I I ll WI l‘lllII‘ I! ' H Hi 1| 1 ‘ W 1 WI 51 W A STUDY OF THE STEFFNESS PROPERTIES QF WQQD FLANGESTEEL W58 [-EEAMg Thesis ('0? fine Degree of M. S. WCEfiEfii'I‘! STATE ERIVERSETY Herbert F. Law 1961 J : 1314/ MM ///// W 9319005 LIBRARY Michigan State University A STUDY OF THE STIFTNESS PROPERTIES OF'WOOD FLANGE-STEEL WEB I-BEAMS By HERBERT F. LAN AN ABSTRACT Submitted to the College of Agriculture Michigan State University of.Lgriculture and Applied.Science in Partial fulfillment of the requirements for the degree or ' MASTERIOF‘SCIENCE Department of Forest Products 1961 Approved rzééi Kéi:;éaégfé2ZL__ ABSTRACT This study was undertaken to investigate the possib- ilities of using thin sheet steel as the web material for built-up I-beams instead of plywood and thus substant- ially reduce shear deflection. This is a serious limitat- ion for the case of woodpplywood I-beams. Twenty scale model test beams with a span of eight feet were fabricated in depths of eight, nine, ten and eleven inches. Two full scale beams, sixteen inches in depth and sixteen feet long, were built and tested in an attempt to correlate results of model beam tests. The- method of fastening flanges and stiffners to the web was by nails only. No adhesive was used. All model beams were tested to failure but full scale beams were not due to the limited capacity of the test machine used. Theoretical and actual stiffness graphs were plotted for all test beam and full scale beam test data. These results were compared. Comparison was also made with a nail-glued wood-plywood I-beam of similar section. The effect of nailing pattern on stiffness was also studied. It was found that wood flange-steel web I-beams, using" either medium or heavy nailing, are superior in resistance to deflection to a comparable nail-glued.l- beam. It was also observed that shear deflection.in the} steel web was less than 2; and thus could be neglected in design calculations for beams of this type. Lateral instability, which gives rise to buckling of the web, is a major problem in beams of this type. However, buckling is not critical until well above the design deflection criteria which is normally recognized to be 1/360 of the span. Further research is recommended’in this field with emphasis on spacing of stiffners, different gages of steel and with an attempt to control lateral stability. In any event, a much larger sample should be used so that the results would be more conclusive statistically. A STUDY OF THE STIFFNESS'PROPERTIES OF‘WOOD FLANGE-STEEL WEB I-BEAMS By HERBERT IR LAW AN ABSTRACT Submitted to the College of Lgriculture> Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of ‘ MASTER OF SCIENCE Department of Forest Products 1961 ACKNOWLEDGEMENTS The author wishes to express his sincere thanks to Professor Byron M. Radcliffe for his help in formulating the problem and for his interest and inspiration in carry- ing this project to a successful conclusion. The author is also indebted to Dr. Alan W. Sliker for valuable assistance given throughout the course of this study. Sincere thanks is also due to Mr. Harry Johnson for his willing assistance in fabricating and.testing of the beams. The author's gratitude is extended to fellow graduate student RichardM. Voelker whose constant help and encour- agement throughout the course of this study were invaluable in.the completion of this thesis. Last, but not least, the writer is indebted to the entire staff of the Forest Products Department for assistance given in the course of studies at this univer- Sitye ll TABLE OF‘CONTENTS Page- ACKNOWLEDGEMENTS......................................ii LIST OF'TABLES........................................iv LIST OF FIGURES....................................... v INTRODUCTION..................................... 1 History of ' Builtdup ' I-Beams Purpose of the Study FABRICATION 0F BEAMSOOOOOOOOOOOOOOOOOOOOOOOOOOOO. 6 A. Model Beams B. Full Scale Beams TESTING PROCEDURE.COOOOOOOOOOOOOOOOOO0.0000000000II A. Model Beams B. Full Scale Beams TET RESULTSOOOOO00.000.00.000...00.0.0000000000020 Loads at Allowable Deflection Modulus of Elasticity' Equivalent Sections Moment of Inertia Stiffness Factor Shear Deflection. . Percentage of Efficiency DISCUSSION OF RESULTSoeoooee00000000000000.00000035 A. Model Beams B. Full Scale Beams CONCLUSIONS AND RECOWD‘TIONSOOO0.00.00.000.00.