Column web strength in steel beam-to-column connections (ASCE Meeting reprint 1524)

Transcription

1 Lehigh University Lehigh Preserve Fritz Laboratory Reports Civil and Environmental Engineering 1971 Column web strength in steel beam-to-olumn onnetions (ASCE Meeting reprint 1524) Wai-Fah Chen David E. Newlin Follow this and additional works at: Reommended Citation Chen, Wai-Fah and Newlin, David E., "Column web strength in steel beam-to-olumn onnetions (ASCE Meeting reprint 1524)" (1971). 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 LEHIGH U I ER IT Beam-to-Column Connetions E TE T lei lu IT f l E by D. E. Newlin W. F. Chen May l,9-,r" Fritz Engineering Laborato.ry Report No

3 Beam-to-Column Connetions STRENGTH AND STABILITY OF COLUMN WEB IN ~~LDED BEAM-TO-COLUMN CONNECTIONS by D. E. Newlin and w. F. Chen Department of Civil Engineering Fritz Engineering Laboratory Lehigh University Bethlehem, Pennsylvania May 1971 Fritz Engineering Laboratory Report No

4 TABLE OF CONTENTS ABSTRACT 1. INTRODUCTION 2. ANALYTICAL METHODS 3. DEVELOPMENT OF BUCKLING STRENGTH FORMULA 4. DEVELOPMENT OF THE INTERACTION FORMULA 5. DESCRIPTION OF SPECIAL TESTS 5.1 Test Program 5.2 Test Proedures 6. RESULTS 6.1 Eentri Load Tests 6.2 Inreased Flange Thikness 6.3 Deformation Capaity 6.4 Slotted Flange Test 7. SUMMARY AND RECOMMENDATIONS 7.1 Parameters 7.2 Formulas 7.3 Reommendations 8. ACKNOWLEDGEMENTS 9. REFERENCES 10. NOMENCLATURE TABLE 1 FIGURES i

5 i STRENGTH AND STABILITY OF COLUMN WEB IN WELDED BEAM-TO-COLUMN CONNECTIONS by D. E~ Newlin 1 'ltv. and 2 F. Chen ABSTRACT In the design of an interior beam-to-olumn onnetion, onsideration must be given to olumn web stiffening. The present AISC Speifiations require stiffening of the ompression region of olumn web on the basis of two formulas. The first formula ompares the strength of the ompression ~egion as a funtion of web and flange thikness to the applied load from the beam flanges. The seond formula preludes instability on the basis of the web depth-to-thikness ratio. If stability is the more ritial, web stiffening is required regardless of the magnitude of the applied load. Both formulas are onservati've. lgraduate Student, Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylvania. 2Assoiate Professor of Civil Engineering, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pennsylvania~

6 ii This report is a further examination of the riteria for stiffening the web opposite the beam ompression flange(s). This ompression region is simulated in a manner allowing rapid and easy testing of speimens. A simple formula is developed for prediting the load arrying apaity of the ompression region for setions in the range of instability. Moreover, the effets of strength and stability are ombined into a single formula. Simulation tests are also made to investigate the effet of olumn flange thikness and less ommon loading onditions on the strength and stability of the ompression region.

7 I N T ROD U C T ION In the present AISC Speifiation [1] there are two formulas governing the requirements for stiffening the ompression region of an interior beam-to-olumn moment onnetion as illustrated in Figure 1. Formula (1.15-1) [1] or (ASCE Man,ual No. 41, Eq [2]) gives the strength a olumn web will develop in resisting the omp~ession fores delivered by beam flanges when expressed in the form p max (1 ) This formula was developed from the onept that the olumn flange ats as a bearing plate as illustrated in Figure 2. It distributes the load aused by the beam ompression flange from an initial width, t b, to some larger width at the edge of the olumn web. The distane from the beam flange to the edge of the olumn web is k (Fig. 2) & The stress distribution proportional to k was developed by urve fitting of test results on 36 ksi steel reported in Ref. 5. The formula was shown to be onservative for high strength steels, as well as for mild steel, by the test reported from previous Lehigh University studies in Ref. 4. The appliation of this formula is limited by the AISC Speifiations to ases where the olumn web depthto-thikness ratio, d It, is small enough to prelude

