Properties of Southern Pine in Relation to Strength Grading of Dimension Lumber

Transcription

1 U. S. FOREST SERVICE RESEARCH PAPER FPL-64 JULY U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WISCONSIN Properties of Southern Pine in Relation to Strength Grading of Dimension Lumber

2 The FOREST SERVICE of the U. DEPARTMENTOFAGRICULTURE is dedicated to the principle of multiple use management of the Nation s forest resources for sustained yields of wood, water, forage, wildlife, and recreation. Through forestry research, cooperation with the States and private forest owners, and management of the National Forests and National Grasslands, it strives - as directed by Congress - to provide increasingly greater service to a Nation.

3 SUMMARY The Research Paper presents the results of an extensive research program designed to establish the strength and related properties of southern pine 2-inch dimension lumber in relation to structural grading. Representative samples of full-sized, kiln-dried lumber were obtained in statistically significant quantities from 10 states and tested as follows: 1,349 in static bending and 495 in compression parallel to the grain on 4 to 10-inch wide pieces, and 1,414 tests of small clear specimens. With respect to dimensions, the average thickness of all grades and sizes equaled or exceeded the standard dressed size of 1-5/8 inches, and the widths, at 15 percent moisture, averaged the respective full standard dressed sizes. The specific gravity, modulus of rupture, and shear parallel to the grain were found to be equal to previously reported values for shortleaf and loblolly pine, while maximum crushing strength parallel to the grain and modulus of elasticity were about 6 percent lower and compression perpendicular to the grain was 16 percent lower. In flexure, only 5.1 percent of the total lumber sample was below the presently assigned bending stress levels, which is very close to the 5 percent exclusion limit associated with structural grading. In compression parallel to the grain there were no pieces below the presently assigned stress values. Based on presently assigned fiber stresses, the efficiency of the present visual structurallumber grading system as compared to the full strength capability of the dimension lumber was 48 percent in flexure and 43 percent in compression. The efficiency of structural grading of dimension lumber on the basis of a flatwise stiffness determination and associated fiber stresses determined statistically, as compared to the full strength capability of the lumber, was 50 percent in flexure and 73 percent in compressionparallel to the grain. The modulus of elasticity (true) for flatwise flexure of the dimension lumber was about equal to that for edgewise flexure and was closely comparable to the modulus of elasticity in compression parallel to the grain. The modulus of elasticity decreased with a decrease in the grade of the lumber. The relationship of the modulus of rupture (edgewise) versus modulus of elasticity (flatwise) for all grades and sizes of dimension lumber gave a correlation coefficient of The correlation coefficient of very close to the same magnitude was obtained for the maximum crushing strength versus modulus of elasticity in compression parallel to the grain relationship. The modulus of rigidity correlated poorly with such properties as modulus of rupture, modulus of elasticity, and shear strength parallel to the grain. This study affords an appraisal of the strength characteristics of the present structural grades of southern pine in different sizes in relation to allowable working stresses; provides a means of evaluating the efficiency of visual grading in bending and compression; and includes pertinent data relating to an appraisal of the possibilities and limitations of grading based on a stiffness evaluation. i

4 CONTENTS INTRODUCTION PURPOSE SCOPE SELECTION OF MATERIAL TEST METHODS Strength Ratio Determination Flexure Torsion Compression Parallel to the Grain Small Clear Specimens PRESENTATION AND ADJUSTMENT OF DATA Flexural Data Adjustment Compression Parallel-to-the-Grain Data Adjustment DISCUSSION OF RESULTS Significance of Differences in Properties of Lumber from 10 States Dimensions of Lumber Visual Grading Grading Potential by Stiffness Evaluation Comparison with Previous Data Modulus of Rupture vs. Flatwise Modulus of Elasticity Flexural Stress at Proportional Limit vs. Flatwise Modulus of Elasticity Modulus of Rigidity vs. Flatwise Modulus of Elasticity Modulus of Rupture vs. Specific Gravity Modulus of Elasticity vs. Specific Gravity Specific Gravity of Dimension Lumber vs. Specific Gravity of Small Clear Specimens. 13 Modulus of Rupture vs. Flatwise Modulus of Elasticity and Specific Gravity Edgewise Modulus of Elasticity vs. Flatwise Modulus of Elasticity Modulus of Rupture vs. Modulus of Rigidity Modulus of Elasticity in Bending vs. Modulus of Elasticity in Compression Parallel to the Grain Maximum Crushing Strength Parallel to the Grain vs. Modulus of Elasticity in Compression Compressive Strength and Related Properties of the Small Clear Specimens Crushing Strength Perpendicular to the Grain Shear Parallel to the Grain Strength Ratio Depth Effect SUMMARY AND CONCLUSIONS APPENDIX Notation., Formulas Used in Computing and Adjusting Data Page ii

5 Properties of Southern Pine in Relation to Strength Grading of Dimension Lumber 1 by D. V. DOYLE, Engineer and L. J. MARKWARDT, Consulting Engineer U. S. DEPAPTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY 2 MADISON, WIS. INTRODUCTION The structural grading of lumber has long been recognized as an essential marketing practice, both from the standpoint of promoting safety in design and improving efficiency of utilization. Among the first structural timber grades were those proposed by the Forest Products Laboratory in 1912, following extensive mechanical tests of timber of various species in different structural sizes. This was followed by additional research at the Laboratory and elsewhere on structural timbers and factors affecting strength. Progressive development has led to the present standards of the American Society for Testing and Materials (ASTM) relating to the principles of visual grading employing the grade-strength ratio system, and the related establishment of working stresses, largely from extensive test data on small clear specimens. A corollary of structural grading is the establishment of safe working stresses to be used in timber design for different grades. One method of deriving such stresses is from the interpretation of data from extensive tests of timber in structural sizes on a species-by-species basis. The species-by-species method is quite valid, but with the availability of large numbers of commercial woods on the market, this approach is not the most economical or practical. The search for a more practical procedure led to the adoption of the present grade-strength ratio system and the related establishment of working stresses, largely from extensive data on tests of small clear specimens. Visual grading under this system has given a long record of satisfactory performance in providing structural lumber for a wide range of design applications and uses. At the same time, it is recognized that visual grading leaves much 1This research was sponsored by and conducted in cooperation with the Southern Pine Inspection Bureau. 2Maintained at Madison, Wis., in cooperation with the University of Wisconsin.

