Determination of Design Values

Transcription

1 Determination of Design Values For Visually Graded Southern Pine Dimension Lumber Southern Pine Inspection Bureau December 2012

2 Contents Introduction... 4 Part I. Determination of Design Values for Southern Pine... 5 Matrix Definition... 5 Data Collection... 6 Data Summary... 7 Assessment of Grade Quality Index... 7 Adjustments to Standardized Conditions Description of Statistical Methods Size Adjustments Characteristic Values Test Cell Data Checks Untested Properties Grouping Species Grade Model Part II. Allowable Design Values Point Estimate Check Final Length Adjustment Adjustment of Compression Strength for Test Method Development of Dense Design Values Adjustment for Duration of Load and Safety Allowable Design Values Mixed Southern Pine Design Values Works Cited

3 List of Figures Figure 1. Summary of GQI checks for Southern Pine strength properties Figure 2. Summary of GQI checks for Southern Pine stiffness properties Figure 3. Test Spans and Gauge Lengths Figure 4. Interpolated MOR Values using the Grade Model Figure 5. Example Grade Model for Modulus of Rupture Figure 6. Interpolated Values for MOE using the Grade Model Figure 7. Example Grade Model for Modulus of Elasticity Figure 8. Dense and Nondense Factors

4 List of Tables Table 1. Bending Test Cell Summary Data Table 2. Tension Test Cell Summary Data Table 3. Stiffness Test Cell Summary Data Table 4. Compression Test Cell Summary Data Table 5. Summarized Test Data Table 6. Test Cell Data Checks for MOR Table 7. Test Cell Data Checks for UTS Table 8. Test Cell Data Checks for UCS Table 9. Characteristic Values - Adjusted for Grade Table 10. Property Estimates Table 11. Section 12.6 Checks for MOR Table 12. Section 12.6 Checks for UTS Table 13. Section 12.6 Checks for UCS Table 14. Southern Pine Design Values Table 15. Mixed Southern Pine Design Values

5 Introduction The original In-Grade Testing Program, undertaken by the major rules-writing agencies in the United States and Canada in cooperation with the U.S. Forest Products Laboratory, culminated in a new methodology for deriving allowable properties for visually graded dimension lumber in This methodology used the results of tests of full-size lumber specimens rather than the small, clear samples identified in ASTM D2555 (ASTM, 2006). This new methodology is documented primarily in two ASTM Standards: ASTM D4761 (ASTM, 2011): Standard Test Methods for Mechanical Properties of Lumber and Wood-Base Structural Material and ASTM D1990 (ASTM, 2007): Allowable Properties for Visually Graded Dimension Lumber from In-Grade Tests of Full-Size Specimens. One of the requirements of ASTM D1990 is to conduct reassessment of the values derived from this practice if there is cause to believe that there has been a significant change in the raw material resource or product mix. To this end, the Southern Pine Inspection Bureau (SPIB) has conducted an annual Resource Monitoring Program each year since This monitoring program was established with the help of the U.S. Forest Products Laboratory and the derivation of the program and initial results were documented in FPL-RP-576: Monitoring of Visually Graded Structural Lumber (Kretschmann, Evans, & Brown, 1999). Based on the results of seventeen years of this monitoring program, the SPIB realized the time had come to perform a full-matrix reassessment of the design values for Southern Pine dimension lumber. This report documents the results of the recent ( ) tests on visually graded Southern Pine dimension lumber and establishes new design values based on these recent tests. 4