“ ”PENDIXOOoooso...ooooooeoeooooooooooooooo00000000000042 LITERATURE CITEDOOOOOO0.000....00.0000000000000000000046 A o . u o . r m ~ V ~ n a p o a L l ‘ l C a a h I I f 0 o 1 n W b a a. I r a c m s t I I I a e . a .. . n O O a I a V 0 t . n . n w n v n b I I v .0 r y o . m r . a I 0 fl 0 L a a n v r v I p o c a l. 2. 3. 4. 5. LIST OF‘TABLES Page Modulus of Elasticity, Model Beams................ 21 Modulus of Elasticity, Full Scale Beams........... 22 Theoretical and Actual Moments of Inertia, Model Beams....................................... 33 Comparison of Stiffness Factors, Model Beams...... 34 Percentage of Efficiency Comparison, Model and Full Scale BeamS...................-........... 35 iv LIST OF FIGURES Figure Page~ 1. Fabrication of Model Beams...................... 7 2. Nailing Schedule, Model and Full Scale Beams.... 9 3. Model Beam Testing Procedure.................... 13' '4. Model Beam'Under:Test........................... l4 5. Model Beam Showing Failure at Point of Loading... 15 6. Flange Slippage, Model Beam, Light Nailing...... 16 7. Full Scale Beam Testing Procedure............... 17 8. Photo of Full Scale Beam'Under Test............. 18 9. Full Scale Beam After Test...................... 19 10. Load vs. Deflection Curves for Model Beams...... 25 11. Effect of Nailing on Stiffness, Model Beams..... 26 12. Shear and Moment Diagrams, Model Beams.......... 28 13. Stiffness Factor Graphs, Model Beams............ 29 14. Load vs. Deflection.Curves, Full Scale Beams.... 30 15. Shear and.Moment Diagrams, Full Scale Beams..... 31 16. Method of Equivalent Sections................... 32 INTRODUCTION History of ” Builtfigp ' I-Beams The use of laminated structural wood members or " Built-up ' beams, as they are often called, dates back to the early 1900's. This process was first used‘in.Eurppe. It dealt mostly with laminated beams but the advantages this method offered were soon adapted to use in laminated beams with.rectangular, I and double I cross sections. Most of the develOpment of structural uses of plywood has taken place since the second world war. Previous to that time, little such deveIOpment had taken place, due to the shortage of plywood and the lack of suitable adhesives. With the advent of the second world.war, a search for structural members, other than steel, took place.The neon essity of conserving materials was responsible for this search. One of the earliest intensive uses of plywood I-beams in this country was a 125,000 sq. ft. warehouse built in 1942 for the RCA Manufacturing Co. at Camden, New Jersey6. A total of 198 identical plywood girders, 36 feet long, were Jab-fabricated using webs that were nailed only to the lumber flanges with 8d cement-coated nails. After ten years of service, the warehouse was taken over by the government. The beams were found to be in excellent condit- ion at that time; they had not sagged and had required no maintenance. The first extensive research and experimentation.on the strength and stiffness prOperties of plywood web I and box:type beams was done by the Forest Products Laboratory. This work was done for the U. S. Government to determine the feasibility of using such sections as structural mem- bers for aircraft. This work was subsequently revised and adapted by the Douglas Fir Plywood Association for design and.use in building constructionz. Methods of construction of plywood web I-beams have been much the same for many years and revised design and fabrication specifications have been published Just recently3. They applied convent- ional engineering calculations using allowable design values of wood and made recommendations concerning the webs, flanges and stiffners of box beams. They were largely concerned with buckling of the web20 21 , and horizontal shear stresses . The Fbrest Products Laboratory found that it made little difference whether the face grain of the plywood webs was horizontal or vertical. Plywood webs oriented at 45 degrees, howevery were found to be substant- ially more efficient22. They also found that for thin beam webs significant increases in web shear resistance could be secured by reducing stiffner spacingao. Dawid Countryman, in full scale tests of plywood beams in 1944, found that nail-gluing was an effective method of 23 ' fabrication . Butt-Joining plywood web splices was also determined to be adequate to develop the full beam strength in