6 to be desired in efficiency, that is, from the standpoint of utilizing the full potential strength of each piece. This results both from the limitations of the techniques of visual grading and the variability in strength of different pieces of lumber, apparently having similar quality and characteristics. The establishment of a minimum quality of material, to which a fixed level of stress is applied to afford safety in design, imposes further limitations on the use of each piece with respect to its full structural capability. Visual grading thus provides lumber generally high in strength capability, as reflected in its long history of generally satisfactory performance. How to grade structural lumber more efficiently than by visual grading has been a continuing challenge to the lumber industry. There has been repeated optimism that this could be accomplished by a nondestructive method of evaluation. The list of possibilities has included X-rays, nuclear radiation, gamma-ray evaluation, sonic and ultrasonic wave transmission, vibration, and simple mechanical or physical tests. Nondestructive testing has been the subject of active research in recent years. Basic requirements are that any such test method must be effective, rapid, safe, simple, and inexpensive. One of the most rapid, simple, and practical nondestructive tests proposed for structural lumber is that for determining stiffness. The interest of industry in the potential of nondestructive test methods has led to the development of commercial machines for the determination of stiffness and extensive research has been directed toward its implementation. The broadest application contemplates the use of the stiffness criterion for the establishment of design values or working stresses through correlation relationships: however, the need for research on the precision of these correlations has been apparent and extensive studies of wood properties related to this problem have been under way in the United States, Canada, and elsewhere. In 1964, the Southern Pine Inspection Bureau (SPIB) inaugurated a research program at the U.S. Forest Products Laboratory to determine the flexural and compressive properties of several structural grades of southernpine dimension lumber for load-sharing framing systems. In the meantime, the increasing interest in the possibilities of machine structural grading based on stiffness evaluation resulted in the broadening of the research program to study this problem as well. AS a result, the study on southern pine covered in this Research Paper represents one of the most comprehensive compilations of data as yet undertaken as a basis for evaluating the potential of machine structural grading. While particularly applicable to southern pine, the results also have a bearing on the problems and factors related to other species. PURPOSE This Paper presents the results of anextensive research program designed to determine the strength and related properties of southern pine in relation to the structural grading of dimension lumber. The data include results of bending and compression tests on full-sized pieces of different dimensions and grades and the results of various' tests of small clear specimens cut from the dimension lumber. Comprehensive statistical data were obtained to enhance the analysis and interpretation of the results. The study thus affords an appraisal of the strength characteristics of the present structural grades of southern pine in different sizes in relation to allowable working stresses; provides a means of evaluating the efficiency of visual grading in bending and compression; and includes pertinent data relating to an appraisal of the possibilities andlimitations of machine grading based on a stiffness evaluation. SCOPE The study of southern pine dimension lumber was planned to provide selection of representative samples in a statistically significant quantity from 10 states in the southern pine region. Six structural grades of material and four different sizes were represented. Grades were NO. 1, No. 1 Dense, No. 2, No. 2 Dense, No. 3 Medium Grain, and Special and sizes 2 by 4, 2 by 6, 2 by 8, and 2 by 10 inches. In all, 1,349 static bending and 495 compression parallel-to-thegrain tests were made on full-sized pieces, together with 1,414 tests of small clear specimens. The tests of small clear material included static bending, compression parallel to grain, compression perpendicular to grain, and shear parallel to grain. FPL 64 2

7 SELECTION OF MATERIAL Material used in this investigation consisted of dimension lumber obtained in most instances from one mill in each of the 10 major southern pine lumber-producing states. The general geographic locations from which the lumber samples were obtained are shown on the map in figure 1. The mills were selected on the basis of a review of their lumber production, which showed that the lumber was representative of the quality and species of lumber produced and marketed in the general geographic location of the mill. Selection of mills was made by the Southern Pine Inspection Bureau in collaboration with the Southern and Southeastern Forest Experiment Stations of the Forest Service. Selection of lumber samples at each mill was supervised by representatives of the U.S. Forest Service and the Southern Pine Inspection Bureau. The grading of the lumber was in accordance with the 1963 Standard Grading which were approved as conforming to the requirements of the American Lumber Standards. The lumber was taken without differentiating between the various southern pine species. It was selected to conform to the kiln-dried grade requirement of not exceeding 15 percent moisture content, All references made to grades in this Paper refer to kiln-dried lumber. The material was sampled to provide specimens for determining flexural and compressive parallel-to-the-grain properties of full-size lum 3 Southern Pine Inspection Bureau standard grading rules for southern pine lumber. 3

8 ber pieces in four sizes and six grades (table 1). In general, 10 pieces of a kind were selected for each grade and size in each of the 10 states for the flexure tests, except that the Special grade was not available for sampling at two locations. In each state, 10 pieces were selected in grades No. 1, No. 2, and No. 3 in the 2 by 4 size and five pieces in the 2 by 6 and 2 by 8 sizes for the compression parallel-to-the-grain tests. The test pieces in each grade and size were randomly chosen from the lumber stock at each mill. At all mills, grades No. 1 and No. 1 Dense were bundled together, as were grades No, 2 and No. 2 Dense, and grades No, 3 MG and Special. One or two bundles of lumber containing a total of 50 to 200 pieces, all of one general grade in one size and length, were selected for sampling. In general, a few extra pieces were chosen randomly from each. group than were required for the study sample. The samples in the compression parallel-tothe-grain series, consisting of 10 pieces (five each in the 2 by 6 and 2 by 8 sizes), were taken in numerical order from each of the randomly chosen groups of pieces. Grades No. 1 and No. 2 included the dense pieces that became available in the selection of each sample. Grade No. 3 included only medium-grain pieces. Moisture content and the grade of each piece were determined by the SPIB lumber inspector and recorded on each piece, All pieces that did not meet the grade required for the sample, or showed a moisture content greater than 15 percent, were eliminated from the group. The next numbered piece meeting required grade and moisture content was chosen in its place. Each piece selected in the test sample was coded on one end, without reference to any particular grain orientation or growth characteristic, to show the geographic location, grade, type of test, and specimen number. Pieces remaining from the initial sampling were then sorted to provide the Dense classification in grades No, 1 and No. 2 and the Special classification in grade No. 3. In most instances, only about 20 to 40 pieces became available in the sample of the Special grade. The pieces required for each sample in these grades were randomly selected by the same method used in the initial sampling. In a few instances, the required lumber was obtained by cutting the samples from longer length pieces. A few 8-foot 2 by 4 s were cut from 16-foot pieces, but only one end from each piece was included in the sample. Such pieces were graded after cutting. At some mills, the lumber in the sample had received a surface treatment of a commercial water-repellent solution. The lumber pieces selected were placed in small bundles, wrapped with a moisture-resistant covering, and shipped by motor freight to the U.S. Forest Products Laboratory. Upon receipt the bundles were opened and the lumber placed on stickers. For several weeks prior to test, the 2 by 4 s and 2 by 6 s were stored at 72 F. and 65 percent relative humidity. The 2 by 8 s and 2 by 10 s were stored in a lumber kiln with controls set to give the wood a moisture content of about 12 percent. TEST METHODS The edgewise static bending test method for full-size pieces followed ASTM Standard D 198, with modifications as to loading and provision for buckling restraint. The flatwise bending and the compression parallel-to-the-grain test methods were for the most part specially developed, as no standard procedures were available. Tests on small clear specimens cut from the full-size pieces followed established ASTM Standard D 143. Formulas used for reducing the test data and notations regarding the various symbols are given in Appendix I. In all tests, the specimens were randomly placed in the testing machine without regard to systematic placement with respect to knots, grain deviation, warp, or other characteristics. A photographic record was made of one wide face of each specimen after test. The moisture content of the material was determined by the ovendrying method on 1-inchlong sections cut from the test specimens. The specific gravity was based on ovendry weight and the volume of the entire piece as determined by measurements at the time of test. Strength Ratio Determination Prior to test, the grade-strength ratio was determined visually for the first five flexure and compression parallel-to-the-grain specimens FPL 64 4

