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TO AVOID FINES return on or before date due. =7 DATE DUE DATE DUE DATE DUE __Jl :| +7 i MSU Is An Affirmative Action/Equal Opportunity Institution “ammonia—9.1 NON-SHEAR COMPLIANCES AND ELASTIC CONSTANTS MEASURED FOR NINE HARDWOOD TREES BY Ying Yu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Forestry 1990 ABSTRACT NON-SHEAR COMPLIANCES AND ELASTIC CONSTANTS FOR NINE HARDWOOD TREES BY Ying Yu Non-shear compliances (SLL: SRL: STL: SR3, SLR: STR: STT: SL3, SRT), Young's moduli (EL, ER, and ET), and Poisson's ratios ('9 , vL‘I‘rkaLv “’R'r: VTL, VTR) were measured at a single moisture content condition using matched samples from nine trees representing six hardwood species. Linear relationships were found between pairs of compliances from the loading of specimens in a given direction (L, R, or T). Most equations were in agreement with previous equations determined by Sliker. Except for ‘QRL there was also good agreement in values for Poisson's ratios. ”LR and ”LT appeared to have the same value for all species. There also appeared to be good agreement between data for SLL: SRR: and STT and empirical equations relating these compliances. ACKNOWLEDGMENTS I would like to express sincere appreciation to Dr. Alan W. Sliker, my major adviser, for his great patience and enthusiasm in the guidance and assistance throughout this study. Also, my sincere gratitude was extended to Dr. Sliker for providing me the funds which made this study possible. Thanks go to my graduate committee members, Dr. Otto M. Suchsland and Dr. Nicholas J. Altiero for giving me helpful suggestions and guidances. I also thank Mr. Timothy G. Weigel for his assistance in the experiment. Finally, I express my hearty thanks to my husband, Zhijun Liu, and my daughter, Mei Liu, for their encouragement and support all the way through my degree. Hearty thanks go to my parents and grandmother for their understanding and moral support of my study abroad. iii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . viii NOTATION . . . . . . . . . . . . . . . . . . . . . . . xii INTRODUCTION . . . . . . . . . . . . . . . . . MATERIALS AND METHODS. . . . . . . . . . . . . . RESULTS. . . . . . . . . . . . . . . . . . . . SUMMARY AND CONCLUSIONS . . . . . . . . . . . . LIST OF REFERENCES . . . . . . . . . . . . . . iv TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE LIST OF TABLES SPECIFIC GRAVITY AND MOISTURE CONTENT MEASURED FOR SPECIMENS MADE FROM NINE TEST TREES O O O O O O O O O O O COMPLIANCES, YOUNG'S MODULUS, POISSON’S RATIOS AND MOISTURE CONTENT FOR SPECIMENS LOADED IN THE L DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE R AND T DIRECTIONS . . . . . . . COMPLIANCES, YOUNG’S MODULUS, POISSON'S RATIO AND MOISTURE CONTENT FOR SPECIMENS LOADED IN THE R DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE T DIRECTIONS . . . . . . . . . . COMPLIANCES, YOUNG’S MODULUS, POISSON’S RATIO AND MOISTURE CONTENT FOR SPECIMENS LOADED IN THE R DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE L DIRECTIONS . . . . . . . . . . COMPLIANCES, YOUNG’S MODULUS, POISSON’S RATIO AND MOISTURE CONTENT FOR SPECIMENS LOADED IN THE T DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE R DIRECTIONS . . . . . . . . . . COMPLIANCES, YOUNG'S MODULUS, POISSON'S RATIO AND MOISTURE CONTENT FOR SPECIMENS LOADED IN THE T DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE L DIRECTIONS . . . . . . . . . . STATISTICAL ANALYSIS OF SLOPES BETWEEN THE CURRENT DATA AND SLIKER’S DATA FOR COMPLIANCE EQUATIONS . . . . . . STATISTICS OF SLOPES AND INTERCEPTS FOR COMPLIANCES EQUATIONS. . . . . . . . STATISTICAL ANALYSIS OF POISSON’S RATIOS BETWEEN THE CURRENT DATA AND SLIKER'S DATA 0 C C O O C O O O O O O O O O O V Page 29 30 31 32 33 34 35 36 37 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. LIST OF TABLES CONTINUED ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCE SR 0 o o o o o o o o o ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPHANCESTT.......... ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCESLL.......... ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCESRL. . . . . . . . . . ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCE STL O C O O O O O O O O ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMMANCE STR 0 e o o o o o o e o ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCE SLR . . . . . . . . . . ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCE Sam . . . . . . . . . . ESTIMATES OF THE VARIABILITY AMONG INDIVIDUAL OBSERVATIONS FOR COMPLIANCESLT......... . SUMMARY OF ANALYSIS OF VARIANCE OVER THE DIFFERENCES AMONG TREES LOADED IN COMPRESSION IN THE L DIRECTION. SUMMARY OF ANALYSIS OF VARIANCE OVER THE DIFFERENCES AMONG TREES LOADED IN COMPRESSION IN THE R DIRECTION. vi Page 38 39 40 41 42 43 44 45 46 47 47 TABLE TABLE TABLE TABLE TABLE TABLE 21. 22. 23. 24. 25. 26. LIST OF TABLES CONTINUED SUMMARY OF ANALYSIS OF VARIANCE OVER THE DIFFERENCES AMONG TREES LOADED IN COMPRESSION IN THE T DIRECTION. . DUNCAN’S T-TEST OVER THE MEANS IN COMPLIANCES AND YOUNG’S MODULUS FOR SPECIMENS LOADED IN THE L DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE R AND T DIRECTIONS . DUNCAN'S T-TEST OVER THE MEANS IN COMPLIANCES, YOUNG'S MODULUS AND POISSON'S RATIO FOR SPECIMENS LOADED IN THE R DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE T DIRECTIONS. DUNCAN’S T-TEST OVER THE MEANS IN COMPLIANCES, YOUNG’S MODULUS AND POISSON’S RATIO FOR SPECIMENS LOADED IN THE R DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE L DIRECTIONS. DUNCAN'S T-TEST OVER THE MEANS IN COMPLIANCES, YOUNG'S MODULUS AND POISSON’S RATIO FOR SPECIMENS LOADED IN THE T DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE R DIRECTIONS. DUNCAN’S T-TEST OVER THE MEANS IN COMPLIANCES, YOUNG'S MODULUS AND POISSON’S RATIO FOR SPECIMENS LOADED IN THE T DIRECTION AND WITH LATERAL STRAIN MEASURED IN THE L DIRECTIONS. Vii Page 48 49 50 51 52 53 FIGURE 1. FIGURE 2. FIGURE 3. FIGURE 4. FIGURE 5. FIGURE 6. FIGURE 7. FIGURE 8. FIGURE 9. FIGURE 10. LIST OF FIGURES COMPRESSION PARALLEL TO GRAIN SAMPLES WITH BONDED WIRE STRAIN GAGES FOR MEASURING STRAIN PARALLEL AND PERPENDICULAR TO THE LOAD AXIS (SLIKER, 1935). . . . . . . . . . . GAGE TYPE A USED TO MEASURE STRAIN IN THE L DIRECTION: GAGE TYPE B USED TO MEASURE STRAIN IN THE R AND T DIRECTION . . . . . . . . . . . . . SPECIMENS FOR LOADING IN THE R DIREflION O O O O O O O O O O O O O SPECIMENS FOR LOADING IN THE T DIREWION O O O O O O O O C O O O O GAGE TYPE USED TO MEASURE SMALL STRAIN IN THE L DIRECTION WHEN SPECIMENS ARE LOADED IN THE R OR T DIRECTION. TEST SPECIMEN A IN THE COMPRESSION “GE 0 O O O O O O O O O O O O O O O SPECIMEN WITH LONG AXIS IN THE L DIRECTION BEING LOADED IN INSTRON TESTING MACHINE . . . . . . SPECIMEN BEING LOADED IN EITHER R OR T DIRECTION BY APPLICATION OF TEN 10-POUND WEIGHTS TO A LOAD HANGER . PLOTS OF THE STRAINS IN THE L, R, AND T DIRECTIONS VERSUS COMPRESSIVE LOAD APPLIED IN THE L DIRECTION FOR YELLOW-POPLAR SPECIMEN YP2-1L . COMPLIANCE SRL PLOTTED AS A FUNCTION OF COMPLIANCE SLL FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . viii Page 54 55 56 57 58 59 60 61 62 63 FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE 11. 12. 13. 14. 15. 16. 