8 instability. The limiting ratio is defined by the formula d t 180 = ICJ y (2) This formula an be derived using the onept of simply supported edge onditions for the olumn web panel with a linear elasti solution for the bukling of a simply supported long plate ompressed by two equal and opposite fores [4]. The test results of Ref. 4 and Ref. 5 show formula (1) to be onservative for all setions tested regardless of de/t (test set-up is shown in Fig. 3). Furthermore, the present AISC Speifiations do not permit onsideration of any load arrying apaity in the ornpression region of seti~ns with de/t ratios greater than 180/~. Development of a feasible and reliable method y of determining ultimate loads for the ompression region of setions with d It ratios greater than 1801;a- will,~ y therefore, be the first objetive of this report. It will be demonstrated herein that strength and stability are not entirely distint; rather that strength and stability are interrelated, espeially when the d ratio is near 180/~. The seond objetive will be to y develop a single formula for prediting the ultimate load arrying apaity of the ompression region regardless of the d It ratio of the olumn setion. It

9 Within the ompression region, the olumn flange simulates a shallow ontinuous beam. The bending stiffness of the flange as a beam is primarily a funtion of its thikness. It is the third objetive of this report to investigate the ontribution of the olumn flange as a shallow beam to the load arrying apaity of the ompression region. It will be shown that the ontribution of inreased flange thikness is relatively insignifiant. Oasionally, the opposing beams of an interior beam-to-olumn moment onnetion will be of unequal depths. This may result in 'a situation where the loads applied to the ompression region are eentri (Fig. 4). Investigation of the effet~of this type of edentriity on the strength and stability of the ompression region will be the fourth objetive of this report. 2. A N A L Y TIC A L MET HOD S A omplete elasti-plasti analysis of a beam-toolumn onnetion using the,finite element method has reently been reported by Bose [3]. Both initial bukling and ultimate strength solutions are obtained. The finite element approah is important to the understanding of the behavior of the onnetione However, a pratiing engineer is not likely to attempt the use of it in the design of steel strutures. Additionally, there

10 remain the questionable areas of boundary ondition stress, residual stress, and degree of auray. In ontrast to the very rigorous approah it is urrent pratie to aept the results of physial experiments oupled with drastially simplified statial analyses as a basis for design rules. This is, indeed, a logial approah for pratial use. The design rules are easy to apply and suffiiently onservative to safely permit use of their inherent approximations~ It is evident, however, that, to gain the auray needed for more effetive and effiient onnetion design, large amounts of experimental data would be required. The quantity of tests needed to?pe with all of the variables affeting onnetion behavior makes further pursuit of this approah unattrative. A ompromise of the rude and rigorous approahes, that optimizes the benefits of experimental tests in ombination with ertain idealized theoretial aspets, of the problem, is the essene of the approah proposed herein. The problem will be treated as an elasti plate with proper interpretation of boundary onditions for the inelasti range. The desired effet is that of inreasing auray while retaining simpliity for design use.

11 D EVE LOP MEN T S T R ENG T H o F B U C K LIN G FOR M U L A One of the major ontributions of the flanges is provision of lateral supported edge onditions for the web panel. The flanges provide web edge supports beause of the very high bending stiffness of the flange in the plane of the flange. The flanges provide simple supports with 36 ksi material beause there is early yielding near the junture of the web and flange. It was observed that further yielding does not spread throughout the ompressian panel until just prior to ultimate load when the panel begins to bukle. with the use of high strength materials this early yielding will not our and the flanges will losely simulate the role of fixed end supports for the web panel. From observations of the test results in the present and previous tests, it appears reasonably justified to assume that the onentrated load ats only aross an effetive width, and this width forms a square panel, de x de. Thus, the ritial bukling stress beomes a r p r = d t = 33,400 (d /t)2 (3 ) as developed in Ref. 4.

12 In Ref. 6 the bukling load of a fixed end long plate ompressed by two equal and opposite fores is twie the bukling load of the same plate when it is simply supported. It was also observed in previous tests [4] that setions made of 100 ksi material with d It ratios greater than Eq. 2 did realize stresses approahing twie the ritial stresses predited by the simply supported theory. This is illustrated graphially in omparison with test results in Fig. 5. It an; therefore, be stated that a r = 33,400/(d It) is a lower bound for 36 ksi material and 2a is an upper r bound for 100 ksi material. 2 This is losely approximated by making G er a funtion of r y as follows: (J r p = d t ra = 33,400 (--Y.) (d /t)2 6 (4 ) If the expression for 0 in Eq. 4 is adjusted to fit r the most ritial test, test No. 21, the resulting equation 4100 t 3 rr p = y r d (5) will be safe for all tests.