9 in each group of 2 by 4 s and 2 by 8 s in grades each pair of weights came to rest on the speci- No. 1, No. 2, and No. 3. The were men. This technique provided data for establish- made in accordance with ASTM D 245, Methods ing load-deflection curves. for Establishing Structural Grades of Lumber. In edgewise the 2 by 4 s and a portion of the 2 by 6 s were loaded as shown in figure 3, Flexure and the 2 by 8 s, 2 by 10 S, and the remainder of the 2 by 6 s (the stiffer pieces as determined Flexure tests were made on 580 pieces of 2 by the flatwise bending tests) were loaded as shown 4--8 feet long, 100 pieces of feet in figure 4. The lateral buckling of the wider long, 580 pieces of 2 by feet long, and specimens was restrained by six sets of vertical 100 pieces of feet long. All speci- guides (fig. 4), which consisted of a flat steel mens were first nondestructively loaded in flat- bar against one face of the specimen and a series wise bending and in torsion for determination of of rollers against the opposite face, Midspan their elastic properties, and then loaded to deflection was measured relative to the points of destruction in edgewise bending. both flatwise support by a taut wire and scale. Deflection, and edgewise bending, the pieces were loaded at readings, beginning with a small initial load on the quarter points of a span equal to the nominal the specimen, were recorded at uniform intervals length of the pieces less 12 inches. of load until maximum load was reached. Loading Stiffness in flatwise bending was determined head rates of travel for the various size speciby dead weight loading at two load points on the mens were as follows: 0.75 inch per minute for specimen as shown in figure 2. Weights of 7-1/2 the 2 by 4 s and 2 by 6 s; 0.69 inch per minute pounds were lowered simultaneously by the test for the 2 by 8 s; and per minute for machine at the two load points until a total load the 2 by 10 s. These rates of loading corresponded of 120 pounds had been placed on the test piece. to a mean rate of extreme fiber strain of approx- The midspan deflection was measured relative to imately inch per per minute for the the points of support by a taut wire and scale as various grades and sizes of specimens. Figure 2.--Method used for determining the modulus of elasticity in the flatwise direction of full-sire dimension lumber. M

10 M Figure 3.--Method used for determining the flexural properties under edgewise loading of 2 by 4 and a portion of the 2 by 6 dimension lumber specimens. Figure 4.--Method used for determining the flexural properties under edgewise loading of 2 by 8, 2 by and a portion of the 2 by 6 dimension lumber specimens. FPL 64 6 M

11 Torsion The torsion test was conducted on each piece as shown in figure 5. The specimen was gripped at its ends and a torque applied at one end at the rate of about 0.01 radian per minute. A weighing at the opposite end measured the torque. The distortion or twist resulting in the specimen was determined over a central gage length equal to the nominal length of the piece less 24 inches. The angular movement was measured at increasing intervals of load up to 800 inch-pounds of toque by reading the movement of a projected reference line, from an illuminated lantern located at one gage point, on a circular scale attached to the piece at the opposite gage point. Parallel to the Grain Compression parallel to the grain tests were made on 300 pieces of 2 by 4 each 8 feet long, 50 pieces of 2 by 6 each 12 long. and 147 pieces of 2 by 8 each 14 feet long. The general arrangement of equipment used in conducting this series of tests is shown in figure 6. Specimens were restrained from flatwise buckling 3/4-inch-diameter steel sliding furniture casters mounted at about 4-inch intervals on two plywood members 8 inches in width by 1-1/2 inches in thickness. The members with the specimen confined between them were restrained from bending by the base I-beam and a 12-inch I-beam. The 12-inch I-beam could be-raised at one end to provide access to the specimen. The pieces were also restrained from edgewise buckling by wood blocks with rounded ends set against opposite edges of the specimen at about 16-inch intervals. A steel plate, 2 by 4 inches by 1/16 inch thick, was placed between each wood block and the specimen. These blocks and plates were held against the specimen with a pair of wood wedges, The specimens were compressed longitudinally between the ram of a 60-ton-capacity hydraulic jack and a steel bearing block. both attached to the base I-beam at opposite ends of the specimen The hydraulic ram traveled a controlled rate which provided a fiber strain of about inch per inch per minute. Average deformation resulting in the specimen was measured by two dial gages over a gage length equal to the nominal length of the specimen minus 6 inches. The gages were attached on opposite edges of the specimen between arms that were pivoted at the midpoints of the upper face of the specimen. Deformation measured by the two dials was averaged and taken as the deformation resulting in the specimen to provide a load-compression curve. M Figure 5.--Method used for determining the modulus of rigidity of fuli-size dimension lumber. 7

12 M Figure 6.--Method used for determining the compression parailel to the grain properties of full-size dimension lumber. The specimen has lateral support in the flatwise as well as the edgewise direction to resist buckling. Small Clear Specimens After the edgewise bending were completed, an undamaged section containing clear wood was cut from the first three 2 by 4 s and 2 by 8 s in grades No. 1 and No. 3 and the first six 2 by 4 s, 2 by 6 s, and 2 by 8 s in grade No. 2 of each group of 10 pieces from each state. From each of the pieces were cut the following small clear specimens: a 1 by 1 by 16 inch static bending, a I by 1 by 4 inch compression parallel to the grain, a compression perpendicular to the grain, and two shear parallel to the grain The compression perpendicular-to-the-grain specimens were 2 inches wide, 6 inches long, of actual lumber thickness. The shear parallel-tothe-grain specimens were 2 inches wide, of actual lumber thickness, 2-1/2 inches long. The static bending and the compression parallelto-the-grain specimens were end matched to one another, as were the compression perpendicularto-the-grain and the shear parallel-to-the-grain specimens. The specimens were stored in a controlled atmosphere of 75 F. and percent relative humidity until representative pieces had attained a relatively constant weight. The specimens were tested in accordance with ASTM Standard D 143. PRESENTATION AND ADJUSTMENT OF DATA The data presented in tables 1-12 and figures 7-38 of this Paper are based on the results of testing full-size dimension lumber specimens (1,349 in flexure and 495 in compression parallel to the grain) and small clear specimens (1,414) from the full-size pieces. All data are based on the actual dimensions of the specimens. The notation and formulas used in computing and adjusting the data are given in Appendix I. FPL 64 8

13 Flexural Data Adjustment The results of the flexure tests on thefull-size dimension lumber specimens are summarized in table 2 and those of the small clear specimens which were cut from the full-size specimens are summarized in table 3. In table 2, the edgewise stress at the proportional limit and modulus of rupture values, which were obtained for the different widths of dimension lumber, were adjusted to a 2-inch depth of beam in accordance with the formula given in Appendix I. 4 No adjustment was made for depth in the modulus of rupture of the small clear flexure specimens. The modulus of elasticity values both in flatwise and edgewise flexure were adjusted for shear deformation to the true elastic modulus. The adjustments were made on the basis of the modulus of rigidity values which were derived from the torsion tests that were conducted on each piece. In flatwise flexure the adjustment was small (about 1/2 percent) because of the large spandepth ratio employed in the tests. The modulus of elasticity values for the small clear specimens (table 3) were adjusted to a true elastic modulus with the commonly used modulus of elasticity to modulus of rigidity (E/G) ratio of 16. In all relationships expressed in this Paper with modulus of elasticity, the true elastic modulus is used. Table 4 and figures 7 and 8 show a comparison of the modulus of rupture values obtained in test and the assigned design stresses for the various lumber grades. The design stress values were adjusted upward for comparison by applying the inverse of the reduction factors of 9/16 (longtime loading) times 10/13 (other factors including factor of safety) times 11/10 (normal loading) = 1/2.1 to the assigned stress ratings for single members which are given in paragraph 201 of the 1963 Standard Grading Rules for Pine 3 (table These adjustment values are at the same level as those recommended by ASTM D 2018 for normal loading except that the factor for beam depth was not included inasmuch as it was already reflected in the test results obtained on different widths of dimension lumber. Table 4 also presents a comparison of the average modulus of elasticity for the tests and the assigned modulus of elasticity unadjusted for grade. Compression Parallel-to-the-Grain Data Adjustment The results of the compression parallel to the grain tests of the dimension lumber specimens are summarized in table 5 and those of the small clear specimens are summarized in table 6. The small clear specimens were cut from the fullsize flexure specimens and are therefore not matched with the full-size compression parallel to the grain specimens. Table 7 presents a comparison of the maximum crushing strength parallel to the grain and the assigned design stresses for the different grades of dimension lumber. The design stresses were adjusted for comparison with the test results by applying the inverse of the reduction factors of 3/5 (long-time loading) times 4/5 (other factors including factor of safety) times 11/10 (normal loading) = 1/1.9 to the assigned stress ratings for single members given in the grading rules 3 (see table 1). DISCUSSION OF RESULTS Significance of Differences of Properties of Lumber from 10 States The southern pine lumber used in this investigation was obtained from 10 states (fig. 1) and represented a wide range of growth conditions. To determine how the properties of the lumber differed between states, an analysis of variance was made of the modulus of rupture and the flatwise modulus of elasticity for the different grades of lumber. The results listed in table 8 show that the level of significance among states for the modulus of rupture was not significant in three grades and was significant at 1 percent level for the remaining three grades, The level of significance of the modulus of elasticity among states was not significant in one grade, but was significant at the 1 percent level in three grades and at the 5 percent level in two grades. 4 Freas, A. D., and Selbo, M. L. Fabrication and design of glued laminated wood structural members. U.S. Dep. Agr. Tech. Bull