both bending and shear. Countryman's tests showed.no buckling in the webs nor were any beam failures caused.by horizontal shear faults,.even though this was the limiting design stress in many of the beams. He concluded that a betterrbalanced‘beam might have resulted had the allowable horizontal shear stresses.for the plywood been higher. Based on the pioneering efforts made by the Forest Products Laboratory, other publications soon appeared from 'various sources. Because of the interest of the Douglas F1r~ Plywood Association in builtdup construction, it soon pub- lished a design handbook which presented to the engineer and architect useable formulae and design.criteria2. The DFPA also published a set of design specifications embody- ing the latest design procedures and methods for plywood I-beams and box'beamsz. The present published reports on the strength propert- ies of plywood I-beams indicate that the design strength may be predicted by existing engineering equations. Recent experimentation.at Michigan State Uhiversity6'l4'18 and previous work done by Radcliffe24 at Purdue University suggest that the recommendedeorking stress for horizontal shear of plywood is conservative and places plywood web structural constructions, such as I and box beams, at a definite design disadvantage. It is important to note that deflection in I-beams has two main components, flexural deflection and shear deflection. Flexural deflection is caused by the lengthen- ing of tension fibers and shortening of compression.fibers and is generally considered the major component of total deflection. Shear deflection, resulting from.horizontal shearing distortion of fibers, is of considerable import- ance in I-beams due to the small cross section of the web. Shear deflection is present in all wooden beams, but the sectional characteristics of an I-beam serve to amplify this deflection. Since shear deflection.has proven to be a significant part of total deflection, there has been, in recent months, an attempt to substitute the plywood.web with a web of thin sheet steel. It was felt that since the shear modulus for steel is much higher than that of wood, that the use of steel would greatly reduce deflection caused by shear. Research has been in progress in Washing- ton, D. C., on an I-beam which incorporates two webs of steela. This thesis is the result of research into the advisability of substituting one thin sheet of steel for the plywood web which has been used in the nail-glued I- beam. Results obtained in this research indicated that the use of steel practically eliminates shear deflection and merits further study in this direction. Purpose offithe Study The purpose of this study was to evaluate the stiff- ‘ness and strength properties of wood flange-steel web I- beams in terms of existing theory and engineering equations. The flexural behavior of half scale wood flange-steel web I-beams was to be compared with theoretically predicted behavior, not only with.actual results obtained for these beams but with plywood I-beams of similar section. This was to be done by comparing the theoretical and actual stiffness factors of the beams being compared. Similar tests were to be conducted on two full scale wood flange-steel web I-beams and to correlate these results with those obtained from model beam tests. Finally, an attempt was made to determine the effect on flexural behavior of the beams tested in relation to the number of nails used in fabrication. FMBRICATION OF‘BEAMS A. Model Beams Twenty half scale model beams of I section were con- structed in eight foot lengths and in depths of eight, nine, ten and eleven inches. There were five beams of each depth. All beams had 1 x 2 inch wood flange members and stiffners applied to both sides of the web. Flange and stiffner material was cut from No. l struct- ural grade 2 x 6 inch Douglas Fir and surfaced four sides to a nominal 1 x 2 inch dimension. Material showing serious defects was eliminated in order that actual full size beam fabrication would be duplicated as closely as possible. Web material was 26 gage cold-rolled galvanized sheet steel having an actual thickness of 0.0184 inches. Method of fastening the flanges and stiffners to web was by No. 6d coated box nails. Glue was not used in fabri- cation. In practical applications to actual beams gluing would add materially to the cost inasmuch as only certain expensive adhesives could be used. Beams were assembled using three different nail spacing arrangements to determine if a correlation existed between nail spacing and stiffness. One beam of each depth was nailed every two inches on both sides. Four inch spacing, on both sides, was used on two beams of each depth. 