'EHE EFFECT OF SLOPE OF GRAIN AND OTHER WOOD VARIABLES ON ELECTRK: RES£STANCE STRAIN MEASUREMENTS Thai: for tho Dogm of M. S. MiCHiGAN STATE UNIVERSITY William Henry Friday 1959 THESIS LIBRAR Y ‘5 iliiciiigjrm 9:81} ‘2' Vms'}:‘.'.‘l ’ A'Vv Unix-1119?. ‘ 4}; L THE EFFECT OF SLOPE OF GRAIN AND OTHER WOOD VARIABLES ON ELECTRIC RESISTANCE STRAIN MEASUREMENTS by William Henry Friday AN ABSTRACT Submitted to the School for Advanced 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 Agricultural Engineering 1959 /\ / fi APPROVED:_// /724>’ , {jaZ;;M/e// WILLIAM HENRY FRIDAY ABSTRACT The sensitivity, accuracy and convenience of SR.“ elec- tric resistance strain gages if applied prOperly on homoge- neous materials like steel or aluminum are well known. Wood research can make use of such a strain measuring device, but the effects of slepe of grain, the most important single characteristic of wood, have not been investigated thor- oughly. The strain measurements for SR-h gages were compared to standard deflection calculated strain values for O, 30, 60 and 90 degree slopes of grain. Because slope of grain can not be isolated from other wood variables, modulus of elas- ticity, Specific gravity or moisture content, they were in— cluded in the study. Randomly selected wood samples were cut from straight grained stock so that the grain made the desired angle with the edge of the test specimen. The results of many tests showed that the slope of grain had an important effect on SR-b strain measurements. A regression equation having a high correlation showed that the percent variation between the two strain measurement methods increased more than one quarter of one percent per degree of grain rotation. However at zero degree slope of grain the percent variation was within experimental error. There were indications that in sloped grain material at high values of modulus of elasticity the percent varia- tion tended to increase in compression and decrease in ten- sion. The equations expressing this were not conclusive because they had poor correlation with randomly located experimental data. On straight grained material it was concluded that the modulus of elasticity had little effect on the percent variation between the strain measurement methods. The percent variation between the strain measurement methods on sloped grain material tended to decrease at high values of moisture and Specific gravity. Again the equa- tions expressing these effects were not conclusive. It was concluded that moisture and specific gravity had little effect on percent variation when the material was straight grained. THE EFFECT OF SLOPE OF GRAIN AND OTHER WOOD VARIABLES ON ELECTRIC RESISTANCE STRAIN MEASUREMENTS by William Henry Friday A THESIS Submitted to the School for Advanced 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 Agricultural Engineering 1959 1/445"? 3—7/?3 ACKNOWLEDGMENTS The author wishes to express his sincere appreciation and gratitude to the following individuals and groups: Dr. J.S. Boyd, Agricultural Engineering Department, under whose guidance, inSpiration and encouragement this study has been conducted. G.R. Blayzor who assisted in testing samples for this study. Applied Mechanics Department whose loan of testing equipment made this study possible. NC-23 Regional Research Committee who supplied the funds for the necessary supplies for this study. My wife, Frederica, for her encouragment and help in preparing this thesis. TABLE OF CONTENTS IIST OF TABLES . . . . . . . . . . . . . LIST OF FIGURES .° . . . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . Problem . . . . . . . . . . . . . Objectives . . . . . . . . . . . . REVIEW OF LITERATURE . . . . . . . . . . . PROCEDURE . . . . . . . . . . . . . . Preparation of the Test Specimens . . . . . Stock selection . . . . . . . . . Establishment of moisture content . . . Sample sizing . . . . . . . . . . SR-h application . . . . . . . . . Testing . . . . . . . . . . . . . Test apparatus . . . . . . . . . Specimen loading . . . . . . . . . Method of Analysis and Calculations . . . . Calculation of strain values . . . . . Regression equation calculations . . . Modulus of elasticity calculations . . . Modulus of elastiCity adjustment . . . Strain difference calculations . . . . Moisture and specific gravity calculations Method of analysis . . . . . . . . 111 Page 4 H \0 CD (I) 0) {Tu N P N N N N N N N N H H H P H WWW N N H H HQU‘KJ‘ #7 N RESULTS . . Modulus of The Effect of Modulus The Effect Percent of The Effect The Effect of Moisture on the Percent of Modulus of Elasticity Variation SUMMARY AND CONCLUSIONS SUGGESTED FUTURE STUDIES REFERENCES . GLOSSARY . . APPENDIX . . Elasticity Variation of Slope of Grain on the Percent of Elasticity Variation of Modulus of Elasticity on the Modulus of Elasticity Variation of Specific Gravity on the Per- cent of Modulus of Elasticity Variation . iv Page 25 30 35 38 42 “5 us 51 52 53 55 LIST OF TABLES Table Page I. Summary of Standard Deviation Range . . . . 26 II. Modulus of Elasticity Straight Grained Samples . 27 III. Modulus of Elasticity All Sample Groups . . . 28 IV. Percent Strain Difference . . . . . . . . 29_ V. The Effect of Modulus of Elasticity on Percent Variation . . . . . . . . . . . . . 38 VI. The Effect of Specific Gravity on Percent Variation . . . . . . . . . . . . . uh VII. The Effect of Moisture on Percent Variation . . #5 10. ll. 12. 13. 1h. LIST OF FIGURES The equilibrium moisture-relative humidity curve 0 0 I O 0 O O O O O O O O O Tension samples in a heat sealed plastic controlled relative humidity container . . . Moisture equilibrium data for sample B—3-0-15 and a graphical plot of weight versus time . . The testing equipment with a Specimen under teat O O O O O O O O O O O O O O A schematic diagram of the testing arrangement Modulus of elasticity variation between two strain measurement methods at 0° grain slope . Modulus of elasticity variation between two strain measurement methods at 30° grain SIOpe . Modulus of elasticity variation between two strain measurement methods at 60° and 90° grain slope . . . . . . . . . . . . The effect of slope of grain on the percent of modulus of elasticity variation . . . . The effect of modulus of elasticity on the percent of modulus of elasticity variation at 0° grain slope . . . . . . . . . . The effect of modulus of elasticity on the percent of modulus of elasticity variation at 30° grain slope . . . . . . . . . . The effect of modulus of elasticity on the percent of modulus of elasticity variation at 60° and 90° grain slope . . . . . . . The effect of Specific gravity on the percent of modulus of elasticity variation . . . . The effect of moisture on the percent of modulus of elasticity variation . . . . . vi Page 10 ll 13 19 31 32 33 37 39 MO #1 “3 M6 I. INTRODUCTION The potential of using electric resistance strain meas- urement of wood can be limitless. Radcliffe (8) with his work on elastic constants of wood and Boyd (2) with his work on truss tests indicate the range through which SR-h elec- tric