'y did, however, provide data points for analysis of the behavior. Tests 3 through 9 omprise the group whose load defletion urves are presented. The two most important variables are the yield strength and the d /w ratio. The allowable d /w ratio is. alulated from AISC Formula (1.15-2) (Eq. 9). Table 1 summarizes the d /w ratios tested. It also lists the d'/w ratios, where d' is the distane between olumn flanges~ The first two test speimens, W-3 and W-4, were A514 steel, with d /w ratios 44% and 71% greater than allowableg The next two speimens, W-5 and W-6, were of A36 steel, with d /w ratios 37% and 4% greater than allow able. Test W~7 was of an A440 speimen almost exatly at the allowable slenderness ratio, followed by speimen W-8, an 8~inh deep heavy setion of A3Q steel, with a slenderness ratio only one-third of allowable. The last test, W-9, was a W12 x 120 A514 ~peimen. Table 2 summarizes the handbook and the measured properties of all test speimens.

11 Test Proedures A test set-up was devised whih permits rapid testing of speimens. It is basially the same one used by Graham et al. (1), but with more omplete instrumentation. The test set-up is shown in Figs. 1 and 2. In this simulation test, a olumn is plaed horizontally between the loading platens of the testing mahine and ompressed by two steel bars plaed in the same vertial plane on the top and bottom surfaes of the olumn. The bar was tak-welded to the olumn flange to simulate a beam flange framing in. All the speimens exept one were tested in the Rhile 800 kip mehanial mahine at Fritz Laboratory. The largest speimen required the 5000 kip hydrauli mahine. The instrumentation onsisted of dial gages to monitor the defletion in the diretion of the applied load (whih is plotted in Figs. 3 through 6) and another gage to monitor the lateral defletion of olumn web. This lateral defletion indiated the onset of buklinge Two tensile speimens were ut from eah speimen, in the orientation shown in Fig. 1, in aordane with ASTM standards. Although the prinipal loading diretion is transverse, the standards all for speimens taken in the longitudinal diretion.

12 RESULTS 4.1 Load-Defletion Behavior The load defletion diagrams are presented in Figs. 3 to 6. Figures 3 and 4 show speimens whose d /w ratio were greater than or,lose to allowable. Note that ultimate load is followed by unloading. Fig. 5 shows the diagram for three speimens with three different d /w ratios: greater than, lose to, and less than allowable. There was an unloading 'for the speimen with safe d /w ratio but it ourred at muh greater values of defletion. All three speimens in Fig. 5 were of steel with 36 ksi yield point. Similar urves for speimens with a 100 ksi yield point are shown in Fig. 6. It should be noted that tests 8 and 9 were of heavy olumn setions. Comparing tests 3,4,5,6, and 7 with test 8 indiates that stokier setions do not have as steep an unloading urve as the slender ones, nor do they reah ultimate load at as small a defletion. This is partly due to the slenderness of olumn web. A great deal of differene may be attributed to the ontribution of the flanges. The heavier speimens had onsiderably thiker flanges. 4.2 Yield Pattern The yield stress pattern at ultimate load varied from test to test. Figure 7 shows an almost perfetly retangular distribution of yielding at the ultimate load

13 of test W-4.,The yielded width is 5 inhes. A dissimilar pattern is found in Fig. 8. It shows the yield pattern at the ultimate load of test W-S, where the yielded width at the toe of the fillet is 6 inhe~. Another type of yield pattern is presented in Fig. 9, from test W-7, where the yielded width was 10 inhes. Ultimate load was marked by the onset of large lateral defletions in all,tests. The yield pattern immediately spread for great distanes as the test was pursued into the unloading region. Two examples of the resulting yield patterns are shown ~n Figs. 10 and 11. Table 3 presents the ultimate load and the predited load for eah test. (summarized in Table 4-), was ombined with this' data and plotted in Fig~ 12. The non~dimensionalizedload, P/(t b + 5k)wa y, is plotted against the normalized slenderness ratio. Figure 12 shows that the predition o~ (t b + 5k) wa is onservative in'all ases but an be anywhere y between 50 perent and 70 perent of the observed load in the safe region. The speimens whose d /w ratios are greater than or lose to allowable are plotted in Fig. 13, with