0n the remaining two beams of each depth nails were spaced at four inch intervals on one side only. All nails were staggered to effectively distribute the holding power. For nailing pattern refer to figure 2. '1! ill!” W/‘(J Awdufillirrnu IIIJ. / \ / , Am I AUIJ) \Jiuinulrfl mu JJAO< or I:O.H and) \lernw OJN:J/Q\/J/\I.v 0.03..» MJZliFO a any Model beams were constructed by fabricating two ident- ical frames of upper and lower flanges and vertical stiff- ners spaced twelve inches on center. The sheet steel web was then inserted between these frames and nailed securely as shown in figure 1. Forty small bending samples, thirty inches in length and nominally 1 x 2 inches in.section, taken at random from the same stock of material used to construct model beams were tested with a.Reitle universal testing machine using testing procedure as outlined in the ASTM, to estab- 1ish an average modulus of elasticity. Moisture content readings were taken for each standp ard bending specimen and also for each model beam at the time of test. An electrical resistance type moisture meter was used in these determinations. B. gull Scale Beams Two full size test beams were constructed for the purpose of correlating results of model beams. Both beams were 16 feet in length and 16 inches in depth. The method of fabrication was identical to that used for model beams. 2 x 4ginch flange and stiffner material used was a mixture of structural grade Douglas Fir and'lestern Hem- lock. It was used as recieved from the lumber yard."eb materiad was 14 gage, cold-rolled sheet steel having an actual thickness of 0.077 inches. No. 12d hardened steel nails were used to fasten flanges and stiffners to the KE'VE. as E. 515%.; / g A) Y4; J ' ' . m 0 A O O Q . O p o 1 g o D ’ 1‘! I. .7 l I C I O ' l ‘ g m I ' o O ‘4 ' o ' .‘ o - - . r'” . o :0 ‘ ‘1. ('7', g ' .‘ ‘ J: .. .- 'Wy'v, . r l . . i ., ,. _ ,, f 1 .7... -, ._ .., ._ . e ,_ . l T . . L a . _. 11 .. . ‘ ‘ 0 -mo_. -_:_ O - ‘ g . ‘ _J_ ' . Agnfln ‘A‘ g .4 A . 4 1 ' 0 To 0 o o . . o o ‘1 g . o O ’ I ' 'I L. ~ . .- i - -. . . -- m. V f 0 " I - 1 Y? I" “1‘I T 1.:— /?/1(7/ )1? I 114;}! I r I 12 i -_- ‘_ __I__ ”0'2: , 1') _ J, HEAVY “gigging KLVEKSE. swab K 0 ~ :0- ‘ _ 3 - I» ' .. . 5 ’ ‘7 ’. ' V‘.":‘“'~"‘-~‘ T41 4 pang-s ru-i ' :i r- b 1 ~ 1J'- '-‘ l ‘ '3. 7 l ‘5 "‘q-Fa‘.“ 3“ - . Lu" 1‘ 'g‘av: ‘ ,7 ‘tfl'u-‘rflanli‘iL" ‘ _f i C . i . . l 1 ‘ L ‘ 4‘ z 4' . A. J i I- - I I I g .. 77/ .1. r I '1. r “f ‘q u 4 1 I'D. 7 - f . . , AELIDILJA UklplkJCi- *-u-m 1%.- V i ——x KhVLR—‘EAE‘. blah—o ' If a I m I l r L o o o o —r T “‘ . P ' {'1 1; ‘ . g I _PF‘ ‘IL, “-1“ . H, .. at: 1 , . 4.. 1" , ~— ~ 1., 4 1 on K i ’ r- ‘ g .. i ". 4 “ I A ‘ e' V .‘J ’ ‘ V ' -___ O ‘9‘ y . ' é ’ "fi 4: F‘ 1 o f . ._.....- .- u A _ . J "ELL 1 1 ._.. 4 A L o " o o 0 fl J o ' i 4 i i_ . i Y r’ —T*—7 4‘ .4- 4” ‘ :7 . O . C ‘ . . i v 1 Q 0 C O m C O J , .. hr. “:3 1m —' ,t, yr 4!" '\ rm... .. . ' O ‘ .4 o r . J o [(5 ’ ‘. . ‘ '1 J r ‘ . - - J O ». ’4 >- 7% t .. ‘3 ‘- . ' ' 4 9 ; l" * - ;- ~ .1 ’ r" r ‘ 3 . 1"" _“_A_ _L ‘— n‘Iflf" “‘1 . m 3. “—1.;4 h. m‘ "L; .‘ ‘ O S ‘ ‘ I . O - ‘ ‘ ' O I f o 4 I 4 0 . o q ' p" " ‘1 LCTlQKJ L—JFT'JKVV’ KJ/XIL..H\JC-ED Luau 6§_/'§..L:.E=:-_-§_D_.E._’£>_L\ afieuzbz '1 HAILIHé SCI—l EDULE/ _ .—._—'— v—T i 5—..- .— 10 web. Stiffners on both sides were spaced at 24 inches on center; See figure 2. Eight 2 x 2 inch small bending samples, 30 inches in length.were cut from the same flange material used in fabricating the full scale beams and tested in bending to establish an average modulus of elasticity. ll TESTING PROCEDURE- L. Model Beams Model beams were tested in static bending in acuprd- ance with.ASTM standards. The load.was applied in a Universal Testing machine at a constant rate of 1/16" per minute mid span deflection. Beams were supported at each end by means of maple blocks and load was applied at two points along the 96 inch span. Loads were applied at 24 inches from each end of span. Refer to figure 3, for loading arrangement. Deflection was measured through the use of a deflect- ion