6 Part I. Determination of Design Values for Southern Pine Matrix Definition This document reviews the determination of allowable properties for all National Grading Rule sizes and grades of dimension lumber (Select Structural, No.1, No.2, No.3, Stud, Construction, Standard and Utility) according to the procedures established in ASTM D1990 (ASTM, 2007). To obtain these properties it was not necessary to test every size/grade combination. Section 7.4 of ASTM D1990 specifies the minimum full matrix of grades and sizes required for deriving allowable properties. For convenience in this document, a grade/size combination is called a test cell. The minimum full matrix consists of six test cells, composed of at least two grades and three sizes for each grade. The grades tested for both the original Southern Pine in-grade program and this recent reassessment were Select Structural (SS) and No.2. The grades sampled in these testing programs were developed using the strength ratio system as defined in ASTM D245 (ASTM, 2011). These grades meet the requirements of Section 7.2, ASTM D1990, in that they are separated by no more than one intermediary grade (No.1) and no more than one quarter of the total possible range in assumed bending grade quality index (GQI). The grade quality index is a scaling parameter which allows modeling of strength and modulus of elasticity (MOE) with respect to grade. For this application, the strength ratios associated with each grade are assumed to be the GQI. That is, SS has a bending strength ratio of 0.65 and No.2 has a bending strength ratio of The difference in strength ratio between these grades is 0.20, which is less than 0.25 (one quarter of the full range). Tests were conducted for four properties: Modulus of Elasticity (MOE), Modulus of Rupture (MOR), Ultimate Tensile Stress (UTS) and Ultimate Compressive Stress (UCS). The sizes tested for each property were 2x4, 2x8, and 2x10. It is also desired to publish allowable properties for dense categories of SS, No.1 and No.2 since these dense grades are currently produced, albeit in limited quantities. Dense lumber is defined in the SPIB Grading Rules (Southern Pine Inspection Bureau, 2002), paragraph 103.1, as follows: Dense lumber shall average on one end or the other of each piece not less than 6 annual rings per inch and 1/3 or more summerwood (the darker, harder portion of the annual ring) measured on a representative radial line as specified. The contrast in color shall be distinct. Pieces that average not less than 4 annual rings per inch shall be accepted as dense in the average ½ or more summerwood. Information on rings per inch and percentage of summerwood was collected for all of the test specimens. The percentage of summerwood was determined using a dot-grid to give a more precise estimation of this characteristic. A 1 x1 grid with 100 dots evenly spaced was placed on a representative portion of the end of each piece and the dots falling in the summerwood bands were counted. Using the rings per inch and percentage of summerwood, the complete unclassified data set 5

7 was sorted into two groups: those pieces that met the dense classification, and those that did not. The pieces that failed to meet the dense definition were considered to be nondense. Factors were determined from ratios of the tolerance limits for strength properties and from ratios of the means for stiffness. These factors were then applied by property and grade to determine dense and nondense design values. Data Collection Section 8.1 of ASTM D1990 stipulates methods for sampling shall be in accordance with ASTM D2915 (ASTM, 2010). The goal of the sampling procedure is to obtain lumber that is representative of the total Southern Pine lumber population. The sampling procedure is described in detail by Jones (Jones, 1988). He outlines the following steps: 1. Divide the entire production area for each commercial species group into homogeneous geographic regions based on topography, climate, and known growth patterns, so that any material sampled in a region can be assumed to representative of the region. 2. Calculate the number of pieces to be sampled in each region in proportion to the production volume of dimension lumber. 3. Establish a list of sawmills in each region for random sampling. (Possible mills included all mills using SPIB or Timber Products Inspection (TP) grademarking services. This accounts for approximately 96% of all Southern Pine lumber production. 4. At each mill, select lumber in lots from a bundle of lumber. Select at least ten pieces (per lot) but no more than two lots from any one mill. (No pieces within the top layer of the bundle were selected, and each piece was judged to be on-grade by and SPIB and a TP Quality Supervisor.) A sample size of 360 pieces per cell was targeted for Southern Pine. Actual samples sizes of were obtained for the unclassified data sets. While the sample sizes for the dense and nondense subsets are less than 360 pieces, the samples sizes were at least 120 pieces per cell, which should be considered adequate given the much smaller production volume of dense (and nondense) material. All tests were performed in accordance to ASTM D4761 (ASTM, 2011). Bending tests were conducted on a Metriguard 312 bending prooftester at the SPIB testing facility. The bending tests used third-point loading with deflection measured at mid-span. Tension tests were conducted on either a Metriguard 403 tension prooftester at SPIB or a Metriguard 412 tension prooftester at the TP testing facility. Compression tests were conducted on a Tinius Olsen Electromatic 60k testing machine at TP or an Instron Universal testing frame Model 5589 with a 135 kip capacity at the Forest Products Laboratory (FPL). For the compression tests, as per ASTM D4761, Annex A1, two short specimens (length = 2.5 * width) were selected from each full length sample to isolate the worst defects. The weaker of these two specimens were retained to represent the strength of the sample piece. 6