17. LIST OF FIGURES CONTINUED COMPLIANCE STL PLOTTED AS A FUNCTION OF COMPLIANCE SLL FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . COMPLIANCE STR PLOTTED AS A FUNCTION OF COMPLIANCE SRR FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . COMPLIANCE SLR PLOTTED AS A FUNCTION OF COMPLIANCE SRR FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . COMPLIANCE SRT PLOTTED AS A FUNCTION OF COMPLIANCE STT FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . COMPLIANCE 3LT PLOTTED AS A FUNCTION OF COMPLIANCE STT FOR SPECIMENS FROM NINE TREES LOADED IN THE L DIRECTION . . . . . . . . . . . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SRL AND SLL FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1985) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN STL AND SLL FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1985) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. ix Page 64 65 66 67 68 69 70 FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE 18. 19. 20. 21. 22. 23. LIST OF FIGURES CONTINUED PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN STR AND SRR FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1988) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SLR AND SRR FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1989) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SRT AND STT FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1988) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SLm AND STT FROM THIS STUDY. 'THE EQUATION DERIVED FROM SLIKER (1989) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN As THE SOLID STRAIGHT LINE. . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SRR AND SLL FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1985 AND 1989) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE . . . . . . . . . . . . PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN STT AND SLL FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1985 AND 1989) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN As THE SOLID STRAIGHT LINE . . . . . . . . . . Page 71 72 73 74 75 76 LIST OF FIGURES CONTINUED Page FIGURE 24. PLOTTED POINTS SHOWING THE RELATIONSHIP BETWEEN SRR AND STT FROM THIS STUDY. THE EQUATION DERIVED FROM SLIKER (1988) EXPRESSING THE RELATIONSHIP BETWEEN THE SAME TWO QUANTITIES IS SHOWN AS THE SOLID STRAIGHT LINE. . . . . 77 xi NOTATION i subscript L, R, or T. j = subscript L, R, or T. L, R, T = longitudinal, radial and tangential axes. E1 = Young’s modulus in the i direction. Gij = shear modulus of elasticity in the ij plane, 1 E j. Sij = compliance with strain in the i direction per unit stress in the j direction for loading in the j direction. ’Dji = Poisson's ratio with strain in the 1 direction to that in the j direction for loading in the j direction; i * j. - stress in the 1 direction. ,3 I strain in the i direction. 61 xii INTRODUCTION The work described here is part of a larger program to collect data on the non-shear compliances Of wood from the testing of wood in compression in the longitudinal(L), radial(R), and tangential(T) directions. An ultimate Objective of this research is to find all the non-shear compliances as functions of the reciprocal Of Young’s modulus in the L direction (l/EL). Previously (Sliker, 1985, 1988, and 1989), data was collected for comparing compliances, which resulted in the finding of linear relationships between pairs Of compliances. In that testing, specimens for loading in the L, R, and T directions were not matched with respect to trees or species, which made a statistical analysis Of the relationships between all the compliances and l/EL more difficult. It is hoped that the use of matched samples as in this report will help clarify the desired relationships. In addition to the samples from nine trees tested for this thesis, another set Of samples from nine additional trees is also being tested. The results Of the two sets of data will be combined for a final comprehensive analysis. Wood is cellular biological material, which can be divided into two categories, hardwood and softwood. Hardwood is the product of broad-leaved species (dicotyledons Of the Angiosperms), and softwood is the product of coniferous trees (conifers of Gymnosperms) (Core et al., 1979). This study emphasized the hardwoods. Hardwoods are also called porous woods because Of their possessing vessel elements, which can be viewed in the transverse section as pores. Based on the change or lack of change of pore size across the growth ring, hardwoods can be separated into two groups, ring-porous woods and diffuse- porous woods (Core et al., 1979). Ring-porous species displays distinct layers Of large pore portion which is composed Of large, thin-wall cells. Because this portion is generally formed at the early part of the growth season, it is called early-wood or spring-wood. In the late season, actually starting in summer, layers Of cells featured with small, thick-wall pores are produced by the cambium Of a living tree. This portion is called late-wood or summer- wood. Early-wood and late-wood form the annual growth ring (growth increment). Oak and ash are in this category. Diffuse-porous species differ in the fact that vessels are generally uniformly distributed within an annual growth ring so that there is no distinct boundaries between early-wood and late-wood. Examples for this category are maple and yellow-poplar. Some woods, such as cottonwood and walnut, are intermediate between ring-porous and diffuse-porous woods, and thus classed as semi-ring-porous or semi-diffuse- porous woods (Panshin and De Zeeuw, 1970). One of the most distinct visual characteristics among woods is whether they are ring-porous, diffuse-porous, or semi-ring-porous species. Woods from different species Show large variations in physical properties due to the variations in cell dimensions and cell wall thicknesses. Woods from different trees Of the same species are also likely to show variations in physical properties due to different growth conditions and genetic variations. Even within a tree, variations exist. In the central region Of a tree near the pith, wood is called juvenile wood (Panshin and De Zeeuw, 1970). The rest of the wood formed away from pith is called mature wood. Juvenile wood and mature wood are quite different in physical properties because of the differences in cell structure and growth ring width. Usually, juvenile wood has wider growth ring than mature wood. Wood is anisotropic so that physical properties are different when tested along its three major directions L, R, and T. In order to get the non-Shear compliances Of wood in compression in the L, R, and T directions, truly orthotropic surfaces on a specimen should be made. This is quite difficult. Wood boards usually have to be resawn to Obtain truly radial and tangential surfaces, since most boards are not truly aligned to these surface. For test specimens, wood grain needs to be as straight as possible on the radial and tangential surfaces. The annual growth rings on the cross-sectional surfaces should have as little curvature as possible. Even when specimens are perfectly aligned with respect to orthotropic axes, there can be large variation in properties in any direction due to change in cell types, change in cell wall thickness of a given cell type, variability in growth ring width and the presence of abnormal wood such as tension wood in hardwoods. There are some problems in using commercially produced gages on wood to measure the strains since these gages are principally designed for use on metals. First, the stiffness of a strain gage can produce a significant