resistance strain gages have been tried. . The sensitivity and accuracy of SR-h gages if applied properly on homogeneous material such as steel or aluminum is common knowledge, and wood research needs this type of sensitive accurate strain indicator. The physical make-up of SR-u strain gages which permits them to be cemented unob- trusively to a structural member coupled with the electric circuitry make remote observations practical. Switching devices make many observations at one time feasible. Such strain measurements made on a wood structure undergoing ac- tual loading conditions would provide data to help modify existing analysis procedures. Since the 58-h gage is an in- expensive instrument and not removable from a test member, structural systems can be tested to failure without damag- ing more expensive reusable instruments. This extended strain data is of value in wood design. Problem Wood structural analysis has been hampered by the fact that wood does not behave as other homogeneous materials. The use of SR-h gages in wood research is still questionable. Their reliability in wood testing is not proved. There is printed material available, but reports that no Special prob- lems were encountered does not provide the fundamental knowl- edge to validate unlimited use of SR-# gages. Because wood is not uniform and is affected by external conditions, there is need for an investigation of the effect of these variable properties of wood on SR—# strain measurements. The surface of a wood member to which an 53-4 gage must be.applied is not homogeneous. There exist areas of differ- ent density due to nonuniform rates of growth during the _life Span of the tree. These areas known as growth rings produce the grain of a wood member. The slope of grain is probably one of the most variable features of wood. To isolate the slope of grain as an independent vari- able is impossible, for the physical constants of wood change with slope direction and density variations which are reSpon— sible for the graining effect. Moisture content of wood al- so influences the physical properties. Objectives The objectives of this study follow: 1. To investigate the effect that the slope of grain has on the reliability of SR-u gage strain meas- urements. To investigate the effect that the modulus of elas- ticity has on the reliability of SR—h gage strain measurements. To investigate the effect that Specific gravity has on the reliability of SR-h gage strain meas- urements. To investigate the effect that the moisture con- tent of wood has on the reliability of SR.“ gage strain measurements. a, II. REVIEW OF LITERATURE Many excellent papers concerning electric resistance gages found in the volumes of the Prgceedings of the Soci- ety for Experimental Stress Analysis (195A) were concerned mainly with metal materials. Hetenyi (1950) presented a thorough treatment of the subject of strain gages and gaging methods. The subject matter in these volumes provided ex- perience in use, Operation and theory of SR-u strain meas- urement. SR-“ strain gages were not new in wood research. Ernst (l9h5) pointed out and illustrated that the SR—h gage had been used for a variety of purposes in the testing of wood and wood products. Yet Radcliffe (1955) expressed that there was a slowness on the part of wood research agencies to realize their potentialities. These statements sounded contradictory, but when compared to the use of 33-4 gages in metals research their use in wood testing was negligible. The major problem Radcliffe (1955) indicated was the large variation of elastic constants in wood which necessitated the calibration and determination of the physical proper- ties for each piece. This calibration would need to be done for all types of strain indicators. Ernst (l9u5) stated that the majority of the SR-h ap- plications in wood testing were done with a scanning recorder to obtain sufficient points for an adequate stress pattern. But Radcliffe (1955) pointed out that enough suc- cess had been obtained at his laboratory using an intermit- tent loading method to conclude reliable results. In either case it was necessary to plot the stress-strain pattern to correct for the inherent creep in wood. Intermittent load- ing provided the possibility of multiple strain readings at the same load levels. Boyd (195A) in preliminary tests of square beams compared calculated stress values with SR-h gage values and found the variation within ten percent. These reporters indicated that no special difficulties were encountered in using the 88-h gage. It was assumed that all the preceding work was done on straight grained wood. The measurement of strain in wood presented several problems not common to most other materials. It has been only in the last thirty or so years that the physical, chemical, and mechanical proper- ties of wood have been sufficiently studied to fur- nish a basis for the use of wood as an engineered , material. Because of woods heterogeneous structure the determination of its basic properties, such as sound transmission and heat conductivity, vary with the longitudinal, tangential and radial direction of each piece of wood it is understandable why the development of basic data on wood has but recently been studied in any degree.1 ~— 1Nicholas V. Poletika (195A), Slope of grain in engineered wood, Jour. of Forest Products Research 800., u, p. 1"01.. Wood, considered to be orthotropic, has twelve physical con- stants instead of three. These constants vary in each of the three planes, longitudinal, radial and tangential. How- ever as Radcliffe (1955) admitted, a piece of lumber was not sawn with the reSpective faces truly radial or tangential. Because of this the strain measured at any point was sub- ject to the variation of the material at that point. When' differences in orthotropic constants were small, wood could be analyzed as other homogeneous materials. A point considered in study of the homogenity of wood was the hollows in the material due to voids in the cell structure. Wood cells are of various sizes and shapes that are firmly united together. In dry wood the cells are gen- erally hollow and empty. As stated in the flggd RanthQE (1955) the strength of wood does not depend upon the length of these fibers (cells) but on the thickness and structure of their walls. In this sense these voids do not constitute weakening the wood but do make a nonuniform surface for the applica- tion of an SR-u gage. To correct this situation Ernst (1945) used a liberal coat of bonding cement applied to the wood exnd allowed to harden before the SR-h gage was cemented in position. Slope of grain occurs when the fibers do not run par- zallel to the main axis of a board. Poletika (195a) believed ‘that lepe of grain was the most important single charac- ‘terdstic of wood. This feature of a wood member influenced practically all of its physical and mechanical prOperties. Slope of grain is inherent in wood and must be contended with in most boards. Boyd (l95b) substantiated the effect of