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Ulllllllllllllfllfllfljl 1293 10063 4 This is to certify that the thesis entitled MEasuring Young's Moduli, Shear Moduli, and Poisson's Ratios for Wood by a Tension Test presented by Ghanbar Ebrahimi has been accepted towards fulfillment of the requirements for Ph .D . degree in Forestry (Wood Science) . .7 \ V ‘ [/ééétx‘ ’§(L [PL b Major professor Date Agril 25, 1222 0-7639 OVERDUE FINES ARE 25¢ PER nu ‘ PER ITEM Return to book drop to remove this checkout from your record. © 1979 GHANBAR EBRAHIMI ALLRIGHTS RESERVED MEASURING YOUNG'S MODULI, SHEAR MODULI, AND POISSON'S RATIOS FOR WOOD BY A TENSION TEST BY Ghanbar Ebrahimi A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Forestry 1979 ABSTRACT MEASURING YOUNG'S MODULI, SHEAR MODULI, AND POISSON'S RATIOS FOR WOOD BY A TNESION TEST BY Ghanbar Ebrahimi To develop a single test method for determinig all elastic constants for wood in a given plane, Young's moduli, shear moduli and Poisson's ratios were determined from the loading of tension specimens at four angels to the grain and at four stress rates and compared with those determined from tension and compression tests made both parallel and perpendicular to the grain and from plate shear tests. Stress rates ranged from 0.3 to 20 Psi per minute; nominal angles of loading to the grain were 20, 35, 50, and 65 degrees. Specially fabricated strain gage rosettes were used to measure strains parallel, perpendicular and at 45 degrees to the load in tnesion specimens. Measurements were made on a radial-longitudinal plane for Liriodendron tulipifera, Sequoia sempervirens, and Tilia americana, and on a tangential-longitudinal plane for Pinus lambertiana. Except for one specimen, the shear moduli calculated from the specimens loaded at an angle to the grain were from Ghanbar Ebrahimi 86 to 130 percent of the values determined from plate shear tests and were from 93 to 116 percent of the plat shear test values when only specimens loaded at 35 degrees or less were considered. Shear moduli increased the most with angle of load to grain for the two species which had the greatest amount of ray tissue oriented parallel ot the surface of the reference plane. Young's moduli parallel to the grain and Poisson's ratios were not accurately predicted from the specimens loaded at angles to the grain. However, modulus of elasti- city perpendicular to the grain could be calculated fairly closely from these same specimens; particularly, at the larger angels of grain to load. For the range of stress rates employed, the rate of loading had very little effect on elastic constants. ACKNOWLEDGMENTS I wish to express my sincere appreciation to the chairman of my doctoral committee and major professor Dr. Alan W. Sliker, for his assistance and guidance throughout the course of this investigation. I appreciate the keen interest and cooperation of other committee members, Dr. Otto Suchsland of the Forestry Department, Dr. Larry J. Segerlind of the Department of Agricultural Engineering, Dr. Robert K. Wen of the Department of Civil Engineering. My thanks to Dr. Victor J. Rodulph for his encouragement and Mr. Ivan G. Borton, for his assistance in fabricating samples and parts for testing apparatus. I also appreciate the cooperation of Michigan State University. I am particularly indebted to the Iranian masses from which, through a scholarship, this graduate work was made possible. ii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . . . V LIST OF FIGURES . . . . . . . . . . . . . . . . . . . Viii LIST OF NOTATIONS O O O O O O O O O O O O O O O O O I X INTRODUCTIOIQ O O O O O O O O O O O I O O O O O 0 O O 0 1 Objective . . . . . . . . . . . . . . . . . . . 3 Chapter I. MEASUREMENT OF ELASTIC CONSTANTS . . . . . . . 4 Measurement of Elastic Constants in an Isotropic Material . . . . . . . . . . . . 4 Measurement of Elastic Constants in Manu- factured Filamentous Composites . . . . . . 5 Measurement of Elastic Constants in Wood . . 6 Wood Structure . . . . . . . . . . . . . 5 Elastic Constants for Wood . . . . . . . 9 Measuring Modulus of Elasticity . . . . . . 9 Standard Test Methods . . . . . . . . . . 9 Other Tension and Compression Tests . . . 10 Dynamic Testing . . . . . . . . . . . . . 11 Plate Testing . . . . . . . . . . . . . . 12 .Measuring Shearing Moduli . . . . . . . . . 14 Plate Shear Test . . . . . . . . . . . . 14 Torsion Test . . . . . . . . . . . . . . 14 Flexure Test . . . . . . . . . . . . . . 15 Vibration Test . . . . . . . . . . . . . 15 Measuring Poisson's Ratios. . . . . . . . . 16 II. EQUATIONS . . . . . . . . . . . . . . . . . . . l7 Shear Modulus . . . . . . . . . . . . . . . . 21 Moduli of Elasticity . . . . . . . . . . . . 22 Poisson's Ratio . . . . . . . . . . . . . . . 24 Maximum and Minimum Strains . . . . . . . . . 25 iii Chapter Page III. PROCEDURE . . . . . . . . . . . . . . . . . . . . 27 Test Materials . . . . . . . . . . . . . . . . 27 Standard ASTM Test . . . . . . . . . . . . . . 30 Manufacture of Tension Test Specimens . . . . . 30 Strain Measurement . . . . . . . . . . . . . . 39 Loading of Tensile Specimens to Failure . . . . 40 Loading of Gauged Tensile Specimens . . . . . . 40 Supplementary Calculations . . . . . . . . . . 45 IV. RESULTS AND DISCUSSION . . . . . . . . . . . . . 49 Standard ASTM Tests . . . . . . . . . . . . . 49 Tensile Specimens Loaded Parallel to Grain . . 50 Tensile Specimens Loaded Perpendicular to the Grain . . . . . . . . . . . . . . . . 55 Young's Moduli and Poisson' s Ratios from Parallel and Perpendicular to Grain Testing . 61 Tensile Specimens Loaded at an Angle to the Grain . . . . . . . . . . . . . . . . . . . 59 Shear Moduli . . . . . . . . 70 Young's Moduli Parallel to the Grain . . . 86 Young' s Moduli Perpendicular to the Grain . 88 Poisson's Ratios . . . . . . . . . . . 39 Suggestion for Further Study . . . . . . . 90 v. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . 93 LITERATURE CITED . . . . . . . . . . . . . . . . . . 100 APPENDICES Appendix A. Tables 26-39 . . . . . . . . . . . . . . . . . 107 B. List of Raw Data . . . . . . . . . . . . . . . 121 iv Table 10. ll. 12. l3. 14. LIST OF TABLES Page Average Value of Moisture Content and Specific Gravity of Conditioned Test Pieces . . . . . . 29 Results of Standard ASTM Compression Parallel to the Grain Tests 0 O O O O O O O O O O I I O 32 Results of Standard ASTM Compression Perpendi- cular to the Grain Tests . . . . . . . . . . . 33 Results of Standard ASTM Plate Shear Test . . . 34 Ultimate Testing Load and Reduction Factor of Hardwood Specimens . . . . . . . . . . . . . . 41 Ultimate Testing Load and Reduction Factor of Softwood Specimens . . . . . . . . . . . . . . 42 Computed Value of Cross-sectional Area and Angle of Load to Grain of Hardwood Specimens . . . . 47 Computed Value of Cross-sectional Area and Angle of Load to Grain of Softwood Specimens . . . . 48 Strain-stress Slope Values of Basswood Specimens . . . . . . . . . . . . . . . . . . 51 Strain-Stress Slope Values of Yellow Poplar Specimens . . . . . . . . . . . . . . . . . . 52 Strain—stress Slope Values of Sugar Pine SpeCimens O O I O O O O I O O O O I O O O O O 53 Strain-stress Slope Values of Redwood SpeCimenS O O O O O O O O O O O O O O O O O O 54 Principal Strains and their Directions Zero- degree Specimens . . . . . . . . . . . . . . 56 Principal Strains and their Directions 90- degree SpeCimenS O O O O O O I O O O O O O O 60 V Table Page 15. Comparison for the Values of Young's Modulus Parallel to the Grain Measured by Tension Tests and Standard Compression Tests an Hardwoods at 12% Moisture Content . . . . . . 62 16. Comparison for the Values of Young's Modulus Perpendicular to the Grain Measured by Tension Tests and Standard Compression Tests on Hardwoods at 12% Moisture Content . 63 17. Comparison for the Values of Young's Modulus Parallel to the Grain Measured by Tension Tests and Standard Compression Tests on Softwoods at 12% Moisture Content . . . . . . 64 18. Comparison for the Values of Young's Modulus Perpendicular to the Grain Measured by Tension Tests and Standard Compression Tests on Softwoods at 12% Moisture Content . 65 19. Comparison of Moduli of Elasticity and Poisson's Ratios from Loading of Zero-degree and 90- degree Tension Specimens . . . . . . . . . . 67 20. Computed Values of Shear Modulus of Basswood by Off-axis Tension Test . . . . . . . . . . 71 21. Computed Values of Shear Modulus of Yellow Poplar by Off-axis Tension Test . . . . . . . 72 22. Computed Values of Shear Modulus of Sugar Pine by Off-axis Tension Test . . . . . . . . . . 73 23. Computed Values of Shear Modulus of Redwood by Off- -axis Tension Test . . . . . . . . . . . . 74 24. Comparison for the Values of Shear Modulus Measured by Off-axis and Standard Plate Tests 0 O O O O O O O O O O O O O O O O O O O 75 25. Comparison for Poisson's Ratios Computed from Zero, 90-degree and Off-axis Specimens . . . 91 26. Poisson's Ratios Computed from Slope of Strain Perpendicular to Load as a Function of Strain Parallel to Load . . . . . . . . . . . 107 27. Computed Values of Elastic Moduli of Basswood by Tension Tests. . . . . . . . . . . . . . . 108 vi Table Page 28. Computed Values of Elastic Moduli of Yellow Poplar by Tension Tests . . . . . . . . . . . 109 29. Computed Values of Elastic Moduli of Sugar Pine by Tension TestS. . . . . . . . . . . . . . . 110 30. Computed Values of Elastic Moduli of Redwood by Tension Tests . . . . . . . . . . . . . . . . 111 31. Computed Values of Elastic Moduli of Basswood by Combining Off-axis Specimens . . . . . . . 112 32. Computed Values of Elastic Moduli of Yellow Poplar by Combining Off-axis Specimens . . . 113 33. Computed Values of Elastic Moduli of Sugar Pine by Combining Off-axis Specimens . . . . . . . 114 34. Computed Values of Elastic Moduli of Redwood by Combining Off-axis Specimens . . . . . . . . 115 35. E6 Computed by Hankinson's Formula and Directly From Off-axis Specimens . . . . . . . . . . 116 36. Computed Poisson's Ratios for Basswood by Combining Off—axis Test Equation 16 . . . . . 117 37. Computed toisson's Ratios for Yellow Poplar by Combining Off-axis Test Equation 16 . . . . . 118 38. Computed Poisson's Ratios for Sugar Pine by Combining Off-axis Test Equation 16 . . . . . 119 39. Computed Poisson's Ratios for Redwood by Com- bining Off-axis Test Equation 16 . . . . . . 120 vii LIST OF FIGURES Figure 1. Relationship between cordinate axes and two orthogonal ones rotated through angle 8 . . . 2. (a) Orientation of Strain Gauges on Test SpeCimen O O O O I O O I O O O O O O O O O O (b) Appearance of Gauges in Forty-five Degree Rectangular Rosette . . . . . . . . . . . . . 3. ASTM Standard Compression Parallel to the Grain Test 0 I O O I O I O O O O O O O O O O O O O 4. ASTM Standard Plate Shear Test . . . . . . . . 5. Laminated Piece from Which Off-axis Test Pieces vqere cut 0 O O O O O O O O O O I O O O O I O 6. Cutting and Trimming Processes for Off-axis Test Piece 0 C O O O O O O O O O C O O O O O 7. Cutting Off-axis Test Piece . . . . . . . 8. Heat Curing Gauged Area on Specimen . . . . . . 9. Geometry of the Three Types of Tension Specimens . . . . . . . . . . . . . . . . . . 10. Loading Tension Specimen . . . . . . . . . . . 11. Slope of Strain-stress Versus Loading Time for Gauge at 45 Degrees to Load Axis on Specimens Loaded Perpendicular to the Grain . . . . . . 12. Shear Modulus Versus Stress Rate for Basswood . . . . . . . . . . . . . . . . . . 13. Shear Modulus Versus Angle of Load to Grain for Bassw00d O O O O O O O O O O O O O I O O O O 14. Shear Modulus Versus Stress Rate for Yellow Poplar . . . . . . . . . . . . . Page 20 20 20 31 31 36 36 37 37 38 44 58 76 77 79 Figure Page 15. Shear Modulus Versus Angle of Load to Grain for Yellow Poplar . . . . . . . . . . . . . . . . 80 16. Shear Modulus Versus Stress Rate for Sugar Pine 0 O O O I O O I O O O I O O O O O O I O O 81 17. Shear Modulus Versus Angle of Load to Grain for Sugar Pine . . . . . . . . . . . . . . . . . . 82 18. Shear Modulus Versus Stress Rate for Redwood . . 84 19. Shear Modulus Versus Angle of Load to Grain for Redwood . . . . . . . . . . . . . . . . . . . 