U.S.D.A.FOREST SERVICE RESEARCH PAPER FPL 148 DECEMBER SOME STRESS-GRADING CRITERIA AND METHODS OF GRADE SELECTION FOR DIMENSION LUMBER

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1 U.S.D.A.FOREST SERVICE RESEARCH PAPER FPL 148 DECEMBER SOME STRESS-GRADING CRITERIA AND METHODS OF GRADE SELECTION FOR DIMENSION LUMBER U.S. Department of Agriculture * Forest Service * Forest Products Laboratory * Madison, Wis.

2 Abstract The availability of several methods of stress-grading provides for an infinite variety of grades of lumber that could be manufactured. Lumber manufacturers and rules-writing agencies need some means of determining, from experimental and other evidence, what grades are most appropriate for manufacture. This paper demonstrates procedures for selecting machine grades based on experimental evidence of what can be produced, along with knowledge of required performance in use. It shows as an example that, for 2 by 8 southern pine floor joists, E-grades with a 1/3 edge-knot limitation are nearly ideal if the joists are used on a 24-inch spacing, or with a 1/2 edge-knot limitation if used on a 12 inch spacing. Relations of bending strength, tensile strength, and compressive strength to full-span modulus of elasticity and strength ratio are given. The methods described can be used for any species.

3 SOME STRESS-GRADING CRITERIA AND METHODS OF GRADE SELECTION FOR DIMENSION LUMBER R. L. ETHINGTON, Technologist Forest Products Laboratory, 1 Forest Service U. S. Department of Agriculture Introduction A decade ago, technology was available for a single method of stress-grading, the visual method (2). 2 Now flatwise quasi-static flexure with visual modifications is in commercial use, and edgewise static flexure, transverse vibration, longitudinal stress waves, and special defect detection systems for stress-grading all appear to be within reach. Each of these methods offers some unique capabilities in grading, and collectively they will provide an essentially infinite number of possible grades. Lumber manufacturers and their respective grading bureaus are faced with the task of deciding which of these grades they should produce and market. When the present machine grades were first described in western rules (10, 11), combinations of modulus of elasticity, E, and allowable bending stress, f, were picked as technological optimums based on the research evidence then available (8). That is, bending strength was regressed on modulus of elasticity, and combinations associated with the regression line were selected as the grade descriptions. As additional research revealed limitations in the ability of these grades to insure the required bending stress, visual overrides in the form of edge-knot limitations were added. Experience with the grades so developed showed that although they might be the optimum technologically, they were not necessarily the optimum economically. For lumber applications where bending allowable stress or the related tensile allowable stress is the most important of the two properties, such as in trussed rafters, the machine grades settled into a niche in the market place. This was particularly true for lumber with relatively small knots and a relatively low average E for the species. For applications where E is the more important of the two properties, such as floor joists, no market for machine-graded lumber developed. One reason is undoubtedly because the edge-knot limitations were imposed to insure a high value of a property where a high value was not important for the final use. The final decision regarding appropriate grades must be made on the basis of both technological capability and performance required, as well as log yield and marketing 1 Maintained at Madison, Wis., in cooperation with the of Wisconsin. 2 Italicized numbers in refer to Literature Cited at the end of this report.