14 Dimensions of Lumber A study was made to determine the amount of variation in the actual measured dimensions (width and thickness) of the lumber used in the flexure tests of this study and to compare the actual dimensions with the standard dressed dimensions. The sample consisted of a total of 1,360 pieces obtained from one or two mills in each of 10 states (fig. 1). The dimensions of the individual pieces were determined prior to test after the lumber had been stored in a controlled atmosphere for some time. The moisture content determinations made after test showed the wood to be at an average moisture content of about 12.2 percent. The lumber had been kiln dried before surfacing and, in general, had a moisture content of 12 to 15 percent at the time of sampling. Only pieces with a moisture content of 15 percent or less were accepted for the lumber sample. The average width, thickness, values of flatwise and edgewise moment of inertia (based on actual dimensions of the lumber), and standard deviations are listed in table 9 for the various lumber grades and sizes. These data show that the average thickness of the lumber in all grades and sizes at about 12 percent moisture content was equal to or greater (by as much as in.) than the standard dressed thickness of 1-5/8, inches for 2-inch dimension lumber. The averages of the widths for the different sizes of lumber were generally very uniform among the various grades. The widths of the 2 by 4 and 2 by 6 sizes were very close to the standard dressed width. For the 2 by 8 and 2 by 10 sizes, the average widths were from 0.03 to 0.04 inch less than the standard dressed width; however, if conditioned to 15 percent moisture content, the width of all the material would average full standard dressed size. The average moment of inertia of the lumber in the flatwise direction was greater in all grades and sizes than the moment of inertia computed on the basis of standard dressed-size lumber, except for grades No. 1 and No. 1 Dense in the 2 by 8 size. The maximum difference for these grades, however, was very small (0.26 percent). The average moment of inertia of the lumber in the edgewise direction was greater in all grades of the 2 by 4 and 2 by 6 sizes but slightly smaller in all grades of the 2 by 8 and 2 by 10 sizes than that computed for standard dressedsize lumber. The maximum differences were 1.23 and 0.65 percent for the 2 by 8 and 2 by 10 sizes, respectively. Table 9 also presents the effect of variation in the dimension of the lumber on stiffness based on the formulas where S.E. (E) = standard error of the modulus of elasticity, S.E. = standard error of the reciprocal of the moment of inertia, and S = product of the average modulus of elasticity determined by flexure test and the moment of inertia based on standard dressed size lumber. These data show that within the 90 percent confidence limit the modulus of elasticity computed on the basis of the actual measured dimensions can vary about 92,000 p.s.i. (pounds per square inch) in the flatwise direction and about p.s.i. in the edgewise direction from the modulus of elasticity based on standard dressed dimensions. Visual Grading An evaluation of the stress ratings assigned in the current standard grading rules- 3 for the several visual grades of southern pine is given in tables 4 and 7 and in figures 7 and 8. Figures 7 and 8 present the modulus of rupture values obtained for the various grades of lumber in the 2 by 4 and 2 by 8 sizes, respectively, in relation to the presently assigned stresses. These data show the relatively large range in modulus of rupture values within each visual' structural grade of each size and clearly illustrate the substantial quantity of material that is not used to its full-strength capacity. A similar substantial range in modulus of elasticity values for a given grade will be noted from the frequency distribution data presented in tables 10 and 11. The data also provided a basis for estimating the efficiency of the visual grades. On the basis of the test data, the strength capability of the visually graded material was evaluated both for bending and compressive stress. The actual total bending-stress value, representing the full- ' FPL 64 10

15 strength capability of all pieces in the 2 by 4 and 2 by 8 sizes and in the combination of all sizes and grades, was determined by applying the 1 reduction factor of to the mean modulus of 2.1 rupture for each grade and size and multiplying by the total number of pieces in each classification. The total design stress obtainable from the same material, on the basis of the current grading rules, was determined by adding the product of the recommended fiber stress in bending for each visual grade and the number of pieces in each grade. The ratio of the total bending stress actually used at present stress levels to the total stress capacity of the material is 45 percent for the 2 by 4 s, 49 percent for the 2 by 8 s, and 48 percent for all sizes combined. In other words, for this sample, visual grading utilizes only about 48 percent of the potential bending strength of the material at the present stress levels. Similarly, the actual total compressive stress value, representing the full-strength capability of all pieces tested in compression parallel to the grain, was determined by applying the reduc 1 tion factor of to the mean maximum com 1.9 pressive strength for each grade and size and multiplying by the total number of pieces in each classification. The total design stress obtainable from the same material may be calculated by multiplying the recommended allow able compressive stress parallel to the grain for each visual grade by the number of pieces for each grade. The ratio of the total design stress actually used, on the basis of present values, to the total compressive strength capability of the material is 43 percent for the 2 by 4 s, the 2 by 8 s, and for all grades and sizes combined. This, together with the fact that no pieces were below the adjusted assigned stress level, suggests that the present compressive stresses are conservative for the quality of material represented by the sample. As indicated, these evaluations of the efficiency of the visual grades were on the basis of presently assigned stress values. For comparison, a theoretical analysis can be made on the basis of stresses derived from statistical data applicable to the population represented in this particular test sample. The theoretical stress value for each grade and size is obtained by multiplying the 5 percent-exclusion value (mean minus 1.64 times the standard deviation) by the reduction factor of for the bending stress and by for the 1.9 compressive stress. This analysis results in a calculated theoretical efficiency for the visual grades of 48 percent in bending and 70 percent in compression parallel to the grain for the test material. This indicates that present stresses are more conservative in compression than in bending. An evaluation of the effectiveness of visual grading for flexure shows that 3 percent of the pieces in the 2 by 4 size and 6.1 percent of the pieces in the 2 by 8 size fell below grade (table 4). In summary, the data show that 5.1 percent of the total lumber sample was below the assigned bending-stress levels, which is very close to the 5 percent exclusion limit associated with structural grading. A comparison of the modulus of elasticity obtained in this investigation and the modulus of elasticity listed for the various lumber grades 3 in the grading rules-is also given in table 4. Grading Potential by Stiffness Evaluation The detailed statistical data obtained from the study provide a means of determining the possibilities and limitations of establishing stress grades based on a flatwise stiffness evaluation. A theoretical analysis of the efficiency of grading based on stiffness was made by using stresses associated with the lower 90 percent confidence 1 1 limit multiplied by for bending, and for compression. The lower 90 percent confidence limit is established from the regression equation for the population by reducing it by an amount equal to the standard error of the estimate multiplied by 1.64, as illustrated in figure 9. The strength potential of the population on the basis of stiffness is then obtained by multiplying the stress associated with each stiffness group by the number of pieces in the group (tables 10 and 11). The full strength capability of the material was determined in the same manner as described for visual grading. This theoretical estimate of the evaluation of strength potential on the basis of stiffness shows an efficiency of 50 percent for bending and 73 percent for compression parallel to grain. 11