8 The following data were collected: 1. Agency, mill, and size 2. Visual grade (gradestamped on the piece as verified by the quality supervisor). 3. Piece number 4. Grade controlling characteristic (identified by quality supervisor) 5. Maximum strength reducing characteristic (identified by quality supervisor) 6. Rate of growth (rings per inch on each end of piece) 7. Percentage of summerwood (on each end of the piece) 8. Presence or absence of Pith 9. Thickness and width (using calipers to the nearest 0.01 to 0.03 inch) 10. Moisture content (using a 2-pin resistance moisture meter) 11. Temperature (if below 47 F) 12. Code describing failure characteristics 13. Failure load (to calculate strength properties: MOR, UTS or UCS) 14. Modulus of Elasticity (in bending mode, collected for all pieces tested in bending or tension) Data Summary The summarizing statistics for each cell include the sample size, mean, median, standard deviation, nonparametric point estimates and tolerance limits, and 75% confidence intervals on the point estimate. The tolerance limit in this document refers to the tolerance limit with 95% content and 75% confidence. The point estimate is an estimate of the 5 th percentile. Note that not all of the pieces were able to be loaded to failure, due to twist and/or capacity limits of the testing machines. A minimum of 36.8% of each size/grade/property sample was loaded to failure (the weakest 36.8% of the pieces), thus permitting accurate estimate of lower tail properties, but estimates of means, medians, and standard deviations are based on maximum loads obtained for each piece, whether the piece failed or not. Tables 1 3 summarize the data collected. All data have been adjusted to 15% moisture content and considered at 73 F. Assessment of Grade Quality Index Section 8.3 of ASTM D1990 requires that the grade quality index of the sampled material be assessed in relation to the assumed grade quality index used to establish the matrix. The observed grade quality index for pieces that failed during testing was calculated for all pieces that did not fail in clear wood and for which a GQI could be calculated, per ASTM D245. There are two facets of the GQI calculation as currently implemented that create inconsistencies. We wish to address these as a matter of record even though this submission is not modified from past practice to correct these inconsistencies: 1) Treatment of combination knots vs. edge knots 2) Non-traditional rounding of the GQI 7

9 The equations in FPL-126 (Evans, Kretschmann, Herian, & Green, 2001) treat narrow face knots the same as edge-of-wide-face knots as shown below. Narrow face and Edge-of-wide-face knots: For members with depth, h, < 6 inches: [ ( ) ] ( ) For members with depth, h, 6 inches: [ ( ) ] ( ) If S is calculated to be less than 45, the strength ratio is recalculated as: [ ( ) ] Where k is knot size measured in inches. A different equation exists for knots located away from the edges of the wide face (i.e. center of wide face knots). Cross sections which include more than one knot (combination knots) are evaluated using the center-of-wide-face knot equations. Center-of-wide-face knots and combinations of knots: For members with depth, h, < 6 inches: [ ( ) ] ( ) For members with depth, h, 6 inches: [ ( ) ] ( ) If S is calculated to be less than 45, the strength ratio is recalculated as: [ ( ) ] Where k is the measured knot size in inches. For combination knots, the percentage of cross-section occupied by the knots is converted to an equivalent knot size. 8

10 A complication arises if a cross section contains a reasonably large edge knot in combination with other center-of-the-wide-face or edge knots. For example, a piece of #2 2x10 contained a edge knot, which occupies 28.4% of the 9.25 cross section. Using the edge-of-wide face equation for depths greater than 6 we see that the strength ratio associated with this single edge knot is: [ ( ) ] ( ) [ ] If this same cross section contained additional knots along with this specific edge knot, and now the total percentage of cross section occupied by knots goes up from 28.4% to 33%, one would expect the strength ratio to drop below But, in fact, when the center-of-wide-face knot equation is used for combination knots, the calculated strength ratio becomes (using a 33% x 9.25 = inch knot): [ ( ) ] ( ) [ ] This can lead to over estimating the strength ratio of the piece if a reasonably large edge knot is included in combination with other, smaller center-of-wide-face knots. The GQI s calculated from the above equations were ranked and the 5 th percentile GQI was used as an estimate of the assumed minimum GQI for the grade. The assumed minimum GQI for SS is 65% for bending and tension (69% for compression) and for No.2 is 45% for bending and tension (52% for compression). The GQI must be calculated for each cell, as well as an average GQI for each grade/property. The GQI for each cell must be within 7 points of the assumed GQI for the grade and the average GQI for each grade must be within 5 points for the grade to be assumed representative of the grade being sampled. If these limits are exceeded, reductions to the data can be taken to enable the assumption of representativeness. The following charts summarize this analysis: 9