slope on the physical properties when he found in pre- liminary tests that the modulus of elasticity varied with the direction of the grain in both plywood and fir. Elastic constants were not only affected by the lepe of grain but also by moisture content and Specific gravity. The flood Handbpok (1955) published data expressing the vari- ations of physical properties with respect to both. In gen- eral the modulus of elasticity decreased as the moisture content increased, and it increased as Specific gravity in- creased. Testing of small clear timber specimens was clearly specified by the American Society for Testing Materials (1952) for compression tests parallel to grain, compression tests perpendicular to grain and tension tests parallel to grain. Moisture determinations of timber Specimens were in- cluded and called for the sample to be dried at a tempera- ture Slightly above 212°F until the weight became constant. The loss of weight divided by the weight of the oven-dry wood was the proportion of moisture in the piece. However Markwardt (19u3) stated that moisture as thus determined was subject to inaccuracy because the loss in weight included substances in wood other than moisture evaporating at 100°C. Such errors usually did not affect the practical application. 5“ r J. III. PROCEDURE For this investigation a representative group of wood test Specimens were prepared with predetermined slopes of grain to measure their effect on SR—h gage strain measure- ment. The group of samples were loaded in a Universal test- ing machine, and the strain was measured two ways. A sta- tistical analysis was made to determine the effect of slope of grain and other variables, modulus of elasticity, mois- ture and Specific gravity, on SR-u strain measurements. Preparation of the Test Specimens Wan Douglas-fir planks, 2 by 12, from which the test speci- mens were sawn, were selected from a local lumber yard on the basis of straight uniform grain. Four of these planks were marked and each cut into sixteen 2 5/8 by 10 inch blocks. The longitudinal axis of each block was positioned with reSpect to the grain so that it intersected the direc— tion of the grain at one of the following angles: 0, 30, 60 or 90 degrees. Four Specimens at each slope were cut from one plank. Sixty of the 6h specimens were used as the com- pression test samples. Three other planks were likewise marked and each cut into ten 2 5/8 by 20 inch blocks. Only 0 and 30 degree grain slepe samples were obtained from the material. These thirty blocks were used as the tension test Specimens. All the test Specimens were later sized more accurately. Esta is m t is ur c tent The test Specimens were divided equally into three groups on the basis of slope of grain, type of testing spec- imen and parent plank. The wood blocks were placed into saturated salt solution controlled humidity containers in an effort to obtain equilibrium moistures of 10, 15 and 20 percent. Markwardt (6) presented an Equilibrium Moisture— Relative Humidity curve, Figure l, which served as the ba- sis for selecting the necessary relative humidity level of the containers. Hodgman (5) supplied the necessary data to produce these relative humidities. Saturated solutions of Aqueous Sodium Bromide (NaRr-2H20), Sodium Chloride (NaCl) and Potassium Chloride (KCl) at 77°F room temperature pro- duced relative humidities of 56, 75.8 and 97 percent reSpec- tively. Heat Sealed two mil plastic bags were used as the con- tainers. An example is shown in Figure 2. These plastic bags provided easy access to the wood samples. Heat seal- ing the bags seemed to provide airtight containers. The ‘Uags were opened and the Specimens weighed at intervals on a Toledo Spring scale. 35 $30 I» Z 25 i=5 /,I / 1’20 77°F , g I J,” ’1’ 2l5 40°F 1” u A,’ am A luff; /’T E3 / ,L‘ ,rw I -_J 5 d/..”" / l D I "’ ‘If’ I .. I / O ’1”::4-’ d U o Lgfi‘m l I o £02030405060708090l00 RELATIVE HUMIDITY (7.) Figure 1. The equilibrium moisture-rela- tive humidity curve. 10 11 .honampnoo huapasss obanmaoa poaaonpnoo caveman poamom use: m a“ endgame nodesoa .N Okawam 12 When the weight of the sample became constant it was assumed that moisture equilibrium in the wood had been ob- tained. This process took a period of from four to five weeks. Figure 3 shows a typical weight-time sheet and a weight-time curve used for the purpose of determining when moisture equilibrium was reached. At the outset of this investigation exact moisture con- tents of 10, 15 and 20 percent were not expected, but it was believed that a narrow range of moisture around the intended moisture could be obtained. The span between the desired moistures of 10, 15 and 20 percent was great enough to per- mit a variation of at least one moisture percentage without overlapping the next moisture band. In practice this was not obtained. There was no attempt made to control the temperature of the sample storage room. A Brown recorder placed in the room recorded only a five degree variation in temperature. This was considered sufficient temperature control for the purpose of the experiment. Sample sizing The specimens originally sawn 2 5/8 by 10 inches and 2 5/9 by 20 inches were sized at a later date to 1% by 1% by 8 inches for compression testing and 1% by 1% by 20 inches for tension tests. This was done to correct any warping or twisting due to a moisture change. The sizing was done af- ter the apparent moisture equilibrium was obtained. At that 13 WHF MAY I955 PROJECT MOISTURE EQUILIBRIUM DATA SAMPLE _a-S-O-Is CONTAINER NO. IO RELATIVE HUMIDITY 75.8% SOLUTION Na Cl DATE WOT/i NOTES DATE weT_/g NOTES 5/l9 l55 start 6/l3 l36 a e 5 /2l l54 6/ 24 I365 test 5 /25 l53.5 6/ 29 l I 9 dry 6/4 l5|.5 6/30 I IS final 6/8 I5l5 6/8 l345 sized 6/l3 l345 l60 A ISO (0 3 0: I40 0 EE ISO GAGE £9 , m .20 DRYING 3 IIO 202428! 5 9 l3 I72! 2529 DAY OF MONTH Figure 3. Moisture equilibrium data for sample B-3-0-15 and a graphical plot of weight versus time. 14 time the Specimens were sawn to dimensions of 1/32 of an inch over size and then sanded to size. A smooth surface for the SR-h strain gage application was obtained. The ends of the compression Specimens were sanded square to the axis of the block to eliminate bending during the tests. r‘ The tension Specimens were drilled with two 3 inch holes L3 a distance of 16 inches apart and equidistant from the center i I line of the block. The tension load was applied at the holes. The tension loading brackets are described under test appara- i tus. The horizontal and vertical axis of the samples were marked so the SR-h strain gages could be positioned. Squared marks were made on the Specimens so that a six inch gage length compressometer could be attached. The Specimens were weighed before and after the sizing Operation and returned to the controlled humidity containers until further tests could be performed. SR-h applicatigg At the time of SR-h strain gage application the samples were removed from the humidity chambers and weighed. A spe- cial precaution was taken to see that the surface