85 ix LIST OF NOTATIONS The following symbols represent used notations in the text; they are, however, properly identified when first introduced. L = Longitudinal direction R = Radial direction T = Tangential direction OR = Stress in the R (radial) direction OL = Stress in the L (grain) direction TRL = Shearing stress in LR plane OX = Stress in the x direction Oy = Stress in the y direction xy = Shearing stress associated with xy plane 8 = The angle of rotation for axis 8R = Strain in the R (radial) direction 8L = Strain in the L (grain) direction YRL = Shearing strain in LR plane Ex = Strain in the x direction 8y = Strain in the y direction ny = Shearing strain in xy plane Ei = Modulus of elasticity (Young's modulus) i = L,R,T Li LR RL max min Shear modulus i = R,T Slope of strain-stress curve i = 1,2,3 . . strain alon R-axis POIsson's ratio = 9 strain along L-axis (when uniform O is applied) L strain along L-axis Poisson's ratio = strain along R-axis (when uniform O is applied) R Maximum strain Minimum strain xi INTRODUCTION Use of wood as a structural material is complicated by the facts that it is elastically anisotropic and that some of its elastic properties are not well documented. There are twelve elastic constants for wood: three Young's moduli, three moduli of rigidity and six Poisson's ratios. Among these elastic constants of wood, moduli of elasticity were more thoroughly investigated in the past. The reasons for this could be ease of measurement of Young's moduli and the greater need for them in timber design. In the more rigorous design procedures of modern times, however, more information is needed with regard to Poisson's ratios and shear moduli. Several different methods are used to determine the elastic constants of wood. The Poisson's ratios and Young's moduli are usually measured by making tensile or compression tests both parallel and perpendicular to the grain on properly instrumented specimens. The shearing moduli are determined by conventional method of shear plate testing. Consequently at least three sets of specimens are required to measure the elastic parameters of wood associated with any one of its three principal planes. The use of excessive sets of speci- mens and the inherent variability in the structure of wood can make it difficult to analyze the elastic properties of a particular specimen of wood. It is possible that some of the current standard test procedures could be improved to measure moduli of rigidity. The expression from which the shear modulus is computed, was derived from small-deflection plate theory. The useful range of that deflection is limited by the assumptions in this theory. Thus if corner displacement of the plate reaches to a limit beyond which middle-plane stretches non-linearly, the validity of the derived expression is no longer acceptable. Less-dense species of wood are probably good example for this case. Therefore a separate formula based on large-deflection theory is needed to compute their shearing moduli. Such a formula has not been published yet. To avoid some of the problems mentioned above, transformation equations for stress and strain were utilized by Greszczuk [24]* to develop a single procedure to determine the elastic constants of anisotropic materials among which wood is included. A combined theoretical and experimental investigation on the applicability of this test method, followed by the design of appropriate off-axis tensile test specimen is the subject of this work and presented here. * Numbers in brackets indicate references. Objective Development of a single test method for determining all the elastic constants for wood in a given plane. CHAPTER I MEASUREMENT OF ELASTIC CONSTANTS For best and intelligent use of engineering materials, their elastic properties are closely investigated. In doing so various experimental techniques are applied to examine elastic constants. The number of elastic constants needed to define a given material depends on whether it is isotropic or anisotrOpic; i.e., whether its properties are independent or dependent on the direction of measurement. Measurement of Elastic Constants in an Isotropic Material For an isotropic material there are four elastic constants of which any one can be determined from a know- ledge of two of the others. The constants are Young's modulus E. bulk modulus E shear modulus G, and Poisson's BI ratio D. The following relationships exist between these constants. 9E - G 3E - 26 E: B 'G=—-—E—— '11:;— (BBB + G) 2(1 + u) 2(3EB + G) To measure these constants for a given isotropic material, tension, compression and torsion tests are made on a proper specimen. Because of the vast usage of isotropic materials such as metals in modern industry, numerous test systems and data monitoring have been developed for measuring the elastic parameters of this group of engineering materials. Measurement of Elastic Constants in Manufactured Filamentous Composites Filament-reinforced composites consist of a rec- tangular array of parallel filaments embedded in a matrix. In planes parallel to the filament axes, the filament rein- forced materials have five elastic parameters. Two Young's moduli, one shear modulus and two Poisson's ratios. A know- ledge of four of the parameters associated with one of these planes is needed to completely define the elastic properties in that plane. These elastic moduli for filaments composites can be analytically determined from a knowledge of elastic proper- ties of constituent materials (filament and matrix). Greszczuk [25] did this for fiber glass embedded in an epoxy matrix. A reasonable agreement (within 10%) between these analytically predicted elastic moduli and their experimental values was observed. To experimentally determine elastic constants of filament-reinforced composites, several methods are avail— able. Tension and compression tests are conducted for the determination of Young's moduli and Poisson's ratios [24]. For the same elastic moduli, dynamic tests can also be used. For shear modulus, the plate shear test is the common one. On properly constructed sample of fiber composite material, triaxial tests could also be made for evaluating their elastic moduli. It is difficult to conduct triaxial test as well as it is somewhat expensive because of requiring sophisticated equipment [24]. One of the latest techniques to measure elastic parameters of filament-reinforced composites, utilizes the anisotropic properties of these materials to generate shear deformation in tension specimens loaded at selected angles to the main filament axis [15, 24, 60, 80]. An advantage of this test method is that, all five elastic constants of a given filamentary composite material can be determined from one type of test specimen. To find the potential of off-axis test, Greszczuk [24] has applied this test technique to measure the elastic moduli of fiber glass. According to his report "good agreement is found to exist among the various properties obtained from tests of specimens with various filament orientations as well as between experimental values and theoretically predicted values of the elastic constants." In addition,off-axis test was regarded well suited for measuring shear modulus. Measurement of Elastic Constants in Wood Wood Structure Wood is a natural product consisting of concentric layers of growth shells. It is produced by trees which grow under diverse ecological conditions that affect their growth rates, shape, structure and strength. Hardwoods are woods from broad-leaved trees and softwoods are woods produced by conifereous species, which have needle-like leaves. Anisotropic properties of wood arise from its cellular structure. Most of the cells are long, hollow tube-like structures, and,with the exception of vessel segments in hardwood, have closed ends. Depending on the species, any- where from 70 to 95 percent of the cells have their long axis parallel to the length of the stem to which they belong. The remaining 5 to 30 percent of the cells are oriented from the center of the stem outward in tissues called rays. Three mutually perpendicular reference directions are recognized for the measurement of wood properties. The grain direction (L) is the direction of the length of the majority of cells, which is parallel to the length of the log con- taining the wood. A radius of the circular cross-section of a log is designated as the radial direction (R). The long axes of rays are in the radial direction. The third reference direction is the tangential direction (T). It would be perpendicular to a radius and tangent to the circu- lar cross-section. Reference planes in wood are denoted by the directions which define them: the RT plane is the cross- sectional or transverse surface of a log where most cells are viewed in cross-section; the RL plane or radial surface is defined by a radius of the log and the grain direction; the TL plane or tangential surface is defined by a tangent to the log cross-section and the grain direction. Rays are seen on side view on the radial surface and in cross-section on the tangential surface. Besides the anisotropy due to the cell orientations, wood is non-homogeneous because of the number of cell types present, their variability in cell wall thickness and dia- meter, and their variability in cell wall structure. Hard- woods have more cell types than softwoods and so are more complex with respect to relative arrangements and numbers of cell types present. Hardwoods are also more variable with respect to the amount of ray tissue present. There is variability of wood in the radial direction from several growth patterns. Some species have very large differences in the anatomy and physical properties of wood grown in the early part of the growing season (earlywood) as compared to the wood formed towards the end of the growing season (latewood). Also, wood formed in the first fifteen to twenty years growth of a tree has shorter cells and differences in cell wall structure from that grown later. If a tree is leaning when it grows, the wood formed on one side of the tree is different from that on the other side. It is difficult to obtain a tangential surface on a wide board because of the curvature of the growth rings. This is not a factor in obtaining a radial surface. Elastic Constants for Wood Although twelve elastic constants can be defined for wood, all of them can be determined from a knowledge of any nine; i.e., there are only nine independent elastic con- stants. A Young's modulus exists for each of the three defining axes R, T, L. For each major plane there are two Poisson's ratios dependent on which of the major axes in the plane is loaded and a shear modulus. Experimental techniques which are used to measure the elastic parameters of wood are similar in principle to those applied for evaluating elastic constants of metals. But there are some differences such as size and shape of specimens and number of constants that are to be measured. Also, measuring equipment for wood testing must possess sensitive load measuring devices, and deflection or strain sensors have to be of low resistance to motion. Test proce- dures for determining different elastic constants of wood are reviewed in the following paragraphs. Measuring Modulus of Elasticity Standard Test Methods.-—Several methods for deter— mining Young's moduli parallel to the grain are described in ASTM standard D143-52[1]. Of the methods mentioned, the compression parallel to the grain test gives the best results [42, 59] although the assumption of a state of pure com- pressive stress in the specimen may be inexact [76]. Young's 10 moduli could be obtained from a tension parallel to the grain test, but the standard sample for this is difficult to fabricate [17, 50]. Values of Young's moduli obtained from a bending test have to be adjusted for a shear deflec- tion component, which makes this calculation subject to additional variables [42, 58, 59]. The only standard test for obtaining modulus of elasticity perpendicular to the grain in ASTM Dl43-52 is a compression perpendicular to the grain test. Although the test prescribes loading in the tangential direction, it could be used equally well for loading in the radial direction. Load-deflection curves for perpendicular-to-grain loading in compression are not as linear as for parallel-to- grain loading. Little information exists on stiffness in tension loading perpendicular to the grain. Other Tension and Compression Tests.--Other than the standard tension specimen, tensile samples of very simple construction have been used to determine Young's moduli and Poisson's ratios of wood [66, 67, 68, 69]. Strain measure- ments were made by two-strand wire strain gages [64]. Rec- tangular tensile samples containing a hole at each end to apply load at an angle to the grain direction, were also used [63] to determine shear moduli [G G G ), Young's LR' LT' TR . . , . moduli (EL, E ET) and Poisson 3 ratios (ULT, ) of R' “LR' “TR wood through measuring deflection on this type of specimen and computing required strain data. Sliker included rate of ll loading as a factor in determining moduli of elasticity in tension. In one paper [68] he found that the effect of rate of loading on modulus of elasticity increased as the angle between the grain direction and the load increased. In an example in another paper [69], modulus of elasticity perpen- dicular to the grain was more than 10 percent less at a stress rate of 0.561 psi per minute than at a stress rate 20.6 psi per minute. In compression testing, standard tests for computing Young's moduli and Poisson's ratios are simple in principle and specimens are readily manufactured. Therefore not much effort was made to improve this procedure except by modi- fying specimens dimensionwise for studying particular factors affecting compression strength of wood [37] and by methods in applying load to specimen [10]. Dynamic Testing.