4 considerations. It is imperative that all be considered if we are to achieve efficient utilization of the timber resource. About 11 billion board feet of lumber is used annually for the framing parts of new residential construction, providing a drain on timber supply and on the home owner s financial resources. If only 1 percent of this raw material can be saved through improvements in stress grades, this represents an annual saving on the order of $11,000,000. An important link in stretching the timber supply is more efficient stress grading. The present research was undertaken to demonstrate how experimental results can be used to select useful grades, where fullspan modulus of elasticity and strength ratio are the sorting criteria. Sources of Data Results of full-size tension, compression, and bending tests of southern pine dimension lumber have been reported by Doyle and Markwardt (3, 4), and those data were used for this analysis. The studies were based on samples of nominal 2 by 4 s and 2 by 8 s selected at random from inventory of one mill in each of 10 states, providing test results on material coming from the entire producing range of southern pine. Table 1 gives details of the sample. For each size and test, an equal number of specimens was selected from grades of No. 1 KD, No. 2 KD, and No. 3 KD, as described in (3). Bending and compression specimens were collected at the same time; tension specimens were collected a year later, and included additional pieces below the No. 3 KD grade. All lumber was conditioned to essentially 12 percent moisture content. Strength ratios were determined by the methods described in Table 1. - Numbers and sizes of southern pine lumber tested ASTM D 245 (2). The full-span of elasticity is a bending, compression, or tension modulus, corresponding to the respective failure test. Analysis Orosz (9) used a technique described by Draper and Hunter (5) to search for a best model relating tensile strength, bending strength ratio, and modulus of elasticity. Best here means an optimum combination of reduction of sums of squares due to lack of fit and transformation of the dependent variable to produce homogeneous variance. Orosz found that a logarithmic transformation of tensile strength worked very well, with no interaction between modulus of elasticity and bending strength ratio. Using Doyle and Markwardt s data (3, 4), the natural logarithm of strength was computed for each piece of lumber. The logarithm of strength (S) was then regressed on modulus of elasticity (E) and strength ratio (SR). Regression coefficients obtained in this manner are given in table 2, along with coefficients of determination. To aid in evaluating the appropriateness of the logarithmic transformation for these data, a study of residuals was made, as described by Draper and Smith (6). To do this, the deviation of each data point from the regression surface in logarithmic space was calculated, and plotted against the ordinate of the regression surface in logarithmic space. Symbolically, if a data point is represented-by (E i, SR i, S i ) and the corresponding ordinate of the regression surface by then values of the residual Si- were plotted against In a plot of this kind any trends apparent in the plot would suggest that the model or fitting methods could be improved upon. Thus, a desirable residual plot is one that shows no Test Bending Tension Compression 2 by 4 s 2 by 8 s Number of Length Number of specimens specimens Ft Length Ft FPL 148 2

5 trend. Figure 1 shows residual plots for each of the testing modes and sizes. No strong trends are evident in the figure. In some cases the variance may be decreasing with increasing predicted strength. In visual stress-grade development, allowable stresses are intended to be less than the value appropriate for 95 percent of the pieces of lumber encountered. Thus, in a plot of strength versus E and SR, a surface is sought that lies below 95 percent of the data. This might be called a 5 percent exclusion surface. It can be approximated by calculating a lower 90 percent confidence limit on individual values of strength for the model used. The method of calculation is described by Freese. 3 Figures 2 to 4 are plots of lower 90 percent confidence limits, where they are represented in two dimensions by plotting contours of the surface for 10 percent increments in SR. Table 3 lists coordinates of the data points that lie below each confidence surface. The amount of deviation of each point from the surface is also listed. The percent of total pieces that lie below each confidence surface are: Percent of pieces below Mode of test Size confidence surface Bending 2by4 2 by 8 Compression 2 by 4 2by8 Tension 2 by 4 2 by The confidence surface is concave upward, with a small positive strength intercept, which seems reasonable on the basis of general appearance of scatter diagrams. Ideally, the sample should contain the complete real range of both E and SR, and the pieces that fall below the confidence surface should be similarly distributed. When these specimens were collected, an effort was made to collect specimens for the tension test that represented the entire range of SR. No such effort was made for the bending and compression specimens. This is evident in table 3, where the pieces listed for 2 by 4 s in tension have strength ratios ranging from 8 percent to 100 percent. The values are not so widely distributed for any other size or test. The line for the lowest strength ratio shown in each of figures 2 to 4 represents the lower limit of the data. We would like to know if the confidence surfaces for the same test but different sizes are alike. If the two graphs in figure 2 are superimposed, (or in figure 3, or in figure 4) and where the graphs are not the same for the two sizes, part of the difference is undoubtedly experimental error. Also a size effect on strength is known to prevail in bending (2), and might be suspected in tension and compression. In general, the confidence lines for 2 by 4 s in bending (fig. 2) lie above those for 2 by 8 s. For compression the lines for 100 percent SR nearly coincided; as the strength ratios decrease, the lines for 2 by 8 s move below those for 2 by 4 s, suggesting an interaction Table 2. - Regression statistics obtained using the model ln strength = Regression statistics Mode of test Size R 2 Bending Compression Tension 2 by 4 2 by 8 2 by 4 2 by 8 2 by 4 2 by ln means natural logarithm, strength is expressed in p.s.i., E in 1,000 p.s.i., SR in percent. 3 Page 81 of U.S. Forest Service Research Paper FPL 17 (7). 3