was pre- pared with a liberal coat of Duco cement to fill pores. The surface of the specimen was again coated liberally with ce- ment and the SR-h gages applied as recommended in the Bald- win instruction manuals. The gages were gently pressed in- to position and squeezed lightly until the extra cement rolled from under the edge. Because of the large number of 15 gages which were to be applied a group of pound weights were cut from 2 by % inch steel flats and these were placed on the SR—h gages for a two hour period. Extreme care was tak- en to square the gage with the axis of the Specimen. Two gages were placed on every Specimen so that average strain values could be obtained to nullify any bending ef- fects. Satisfactory application of the gages was obtained as only one dead gage occurred in the 192 tested. Testing Tgst gppgratgs A Tinius Olsen 60,000 pound hydraulic testing machine was used to load the Specimens for this research. Care was taken that a consistent loading rate of.05 inches per minute as indicated on the load control panel was applied through- out each trial. The machine performed well, and it was found that a load level could be held constant while a series of strain readings were taken. A standard four dial compressometer having a gage length of six inches was used to measure the deflection of the Spec- imen. The Ames deflection gages were estimated to the ten thousandth of an inch. Upon completion of the tests the gage length was checked by measuring the distance between the gage insert marks on the specimens. It was determined that the gage lengths were consistent. 16 The 0 degree slope compression tests followed ASTM pro- cedure. The same size Specimens were used for the 30, 60 and 90 degree slopes. ASTM standards were deviated from for the tension test so that sufficient Space would be available for theapplication of the SR-h gages. The resulting Spec- imen was prismatic throughout and of the same cross section- al area as that of the compression sample. It was necessary to devise a bracket to suSpend the tension samples in the testing machine. A standard metal test Specimen was cut in two, and a three inch piece of channel was attached to each half. These channel sections were bolted to the Specimen with i inch bolts. The metal test Specimen ends permitted the use of the standard Spherical tension test mounts. Ax- ial loading resulted from their use. A type AM strain indicator manufactured by the Young Testing Machine Company was used to read the SR-h strain values. This strain indicator was calibrated to read di- rectly in microinches of strain. Because there were two sets of SHAH strain readings to take on every Specimen a switching mechanism was devised. The basic element of this was a war surplus Air Force radio communication channel selector. At first it was thought that all the 83-h leads would have to be soldered into the circuit so the channel selector was wired for all seven chan- nels. This would permit three Specimens to be soldered in the circuit at one time. However a circuit using alligator 17 clips was tried, and it was found that only a difference of one tenth an ohm existed between the two types of circuits. It was decided to use the alligator clips not only because they would provide a quick connection but also all the Spec- imens could be handled with the same circuit throughout the investigation. During the investigation of the SR-“ circuit a reading consistency test was performed with both potential operators alternately reading the instrument. The results of this test using two SR-h gages under a load showed that the two channels selected for use could be read within a Spread of 1.7 microinches of strain. A temperature compensating dummy SR-h gage was used during the tests. The actual test equipment is pictured in Figure 4, and a schematic diagram of the testing arrangement is found in Figure 5. mm It was planned that during this investigation all load- ing would be done within the plastic range. To predetermine the load level and gain experience operating the hydraulic testing machine three blocks at each slope similar to the test Specimens were loaded until failure. The average loads required to produce failure of these blocks were 517, 36h7, l7#7 and 1160 pounds for 0, 30, 60 and 90 degree slope reSpec- tively. The,flggg,flandhggk_(10).allowable stress values I ,..I...vllitl|. ill.|l i .. ,I. - 18 who so u can noaaooam m and: agenda; madame» one .3 onswdm ,ii\.l. Hi Ly>u b. it ZSIR-4‘s 19 7—3 TEMP. COMPENSATING GAGE D] [GK—— DEFLECTION DIALS ATEST SPECIMEN [i \m MACHINE SWITCHING DEVICE \ TRANSFORMER Figure 5. A schematic diagram of the testing arrangement 20 would.permit using 3500 psi stress parallel to the grain and 800 psi stress perpendicular to the grain for Douglas-fir. Maximum test loads for the slopes of 0, 30,60 and 90 de- grees were set at 8000, 2000, 1200 and 800 pounds respec- tively. These loads were slightly over 50 percent of that required to produce failure and would be 3555 psi for the 0 degree samples, 889 psi for the 30 degree samples, 533 psi for the 60 degree samples and 355 psi for the 90 degree sam- ples. During testing it was not possible to obtain the maxi- mum load for all the higher slope Specimens due to premature failure. The data in these cases was taken only to that point at which a constant strain could be maintained for a specific load. It was impossible to read either a continu- ally moving deflection dial or an unbalanced galvanometer needle. The procedure for loading the Specimens was as follows: 1. An initial load of 200 pounds was placed on the sample; the deflection dials were zeroed, and ini- tial 53-4 strain readings were taken. 2. Intermittent deflection and SR-h strain readings were taken at loads of #00, 600, 800, 1000, 1200, 1500, 2000, 3000, 5000 and 8000 pounds. In some cases intermediate readings were taken in the high sloped samples so that more points would be avail- able for analysis. 21 Method of Analysis and Calculations C c t t The calculation of the deflection determined strain value was done by summing the four compressometer readings at each load and dividing by four. This average was then divided by the gage length of six inches to produce the strain value in inches of deformation per inch of length. The $3.4 readings were made on a Young type AM strain indicator which read directly in microinches of strain. The zero load strain reading for each gage was subtracted from the strain value at each load position. The two strain differences at each load were averaged to eliminate bending effects on the sample. The result was an average SR-h strain value for each load increment. R ess n t 0 Each set of data, both by SR-h and deflection method, was plotted on a strain—load graph. The regression equation for this data was determined using the following general formula: e s a + b (L -lf) _ z. where a a e s.... N Z(L-I)e and Z (L -'i')2 The resulting b value was the reciprocal of the slope of line for a load-strain curve. 