11 Figure 1. Summary of GQI checks for Southern Pine strength properties +/- +/- Size MOR (SS GQI = 0.65) UTS (SS GQI = 0.65) UCS (SS GQI = 0.69) SS n OS GQI +/- n OS GQI n OS GQI PE (1) 7% PE (1) 7% PE (1) 7% 2x yes yes yes 2x yes yes (4) yes 2x yes (2) no (5) yes Avg: ok Avg: > +/- 5% Avg: >+/- 5% +/- MOR (No.2 GQI = 0.45) UTS (No.2 GQI = 0.45) UCS (No.2 GQI = 0.52) #2 n OS GQI +/- n OS GQI +/- n OS GQI PE (1) 7% PE (1) 7% PE (1) 7% 2x yes yes yes 2x yes yes yes 2x yes (3) no yes Avg: ok Avg: ok Avg: ok (1) Order Statistic used to calculate 5 th percentile Point Estimate, based on given sample size, n. (2) Factor applied to SS 2x10 Tension = (3) Factor applied to No.2 2x10 Tension = (4) Factor applied to SS 2x8 Compression = (5) Factor applied to SS 2x10 Compression = While it is undocumented in ASTM standards, in a prior submission documented in the History of Lumber Submissions under ASTM D1990, it appears the ALSC Board of Review adopted a policy of using non-standard rules for rounding numbers when applied to strength ratios, in an effort to be conservative. Any number in the hundredths digit would force the tenths digit to be rounded up to next tenth. For example, for #2 2x10 tested in bending, the calculated 5th percentile strength ratio is Traditionally, this would be rounded to 50.0, but under the non-traditional procedure would round to In most instances this slight variation in procedure is insignificant. On certain occasions, though, it does make a significant difference. In the case of the Select Structural lumber tested in compression, each cell is within the 7% tolerance permitted. But the average for all three sizes calculated to According to traditional rounding rules, this would be 74.0 when rounded to the nearest tenth. But because the hundredths digit is greater than 0, the non-traditional procedures would round this up to 74.1, which exceeds the 5% tolerance permitted (69% + 5% = 74%) for the average of the combined sizes. This, in turn, requires a reduction to the SS 2x8 and 2x10 compression strength values. It should also be noted that the requirements of the GQI provision have been significantly modified and made much more specific and encompassing than was used for the original submissions of major species in-grade data submitted over 20 years ago. Furthermore, Appendix X12.5 of ASTM D1990 documents that the evolution of these additional rules and adjustment procedures were primarily created to address new species being introduced for approval in North America that had very limited production using North American grading rules. The limits and rules were developed assuming that the original samples tested in the 1970 s and 1980 s for the North American In Grade Testing Program were 10

12 assumed to be representative due to the extensive sample size and sampling procedures. These same sampling procedures were used for this re-evaluation of Southern Pine with additional measures, namely having two agency quality supervisors present during sample selection, were taken to ensure the sample was not biased by the selection process. Except as noted in the footnotes of Figure 1, the GQI checks for each cell and for the average of each grade/property are within acceptable limits. The reduction factors indicated in the footnotes are calculated from ASTM D1990, Section , equation 1. Even though the Average GQI for all SS in tension is more than 5 points above the grade GQI, no further reduction is required, since the offending cell of 2x10 has already been reduced. For stiffness, the MOE data collected on both the bending and tension samples were considered because this represents the most extensive collection of MOE data. Figure 2. Summary of GQI checks for Southern Pine stiffness properties Size MOE (SS GQI = 0.65) SS n OS PE (1) GQI +/- 7% 2x yes 2x yes 2x (2) no Avg: ok MOE (No.2 GQI = 0.45) #2 n OS PE GQI +/- 7% 2x yes 2x yes 2x (3) no Avg: ok (1) Order Statistic used to calculate 5 th percentile Point Estimate, based on given sample size, n. (2) Factor applied to SS 2x10 = (3) Factor applied to #2 2x10 = While the strength ratio equations from ASTM D245 have been used for many years, when applied as part of the GQI check for ASTM D1990, the actual fifth percentile GQI can be greatly overestimated depending on the number of combination knots coded in the failures. To get a feel for the magnitude of this issue, consider the number of pieces coded with combination knots: For each size/grade/property cell, anywhere from 23% to 74% of the pieces for which a strength ratio could be calculated were coded as combination knots. The cell with the greatest percentage of combination knots (74.1% of pieces with a strength ratio calculation) was the SS 2x10 tested in tension, which is also the cell with the highest GQI above the target as shown in the charts above. This also reduces the calculated stiffness values for the 2x10 s. The No.2 and SS 2x10 failed cross sections containing combination knots were additionally evaluated for strength ratio based solely on the largest edge knot present, using the equation for edge-of-wide-face knots. Using strength ratios calculated in this manner, no reduction is 11