16 Comparison with Previous Data A comparison of results obtained in this investigation with those previously published 5 is given in tables 3, 6, and The data for the small clear specimens in this study show that specific gravity, modulus of rupture, and shear parallel to the grain are very close to the previously published data for loblolly and shortleaf pine, while modulus of elasticity, compression parallel to the grain, and compression perpendicular to the grain are somewhat lower. Modulus of Rupture vs. Flatwise Modulus of Elasticity The relationship between the modulus of rupture and the flatwise modulus of elasticity is presented in figures 9 to 12 for the dimension lumber specimens of all grades of 2 by 4, 2 by 6, 2 by 8, and 2 by 10 sizes, respectively. The coefficient of correlation- 6 based on a linear regression was for 2 by 4 s, for 2 by 6 s, for 2 by 8 s, and for 2 by The relationship between the modulus of rupture and the flatwise modulus of elasticity for all grades and sizes is shown in figure 13. The modulus of rupture values obtained for the lumber of different sizes were placed on a comparable basis by adjusting them to the values associated with a beam that is 2 inches in depth (Appendix I). The coefficient of correlation between modulus of rupture and modulus of elasticity was for all grades and sizes of lumber. The relationship between the modulus of rupture and the modulus of elasticity for the small clear specimens as well as for the matching dimension lumber specimens from which the small clears were cut (grades No. 1, No. 2, and No. 3) is shown in figure 14. The modulus of rupture of the dimension lumber specimens was adjusted to a 2-inch depth of beam but no adjustment was made for the small clear specimens. These data show that the slope of the regression line differs somewhat for the two types of specimens. As would be expected, the coefficient of correlation 6 between modulus of rupture and modulus of elasticity for the small clear specimens was higher (0.771) than that for the corresponding dimension lumber (0.660). Flexural Stress at Proportional Limit vs. Flatwise Modulus of Elasticity An appraisal of the relationship between the flexural stress at proportional limit and the flatwise modulus of elasticity showed that the coefficient of correlation for the different grades and sizes varied from to 0.814, with an average of for all grades and sizes. For each grade and size, except for the No. 2 Dense in the 2 by 4 size, the coefficient of correlation was higher for the flexural stress at the proportional limit versus modulus of elasticity relationship than for the modulus of rupture versus modulus of elasticity relationship. Figures 15 and 16 show the linear regression lines that were obtained for the modulus of rupture versus the flatwise modulus of elasticity relationships and the flexural stress at the proportional limit versus the modulus of elasticity relationship for the different grades in the 2 by 4 and 2 by 8 sizes, respectively. Modulus of Rigidity vs. Flatwise Modulus of Elasticity A study to determine the relationship of modulus of rigidity versus flatwise modulus of elas 5 U.S. Forest Products Laboratory. Wood Handbook. U.S. Dep. Agr., Agr. Handb In the analysis of the results, the correlation coefficient is one of the important statistical relationships among properties. A correlation coefficient of 1.0 denotes a perfect linear relationship between the properties, in which an increase in one property is associated with a direct increase in another. A correlation coefficient of 0 means there is no relationship between the properties under consideration. In the positive correlation coefficients presented, the nearer the value is to unity, the more perfect is the relationship. In connection with the lnterpretation of data for grading by mechanical means, no minimum values of correlation coefficients for acceptable relationships have been established; however, values under 0.70 leave much to be desired in affording a satisfactory degree of relationship, as a 0.70 correlation Coefficient is associated with a probability that only about one- half of the variation in the dependent variable (modulus of rupture, for example) is explained by the variation in the independent variable (modulus of elasticity). FPL 64 12

17 ticity shows that for the different grades and sizes, the coefficient of correlation varied from to with an average of for all grades and sizes. The data showed that, for the most part, modulus of rigidity did not vary with the grade or size of the dimension lumber (table 2). Modulus of Rupture vs. Specific Gravity The relationship between the modulus of rupture and specific gravity based on ovendry weight and volume at test is given in figure 17 for the small clear specimens and the dimension lumber specimens of grades No. 1, No. 2, and No. 3 from which the small clear specimens were cut. These data show that the correlation coefficient was for the small clear specimens and for the full-size specimens. The regression lines for the two sets of specimens have about the same slope. The correlation coefficients for the different grades and sizes of dimension lumber ranged from to for the modulus of rupture versus specific gravity relationship and was for all grades and sizes combined. These relationships reflect the limitations of specific gravity in evaluating the bending strength of dimension lumber containing strength-reducing characteristics. Modulus of Elasticity vs. Specific Gravity The relationship between the flatwise modulus of elasticity of dimension lumber and specific gravity is given in figure 18 for all grades and sizes of lumber. The correlation coefficient for these data was The relationship between the modulus of. elasticity of the small clear specimens and specific gravity is shown in figure 19. These data do not show as good correlations as those obtained for the dimension lumber specimens. The coefficient of correlation was These relationships are all low for reliable correlations. Specific Gravity of Dimension Lumber vs. Specific Gravity of Small Clear Specimens A comparison of the specific gravity of the small clear specimens and the specific gravity of the dimension lumber specimens from which the small clear specimens were cut is given in figure 20. These data show, in general, a slightly higher specific gravity for the dimension lumber (0.521) than that for the matching small clear specimens (0.513). This difference is less than 2 percent and may result from a combination of factors such as knots, resin deposits, nonuniformity in moisture content, nonuniformity in size, etc. Previous standard tests on small clear specimens at the Forest Products Laboratory have shown an average specific gravity of 0.51, based on ovendry weight and volume at 12 percent moisture content, for loblolly and shortleaf 5 pine.- A graph of the frequency distribution of specific gravity for the dimension lumber and small clear specimens on the basis of 0.01 class is given in figure 21. These data illustrate the relatively wide range in the specific gravity of the southern pines. Modulus of Rupture vs. Flatwise Modulus of Elasticity and Specific Gravity Multiple correlations were made to determine the effect of including specific gravity as well as modulus of elasticity as independent variables in evaluating modulus of rupture for the different sizes and grades of dimension lumber, The correlation coefficients for modulus of rupture versus modulus of elasticity alone for the 2 by 4, 2 by 6, 2 by 8, and 2 by 10 sizes for all grades are 0.678, 0.607, 0.674, and respectively. The correlation coefficients for modulus of rupture versus specific gravity for the above sizes are 0.561, 0.405, 0.543, and The comparable multiple correlation coefficients for modulus of rupture versus modulus of elasticity and specific gravity for the 2 by 4, 2 by 6, 2 by 8, and 2 by 10 sizes are 0.700, 0.620, 0.693, and respectively. These data show but a very small improvement in the correlation coefficient by considering specific gravity in addition to modulus of elasticity in estimating modulus of rupture. This reflects the limited influence of specific gravity on the bending strength of dimension lumber in the common commercial grades. It does not indicate any encouragement for the 13