--Moduli of elasticity (EL, ER’ ET) can also be obtained from dynamic tests. Some types of dyna- mic tests for this purpose are flexure vibration, vibration of a column and pulse transmission. Dynamic tests are reported to be less accurate for determining elastic moduli than are static ones [40, 42, 78]. All three Young's moduli measured from dynamic tests were about 10 percent higher than their static value [6, 78]. Hearmon [28] sug- gests that for evaluating moduli of elasticity from vibration tests, frequency of many modes be measured and statistically analyzed. There are some advantages of dynamic tests as 12 (a) they are nondestructive, (b) individual specimens can be tested more than once, (c) Young's moduli and shear moduli may be measured from a single test sample, (d) speci- mens can be tested in service scale with pulse methods. Russian investigators [3] have recently used an impulse method to determine elastic moduli of wood. They conducted vibration tests and static tests with the appli- cation of strain gages. Their report indicates that the results from impulse technique differed from that of strain gage by 4 percent for E 17 percent for E E was L' T' R estimated 12 percent smaller by impulse method. A disad- vantage of this procedure is that it requires some infor— mation of Poisson's ratios as well. Plate Testing.--P1ate tests have been used for determining Young's moduli, shear moduli and Poisson's ratios of orthotropic materials and studies were made on the validity of this test technique. In conjunction with the idea of plate testing, Hearmon and Adams [30] have compared the experimental values of modulus of elasticity, shear modulus and Poisson's ratio from tests made on plywood plates and theoretically predicted values of these constants. They report that the general agreement between these two sets of values was close (within 10 percent), although in some cases, fairly large (30%) discrepancies were observed. They relate these to the variability within plywood itself. The aptness of plate testing (with 6% differences in value 13 of modulus of elasticity) was confirmed in another study [79], but it must be realized that this experiment is appli- cable for orthotropic materials in which linear strain-stress relations exist over a definite range of stress. To evaluate components of compliance matrix (Sij' Ei = Sijoi) by making tests on orthotropic plates, Tsai [73] has proposed three steps of testing. Bending a beam (strip) sample with orientation of an elastic symmetry axis at 90 or zero degree. Twisting square plates, one along and another at 45-degree with respect to an elastic symmetry axis. He claims that, the procedure is easy to implement and reliable data are obtained. The idea was carried into effect for determination of elastic constants of plywood and sandwich boards and corresponding report shows that excellent agreement (maximum error 3.3% for all compliance) between theory and experimental results was observed [16]. Plate test was applied to measure Young's moduli, shear moduli and Poisson's ratios of solid wood by Gunnerson et a1. [26]. Their observations confirmed the existence of large two-way bending moments in the plates. It was believed that two-way bending effects were created by a tri- angular load pattern and could cause large deformations in the plate sample. These two-way bending effects were noticed to vary from plate to plate depending upon grain orientation. Finally by making use of orthotropic plate theory, a cor- recting method was found to treat two-way bending effects 14 which may improve this test procedure, but the calculations for Poisson's ratios remain inaccurate. Measuring Shearing Moduli Shear moduli of wood could be determined through one of the following experimental procedures. Plate Shear Test.--This method of test was recog- nized as being the most useful to determine shear moduli of plywood and solid wood [42]. The expression from which shear modulus is computed, was derived from linear, small- deflection, plate theory. It is valid for an orientation of the principal axes of elastic symmetry in x, y plane [21], but the useful range of deflection is limited by the assumptions in this theory. If corner deflection reaches to a limit beyond which middle-plane stretches nonlinearly, the aptness of derived expression for shear moduli is not acceptable. In a study of shear modulus of particleboard and plywood by plate shear test, Biblis and Lee [7] observed more accurate values of shear modulus can be obtained by measuring the required deflection at extremities of diagonal of plate. Torsion Test.--In torsion test on wood, it was noticed that at least two of the shear moduli are involved [27, 42]. Kuenzi [42] states that it is possible to perform torsion test on two sizes of matched specimens and compute apparent shear modulus by solving simultaneous expressions. 15 The accuracy of doing so is questionable unless extreme care is exercised in matching samples and in measurements. If involvement of two shear moduli in torsion test is true, then plate shear and torsion test on a given species should not produce the same results. DeSpite this observation Tang et a1. [70] report "the results calculated from rod twisting are in close agreement with the values obtained from the experiments of plate deflections." They concluded this from the testing of scarlet oak and graphi- cally comparing the results of the two test methods. Flexure Test.--Theoretically it is possible to compute shear modulus by making a flexure test on a beam sample [58]. A complementary compression test on a matched specimen is needed to obtain true Young's modulus of test piece for this calculation. No experimental verification has been made. Vibration Test.--For vibration test the same objec- tion as to torsion test exists [42]. That is a mixed measurement of two shear moduli would be made by vibration test. Becker [5] has attempted to apply torsional vibra- tion, to determine shear moduli. In this method of testing, he measured the torsional rigidity along an elastic symmetry axis to obtain the values of shear moduli. Ashkenazi et a1. [3] have recently studied an impulse method of measuring shear modulus. Their report 16 indicates that the results of impulse method differed by 30 percent from that of their control method. Measuring Poisson's Ratios All six Poisson's ratios of wood can be directly measured by making tensile or compression tests on wood samples and recording strains parallel and perpendicular to the load direction. and “TL are very small quantities “RL and are difficult to measure, but they are subject to the following relations: u =1] 53 RL LR EL E = .;I “TL “LT EL Other than strain measurements technique, according to Carrington [12], Poisson's ratio is numerically equal to lateral curvature divided by longitudinal curvature in a flexure test. This procedure was of less interest, perhaps because of lack of accuracy and has not been applied in the past. CHAPTER II EQUATIONS Elastic constants of synthetic anisotropic materials have been determined by loading the materials in a direction other than parallel to one of their axes of symmetry [15, 24 60, 63, 80]. This test method is capable of evaluating up to five elastic parameters for a given anisotropic material. The basic stress and strain transformation equations for determining elastic constants are described in the following paragraphs and in References 24, 56, 57. If normal and shearing stresses or strains in a plane are given with respect to a set of coordinate axes x and y, stresses or strains associated with another set of coordinate axes R,L in the plane which has a rotation angle of "8" from the initial set of axis, can be obtained through transformation equations. " 2 .2 . q . 1 [ OR] cos 8 Sln 8 Sln28 Ox 0 = Si% 8 co% 8 -sin28 O (l) 4 L ' 4 y l T —%sin28 %sin28 c0528 T L RL‘ L _ L ny l7 18 cos 8 Sig 8 ksin28 [ ex] .2 2 . Sln 8 cos 8 -%51n28 ‘ 6y. (2) -sin28 sin28 c0528 - LYXY. stress in the R (radial) direction, stress in the L (grain) direction, stress in the x direction, stress in the y direction, Tyx = shearing stress associated with xy plane, TLR = shearing stress in LR plane, strain in the R (radial) direction, strain in the L (grain) direction, Y = shearing strain in xy plane, yx shearing strain in RL plane, the angle of rotation for axis. Figure 1 indicates the referred to axes and direction of rotation. Now if R and L are the axes of elastic symmetry of the material, relationship between the components of stresses and strains could be written as: 19 R ER LR EL (3) E ._. °_L _ u is L L RL ER (4) T RL YRL = G— (5) LR where: E Young's modulus parallel to L axis, L ER = Young's modulus parallel to R axis, GLR = GRL = shear modulus for RL plane, . . Strain along L—axis = ' = . . LlRL P01850n 8 ratio Straln along R-aXIS (when uniform OR is applied) = . , . = Strain along R-axis ULR POISson S ratio Strain along L-axis (when uniform O is applied). L LR' EL and ER some measure- ments of stress and strains need to be made. A uniaxial In order to evaluate G tension test on off-axis (Figure 2a) sample would provide the required data as explained next. If a uniaxial stress is applied, Ox = T = o and Equation 1 will be simplified into: . 2 R Oy Sln 8 (6.1) O 2 O = OY cos 8 (6.2) TLR = toy Sln28 (6.3) 20 #-< R J 8 O L" Figl Relationship between coordinate axes and two orthogonal ones rotated through angle 9 F .. \ and er’ I l I I I I I I I I 0‘ (a) Orientation of strain (b) Appearance of gauge: gauges on test Spacing." in forty-five degree rectan- gular rosette. Fig. 2 21 When strains are measured with a rectangular rosette with gauges parallel and perpendicular to the load and with a third gauge at an angle of forty-five degrees to the other two (see Figure 2), the strains are as follows: y 1 Ex = E:3 (7) ny = 262.61-53 e = e c0528 + s sin28 - 5(26 -€ -€ ) sin28 (8.1) L l 3 2 l 3 (D ll 6 sin28 + e c0328 + 5(262-8 R l 3 -e3) Sln28 (8.2) l (262-61-63) c0528 + (El-e3) Sln28 (8.3) Thus normal stress and strain associated with sym- metric axes R and L are obtained. Shear Modulus An equation for determining shear modulus from off- axis tensile specimens can be derived from Equations 5, 6.3, and 8.3. 22 G :38 LR YLR 50 sin28 G = Y LR . (El 23) Sinz8+ (262-81-83) c0528 G = 1 LR 2(Sl-S3) + (252-81-S3) (cot8- tan8) (9) S1 = 81 - Cy S2 = 62 i 0y (9.1) S3 = E3 - 0y Moduli of Elasticity Modulus of elasticity parallel to the direction of loading of a test specimen equals simply stress divided by strain: E = .1 = __ (10) If the grain direction coincides with the load axis, then the modulus of elasticity of the wood parallel to the grain is obtained from Equation 10. If the perpendicular to the grain direction is parallel to the load, then the modulus of elasticity perpendicular to the grain is obtained. E refers to modulus of elasticity in the radial direction R and ET to the value in the tangential direction. Moduli of elasticity at angles other than parallel or perpendicular 23 to the grain are related approximately as described by Hankinson's Equation: EE E = 'ELR 2 (11) ELSl 8 + ERcos 8 A technique in data reduction on off-axis test for L' ER and/or E expression for each by combining and simplifying the sets determining E is to derive computational T of Equations 6 and 8 as well as 3, 4. In doing so at least one Poisson's ratio of the plane being tested, must be known. Then by making use of Maxwell's Reciprocal Theorem E - _R - RL — “LR EL) and Equations 3, 4, 6.1, 6.2, 8.1, 8.2 the following relations are obtained: (L » = OJ: _ is L EL RL ER C = E _ IJ E_R (O_R) L EL LR EL ER 7, OR B : ._'LJ. -- L; —. L EL LR EL 2. . 2 EL = chos 8 - ULROy Sin , 2A . 2 _ _ _ . LlCOS C+ €351n 8 (26:2 61 E3)Sin€cos8 2 l - “LR tan 8 - — — - 8 L Sl + SBtan 8 (ZS2 S1 S3) tan 24 In similar fashion: 1 S + S cot28 + (2S -S -S ) t8 + :95 t28 (13) 1 3 213°° EL°° S S S are defined by Equation 9.1. 2' 3 A third method for calculating Young's moduli 1' requires data from two off-axis tension specimens with dif- ferent angles of load to grain. From combination of Equations 3, 6 and 8: O O O U C U U U E = Ll R2 ' L2 R1 R1 L2 ‘ R2 L1 (14) L OR EL _ OR EL — 2 1 1 2 The quantities OL'S ......€R's are computed from test data by the following expressions. 2 2 2 . = = ' - 2 - - Sin29 0L 0y cos 61 EL €3151n 61 + Ellcos 91 %( 821 E31 €11) 1 l 1 1 O = O sin28 e = e c0528 + e sin26 + 5(25 -5 -e ) sin29 Rl yl 1 R1 31 1 11 1 21 11 31 1 0 = O c0526 6 = € sinze + E c0328 - 5(26 -€ -€ ) 81029 L y 2 L 32 2 12 2 22 32 12 2 2 2 2 O = O sin28 e = e c0528 + e sin28 + 5(26 -6 -€ ) Sin29 R2 y2 2 R2 32 2 12 2 22 32 12 2 Poisson's Ratio In a given plane such as the RL plane, there are two Poisson's ratios “LR and URL' is the ratio of strain in “LR the R direction to that in the L direction when a force is 25 applied in the L direction. is the ratio of the strain “RL in the L direction to that in the R direction when a force is applied in the R direction. and “LR are related by uRL the equation: LR = RL EL ER (15) “LR can be determined from the zero-degree specimen by dividing strain perpendicular to the load by strain parallel to the load. And URL can be determined from the 90-degree specimen in similar fashion. When the load is applied perpendicular to the grain, however, the strain perpendicular to the load is difficult to measure so that URL is often calculated from measurements of the other three quantities in Equation 15. A second method for determining Poisson's ratio is to combine data from two off-axis tensile members with different angles of axis to load as follows: R uLR = 0:1e:2 : 0:25L1 2 1 1 2 (16) u... = :9?” ' :13?