STRESS AND STIFFNESS PROPERTiES OF REENFORCEE) WOOD BEAMS Thais {'oc eh. Dogma ei‘ M. $. MECHIGAN STATE UNIVERSITY iarflan A Tseiakfies 1962: IIIIIIIIII IIIIIIIIIIIIIIIIIIIIIII L/ 31293 01059 3659 L I B R A R Y 1] Michigan State University FE STRESS AND STIFFNESS PROPERTIES OF REINFORCED WOOD BEAMS BY JORDAN A. TSOLAKIDES AN ABSTRACT Submitted to the School of Graduate Studies of 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 1962 ApprovedLMlM/ ABSTRACT This study describes the manufacturing and testing of twelve reinforced wood beams with cross section of 1.5 by h.S inches. Nine of the beams were 96 inches long and three AS inches long. The beams were divided into three groups accord- ing to the board from Which they were cut. Each group was constisted of four beams, each one of different type. Three beams of each group were reinforced with steel strips. One was reinforced in the sides (Type A), one on top and bottom (Type B), one the same as Type B but of MS inches length (Type b), and one left unreinforced(Type C). The purpose of this problem was to evaluate and compare stress and stiffness properties of the beams when subjected to static bending. Also, an attempt was made to obtain certain information about the behavior of the reinforced beam within the two different types of reinforcement used in this study. Stiffness properties (a function of the modulus of elasti- city and section properties) calculated for all beams were found to be 2 to 3 times greater for the reinforced beams as compared to the unreinforced ones. Among the two types (A and E) Type B indicated 10 percent higher values. The load carrying capacity of the reinforced beams was also increased. Calculations at proportional limit showed an increase between 35 and 50 percent. At maximum load the ir- crease was much greater. Eleven of the beams failed in tension and one (reinforced) in compression with buckling in the compression side. Theoretical stiffness values were also calculated. A mathematical model of the beans' cross section was built, using the weighed ratio of the two moduli of elasticity of the composite beam. This gave an I form cross section in which the neutral axis was located and the inertia of the whole transformed cross section was calculated with the parallel axis theorem. In general, a close agreement was observed between theoretical and practical stiffness values within groups; but a small variation was indicated among the groups. The grooves used for the placement of the steel strips proved to be critical for the whole construction, and further study is needed toward this direction. STRESS AND STIFFNESS PROPERTIES OF REINFORCED WOOD BEAMS By Jordan A. Tsolakides A THESIS Submitted to the School of Graduate Studies of 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 1962 ACKNOWLEDGEMENTS I welcome this opportunity to express sincere thanks. The following study has been achieved through the cooperation, understanding, patience and guidance, of numerous individuals who have assisted the author in this specific endeavor and in his general education. Special thanks to Dr. A. Sliker for his indispensable help, direction and criticism, without which the fine points of this study could not have been worked out. I am indebted to Dr. A. Wylie and Dr. 0. Suchsland for overall advice and general assistance. Finally, I most sincerely express gratitude to faculty and staff members of the Forest Products Department at Michigan State University who have come to my aid in count- less ways. ii 2. TABLE OF CONTENTS Ammmmmmmmms. ... ... ... LIST OF TABLES . . . . . . . . . . . LIST OF FIGURES . . . . . . . . INTRODUCTION . . . . . . . . . . . . 1.1 "' Definition 0 o o o o o o l. 2 - Historical Background . . . 1.3 - Testing of Reinforced Importance . . . . . . l. h- Purpose of the Study . . . PRO CEDURE o o o o o o o o o o o o o 2.1 Description of Test Beams 0 Materials Used. 0 o o . Lumber Preparations . Steel Preparations . Adhesive Preparations - Assembly Procedures . - Strain Gauges . . . . O «Jownfirunu l 0.00.. 00.00. 000.000 NNNNNN TESTING PROCEDURES . . . . . . . . . 301 " Static Bending . o o o o o 3.2 - Compression Parallel to ANALYSIS OF DATA . . . . . . . . . u.1 - General Considerations . . 14.02 "' TeSt Data 0 o O O o o o o h.3 - Theoretical Data . . . . . RESULTS AND DISCUSSION . . . . . . . 5.1 - Stiffness and Load Carrying Long Beams . . . . . 5.2 — Stiffness and Load Carrying Short Beams . . . . . . . . 5.3 — Stresses in Beams . . . . . 