18 application of this combination of variables in further analysis of the data. Edgewise Modulus of Elasticity vs. Flatwise Modulus of Elasticity The relationship of the modulus of elasticity (true) of dimension lumber for six grades loaded flatwise and the modulus of elasticity for the same pieces loaded edgewise is given in figures 22 and 23 for 2 by 4 and 2 by 8 sizes. These data show that except for a few scattered points, the flatwise and edgewise modulus of elasticity are closely related with a coefficient of correlation of for all grades in the 2 by 4 size and for all grades in the 2 by 8 size. For the 2 by 4 size, the average modulus of elasticity flatwise (1,605,000 p.s.i.) was slightly higher than that of the modulus of elasticity edgewise (1,598,000 p.s.i.), while for the 2 by 8 size the average modulus of elasticity edgewise (1,675,000 p.s.i.) was slightly higher than that of the modulus of elasticity flatwise (1,644,000 p.s.i.). The relationships of the modulus of elasticity flatwise and edgewise in all the individual grades and sizes gave a coefficient of correlation of 0.9 or better, except that the 2 by 8 size in the No. 3 grade and the 2 by 10 size in the No. 2 grade gave coefficients of and A review of the notes made at time of test and of the photographs taken of the dimension lumber pieces after test indicates that variations between the edgewise and flatwise stiffness could not be associated with any particular one of the commonly recognized strength-reducing characteristics. The relationship of the modulus of elasticity of the small clear specimens and the flatwise modulus of elasticity of the dimension lumber pieces of grades No. 1, No. 2, and No. 3 in 2 by 4, 2 by 6, and 2 by 8 sizes from which the small clear specimens were cut is given in figure 24. These data show a rather wide scatter of the points and, as would be expected, the modulus of elasticity values for the small clear specimens were higher, in general, than those of the matching dimension lumber specimens. A frequency distribution of the specimen population, on the basis of 200,000 p.s.i. classes of modulus of elasticity flatwise, is given in figure 25 for all grades in the 2 by 4 and 2 by 8 sizes of dimension lumber. Similar distributions are also shown for the individual grades in the 2 by 4 size in figure 26 and in the 2 by 8 size in figure 27. A tabulation of these data are presented in table 10. These data show that the modulus of elasticity of the material ranged from about 500,000 to 3 million p.s.i. with about 77 percent of the specimens having a modulus of elasticity of between 1 and 2 million p.s.i. Figures 26, 27, and 28 show a general decrease in modulus of elasticity with decrease in the grade of the dimension lumber. Modulus of Rupture vs. Modulus of Rigidity The modulus of rigidity of the dimension lumber averaged about 140,000 p.s.i. and for the most part did not show any consistent relationship with the grade or the size of the lumber (table 2). On the basis of these data it is evident that modulus of rigidity would not provide a very satisfactory basis for predicting the flexural properties of dimension lumber. The coefficient of correlation of the modulus of rupture versus modulus of rigidity for the different grades and sizes varied from to 0.468, with an average of for all grades and sizes. Modulus of Elasticity in Bending vs. Modulus of Elasticity in Compression Parallel to the Grain A comparison of the modulus of elasticity in flexure and in compression is provided in tables 3 and 6 and in figure 28 for three grades and three sizes of dimension lumber and for the small clear specimens cut from the dimension lumber, The comparison is made on the basis of average values, as the full-size dimension lumber compression specimens were not matched with the small clear compression parallel-tothe-grain specimens. All modulus of elasticity values in flexure were adjusted for shear deflection to a true modulus of elasticity. Figure 28 shows that within grades the moduli of elasticity in flatwise and edgewise flexure are about equal and are closely comparable to the modulus of elasticity in compression parallel to the grain of the dimension lumber. The modulus of elasticity of the dimension lumber decreased as the grade of the lumber decreased (tables 2 and 5), with the values for grade No. 2 being more closely comparable with those of grade No. 3 than with FPL 64 14

19 grade No. 1. As would be expected, the small clear specimens gave somewhat higher values of modulus of elasticity than the dimension lumber, particularly in comparison with the lower grades of lumber from which they were cut. Some decrease was noted in the modulus of elasticity of the small clear specimens with grade. This is no doubt associated with the density of the material, as the specific gravity of the small clear specimens decreased with a decrease in the grade of the dimension lumber. The modulus of elasticity in flexure, ingeneral, closely paralleled the modulus of elasticity in compression for the closely matched small clear specimens. The modulus of elasticity in flexure for the small clear specimens was adjusted for shear deflection on the basis of the ratio of 16 for modulus of elasticity to modulus of rigidity, which is an average value commonly used when specific data for a given species are not available. The modulus of rigidity of the southern pine dimension pieces was found in the torsion tests to be somewhat higher than that reported for other species. The average ratio of modulus of elasticity to modulus of rigidity for southern pine is shown to be 13.1 when based on the modulus of elasticity for small clear specimens and 11.6 when based on the modulus of elasticity for the dimension lumber. The use of the smaller E/G ratio would decrease the adjusted value of true modulus of elasticity for the small clear specimens by less than 2 percent compared to the values based on the assumed E/G ratio of 16. Ratios of the average flatwise modulus of elasticity (true) to the modulus of rigidity for different grades and sizes of dimension lumber are listed in table 2. The ratios decrease with grade and range from 8.1 to 13.4, with an average of about 11.6 for all grades and sizes. Maximum Crushing Strength Parallel to the Grain vs. Modulus of Elasticity in Compression The relationship of the maximum crushing strength parallel to the grain and the modulus of elasticity in compression parallel to the grain is given in figure 29 for grades No. 1, No. 2, and No. 3 in the 2 by 4 and the 2 by 8 sizes. The coefficient of correlation for each grade and size ranged from to and was for all grades and sizes combined. A frequency distribution for the modulus of elasticity in compression, based on 200,000 p.s.i. classes, is given in figure 30 and table 11 for the dimension lumber specimens. These. data show about the same range and distribution of modulus of elasticity as are shown in figure 25 for modulus of elasticity in flatwise bending. Compressive Strength and Related Properties of the Small Clear Specimens The strength and related data obtained for the small clear compression parallel-to-the-grain specimens cut from the dimension lumber flexure specimens are listed in table 6 and related graphically in figures 31 and 32. The relationship of the maximum crushing strength and the modulus of elasticity in compression shown in figure 31 has a coefficient of correlationof The coefficient of correlation of the compressive stress at the proportional limit and the modulus of elasticity was The relationship of maximum crushing strength versus specific gravity (fig. 32) and modulus of elasticity versus specific gravity (fig. 33) of the small clear specimens show coefficients of correlation of and 0.377, respectively. Crushing Strength Perpendicular to the Grain The crushing strength in compression perpendicular to the grain for the various grades and sizes of lumber from which the specimens were cut are listed in table 12. These data show that the average stress at the proportional limit for all grades and sizes was about 850 p.s.i. This value is somewhat lower than the average values of 980 p.s.i. for loblolly, 1,000 p.s.i. for shortleaf, and 1,190 p.s.i. for longleaf pine, previously reported. 5 The relationship of the stress at the proportional limit in compression perpendicular to the grain and the modulus of elasticity in flatwise bending of the dimension lumber pieces from which the specimens were cut showed a coefficient of correlation of for all grades and sizes. The relationship of stress at proportional limit and specific gravity of the specimens showed a coefficient of correlation of for all grades and sizes. 15