22 The standard deviation was determined for each equa- tion. A t test for significance was performed upon the sample slope values at the 90 percent confidence level. The equation used for the t test was as follows: ba-bd t- svz {@sz $2.Z(°8';l)2+z(°d';d)2‘ (b§+b§)Z(L-f)2 ' NB+Nd-l+ where The modulus of elasticity for each sample and by both strain measurement methods was determined two ways. The first was to divide the b term of the regression equation into the reciprocal of cross sectional area for each sam- ple. The second method was to divide the maximum load by both the cross sectional area of each sample and the strain value at the maximum load. Both methods produced identical values for the modulus of elasticity. W The modulus of elasticity is known to vary with mois- ture change. Adjustments were made to correct each E value to its equivalent at the 12 percent moisture level. The following equation was used for these calculations (10): (up - 12) LOSE'LOS El + (”1 - 12) . “r“— 1: . Aug-7 .‘J’l‘ 1...”; -. 23 St a 3 Strain difference between the two strain measurement methods was calculated for each sample at the maximum load level by using the regression equation. Two calculations were necessary for the strain difference (one at the maximum load and the other at zero load). The true maximum strain was the algebraic sum of the strain at the maximum load and the strain at zero load. The strain difference at the maxi- mum load between the measurement methods was the difference between the two maximum values. The strain difference at any intervening load would be directly proportional. t c v t a t s The percent moisture (N) content of the samples was calculated by the standard manner of dividing the weight loss of an oven—dry sample by the final sample weight. Care was taken that the gage weight was subtracted from the divisor or final weight before it was divided into the weight loss of the oven dried sample. Specific gravity (G) was the resultant of the final weight of an oven dried sam- ple less the gage weight divided by the weight of an equal volume of water. M a s The method of analysis for this research was to estab- lish statistically the constants and physical prOperties of each sample and to plot graphically and to determine statistically the prediction equations for this data with respect to the variable. The following investigations were made: 1. 2. Modulus of elasticity variation. Percent modulus of elasticity variation-slope of grain relationship. Percent modulus of elasticity variation— modulus of elasticity relationship. Percent modulus of elasticity variation- Specific gravity relationship. Percent modulus of elasticity variation- moisture relationship. 21+ d‘l-.-hp ”V , ' . _.. A; ‘ ‘0'“ ~‘ 25 IV. RESULTS For convenience and easier reading the following short- ened forms are used in this section: ' l. The percent of modulus of elasticity variation is $13 referred to as the percent variation. } m 2. A slope of grain sample or group is referred to by F the numerical value of its slope followed by the first letter of the type load applied; for example, é 30°C group means the 30 degree compression loaded slope of grain group. 3. The terms modulus of elasticity, specific gravity and moisture content are referred to by their com- mon notations of E, G and M respectively. The standard deviations of the load-strain regression equations increased as the slope of grain increased (Appendix Tables A and B). Table I presents a summary of the range of the standard deviations for all lepe of grain groups and the coefficients of variation within each group. The range of standard deviations for the load-strain equations widened as the slope of grain increased for both the SB.“ and deflection gage methods indicating difficulty in making accurate strain measurements. The coefficient of variation of the standard deviations was less in each group for the deflection calculated equations than its counterpart by 88-“. rate than the other but that one was influenced less other factors; for example, Poisson's ratio or shear grain line. mation between two pairs of points without regard to took place between while the 38-h was adhered to the This did not mean that one method was more The deflection gage measured an average by what 8111‘- face of the wood in a small increment of length and was subjected to local variation. TABLE I SUMMARY OF STANDARD DEVIATION RANGE 26 accu- in the defor- F1 .5 . ,____ .. .-- a I . c ' . -»- ant.— Grain 58-“ Method Deflection Method- Slope Bange Coef. of Range Coef. of xlO'u variation xio-“ variation 0°C .05-1.12 lll .ll-l.0# b6 30°C 019-108“ 70 018-1018 ’48 60°C .oz-u.u6 77 1.13-9.12 64 90°C .h4-3.82 69 1.16-5.25 no O°T .02-0.18 61 .02-0.18 51 30.1. 003-0035 85 005-0085 96 The two E values calculated for each sample varied through a wide range (Appendix Tables C and D). Table II compares the mean E values of the 0°C group and the coef- ficient of variation for each method with the flood flandp bank (10) values. 27 TABLE II MODULUS 0F ELASTICITY STRAIGHT GRAINED SAMPLES Source No Moisture Correction Moisture Corrected to 12% Exlo5 Coef. of 3x105 Coef. of variation . variation 83.4 175.17 22.5 182.72 22.6 ‘Deflection 179.17 19.9 187.25 20.1 Handbookl __ 195.00 22 .o The mean experimentally determined E values were slightly less than accepted handbook values. This was at- tributed to a lower than average G value for the experimen- tal samples. The mean G value for the samples was determined to be .#h and a handbook value was given at .h8. The mean E value by both methods was within the 22 percent coeffi- cient of variation range given. The coefficient of varia- tion for the experimentally determined E values was similar to the handbook value. This illustrated that the wood sam- ples were quite typical of average Douglas-fir. As expected E decreased as the slope of grain increased, and the coefficients of variation increased with the slope of grain. Table III summarizes these facts. — ww— 1Handbook values mentioned in this section were taken from the Egan.flanlh29k (10). 28 TABLE III MODULUS OF ELASTICITY ALL SAMPLE GROUPS .I Sample SB-h Method Deflection Method Groups Mean E Coef. of Mean E Coef. of x105 Variation x105 variation 0°C 182.72 22.6 187.25 20.1 30°C 27.75 24.0 32.1“ 2#.8 60°C 6.25 #7.5 5.22 25.9 90°C 3.52 38.9 2.86 21.3 0°T 2h7.63 19.2 267.57 l9.h 30°T ui.58 26.9 , 39.07 26.6 There were no handbook E values for wood sloped 30 and 60 degrees and no specific value for E perpendicular to the grain listed, but there was an Er/El handbook ratio which would compare to an Ego/Bo ratio of the data presented in Table III. The handbook ratio value for Er/El was .068. The experimentally determined E90/EO value of .019 for the SR-# method and .015 for the deflection method was unusu- ally 1ow. The E values obtained for the tension samples were higher than handbook values. The coefficient of variation values followed the same pattern for both measurement methods increasing through the 60°C and falling off for the 90°C groups. The 30°T coeffi- cient of variation value was higher than 0°T in both methods. ltJv 29 Table Iv presents the extremes in percent strain dif- ference and the average percent difference for the slope of grain groups. TABLE IV PERCENT STRAIN DIFFERENCE *— v__ v, _— Wv.