50L). " Failure 0 o o o o o o o o 0 CONCLUSION AND SUMMARY . . . . . . . APPENDIX . . . . . . . . . . . . . LITERATURE CITED 0 . . . . . . . o o o o o o O O O O O O O O o o O o o o O O O o o O o O O O O O O O 0 0 O o 0 o o o O O O O O 0 Capacity of Capacity of Page . ii . iv . v . 1 . l . l . 5 . 6 . 7 . 7 . 7 . 9 . 10 0 10 o 13 . 13 . In . 1h . 17 . l9 . l9 . 22 O 28 . 38 . 38 . lIB . LIE . no 0 1+8 . S2 . 56 Table l. 2. 3. LIST OF TABLES Page Actual Size of Specimens . . . . . . . . . . . . . . 12 Moduli of Elasticity in compression parallel to grain as determined from.2" x 8" x 8" test specimens . . . 18 Experimental and Theoretical Stiffness values for test bems O O O O O O O O O O O O O O O O O O O O O 35 Bending and Shear Stress for test beams . . . . . . 36 Strength and Strain Data . . . . . . . . . . . . . . 37 iv Figure No. l. 2. ll. l2. 13. IR. 15. 16. 17. 18. LIST OF FIGURES Page Steel reinforced wood beam according to a German patent No. 233658 (1906) . . . . . . . . . . . . . . . 2 Reinforced wood beam.with longitudinal reinforcement, in both tension and compression sides . . . . . . . . 2 Various types of reinforced solid timber . . . . . . . 3 Cross sections of reinforced beam types used in th e S tu dy O O O O O O O O O O O O O O O O O O O O O O 8 The two types of reinforced beams used in the study and the location of the reinforcement . . . . . . . . ll 15 SR-h static strain indicator . . . . . 16 Testing procedures of Type A and Type B beams . . . . Baldwin type M, Load deflection curves for long beams . . . . . . . . 23 . . . . . 2h 25 curves for short beams . . . . . . . . 26 Load deflection curves for long beams . . . Load deflection curves fer long beams . . . . . . . . Load deflection Strain.measurements recorded surfaces at mid-span of long Strain.measurements recorded surfaces at mid-span of long Strain.measurements recorded surfaces at mid-span of long Strain.measurements recorded on tension and compression beams . . . . . . . . . . 29 on tension and compression beams . . . . . . . . . . 30 on tension and compression beams . . . . . . . . . . 31 on tension and compression surfaces at mid-span of short beams. . . . . . . . . . 32 Experimental and Theoretical beams Types of Failures in static bending . . . . . . . . Shear and Bending Moment Diagram.. . . . . . . . . V stiffness values of all ooooooooooooo39 . 52 . . Sh 1. INTRODUCTION 1.1 Definition of Reinforced wood beams: A reinforced wood beam.is a wood beam assembled in com- bination with some other material in order to improve a desirable strength property. In the present problem.the term "reinforced" is used to describe a wooden beam with steel strips inserted in milled grooves in the span direction. 1.2 Historical Background: Although a number of papers have been published on the general subject of wood reinforcement very few were close to the subject of this particular problem. One of the first ideas for reinforcing wood was presented by C. Volk in Germany in 1907.6 His construction was of a very primitive nature, con- sisting of wooden boards placed on top of each other, and tied together with metal strips (see Fig. 1). In 1921 J. B. Aatila from.Chicago, Illinois, registered a type of hollow rectangular wooden beam comprising solid upper and lower flanges that were thick and slab-like, and thin parallel connecting webs of flat laminated wood veneer 13 (see Fig. 2). Later in 1926 a German patent (D. R. P. 5u7576) was filed by A. Fischer. In this patent another type of solid timber, reinforced with steel rods, was introduced. Steel rods were fastened to the timber with a type of elastic cement (Fig. 3). hi ’4. (I. O H 0 Steel rein‘orced wood tease according to a German patent No 233653 (1507 . Bram consists of a numter of boards. which are connected by crosswise glued reinforcenents. Fig. 2. Reinforced wooden team, with longitutinal reinforcement in both tension and compression sides. qO Various types of reinforced solid timbers. Fastening of metal to wood was done with an elastic cement. LI Fischer's results wenadoubtful because of the glue used. The concept of combining solid wood with steel is particularly important today, due to the fact that adhesives have been imp proved tremendously. J. F. Seiler, in 1932, introduced an original work of outstanding value to this field; the development of a proce- dure for the structural assembly of composite laminated wood- concrete construction.h This combination has become a rather common practice today, for bridges, pier decks and miscelaneous heavy duty services. Trilaminated wood-steel beams are sometimes