“ L2 R1 ' L1 R2 26 Maximum and Minimum Strains To compute the magnitude of principal strains, the following equations are applied: ems—J- leg—alter (17) e e e _ e 2 y 2 emf—479.4) we) The plane on which the maximum and minimum strains act are defined by the Equation 18. Y Tan 29 = r—i—{XE— (18) X Y E = maximum strain, max t . = minimum strain, min 8 = angle, locating the direction of principal strains with respect to x,y. CHAPTER III PROCEDURE The strategy for the project was to determine elastic constants from strain gauge rosettes mounted on tensile Specimens. Each specimen was to be loaded four times, each time at a different rate to see if rate of loading would affect the results. In order to determine safe load limits for the specimens with rosettes, a set of matched specimens was loaded to failure. Shear moduli and Young's moduli parallel and perpendicular to the grain were also determined by Standard ASTM tests for purpose of comparison. Test Materials Four species of wood were chosen for testing. These were basswood (Tilia americana L.), yellow pOplar (Liriodendron tulipifera L.), sugar pine (Pinus lambertiana Dougl.), and redwood (Sequia sempervirens [D. Don] End L.). Major considerations in this selection were uniformity of cell structure and availability. In addition, quarter sawn or vertical grain boards were favored because the curvature of the growth rings would not be a factor as they would be in plain sawn or flat sawn boards. 27 28 Selected trees of basswood and yellow poplar were cut down in the experimental forests of Michigan State Uni- versity, to obtain 5/8-inch quarter sawn boards and nominal 2 1/2 x 2 l/2—inch squares. The diameter breast high of the yellow poplar tree was 36 inches and that of the basswood was 32 inches. Out of a log from each of these species, a single segment 32 inches long was cut and split parallel to the grain into pie-shaped pieces. The revelant pieces were individually mounted on a positionable carriage and sawn radially into 6/8-inch thick boards and 2 1/2-inch squares. These were end coated and stacked for air drying. A quarter sawn redwood board (1" x 11" x 14') was selected from the available vertical grain boards of this species in the lumber yard of a wholesale company. Parti- cular attention was paid to straightness of grain and uni- formity of growth rate. Moisture content of redwood board at time of purchase was measured 10 percent by a moisture meter. A flat grain board (1 3/4" x 17" x 16') of sugar pine was already available in the laboratory of wood techno- logy at Michigan State University. Test materials were stored in the conditioning room (68°F, 65% RH) for three and a half months. By the use of moisture meter, the moisture content of the conditioning materials were inspected at interval until equilibrium was reached. Their moisture contents and specific gravities 29 were determined by the oven-drying method prior to the specimen fabrication (Table l). Equilibrium moisture con- tents of nominal 2 1/2 x 2 l/2-inch squares from basswood and yellow poplar were slightly higher (0.66%, 0.93%) than for the 5/8-inch material which indicates they might still have had a slight moisture gradient. The number of rings per inch of test materials were found as 7, 8, 12, and 17 for basswood, yellow poplar, sugar pine and redwood, respectively. Table 1.--Average Value of Moisture Content and Specific Gravity of Conditioned Test Pieces. T Specific Gravity* Moisture Species l . On oven-dry 1 At 12% Content %: At test Weight MC 1 i 7 9T Basswood 11.69 ‘ 0.39 0.42 0.39 Yellow Poplar 13.09 F 0.51 f 0.54 0.51 Sugar pine ; 9.37 0.37 § 0.40 0.36 Redwood é 10.20 0.39 . 0.42 0.39 *Based on oven-dry weight and on volume at moisture content of measurement. 30 Standard ASTM Test To determine modulus of elasticity Ei (i = L,R,T), standard specimens were made out of materials from the four species and tested (Figure 3) according to ASTM Specification (D143-52). For sugar pine and redwood, standard test speci- mens (2 x 2 x 8-inch, 2 x 2 x 6-inch) were made by gluing board pieces together for the required two inches dimension. The cross-head speed of testing machine (Instron) was set at 0.02 in/minute for compression test parallel to the grain and 0.01 in/minute for compression test perpendicular to the grain. The number of specimens for these tests are shown in Tables 2 and 3. Standard shear plate Specimens were manufactured with their length and width equal to twenty-eight times their thickness (28 x 0.5-inch). For yellow poplar, basswood and redwood, two boards were edge glued to fabricate a shear plate specimen. The sugar pine board was wide (17 inches) enough to produce the desired shear plate specimen without any gluing process. In this standard test (Figure 4), ASTM specification (D3044-76) was followed and the cross-head speed of testing machine was set at 0.02 in./minute (0.012 x l4-inches). The number of specimens for each species is Shown in Table 4. Manufacture of Tension Test Specimens For tension test, three types of specimens were made out of the materials from the four Species. Type A, 31 Figure 3. ASTM Stand Compression Parallel to the Grain Test. Figure 4. ASTM Standard Plate Shear Test. 32 Table 2.--Resu1ts of Standard ASTM Compression Parallel to the Grain Tests. : l .. S ecimen EL* . Average i Standard I Coeffic1ent Species p . E . Deviation i of Number PSl L . - . . . PSi ! Variation % PSl l 1 1,822,500 . 2 3 1,507,000 ‘ Basswood 3 ; 1,557,000 . 1,610,000 144,000 9.0 4 ; 1,553,000 , . i 1 ; 1,701,000 f ; $2112: 2 : 1,687,000 i 1,705,000 l 20,000 i 1.2 P 3 l 1,727,000 a ‘ s ’ l l i i v + . Sn ar 1 g 1,476,900 ! 3 ; Pige 2 : 1,314,400 ‘ 1,429,000 ; 100,000 1 7.0 3 ; 1,496,100 ' l l ' 1 ; 1,204,500 . l 7 Redwood 2 i 1,479,200 1,342,000 l 194,000 . 14.5 l *This value for Young's modulus was measured at approximately 12% moisture content. 33 Table 3.--Resu1ts of Standard ASTM Compression Perpendicular to the Grain Tests. i . ' E ** Average Standard ! Coefficient . SpeCImen R . , . Spec1es s . E Dev1ation l of Number i (PSI) R s . . l . PSI l Variation % l (PSI) ; 1 . 114,000 Basswood 2 110,000 114,700 5,000 4.4 3 120,000 1 190,000 Yellow 2 150,000 77 2.4 Poplar 3 170,500 1 '600 22'100 l 4 200,000 Su ar 1 80,000 P138 2 55,000 72,300* 15,000 20.7 3 82,000 1 110,000 Redwood 2 90,000 100,000 14,100 14.1 *ThiS value is ET for sugar pine. **This value for Young's modulus was measured at approximately 12% moisture content. 34 .UCOHCOU OHSHWHOE WNH >HoumEonqum um UOHDWwOE mm3 mflHDGOE Hmmfim HOW ODHM> mflfififit .OCHm ummsm How 9H0 DH osHm> DHcee 1 iii iii oom.NmH oom.NMH m H voozpmm n. i . . . oom.vOH N asam mu N oom N m Room NOH . Hamsm 1 com 00H H oom.mNH N HnHmom so.H OCH.N oom.s~H onHo» oom.mNH m H _ oom.mm N m.o oon oom.nm poozmmnm CON.>m H w coHumHHn> Hum _ mo coHumH>oa 1 Hum “Mm CMWMWMM mmHoomm Damsoanoooo onmoomum m app 44 o . m l-_ _ .umme Hmonm oumHm 28m< puppcmum mo manmwmii.v OHQUB 35 the off-axis specimens, had an angle of inclination (8) between grain and load directions, where 8 represented angles between 20 and 65 degrees. Type B specimens were those in which the grain was parallel to the load direction. Type C specimens had their grain perpendicular to the load direction. Specimen types are also frequently referred to in this report by the angle between load and grain directions. Each tension Specimen required a l/2-inch thick by 4-inch wide by 25-inch long board in which the angle between the grain of the wood and the 25-inch dimension of the board was the specified test angle. A board of this dimension could easily be made for the zero-degree specimen but for the other angles extra boards had to be glued to sides as shown in Figure 5. The central test boards had a minimum width of 8 inches. All bonding was with polyvinyl adhesive. Cutting of the boards to achieve the desired angle was done as shown in Figures 6 and 7. To complete the tensile specimens, boards of red oak were bonded at the ends of the test boards and grooves were cut into them to receive 2 1/2 inches diameter shear plates as shown in Figure 9. Materials for basswood, yellow poplar and sugar pine were sufficiently available to prepare four off-axis tension specimens with the angle of inclination of 20°, 35°, 50°, and 65°. For redwood there was only enough material to make specimens with 35°, 50°, and 65° inclina- tion angles. Grain Direction ‘— Figi5 Laminated piece from which off- axis test pieces were cut. a , c= stress- transmitter board b= test board (a) ‘\\\\, 25 in. F\Q Fig.6 Cutting and trimming processes for off-axis test piece. (c) 37 Figure 7. Cutting Off-Axis Test Piece. Figure 8. Heat Curing Gauged Area on Specimen. 74 [OIV it 'e I! 1 Off-axle acumen Type A HO] lll©l 1.3.. BIT) Ill HO” .— 1 Mr) F Typec Fig.9 Geometry of the three types of tension specimens. 39 Two sets of Type A and Type C specimens were made. Those from one set were loaded to their breaking point. Those from the other were used for determining elastic con- stants at the specified loading rates. Strain Measurement Strain was measured in the wood with rosettes of free-filament bonded electrical resistance strain gauges. These gauges allow rapid reading of strain and at the same time are less apt to restrain movement of their substrate then are gauges with rigid backing materials. Gauges were made essentially as described by Sliker [64] except that the length of the one mil diameter strain sensitive wire in a given gauge was only about four inches. This produced a gauge with a resistance of 90 ohms. After bonding the gauges to the wood in a 2-inch long U-shaped pattern with thinned nitrocellulose cement, the gauge installations were allowed to air cure for 24 hours. This was followed by a condi- tioning at 100°F for 4 hours (Figure 8). The gauges were installed as rosettes on the center of opposite broad faces of each test specimen and on matched boards for use as compensating gauges. One gauge was parallel to the member's length, another was perpendicular, and a third was at an angle of 45 degrees to the member's length. This arrangement is shown in Figure 2. Resistance of each gauge to the nearest 0.02 ohms was determined with a Hewelett Packard Digital Multimeter, Type 34072A. 40 Precautions were taken to protect the gauges and boards from slight fluctuations in the relative humidity and temperature in test area. One of these was to coat end grain surfaces on the narrow edges of boards with wax. Then saran wrap was wrapped around the gauged area and its proxi- mity. In addition a one-inch thickness of a low-density rubber cushioning material was placed over gauges during a test. Loading of Tensile Specimens to Failure As was mentioned earlier, by loading one set of tension specimens to their breaking point, the ultimate strength of unbroken specimens could be estimated. This loading was done on an Instron model TTD testing machine with a cross-head speed setting of 0.002 inch/minute. Failure loads were recorded (Tables 5, 6). The zero-degree specimens were not included in this testing because their strength would have exceeded the capacity of the testing machine. Loading of Gauged Tensile Specimens The magnitude of maximum test load for each Speci- men used in strain determinations was proposed. Then it was divided by the corresponding measured ultimate load to compute the reduction factor. Rounded reduction factors ranged from 0.07 to 0.320 (Tables 5, 6). The maximum test load was applied to each specimen four times, each time at a different rate of loading. Rates 41 .mcofiHommm mmummpiouwu now comomonm mm3 cmoH mo OSHm> MHEBR H ” coH.c com coca _ omH.o m cos oooH co HcH.c _ com oNHN . oo~.c w com coma oo cmH.o _ com ommm W omH.c com coHN co ooc.o com comm _ ccH.o com ccom om cco.o coo coco 1 ooo.o M coo ommo cm . in coo in nu _ .oco in o _ _ cocooc EH coon come EH coon nouooc oH coon poms EH coon monomeric coHuospom ESEmez oumEHuHD coHpospmm w EDEmez mumEHuHD GOHDMGHHOGH mo HUHmom 3oHHow ooozmmnm mHmsd anHEoz .MOHOOQm moospum: mo Houomm coHuospom can pnoq mcHumme oumEHuHDIi.m OHQUB 42 .poozomu How pmumoHunnw mm3 smEHommm omumopioN 024 cms.o 1 ocH ocMH m cc~.c W coH coo cc cmm.c w com mom 1 cH~.c cos occ oo c-.c _ coo comH cc~.c cos coo co co~.c 1 coo ommm ccH.c 1 com cch mm 4 . 4 . ccc.c w com ocom cm in W coo in in ” coo m in M o (I m nocooc 1 pH ooog come as coco 660666 as coco come as coon monomers coHuuspmm W ESEHRUZ mumEHuHD w coHuoDUmm ESEHxUZ mumEHUHD :oHumocHHocH mo poozoom och unmom _ ons< anHEoz . II.I. I III IIIIII liIIIIl III I I) I‘ll-III]. IIIII.II. I . tl.III III .I .I I I. III! III IIIIIII III .mmHoomm COOBDMOm mo Houomm coHuosoom can coon mcHummB mumEHuHDII.w mHnt 43 of loading were based on the time to reach the maximum load at total test times of 15, 40, 100 and 240 minutes. The order of testing at these rates was randomly chosen for each specimen. The recovery time between two consecutive loading was 7 days at least. Loading of a specimen at a given test speed was accomplished by adding water to a five-gallon bucket at a constant rate from a twenty-gallon reservoir with a constant head. Calibrated plastic tubes leading from the reservoir to the bucket provided the outlets for different rates of loading. The five-gallon bucket was suspended from one end of a moment arm which was attached at its other end through a load cell to the specimen. The mechanical advantage of the moment arm was 20 to 1, so the weight of water in the bucket was multiplied by 20 at the test specimen. The test frame containing the moment arm is Applied Test System Model 2410. Test Specimens were mounted (Figure 10) individually in series with 1000 pound capacity load cell in the test frame. Two 2 1/2-inches diameter shear plates, one on either side of a specimen's end blocks and a single bolt provided a pin type connection at both extremities of a specimen. Between the specimen and the bottom of the test frame there was a pin-type joint that allowed rotation at 90 degrees to the axis of rotation of the bolt in the specimen. Between the specimen and the load cell there was a universal joint. The load cell was connected by a pin-type joint to the loading 44 Figure 10. Loading Tension Specimen. 