‘ j.— _— .r _ ._ .7_—_.. .1 .9.“ - AID-1" ‘ ’5‘. ‘5 a Slope Groups Range (percent) Average (percent) 0°C 1.29-2u.72 7.70 L; 30°C .82-58.80 16.00 *3 60°C .03-88.56 26.45 90°C 2.66-55.79 23.67 O’T 1.03-24.79 10.71 30°T 2.12-56.06 21.81 The difference between the extremes of percent strain difference widened with increased slope of grain as did the load-strain curve standard deviations (Table I). The in- crease of the average percent strain difference to the 60°C group and the slight drop for the 90°C group was similar to the results obtained for the E coefficient of variation (Table III). The tension groups followed the same pattern with higher values. The indicated strain by 88-“ was both higher and lower than the strain calculated by the deflection method. This occurred about equally for all grain slopes except for the ' ii: 30 30°C group. In this group the 53-4 strains were almost all greater than the deflection calculated values. In this section it was shown that the slope of grain increased variability of strain readings in three different ways. These were: 1. The increase of the range and coefficient of vari- F? ation of the standard deviations for the load- ' strain curves. 2. The increase in the E coefficients of variation. 4] 3. The increase in the range and average value for percent strain difference between the two methods of strain measurement. Modulus of Elasticity Variation The best criteria for discussing variations between the two methods of strain measurement is the modulus of elastici- ty (E). This is the most direct and meaningful comparison which can be made because E is a function of both stress and strain. If actual strain difference is used it would have to be qualified as a percentage and for a specific load. The deflection method E values will be used as the standard or basis for comparison because they are influenced less by the orthotropic properties of wood. Figures 6, 7 and 8 are graphs which plot E determined by 53-“ and deflection methods. They show the E variation between the two methods. Variation limits of 10 percent 31 o - O'OOMPRESSION i x - O’TENSION + L ' 3340 5. z 9 p. o I.” _l Em ,‘_ E / E220 o O i: f 0" 5 :00 ° / In -0 O a / 0’ I40 / / g / :E MODULUS OF ELASTIOITY BY SR-4('IIIO5psi) Figure.6. nodulus of elasticity variation between two strain measurement methods at 0° grain slope. 32 A 9" 30' TENSION '3, x - 30° cowpaessnou 22 z 9 P [ 870 .J lb (3 )- m >- / 550 :3 . x . / ‘ 1 3:41 ,° / / ° IL / / o a / 83 25/ 5' / 4 o o i x o O 3 / / / IO IO 20 3 O 40 50 60 7O MODULUS 0F ELASTICITY BY SR-4 (in I05psi) Figure 7. Modulus of elasticity variation between two strain measurement methods at 30° grain slope. Va-.. 33 x - GO‘COMPRESSION 6 - 90’COMPRESSION (In 0023'!) ab OI 0 l/ o MODULUS OF ELASTIOITY BY DEFLEOT ION Figure 8 . 2 3 4 5 6 94000103 0F ELASTIOITY sv SR-4(inl05psi) Modulus of elasticity variation between two strain measurement methods at 60° and 90° grain slope. 7 . 15.x: 34 were established because the 10 percent figure is generally considered to be allowable error in wood research. Figure 6 is a plot of the 0°C and 0°T groups. Only two of the compression samples had a variation which exceeded 10 percent while eight of the tension samples exceeded the limit. All the tension samples which had greater variation than 10 percent had higher E values by the deflection method than by 83-0 gages. This might be due in part to the dif- ficulty of attaining uniform stress distribution in wood' tension samples. Figure 7 is a plot of the 30°C and 30°T values. Seven compression and eleven tension samples exceeded the 10 per- cent variation.level. Samples in the 30°C group exceeded the 10 percent variation limit 3.5 more times than did samples in the 0°C group and 1.25 more times in the 30°T group than the 0°T group. In the 30°T group SB-h method variations were both higher and lower than the deflection method values when in excess of 10 percent. This differed from the 0°T group. In Figure 8, for 60°C and 90°C groups, ten of the 60°C and eleven of the 90°C samples exceeded the 10 percent vari- ation level. This represented an increase of 5.0 and 5.5 times the samples exceeding the 10 percent variation in the 0°C group. It was found that E exceeded the 10 percent variation limits more frequently as the slope of grain increased. 35 This was not in agreement with the work done by Youngquist (11) in 195?. He found little difference between compression E values obtained by 88—0 and other deflection calculated meth- ods for slopes of grain of 0, 45 and 90 degrees. This dif- ference was probably due to different gage lengths. In all cases Youngquist used a short deflection gage length, and this might have subjected the gage to local variation and the influence of slope of grain. A t test performed on the regression equation slope coefficient, the reciprocal of the E value when corrected to the proper units by the area, showed that at the 90 per- cent confidence level nine of the fourteen 0°C samples had slope coefficients which were significantly different (Ap- pendix Tables A and B). It also showed that slope coeffi- cients of eleven of fifteen 0°T samples, ten of fifteen 30°C samples and twelve of fourteen 30°T samples were signifi- cantly different. No t tests were performed on the 60°C and 90°C samples. In all cases samples which exceeded the 10 percent variation limit had slope coefficients which were significantly different. The Effect of Slope of Grain on the Percent of Modulus of Elasticity Variation The slope of grain was assumed to be the most impor- tant variable considered because as reported (7) the physi- cal properties of wood are influenced more by slope of grain 36 than by any other factor. Figure 9 is a graph representing the effect of slope of grain (¢) on the percent variation (P). This graph shows that the assumption was correct. The regression equation for the weighted percent varia- tion means of the compression loaded slope of grain groups was: P = 7.296 + .281 0 This equation had a correlation coefficient of .965 which indicated a good linear fit of the data and high correla- tion of the variables. The equation indicated that the ex- pected variation between the two strain measurement methods at zero 310pe of grain was seven percent. This figure was good considering the methods of measurement and the materi- al under test. The most important result was that the slope of the regression equation line showed that the effect of slope of grain was greater than one quarter of one percent variation per degree of angle rotation. This was ascertained to be greater than allowable experimental variation and represented a sizable influence on strain measurements. The regression equation for tension loading plotted from only two mean percent variation values was: . P = 9.37 + .561 ¢ This equation, having only two points, was not of signifi- cant value, but its slope of line agreed with the slope of line obtained for the compression loaded group. The above equation had a lepe or rate of change of percent variation “Rec pm I: _l- “’1‘- -Ifl I ' I you. . l 37 e O _ eeufis 0.8:. _9 0|. 