13 required for the No.2 2x10 in tension or E, and the factor applied to SS 2x10 tension strength increases from to While the intent of this provision is laudable, the implementation leaves something to be desired. We have several issues with how this check is implemented. First, to take the strength ratios associated with the failed cross section of pieces that did not fail in clear wood and apply this to force reductions in a nondestructive property like MOE seems nonsensical. Secondly, with the identification of vastly different strength ratios being calculated for edge knots and combinations of knots that include edge knots, it seems inappropriate to require the use of the center-of-the-wide-face knot equation, which inflates the calculated strength ratio. Thirdly, given the ball park nature of these calculations, it seems illogical to abandon traditional rules of rounding in an effort to be conservative. Adjustments to Standardized Conditions Strength properties can vary with the moisture content and temperature of the piece. Therefore, to treat each piece equitably, strength values were adjusted to certain standardized conditions. Both ambient and wood temperatures were observed and recorded if they were below 47 F. Temperature conditions can vary because the tests were conducted at various locations and different times of the year. Wood moisture content was recorded using a 2-pin DC resistance meter specifically calibrated for Southern Pine. When available, temperature adjustments were made to the moisture content readings as described by Garrahan (Garrahan, 1988). Temperature Adjustments A complete description of adjustments to strength properties for temperature is given in Barrett et al (Barrett, Green, & Evans, 1988). These adjustments vary with moisture content, grade, and property. For all properties and grades of Southern Pine, there is no adjustment for temperatures greater than 46 F. The temperatures for all tests of Southern Pine were above 46 F, so no adjustments for temperature were required. Moisture Content Adjustments Moisture content adjustments were performed in accordance with Annex A1 of ASTM D1990. For lower levels of each strength property, no adjustment is made for moisture content. For strength levels greater than the specified limits, the equations are as follows: For MOR > 2415 psi: For UTS > 3150 psi: 12

14 For UCS > 1400 psi: All values of MOE were adjusted for moisture content as follows: Where subscripts 1 and 2 denote the conditions at original and adjusted moisture content levels respectively. Note that if the measured moisture content was below 8% or above 23%, then 8% or 23% respectively was used in the moisture content adjustment equation. These adjustments were made when the strength values were considered at the test size and span. Example: Adjustment for moisture content Given: No.2 2x10, tested at 19% MC to have an MOR of 2520 psi Find: The MOR, when adjusted to 15% MC Solution: Using the MOR moisture content adjustment equation: Span to depth Adjustment for MOE While E values were tested on a span to depth ratio of 17:1, the published design values assume a uniformly loaded piece with a span to depth ratio of 21:1. Therefore, all E values were adjusted by the following equation from ASTM D2915: ( ) ( ) ( ) ( ) Where: K 1 = for concentrated loads with deflection measured at the midspan K 2 = for uniformly distributed loads with deflection measured at midspan. (h 1 /L 1 ) = (1/17) (h 2 /L 2 ) = (1/21). E/G is the ratio of the shear free modulus of elasticity to the modulus of rigidity, (assumed to be 16 for lumber). ( ) ( ) 13