13 It should be noted that beause t is ubed while d remains first order, web thikness is a more signifiant parameter in determining the bukling load, P. Graphir al omparison of formula (5) is made with test results in Fig. 6 using nominal values of yield stress. A good agreement is observed. 4. D EVE LOP t1 E N T OFT H E I N T ERA C T ION FORM U L A Figure 7 is a results with AISC non-dimensional omparison of test design formulas for strength and stability. There are some inherent drawbaks. The first is that when a setion's d It ratio exeeds the allowable values of l80/;a-, the speifiations delare that the y setion has no load arrying apaity and is to be stiffened regardless of the magnitude of the applied loade In the range where d It is within the allowable. limits and the load apaity of the setion is ontrolled by the strength formula, P = (t b + 5k)ta y, other diffiulties arise. The test data is muh too sattered to make an aurate predition of the ultimate load ap'aity. It is readily determined that, although the AISC strength formula is onservative for normal rolled setions, it does not desribe what really ours in the olumn ompression region of a beam-to-olumn onnetion. If we return to the assumption that the ompression region of the olumn is effetively a square web panel with

14 dimensions d x d and thikness, t, a different perspetive reveals itselfe Compressive stress in the olumns is now determined as r = P/d t. From the results plotted against d It on a non-dimensional form in Fig. 8 it is observed that the data is onsiderably less sattered. However, if the formula P = d to was used to predit ulti y mate load instead of the AISC formula, P = (t b + 5k)to y, premature failure would our as values of d It approah 180/~. This is observed beause of test failures oury ring within the limits of the two formulas. There is a logial onlusion to be drawn from this behavior. It is supported both intuitively and by observation of the plotted results. Interation between strength and stability riteria does our near the beginning of the stability riteria range as desribed by 180/1r-. In y Fig. 8 this interation is onservatively desribed by a straight line from 1.75 on the absissa to 1.75 on the ordinate. The equation of this line an be written as (6 ) In omparing values predited by this formula to test values it was disovered that the equation provided exellent results for all tests exept on those speimens made of 100 ksi material. For these speimens the axis

15 intersetion point in Fig. 8 would have to be at least 2.2 or 2.3. Making the onstant 1.75 a funtion of the yield stress presented itself as a possible way of aomplishing the desirable effet of shifting the interation line upward for high strength steel. Changing 1.75 to 1.75(~/136) pray dued premature failures in 50 ksi materials. Changing 1.75 to ( ra-/ he;) provided the desirable effet. For y a = 100 ksi, 1.70 is hanged to 2.17 and 1.85 for 50 ksi y material. The interation equation takes the form: 1.70 ra p = ( y t36 ( 7) whih redues to P = 61.2 d t d 2 (0 = 36 ksi) y (7a) and P = d t d 2 (0 = 100 ksi) y (7b) When the formula 16 solved for t it takes the form: t'= d 2 ~ C 1 A f 125 d' &rae y ( 8)

16 this an be similarly redued (0 = 36 ksi) y (8a) where C 1 is the ratio of beam yield stress to olumn yield stress and A f is the area of the beam flange delivering the onentrated load, P. Thus, C A 1 f = PlOy. Then t beomes the required web thikness in the olumn ompression zone regardless of d The predited <ultimate loads from this formula for reent Lehigh University tests are tabulated on Table 1 and omparatively plotted against atual values in Fig. 9. Fig. 9 shows the interation formula (7) to be as aurate as the stability formula (5) and for 100 ksi material the interation formula provides better auray than the It. stability formula. In the range where the stability formula is not appliable, i.e. d It < 180/;a-, the interation y formula is ompared with AISC preditions in Fig. 9. Where the stability formula is appliable, AISC makes no predition.

17 o F DES C RIP T ION S PEe I A L T EST S 5.1 TEST PROGRAM Fifteen tests were performed investigating web rippling, in general, as affeted by various types of loading onditions and olumn flange variations. Refer to Fig. 3 for a shemati of the web rippling test setup. The first series of tests simulated the ompression zone of a olumn loaded by moments from two opposing beams of unequal depth. This is illustrated shematially in Fig. 4. To observe the effet of inreased olumn flange thikness, a set of tests were performed on sample speimens with and without over plates. Cover plates used were 1 inh thik, 20 inhes long, and slightly wider than the speimen flanges to permit fillet welding all around. The role of the olumn flange as a ontinuous stiffening beam was analyzed by another set of tests. The speimen flanges were slotted from the outside edges to the web on both sides of the load points. The ends of the uts near the web were pre-drilled to insure rounded smoothness and prevent nothes. On one test the distane between the slots was equivalent to t b + 5k and equivalent to d' on ~nother speimen.