reinforcing effect when the gage is installed on a material with a low elastic modulus (Perry, 1985). Wood in the R and T directions belongs to the low elastic modulus material. Most commercial strain gages are stiffer than wood so that movement Of wood is restrained under the gages. Secondly, "when most commercial types Of bonded electrical resistance strain gages are used on dielectric materials, undesirable drifts of the gages occur as they are energized in the measuring circuit"(Sliker, 1959). These are mainly due to the poor heat dissipation properties Of wood and the accumulation of heat in the vicinity of the gages. Drift of gages is generated by the thermal expansion of either the gage itself or the wood or both the gage and the wood, SO it is called thermal drift. Shrinkage Of the wood underneath the gage may also occur due to the heating Of the wood. In order to overcome these problems caused by commercial produced gages, it is desirable to make our own 5 bonded wire electrical resistance strain gages for use in wood strain tests. These gages have no backing material such as paper or plastic, which greatly add to the stiffness of commercial gages. The wire used to make gages is very thin and does not add much restraining effect to the wood. And the gages are made with only one or two strands or have a comparatively wide spacing between adjacent strands to reduce heat concentration (Sliker, 1959). There are twelve elastic constants and related compliances for wood, which correspond with three major orthotropic surfaces. The elastic constants are Young's moduli in the L, R, and T directions--EL, ER, and ET; six Poisson’s ratios-40m, ”LT: VRT, VRL: ”TR: ”TL? and three shear moduli GLR: GLT: GRT- The compliances are combinations Of the elastic constants as indicated in the next paragraph for the non-shear compliances. The only elastic constant that is readily available for use in structural design for most species is EL. It is difficult to obtain appropriate values for the other elastic constants (Sliker, 1988). Because Of developments in scientific test equipment and computer technology in the 80's, the difficulty could be solved. In order to Show three dimensional relationship Of strain to stress for an orthotropic material, a matrix equation can be written in terms of compliances or the engineering elastic parameters (Bodig and Jayne, 1982): ' 1 ’ r 4 ' 1 EL SLL SLR SLTi 0' L 1/EL "’RI/ER ' TL/ET ”Ii 6R ' sRL SRR SRT O’R " ‘vLR/EL 1/ER 'vTR/ET 0" R LET LSTL STR STT LO'T L‘vLT/EL " RT/ER 1/ET 0' T This also can be written into the following form:‘ 61] ' ago-L new}; -81/o'Ti '01] 8R =' '3R/0'L €R/0’R ‘5R/0‘T O‘R . .. [ET/7L ‘8T/0'R eT/O’T‘ (O‘T‘ In a previous study, Bodig and Goodman (1973) reported the information about determining the elastic parameters for 18 softwood species from his own data and the other data from Hearmon by plate-bending and plate-twisting method. As an exponential expression, the relationship between the combination of density and elastic parameters showed significant regression within these parameters, except Poisson's ratios, which were constant. Also, EL might be used to predict the other five elastic parameters, excluding Poisson’s ratios. In 1987, Guitard and Amri found significant multiregressions within the following parameters: specific gravity and elastic properties for 80 different wood species. The complete elastic compliance matrix for a certain wood could be predicted. However, the data used was a mixture from many sources done by different methods. Sliker had tested a broad range of species which included hardwoods and softwoods as loaded in the three major directions L, R, and T to obtain non-shear elastic constants and related compliances in 1985, 1988, and 1989. His researches have found the following results at a controlled room condition with 68°F temperature and 65% relative humidity(RH): 1. SRL = 0.022 x 10'6 - 0.405 SLL R2 = 0.900 2. STL = 0.021 x 10'6 - 0.500 SLL R2 = 0.925 3. STR = 1.260 x 10‘6 - 0.887 SRR R2 = 0.911 (1) 4. SLR = 0.029 x 10"6 - 0.0483 SRR R2 = 0.593 5. SRT = -0.659 x 10'6 - 0.255 STT R2 = 0.980 6. SLm = -0.022 x 10‘6 - 0.0274 STT R2 = 0.980 Equilibrium moisture content Of specimens that were tested by him was between 9 and 12%. In 1990, test specimens were loaded in the L, R, and T directions at three different moisture conditions--40% RH and 68°F, 65% RH and 68°F, 83% RH and 80°F to examine the effect Of moisture contents on relationships of non-shear compliances. The EMC Of specimens were 5-9%, 9-12%, and 15-20% with respect to the three moisture conditions. Results showed that moisture contents had very little effect on the relationships between pairs Of compliances (Sliker et al., in press). The current study focuses on finding the non-shear compliances for wood from nine different trees, which all belong to hardwood species, using matched samples for loading in the L, R, and T directions. Emphasis will be placed on analyzing the variability of individual measurements and on how well the data fits the Equations 1, which have already been published. Because Of the use of matched samples, this new data set also provides an 8 opportunity to compare relationships between l/ER and 1/EL and between 1/ET and 1/EL, and to make a rigorous statistical analysis of subsample differences (Sliker et al., in press). Ultimately the data from this thesis will be combined with that from another thesis to provide another estimate of the relationships between pairs of non-shear compliances and between all the non-shear compliances and l/EL. MATERIALS AND METHODS The test material was selected from nine trees and six species, which were cottonwood(£gpulu§ ggltgiggs 8.), hard maple(Agg; species), red oak(ng;gg§ species), soft maple(Agg; species), white oak(Que;§us species), and yellow- poplar(L1;igd§ngzgn,gulipifgzg L.). There were two red oaks, two soft maples, and two yellow-poplars among them (see Table 1). The diameters of the trees were over 30 inches. Only mature wood was used for test specimens by selecting only wood which was at least 15 growth rings (preferably 20 or more) from the pith. The trees were all sawn into three and half inches thick planks and then dried in a kiln for about 30 days with a slow schedule to reduce drying defects. For each tree, three types Of Specimens and a moisture content (MC) sample for each type Of test specimen were made according to three different loading directions--longitudinal(L), radial(R), and tangential(T). In order to make truly orthotropic surfaces for each specimen, the boards were resawn to follow grain and to have truly radial and tangential surfaces. For woods where the grain direction was hard to see, a red dye in kerosene was placed on the woods tO see its major direction Of flow. Each type of specimen has a matched sample in order to make 10 possible a rigorous statistical analysis of subsample differences (Sliker et al., in press). After kiln-drying, a wood block from each board where the specimens were made was cut, weighed, measured in its dimensions to get its kiln-dry weight and kiln-dry volume, and then dried in an oven at 103°C to Obtain its oven-dry weight and oven-dry volume. Based on these values the moisture content and the specific gravity of each test board was obtained at the time of specimen preparation (see Table 1). All of the test specimens and MC samples were weighed after they were made, and the MC samples were