fabricated.2 In such a construction the core lamination is of wood and the flanges are of steel. Another type consists of a wooden core encased by a welded steel shell. Fastening of the metal to the wood (in both cases) is usually done by mechanical fasterners, such as bolts or pins, which secure the wood core to the flanges or to the metal shell. The subject of reinforcement with metal strips of various cross sectional areas, placed in milled grooves and glued with wood, was experimented by H. Granholm.in 195k.6 Today many workers are engaged in studying the technical possibilities of combining timber and metal of various forms in order to obtain beams that could be used in practical engi- neering construction. Wood-aluminum beams were investigated by R. Mark.hr Also, an experiment of laminated wood beams reinforced with.aluminum was recently done by A. Sliker.ll A number of other workers have been engaged in research of I beams, reinforced with steel bars or trellis beams with braces, built of wood members, and sheet steel strips.10 All the above mentioned experiments by various people present a historical picture of the progress in reinforcement work to date. 1.3 Testing of Reinforced Beams and their Importance: Wood as a structural material has good strength properties, it is easy to work, is light in weight, has good insulating values, and is moderate in cost. Metals on the other hand are characterized by high strength, are heavy, and when in thin sheets lacking of stiffness. A reinforced wood beam combines the good qualities of both, and compensates for the less desirable qualities of each. Where a strength/weight ratio is of great importance, the combination of wood with.metal can be of maximum value. Im- provements in strength, stiffness, dimensional stability, and other advantages, such as light weight compared with.metals or concrete, more fire resistance, and improved resistance to weather and decay, make the wood-metal combination an.important product. Adding to this the decreasing amount of first grade timber, and the competition that wood faces in the market to- day, a broad field of applications would be available for wood derived products. l.k Purpose of the Study: The object of this study was to evaluate and compare the stiffness and strength properties of two types of reinforced wood beams and one of the conventional type (unreinforced). The beams were constructed in an attempt to determine: 1) Whether or not there was any increase in stiffness by changing the orientation of the stiffening material. 2) The differences between theoretical and experimental stiffness values. 3) The load at failure, the type of beam failure, and the behavior of reinforced beam as compared to unreinforced. 2. PROCEDURE 2.1 Description of Test Beams: A total of twelve beams with like cross sectional dimen- sions (1.5 by h.S inches),were prepared in this study. Nine of them.were 96 inches long, and three were 45 inches long. Typed as follows, the separate groupings included: Type A: Three beams, each reinforced on two opposite vertical sides. Type B: Three beams reinforced top and bottom. Type b: Three beams reinforced as Type B, but of shorter length. Type C: Three beams with no reinforcement. The above specimens were divided into three groups. The members of each given group were cut from a single board and consisted of four beams, one beam of each type. For the sake of simplicity each group was given a number which together with the letter characterizing the beam type would be the code number in the following pages (see Fig. A). 2.2 Materials Used: Defect free and kiln dry Redwood (Sequoia sempervirens) was used in this study. The lumber was flatgrain. Three pieces of nominal 2 by 12 inches and 16 feet long, boards were used. In selecting the lumber, attention was paid as to the slope of grain and growth rings, in order to elimi- nate variations between the three pieces as much as possible. Fig. 1;. Cross sections of reinforced beam types. Both beams have been cut from the same board. Their moisture content, tested by a resistance type moisture meter, was found to be approximately nine percent. As a stiffening material a mild hot rolled steel was used. Data given by the manufacturers, indicate an average modulus of elasticity for tension and compression of 30 times 106 pounds per square inch, a yield point of 70,000 pounds per square inch, and hardness 163, under the Bernoll Scale. The nominal dimension of the individual pieces was 1/8 by 1/2 inch. Because of the nature of beam types (milled grooves) which did not permit application of sufficient pressure when steel strips were placed in the milled grooves, it was im- portant that a gap filling glue be used. The epoxy resins were best suited for the purpose of the project, since they eXhibit little or no shrinkage from.loss of solvent. A comp mercial epoxy-resin adhesive, Hysol 2030, and catalyst 0-1 was utilized for wood to metal bondings. 