14 an ordinate o~ a = P/dw. The solid urved line (Eq.7) is the predition by the theoretial analysis developed in Setion 2. It is seen that exept for Tests 3 and 4, the theoretial urve is in good agreement with test results. Tests 3 and 4 are seen to develop a bukling strength far in exess of that indiated by the theoretial urve. This may be expeted beause Tests 3 and 4 are speimens of high strength steel with d /w ratios muh greater than allowable. In suh ase, bukling may take plae only after small areas of inelasti strain developed near the immediate areas of the onentrated fores, and the web plate remains essentially in the elasti range. The effetive width onept, upon whih the inelasti bukling stress was alulated, does not apply, beause the elasti behavior of the web plate is no longer a loal matter but depends upon the geometry and loading of the entire web plate. In the elasti bukling ase, the olumn flanges appear to provide some additional moment restraint for the web plate, beause of the very limited loal yielding at the depth of the base of the olumn flange fillet (k-depth) Timoshenko shows that the bukling load of the lamped long plate is exatly twie the value given by Eq. 3 [ 4] For Tests 3 and 4, these bukling loads are found to be 328 kips and 274 kips, whih give 253 kips and 260 kips as the upper limits for the test values respetively. Thus the previous disussions on the plate

15 edge onditions is reasonable in suh ases. All of the earlier data from Ref. 3, was ombined with present data and plotted in Fig. 140 The non-dimensionalized load, a/o, y normalized slenderness ratio. is plotted against the The straight line is a=a and the urved line (Eq. 10) is the theoretial y predition. The theoretial urve fits well in the slender range, where d /w is greater than allowable. Figure 15 substitutes, d', the web depth between flanges, for d in Fig. 14. It an be seen that the agreement is omparable to that of Fig. 14~ 4.4 Deformation Capaity When the olumn web has the requisite strength the desired rotation apaity of the onnetion is supplied jointly by the olumn web and the end portions of the beam. A rough idea of deformation apaity of the olumn web an be estimated by setting 8, the hinge angle rota~ tion, equal to ~, the measured deformation, divided by the depth of the beam, db. For ~ult~o.2 to 005 inhes (see Tests 3 to 7), 8 ult is in the range of neessary rotation (this varies from struture to struture). It is possible that suh a hinge will not deform suffiiently to re-distribute its moments. A safe setion (Tests 8 and 9) probably will develop suffiient rotation.

16 SUMMARY AND COr~CLUSIOt~S (1) The two most important variables in the present study are the yield strength and the web depth-toweb thikness ratio. with regard to strength and stability, the results show that the present AISC Speifiations are onservative for all grades of steel. (2) It is found that strength and stability of olumn web ould be more aurately predited by the urves shown in Fig. 14 or 15. It should be kept in mind, however, that if a slender shape is used, the uanger of unloading as well as the deformation apaity must be onsidered.

17 ACKNOWLEDGEMENTS The work is a part of the general investigation on "Bearn-to-Column Connetions,H sponsored by AlSI and WRC at the Fritz Engineering Laboratory, Lehigh University.. Tehnial advie for the projet is provided by the WRC Task Group on Beam-to-Column Connetions, of whih J. A. Gilligan is Chairman. This work is based largely on a speial ourse program prepared by the seond writer under the diretion of the first, in the Department of Civil Engineering of whih Dr. D. A. VanHorn is Ch~irrnan. The writers are espeially thankful to Messrs. J. A. Gilligan, and o. W. Blodgett for their review of the preliminary report, to Drs. L. S. Beedle and G. C. Drisoll for their review of the manusript, to G. L. Smith for his help in testing and redution of data, to P.' A. Ral1denbllsh for her help in typing the manusript, and to S. Balogh for preparing the drawings.

18 REFERENCES 1. AISC Speifiation for the Design, Fabriation, and Eretion of Strutural Steel for Buildings, Amerian Institute of Steel Constrution, February, 1969Q 2. ASCE Manuals of Engineering Pratie No. 41, Commentary on Plasti Design in Steel, the Welding Researh Counil and the Amerian Soiety of Civil Engineers, 1961 (Revision to Appear in 1970). 3. Graham, J. D., Sherbourne, A. N., Khabbaz, R. N., and Jensen, C. D.,WELDED INTERIOR BEAM-TO-COLUMN. CONNECTIONS, AISC PUbliatiop, 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, MGraw-Hill, New York, 1961.