45 bar, see Figure 10. The rated accuracy of the 1000 pound capacity load cell was plus or minus 0.1 percent. It was calibrated by suspending 100 pounds of dead weight from it. In preparation for a loading sequence, recording instrumentation was calibrated and then the loading mechanism was attached. Four channels on a B and F Type 161 Data Aquisition System were reserved for load and strain measure- ment. The channel for the load cell was calibrated as pre- viously mentioned to indicate loads to the nearest 0.20 pounds. The three pairs of strain gauges on the test speci— men were calibrated with the specimen hanging freely from the load cell. After calibration, the lower end of the specimen was secured, and the bucket plus a small balancing weight were placed in position at the loading end of the moment arm. The indicated load on the test specimen at this point was about 15 pounds. Load and strains were measured at specified incre- ments of time during the loading cycle, which began with turning on of the flow of water into the five-gallon bucket. These increments of time are included in the list of raw data (Appendix B). At each of the designated times, the recording channels in the data aquisition system were scanned and the readings were recorded by a printer in the system. Channels were scanned at the rate of two channels per second. Strains were read to the nearest one microstrain up to a strain of 2000 microstrain and to the nearest 2 microstrain beyond that point. 46 Supplementary,Calculations To calculate stresses, the cross-sectional area of every specimen was computed (Tables 7, 8). In off-axis specimens, the angle of inclination between grain and load direction (Tables 7, 8) was measured in several spots on each constructed specimen, ‘UD obtain a more precise value than the nominal one. To examine the correctness of recording of all data points obtained in any particular speed of loading, a cor- responding strain-stress curve was plotted by computer. To compute the required slope of strain-stress curve, multiple regression analysis was made through an available least square subroutine [51] on system of CDC 6500 at Michigan State University. For this analysis simple and quadratic regression equations were tried. Simple regression between strain and stress was found highly valid. The main calculations for elastic constants were carried out in accordance with three methods of theoretical analysis on off-axis tension tests. Conventional methods were also applied to compute elastic parameters from the results of standard tests. 47 oo.om om.H oo.om om.H om o.mo om.H m.mo oa.H mo H.Nm om.H w.Hm mm.H om o.om cm.H h.vm vm.H mm v.mH vm.H m.mH om.H ON 0 mm.H o mm.H o mmnmopio mHmc< .sa noun 1 wmummpio OHmcm soHumcHHocH mo N . coHumcHHosH no N ownmaono man> consume: HmcoHuUOMImmoHU W man> consume: HUGOHDOOMImmoHU MOHmom 3OHwa j ©003mmnm soHuncHHocH mo onc¢ HmcHaoz .mcoEHoomm poo3pnmm mo chuo ou Coon mo OHmc< can mou< HmcoHuommimmoHO mo osHm> CODDQEOUII.5 OHQDB 48 oo.oc Hc.~ A cc.cc Nc.H W cm 1 1 o.~o cc.H m c.oo co.H 1 oo c.cc co.H _ c.co cc.~ 1 co c.mm cc.H _ c.mm oc.m om in in H.om cc.H om o cc.H c cc.H o 3 omnmmcro mHms< .cH noun m woummcuo OHms< .ca noun coHumcHHocH mo N . A coHumcHHocH mo N . moummnio ODHU> consumes HUCOHDUOMIMMOHU W osHm> pmusmmmz HUGOHDOOMImmoHU COHumcHHocH mo 1 OHms< HmcHEoz poozpom m mch Hmmsm .mcoEHommm ooozumom mo chuo 0p Upon mo OHmc< paw poem HmCOHuuomimmoHU mo OSHm> cousmfiooii.w OHQUB CHAPTER IV RESULTS AND DISCUSSION Standard ASTM Tests The average moduli of elasticity from standard ASTM tests in compression parallel to the grain and in compres- sion perpendicular to the grain at approximately 12 percent moisture content are given for the four test species in tables 2 and 3. Standard deviations and coefficients of variation for these moduli are also included. For compres- sion parallel to the grain the coefficients of variation were 9.0, 1.2, 7.0, and 14.5 percent for basswood, yellow poplar, sugar pine and redwood respectively. For compres- sion perpendicular to the grain these coefficients were 4.4, 12.4, 20.7, and 14.1 percent in the same order. Part of the reason for these large standard deviations were the small number of samples taken. Also, strain and stress data were not as linear in the perpendicular to grain loading as in the parallel to grain loading. Average shear moduli from standard ASTM tests for the four species are given (Table 4) along with the individual test values. The differences between the paired values for basswood, yellow poplar and sugar pine were less than 4 percent. Only one sample of redwood was tested. 49 50 Tensile Specimens Loaded Parallel to Grain The slope and associated standard errors of strain versus stress parallel (Sl), perpendicular (S3), and at 45° (82) to the load is shown in tables 9-12 at four loading rates for individual specimens of each species loaded parallel to the grain. Since the grain is also parallel to the load, the strains are parallel, perpendicular and at 45° to the grain. Most of the standard errors of the slopes are in the range from 0.002 to 0.004. In all but two cases this is less than 0.6 percent of the slope reading parallel to the grain and 1.0 percent or less of the reading perpen- dicular to the grain for the sixteen recorded slopes at each angle. Percent errors for the perpendicular to the grain readings are about double those of the parallel to grain slopes because the perpendicular readings have the same standard errors as the parallel ones but are about half as great in magnitude. For the gauges at 45° to the grain, the magnitude of errors would be much larger percentage-wise because the slopes are smaller. There is no consistent pattern of strain-stress slopes as a function of loading time for the four species. Variations among the slopes taken at different loading rates are apparently related to variables in the reapplication of loads such as specimen alignment, gauge calibration, etc. Coefficients of variation for the four parallel to the grain slope measurements for a given specimen ranged from 1 51 TABLE 9.--Strain-Stress Slope Values of Basswood Specimens. Angle of Load 15 40 100 240 to Grain Minutes Standard Minutes Standard Minutes Standard Minutes Standard 8 (degree) Loading Error Loading Error Loading Error Loading Error 5 - 6 i O (10'6 % psi) 1 l 0 0.602 0.002 0.604 0.002 0.636 0.003 0.617 0.004 19.8 1.531 0.002 1.541 0.001 1.596 0.003 1.577 0.005 34.7 3.501 0.004 3.511 0.004 3.572 0.004 3.608 0.004 51.8 7.520 0.142 7.176 0.089 7.442 0.129 7.568 0.063 63.9 8.911 0.016 9.152 0.024 9.113 0.023 9.166 0.028 90 11.875 0.014 12.102 0.020 12.328 0.027 12.303 0.031 S - c = c (10.6 4 1) 3 3' '95 0 -0.280 0.002 -0.274 0.002 -0.270 0.003 -0.238 0.003 19.8 -0.158 0.001 -0.124 0.001 -0.l45 0.003 -0.128 0.003 34.7 -0.012 0.002 0.00003 0.00001 0.00009 0.00001 0.095 0.004 51.8 0.010 0.00002 0.001 0.00003 0.002 0.00003 0.003 0.0001 63.9 0.181 0.010 0.011 0.0003 0.839 0.098 0.007 0.001 _ -3 —4 -3 -3 —-2 _ - 90 49136.10 0.450t10 -0.358xlO 0.1687410 -0.105x10 -O.259>.10 0. 121 0. 125 . -6 . S2 - £2 7 o (10 ? psi) 0 0.222 0.002 0.215 0.001 0.233 0.001 0.253 0.004 19.8 2.111 0.005 2.183 0.004 2.225 0.006 2.248 0.005 34.7 4.130 0.018 4.057 0.006 4.272 0.020 4.344 0.005 51.8 5.638 0.013 5.700 0.008 5.845 0.011 5.847 0.007 63.9 6.925 0.012 7.054 0.029 7.226 0.014 7.308 0.011 90 7.793 0.015 7.849 0.009 8.122 0.017 8.353 0.077 52 TABLE lO.--Strain-Stress Slope Values of Yellow Poplar Specimens. Angle of Load 15 40 100 240 to Grain Minutes Standard Minutes Standard Minutes Standard Minutes Standard 6 (degree) Loading Error Loading Error Loading Error Loading Error . -6 . S1 I 61 7 o (10 7 psi) O 0.624 0.003 0.614 0.003 0.620 0.002 0.606 0.002 18.4 1.301 0.002 1.285 0.002 1.274 0.003 1.346 0.003 36.6 2.538 0.009 2.524 0.006 2.594 0.003 2.601 0.008 52.1 3.482 0.005 3.485 0.013 3.634 0.015 3.590 0.007 65.6 5.269 0.021 5.259 0.010 5.484 0.006 5.330 0.011 90 5.998 0.023 6.206 0.022 5.954 0.013 8.368 0.076 S - t + C (10-6 % psi) 3 3 0 -0.247 0.002 -0.261 0.002 -0.250 0.002 —0.219 0 003 13.4 -0.220 0.001 -0.197 0.001 -0.210 0.002 -0.173 0.002 36.6 -0.253 0.005 -0 243 0.005 -0.247 0 005 -0.244 0.004 52.1 -0.377 0 004 -0 375 0.003 -0.399 0.005 -0.320 0.006 65.6 -0.137 0.006 -0.177 0.004 -0 149 0.007 -0.107 0 005 90 -0.177 0.007 -0.137 0.007 -0.177 0.007 -0.253 0.003 s - e e 3 (10"6 4 psi) 2 2 0 0.213 0.003 0.249 0.0002 0.214 0.001 0.231 0.005 13.4 1.544 0.001 1.576 0.003 1.532 0 002 1.535 0 002 36.6 2.030 0 005 2.093 0 003 2.166 0 003 2.149 0.004 52.1 2.772 0.004 2.733 0 005 2.312 0.003 2.973 0 011 65.6 3.923 0.013 3.944 0.007 4.164 0.013 3.949 0 006 90 3.105 0.009 3.105 0.006 3.163 0.003 3.169 0.011 53 TABLE ll.--Strain-Stress Slope Values of Sugar Pine Specimens. Angle of Load 15 40 100 240 ’to Grain Minutes Standard Minutes Standard Minutes Standard Minutes Standard c (degree) Loading Error Loading Error Loading Error Loading Error 5 - c i c (10.6 % psi) 1 1 0 0.837 0.005 0.789 0.010 0.821 0.012 0.900 0.003 26.1 1.854 0.030 2.051 0.016 1.969 0.008 2.086 0.011 32.4 3.668 0.005 3.718 0.005 3.727 0.003 4.483 0.066 50.9 8.532 0.081 8.776 0.099 8.099 0.058 7.950 0.086 65.4 9.143 0.025 9.078 0.029 9.465 0.033 9.615 0.080 90 12.431 0.048 11.898 0.079 12.895 0.137 12.006 0.071 S I E % t (10.6 % psi) 3 3 0 -0.523 0.003 -0.508 0.001 -0.528 0.002 -0.514 0.003 26.1 1.197 0.017 1.636 0.013 1.471 0.018 1.375 0.024 32.4 0.831 0.007 0.857 0.004 0.890 0.006 0.862 0.017 50.9 0.972 0.007 0.967 0.009 1.026 0.008 1.089 0.015 65.4 0.151 0.004 0.184 0.008 0.192 0.006 0.202 0.007 90 -0.341 0.013 -0.345 0.004 -0.421 0.009 —0.426 0.015 52 - :2 4 o (10.6 % psi) 0 0.196 0.002 0.204 0.001 0.196 0.002 0.189 0.003 26.1 2.472 0.004 2.446 0.004 2.396 0.006 2.455 0.015 32.4 4.268 0.008 4.274 0.008 4.293 0.005 4.371 0.045 50.9 6.576 0.021 6.626 0.024 6.725 0.027 7.050 0.052 65.4 7.295 0.057 7.320 0.046 7.380 0.059 7.708 0.068 90 6.578 0.016 6.567 0.037 6.798 0.037 6.766 0.02] 54 TABLE 12.-~5train-Stress Slope Values of Redwood Specimen. Angle of Load 15 40 100 240 [to Grain Minutes Standard Minutes Standard Minutes Standard Minutes Standard 3 (degree) Loading Error Loading Error Loading Error Loading Error . -6 4 s1 61 . o (10 - psi) 0 0.706 0.001 0.691 0.002 0.686 0.002 0.686 0.003 32.9 2.491 0.003 2.498 0.003 2.544 0.005 2.544 0.003 47.7 3.617 0.006 3.632 0.006 3.593 0.005 3.619 0.015 62.6 4.193 0.011 4.197 0.012 4.365 0.024 4.335 0.021 90 6.373 0.030 6.500 0.013 6.662 0.025 6.636 0.016 6; S3 - £3 % C (10- psi) 0 -0.286 0.002 -0.281 0.002 -0.302 0.003 -0.307 0.003 32.9 ~0.468 0.002 -0.453 0.001 —0.451 0.007 -0.466 0.002 47 7 -0.380 0.012 -0.363 0.006 -0.397 0.009 -O.425 0.012 62.6 -0.417 0.003 ~-0.403 0.003 -0.405 0.004 -0.399 0.005 90 -0.401 0.005 -0.411 0.007 -0.420 0.009 -0.377 0.007 So - E i C (10'.6 % psi) - 2 0 0.280 0.002 0.286 0.002 0.277 0.002 0.289 0.003 32.9 2.116 0.010 2.155 0.007 2.127 0.014 2.279 0.009 47.7 3.052 0.010 3.046 0.004 3.065 0.010 3.060 0.007 62.6 2.829 0.004 2.864 0.005 2.959 0.005 3.165 0.017 90 2.972 0.020 3.039 0.008 3.134 0.010 3.104 0.008 55 percent to 5 percent for the parallel to grain gauges, from 1 percent to 7 percent for the perpendicular to the grain gauges and from 2 percent to 8 percent for the gauges at 45° to the grain. In order to obtain some verification of the accuracy of the rosettes and measuring system, maximum strain (Emax) per unit stress, minimum strain (8min) per unit stress and the direction of the principal strains were determined from the three rosette guagues under the assumption that maximum and minimum strains and their directions were unknowns. The calculated values for Emax and 6min were generally within one standard error of the measured ones, see Table 13. The calculated principal strains were acting at an angle of 5° or less with the direction of measured strains. The reasons for this deviation in the sense of principal strains could be rosette construction, grain direction not parallel to specimen load axis, grain deviation along the gauge and non-uniformity in strain field due to non-homo— geneous nature of wood. Tensile Specimens Loaded Perpendicular to the Grain The arrangement of the three gauges in the rosette in the specimens loaded perpendicular to the grain was such that the gauge parallel to the load was oriented perpendi- cular to the grain, the gauge perpendicular to the load had its long axis parallel to the grain and the gauge at forty- five degrees to the grain had its long axis at forty-five 56 .mmauum mo COflUUCDM fl mm wEMH UCwEQHmew—z SUMO um a x> mo woodme .mcoefioomm moummcIouoN MOM wcofluoouwo mm.vI vam.OI mmo.o moo.o som.0I moo.o mmo.o on~.o cvm om.vI mom.0I maw.c moo.o Nom.0I moo.o mmo.o on~.o ooH coo3cmm so.vl hm~.oI hmo.o moo.o Ho~.ol ~oo.o Hmm.o omH.o ov Ho.vI oa~.OI lo.o ~oo.o www.cI Hoo.o oo>.o ovH.o ma HNH.o «Hm.OI oom.o moo.o vam.oI moo.o oom.o moo.0I ovm HH.