weighed again during the test to keep track of moisture contents of specimens (Tables 2-6). Final moisture content conditioning and testing was conducted in a room where temperature and relative humidity were maintained at 68°F and 65%. Equilibrium moisture content for selected types of wood at such an environment was between 7 and 13 percent. The positions where strain gages were to be installed were drawn on specimens before the gages were placed, and then a thin layer of Duco cement was put on these areas. After the adhesive dried, the specimens were lightly sanded by sandpaper with grit No. 180 to make the areas smooth. Following this step, strain gages were mounted on the specimens in specified patterns for each type of loading. The specimens loaded in the longitudinal direction were approximately 7 inches (18.78 cm) long and 1.25 by 1.25 inches (or 3.20 by 3.20 cm) in cross-sectional dimensions 11 (Figure 1). "Great care was taken in trying to have the grain of the wood parallel to the length of the specimen and to have the side surfaces be radial and tangential" (Sliker, 1985). The free-filament strain gages, which were designed by Sliker from 4-inch lengths of 1-mil diameter constantan wire having a resistance of 290 ohms per foot soldered to 12-mil diameter constantan lead wire, were used (Sliker, 1985). "Resultant gage resistance was approximately 97 ohms“ (Sliker, 1985). Electrical resistance strain gages bonded on a specimen are shown in Figure 1. The gage along the grain direction Of specimens was kept at 2 inches long by making one 360 degree bend in the l-mil wire around a steel straight pin, and the gage perpendicular to the grain direction was kept 1-inch long by making three 360 degree bends in the 1-mi1 wire around three steel straight pins (Sliker, 1989) when they were bonded to the specimen with a nitrocellulose adhesive (Duco Cement). The gage construction is demonstrated in Figure 2. "Parallel gages on opposite faces of each specimen were connected in series to make one arm of a Wheatstone bridge" (Sliker, 1985). The method of making individual specimens that were loaded in either the R or T direction was to take a board and cut from it five pieces measuring 1.5 inches by 1.25 inches by 12 inches with the 12-inch dimension being in the L direction and the 1.25-inch dimension being in either the R or T direction according to the specimen type to be made (Sliker, 1988). Then, these five pieces were laminated with 12 polyvinyl acetate adhesive into blanks measuring 1.5 inches by 6.25 inches by 12 inches (Sliker, 1988). The final size of a specimen was about 6 inches long and 1.25 by 1.25 inches in cross-sectional dimension by machining the blanks to a thickness of 1.25 inches and by cutting 6.25-inch dimension at 1.25-inch intervals in the L direction (Figures 3 and 4) (Sliker, 1988). The free-filament strain gages mentioned before were also used here. Gages were mounted only on the central section of each five-layer laminated specimen with thinned Duco Cement adhesive. There are two types of gage installations for specimens loaded in the R or T direction. One is shown in Figure 3 for loading in the R direction and the other is shown in Figure 4 for loading in the T direction. The mounting method in Figure 3A and Figure 4A.was similar to that for the gages perpendicular to the grain direction of specimens loaded in the L direction (refer to Figure 28 for gage construction). Four gages were mounted per specimen with gages on Opposite faces being connected in series to eliminate the recording of bending strains (Sliker, 1988). In Figure 3B and Figure 48, each specimen has two 4-inch free-filament strain gages installed along either the R or T direction on the opposite sides. The way of the gage installation was similar to that for the gages perpendicular to the grain direction of specimen loaded in the L direction. ”Although there might be a slight sensitivity to strain in the L direction in this design, the strain pickup 13 in the L direction would be small compared to those in the R and T directions" (Sliker, 1989). There is a special concern when strain gages are mounted along the L direction while loading in the R or T directions. This is that they may pick up some of the large strains in the R and T directions with a gage oriented to measure the small strain in the L direction (Sliker, 1989). Many commercially produced strain gages with loops perpendicular to the main strain axis have this problem in particular. Therefore, if strain gages were made in which all the strain sensitive wire was oriented in the L direction (Sliker, 1989), that could overcome the problem. This was accomplished by making strain gages with 12-mil diameter constantan leads soldered to 1-inch lengths of 1-mil diameter constantan strain gage wire having a resistance of 290 ohms per foot, then placing four of these gages parallel to each other along the L direction on one side of a specimen's middle section with quarter inch intervals (Sliker, 1989). These four gages were connected in series and then were connected in series with a similar arrangement Of 1-inch gages on the opposite side of the specimen (Sliker, 1989). Figure 5 shows the scheme for gage construction. Also, there was another problem, which was amplification of the low signal emanating from the gages in the L direction when the specimens were loaded in the R or T direction (Sliker, 1989). Measurements Group's Model 3800 Wide Range Strain Indicator could solve this problem because it could indicate strain to 10‘7 inches 14 per inch. Shielded cable was used between the strain gage and the measuring instrument in order to keep the noise to signal ratio low (Sliker, 1989). Test specimens to be loaded in the L direction were placed in a compression cage (Figure 6) for load application. A tensile force on the compression cage applied a compressive force on the test specimens. A key feature of the compression cage, which was made of steel and aluminum, was the placement of a three-eighth-inch spherical bearing between the top and bottom sections of the compression cage and the blocks that bore on the ends of the test specimen (Bodig and Goodman, 1969). "This allowed rotation of the bearing blocks so that equal pressure would be applied over the ends of the specimens” (Sliker, 1988). "Loosely fitting guides near the ends of the specimen keep it centered on the bearing blocks" (Sliker, 1989). An Instron testing machine 4206 was used for loading specimens with the crosshead speed setting at 0.005 in/min (Figure 7). Three direction strains and load in the L direction were recorded at increments of 50 microstrain in the L direction until it was up to 600 microstrain. The strains were read from the Measurements Group's Mbdel 3800 Wide Range Strain Indicators. The range of maximum loads placed on the specimens is from 1099 pounds on COTl to 1975 pounds on HMZ. For compression loading in the R and T directions, specimens shown in Figure 3 and 4 were placed into the compression cage described previously. "The upper end of 15 the cage was connected to a structural frame by a universal joint, while a load hanger was suspended from the lower end of the cage through another universal joint” (Sliker, 1989). The scheme is shown in Figure 8. Loads were applied by putting ten 10-pound weights on the suspended hanger in quick succession. Less than two minutes elapsed for a given total loading of 100 pounds. Strain