7% mu m a: mu m m .01.. o #000,: 0 T nonclseilIOIOIG] O o 0 (alone-000luluol L AU." N m T. A Sle 0'0 [0... .erIeoeolee. M E S a M E o ... m o M 0 w m . 1.9.1 Oh P a j _ p .b _ a n p m o 7 s w m w m m o no 202332) >550.th to 94.500! to hzuomua 900 SLOPE OF GRAIN (DEGREES) 60 30 The effect of slope of grain on the percent of modulus of elasticity variation. 0 Figure 9. 38 equal to twice that for the compression group. This was not considered valid. It was noted that the percent vari- ations for the tension groups were larger than for compar- able compression samples. This was true for E and C values also. It was expected that the rate of change of percent of variation would be higher for the tension samples due to these results. The Effect of Modulus of Elasticity on the Percent of Modulus of Elasticity Variation Another wood variable considered with slope of grain was modulus of elasticity (E). Figures 10, 11 and 12 show the plotted experimental data (Appendix Tables C and D) and the regression equation line for each slope of grain group. Table V presents the regression equations and their correlation coefficients for each slope of grain group. TABLE V THE EFFECT OF MODULUS OF ELASTICITY ON PERCENT VARIATION —. ‘ ——__— 510pe Regression Correlation Group Equation Coefficient 0°C P = 10.980 - .0173E .013 30°C P = -6.857 + .629E .237 60°C P = 25.063 + 9.5793 .298 90°C P = 8.220 + 8.121E .027 0“T P = -2.909 + .0459E .162 30°T P = 71.940 - 1.1713 .220 n; 39 .cooam madam 60 pm scapmdpm> mpaodpmmao mo msHspoe mo scoopop as» no madcapmmam mo wsazpoe mo hookup 0:8 .oa manuam 288:5 $6.548 do 3382 com com can own one 08 oo. ‘ 8. c: on. 06. x o T x a m X 0 X X X IIIIIIIII |||||I||Il 0 m “MHH‘IIIII I. .0 e 0 II .1 x I x Y\\\i Au_mu 0 to 00.0 m (XI! 1 T 1--) IO): ‘0 AONW 0 I3 3 -Il: iflll1- I T I T) I ) I n ,l,1-iwlllll-t. 1Y1! (til W n on% m I. 26...".sz - x i 9.1 zemmmmdzooo m w - u am no lF' I l. L: l. E. .oaoam madam can no meanness» madcapmmao mo msHSpos mo espouse on» no madcapmmao ho moaspoa mo poommo one .aa madman 238.5. E32; .6 mangoes. n m on as ow on on mm Cu Jaw O / Ge 0 0 f x \Y /Lr \\ m o C) 9 \Wfl/ 0 Au .IIIIIII Kazan x / zo.mzw._.oom - x zo.mmmmazoo..om .. O _ _ C) N :10 Sfl'anOW :IO .LNBOHBd C) H) (3 ¢ NOLLVIHVA AllOl .LSV'IB C) K) C) (O IOO 90L X 0" GO'COMPRESSION 80 X- QO’OOMPRESSION z 9 L I- 570 m X "i g... gflj; g... ‘° / 2; 6&YT)-4:>////r O -/ / g 90°C ‘V / / 230 {f / o u. o /L/ x o / '22 / Ill x 0 x o :5 / o “no “ /x3 p o K x 0 O l 2 3 4 5 6 7 MODULUS OF ELASTIOITY (IIIO5psi) Figure 12. The effect of modulus of elasticity on the percent of modulus of elasticity variation at 60° and 90° grain slope. ‘4 5.. a. A; a nu. Au ‘1 . a. as '1. Co ‘. A- O- A. :4 1.15.". - I. a .i.. Vut ....1.. .II.. I.u.~...1.....‘ I.|.. 1:1. .. . U #2 The low correlation coefficients indicated a poor lin- ear fit of the experimental data, but no reason was found to use nonlinear equations. The random location of the data contributed to the poor correlation coefficients. Al- though the 30°C, 30°T and 60°C groups showed a higher cor- relation between the percent variation and E, this was not considered sufficient to indicate reliable prediction equa- tions. The effect of E on the percent variation illustrated by the regression equations for both zero degree groups was almost negligible although the slope of the lines disagreed. The remaining compression loaded groups indicated a greater effect of E on the percent variation which increased as E increased. This was not expected but showed the influence of slope of grain. The 30°T group had a lepe of line 0p- posite that for the 30°C group. This followed the slope of line disagreement for the 0°C and 0°T groups. It was be- lieved due to the stress reversal. The Effect of Specific Gravity on the Percent of Modulus of Elasticity Variation Specific gravity (G), another wood variable to affect the physical properties of wood, had less effect upon the percent variation (P) than E. Figure 13 shows the plotted BXperimental data (Appendix Tables C and D) and the regres- sion equation line for each slope of grain group. Table VI presents the regression equation for each grain slope group. zma—rntir- ‘ - - a 1 1, | ..~ 3“ PERCENT OF MODULUS OF ELASTICITY VARIATION 43 + 1 0° GROUP X-TENSION 6>-cowu=mzssuon 30‘: 60° 890° GROUP 9 ' 30° COMPRE SS ION m - 60°COMPRE$SION a- 90°COMPRESSION_ X'3O" TENSION 8‘ T . . T . X X‘— " - 0°T :1. ...—C .1...—- - . 90 44 48 .52 .56 .60 .64 SPECIFIC GRAVITY Figure 13. The effect of specific gravity on the percent of modulus of elasticity variation. . 2"». '4 I an TABLE VI THE EFFECT OF SPECIFIC GRAVITY ON PERCENT VARIATION Slope Regression Correlation Group Equation Coefficient 0°C P = 5.918 + 0.211G .00083 30°C P = 26.228 - 29.513G .0082 60°C P = 107.325 - 188.5396 .047 90°C P = 100.363 - 160.210G .024 0°T P = -1.913 + 20.398G .056 30°T P = 36.522 - 19.5690 .0017 The very low correlation coefficients for all the slope groups indicated a very poor linear fit of the ex- perimental data. The random location of the points justi- fied the linear relationship. The prediction equations al- though not reliable indicated that the effect of G on the percent variation was small for all slope of grain groups except 60°C and 90°C. The small effect that G had on the percent variation at zero grain slope was to increase the percent variation with an increase of the variable. This was shown by the positive slope of the 0°C and 0°T lines, Figure l3,and the positive regression equation slope terms, Table VI. For all other slope of grain groups the G effect was to decrease the percent variation with an increase of the variable. I. . ..u ..I’ 1*5 This was illustrated by negative line slones, Figure 13, and negative regression equation slone terms, Table VI. The Effect of Moisture on the Percent of Modulus of Elasticity Variation Experimental data (Appendix Tables C and D) plotted in Figure 14 shows the effect of moisture (M), another wood variable, on the percent variation (P). The regression equations and their correlation coefficients for the lines of Figure 15 are given in Table VII. TABLE VII THE EFFECT OF MOISTURE ON PERCENT VARIATION Slope Regression Correlation Group Equation Coefficient 0°C P = -l.05l + .612M .028 30°C P = 57.967 - 3.120M .204 60°C P = 14.601 - .890M .0038 90°C P = 66.458 - 2.581M .024 0°T P = 6.977 + .209M .0024 30°T P = -3.770 + 2.516M .018 The low correlation coefficients for all the slope groups indicated a very poor linear fit of the experimental data, but the random location of these points gave no justi- fication to use nonlinear equations. The random point 2 AJRIATIO CENT OI: moouws PER h) C) 0 C 46 QZEBQHP 70 x -TENSION a o- COMPRESSION 30160‘8 90° GRQUP O— 30°COMPRE$SION 13- 60°COMPRESSION A— 90°COMPRES$ION x --30" TENSION I C) II OF gLASTlCITY V I hD <3 / C) o w 0 O O . - _ 07 I0 II I2 I3 PERCENT MOISTURE Figure 14. The effect of moisture on the percent of modulus of elasticity variation. 