18 TEST PROCEDURES A test set-up was devised whih permits rapid testing of speimens. It is basially the same one used by Graham et al [5]. The test set-up is shown in Figs. 2 and 3. 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. The speimens were tested in the Rhile 800 kip mehanial mahine at Fritz Laboratory. The instrumentation onsisted of dial gages to monitor the defletion in the diretion of the applied load and another gage to monitor the lateral defletion of olumn web. This lateral defletion indiated the onset of bukling. Two tensile speimens were ut from eah setion in the orientation shown in Fig. 2, in aordane with ASTM standards.

19 RES U L T S Table 1 summarizes the measured properties of all test speimens inluding the tests reported in Ref. 4. Table 1 also summarizes the test results and the theoretial preditionse 6~1 ECCENTRIC LOAD TESTS It an be observed from the load-defletion urves in Fig. 10 and Fig. 11 that the ultimate load is essentially unaffeted by the eentri load ondition. Loading eentrially has the effet of adding a small amount of stiffness to the web. Design based on the assumption of non-eentri loading will be onservative. Fig. 12 shows the omparison of the yield pattern of the ontrol speimen with the eentriity speimen at the end of tests. 6.2 INCREASED FLANGE THICKNESS The load defletion urve of the ontrol test, Fig. 13, exhibits the usual properties of a beam of this size made of 36 ksi material. From no load to approximately half of ultimate load the urve is almost linear and reasonably steep. The upper half of the urve to ultimate load is at a lesser slope indiating the ourene of some yielding and redistribution of stresses from the inreasing load. The maximum design load, as determined by the AISC formula (t b + 5k)ta is reahed soon after the initial yield point, y on the load defletion urve with onsiderable reserve apaity remaining.

20 with the addition of a heavy over plate, reasonably long, a signifiantly different situation exists. The load defletion urve is essentially linear all the way to ultimate load with no stress redistribution exhibited. The (t + 5k)to formula leaves only 4.8% of ultimate load b y as reserve apaity as ompared to 43% in the WIO x 29 setion without over plate. These figures are 4.8% and 33% respetively for the W12 x 27 setion. Also, though the flange thikness is tripled, the ultimate load is inreased only by a fator of 1.3. It an be onluded that for very thik flanges the t b + 5k formula does not meet present standards of reliability. Thus, in the design of beam-to-olumn onnetions the presene of a over plate on a olumn flange should not be onsidered as part of the k dimension. These results further support the relative insignifiane of the olumn flange thikness as ompared with web dimensionse 6.3 DEFORMATION CAPACITY In Refe 5 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 mehanism, is M L/6EI. In the pratial ase of a W16 x 36 beam p spanning 24 feet the required rotation is alulated in Ref. 5 to be 702 x 10-3 radians. If this deformation was to be absorbed by an interior olumn, the required, ompression deformation would be 2 x 8 x (7.2 x 10-3 ) or about 0.12 inhes.

21 In the test ase represented in Fig. 13 the ontrol olumn develops the required deformation within the load requirements of the interation formula with onsiderable reserve apaity. Inreasing the flange thikness without hanging the web properties produes a stiff setion, barely apable of developing deformation, that fails suddenly. 6.4 SLOTTED FLANGE TEST Slotting the flanges as shown in Fig. 14 little effet on the load defletion urve. had very Stiffness was essentially unhanged and ultimate load dereased only slightly. This adds support to the theory that ompression region analysis is basially a loal problem. Speimens at the end of the test are shown in Figs. 15 and SUM MAR Y AND R E COM MEN D A T ION S 7.1 PARAMETERS It has been shown that the parameters most pertinent to the strength and stability of the olumn ompression zone in a beam-to-olumn onnetion are four fold. They are web thikness, t, olumn depth, d, yield stress, a, y and the role of the ~olumn flanges as supports for the web panel. The olumn flanges vary in their support effet from a lower bound of simple edge supports to an upper bound of fixed edge supports with inreasing yield stress. Flange thikness has been shown to be a parameter not espeially signifiant or needed. Inlusion