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7 Figure 2.--Five percent exclusion surface in bending for 2 x 4's (left) and 2 x 8's (right). M M

8 Figure 3.--Five percent exclusion surface in compression for 2 x 4's (left) and 2 x 8's (right). M M

9 Figure 4.--Five percent exclusion surface in tension for 2 x 4's (left) and 2 x 8's (right). M M

10 Table 3.-Coordinates of all data that lie below the confidence surface, with amount of deviation from the surfaces Bending Compression Tension Modulus of Strength Deviation Modulus of Strength Deviation Modulus of Strength Deviation Strength elasticity ratio from Strength elasticity ratio from Strength elasticity ratio from surface surface surface 1,000 Pct. P.s.i. P.s.i. 1,000 Pct. P.s.i. P.s.i. 1,000 P.s.i. P.s.i. p.s.i. p.s.i. p.s.i. Pct. 2 BY 4 5,430 2, ,124 3,070 1, ,547 2, , ,785 1, ,209 2, ,444 1, ,357 1, ,026 2, , ,230 2, ,067 3, , ,639 1, , ,229 3,464 1, , , , ,419 1, , ,309 1, , , ,569 1, , ,300 2, ,000 1, , , , , , , ,563 1, , ,045 1, BY 8 4,180 1, ,644 1, , , ,137 1, ,650 2, ,087 2, , ,823 1, ,605 2, , ,192 2, ,368 1, , , , , ,364 1, ,561 1, ,489 2, , , , ,005 1, ,417 1, , FPL 148 8

11 of size with strength ratio. For tension, the lines corresponding to 10 percent SR are similar, and as strength ratio increases, the lines for 2 by 4 s move above those for 2 by 8 s. Use of the Grading Criteria A Family of Grades for Any Strength Value Using any one of the figures 2 to 4, it is possible to estimate combinations of E and SR that will assure a 5 percent exclusion limit in strength. The most common situation that the developer of a grading criterion encounters is the need to achieve a specified allowable stress. The allowable stress is related to strength by a factor given in reference (2). As an example, suppose that an allowable stress in bending of 1,500 p.s.i. is desired. From reference (2), the associated bending strength should be (2.1) (1,500) = 3,150 p.s.i. This value is graphed in figure 5, which has the same confidence lines as figure 2 for 2 by 4 s. Any combination of E and SR represented by a point on the horizontal line would provide a suitable grading criterion. For example, the visual requirements of machine grade rules now in existence specify edge knots having a displacement of 1/2, 1/3, 1/4, or 1/6 of the cross section. These correspond to bending strength ratios of 25, 47, 58, and 71 percent, or compression strength ratios of 53, 69, 77, and 84 percent (2). Expressions of three sizes of edge knots are represented by vertical lines in figure 5. They correspond to moduli of elasticity of about 1.75, 1.20, and 0.92 x 10 6 p.s.i., respectively. The locus of points representing 71 percent strength ratio lies entirely above 3,150 p.s.i., suggesting that a 1/6 edge-knot limitation is sufficient to achieve the desired strength for all moduli of elasticity within the range of the experiment. Also, the 1,500 f could be supplied in a grade with E>0.92 x 10 6 p.s.i. and a 1/4 edge knot; or E>1.20 x 10 6 p.s.i. and 1/3 edge knot; or E >1.75 x 10 6 p.s.i. and a 1/2 edge knot. Thus, there is a family of E s and SR s that are technically satisfactory for a grade assigned 1,500 f or any other allowable strength value. The figures must necessarily be used with a certain amount of caution. The size effect discussed earlier suggests that extrapolations to other sizes may cause anomalies. Inferences have been drawn above about the effect of edge knots, but the pieces of lumber that made up this sample were not confined to pieces containing edge knots. The modulus of elasticity was measured over full span, but differently for each testing mode. It would likely be measured in a single mode in a grading process. Relations between full-span moduli measured in bending, tension, and compression are needed for conversion to any testing mode that may be used in a grading process. However, there appears to be no literature to supply this information. Choice of Family Members There are a redundancy of grading criteria available from figures 2 to 4, all technically feasible. From these many possible grades, it will be necessary to select from one to a few that are particularly useful. This task is normally performed in the United States by a rules-writing association, or occasionally by an individual manufacturer with special product demands. Picking appropriate grades involves judgment on such things as performance required of the lumber in typical use, probable yield of any particular grade from available raw material, the economics of alternative uses for the wood, and problems in merchandising. The number of alternative grades can be narrowed somewhat by focusing on the performance required of the lumber in typical. use. Consider, for example, use of 2 by 8 lumber for floor joists. Given a maximum permitted deflection and floor load, and assuming that each joist acts independently (a common assumption in the development of joist span tables) it is possible to calculate the bending stress that will prevail in a joist having any E, and calculate the permitted span. This gives an E and f that are in balanceany additional bending strength would be superfluous, since the design would be limited by the permitted deflection, and thus by the E of the joists. Curves of balanced E s and f s (joist performance requirement lines) are graphed in figure 6 for four floor joist spacings. A deflection limitation of 1/360 of span was as- 9