15 Description of Statistical Methods The mean and standard deviation of each data set were obtained using EXCEL algorithms. The order statistics required to obtain nonparametric estimates for median and fifth percentile were obtained using the nonpar.exe program suggested by FPL-GTR-126 (Evans, Kretschmann, Herian, & Green, 2001). To avoid being nonconservative, the value for the order statistic is truncated for lower limits and the next higher integer is used for upper limits. Interpolation between order statistics was used for point estimates and medians when necessary. Size Adjustments There are two potential adjustments related to the size of the member tested. The first adjustment accounts for the shrinkage or swelling in dimensions due to changes in moisture content. Appendix X1 of ASTM D1990 provides an equation to adjust specimen dimensions to a moisture content of 15%. The following equations were used to adjust specimen width (w) and thickness (t) for moisture content: The second size adjustment accounts for observed differences in test properties due to the size of the member tested. So that data from all sizes could be pooled together for further calculations, the data from each size were adjusted to the characteristic size, i.e. 2x8 12 long. The equation for adjusting the various properties from one size to a second size is found in ASTM D1990 Section and is shown below. The subscripts one and two denote conditions at the original size and the new size respectively. The exponents vary with property and are listed below. ( ) ( ) ( ) Property w l t MOR, UTS UCS MOE Due to the zero exponents, no properties are affected by changes in thickness, UCS is unaffected by length, and MOE is not affected by size at all. A 10% increase in bending design values for lumber 4 thick (nominal) was identified by research outside the In-grade program (Madsen & Stinson, 1982) and is permitted by ASTM D1990 Section The characteristic size to which all data is adjusted is a nominal 2x8, 12 long. Therefore, when adjusting data to the characteristic size, W 2 is 7.25 and L 2 is 144. The original sizes and lengths (test spans) are listed below: 14

16 Figure 3. Test Spans and Gauge Lengths Nominal Size Actual Size Bending Test Span Tension Gauge Length Compression Length 2x4 1.5 x x8 1.5 x x x or The bending test spans correspond to a span to depth ratio of 17:1. A small portion of the 2x10 s could only be obtained in a 12 length and they were tested on a 138 test span. Compression lengths are documented as a matter of record no volume adjustment is made based on test specimen length. Example: Adjustment for size Given: No.2 2x10, MOR = 2540 psi, tested on span Find: MOR value when converted to Characteristic Size Solution: Using the volume adjustment equation: ( ) ( ) Note: for purposes of adjusting individual strength data to characteristic size, the measured width dimension, adjusted to 15% MC, was used in the above equation. Characteristic Values Summarized test data are provided in Table 5. The data from each size were converted to characteristic size. This allows the data to be pooled into one data set for each grade/property combination. Table 4 summarizes the initial characteristic values, while specific data checks and adjustments described below are required to obtain final characteristic values. Test Cell Data Checks Section 9.3 of ASTM D1990 discusses a Test Cell Data Check. This check compares the predicted values for each size that are derived from the values for the characteristic size to the upper 75% confidence limit for each cell. If the value predicted from the size model is larger than the upper 75% confidence limit for the cell, then the characteristic value must be lowered until the condition does not exist. Tables 6-8 show these Test Cell Data checks. Untested Properties Because tests were performed for all four properties (MOE, MOR, UTS, and UCS), no properties need be estimated from test data of another property. Compression Perpendicular Values Compression perpendicular to the grain is not addressed in ASTM D1990. The current (2002) SPIB Grading Rules currently list compression perpendicular to grain design values for Dense, Unclassified, 15

17 and Nondense sorts, based on procedures defined in ASTM D2555 and D245. No change is proposed for the compression perpendicular design values for Southern Pine. Horizontal Shear Horizontal shear is another property that is not addressed in ASTM D1990. The current (2002) SPIB Grading Rules currently list horizontal shear design values based on procedures defined in ASTM D2555 and D245. No change is proposed for the horizontal shear design values for Southern Pine. Density classifications do not affect horizontal shear values. Grouping Species Section 10 of ASTM D1990 discusses grouping data from various species to form a new species grouping. While Southern Pine does consist of several species, no grouping of the data is required (or possible) because major species Southern Pine is an existing grouping and was not sampled as individual species. Grade Model After characteristic values have been reviewed using the Test Cell Data Check of Section 9.3, a grade model is used to determine characteristic values for those grades which were not tested. The untested grades are No.1, No.3, Stud, Standard, Construction, and Utility. This grade model is fully documented in Section 11 of ASTM D1990 and examples for MOR and MOE are provided here. Figure 5 shows the grade model for the unclassified MOR data. The model was developed using the data from the SS and No.2 grades. Straight lines were drawn between the origin and the No.2 data point (strength ratio = 0.45, MOR = 1944 psi), and between the No.2 data point and the SS data point (strength ratio = 0.65, MOR = 4109 psi). Values for the other strength ratios were interpolated from these lines based on the strength ratios associated with the untested grades. The interpolated MOR values shown in Figure 4. Figure 4. Interpolated MOR Values using the Grade Model Grade Strength Ratio MOR (psi) No No Stud Construction Standard Utility As identified in Section 11.1, Note 16, of ASTM D1990, the characteristic value for the grade of No.1 is 85% of the interpolated strength value for MOR and UTS (0.85 * 3027 = 2573 psi). For UCS, 95% of the interpolated value is used. 16