2.3 Lumber Preparations: Each 16 foot board was sawed lengthwise into two halves and each.half was cross-sawn into two pieces. In this manner four beams, one of each type, were obtained from each board. Then each beam was planed into final dimension of 1.5 by h.5 inches, and the grooves corresponding to the orientation of reinforcement in three of the beams were made with a circular saw. 10 In Type A beams, the size of the grooves was 1/8 by 1/2 of an inch, and in Type B, 1/8 by 9/16 of an inch. An essential condition in designing the beams, was to safeguard the reinforcement against buckling. This was done by placing the milled grooves in Type A one half of an inch (including the grooves) inward from.the top and bottom of the beam, and for the Type B, one half of an inch inward of the sides of the beam (see Fig. 5). In Type B beams, the depth of the groove was 1/16 of an inch larger than that of Type A. The reason for this was that it was not desirable to apply the load directly against the steel, during the testing procedure. Table 1 gives the actual size of specimens and the loca- tion of the steel strips in the grooves. 2.u Steel Preparations: The surface of the steel was prepared for bonding, by sanding it with a No. 50 Aluminum Oxide abrasive. During this process the surface of the metal was slightly scratched and some metal was removed. 2.5 Adhesive Preparations: The adhesive was mixed at a weight ratio of 100 parts of epoxy (Hysol 2030) to 8.8 parts of catalyst (0-1). The catalyst was poured into the epoxy and the mixture was stirred for five minutes. as... .5 3 3:. :33 :35... no .25 23 3a .m 6: < 11 Had T l a: » Z 1 I. 12 2010 1 - mm 01.0 of ”no. in: 110.6 00001 Tic-{tun 0: Jul , lantern-non“ Length Into: :16“ noun '1“! 3m: ‘ 1 1 - 1’ 1.500 10.512 .12: .511 .576 .m - 96 a. 1 1.500 1.500 .m .500 .379 .500 .037 96 0 - 1 1.505 6.500 -‘ - - - - 96 A - 2 1.505 11.510 .125 .516- .375 A73 - 96 l- 2 1.500 0.990 .125 .519 ‘ .380 .1090 .009 96 o - a 1.505 #510 - - - - - 96 A - 3 1.995 3.995 .m .507 .375 .1081 - 96 3- 5 1.1095 10.595 .126 .507 .375 .993 .027 96 0 - 5 1305 b.1995, - - - - - 96 b- 1 1.505 M505 .125 .500 .360 .535 .032 #5 b - 2 ~ 1.505 6.500 .125 _ .506 .55» .507 .036 45 b - 3 1.500 15.505 .12» .506 .350 .552 .036 A5 0 1.000020 ”for to the up. of been. labor actor to board from Not «Ah Mu m .40. 13 2.6 Assembly Procedures: Immediately after the adhesive was mixed, it was applied into the grooves with a small brush and the steel strip was imbedded. When all four strips were placed, wooden clamps were used to secure the strips in the grooves and to apply a small pressure. Then the beams were left for 2h.hours to cure at room temperature and were removed to a conditioning room at 70°F. temperature and 60 percent relative humidity, for a week. 2.7 Strain Gauges: Wire, electrical resistance strain gauges were placed on the top and bottom of each beam. The gauges were made from 120 ohm.lengths of 1 mil constantan wire which were formed into the shape of a hairpin when bonded to the test members. 1LI 3. TESTING PROCEDURES 3.1 Static Bending: In general the testing procedures prescribed by the American Society for Testing Materials (Designation D 198-27) were used.1 The test was performed in a 100,000 pound Reihle Universal Testing Machine. According to A. S. T. M., the specimens were measured to a nearest of 0.001 inch 1’0.003 inches for the cross section and the results were recorded (see Table l). The beams were loaded at third point and the load was applied at a rate of 1/16 inch per minute. This speed is not the one recommended by A. S. T. M. but it was used in order to facilitate strain gauges reading at each deflection interval measured. The span of the long beams was 90 inches and of the short ones 39 inches. The method of testing and the apparatus used are illustrated in figure 6. Loads were recorded to the nearest 10 pounds at 0.025-inch intervals of mid-span deflection with an Ames dial gauge read— ing to 0.001 inch. This gauge was held by a yoke, supported at the beams' end and was mounted on the neutral plane of the specimen. Strain readings were also recorded at the same intervals (0.025 inch) of the deflection gauge, with two strain gauges mounted on the mid span top and bottom.surface of the beam. These gauges were connected with SR-h Baldwin Strain indicator, measuring microinches per inch (see Fig. 7). I: .mpnmaohdmwme cowpooHMod you omsww Head esp mo newBEOOH as» new .QOHpEOAngm chH Mo venues on» opez .Emop 4 make a macaw oaseofie.u£w«u cue .smop m mama mo wuwmep macaw endpoam when .m 0mg 16 Fig. 7. Baldwin Type M, SR-LI, static strain indicator for making strain measurements. 