47 location and the low correlation coefficients indicated that the prediction equations for the effect of M on the percent variation were not reliable. The small indicated effect that M had on the percent variation at zero grain slope was to increase the percent variation with an increase of the variable. This was 11- lustrated by the positive slopes of the regression equa— tion lines but was considered negligible. For all other grain slopes under compression load the indicated M effect was to decrease the percent variation with an increase of the variable. In the 30°T group the percent variation in- creased as M increased. awn—...: _ .4" ”n 48 V. SUMMARY AND CONCLUSIONS It was found that differences existed between SR-4 and deflection determined strain measurements. Using the deflection measurements as the basis this strain differ- ence increased as the lepe of grain increased. The range of these strain differences increased as did the-average percent of difference. Although neither measurement could be considered accurate, the deflection calculated strain was subject to less variation from angled grain distor- tion. The modulus of elasticity variation was considered the best method for comparing differences between measure- ment methods. The frequency of exceeding ten percent mod- ulus of elasticity variation increased with the slope of grain. The slope of grain had the most effect upon the per— cent of modulus of elasticity variation. A regression equation having high correlation showed that the percent of modulus of elasticity variation increased one quarter of one percent per degree of grain rotation. This had serious implications because transverse sensitivity read- ings made with SR-4 gages at an angle to the grain would be in error as well as stress calculations based on the measured strain. BITS-“‘7'. ILE‘H ‘— It was concluded from the prediction equation that the modulus of elasticity of straight grained material had little influence on the percent of modulus of elasticity variation. Low equation correlation coefficients for the remaining slope groups made it impractical to draw con- clusions. The other equations indicated that the effect of the modulus of elasticity was to increase the percent of modulus of elasticity variation for compression loaded slooed grain groups. The effect in tension was opposite the effect in similar compression groups. A The indicated effect in compression of the Specific gravity on the percent of modulus of elasticity variation was that the variation decreased with the variable for all, grain lepes other than zero. At zero degree grain slope the effect of Specific gravity was negligible. The effect in tension was comparable. The Specific gravity indicated less effect than the modulus of elasticity. Because the prediction equations had very low correlation coefficients no conclusions were made except on straight grained ma- terial. The indicated effect in compression of the moisture content on the percent of modulus of elasticity varia- tion was that the variation increased with the variable at zero degree grain slope and decreased with all other slopes. The effect in tension was that the variation increased for all slopes as the moisture content increased. I E K t‘fiiL‘fi—il-J. Very little reliance was placed on these equations because they had low correlation coefficients. The line slope for straight grained material was almost negligible, and it was concluded that this constituted little effect. The following conclusions were drawn from this study: 1. It became increasingly difficult to make reli- gEfi” able strain measurements as the slope of grain g increased. (pages 26, 29) 2. The lepe of grain had a significant effect on E w J I? 38.4 strain measurement variation. (page 36) K») . The percent variation between the two strain measurement methods on straight grained mate- rial was within experimental error. (page 36) u. Modulus of elasticity had little influence on <9-u strain measurement of straight grained material. (page #2) 5. Specific gravity had little influence on sa-u strain measurement of straight grained mate- rial. (page b4) 4. Voisture content had little influence on 33-4 strain measurement of straight grained mate- rial. (page ”5) 51 VI. SUGGESTED FUTURE STUDIES The results of this study indicated that a difference existed between the two methods of modulus of elasticity determination. Both methods were dependent upon axial de- formation of the member and the calculations were based up- on isotropic behavior of the material. In order that more accurate stress analysis of wood can be made the following studies appear worthy of future investigation: 1. A study of the variation of SR—u determined strain values from deflection calculated strain when they are evaluated or corrected in terms of the ortho- tropic properties of wood. 2. A study of the 58-h measurement of combined stresses in wood. 3. A study of the effect that gage lengths have on strain measurement of wood. DIR—.1 .‘Ffi; a an: «all m1 3'“: MI I ,__m.:‘ Vein. 10. 11. REFERENCES American Society for Testing Materials (1952). ASTM Standards. ASTM, Philadelphia. Des. 143-52. pp. 720-775. Boyd, J.S. (195U). Secondary stresses in trusses with rigid joints, Special applications to glued wooden trusses. Thesis for degree of PH.D., Iowa State College, Ames. (Unpublished). ’3 Ernst, G.D. (1945). The use of SR—h strain gages in the testing of wood and wood base materials. United States Department of Agriculture, Forest Products Laboratory, Madison, Wisconsin. 3 pp. Hetenyi, M. (1950). flandbggk g£_§xpegig§nta1 Stress Ana - 1§;§. John Wiley and Sons, Inc., New York. 1077 pp. 3 7"—'_- .' l r. *mmzm ..‘n amp-1g v c‘._ . . “a: a Hodgman, Charles D., Robert C. Weast and Samuel M. Sel- by (195“). Hangbgok 9;,Chemistgy and Pnygigs. 35th ed. Chemical Rubber Pub. Co., Cleveland, Ohio. 3213 pp. Markwardt, L.J. (1943). Wood as an engineering material. Reprint from Egggeggiggg g; the Amggican Sgciety f9: Testgng Materials. ASTM, Philadelphia. 58 pp. Poletika, N.V. (195M). Slope of grain in engineered wood. Jour. of Forest Products Research Soc. h:h01-403. Radcliffe, B.M. (1955). Method for determining the elas- tic constants of wood by means of electric resistance strain gages. Forest Products Jour. 5:77-80. Society for Experimental Stress Analysis (1954). Ezgr cegdings f r the §ggigt1 fgr Experimental Stagss Anal? The ngd Handngk (1955). United States Department of Agriculture, Forest Products Laboratory, Madison, Wis- consin. No. 72. 528 pp. Youngquist, v.0. (1957). Performance of bonded wire strain gages on wood. United States Department of Ag- riculture, Forest Products Laboratory, Madison, Wiscon- sin. No. 2087. 26 pp. . I y . ()1. ... .n .....c... sL» 3.1 u S} 1! l l .diMjR—osps