18 MOR, psi December 2012 Figure 5. Example Grade Model for Modulus of Rupture Grade Model Development for MOR Unclassified Data Strength Ratio An example of the MOE grade model is shown in Figure 7, using the mean values of the unclassified data. The model is anchored by the No.2 data (SR = 0.45, MOE = 1.451) and SS data (SR = 0.65, MOE = 1.807) Rather than using the origin as the third data point, 80% of the No.2 value is used, corresponding to a strength ratio of Interpolated mean MOE values are shown in Figure 6. Figure 6. Interpolated Values for MOE using the Grade Model Grade Strength Ratio MOE (million psi) No No Stud Construction Standard Utility For stiffness properties, for the No.1 grade, 100% of the interpolated value applies. 17

19 MOE, million psi December 2012 Figure 7. Example Grade Model for Modulus of Elasticity Grade Model Development for MOE Unclassified Data - Mean Values Strength Ratio Part II. Allowable Design Values The complete set of characteristic values for all grades of Southern Pine is shown in Table 9. These characteristic values are used, in conjunction with the size model, to generate property estimates for each size and grade. The property estimates are shown in Table 10. These estimates are given at the characteristic length, 144, and each width as indicated. Point Estimate Check Section 12.6 of ASTM D1990 describes one final data check to be made. This check is used to compare the values that are generated from the size and grade models to the point estimates for the original data cells. This check only applies to cells where original test data exists, namely 2x4, 2x8 and 2x10 sizes of the SS and No.2 grades. If any value predicted by the size and grade model was larger than the point estimate plus 100 psi or plus 5% (whichever is smaller), the predicted value must be reduced so this condition does not exist. These data checks are shown in Tables Some reductions were needed based on this check, as indicated in the tables. Final Length Adjustment The allowable design properties were converted to appropriate lengths based on the size of the material. A 12 length represents a reasonable end-use length for 2x4, 2x6 and 2x8 widths. A 20 length was used for the 2x10 and 2x12 widths. These length adjustments have been performed using the size model. 18

20 Adjustment of Compression Strength for Test Method Short-segment compression samples were tested in this testing program. Supplemental testing had been performed (Green & Evans, 1992) to compare compression strength values obtained using short vs. long compression specimens. The source of the difference in strength values obtained using short specimens vs. full length specimens seems to stem from the likelihood of being able to select the true weakest section to be isolated within the short specimen. The likelihood of isolating the true weakest section increases as more defects are present (i.e. in lower grades of lumber.) During the original submission of Southern Pine In-Grade testing in the 1990 s, a 5% reduction was applied only to Select Structural UCS values. No reduction was applied to No.2 values. The No.1 UCS values were calculated by applying the grade model to each size of the No.2 UCS values and the reduced Select Structural UCS values. Upon subsequent discussions with current FPL staff, it is preferred to take this 5% reduction for both the SS and #2 characteristic values. It should be noted that this 5% reduction is not documented in either ASTM D4761 or ASTM D1990. Development of Dense Design Values It is desired to publish allowable properties for dense categories of SS, No.1 and No.2 since these dense grades are currently produced. The development of design values for a subcategory of a major species is not specifically addressed by ASTM D1990. While it is true that the minimum sample size of 360 pieces per cell was not achieved when the data was subdivided into dense and nondense categories, it is our assertion that the resulting sample sizes are nonetheless sufficient to represent the very limited production of dense grademarked lumber. According to agency shipment records for 2011, the amount of lumber grademarked as dense is approximately 1.7% of all Southern Pine production. The data were sorted into three categories: unclassified using all of the available data, dense - using the data for which the recorded density information could classify the pieces as dense, and nondense using the data for which the recorded density information could not classify the pieces as dense. As suggested by the Forest Products Lab, factors were determined from ratios of the tolerance limits for strength properties and from ratios of the means for stiffness. These factors were then applied by property and grade to determine dense and nondense design values. The factors are as follows: Figure 8. Dense and Nondense Factors Grade Property Dense Nondense MOR SS MOE UTS UCS MOR #2 MOE UTS UCS