yoke, supported at the neutral axis of the beam over' the bearing points. Deflection at the neutral axis at the center of the beam span.was determined by an Ales dial as: shown in figure 3. Deflection readings were taken for every 200 pounds force to failure. Loading was at 1/4.points. B‘. gull Scalem Two full scale beams were tested in static bending on a hydraulic floor type testing machine. Refer to fig- ure 7 for graphic illustration of testing set-up. The beams were strapped to the concrete floor in four places by means of angle iron and metal rollers and plates were used at every point of friction to provide freedom of movement. See figure 7. This was done to restrict buckling and assimilate practical use situations. Buckling had been the cause of failure in all model beans and every attempt was made to restrict it in these tests 12 by using the metal straps as referred to above. Load was applied by means of seven hydraulic.cylinders; spaced two feet on center; Beams were supported at each end of the span. There was no load applied at either end which resulted in a load being applied at each stiffner' excepting those located at each end of the beam. The area of each cylinder was 2.94 inches and therefore the indic- ated loads were multiplied by the area of each.cylinder to give the actual load applied in p. s. i. The seven cylinders were connected hydraulically with gages at each end of the hydraulic system. Loads were applied in incre— ments of 25 p. s. 1. These, as mentioned above, were the indicated readings and.were adjusted by the multiplying factor, 2.94, as discussed above. in Ames dial deflection gage was placed at mid span and readings were taken at every 25 p. s. i. to the closest 0.001". Readings were taken at the bottom flange rather than the neutral axis as in the case of the model beams, due to the type of test set-up used. Refer to figure 7. 13 JIIINDOJUOMQ GDFWJF (>407... JJ00/\\ M . .ijnwli. J].1.U/4/\ alfrnvlk. w. V..U.JD-- . t y 0 I J .,\ , ‘ . 3...... r... J .rJ/K W 10340 .JOFUJJudfl is. .5, I .n pascal - .. _ - 1 3 \I. {v . -la etyirlw. (Cu. a,-s.+x,1¢ at ,,...Ia..l.t. .J.nV. J..... 4-1.)...“ unhm 4...... .J..@.4..NW%. mam.“ :0” « Ki: u: .x.. .01 . , . I \ w. 3... a w . (:30 340 2.3. ..<.4 r \ \ _ / A / . , P\0 039. JIUPDJJ k4 \ \\ 1:1] .vjrrdoahan «with / dJJJON. .1352..- \n \dukju JKFJI.‘ .. Figure 4 Half Scale Madel Beam Under Test 14 Ei gure 5 Model Beam Showing Failure At Point Of Loading 15 16 Figure 6 Flange Slippage, Model Beam, Light Nailing. #7 .JdDOJUOdh 02.5:qu 3A. J44. mm “..ij .... .....N in \h.w\ . x. z. 2 A 3003. Saul JPJUUJOU 2. flatten + 3.50m 1.4.57». 6333.50 .58...an . . _ . . . 2 .2 .. . . / \Or 03.54.30 445/... 5.4.0. . . . / . . . .. . .. . . .. 2.20. w \- . . .... h3fl..d_Jfloa . .2 _ . .. _,..2J5s.ujoU_1. Jungle _ .u . 0 I I u v.‘ . .| . a M i” v \ . .vi / t . . .. L . . J. .11 . Jud; . . c . . . 4 . u .. . . . , c x... -... . ~ . 2 . . .--. 25% r. .2... inc? . _ .2 .. a . .2 .2 m A. . . . r 2 . . . ; . . . ..I If . . , ., . at f . 2 I .. . u . J . 1 .. r1 . .... . .; . _. ~ . . . I . . .. r. . . o . . .. .....- . o. - .. ... n\ . . . 4‘. ......G. - l . . . . . ... . ...! . . ...4 .. . .. , . . av.) . ... .. u .4 f e- f. ~ . . v . . . . . . . _ . . . . . . . u. ‘9" .D ‘. 2...! . \. a N FN I |.':H» vi. . . I .* . - .~ r l . . n. r |I 2 . «I q . |.' . . . x u! . q . - . . . . . .... . -. . -- a .2 .- . A - . . 2 . , . , A L . 2 ~ 1“ I JFvLIWI 1.. v7 V"! A\ . / / h mudalflru 033180)] . .0000 .vujiukmbm . v/ / (“HP“)D U.JD4N_O&LJ 0JO0JU Joustiu Juanndah .5340 duanmdaa I. JAG—1‘1...“ 000) IUJ‘UO JJDu Figure 8 Full Scale Beam Under Fall Load in Hydraulic Testing Machine 18 Elgure-9 View of Full Scale I-Bean Lgter'rest l9 20 TEST RESULTS Eggds a345llowable Deflection A load versus mid span deflection curve was plotted for both halt scale and full scale beams. The graphs are shown in figures 10, ll, 14. Graphs were plotted to show the relative stiffness comparison of both half scale and full scale beams due to spacing arrangement of nails. Results are shown in figures ll and 14. godulus o;:§lasticity An average modulus of elasticity ( Ea.) was establish- ed for the half scale and full scale beams. Small bendp ing samples or the same stock were used for this purpose. The formula used was: 1:. PL3 18—171 Where: ‘ - lodulus or Elasticity, p. s. i. a Total Load.on Sample, pounds. 