17 3.2 Compression Parallel to Grain Tests: After each beam.was tested in bending, two pieces of wood were cut from between reinforcements, close to the failure and laminated together to form a standard A. S. T. M. compression parallel to grain specimen. The procedures described by the A. S. T. M. (Designation lh3-52) were followed in this test. The specimens were weighed and measured to an accuracy of 0.001 inch for the cross section, and 0.01 inch for the length and the results were recorded. A Reihle 50,000 pounds testing machine was used, for the compression testing. Following the test, the specimens were placed in an oven at a 103 : 2°C. for moisture content, and specific gravity calculations. This test was done in order to find out the modulus of elasticity of the wooden part of each beam. The results of this test are illustrated in Table 2. 18 1.010 2 «- nodal: 0! 1100010109 in Output-1011 parallel to ("in u determined from 2' x 2" x 8' tut spout-0110 In- let-taro 99001!“ locals. of In»: 0000.00 01-17107 ’ Dummy noun. Pomnt ' 1000 10.0.1. ‘- 1 806 .2. 90802 n -, 1 ' 0.5 .29 1,052.6 0 - 1 0.0 .29 1,000.9 A - 2 0.0 .00 1.595.} n - z 9.3 .02 1,726.9 0 - 2 0.9 .00 1,505.5 A- 3 0.5 .30 1,051.5 ' 3 ° 3 9-9 .39 1,291.1 o -‘ 3 9.3 .39 1.302.0 b . l - «- 1,010.0 Average of b - 2 - ~ .._. 1,570.0 01.0 m "I10.- 0 - 3 ‘- - 1.21.0.0 are and. .Iand 011 mu 0:: night and vols-0 at 0000. 19 M. ANALYSIS OF DATA h.l General Considerations: The two material beams have different moduli of elasticity for their components. When these beams are subjected to bending within the elastic range of each material, the following assump- tions of the flexure theory are valid: a) Plane sections at right angle to the axis of a beam remain plane. Therefore the strain.must vary linearly from.the neutral axis. b) The neutral axis passes through the center of gravity of the section. 0) The modulus of elasticity of each component is the same in tension and compression. Then, since the elastic case is considered, stress is proportional to strain, and the stress distribution follows a pattern depending upon the position of the reinforcement on the cross section of the beam. Because M.E. of steel is greater than that of wood, stresses are greater in the stiffer material, at the same distance from the neutral axis. A common technique for calculating moment of inertia and stresses in composite members is used, as described in Popov,9 by constructing an equivalent cross section of one material. For the reinforced test beams, an I shape results. This I form cross section is termed, transformed cross sectional area. The two material beam, when transformed in I cross section beam, is considered as a one material beam and the usual Flexure Formula applies. In order to achieve this I form 2O cross section, Popov utilizes the E steel/ E wood ratio. Through the use of this ratio, multiplied by the width of the steel strip, the breadth of one of the flanges of the I form cross section was found (in terms of wood). Est b1”? bl = the breadth of one of the flanges in inches. b = the width of the steel strip in inches. Est: modulus of elasticity of steel in p.s.i. E = modulus of elasticity of wood in p. s. i. The modulus of elasticity for steel was known and modulus of elasticity of wood was calculated in a test with compression parallel to grain. Then the bl value multiplied by two (in this problem) plus the width of the intermediate wood (web) gave the total width of either upper or lower flange of the transformed I section. The stresses and strains of the I form beam.vary linearly from its neutral axis, and the stresses for the material of which.the transformed section was made can be calculated from the conventional stress formula. For the steel the following formula has been adopted for 21 the purpose of this problem. Ic "Est 6813:]: XE Ky w c which simplified gives _ M OSt _ fx_'x n where 0': stress in extreme fiber (subscripts refer to wood or steel) p.s.i. M = maximum.bending moment, pound - inches. c 2 distance