~I mNm.oI N~w.o ~oo.o owm.OI «Ho.o Hmm.o oo~.o ooa moan . unusm ov.~I cam.OI oom.o Hoo.o wom.0I o~o.c mah.c cam o co hv.HI m~m.OI hmm.o noo.o mwm.OI moo.o 5mm.o ono.o ma ~v.~I oNN.OI new.o moo.o mAN.oI woo.o oom.o ono.c ovw hm.~I Hm~.0IV Hmo.o ~oo.o om~.oI ~oo.o omm.o owo.o ooa unamom soHHow mm.mI www.cl hao.o ~oo.o HmN.OI moo.o vam.o oHH.o ow vo.~I he~.OI «No.o ~oo.o nvN.OI moo.o «No.o omo.o ma mm.mI NnN.OI Hmm.o moo.o mmm.OI coo.o nam.o oma.o ovw va.mI ~h~.oI mmm.o moo.o osN.OI moo.o omm.c ooa.o cog poozmmmm m~.mI wn~.oI moo.o ~oo.c whN.OI moo.o vow.o ooH.o ow hm.mI vm~.oI wow.o Noo.o om~.0I ~oo.c moo.o o~H.o ma Amouowoy c and m mIoH and m mI swam eIoa and . oIOH and monoa and m oIoH «mm m oIOH Amusedev mcwmuum cae on uOuum uouum oEwu mmflommw Hoawocfium o m . 3 o m cuwccmum o I o cumocmum : I o I mcwomoq no newuowufio .xvm. I .xvfi. I n IINMHI I m causasodmo , 6 Eghflh .INIV..LT I III! .71 "U .II 61“.! III-Inn!” .I r n. H 1-... I I In .4. -. .I . II u at I i .I.... II. "'uIIuMILLIIUI ‘ II. ".14'13. .. 1|-.IIIV.I.!I Mamas 0cm mcwmuum HmaflocflumII.ma wanna 57 degrees to the grain. The slopes of the strain-stress curves of these gauges and corresponding standard errors are given in tables 9-12. With the exclusion of basswood readings perpendicular to the load, the range of standard errors is at most 2.2, 75, 4.5 percent of slope readings for parallel, perpendicular and 45-degree to load gauges of all test species respectively. The reason for the large error percentages for the strains measured perpendicular to the load was that the strains were very small in this direction. Even for basswood the magnitude of the standard errors perpendicular to the load were not any larger than in the other two directions. Generally, most researchers do not try to make this type of strain measure- ment because it is so small. The coefficients of variation for the four computed slopes of strain-stress curves for each specimen varied from 2 percent to 18 percent for the gauge perpendicular to the grain (parallel with the load), from 5 percent to 18 percent for the gauge parallel to the grain (excluding basswood) and from 1 percent to 5 percent for the gauge at 45° with respect to the grain. If one reading for the yellow poplar specimen parallel to the load is ignored, the coefficients of vari- ation for these slopes were 2 percent to 4 percent. When the slopes of the strain-stress curves were plotted against loading time, a slight increase in most of these slopes was observed with loading time. This is shown in Figure ll for the gauges oriented at forty-five degrees to 58 .3555 5 me: 0533 EEO of 2 5.3.9393 6360. 2856on :0 9.6 coo. o. 3802. no 6 ~08 to. 9:: 9.68. 35? $872.93.. 6 82m ocm oom ow. ON. 00 0v 0 «1 0 86368 .v 9.5 608 n r... 538 32.2 N noozmmon _ c .I. m N W IflIl 1W u no w n w! . n 6 ms K‘IIIII‘I III||I\\|III _rII II|III |II||||I| IIIIIIII.|I I‘IIIIIIu 1K7 : a; (lSd 89,00 PDOI 0: IaIIOJDd 583498.917 Io wows 59 the grain for the specimens loaded perpendicular to the grain. The three gauges on the basswood specimen showed greater change with loading rate than the gauges on any of the other species. More replications and a greater range of loading times is probably needed to certify the changes of strain- stress slopes with loading rate. However, the implications are that apparent modulus of elasticity perpendicular to the grain should decrease with increase in loading rate since it would be equivalent to the reciprocal of the strain-stress slope parallel to the load. The accuracy of measurement of this type Specimen was also examined with readings from the rosette by assuming that the magnitude of the principal strains and their direction was not known (see table 14). Except for the basswood, the calculated maximum strain per unit stress parallel to the load (perpendicular to the grain) was within one standard error of the value measured by the gauge parallel to the load. A similar situation existed in many cases for the calculated minimum strain per unit stress and the strain per unit stress measured perpendicular to the load. In the cases where the differences between minimum strain and the measured strain were larger than one standard error, the direction of principal strains from the load axis was more than two degrees. For the basswood, the indicated deviation from the load axis was about nine degrees for all four loadings. Also, for the basswood, calculated maximum .mwwhum MO COMuUCDM M mm mafia UCGEQHDmMQE SUMQ um i x» we 6&06m6 60 666.6 666.6- 66.6 666.6 666.6- 666.6 666.6 666.6- 666 666.6- 666.6- 66.6 666.6 666.6- 666.6 666.6 666.6 666 U003pmm 666.6 666.6- 66.6 666.6 666.6- 666.6 666.6 666.6- 66 666.6 666.6- 66.6 666.6 666.6- 666.6 666.6 666.6- 66 66.6- 666.6- 66.66 666.6 666.6- 666.6 666.66 66.6 666 66.6- 666.6- 66.66 666.6 666.6- 666.6 666.66 66.6 666 0:66 uwmsm 66.6- 666.6- 66.66 666.6 666.6- 666.6 666.66 66.6 66 66.6- 666.6- 66.66 666.6 666.6- 666.6 666.66 66.6 66 66.6 666.6- 66.6 666.6 666.6- 666.6 666.6 66.6- 666 66.6- 666.6- 66.6 666.6 666.6- 666.6 666.6 66.6 666 666606 66.6- 666.6- 66.6 666.6 666.6- 666.6 666.6 66.6 66 306666 66.6- 666.6- 66.6 666.6 666.6- 666.6 666.6 66.6 66 66.6- 666.6- 66.66 666.6 666.6 666.6 666.66 66.6 666 66.6- 666.6- 66.66 -66x666.6 6-66x666.6- 666.6 666.66 66.6 666 66.6- 666.6- 66.66 6-66x666.6 6-66x666.6- 666.6 666.66 66.6 66 60036666 66.6- 666.6- 66.66 -66x666.6 6-66x666.6- 666.6 666.66 66.6 66 6666666. 6 666 6- 666 . 6- 6666 6-66 666 H 6-66 666 N6-66 . 6-66 666 m 6- 60666656 wcflmuum neuum acuum msau mm6owom CHE XME . . 6mawoc6uo H . 6 6 pumocmum : I o cumpcmum : I 6 I mcwvooq 60 606600666 6x66. - 6.6. - 6x» - cmum6so6mo a 1’; i.- .I.| ‘- .mcoE6Uomm omuwopI06 606 mco6uoou6o IIIlI’II‘ '1-14 I 1|“- 666:6 6:6 6666666 666606666-.66 66666 61 and minimum strains per unit stress were considerably differ- ent than the strains per unit stress measured parallel and perpendicular to the load. Why this should be consistently so for the basswood is difficult to explain, but it indicates why very samll negative strains or even positive strains were recoreded perpendicular to the direction of loading. More realistic numbers for Poisson's ratio are obtained if the cal- culated maximum and minimum strains per unit stress are used. Young's Moduli and Poisson's Ratios from Parallel and Perpendicular to Grain Testing Except for the sugar pine, the difference between the average modulus of elasticity from the parallel to grain ten- sion test and that from the ASTM standard compression test differed by less than 7 percent (Tables 15, 17). For some reason in the case of the sugar pine, the modulus of elasti- city from the ASTm test was 20 percent greater than the value in the tension test. The moduli of elasticity from the four replications at different loading rates of the tension speci— mens showed only random variation of a very small order (5% at most), which was expected. When comparing the muduli of elasticity perpendicular to the grain from the ASTM test and the tension test perpen- dicular to the grain, relative large differences were noted. Based on average these ranged from minus 34 percent to plus 39 percent of the tension test value (Tables 16, 18) . Several reasons might be noted for these differences. One of them is that there 62 .moumu mc6c606 6306 um mummy scum 6:66> poundaoamo ommuo>< oomuo>¢ 0‘11 .1! f'. ..I. z .. h.”- mcwfiwomam m6x6Imuo Eouu poc6suwuwo 66m INfuln-H u.H.-r-|“I.-‘Hu|¢ -OI'IMII-W'h ”flair-I'll, l.” I,» III. 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Godumsvw 60 mm: wocmumuuflo monum>< womum>¢ 660560066 mwxmlumo EOuu GwCMEuwumo «9m .ucwucou musumwoz wNH um voo3uuom :o mumws cofimmmuasou cumccmum 6cm mumma mcoflwcme >2 cwusmmmz samuo ocu Ou undaowccmmuwm mafisnoz 6.06506 60 mmsam> ms» H06 comwquEOU|u.mH manna 66 were large standard deviations associated with ASTM com- pression perpendicular to the grain tests. Also the load— deflection curves for this testing were not as linear as those for the parallel to grain testing and so were Open to more interpretation. In addition, modulus of elasticity perpendicular to the grain is sensitive to loading rate. This was noticeable for the yellow poplar and basswood. For these two species, the apparent elastic modulus perpin- dicular to the grain was greater for the relatively fast ASTM test and decrease of modulus with decrease of loading rate was not evident for the tension test. R = “LR % EL can be used to check the accuracy of measurements of these The reciprocal relationship “RL % E elastic constants made in a given plane. is the one “RL which usually contains the greatest error since its strain perpendicular to the load is small. The results of dividing Poisson's ratios by elastic moduli are given in Table 19. Except for the basswood, agreement between the relationships from the parallel to grain loading and those from the perpendicular to the grain loading are good. (URL é ER) % (“LR + EL) was from 0.65 to 1.47. In the case of the basswood, however the indicated Poisson's ratios were very small for the loading perpendicular to the grain which resulted in an extremely small number for Poisson's ratio 67 n~.~ n~.~ 0~n.0 00n0.0n 0~n.0| 00.0 0~n.0 0000.0 00n~.0 0nn.0| 0n0.0 ~0n.0 000.0 0n0.~ ~0n.0| 000.0 00w on.~ 0n.~ 0N0.0 ~n0.0l 0N0.0I 00.0 0~0.0 ~n00.0 Now—.0 0N0.0I N00.0 ~0n.0 000.0 0n0.— N0fi.0l 000.0 00m ~0.~ n0.~ ~—0.0 0n00.0l -0.01 0n.0 N~0.0 0n00.0 0nn~.0 N~0.00 00n.0 ~0~.0 «00.0 ~00.~ ~0N.0I ~00.0 00 N0." N0.“ «00.0 un00.01 «00.01 nn.0 N00.0 «n00.0 05n~.0 «00.0! nun.0 00~.0 n00.0 5N0.~ 00~.0I 00h.0 an “00030fll no.0 n0.0 000.0 0~00.0I non.0n 00.N~ s~0.0 0nn0.0 nn00.0 «N0.0I 000.N~ 0—n.0 ~nn.0 -~.H 0~n.0l 000.0 00w 00.0 00.0 000.0 00n0.0| 000.0! 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V Ama v mcflvmoq mcflvmoq msflwmoq mcficwoq Ammummcv o coHuMH>mo w mmuocwz mmuscflz mmuscflz mmuscflz cflmuo ovm ooa ov ma 0» nmoa oumncmum ommum>< mo waved mecmeueuoocHHmum u mHo HHmmv .‘qlul‘llll‘ll ’v‘. .‘I' .01.’!i|l|llvllll|| t’lllll' I. Il'll‘lul' I' 2' Ill, l‘l‘b'v’ll}. 01"!!! ..l n I: , V» . . n.!.‘..v. llll‘filll'.l Vii... mummmv+xmmnHmvm_ m H '. .rr n 6 v.1: II? .l'l. OIIII'.‘ III .umwB coflmcwe mflxmlwwo >3 HmHoom 3oHHo> mo mostoz Hmmcm mo mooam> UmuDQEOUIu.HN manna 73 oom.m oom.oaa oom.moa ooh.moa oom.>HH ooH.MHH «.mm ooo.n oom.hh M ooa.mm coo.Hm oo>.on oom.m> m.om ooo.m oom.moa M oom.mm oom.mo~ oom.moa oom.moa v.mm ooa.mm oom.oom oom.mhm oom.mmm oom.onm ooo.mmm H.mm HHmmO HHmmO W BA mcwomoq M mcflomoq mcflwmon mewomoq Hmwummcv o coflumw>mo U mmuscwz “ mouncwz mmuocflz mmuscflz chHw OOH m OOH OO mH on OmoH wumccmum momum>< mo mamc< m AH. O H1O:OH-OHOOOHHmumm-~m~O+imm-HmO~O . H u 9H6 .umme coflmcwe mflxmuwwo an ocflm Hmmsm mo moaswoz Hmmnm mo mosam> wmusmfioonl.mm wanna 74 oom.o oom.vma ooo.¢ma i oom.hwa oom.vma oom.mma m.~m oom oom.mmH oom.~ma _ oom.vma ooa.vma oom.vma 5.50 oom.~ ooo.mNH oo~.H~H ooa.m~a ooo.m~a oom.mma m.~m HHmmv HHmov mg msfiwmoq mcwcmoq mcwomoa mcficmoq Amwnmmwv :oflumfl>mo w monocwz M mousswz mouscflz mousse: CHMHU OON . OOH OO OH on nmoH cnmvcmum womuw>¢ , mo mamcd HHme m mH HA Owe- HOOOAHO- mummmv+immuHmcmi .umma coflmcoe mflxMImmo an poo3cmm mo msasvoz Hmwnm mo mosam> cmusmfiouul.mm manna 7 5 Table 24.--Comparison for the Values of Shear Modulus Measured by Off-axis and Standard Plate Tests. _ * , Angle of GLR (P51) Differences S ecies Load to . in Percent p Grain Off-axis Average From 1_2 (degrees) Tests ‘ Standard Plate -7— x 100 (l) Shear Test (2) 19.8 94,700 8 34.7 93,500 7 Basswood. 87,700 51.8 77,700 -11 5 63.9 100,000 14 E 18.4 118,000 2 —7 i 3 Yellow ; 36.6 147,300 g 127 300 16 Poplar i ! ' 2 52.1 152,300 = 20 5 65.6 165,100 3 30 i 26.1 300,300 3 193 Sn ar g 32.4 103,300 1 1 Pige ; 3 102,500 3 50.9 77,800 -24 3 65.4 110,600 8 i 32.9 125,000 1 -6 E I - Redwood ; 47.7 | 133,900 ; 132,900 1 2 3 ' g 62.6 154,600 2 16 *This is G L T value for Sugar Pine. 76 1050.00 1012.50 NORM (DGDCDC) xxxx xxxx HHHH zzzz xxxx 2222 (363636) rrrr mmmm mmwm memo 0000 mmmm CDGDCDGJ r0.80 4160 8170 18.80 18.80 21.00 STRESS RRTE PSI/MINUTE Fig. 12. Shear Modulus Versus Stress Rate for Basswood. 