1 Length of Span, inches. 4 a Moment of Inertia, inches . no r* 'U I! A e Deflection, inches. The average modulus‘or elasticity for the half scale beams was found to be 1.95 x 106. Fer the full scale beams it was 1.68 x 106. MoistureLcontent readings were* also taken and the average for the half scale beams was found to be 8%. For the rull scale beams the average was 13.2%. Refer to tables 1 and 2. Moment of inertia was calculated.ror the small MODULUS OF'ELASTICITY TABLE 1 MODEL BEAMS Sample Modulus of b d Moisture‘ No. Elasticity Least Dim. Great.Dim. Content 1. 2.0; x 106 .95" 1.91" 0.05 2. 2.2 .95 1.90. 8.0 3. 1.79 .96 1.32 6.5 4. 1.73 .97 1. 9 5.0 50 2049 '095 1092 05 6. 2.14 .96 1.92 7.5 7. 2.45 .97 1.89 8.5 8. 2.51 .97 1.89 8.5 9. 2-59 .94 1.90 7.5 10. 1.68 .98 1.89 6.5 11. 1.62 .96 1.92 6.5 12. 1.85 .97 1.91 6.5 13. 1.82 .97 1.91 6.5 14. 1.58 .97 1.91 6.5 15. 1.72 .9 1.91 6.5 16. 1.57 .9 1.93 6.5 1 . 2.72 .9 1.90 7.0 1 . 1.53 .9_ 1.92 6.5 19. 1.56 .98 1.90 7.0 20. 1.74 .98 1.88 5.0 21. 2.22 .95 1.93 3.0 22. 2.1 .97 1.89 6.5 23. 2.58 .98 1.90 9.0 24. 1.48 .97 1.g3 6.5 250 2049 09 lo 9 ;05 26. 1.97 :9 1.92 .0 25. 1.99 .93 1.89 7.0 2 . 1.51 .97 1.94 g.0 29. 1.97 .93 1.93 .0 30. 2.25 .9 1.93 7.5 31. 1. 2 .9 1.96 11.0 32. 1. 5 .99 1.97 11.0 33. 1.53 .99 1.9 11.5 34. 1.70 1.00 1.9 11.0 35. 1.79 1.00 1.99 10.0 36. 1.75 .98 1.98 12.0 350 1093 098 109 1205 3 . 2.11 .9 1.9 11.0 39. 1.83 .9 1.98 12.0 40. 2.04 .98 1.98 10.5 Total: 78.15 x 106 38.70" 77.05” 327.5% average: 1.95 x 106 .97” 1.93” 8.2% 21 MODULUS OF‘ELASTICITY FULL SCALE BEAMS TABLE 2 22 Sample Modulus of b d Moisture‘ No. Elasticity Least Dim. Great.Dim. Content 10 1085 x 106 1060" 1070" 15.5% 2. 1.40 1.61 1.72 14.8 3. 1.40 1.61 1.73 15.5 4. 2.10 1.59 1.77 15.5 5. 1.92 1.52 1.72 11.0 6. 1.92 1.58 1.75 11.0 7. 1.55 1.55 1.74 11.5 80 1036 1060 1077 1008 Total: 413.50 x 106 12.667 13.90" 105.6% average: 1.68 x 106 1.58" 1.74“ 13.2% These calculations were derived from eight small bending samples, 30 inches in length, using the equation: 91.3 E' 4810. Where: . Modulus or Elasticity, p. s. i. . Load, pounds. - Length of Sample, inches. 4. HF'UH - Moment of Inertia, inches A . Deflection, inches. 23 bending samples for the purpose of determining the above modulus of elasticity ( Ea ) using the equation: 0113 I a 12 Where: I”: Moment of inertia, inches4. b a Least dimension, inches. h.: Greatest dimension, inches. Eguivalent Sections In order that standard equations could be used in comparing wood flange-steel web I-beams with nail-glued wooden I-beams or similar section it was necessary to convert the steel web to an equivalent section or wood. This was done by using the equation: 8 t'n_xts Where: t' . Thickness of equivalent web or wood, inches. Es 3 Modulus of elasticity of steel, p. s. i. E. a Modulus of elasticity of wood, p. s. 1. t8 w Thickness of steel web, inches. This method.was used for both halt scale models and full scale beams in order to calculate the theoretical moment of inertia ( 1th ) and the theoretical stiffness factor ( Elth.)’ For these'values refer-to tables 3 and 4. 24 Moment of Inertia The theoretical moment of inertia was calculated for each beam using the equation: b h3 - 2 b1 h13 I a th 12 'Where: 1 b g Total width of beam, including both th2' Theoretical moment of inertia, inches4. flanges and web, inches. h a Total depth of beam, inches. b e Flange width, inches. h g Total beam depth less twice flange depth, inches. These theoretical moment of inertia ( I h.) values were t used in computing the theoretical stiffness factors ( Elth ). These values can be found in table 3. $11 ffness Factor For each model beam and full scale beam a stiffness factor, both theoretical ( 81th.) and actual ( Elact ), was computed. A theoretical E1 value was also calculated for an equivalent nail-glued I-beam of similar section. This E1 value was calculated without subtracting that amount due to shean‘so that a more accurate comparison could be made with the wood flange-steel web I-beams being tested in this research. The equation.used to 25 30:0...0 0.30.33 ...... nw U DQFUJJumalalqO... .. Q. 4.1“- anw 0033.43 F103 nlil .. . 073.43 (3534. lull. . $3.123]. ..\/\/14JT. u £030..» L\.\ \ i \ \ \ 1#— x . Ilka"! 14...] lIII-IIIIInIl-Illllrl go “.0 0.0 70 Av 0.9103. 3. .JOFUJJido r _ . . _ «WIFOJO V0 F‘lflOd 1% 26 @110]. I 30.1rUstlmmn. V0 0.0 0.0 ..0 My ‘ - 1‘ 1‘4 4. i A. . l . a H W; a ‘ m fl<.