12 Figure 5.--A family of grades having the same allowable bending stress. M FPL

13 Figure 6.--A graph used to search for efficient joist grades. M

14 sumed, 40 p.s.f. live load, 10 p.s.f. dead load, and nominal 2 by 8 floor joists (actual size 1-1/2 by 7-1/4). The live load was assumed to cause deflection, and the total load contributed to the stress. The plotted points shown in figure 6 are allowable properties for some possible grades. These points were obtained from figure 2 by restricting edge knots to 1/2, 1/3, 1/4, or 1/6 of the cross section, and by arbitrarily considering E in 200,000 p.s.i. increments. Although the points are plotted in figure 6 at the midpoint of each E class, they were obtained from figure 2 using the class lower limit, to provide a small additional margin of safety in selecting f. (To select points plotted at E = 1.2 x 10 6 in figure 6, figure 2 was entered at E = 1.1 x 10 6.) The ordinate of each point was increased by 15 percent, as permitted for repeated member systems in reference (2). Figure 6 is a very useful device for selecting grades that are efficient as well as safe for floor joist use. 4 The rectangle having any one of the points (grades) as its upper righthand corner delineates a region in which the grade will perform adequately. The grade can be used satisfactorily for any situation represented by the portion of a joist performance requirement line that passes through the rectangle. The grade prescribed by E>1.2 x 10 6 p.s.i. and a 1/2 edge knot is used as a demonstration. Joists of the size specified and of this grade can be used for spans that require f<910 p.s.i. This includes some situations for all of the spacings. Graphically, points that fall close to a line in figure 6 represent very efficient grades in the sense that E and f are well balanced. The figure shows that a series of grades permitting a 1/3 edge knot should be relatively efficient for southern pine used with a 24-inch spacing, and a series permitting a 1/2 edge knot are similarly efficient with a 12-inch spacing. Figure 6 can be used conveniently with a span table. Table 4 was calculated using the same criteria that gave the lines in the figure. Consider a southern pine grade having E>1.2 x 10 6 p.s.i. and a permitted 1/3 edge knot. The figure shows that this grade can be used for spans that correspond any bending stress up to 1,160 p.s.i. The span table then shows that the grade could be used on 12-foot 10- inch spans with 12-inch spacing, or 11-foot 8-inch spans with 16-inch spacing, or 11-foot 0-inch spans with 19.2-inch spacing. Can the grade be used on a 24-inch spacing? The span table indicates an allowable stress of 1,185 p.s.i. is needed with a span of 10 feet 2 inches. The grade isn t quite strong enough for this application, and this is graphically apparent in figure 6 because the point representing the grade is slightly below the 24-inch spacing line. However, by treating the grade as if it were one grade lower, it can be used with a 24-inch spacing and a span of 9 feet 7 inches. Grade descriptions developed using these concepts would be assigned a bending allowable stress less than those plotted in figure 6 by the 15 percent permitted for repeated members. Figure 7 is a plot of the same points reduced by 15 percent. The points are connected, and any point on any of the lines is a possible grade. A particular set of grades might well be decided upon based on certain properties essential to the use, as with the floor joists described above. Because the manufacturer cannot control the final use of the lumber he makes, it may be desirable to associate other allowable properties with the grade. Companion allowable stresses in tension and compression parallel to grain for the 2 x 8 joists can be gotten from figures such as 3 and 4, assuming no difference in modulus of elasticity in bending, tension, and compression. For example, for a grade with E>1.4 x 10 6 p.s.i. and a permitted 1/3 edge knot, strengths of 3,200 p.s.i. in compression and 1,100 p.s.i. in tension are obtained from the graphs. These correspond to allowable stresses of 1,680 p.s.i. and 520 p.s.i., respectively (2). 4A device first to the author by D. V. Snodgrass. FPL