77 .00 7 59.00 fl 0 G 478 . L H L R 0 0 377 00 RNGLE (DEG. Shear Modulus Versus Angle of Load to Grain I U I U M N H N 2'8 00 for Basswood. E 5004 x: A <0 22 500 1 . - q 8.82 84.8: 84.me Owémm OO.OOO OO O OO.O~.O 8.5M 8.8:. you; Hm; 024300: mamzm 00 l 13. Fig. 78 For yellow poplar samples the shear moduli ranged from 92 percent to 132 percent of the average from the plate shear test. There was little if any change of shear modulus with loading rate, but the shear modulus increased greatly with the angle of load to grain variable (Figure 14, 15). The average shear modulus for the specimen with the grain at 65 degrees to the load was 1.4 times that calculated for the specimen with the grain at 20 degrees to the load axis. The shear moduli from the 20-degree and the 35-degree tension specimens were closest to those from the plate shear test. They averaged 92 percent and 115 percent respectively of the shear moduli from the plate test. For sugar pine samples, the shear moduli ranged from 69 percent to 361 percent of the average from the plate shear test. If the specimen with the load at 26-degree to the grain is ignored the range of values is reduced to 69 percent to 115 percent. There is little if any change of calculated shear moduli with either loading rate or angle of load to grain (Figure l6, 17). The shear moduli from the specimen with angle of load to grain of 32-degree were the closest to the average of the plate shear test. They were from 93 to 104 percent of this average. The large discrepancy of the shear moduli from the 26-degree specimen suggests a special problem. The one that comes to mind and the most obvious is the fact that the measurements were made on the longitudinal-tangential plane in the sugar pine specimens, and that in the 26-degree specimen the rosette is the least 79 1606 .25 1670 .00 1542.60 NODX (73900 20202020 13332033 o—n—u—u—o 25252525 33332320 2222 0000 l—r-r'l— rnrnrnrn CDCDCDPO 010010 0000 rnrnrnrn 0000 1223.75 4 \7 + .50 4180 8170 11.80 {8.90 21.00 STRESS RHTE PSI/MINUTE c}160.00 Fig. 14. Shear Modulus Versus Stress Rate for Yellow Poplar. 70.00 80 j 59.00 40.00 1 37.00 HNGLE (DEG. 1 26.00 OO.OOOH O~.OOmH Om.~OmH wpqow m0.0~mH 00.00— “15.00 Shear Modulus Versus Angle of Load to Grain for Yellow Poplar. 15. Fig. 81 nunUnunu ELELCLEh nunununu nucunuco 04000000 ELELtLEL ILILILIL nUnUnUnu MHMHMHMH nfinflnfinfl MHMHMHMH IIII nfinflnfinfi DnDnDnDn nUnUnunu HAG—x. *x—I oo.m>m NH.OmO ON.Om~ OO.OnH uzw A / bo.bo~ 11.00 T 8.86 STRESS 88T5 PSI/MINUTE 1 6.72 ——o 4'58 2-44 30 O0.0mu Shear Modulus Versus Stress Rate for Sugar Pine. 16. Fig. 373.00 82 335.12 Fig. 5.00 17. 37.00 48.00 59.00 RNGLE (DEG. 1 1 26.00 Shear Modulus Versus Angle of Load to Grain for Sugar Pine. 7|. 83 likely to be in a true longitudinal-tangential plane. The reason for this latter observation is that there is only a small area on the specimen surface that very closely approxi- mates a tangential surface and this area changes very rapidly from one side of the specimen to the other when the angle of load to the grain is small. It could be easily seen that some parts of the strain rosette on this particulr specimen were on locations that were distinctly different from a tangential-longitudinal plane. With greater angle this problem becomes less drastic. For the redwood samples, the shear moduli ranged from 91 percent to 123 percent of the value from the plate shear test. If just the two lowest angles of loading to the grain (in this case 33-degree and 48-degree are considered) the shear moduli for the tension specimens were from 91 per- cent to 101 percent of that from the plate shear specimen. There is little if any change of shear modulus with loading rate but shear moduli increases as the angle between the load and the grain increases (Figure l8, 19). When the data for all the shear tests are examined as a group, the shear moduli from all the tension tests (excluding one sugar pine specimen) were from 69 percent to 130 percent of the shear moduli from the plate shear tests. If specimens with angle of load to grain less than 37-degree only are considered (with the exception of the sugar pine with angle of 26 degrees) the shear moduli from the tension tests ranged from 93 percent to 117 percent of the average values from the shear plate tests. The shear moduli of the Fig. 84 1050.00 L 1593.75 1537.50 1 1256.25 J 1 aka» cacaca R R R 333333 HHH 252525 333333 252525 C353q3 rnrnrn C3C3C3 LE 3 LE 5 LE 6 CHCDCfl C3C3C3 c1200.00 18. 4. 40 ST 30 STRESS RHTE PS _' 120 18J0 I/H INUTE 2 Shear Modulus Versus Stress Rate for Redwood. 0.00 85 70.00 62.00 I 54.00 HNGLE (DEG. Shear Modulus Versus Angle of Load to Grain for Redwood. I I 46.00 38.00 00.0mm ; OO.OOmH OO.OOmH m~.OmmH oo.co~ “30.00 19. Fig. 86 redwood and yellow poplar increased with the angle of load to the grain while that for the basswood and sugar pine did not. Also, Gresczuk [24] did not have any such change for his fiber glass laminates. A possible reason for the increase in shear modulus with the yellow pOplar and the redwood is that they have a relatively large percentage of ray tissue oriented perpendicular to the grain direction: the volumetric percentages of ray tissue for these two species are 14 percent and 8 percent respectively [55]. The ray tissue might provide a reinforcement perpendicular to the grain. Basswood is listed as having 6 percent ray tissue, the sugar pine was tested in a plane where the ray tissue did not act as a reinforcement, and the fiber glass had no comparable structure. It would seem with the experience with the sugar pine, that more care has to be taken with tension specimens made on a longitudinal-tangential plane than with those on a longitudinal-radial plane because of growth ring curvature. Larger angle between load and grain direction would seem to be best. A plus factor is that shear measurements on a tangential-longitudinal plane will not be influenced as much by the rays as those in radial plane. Young's Moduli Parallel to the Grain.—-Young's moduli parallel to the grain were calculated from the off-axis tensile specimens in two ways. The first of these presupposed a knowledge of “LR but then only 87 required the data from one specimen to obtain EL from Equation 12. from the parallel to the grain tension “LR samples was used for these calculations. If “LR was not known, data from two off-axis tensile specimens could be combined as per Equation 14. The results of the calcula- tions for EL by these two methods are given in Tables 15, 17 and in Tables 27—30, 31-34, Appendix A. In Gresczuk's tests [24], the largest percentage errors for any of the elastic constants occurred in the determination of EL particularly at the larger angles EL was more "sensitive" to error. Determination of BL using Equation 12 and the Poisson's ratio from the parallel to grain loading did not produce many numbers for Young's moduli that were very close to those found from testing the parallel to grain specimen. In fact the differences were mostly large. The EL values for a given specimen at the four loading rates were averaged for comparison purposes. Of the fifteen such calculations made for the off-axis specimens for all species, only four differed from the expected EL by less than 30 percent. These were for a basswood loading at 20- degree, yellow pOplar loadings at 18-degrees and 52-degree, and a sugar pine loading at 65-degree. EL from the two yellow pOplar loadings mentioned were within 3 percent of the EL value obtained from the parallel to grain loading. Young's moduli obtained from the combining of the data from two off-axis tensile specimens in Equation 14 did not give much better results. Combinations where the 88 calculated EL differed from the EL obtained from parallel to the grain testing by less than 30 percent were: basswood-- 20 and 35 degree specimens, 35 and 50 degree specimens; yellow poplar--20 and 35 degree specimens, 20 and 50 degree specimens, 20 and 65 degree specimens, 50 and 65 degree specimens; sugar pine--20 and 50 degree specimens; redwood—- none. At this point it does not seem as though an off-axis tensile specimen would be very reliable in determining Young's modulus parallel to the grain for wood. Young's Moduli Perpendicular to the Grain.--Young's moduli perpendicular to the grain were also calculated from the off-axis tensile specimens in two ways by equations either requiring one sample if “LR was known or two if it was not. See Equations 12 and 14. The results of the calculations for ER by these two methods are given in Tables 16 and 18 and in Tables 27-30, 31-34 of Appendix A. In Gresczuk's tests, the moduli of elasticity calculated perpendicular to the fiber axis were within plus or minus 10 percent of the expected. The perpendicular modulus was expected to be "sensitive" to small errors when the angle of axis to loading was small. Calculated Young's moduli perpendicular to the grain using Equation 13 and Poisson's ratios from parallel to grain loading were close to the values obtained from loading these species in tension at 90 degrees to the grain. If the average moduli calculated from the loadings of a given speci- men are compared to the modulus obtained from the 90-degree 89 specimen, all of the calculated values except two are within plus or minus 25 percent of the test value from the 90-degree specimen. For three of the four species, the calculated averages for the 65-degree samples are within 10 percent of the test value. Young's moduli obtained from the combining of the data from two off-axis tensile specimens in Equations 14 gave even better results except for the redwood. Over one-half of the differences between calculated and test values were within plus or minus 10 percent of the test value. Except for the redwood, all of the combinations of 50-degree with 65-degree specimens and 35-degree with 65- degree specimens produced calculated moduli within plus or minus 10 percent of test value of the 90-degree specimen. It could be concluded then that it is possible to make accurate calculations of modulus of elasticity perpen- dicular to the grain from off-axis tensile specimens. This is particularly true if the angle of load to grain direction is around 65 degrees. The presence of large errors in the values used for E in the calculation of E or E does not L R T seem to affect the accuracy of ER or ET very much. Poisson's Ratios.--Poisson'a ratios “LR' from “RL basswood, yellow poplar, redwood and “LT from sugar pine were computed from the off-axis tensiel samples through Equation 16. The results are compared with the average values of these constants measured by zero and 90-degree 90 specimens (Table 25) for all four species. Some cases of combining off-axis specimens resulted in values for ”LR and “LT that had less than 42 percent discrepancy from parallel to grain testing on zero-degree samples. These combinations were 20 and 35, 50 and 65-degree specimens of basswood; 20 and 35, 35 and SO-degree specimens of yellow poplar; 20 and 35, 20 and 50-degree samples of sugar pine, 35 and 50-degree samples of redwood. Almost all cases of off-axis data com— binations for URL and “TL resulted in values which differed by more than 60 percent from the corresponding values obtained from perpendicular to grain testing on 90-degree specimens. The exception was in combining data of 50 and 65-degree samples of basswood from which this difference was only 12 percent. It is clear that Poisson's ratios are very sensitive and u - transformed data from RL TL' off-axis test practically could not provide the required to errors particularly 0 accuracy. Suggestions for Further Study In view of the results obtained in this study, it is felt that investigation could be conducted in the following areas: 1. An analytical and experimental investigation on the effect of length and width of off-axis tensile samples and developing smaller samples which are convenient to construct and use. 91 Table 25.-~Comparison for Poisson's Ratios Computed from Zero, 90-degree and Off-axis Specimens. it fit Nominal LR RL Species gnziimZEs Use of Zero** Difference Use of 90-degree'* Differences p Equations Degree in \ Equations Specimen in \ (degree) (1) 16 Specimen 2_3 16 (6) 5-6 (2) (3) "3— X 100 (5) T x 100 (1) (2) (3) (4) (5) (6) (7) 20—35 0.579 34 0.062 157 20-50 0.990 129 -0.158 -755 20-65 0.950 120 —0.057 -336 Basswood 0.431 0.0241 35-50 0.031 -92 -O.144 ~69? 35-65 -0.033 '107 -0.081 -436 50-65 0.253 -41 -0.021 -187 20-35 -0.242 -161 -O.182 -660 20-50 -0.056 -ll4 0.069 112 Yellow 20-65 0.170 -57 0.075 131 0.396 0.0325 Poplar 35-50 0.300 -24 0.208 540 35-65 0.887 124 0.091 180 50—65 2.96 647 0.061 88 20—35 0.658 6 -0.070 -303 20—50 0.478 -22 -0.181 '624 Sugar 20-65 0.168 -73 0.057 65 Pine 0.618 0.0345 35-50 0.158 -74 -0.200 -679 35-65 0.022 -96 0.064 85 50-65 -0.167 ~127 0.160 364 35-50 0.517 21 0.216 251 Redwood 35-65 0.132 0.425 ~69 0.124 0.0616 101 50-65 -3.76 ‘ -984 0.107 74 a ' - - For Sugar Pine these constants are "LT and uTL' '* Average of four readings from table 26 for Zero-degree sample and Em. from Table 14 for 90-degree specimen. 1!! max 92 The interaction of loading time and angle of load to grain on specimens with investigated Optimal length and width, along with a greater range of stress rate. The uniformity of stress-strain field on off-axis tensile samples through experimental investigation. The range of linear behavior of off—axis tensile specimens with optimal length and width. Measurement of all elastic constants associated with a given plane, especially shear modulus, at large strain level. Find out if there are any unusual elastic properties of basswood when loaded at 90 degrees to the grain. Seeing if rays affect shear moduli determination in tensile specimens. CHAPTER V SUMMARY AND CONCLUSIONS Shear moduli, moduli of elasticity and Poisson's ratios obtained from loading wood tension specimens at four angles to the grain were compared with elastic constants obtained from parallel and perpendicular to the grain ten- sion loadings and from standard ASTM compression and shear plate tests. Measurements were made on a radial-longitudinal plane for basswood, yellow poplar and redwood, but on a tan- gential-longitudinal plane for sugar pine. Moisture contents of test materials were close to 12 percent. Tension speci- mens were so constructed that the angles between load axis and the grain direction were 0, 20, 35, 50, 65 and 90 degrees. Specially manufactured strain gauges were applied on each specimen in a rectangular rosette configuration with gauges parallel, perpendicular and at 45-degree to the load axis. Hardwood samples were loaded at most to 15 percent and softwood samples at most to 32 percent of their load carrying capacity at stress rates ranging from 0.3 to 20.0 psi per minute. At least seven days elapsed between suc- cessive loadings of a specimen to allow for recovery. 