\. M J30 123k . J02 down) a fi 36: f - -.w . _ . \\\\\ L N}. X“ ‘ . fl _ i I\ ‘ , . .‘ _ I \ ‘ h .k a " \I . y \‘ ‘ '1 L \ l ‘. "Y‘ .rJJO Jazw \ - .fidflfi. “wa ..mmopm 75/ \wjoéjoéanfi \\ . . 15.0-016430 .V “WinA Ikoouwjadonh. ///1 x m ....an3322 <35J< . - . @333] >231 V _ u . . ¢ . _. w . H. _ _ ‘ calculate these EI values was: 6 A i 81 . A Where: E a Modulus of elasticity, p. s. i. I a Homent of inertia, inches4. Ai a The sun of i of the area of the bending moment diagram, shown in figure-15, multiplied by the distances of their respect- iwe centroids from the left edge of the diagram, inches3.‘ This is sometimes referred to as the second area moment theorem. A: Total deflection measured at mid span, inch. For results of this El comparison refer to table 4. Graphic: illustrations of RI plots are shown in figure 13. The effect of nail spacing on the stiffness factor can also be seen in figure 13. Shear Deflection Shear deflection was calculated for one model test beam to show that it was insignificant and thus could be ignored. For the method of calculation refer to Appendix. In order‘ that a true comparison of these beans with a nail-glued I-heam of similar section could be made, it was necessary to calculate the shear deflection of an equivalent nail-glued I-beam and add it to the deflection 27a attributable to bending. It was felt that only in this way, could a true comparison be made. Refer to Voelker 18 thesis for calculations . fiercentagg of Efficiengz The effect of nail spacing on the stiffness factor- of both model and full scale beams, mact values were.- divided" by the El values to find the percentage of th efficiency. These results are shown in table 5. _D/7 . -. -. 9/7 ’24“ 45" . ”24‘ ---- - . . - X . . - . . . I .J‘RE'E: waggégfsgzz. R 'D/’1 Rq'P/Q V3 LBS. + 9’1 P/‘D // //'~' 7. // I //* Qfléégu$$éQAA / 1 o/./// / r‘ //,/"‘l / . . //) - f' .1 / I ” / / / 9/7 pm « 2' : Jab/A EEUDIHS /\O/’\E.HT —‘t r r 7 Iv Ir r/V/v‘f/Y 7 f , ’7 7 V—V 7 V 7 ' / , ’1‘ / I, I, I I ’ '( ’/,/‘ r " I . n / // / ’, . I, / . / .fl [1 / / l ’1 ,4" / / // I / / J / / /_,/ ,7, / ' // . __’I J '/ / . / ' l/I ’ . / [I .’ / . /' /’ [I / l/ ' o / ' 2. , , , / . / /'/ , / / — I I / L4, 4% g '1 1 1 i l I" L A ¥ . /’ 4 4 gauge: to buaAQ + aauanue mgur 51W “- f“ 40d” .WLL Wemaa.(u..+_azn)_ Mgaaza; -- -- l - L ”I.” f" ’“ ‘ ‘ ‘ L7 5": TUBOREJ’LCAL. (:31)? 5-: ... HEAVV LJALLLUG i; E -——-— -—-——--~—- 5.1: .... AabLuA umuue L E -------r- k“ LIGHT Hklpluéa “ I T' .1 ‘ UJJL. -C—Z:>L..LJE=.b (V)? 3 i « “(VATHOUT :UbTQAcn L i L ! SHEAR. mac-Lennon !! i i: .z E L L i ‘ i L L I i e 9“ L0” 11" . POUNDb PL; CYLJHELQ LOAD IO'Z‘B 081 - 735 06‘2- 5 NA“: ‘ r---__.._..- _. . r-w-w f 'zbre‘/c.YL.\uDao. t: ‘ LQUIVALBHT To “1000‘ 701“. nous - ‘1 cvuucmml _£.IG5UI_2,LE=,: IA- 'f [HOAD umbLF-LLCT\OU CURVE. FULL. 5CALE,_ t DLFLECT‘OU ‘m IUCHEB‘ bEAAD L . - . : L : i g 0-3” o-A' ‘ 0-5“ 0-6“ 0-7 ~ 31 P D D D D D D 1' g ' - 4' x H, IG' (2. :3-59 R,u 3-59 5-59 '77, 7* fl 0 :4 -, « - twp/’4‘ :6??? ,7," 71 - .50," ///, /, I"// lg/l. //// /’_/", If .74 0 WA 51/. 5/. Z 42/ 12.51: if”: ,7l-f7—7/7/ ,7 why, //Vrv,’7/ [/1 V // ' / / .4 L/// ////// y/ / / /"/ ’ -./,,I , / // / /// I. /4 1.54)1 A 2, C -I////: /'tests correlated very closely with results from model beam tests. Elth and EI werezcalculated.and the percentage act of efficiency worked out and compared with model beam results. The correlation was excellent. These can be seen in table 5. Because of the.load limitations of the testing machine used, the proportional limit was not evidenced. At no point‘was any damage to the beans observed and only a very slight buckling occurred.when maximum load ‘was applied. When pressure-was released, no damage of any description was evidenced. In neither the model nor" the full scale beam tests was; an attempt made: to correlate the modulus of elasticity values. Average modulus of elasticity values were deter- mined for both types- of beams and an analysis of variance calculated for small bending samples, of the same stock as used in model beam fabrication. The results of this analysis can be seen in the Appendix. 99% of the samples: fell within two standard deviations with the majority fall- ing within one standard deviation. 