from.neutral axis to the furthest point of the wood in inches. I = moment of inertia of the transformed cross section in inchesu. y = distance from the neutral axis to the furthest point of the steel in inches. n = ratio of the elastic moduli Est / Ew- The reinforcement of the beams was symmetrical; therefore, the neutral axis was located at the center of the cross sectional area. The moment of inertia I, of plane area with respect to an axis in its plane is given by: _ 2 Ix — ‘jly dA In a composite beam.as in our case, the cross sectional area was broken in small components and its component's moment 22 of inertia was determined by the parallel axis theorem: I = ....l ab3 + (ab) 02 12 where a = width of the area in inches. b = height of the area in inches. 0 = distance from neutral axis of the beam to the centroid of the area in inches. Then the total moment of inertia around the neutral axis was fOund as the sum of the inertias of the components. I = I + .... = I T 1 I2 In n A.2 Test Data: From the data recorded for each beam, loads were plotted versus mid-span deflection, and curves were drawn (see Fig. 8, 9, 10, 11). The usual deflection formula? for a third point loading was used to calculate the practical stiffness values: E1 = 23PL3 6h8y where slope of load deflection curve in pounds / inch. w fists one of two equal concentrated third point loads in pounds. L = beam span in inches. W m 2? (HWSANDS OF POUNDS) 3.5 3.0 2.5 2.0 1.5 . 23 1'13. 8. Load deflection cum. for long boa-o summon AT KID-SPAN (INCHES) / / 7 / + / + + O / O 1 D +09 ,, +0 ," / e L; “I 7' 0 I’d x 7J/ ”IA . ’00 A); ’0/1‘ + / / / at}! fl/Aa 4 o 77 0r“ . x M; —0— ho. Type A - 1 I} A9 ——+-- In: Type I - 1 ,5 AAA, "-6"- lon '1'pr C - 1 If“ A/ / A 09 0159/, OJAAII/ e ,’ l/ 5 1.0 1.5 2.0 2.5 TOTAL 1.010 2? (HWSANDS OP POUNDS) 2h 3.5 + 3.0 ‘L , f . o x / / 4‘. O // / O l/ 2.5 1F 0 fl, + 0 ll .1. 0 /’¢ / .0 .1. MD I, ’43 2.0 f if 1 I I’D I .4 [P a i, [A [/3 A [A] ,6 ’9 A —0— Been Type A - 2 __r_.lee- Type I - 2 “4-" lee- Type C - 3 1.0 L5 2.0 DIRECT!“ AT HID-SPAN (INNS) r13. 9. Loed deflection curvee for long bee-e TOTAL LOAD 2P (THOUSANDS OF POUNDS) 3.5 3.0 25 —:»- lean Type A - 3 --*-- Been Type I - 3 ---A--- Been Type C - 3 1.0 1.5 2.0 DWCTIW AT HID-SPAN (INNS) Fig. 10. Loed deflection come for long bee-e 2.5 TOTAL m 2? (nonsense (I W) 7.0 6.0 5.0 6.0 3.0 2.0 1.0 26 A A o - Q / I o I I + / s O O I + /°‘ / + I q/ I .6 / + 4g : '1’ I /+ _ I I I I I+ I / I T 7 . I +/ I I _I .: / ——o— lee- Typeb' - 1 / e / . “1....-. f / “4’“ I... T7,. 5 - 3 I / , , + -' I I / I .0 I l .1 O! 03 DIPLICTICI AT KID-SPA! (IICIIS) Fig. ll ._ Loed deflection came for ehort bee-e 27 The bending stress calculations for steel were done by the formula I E c where I is the inertia of the transformed cross sectional area. The weighed ratio of the two different moduli of elasticity becomes equal to one as far as wood is concerned. For wood the following formula was used: (7:31in I c This formula gives the stress at any infinitesimal area of the cross section at distance y from the neutral axis. When y equals 0, the distance from the neutral axis to the extreme fiber, 0’, represents the maximum stress ( O'max. ). By transforming the cross sectional area of a two material beam, we obtain a new cross sectional area consisting only of wood and then can use the regular shear stress equation. 13:13... It where T = shear stress in p.s.i. V = total shearing force at a section in pounds. I = moment of inertia of the whole transformed cross section in inches . Q.= statical moment of the transformed cross sectional area above the shear plane around the neutral axis in inches cubed. t = width of the beam of the shear plane in inches. 28 For T max., Q obtains its largest value by considering the shear plane at the neutral axis. A comparison of load carrying capacity (apparent bending stress) of the reinforced beams at a maximum.load and at pro- portional limit war evaluated by dividing the corresponding bending moment by the quantity bh2/6. P x L/3, bh2/6 where P = load at maximum carrying capacity or at proportional limit in pounds. (One of two equal third point loads.) L = span in inches. b 2 actual beam width in inches. h = actual beam depth in inches. Strain development informations were provided by strain gauges mounted on tops and bottoms of the beams. Strain read- ings were plotted versus deflection, and the proportional limits in the compression and tension surfaces were observed (see Fig. 12, 13, 1h, 15). 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