22 of flange thikness effets would unduly ompliate the design equations and is therefore unwarranted. 7.2 FORMULAS The formulas developed or under onsideration in this study are summarized below. They are shown both in a form readily useful to the designer and in a form for prediting the maximum permissible load that an be arried by the olumn ompression zone in a beam-to-olumn onnetion. strength governs when t > d f(j y 180 Stability governs when t < d y Ultimate Load Form Design Form ~ Strength strength C A p = (t b + 5k)ta 1 f Y t.:5 t +5k b AISC Stability Stability p = 0 Stiffener Required strength & Stability a 3/2 d p = y [125t _ d ] 180 ~ y Strength p = (t + 5k)ta b y Stability strength & Stability d 2 ;a C 1 A f t < y ~ d y strength C A l f t.:5 t +5k b Stability Interation AISC and Bukling Formula p = 4100 t 3 IC1 y d d

23 The present AISC formulas are onservative. This has been shown previously and is reonfirmed in this report. The AISC formulas are inomplete in that they offer no estimate of the load apaity of the ompression zone when d/t exeeds 180/lo. The (t y b + 5k)to y formula is not an aurate expression of strength and, in the ase of very thik flanges, is unonservative. The interation formula is onsiderably more aurate. It has the advantage of being a onservative fit to data that is far less sattered than the data pertaining to the AISC formula. This fat alone makes it more pertinent than the AISC formula. Another important 'advantage is that it permits the designer to make a one step analysis of the ompression zone of a onnetion to determine whether a st~ffener is advisable. The last set of formulas, herein referred to as Modified AlBe, adds to the present AISC approah the advantage of being able to predit ultimate loads in the stability range very aurately. When the onstant in the formul~ P = 4100t 3 ~/d is inreased to 4400 this y equation is an exellent fit to the test results of speimens made of 36 ksi and 50 ksi material and is onservative for 100 ksi material. When the onstant is left at the onservative 4100 value, it is a reliable design aid.

24 RECOMMENDATIONS After thorough evaluation of the test results set forth in this report, it is the onsidered opinion of the authors that the proposed l1interation formula" offers a deided improvement to the present AISC approah on the basis of simpliity, safety, auray, and thoroughnessg Also the addition of the stability formula P = 4100t 3 ;r'/d to the AISC ommentary would be an asset y to that text and to persons interested in greater auray for determining bukling loads of rolled setions of 36 or 50 ksi material.' 80 A C K NOW LED G EO MEN T S The work is a, part of the general investigation on "Beam-to-Column Connetions,1I sponsored by AlSI and WRC at the Fritz Engineering Laboratory, Lehigh universityg Tehn~al advie for the projet is provided by the WRC Task Group on Beam-to-Column Connetions. This work is based largely on a speial ou~se program prepared by the first writer under the diretion of the seond, in the Department of Civil Engineering of whih Dr. Do A. VanHorn is Chairman. The writers are espeially thankful to Messrs. J~ Ao Gilligan, W. E. Edwards, Dro A. No Sherbourne,

25 and members of the WRC Task Group for their omments following presentation of the preliminary report, to Drs. L. S. Beedle and G. C. Drisoll for their review of the manusript, to G. L. Smith for onduting tests and redution of data, to P. A. Raudenbush for her help in typing the manusript, and to J. Gera for preparing the drawings. 9. REF ERE NeE S 1. AISC SPECIFICATION FOR THE DESIGN, FABRICATION, AND ERECTION OF STRUCTURAL STEEL FOR BUILDINGS, Amerian Institute o Steel Constrution, February, ASeE MANUALS OF ENGINEERING PRACTICE NO. 41, Commentary on Plasti Design in Steel, the Welding Researh Counil and the Amerian Soiety of Civil Engineers, Bose, Somesh K. ANALYSIS AND DESIGN OF COLUMN WEBS IN STEEL BEAM-TO COLUMN CONNECTIONS, Ph.D. Dissertation, Department of ivil Engineering, University of Waterloo, Marh, Chen, W. F. and Oppenheim, I. J. WEB BUCKLING STRENGTH OF BEAM-TO-COLUMN CONNECTIONS, Fritz Engineering Laboratory Report NOG , Grah~m, J. De, Sherbourne, A. N., Khabbas, R. NQ' and Jensen, C. De WELDED INTERIOR BEAM-TO-COLUMN CONNECTIONS, AISC Publiation, Fritz Engineering Laboratory Report No , 1~59. 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.