parallel and perpendicular to the loading direction were quickly read from Measurements Group’s Model 3800 Wide Range Strain Indicators at zero load and after each 10-pound weight being added (Figure 8). When measuring the small strains in the L direction, the gage factor was changed from 2.050 to 0.2050 for increased sensitivity in strain readings. RESULTS Linear regression analysis was applied to the strain versus load data for each specimen in order to Obtain a best fit value for the slope used to determine the compliance for the specimen. The coefficients of determination for these equations ranged from 0.986 to nearly perfect. Plots of strain in the L, R, and T directions versus load are given for one test sample in Figure 9. Compliances expressed as SLL: SRL: STL: SRR: STR: SLR: STT: SRT: and 3LT were derived from the slopes of the curves of each individual specimen by multiplying the slopes by cross-sectional areas of the specimens, which converts load to stress. Compliances, Young's moduli, and Poisson's ratios for all test specimens are presented in Tables 2 through 6. Young's moduli EL, ER, and ET are the slopes of strain versus stress where the strain and the stress are measured in the same direction. Poisson's ratios are the slopes of curves of strain perpendicular to the load axis divided by strain parallel to the load axis. The signs for the compliances are reversed from those in previous publications by Sliker in 1985, 1988, and 1989 in order to conform with more traditional practice (Sliker et al., in press); i.e. SLL: SRR: STT: EL, ER, and ET are shown as positive numbers 16 17 despite being derived from negative strains. Similarly, SRL: STL: SLR: STR: 3LT: and SRT are shown as negative numbers despite being determined from positive strains. Linear relationships can be found between pairs of compliances taken for a given direction (L, R, or T) Of loading. Regression equations relating pairs of compliances from the data in Tables 2 through 6 are as follows: 1. SRL = -0.016 x 10'5 - 0.353 SLL R2 = 0.613 2. STL - -0.062 x 10‘6 - 0.360 SLL R2 = 0.566 3. STR = 1.224 x 10'6 - 0.967 833 R2 = 0.858 4. SLR a -0.210 x 10‘5 - 0.0143 SRR R2 = 0.332 (2) 5. Sam = -0.309 x 10'6 - 0.288 STT R2 a 0.936 6. SL3 - -0.266 x 10"6 - 0.00605 STT R2 = 0.100 Plots of the data and the associated compliances are given in Figures 10 through 15. The slopes and intercepts of Equation 2 are slightly different from these reported on by Sliker in 1985, 1988, and 1989 (Equation 1) and, also, the R3 are smaller. Two possible reasons for this are the smaller number of samples involved for any one equation and the concentration of the samples in the higher specific gravity species in the current testing. The additional testing being done for another thesis contains more lower specific gravity species. One of the poorest correlations _ is between SET and STT- If the cottonwood is removed from this set of data, the equation (SL3 a 0.107 x 10‘5 - 0.047 STT: R2 = 0.455) becomes more like that on Equation 1. 18 In order to examine how my data points are distributed around a regression line of each of the Equations 1 established by Sliker in 1985, 1988, and 1989, six graphs are generated that contain my data points along with regression lines for Equation 1 (Figures 16-21). In the plots, the data points from nine trees of this study represent the relationship between the strain perpendicular to the loading direction per unit stress parallel to the load direction and the strain per unit stress parallel to the load direction. Each data point represents the average of two replications. The solid straight lines from the Equations 1 found by Sliker also express the relationship between the same two quantities. The plots show that there is a general agreement between the current experimental data and Sliker's data. Statistical analysis as shown in Table 7 indicates that all of the slopes except for one in Equation 2 are not significantly different from the slopes in Equation 1 at the 95% probability level. In other words, common slopes from the two independent experiments can be found. The one exception is the relationship between SL3 and STT- In addition, the current data for SLR versus SRR does not match well with the regression line from Equation 1. Y-axis intercept rather than slope may account for this. SLR and SL3 are the two most difficult compliances to measure. For an orthotropic material, SRL = SLR: STL = 5LT: and STR - SRT- In this data, there is very good linear 19 correspondence between STR and SRT- To a lesser extent there is linear correspondence between SRL and SLR and between STL and SL3. These latter discrepancies may be because of the greater difficulty in measuring SL3 and SLR than in measuring the other compliances or it may be related to different viscoelastic responses in loading parallel and perpendicular to the grain. The accumulation of more data should help to better show that there are solid relationships between all these pairs of compliances. If assuming SRL - SLR: STL - 3LT: and STR - SRT: three other equations can be obtained from the Equations 1 found by Sliker: 1. SRR - 0.145 x 10“ + 8.39 SLL 2. STT - -1.57 x 10"6 + 18.25 SLL (3) 3. 833 - 2.19 x 10‘6 + 0.291 STT By using each of these three equations as a solid straight line and the averaged values of SLL: 3RR and STT from nine trees of this report, three plots are obtained and shown in Figures 22-24. The data points from this study in each plot generally fit the straight line except that the cottonwood data point in Figure 23 is far Off the straight line found by Sliker. This suggests that either the value for SL3 or STL for cottonwood is not a representative number. The statistics of regression analysis is given in Table 8. All the slopes except the ones in the equation relating SLR to SRR and the equation relating SET to STT are statistically significant at a minimum of 95% probability 20 level. This indicates that there exist linear relationships between the various pairs of compliances listed in Tables 2, 3, and 5 among nine trees tested in this experiment. This may also suggest that linear relationships between compliances exist in a broader range of hardwood species. Due to the statistical significance of intercepts in equations 4 and 6 in Table 8, these values can be used in establishing the predictive equations for Poisson's ratios, since they can be determined by quotients of compliances: «1m. - (euro/(cams) and 9n. - (sum/(swam If each term in equation 4 in Table 8 is divided by SR3, it will become: SLR/SR}; -- - 0.0143 - 0.210 x 10"5 l/SRR. The term in the right Of the above equation equals the Poisson's ratio‘th. It is obvious that it can be predicted from SRR- similarly, if each term in equation 6 in table 8 is divided by STT: it will become: SLT/STT - -0.00605 - 0.266 x 10'6 1/STT- Poisson's ratio'vfiL then can be predicted from this equation through the use of STT obtained experimentally. The rest of the equations in Table 8 showed that intercepts were not significantly different from zero. Therefore, the best way to estimate these Poisson's ratios could be the averages of the test values (Sliker, 1989). The averaged values and their standard deviations for all Poisson's ratios of all the tested trees are shown in Table 9. In order to compare the Poisson's ratios obtained from this study with those reported by Sliker in 1985, 1988, and 21 1989, a statistical method (t