20 Shear Parallel to the Grain The summary of the shear parallel to the grain properties for the clear specimens cut from the dimension lumber flexure specimens is given in table 12. The average shear parallelto-the-grain value for all grades and sizes was 1,370 p.s.i. This compares favorably with the values of 1,370 p.s.i. for loblolly, 1,310 p.s.i. for shortleaf, and 1,500 p.s.i. for longleaf pine previously reported. 5 For most grades and sizes, the shear across the growth rings (radial shear) was somewhat greater than the shear along the growth rings (tangential shear). The relationships of shear parallel to the grain with other properties showed rather poor correlations. Correlation coefficients for the matching dimension lumber specimen relationships were as follows: with modulus of elasticity in flatwise bending, with specific gravity, and with modulus of rigidity; and for the matching small clear specimen relationships, for the modulus of elasticity. Strength Ratio The flexure tests which were made on the dimension lumber and the small ( 1 by 1 by 16 inch) clear specimens at about 12 percent moisture content provide data for comparing the actual and the visually estimated strength ratio of the different lumber grades. The actual strength ratio was obtained by dividing the modulus of rupture of the dimension lumber specimens by the modulus of rupture of the matching small clear specimens. The visually estimated strength ratio was determined on the same pieces of dimension lumber in accordance with the method developed for green lumber and given in ASTM D 245. Since effects of drying on strength may not be the same in dimension lumber as in small clear specimens and may vary with species, this factor should be kept in mind when comparing the actual with estimated strength ratios. The relationships between the actual and estimated strength ratios and the modulus of rupture of the matching dimension lumber specimens are given in table 3 for grades No. 1, No. 2, and No. 3 in the 2 by 4 and 2 by 8 sizes. A comparison of the estimated and actual strength ratios is also given in figure 34 for the 2 by 4 and 2 by 8 sizes. In calculating these ratios (fig. 34), an adjustment for depth of beam was made in the modulus of rupture values for the dimension lumber. 4 These data show a correlation coefficient of between the estimated and actual strength ratios. Depth Effect The flexure tests of dimension lumber in this study provide data on the effect of beam depth on the bending strength of wooden beams. Figure 35 presents the relationship of the average modulus of rupture, obtained for the various lumber grades, to the standard dressed widths. In line with results of previous studies, these data show a general reduction in modulus of rupture with increasing depth of beam. The average reduction was about 2.03 percent per inch of depth from the 2 by 4 to the 2 by 10 size in the No. 2 grade. The data also reflect the effect of grade. For the other grades, the percent reductions per inch of depth from a 2 by 4 to a 2 by 8 were 0.58 for No. 1, 1.36 for No. 1 Dense, 4.35 for No. 2 Dense, and 6.15 for No. 3. There was little difference for the Special grade. The average reduction in modulus of rupture between the 2 by 4 and 2 by 8 sizes for all grades was 2.4 percent per inch of depth. While these data show a considerable variation in the reduction among the different grades, they add to the general knowledge relating to depth effect. Information on the effect of beam depth on modulus of rupture is referenced in footnotes 4, 5, and 7. A further appraisal of the effect of beam depth on strength is given in figures 36 and 37. Figure 36 shows the relationship of depth to the ratio of the flexural properties of the full-size dimension lumber specimens to the flexural properties of the small clear matching specimens. These data show that the ratios of the stress at the proportional limit as well as the modulus of rupture tend to decrease with an increase in the depth of the lumber beams. Figure 37 shows the relation of the ratio of 7 Bohannan, Effect of size on bending strength of wood members. U.S. Forest Serv. Res. Pap. FPL Forest Prod. Lab., Madison, Wis. FPL 64 16

21 the flexural to the compressive properties of dimension lumber specimens to the depth of the lumber beams. These data also show that the ratios both at the proportional limit and at ultimate tend to decrease with an increase in the depth of the beam. The relationship between maximum crushing strength parallel to the grain and width of the dimension lumber is shown in figure 38. These data show, as would be expected, that in general there was little change in compressive strength with an increase in lumber width. SUMMARY AND CONCLUSIONS The study provides a wealth of data on the strength and related properties of dimension lumber and matched small clear specimens of southern pine from 10 states. Included are pertinent statistical data to aid in the interpretation and application of the results. Data are provided for an appraisal of structual grading and the establishment of working stresses both on the basis of the grade-strength ratio procedure or from the data on the structural size lumber. The report presents pertinent findings based on an analysis of the data and also detailed data appropriate for further analysis and interpretation of property relationships and details of lumber grading. The results are based on 1,349 static bending, 495 compression parallel-to-the-grain dimension lumber pieces, and 1,414 matching small clear specimens. The dimension lumber was randomly selected in 2 by 4, 2 by 6, 2 by 8, and 2 by 10 sizes from mills in 10 states in the southern pine region. Six grades were represented. The material had been dried at the mills to about 15 percent moisture content and was further conditioned to about 12 percent prior to test. An analysis of the variance of modulus of rupture and flatwise modulus of elasticity did not reveal any marked difference in these properties with respect to the state of origin. From the data of table 3 it will be noted that the average specific gravity (0.513) of the small clear specimens, which were selected without regard for species, is identical to that previously 5 reported- for loblolly and shortleaf pine. The modulus of rupture and shear parallel-to-thegrain values are equal to the previously reported 5 values for these species, while maximum crushing strength and modulus of elasticity are about 6 percent lower, and compression perpendicular to the grain 16 percent lower. In the analysis of the visual grades it is shown that in bending, for all grades and sizes, 5.1 percent of the pieces, fell below the level of the presently assigned allowable design stress. This is close to the 5 percent exclusion limit associated with stresses in grading. In two of the grades in the 2 by 4 size, there were no pieces below the allowable design stress. In compression parallel to the grain, no pieces in any of the sizes or grades were below the allowable design stress level for the grade. In general, the visual grades contain a large number of pieces high in strength which as yet cannot be accurately identified so as to be used safely to their full-strength capability. It is recognized that modulus of elasticity, as well as most other strength properties, is affected by the grade of material. The data on modulus of elasticity obtained for different grades of southern pine provide information to assist in establishing reduction factors applicable to other than clear material in timber design. The test data obtained afford a means for evaluating the efficiency of the visual grades with respect to bending and compressive strength. Taking efficiency as the ratio of the total stress actually used, on the basis of presently assigned stresses in the grading rules, to the total stress representing the full-strength capability of all pieces as determined by tests, the visual grades show an average efficiency of 48 percent for bending and 43 percent for compression. This illustrates in another way that the visual grades contain large quantities of material high in strength that are not used to their full capability. A similar estimate was made of the efficiency associated with structural grading on the basis of flatwise stiffness determinations. The stresses used were those derived on a statistical basis from the 90 percent confidence limit associated with the regression equations for modulus of rupture versus flatwise modulus of elasticity and for compressive strength versus flatwise modulus of elasticity. The estimated efficiency obtainable on the basis of this stiffness evaluation, as compared to the full-strength capability of the material indicated by the tests, was 50 per 17