26 NO MEN C L AT U R E A f area of one flange (of the beam framing in); C 1 ratio of the beam yield stress to the olumn yield stress; d db olumn web depth between olumn k-lines or between toes of fillets; depth of beam; d' distane between olumn flanges, Fig. 2; E k Young's modulus of elastiity; distane from outer fae of flange to web toe of fillet, Fig., 2; P t b t a onentrated load; thikness of the beam flange; olumn web thikness; normal stress; r yield stress in ksi; y ~ vertial displaement, Fig. 3.

27 Table 1 SECTION PROPERTIES AND PREDICTED CRITICAL LOADS WITH NOMINAL STRESS VALUES Inter- Measured Dimensions AISC Bukling ation a a P P P Tests y y r r r d Test (Nom. ) Atual t k Eqs.l,2 Eqs.S,2 Eq. 7 Fult Setion No. ksi ksi in. in. In. kips kips kips kips W-3* WIQ x W-4* W12 x W-5* W12 x W-6* WID x W-7* WID x ISS 215 W-8* W 8 x f W-9* W12 x W-IO HID x W-12 W12 x J I W-1S W12 x W-17 WIQ x W-20 W12 x I a W-21 W12 x I *Reported in Ref I l\j...

28 -22.. T... J ~ M /.. I... T \ I ~ t ""-Compression Region Fig. 1 Shemati of Typial Interior Beam-To-Column Moment Connetion p -Vrtb,; 2.5:1 o-y t t t t t t t t --f r-tb +5k ry I I I I I I t ~ I Fig. 2 Simulation of the Compression Region

29 -23 e - Eentriity Fig. 4 Shemati of,eentriity Problem BOOk Mahine Fig. 3 "Test Set-up

30 ksi o 50 ksi o 36 ksi Clamped Support 0-= 66,800 (de/t ) KSI 40 Simple Support (y =_p :: _33_,_40_0_ det (d e ft)2 o 20 delt 40 Fig0 5 Comparison of Theory Developed in Ref. 5 Using Tests of Speimens with d It Ratio Greater than or Close to AllowaBle

31 CTr _ 4100 JaY -(d e /t)2 p = de t JU"y ksi 5 P ksi (J 36 ksi o Fig. 6 Comparison of Stability Formula with Tests of Speimens with 'd It R'atio Greater than or Close to Allowable C

32 -26 p IT: (tb + 5k) t r ry rr ( dtc)o Jry P DO [J 1.5 [J C AISC Eq I DO ksi 0.5 Safe Region C\J I LO -. - W o o 50 ksi 36 ksi U (J) <t a (d/t) (d/tl o Fig. 7 Comparison of Test Results with AISC Formulas

33 = 1 =--""!!""'" (d e /t) o (del t)o !L ry D o ~~ ksi ksi 4 15 lj 36 ksi o Fig. 8 Comparison of Test Results with Interation Formula. Ref. 5 Points not Numbered

34 -28 P u1t KIPS Test No _ opr...--_...o: """'""" vi 0 1--D~------O pilii" 100 DAise e Stability o Interation o Per ' KIPS Fig. 9 Composite Comparison of Ultimate Test Load with Predited Ultimate Load as Determined by the Various Formulas

35 -29 P KIPS '----Test I '----Test Control Test R Control Test Test I 120 WI2 x Test P WI2 x 36 50" 100 ksi o O~5 li t INCH Fig. 10

36 -30 P KIPS Eentri Test 150 Control Test p 100 WI2 x ksi l.p 4- Eentri Loading 3 p 4 50 Control Test o ~_~~~~~~--.J~_~ ~, INCH Fige 11 Eentri Loading Results

37 a) Eentriity Test b) Control Test Fig. 12 Yield Pattern at the End of Tests W-ll and W-12

38 -32 P KIPS 120 (t +5k) t C1\ Inreased Flange Thikness IIIlilli'-- (I nferaet ion) Control Test 60 p p ksi WIO x29 20 p Atual Test p Control Test o ~, INCH Fig. 13 Contribution of Inreased Flange Thikness, t

39 -33 P KIPS Test I - Control Test Test 2 - L =d - 2 tf Test 3 - L =tf + 5k P P 60 P Control 40 Test WI2 x 45 }.OO" 20 SI"otted Flange Test o A, INCH Fig. 14

40 a) Side View Slotted Flange Test b) Top View, Width - t b + 5k Fig. 15 Slotted Flange Speimen after Test

41 a) Side View Slotted Flange Test b) Top View, Width = d' Fig. 16 Slotted Flange Speimen After Test