test) was conducted (Table 9). The Poisson's ratios ”LR: YLT: 1’31), ”TR: and 1,11, derived from current study are not significantly different from those found by Sliker with 95% probability level, and the Poisson's ratio‘VRL derived from this report is significantly larger than that found by Sliker with 95% probability (Table 9). Coefficients of variability (CV) of SRR among individual specimen are listed in Table 10. There are four specimens from each tree for the measurements of compliance SRR: of which two are matched samples with the same gage installation (see Figure 3A) and the other two are also matched samples but with another type of gage installation (see Figure 3B). The coefficients of variation among the nine trees tested range from 0.14% in 8M2 to 4.18% in W01 for specimens shown in Figure 3A and 0 in R02 to 2.98% in SMl for specimens shown in Figure 3B. Coefficients of variability of STT along individual specimen loaded in the T direction are listed in Table 11. There are four specimens from each tree for measuring STT: of which two are matched samples with the same gage installation (see Figure 4A) and the other two are matched samples, too, but with another type of gage mounting (see Figure 4B). The variabilities among the nine trees tested range from 1.34% in R01 to 5.42% in 8M1 for specimens shown in Figure 4A and 1.00% in R01 to 4.90% in YPl for specimens shown in Figure 4B. 22 Coefficients of variability (CV) of SLL: SRL: STL: STR: SLR: SRTI and SL3 among individual specimen are listed in Tables 12 through 18. There are two matched samples from each tree for measuring these compliances. The coefficients of variation of SLL: SRL: STL: STR: SLR: SRT: and SLE among the nine trees tested range from 0.60 to 13.61%, 0.33 to 22.22%, 1.43 to 25.93%, 0 to 3.33%, 1.10 to 5.66%, O to 3.72%, and 0.49 to 6.88%, respectively. The experimental data collected was analyzed with the procedure Of analysis Of variance (ANOVA) to determine the differences existing among the nine tested trees in compliances and elastic constants. Results demonstrated that trees, loaded in compression in the L direction, exhibited significantly different responses in compliances, i.e. SLL: SRL: STL: and Young's moduli, but did not differ in Poisson’s ratios (Table 19). When loaded in compression in the R direction, trees tested showed significant differences in all the parameters investigated, regardless of the orientation Of the gage settings (Table 20). Similarly, there were significant differences in the nine trees tested when loaded in compression in the T direction in all the compliances and elastic constants studied, no matter which method was used in the gage installation (Table 21). Trees that showed significant differences in compliances and elastic cOnstants from the ANOVA tables were further tested for their means with Duncan's t-test. Mean 23 values of compliances and EL for trees that were loaded in compression in the L direction were presented in Table 22. There is clear exhibition of groups in SLL- COT1, R02, SM1 and SM2 fell in one group and ranked the highest in the nine trees. SM1 and SM2 are not significantly higher than YPl and R01 which, however, were different from COT1 and R02. YP2, W01, and HM2 belonged to the same group and Showed lowest value in the nine trees. The differences can be scaled up to 44% between the highest and the lowest groups based on the group mean values. Young’s moduli showed the same order but Opposite pattern due to the nature Of SLL = EL'l. In SRL: SM1 showed highest value in magnitude, and YP2 the lowest, with 83% difference. In STL: SM1 and SM2 showed the same and highest values in the nine trees. They are significantly higher than YP2, W01, and HM2. Mean values of compliances, ER, and ‘9er for trees that were loaded in compression in the R direction are shown in Table 23 for one type Of gage installation (refer to Fig. 3A). In SRR: COT1 had the highest compliance value, and W01 the lowest. In between were YP2, SM2, R02, SM1, YPl, R01, and HM2. COT1, which was significantly higher in SRR than W01, yielded more than two-fold value to W01. In STR: COT1 had significantly higher value than the rest of the trees, and the difference was up to about triple fold over W01, one with the lowest value. The Young’s moduli showed an Opposite pattern to SRR- In Poisson's ratios, trees exhibited clear grouping patterns. COT1 and HMZ were in the 24 same group and ranked the highest, followed by SM2, SM1, and YPI group, YP2 and W01 were in the next group, followed by R01, and finally, R02, the lowest ranking. The other results are listed in Table 24 for the gage settings shown in Fig. 38. There was more than two-fold difference in SRR within the nine trees. The order can be demonstrated as: COT1 > SM2 = R02 = YP2 > SM1 = YPI > HMZ = R01 > W01. In SLR: the ranking pattern was different, with SM2 and COT1 in the highest group, and YPl and HMZ in the lowest group. The Young's moduli indicated an opposite pattern to SRR- For Poisson’s ratios, R01 and W01 were in the same group and had the highest value. COT1, on the other hand, had the lowest value. Mean values of compliances, ET, andeTR for trees loaded in compression in the T direction are shown in Table 25 for the gage installation method displayed in Fig. 4A. In STT: COT1 ranked the highest, and displayed about a triple-fold higher value than R01. Even the second-highest tree YPI showed only about half of the value in COT1. In SRT: the order can be demonstrated as COT1 > SM1 = SM2 = YPl > YPZ > HMZ > R02 > R01 = W01. Similarly, Young’s moduli displayed an opposite pattern to STT- In Poisson's ratios, SM1, YP2, HMZ, and SM2 fell in the same group and ranked the highest. 0n the other extreme, W01 and COT1 fell in one group. The other results are shown in Table 26 for the gage installation method displayed in Fig. 4B. COT1 exhibited a 25 significantly higher STT value, about doubled the second highest value and tripled the lowest. The pattern can be displayed as a series Of orders: COT1 > YP1 = SM2 = SM1 > R02 = HM2 = YP2 > R01 = W01. In 5LT: SM1 showed highest value in term Of magnitude, followed by SM2, COT1 and YP1 in the next group, followed by YP2, R01, W01 and R02, and lastly HM2. The order Of Young’s moduli are Opposite to STT due to ET = 1 / STT- Poisson's ratios also showed variation among the nine trees tested, ranging from 0.0177 Of COT1 to 0.0459 of SM1. The order can be displayed as SM1 > SM2 > R01 > YP2 = W01 > YP1 = R02 = HM2 > COT1. SUMMARY AND CONCLUSIONS Strains parallel and perpendicular to the load axis were recorded for specimens from nine different hardwood trees representing six species loaded in the L, R, and T directions at moisture contents between 7% and 13%. Non- shear compliances in terms of strain in the L, R, and T directions per unit of stress in the loading direction (either L, R, or T) were calculated from this data. Conclusions were as follows: 1. Linear relationship were found between pairs of compliances: SRL = f(SLL), STL - f(SLL), Sm = f(SRR), SRT f (ST-1v), SLR - f (SRR), and Sm - f(Sc1-r). The correlation factors R2 for the first four equations were 0.566 or greater. However, R2 for the last two equations were 0.332 and 0.100. In part this can be explained by the greater difficulty in measuring SLR and 5LT than in measuring the other compliances. 