41 CONCLUSIONS AND RECOMMENDATIONS As a result of this research project, it is concluded that: 1. Wood flange-steel web I-beams are stiffer than nail- glued plywood I-beams of similar section. This is true where heavy or medium nailing is used. However; where relatively few nails are used, as in the caseof light nailing, the nail-glued I-beam appears to be slightly ‘ superior. This conclusion is based on the assumption that shear deflection is not deducted from total deflection in calculating the stiffness of the nail-glued plywood I- beam. It is felt that this is the only accurate method of comparison since the ultimate ' on-job ' strength should be the only consideration in evaluating the two types. 2. Nailing is an effective method of fastening the wood flanges and stiffners to the sheet steel web. The effic- iency of this method of bonding increases;proportionately with the number of nails used. Gluing would add mater- ially to the cost because of the type of adhesive required to give an adequate bond between wood and metal. 3. Shear deflection is of practically no consequence in design of this type of beam and can be ignored.since it is less than 2%. 4. That lateral instability is a most important consider- ation in the design of this beam for ultimate failure. It becomes more critical as the span-depth ratio increases. However, it should be noted that it does not become a problem until well beyond the recognized.allowable design deflection which is normally taken to be 1/360 of the span. The results obtained in this study tend to indicate that the beam has considerable merit. The negligible effect of deflection due to shear as well as the fact that an adequate bond can be achieved without the use of an .adhesive, would make this type of beam more practical, than the nail-glued plywood I-beam, for many job situations. It is felt that the cost of these beams may be slightly higher than for the nail-glued beam. However, the added strength, stiffness and the ease of fabrication may well offset the additional cost. Further steps should be taken to evaluate the comparative cost factors involvedh Further study should be undertaken with a much larger sample to arrive at more conclusive results. The results presented, indicate the need for further work, to arrive at empiracle design equations. Further experiment- ation could be done with different spacing of stiffners, i. e., four feet on center instead of two feet. Other types and gages of steel could be tried. APPENDIX ANALYSIS OE VARIANCE N«u 40 Small Bending Samples. E - Modulus of Elasticity No. R No. Bi 1. 2.0 1'10 21. 1.24 x 106 2. 2.2 22. 1.16 3. 1.80 23; 2.58 4. 1.73 24. 1.48 5. 2.50 25. 2.49 b. 2.14 26. 1.97 g. 2.45 2 . 1.99 . 2.51 2 . 1.51 9. 2.59 29. 1.97 10. 1.68 30. 2.25 11. 1.61 31.. 1.32 12. 1.85 32. 1. 5 13. 1.82 33. ’ 1.53 15. 1.72 35.« 1.79 16. 1.57 36._ 1.75 1;. 2.72 3 . 1.93 1 . 1.53 3 . 2.11 19. 1.56 39. 1.83 20. 1.74 49. 2.04 C 1095 x 106 average €5.o C51? -‘«EEX’2 . N {I . “3.760.283 . 3.623.312 GE.: Therefore; 1 standard deviation . I vrliflaéll3.r 40 ".29 .4 111., 6.1 2 E40) .29 a V .082,971 45 S HEAR DEFLECII‘I ON A.m4Ab §.A, and for uniform loading, simply supported beam tAb‘m 5‘w L4 384 E r ‘s g x L2 I 8 A G Wheres A m Deflection at mid span, inches I m Load, lbs. per inch of span L s Span, inches; E m Modulus of elasticity, p. s. i. I m Centroidal moment of inertia of area, inchee4 A a Cross-sectional area, inches? 6.: Modulus of rigidity, p. s. i. K.g Shear deflection constant depending on geometry of section.. For the:case~of an l-beam sections 2 2 . KIA. ....bh -411. b11[8 8 (b-bl] Where! bl m Web thickness, inches b m Flange width, inches‘ hl s Web height, inches: h, m Total height'of section, inches. Forrthelcase of a beam with 14 gage steel web and nominal 2“ x 4” flangesg an equivalent section is used for the- case of computing the relative portion of deflection due to shear. 46 Thus, for a beam of 16 inch total depth: bl a 0.0766 inches 6 m 0.0766 . 2(l.63) €39;§I%%-»e 0.295" m 0.295(‘16 )3 - 0,9166 1 1.26 )3 m 96.8 in4 12 :106 p. 9.1I. 30 x 100 p. s. i. 16.0“ 8.74” 2.445( from solution of the above equation ) was)”: 5' ...- ‘ II a I. II x A . 2.77 in2 Bl For an arbitrary load, W, below the prOportional limit Ab and"8 may be computed. For the fraction due to shear deflection as a percentage: A s % ‘9 ' x. 100% m 2% for this case. we LI TERATUREC CI TED) L. 2. 3. 4i. 5. 6. 7. 8. 9. IO. 11.. 12. 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