19 NOMENCLATURE d d' E k p w a 0 Y e = = = = = = = = = = = := = = = = area of one flange (of the beam framing in); ~atio of the beam flange yield stress to the olumn yield stress; olumn web depth between olumn k-lines or between toes of.fillets; dept'h of beam; distane petween olumn flanges, Fig. 1; Young's modulus of elastiity; distane from outer fae of flange to web toe of fillet, Fig. 1; onentrated load; thikness of the beam flange; olumn web thikness; normal stress; yield stress in ksij Poisson's ratio; lateral displaement, Fig. 1; vertial displaement, Fig. 1; hinge angle rotation;'

20 TABL E 1 TEST PROGRAM Atual Allowable Atual d /w d'/w Test No. Setion ry d /w d/w (d/w)a d'/w ksi 180 = TO y (d/w) a 3 W10x W12x W12x WIOx WIOx W 8x W12x

21 TABLE 2 SECTION PROPERTIES Handbook Measured a d w k d' a d w k y d' y Test No. Setion ksi in. in. in. in. ksi in. in. in. in. 3 WIOx W12x W12x WIOx W10x W 8x W12x ' TABLE 3 TEST RESULTS Computed Test P u1t Pult t b (t b + Sk) way P u1t de way d' W(J y Test No. in. kip kip

22 TABLE 4 Test results reported by Graham, Sherbour~e, Khabbaz and Jensen (see Ref. 3) Atual Allowable Atual Computed Test Test No. Setion t b r d 180 d d" (t b + 5k)wa P P P y - ---TO y u1t u1t u1t w in. ksi w y w kip kip d wr d.' wr C y Y E 1 W12x < El.4- W 8x EIS W 8x E16 WIOx ~ E17 WIOx E18 W12x eO El9 W12x E20 W14x E21. W14x68. 0 ~ E22 \v14x eo eO E23 W14"xlO ,, i I..., 00

23 d' t p Fig. 1 Simulation of the Compression Region SOOk Mahine Fig. 2 Test Set-up

24 P KIPS Test w- 3 A514 Steel o ~ OR 8 (IN.) Fig. 3 Load-Defletion Curves

25 W-7 P KIPS (tb+5k ) w ry A 440 Steel a 0.5 ~ (IN.) 1.0 Fig. 4 Load-Defletion Curve

26 A 36 Steel P KIPS -125 k (tb+5k) w CTy 100 W-5 a (IN.) 1.0. Fig. 5 Load-Defletion Curves

27 P ULT =980. W P KIPS, A 514 Steel' a ~ (IN.) Fig. 6 Load-Defletion Curves

28 Fig. 7 Retangular Distribution of Yielding at the Ultimate Load of Test w-4

29 Fig. 8 Yield Pattern at the Ultimate Load of Test W-5

30 Fig. 9 Yield Pattern at the Ultimate Load of Test W-7

31 Fig. 10 Yield Pattern Immediately After the Ultimate Load of Test W-7 was Reahed

32 Fig. 11 Yield Pattern at the End of Test W-7

33 p u= (fb +5k)w a [J 9 ~a a 5 0 (~)= 180 W a../by AISC EQ.I [J[] [] Safe Region l>... (f) o JTI P U1 N o (d/w) (d/w)a Fig. 12 Comparison of Test Results With AISC Formulas

34 CT KSI 100 U y ksi o 50 ksi, 36 ksi ksi (Ref. I) p 33,400 (1"= - 60 de W (d /w)2 40 Eq o 20 de - w Fig. 13 Comparison of Analytial Results with Tests for Speimens with d/w Ratio Greater Than or Close to Allowable

35 ry 2.0 \ 8 0 \ 100 ksi 0 50 ksi, 36 ksi 0 36 ksi (Ref. I) \ u P I 0 -= - \ ry de w fry (dc/wi [] I.5 9\., (de/w)a.. u - \ d.,.7 o-y [J I.0 [J CJ \ Cut- Off \ Eq.IO o (de/w) (de /w)o Fig. 14 Comparison of Analytial Results de With Tests (For all W- )

36 o d'/w (d/w)a Fig. 15 Comparison of Analytial Results With Tests (Note: using d l instead of d in Fig. 14)