2. With the exception of the relationship between SLE and STT: slopes of equations from this report (Equation 2) relating pairs of non-shear compliances to each other were in general agreement with those in Equation 1 published 26 27 previously by Sliker (1985, 1988, and 1989). The slope of the equation with 3LT as a function of STT showed a significant difference from Sliker’s equation (1989) at the 95% probability level. 3. Intercepts for the equations SLR = f(SRR) and 5LT = f(STT) were the only intercepts statistically significant at the 95% probability level. Dividing SLR = f(SRR) by SRR and SET - f(STT) by STT provided equations for predicting the Poisson’s ratios VRL and “TL- 4. The averaged values Of Poisson's ratios Obtained from current study are not Significantly different from those reported by Sliker except the Poisson's ratio vRL that is significantly larger than that found by Sliker with 95% probability level (Table 9). 5. Trees studied in this experiment differed significantly in compliances and Young's modulus but did not show differences in Poisson's ratios when the specimens were loaded in compression in the L direction (Table 19). 6. Trees that were loaded in compression in either the R or T directions displayed significant differences in compliances and elastic constants investigated (Tables 20 and 21). 28 7. For this data STR very closely equaled SRT- There was not sufficient data to test that SRL = SLR and STL = 5LT- 8. 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Amuo6 x 6. >0 0600\6. 0600\6. >0 0600\6. 0600\6. .>00 .060 000: .>00 .060 0002 000060000 60 600002 60060000 6690 N880 980 0000660000 600 000660>60000 60006>6006 60000 6666600660> 006 00 006006600 .66 06006 40 Table 12. Estimates of the variability among individual observations for compliance SLL SLL Species* Number of specimens Mean Std. dev. (l/psil6 (1/95115 CV (1 x 10 ) (1 x 10 ) (2;) COT1 2 0.748 0.1018 13.61 YP1 2 0.625 0.0346 5.55 YP2 2 0.514 0.0205 3.99 SM1 2 0.707 0.0042 0.60 SM2 2 0.658 0.0127 1.93 R01 2 0.624 0.0078 1.25 R02 2 0.726 0.0071 0.97 HM2 2 0.478 0.0170 3.55 W01 2 0.487 0.0163 3.34 *the numbers after the abbreviation of species represent trees. 41 Table 13. Estimates of the variability among individual observations for compliance SRL SRL Species* Number of specimens Mean Std. dev. (l/psi) (l/psi) CV (1 x 10'5) (1 x 10‘5) (%) COT1 2 -0.271 0.0601 22.22 YP1 2 -0.214 0.0311 14.54 YP2 2 -0.167 0.0071 4.23 SM1 2 -0.305 0.0064 2.09 SM2 2 -0.228 0.0049 1.72 R01 2 -0.232 0.0014 0.61 R02 2 -0.238 0.0276 11.61 HMZ 2 -0.214 0.0007 0.33 W01 2 -0.181 0.0106 5.88 *the numbers after the abbreviation of species represent trees. 42 Table 14. Estimates of the variability among individual observations for compliance STL STL Species* Number of specimens Mean Std. dev. (1/psi) (l/psi) CV (1 x 10'5) (1 x 10'5) (z) COT1 2 -0.300 0.0778 25.93 YP1 2 -0.288 0.0502 17.46 YP2 2 -0.237 0.0127 5.37 SM1 2 -0.347 0.0064 1.84 SM2 2 -0.347 0.0049 1.43 R01 2 -0.323 0.0389 12.06 R02 2 -0.274 0.0177 6.46 HMZ 2 -0.228 0.0163 7.15 W01 2 -0.217 0.0120 5.55 *the numbers after the abbreviation of species represent trees. 43 Table 15. Estimates of the variability among individual observations for compliance STR STR Species* Number of specimens Mean Std. dev. (l/psi)_6 (1/psi)_6 CV (1 x 10 ) (1 x 10 ) (%) COT1 2 -6.390 0.1556 2.43 YP1 2 -3.325 0.0778 2.34 YP2 2 -3.330 0 0 SM1 2 -3.495 0.0636 1.82 SM2 2 -3.950 0.0283 0.72 R01 2 -2.275 0.0354 1.55 R02 2 -2.585 0.0495 1.91 KHZ 2 -3.185 0.1061 3.33 W01 2 -2.160 0.0283 1.31 *the numbers after the abbreviation of species represent trees. 44 Table 16. Estimates of the variability among individual observations for compliance SLR SLR Species* Number of specimens Mean Std. dev. (1/psi)_6 (1/psi)_6 CV (1 x 10 ) (1 x 10 ) (%) COT1 2 -0.311 0.0085 2.73 YP1 2 -0.250 0.0120 4.82 YP2 2 -0.279 0.0078 2.79 SM1 2 -0.289 0.0078 2.70 SM2 2 -0.325 0.0071 2.18 R01 2 -0.290 0.0035 1.22 R02 2 -0.275 0.0156 5.66 HMZ 2 -0.238 0.0042 1.78 W01 2 -0.258 0.0028 1.10 *the numbers after the abbreviation of species represent trees. 45 Table 17. Estimates of the variability among individual observations for compliance SRT SRT Species* Number of specimens Mean Std. dev. (1/psi) (l/psi) cv (1 x 10‘5) (1 x 10‘5) (%)‘ COT1 2 -6.250 0.0990 1.58 YP1 2 -3.620 0 0 YP2 2 -3.135 0.0071 0.23 SM1 2 -3.635 0.0071 0.19 SM2 2 -3.565 0.0495 1.39 R01 2 -2.280 0.0849 3.72 R02 2 -2.380 0.0849 3.57 HMZ 2 -2.960 0 0 W01 2 -2.185 0.0212 0.97 *the numbers after the abbreviation of species represent trees. 46 Table 18. Estimates of the variability among individual observations for compliance 5LT 3LT Species* Number of specimens Mean Std. dev. (1/psi) (l/psi) CV (1 x 10‘5) (1 x 10'5) (%) COT1 2 -0.356 0.0113 3.18 YP1 2 -0.329 0.0226 6.88 YP2 2 -0.297 0.0057 1.90 SM1 2 -0.463 0.0028 0.61 SM2 2 -0.425 0.0297 6.99 R01 2 -0.290 0.0014 0.49 R02 2 -0.271 0.0078 2.88 HMZ 2 -0.262 0.0127 4.86 W01 2 -0.265 0.0014 0.53 *the numbers after the abbreviation of species represent trees. 47 Table 19. Summary of analysis of variance over the differences among trees loaded in compression in the L direction Parameter Number of n F value Pr > F trees tested sLL 9 18 15.07 0.0002 SRL 9 18 7.01 0.0043 STL 9 18 4.00 0.0269 EL 9 18 26.21 0.0001 913 9 18 2.72 0.0774 ‘9Lm 9 18 3.03 0.0597 Table 20. Summary of analysis of variance over the differences among trees loaded in compression in the R direction Parameter Number of n P value Pr > F trees tested sRnl 9 18 343.81 0.0001 STR 9 18 565.26 0.0001 ER1 9 18 147.22 0.0001 ‘vhm 9 18 41.57 0.0001 SRRZ 9 18 412.17 0.0001 SLR 9 18 21.38 0.0001 ER2 9 18 233.38 0.0001 JDRL 9 18 43.90 0.0001 1gage installation displayed 2gage installation displayed in Fig. 3A. in Fig. 3B. 48 Table 21. Summary of analysis of variance over the differences among trees loaded in compression in the T direction Parameter Number of n F value Pr > F trees tested sTTl 9 18 336.16 0.0001 SRT 9 18 1013.29 0.0001 8T1 9 18 192.21 0.0001 ‘VTR 9 18 16.93 0.0001 STTZ 9 18 296.12 0.0001 3LT 9 18 53.41 0.0001 ET2 9 18 131.39 0.0001 «Ln, 9 18 78.32 0.0001 1gage installation displayed in Fig. 4A. 2gage installation displayed in Fig. 4B. 49 Table 22. Duncan’s t-test over the means in compliances and Young's modulus for specimens loaded in the L direction and with lateral strain measured in the R and T directions SLL SRL STL EL Species* (l/psi) (1/psi) (l/psi) (psi) (1 x 10") (1 x 10’5) (1 x 10'5) COT1 0.748a -0.27labc -O.300abc 1.350c R02 0.726a -O.238bcd -0.274abc 1.378c SM1 0.707ab -0.305a -0.347a 1.414dc SM2 0.658ab -0.288ab -0.347a 1.520bc YP1 0.625b -0.2l4cde -0.288abc 1.604b R01 0.624b -0.232bcd -0.323ab 1.604b YP2 0.5140 -0.167e -0.237bc 1.949a W01 0.487c -0.181de -0.217c 2.057a HMZ 0.478c -0.214cde -0.228c 2.094a *the numbers after the abbreviation of trees. species represent Means in different letters within the same column are significantly different from each other at 95% probability level with Duncan's multiple range test. 50 Table 23. Duncan’s t-test over the means in compliances Young’s modulus and Poisson’s ratio for specimens loaded in the R direction and with lateral strain measured in the T direction SRR STR ER Species* (l/psi) (l/psi) (psi) JVRT (1 x 10's) (1 x 10'5) COT1 7.6203 -6.390a 131500f 0.839a YP2 5.130b -3.330¢d 195000e 0.650c SM2 5.085bc -3.950b 196500e 0.777b R02 4.895cd -2.585e 204500de 0.5288 SM1 4.690de -3.495c 213500Cd 0.746b YP1 4.5058 -3.325¢d 2220000 0.738b R01 3.850f -2.275f 260000b 0.591d HMZ 3.795f -3.185d 263500b 0.840a W01 3.5559 -2.160f 2815003 0.608cd *the numbers