22 cent for bending and 73 percent for compression parallel to the grain, Previous research has shown the presence of a depth factor that results in lower bendingstrength values with increase in depth of the member. The data obtained in the study show an approximate 2 to 2.4 percent reduction in modulus of rupture per inch increase in depth of member over the range of nominal 2 by 4 to 2 by 10 sizes. Exact measurements were made of each piece of dimension lumber at about 12 percent moisture content in connection with the strength study. Each grade and size averaged a full standard 1-5/8 inches in thickness. In width, the nominal 2 by 4 s averaged a full 3-5/8 inches, and the 2 by 6 s averaged a full 5-5/8 inches. The 2 by 8 s and the 2 by 10 s in some of the grades were 0.04 inch scant. On a basis of 15 percent moisture content, all of the material would meet the minimum size standard. Considering the 10 different states of origin, the material was remarkably uniform in cross-sectional dimensions. A good relationship exists between the modulus of elasticity values obtained in edgewise and flatwise tests of southern pine dimension lumber. The correlation coefficient 6 of edgewise modulus of elasticity to flatwise modulus of elasticity is The average modulus of elasticity in compression parallel to the grain for all grades and sizes corresponded closely to the average true modulus of elasticity in flexure, with a mean difference of only 2-1/2 percent; likewise, the values by individual grades and sizes were in reasonably close agreement. With respect to the relationship of modulus of rupture (edgewise) and modulus of elasticity (flatwise), the data show a relatively large range in correlation coefficients among the various sizes and grades. The correlation coefficient based on linear regression was for the 2 by 4, for the 2 by 6, for the 2 by 8, and for the 2 by 10 size. For fiber stress at proportional limit, the correlation coefficient for fiber stress at proportional limit in bending versus modulus of elasticity was higher than for the modulus of rupture versus modulus of elasticity relationship. For maximum crushing strength parallel to the grain versus modulus of elasticity in compression parallel to the grain, the coefficient of correlation was found to be for the average of all 2 by 4 s and for all 2 by 8 s. These values closely parallel those in bending for modulus of rupture versus modulus of elasticity in the same sizes. The data also show about the same range and distribution of modulus of elasticity in compression as for modulus of elasticity in flatwise bending. Because specific gravity is a general index of the properties of clear wood, an evaluation of its relationship to the properties of dimension lumber was also made. The data show a correlation coefficient of between the flatwise modulus of elasticity and specific gravity for the small clear specimens and for all grades in the 2 by 4 and 2 by 8 sizes. The similar correlation coefficients for the No. 2 grade were for the 2 by 4 s) for the 2 by 6 s, for the 2 by 8 s, and for the 2 by 10 s. For modulus of rupture versus specific gravity, the correlation coefficient was for the small clear specimens, and for the fullsize pieces. Multiple correlations were made to determine the effect of including specific gravity as well as modulus of elasticity as independent variables in evaluating modulus of rupture. The data show but very small improvement in the correlation coefficient by adding specific gravity as an additional factor. For example, in the 2 by4 size the correlation coefficient between modulus of rupture and modulus of elasticity is for all grades; between modulus of rupture and specific gravity, 0.561; and between modulus of rupture versus modulus of elasticity and specific gravity combined, These data show that specific gravity has but minor influence in the evaluation of properties in dimension grades of lumber and that other factors such as knots and cross grain are the major influence in establishing grade. The results show that modulus of rigidity has a poor correlation with other properties such as modulus of elasticity and modulus of rupture. The correlation coefficient between modulus of rigidity and modulus of elasticity for all grades and sizes of southern pine was andbetween modulus of rupture and modulus of rigidity was The correlation coefficient between shear parallel to the grain and modulus of rigidity was As comprehensive as this research program was in evaluating the principal properties of FPL 64 18

23 southern pine dimension lumber in making strength of structural lumber, and concerning comparisons between properties, it is obvious the effect of such factors as cross grain, density, that some gaps and omissions still exist in the growth rate, machining imperfections, and other data. For example, more information is needed characteristics on the strength and stiffness of on such properties as tensile strength and shear dimension lumber. Table 1.--Southern pine dimension Iumber seiected for evaiuation of strength and related properties 19

24 Table 2.--Summary o f flexural properties of full- size southern pine dimension lumber

25 Table 3.--Comparison of flexural properties of southern pine

26 Table 4.--Comparison of actual and assigned flexural strength and stiffness values for southern pine dimension lumber Table 5.--Summary of compressive properties parallel to grain of full- size southern pine dimension lumber FPL 64 22

27 Table 6.--Comparlson of compressive parallel to grain properties of southern pine

28 Table 7.--Comparison of actual and assigned compression parallel to Grain strength and stiffness values for southern pine dimension lumber Table 8. --Significance of differences of moduli of rupture and moduli of elasticity of southern pine dimension lumber from IO states FPL 64 24

29 Table 9.--Summary of size measurements and related moduli of southern pine dimension lumber

30 Table 10.--Frequency distribution of southern pine dimension lumber flexure specimens by 200,000 pounds per square inch modulus of elasticity flatwise (true) classes Table requency distribution of southern pine dimension lumber compression parallel to the grain specimens by 200,000 pounds per square inch modulus of elasticity classes FPL 64 26

31 Table 12.--Summary of compression perpendicular to grain and shear parallel to grain properties of southern pi ne 27

32

33 Figure 8.--Relation of modulus of rupture to design stresses for six grades of KD southern pine 2 by 8 dimension lumber. 29

34 M Figure 9. --Relation of modulus of rupture to flatwise modulus of elasticity (true) of six grades of KD southern pine 2 by 8 dimension lumber. FPL 64 30

35 M Figure 10.--Relation of modulus of rupture to flatwise modulus of elasticity (true) of six grades of KD southern pine 2 by 4 dimension lumber. 31

36 M Figure 11.--Relation of modulus of rupture to flatwise modulus of elasticity (true) of NO. 2. KD southern pine 2 by 6 dimension lumber. FPL 64 32

37 M Figure 12.--Relation of modulus of rupture to flatwise modulus of elasticity (true) of the No. 2 KD grade of southern pine 2 by 10 dimension lumber.

38 Figure 13.--Relation of modulus of rupture adjusted to a 2- inch depth of beam to flatwise modulus of elasticity (true) of six grades and four sizes of southern pine dimension Iumber. FPL 64 34

39 Figure 14.--Relation of modulus of rupture of three grades and three sizes of KD southern pine dimension lumber (adjusted to a 2-in. depth of and of the matching small clear specimens (unadjusted for depth of beam) to the modulus of elasticity (true). 35

40 Figure 15.--Relation expressed by the linear regression lines of the modulus of rupture to the flatwise modulus of elasticity (true) and the flexural stress at the proportional limit to the flatwise modulus of elasticity (true) of KD southern pine 2 by 4 dimension lumber of six grades.

41 Figure 16.--Relation expressed by the linear regression lines of the modulus of rupture to the flatwise modulus of elasticity (true) and the flexural stress at the proportional limit to the flatwise modulus of elasticity (true) of KD southern pine 2 by 8 dimension lumber of six grades.

42 Figure 17.--Relation of modulus of rupture to specific gravity of KD southern pine 2 by 4, 2 by 6, and 2 by 8 dimension lumber specimens and of the matching small clear specimens. FPL 64 38

43 M Figure 18.--Relation of flatwise modulus of elasticity (true) of six grades and four sizes of KD southern pine dimension lumber to specific gravity.

44 Figure 19.--Relation of modulus of elasticity (true) of small clear southern pine specimens and specific gravity.

45 M Figure 20.--Relation of the specific gravity of small clear southern pine specimens and the specific gravity of the dimension lumber specimens from which the small clear specimens were 'cut.

46 Figure 21.--Frequency distribution of the small clear specimens and the 2 by 4, 2 by 6, 2 by 8, and 2 by 10 sizes of southern pine dimension lumber by 0.01 classes of specific gravity.

47 Figure 22.--Relation of the edgewise modulus of elasticity (true) to the flatwise modulus of elasticity (true) of the same pieces of southern pine 2 by 4 dimension lumber. 43

48 Figure 23.--Relation of the edgewise modulus of elasticity (true) to the flatwlse modulus of elasticity (true) of the same pieces of southern pine 2 by 8 dimension lumber. FPL 64 44

49 Figure 24.--Relation of the modulus of elasticity of the small clear specimens to the flatwise modulus of elasticity (true) of the southern pine dimension lumber specimens from which the small clear specimens were cut. 45

50

51 Figure 26.--Frequency distribution of the specimen-population in-the six grade's of 2 by 4 KD southern pine dimension lumber by 200,000 pounds per square inch classes of flatwise modulus of elasticity (true).

52 M 129 Figure 27.--Frequency distribution of the specimen population in the six grades of 2 by 8 KD southern pine dimension lumber by 200,000 pounds per square inch classes of flatwise modulus of elasticity (true).

53 M Figure 28.--Comparison of the modulus of elasticity in edgewise and flatwise flexure and in compression parallel to the grain for three grades and three sizes of KD southern pine dimension lumber and of the small clear specimens cut from the dimension lumber.