15 Table 4. - A span table for 2- by 8-inch lumber, based on a deflection limitation. 1 Joist spacing Modulus 12 Inches 16 Inches 19.2 Inches 24 Inches of elasticity Permitted Required Permitted Required Permitted Required Permitted Required span allowable span allowable span allowable span allowable stress stress stress stress 10 6 P.s.i. Ft. - In P.s.i. Ft. - In P.s.i. Ft. - In P.s.i. Ft. - In P.s.i , , , , , , , , , , , , , , , , , , , ,666 Calculated using the following assumptions: (a) Actual size of 2 x 8 = 1½ x 7¼ inches. (b) Permitted deflection = 1/360 of span. (c) Load for calculation of span = 40 p.s.f live load. (d) Load for calculation of required allowable stress = 50 p.s.f. live load + dead load. 13

16 Figure 7.--AII possible allowable f's and E's for southern pine 2 x 8's with certain edge knot limitations. M FPL

17 Summary It has been shown in the literature that bending strength and tensile strength of lumber are reasonably well related to modulus of elasticity and strength ratio. This is probably also true for compressive strength parallel to the grain. Confidence surfaces associated with multiple regressions relating these variables, after logarithmic transformation of strength, provide a set of grading criteria. However, they provide us with a redundancy of grading criteria, and it is necessary to find some way to select especially useful members from that redundancy. Selection can be made, in part, on the basis of performance required of the lumber. A useful grade is one with allowable properties established at the levels required in application. Additional restriction of some of the mechanical properties would make an unbalanced grade that does not provide optimum use of the raw material. An example is given of grades selected for floor joists. More efficient stress grading appears to be an important link in stretching the timber supply. Literature Cited (1) American Society for Testing and Materials Standard methods of static tests of timbers in structural sizes. ASTM D (2) Standard methods for establishing structural grades for visually graded lumber. ASTM D (3) Doyle, V., and Markwardt, L. J Properties of southern pine in relation to strength grading of dimension lumber. U.S. Forest Serv. Res. Pap. FPL 64. Forest Products Lab., Madison, Wis. (4) Tension parallel-to-grain properties of southern pine dimension lumber. U.S. Forest Serv. Res. Pap. FPL 84. Forest Products Lab., Madison, Wis. (5) Draper, N. R., and Hunter, W. G Transformations: some examples revisited. Technometrics 1l(1): (6) and Smith, H Applied regression analysis. New York. John Wiley & Sons. (7) Freese, F Linear regression methods for forest research. U.S. Forest Serv. Res. Pap. FPL 17, Forest Products Lab., Madison, Wis. (8)McKean, H. B., and Hoyle, R. J Stress-grading method for dimension lumber; ASTM Spec. Tech. Pub. No. 353: 3-18 (9) Orosz, I Modulus of elasticity and bendingstrength ratio as indicators of tensile strength of lumber. J. Material 4(4): (10)West Coast Lumber Inspection Bureau Standard grading and dressing rules No. 15. (11)Western Wood Products Association Rules for grading western lumber

18 ABOUT THE FOREST SERVICE.... As our Nation grows, people expect and need more from their forests--more wood; more water, fish and wildlife; more recreation and natural beauty; more special forest products and forage. The Forest Service of the Department of Agriculture helps to fulfill these expectations and needs through three major activities: * Conducting forest and range research at over 75 locations ranging from Puerto Rico to Alaska to Hawaii. * Participating with all State forestry agencies in cooperative programs to protect, improve, and wisely use our Country s 395 million acres of State, local, and private forest lands. * Managing and protecting the 187-million acre National Forest System. The Forest Service does this by encouraging use of the new knowledge that research scientists develop; by setting an example in managing, under sustained yield, the National Forests and Grasslands for multiple use purposes; and by cooperating with all States and with private citizens in their efforts to achieve better management, protection, and use of forest resources. Traditionally, Forest Service people have been active members of the communities and towns in which they live and work They strive to secure for all, continuous benefits from the Country s forest resources. For more than 60 years, the Forest Service has been serving the Nation as a leading natural resource conservation agency.