after the abbreviation of species represent trees . Means in different letters within the same column are significantly different from each other at 95% probability level with Duncan’s multiple range test. 51 Table 24. Duncan's t-test over the means in compliances Young’s modulus and Poisson’s ratio for specimens loaded in the R direction and with lateral strain measured in the L direction SRR SLR ER Species* (l/psi) (1/psi) (psi) ‘VRL (1 x 10'5) (1 x 10'5) COT1 7.4803 -0.3113 134000e 0.0416f SM2 5.050b -0.3253 198500d 0.0644b R02 5.050b -0.275b0 198000d 0.0545de YP2 5.025b -0.279b 199000d 0.0555de SM1 4.7500 -0.289b 2105000 0.0608b0 YP1 4.6650 -0.250d 2145000 0.0535e HMZ 4.050d -0.238d 247000b 0.05880d R01 3.925d -0.290b 254500b 0.07383 W01 3.535e -0.2580d 2825003 0.07303 *the numbers after the abbreviation of species represent trees. Means in different letters within the same column are significantly different from each other at 95% probability level with Duncan’s multiple range test. 52 Table 25. Duncan’s t-test over the means in compliances Young’s modulus and Poisson’s ratio for specimens loaded in the T direction and with lateral strain measured in the R direction ST'I‘ SRT ET Species* (l/psi) (l/psi) (psi) ‘VER (1 x 10'5) (1 x 10‘5) COT1 21.1153 -6.2503 ' 47350f 0.296de YP1 11.175b -3.620b 89550e 0.325bc SM2 10.510b0 -3.565b 95200de 0.3403b SM1 9.9200 -3.635b 101050d 0.3673 YP2 9.040d -3.l350 1105000 0.3473b R02 8.650de -2.380e 1150000 0.2760 HM2 8.610de -2.960d 1160000 0.3443b W01 8.080ef -2.185f 124000b 0.271e R01 7.400f -2.280f 135000a 0.3080d *the numbers after the abbreviation of species represent trees. Means in different letters within the same column are significantly different from each other at 95% probability level with Duncan’s multiple range test. 53 Table 26. Duncan's t-test over the means in compliances Young’s modulus and Poisson’s ratio for specimens loaded in the T direction and with lateral strain measured in the L direction STT, 5LT ET, Species* (l/psi) (I/psi) (ps1) 9n. (1 x 10'5) (1 x 10'5) COT1 20.1853 -0.356c 49600d 0.0177: YP1 10.6705 -0.329c 938500 0.03096 SM2 10.2805 -0.4255 972506 0.04145 SM1 10.0955 -0.463a 991506 0.0459a R02 9.2106 -O.27lde 1085005 0.0294e HMZ 8.9750 -O.262e 1115005 0.0292e 292 8.6900 -0.2976 1150005 0.03426 R01 7.775d -0.290de 129000a 0.0373c w01 7.7606 -O.265de 1290003 0.03426 *the numbers after the abbreviation of species represent trees. Means in different letters within the same column are significantly different from each other at 95% probability level with Duncan's multiple range test. 54 275 3. 5" z 025' GRAIN DIRECTION 2: 1” JL 11 L__3_L_LL .___.. L— l.25"-J -|.2s'.'.( Figure 1. Compression parallel to grain samples with bonded wire strain gages for measuring strains parallel and perpendicular to the load axis (Sliker, 1985). 55 Figure 2. Gage type A used to measure strain in the L direction; gage type B used to measure strain in the R and T directions. 12-mil diameter constantan lead wires are indicated by the number 1; l-mil diameter constantan wires for measuring strain are indicated by the number 2; straight pins around which strain wire is looped are indicated by the number 3 (Sliker, 1989). 56 “D A LOAD DIRECTION V Figure 3. Specimens for loading in the R direction. In specimen A, the gage measuring strain in the R direction is on the radial surface and the gage measuring strain in the T direction is on the cross-section. In specimen B, the gage measuring strain in the R direction is on the cross-section and the gage measuring strain in the L direction is on the radial surface. 57 1. A LOAD DIRECTION Figure 4. Specimens for loading in the T direction. In specimen A, the gage measuring strain in the T direction is on the tangential surface and the gage measuring strain in the R direction is on the cross-section. In specimen B, the gage measuring strain in the T direction is on the cross-section and the gage measuring strain in the L direction is on the tangential surface. 58 T HM‘fll/‘I‘LHMQ- N "J \ 7m: Figure 5. Gage type used to measure small strain in the L direction when specimens are loaded in the R or T direction. 12-mil diameter constantan lead wires are indicated by the number 1: l-mil diameter constantan wires for measuring strain are indicated by the number 2 (Sliker, 1989). 59 Figure 6. Test specimen A in the compression cage. 8 is end block. C is end bearing block. D is centering guide. E is hole for metal dowel connection to universal joint. 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O O l I O I r©.Oll (o-Ol x l) “S 75 .maH unmfimuum vfiaom ms» nu csonm ma mmfluwucmav 039 mfiwm may :mw3umn QHQmQOfiumHmu may mcwmmmumxm Ammma can mmeV umxflflm scum cm>fiumc :ofiumsvo use .aunum was» scum dam was mam cmmsumn mflsmcoflumamu may unasosm mucwom vmuuon .mm mhsmwm Al: x 3 am 2 2 o._ mpo fio who who who To No Nd _ _ _ l (0 (.-0L x L) “s 1m and + 79 x 91.0 n 5m OF 76 .mcwa unvamuum uflaom an» an c3onm aw mowuflucnsv osu mama map cmmaumn Qanmcoaumamu an» unammmumxo .mmma can mmmav umxfiam aouu om>wumc cofiumavo mna .muaum «any song Adm can 89m cmmsumn QflanOflumaou may unwzonm mucfiom vouuoam o7? x 5 jm N; F; 0; who who who who who Jo nbo N. .nm madman noozcoxoolwloo am 3.? + L: x $4: n pm 77 .maH unmflmuum vwaom mnu mm caonm mw mmfluwucmzv 03» mamm may :mmzumn mwnmco«umamu 0:» mewmmmhmxm Ammmav mefiam Bonn cm>wumc acaumavm oak .aoaum man» aoum 99m can mum :mm3umn mfinmcofiumHmu ms» mcwsonw mucwom cmuuon .vm mnzvflm AL: x 5 pm ommNmNVNNNONm—va—Npowm m ¢ N O _ rxxL _ _ _ L, _ _ _ _ pm ado + L: x 3N n 5m LIST OF REFERENCES LIST OF REFERENCES Bodig, J. and J.R. Goodman. 1969. A new apparatus for compression testing of wood. Wood Fiber 1(2): 146-153. Bodig, J., and J.R. Goodman. 1973. Prediction of elastic parameters for wood. Wood Science, 5(4): 249-264. Bodig, J., and B.A. Jayne. 1982. Mechanics of Wood and Wood Composites. Van Nostrand Reinhold Company. 712p. Core, H.A., W.A. Cote, and A.C. Day. 1979. Wood Structure and Identification. Second Edition. Syracuse University Press. 182p. Guitard, D., and F.EL Amri. 1987. Modeles previsionnels de comportement elastique tridimensionnel pour les bois feuillus et les bois resineux. Ann. Sci. For., 44(3): 335-358. Panishin, A.J., and C.De Zeeuw. 1970. Textbook of Wood Technology. Third Edition. Volume 1. Structure, Identification, Uses, and Properties of the Commercial Woods of the United States and Canada. McGraw-Hill Book Company. 705p. Perry, C.C. 1985. Strain-gage reinforcement effects on low-modulus materials. Experimental Techniques, May: 25-27. Sliker, A. 1959. Electrical resistance strain gages-their zero shift when bonded to wood. Forest Products Journal, 9(1): 33-38. Sliker, A. 1971. Resistance strain gages and adhesives for wood. Forest Products Journal, 21(12): 40-43. Sliker, A. 1985. Orthotropic strains in compression parallel to grain test. Forest Prod. J. 35(11/12): 19-26. Sliker, A. 1988. A method for predicting non-shear compliances in the RT plane of wood. Wood and Fiber Science, 20(1): 44-55. 78 79 Sliker, A. 1989. Measurement of the smaller Poisson’s ratios and related compliances for wood. Wood and Fiber Science, 21(3): 252-262. Sliker, A., J. Vincent, W.J. Zhang, and Y. Yu. In press. Compliance equations for wood at three moisture content conditions. Steel, G.D. Robert and James H. Torrie. 1980. Principles and procedures of statistics. Second edition. McGraw-hill Book Company. 633p. O‘ "‘Illnjmmmm)“