93 94 The findings of this study were: Strains parallel, perpendicular and at 45-degree to the load axis were linear functions of stress. This indicates that specimens were loaded within their elastic limit. The accuracy of the strain gauge rosettes was checked on the specimens loaded parallel to the grain and those loaded perpendicular to the grain by assuming the principal strains per unit stress and their directions were unknowns. a. For specimens loaded parallel to the grain, the magnitudes of computed principal strains per unit stress were within one standard error of measured ones. b. For specimens loaded perpendicular to the grain, the magnitudes of maximum computed strain per unit stress were within one standard error of the strains per unit stress measured parallel to the load for all species except basswood. This was also true for most of the minimum computed strain per unit stress and the strains per unit stress measured perpendicular to the load direction. c. For all the specimens loaded either parallel or perpendicular to the grain, the calculated angle between the load direction and the maximum strain was less than plus or minus five degrees except 95 for the basswood loaded perpendicular to the grain. The angle difference for the latter was about nine degrees. d. The small calculated angular deviations between the load axis and the principal strains probably represent such things as imperfect grain align- ment in the specimens, load not parallel to the specimen length, imperfect rosette construction, and non-homogeneity of wood. e. Reasons for the basswood specimen loaded perpen- dicular to the grain being so different from the others is not known. The average modulus of elasticity parallel to the grain computed from the tension specimens was greater than that from the ASTM compression tests by 0.4 percent for basswood, 5 percent for yellow poplar, 20 percent for sugar pine. It was 7 percent less for redwood. The large difference between the two test methods for EL of sugar pine had no clear reason. The average moduli of elasticity perpendicular to the grain computed from the tension specimens differed by minus 34 to plus 39 percent from the average values from the ASTM tests. The large coefficient of varia- tion (from 4.4% to 20.7%) for the ASTM tests help to explain the differences. Of particular note is the non-linearity of the load-deflection curves in the 96 perpendicular to grain testing. Also, one might expect the ASTM test to produce a larger modulus value as a result of having been done at a faster loading rate. Quotients of (URL % ER) (“LR 0.65 to 1.47 excluding basswood. This result com- — EL) ranged from pares very favorably with that of other researchers. Basswood fell into this range if the maximum and minimum strains computed from the rosette analysis were used instead of the strains measured parallel and perpendicular to the load direction. Shear moduli calculated in the radial-longitudinal plane (all species except sugar pine) from the tension specimens were from 86 percent to 130 percent of the values calculated from the ASTM plate shear test. When only specimens loaded at angles of 20 and 35- degree to the grain in the radial-longitudinal plane were considered, the shear moduli from the tension specimens were from 93 percent to 116 percent of those from the plate shear specimens. Shear moduli calculated in the tangential-longitudi- nal plane for three of the four sugar pine specimens loaded at an angle to the grain were from 93 to 103 percent of the values calculated from the plate shear samples. The shear modulus calculated from the 26-degree tension Specimen was about twice the plate 10. ll. 97 shear value. It was observed that the strain gauge rosette was not in a truly tangential-longitudinal plane for this specimen because of growth ring curvature and the rapid change of the curvature factor with specimen length. Shear moduli increased the most with increasing angle of load to grain for the two Species which had the greatest amount of ray tissue oriented parallel to the surface of the reference plane. Young's moduli parallel to the grain were not accu- rately predicted by the equations used with the data from specimens loaded at an angle to the grain. In most instances the values calculated from these specimens differed by more than 30 percent from those determined from the parallel to grain specimens. The moduli obtained from combining the data of two speci- mens loaded at an angle to the grain were closer to the expected than were those obtained from the data of one sample and a known value of Poisson's ratio. The Young's moduli perpendicular to the grain were predicted fairly closely by the equations used for the data from the specimens loaded at angle to the grain. When using the equation which took data from one specimen and a known Poisson's ratio, all calcu- lated values were within :25 percent of the values obtained from loading specimens at 90 degrees to the grain. The calculated average moduli from the 13. 98 65-degree samples for all species were within 10 percent of the expected value except for redwood which was within 20 percent. The moduli obtained from combining data from two specimens were equally as good. The effect of stress rate on the slope of stress- strain curves and elastic constants was a minor variable for the range of stress rates in the experiment. a. For specimens loaded parallel to the grain there were no consistent patterns of change of slope of strain-stress curves with stress rate. b. For specimens loaded perpendicular to the grain, there were slight increases in slopes of strain-stress curves with loading time. This was particularly true for the slopes of strain- stress data recorded at 45 degrees to the loaded axis. c. For specimens loaded at intermediate angles to the grain, about half of the slopes of the strain-stress curves showed consistent change with stress rate. d. There were few if any consistent patterns of change of moduli of elasticity parallel to the grain, of Poisson's ratios or of shear moduli with stress rate. 14. 99 e. There were slight indications of decrease of moduli of elasticity perpendicular to the grain with decrease in stress rate. Off-axis test was found to be productive for measur- ing shear modulus and modulus of elasticity perpen- dicular to the grain, but not accurate for determin— ing Young's modulus parallel to the grain and Poisson's ratios. LITERATURE CITED 10. L ITERATURE C I TED American Society for Testing and Materials. 1978. ASTM Standards, part 22: Wood; Adhesives. Philadelphia, PA. Anon. 1956. Stress-strain relations in wood and plywood considered as orthotropic materials. USDA Forest Service Report No. 1503. For. Prod. Lab, Madison, Wis. Ashkenazi, E. K., M. V. Gershberg, and M. G. Kapustin. 1976. Impulse method of determining moduli of elasticity and the shear moduli of wood. Industrial Laboratory (Zavodskaya Lab.) 42(8):129l-1295. Barkas, W. W. 1938. Recent work on the moisture in wood in relation to strength and shrinkage. Forest Products Research Special Report No. 4. London. Beker, V. H. F. 1973. Measuring the moduli of rigidity of solid wood by torsional vibration test. Holz als Roh-und werkestoff 31:207-210. Bell, E. IL,, E. C. Peck and N. T. Krueger. 1953. Modulus of elasticity of wood determined by dynamic method. USDA Forest Service Report No. 1977. For. Prod. Lab, Madison, Wis. Biblis, E. J., W. C. Lee. 1976. Simplification on the experimental method for determining plate shear modulus of plywood and particleboard. For. Prod. J. 26(4):38-42. Bodig, J. 1965. 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Popov, E. P. 1968. Introduction to Mechanic of Solids. Prentice—Hall, Inc., Englewood Cliffs, NOJO Radcliffe, B. M. 1953. Shear deflection in timber beams and method for determination of shear moduli. Purdue Univ. Agr. Expt. Sta. Bul. 589. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 105 1953. Proposed new methods for determination of the stiffness of timber beams and the strength of wood columns. Purdue Univ. Agr. Expt. Sta. Bul. 596. Richards, G. L., T. P. Airhart and J. E. Ashton. 1969. Off-axis tensile coupon testing. J. of Composite Materials 3(3);586-589. Rizzo, R. R. 1969. More on the influence of end constraints on off-axis tensile tests. J. of Composite Materials 3(2):202-219. Schniewind, A. P. 1959. Transverse anisotropy of wood. For. Prod. J. 9(1):350-359. Schuldt, J. P. 1972. Unified testing procedure for determining the elastic parameters of wood. Ph.D. Thesis. Colorado State University. Sliker, A. 1967. 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McGraw-Hill Book Company, N.Y. Tsai, S. W. 1965. Experimental determination of the elastic behavior of orthotrOpic plates. Journal of Engineering for Industry 87(3):315-318. U.S. Forest Products Laboratory. 1974 wood handbook wood as an engineering material (USDA Agr. Handb. 72, rev.) Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Vafai, A., M. Farshad, and A. Ahmadieh. 1976. Determination of modulus of elasticity of wood from vibration reed measurements. Fiber Sci. and Technology 9(1):1-10. Walker, J. N. and A. C. Dale. 1963. Interpretation and measurement of strain in wood. Transactions of ASAE 6(1):68-72. Wang, C. T. Sc.D. 1953. Applied elasticity. McGraw-Hill Book Company, N.Y. Wen/Nuri, P. R. and N. Mohsenin. 1970. Application of pulse technique for determination of elastic modulus of yellow poplar. Material and Research and Standard, pp. 25-27. Witt, R. K., W. H. Hoffman and R. S. Buxbaum. 1953. Determination of elastic constants of orthotropic materials with special reference to Laminates ASTM Bulletin 194:53-57. Wu, E. M. and T. L. Rodvey. 1968. Off-axis test of a composite. J. of Composite Materials 2(4):523-526. Young, R. L. 1957. The perpendicular-to-grain mechanical properties of red oak as related to temperature, moisture content and time. USDA Forest Service Report No. 2079. For. Prod. Lab, Madison, Wis. APPENDICES APPENDIX A 1(37 .He: can 94: ohm ommcu mama umosm mom. va.o vo.H| Hoo.o wmo.o Nem.o mm.m Hoo.o th.o cow me.o mw.~ Hoo.o nmo.o mmm.o o~.HI voo.o 900.0 00H NHoo.o mmv.o poozpom hm.o hc.H| Hoo.o moo.o Hmm.o we.mu voo.o wov.o ow wH~.o Hw.HI hooo.o moo.o omv.o om.Hu noo.o mov.o ma Ova.o mv.~| Hcc.o mno.o mhv.o mm.~u moo.o Hum.o ovw Omv.o mH.HI Hooo.o mno.o mv.H ~m.~ moo.o va.o oOH . mHo.o och vnm.O H~.H| mOOO O mOO0.0 O~O.O m~.H O... 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Hmm.MH m-.OvO OOO.~mO OOO.m~O OO0.000 _ OOO.an O0.0H coHuoH>mO OcHOmoO OOHOOoH OOHOmoq Ochmoq coHumH>mO OOHOmoO OcHoooq OOHOOOH _ OOHOmoH . . womuw>< mmuacmz nouns“: mwusc : nausea . . womuv> mwuscH mm :cH mm OCH . mm :cH Ouaocoum Ov~ OOH OOH OH 2 Oumccmum < Oe~.: WOH.z uov.z , umH.z wouOmO O M :oHuMOMHocH wwwuwmm 0 Hm; . . - , Ham 00 OHOc< AOHOEOOO m.cow:chw: >3 0Oum~=UHmov m AmcwEHuvzm mewuuuo £030 >Huucuwc 0&30330Hmuv m . ..E.fllfivk "unyflhlhh:ul.‘u “II'IVNF 0‘th ” "I’lkuhh ”In- ““tun I ‘Inrh thhuhn ”‘khhh .k .N ”Lu kl”.LI““L”"I‘JLH ““"pNhln hhlh.|llh.lnhhlnh.,.hru‘"E "hr":h|""" I Ethgu“ O ulu.mm wand? 117 ma0.0l a0000.0l OOH.0I NOH.0 v~0.0 vam.0 0~>.0I 000.0 00100 Ovo.0| 0HH.0I H0H.0I H00.0| >00.0| 000.0: 000.0: OON.~ 00Imm 0HN.0I HHH.0I 0NH.0I 0NH.0I 00H.0 00~.0 m0m.0| 000.0 00:00 Om0.0l mmo.0l OOH.0I 0H0.0 H50.0 000.0 Om~.H ~H0.0 m0|0m 0>H.0| vma.0| mma.0| 00H.0| vmo.a H00.0 mm0.0 00H.H 00I0N .r 000.0 HO0.0 000.0 m>0.0 0H0.0 «00.0 000.0 000.0 mmlom mcflvmoq mcficmoq ocflwmoq mcwomoq OCHUMOA Ocawmoq mcflnmon mcflnmoq 0000002 ” 0035002 mmuscflz mwuncwz mmuscflz mmuscwz mmuscwz mmuscwz 00m ~ 00H 00 ma 00m 00H . 00 ma Awwummov . . 000800000 ma: mo mamcm _ HMOHEOZ 000000 0.0000000 .0H coflumswm u009 maxMImmo mcflcwnfioo >3 00030000 000 mowumm 0.0000fiom wmusmfioonl.0m manna 118 0009 00x0:mmo 000000000 >3 000000 300000 «00.0 000.0 000.0 000.0 000.0: 000.0 000.0 000.0 00:00 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 00:00 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 00:00 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 00:00 000.0 000.0: 000.0 000.0 m 000.0: 000.0: 000.0: m 000.0: 00:00 000.0: _ 000.0: m 000.0: 000.0: 000.0: 000.0: 000.0: m 000.0: 00:00 , 0 0 0000000 m 0000000 0000000 0000000 _ 0000000 0000000 0000000 . 0000000 0000002 _ 0000002 0000002 0000002 . 0000002 0000002 0000002 _ 0000002 OON OOH OO mH OON OOH OO mH AmmuOmOO 000000000 00: 00: mo mHOc< 0000002 000000 0.0000000 .00 00000000 000 000000 0.0000000 00000000::.>0 0030B 119 0 000.0 000.0 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