21 Note: These factors were applied after any required cell-specific reductions from the Section 12.6 data checks. The grade model was then used to calculate values for #1D and #1N. Using this factor approach helps to ensure representation of all regions for the dense and nondense material. Adjustment for Duration of Load and Safety The strength properties that have been generated must also be reduced by a factor of safety and a duration of load adjustment to normal (10 year) loading. These factors are identified in ASTM D1990 Section A factor of 2.1 is used to reduce MOR and UTS values, and a factor of 1.9 is used for UCS. A factor of 1.0 is used with MOE. Allowable Design Values The allowable design values for Southern Pine are presented in size-specific tables in Table 14. All properties are rounded according to the rounding rules in ASTM D1990. Mixed Southern Pine Design Values Virginia pine and pond pine are known as minor species of Southern Pine and can be grademarked together with the major species as Mixed Southern Pine. While the clear wood strength properties of these minor pines are on the same order of the values for the major species, the stiffness properties are somewhat lower. When the original In-Grade testing program was conducted, pieces of mixed Southern Pine (Virginia Pine and Pond Pine) were also sampled and tested, but in smaller quantities. It is difficult to identify these minor species of Southern Pine once the wood is cut into lumber. The primary identifiers are related to the bark and the color of the pith and summerwood bands. Consequently, the pieces of lumber identified as Virginia pine and pond pine had lower strength values associated with them as compared to the major species of Southern Pine. When lumber from Virginia pine and pond pine is produced, it very commonly has a significant portion of major species Southern Pine packaged along with it, but the combined lumber must be grademarked as Mixed Southern Pine and carries lower design values. Because of some of the current reductions of design values for Southern Pine, there are some cases, primarily No.2 and lower grades, where some properties of Mixed Southern Pine would have higher design values for some properties than for the major species of Southern Pine. This creates logistics issues when one considers that a very great percentage of the Mixed Southern Pine consists of the major species of Southern Pine. Therefore, the values to be published for the classification of Mixed Southern Pine are proposed to be the lower of: 1) the previous Mixed Southern Pine design values or 2) the newly proposed values for (major) Southern Pine. The proposed values are shown in Table 15. Note that Mixed Southern Pine does not include the dense and nondense classifications. 20

22 Works Cited ASTM. (2007). Standard Practice for Establishing Allowable Properties for Visually Graded Dimension Lumber from In-Grade Tests of Full-Size Specimens. ASTM D1990. ASTM. (2011). Standard Practice for Establishing Structural grades and Related Allowable Properties for Visually Graded Lumber. ASTM D245. ASTM. (2010). Standard Practice for Evaluating Allowable Properties for Grades of Structural Lumber. Philadelphia: ASTM. ASTM. (2006). Standard Test Methods for Establishing Clear Wood Strength Values. ASTM D2555. ASTM. (2011). Standard Test Methods for Mechanical Properties of Lumber and Wood-Base Structural Material. ASTM D4761. Barrett, J., Green, D., & Evans, J. (1988). Temperature Adjustments for North American In-grade Structural Lumber. Workshop on In-Grade Testing of Structural Lumber (pp ). Madison: Forest Products Research Society. Evans, J., Kretschmann, D., Herian, V., & Green, D. (2001). Procedures for Developing Allowable Properties for a Single Species Under ASTM D1990 and Computer Programs Useful for the Calculations, FPL-GTR-126. Madison: US FPL. Garrahan, P. (1988). Moisture Meter Correction Factors. Workshop on In-Grade Testing of Structural Lumber (pp ). Madison: Forest Products Research Society. Green, D. W., & Evans, J. W. (1992). Compression Testing of Lumber: A Comparison of Methods. Journal of Testing and Evaluation, Jones, E. (1988). Sampling procedures used in the in-grade lumber testing program. Workshop on the In- Grade Testing of Structural Lumber, Kretschmann, D., Evans, J., & Brown, L. (1999). FPL-RP-576: Monitoring of Visually Graded Structural Lumber. Madison, WI: U.S. Forest Products Laboratory. Madsen, B., & Stinson, T. (1982). In-Grade Testing of Timber 4 or more inches in thickness. Vancouver: Department of Civil Engineering. Univeristy of British Columbia. Southern Pine Inspection Bureau. (2002). Standard Grading Rules for Southern Pine Lumber. Pensacola: Southern Pine Inpection Bureau. 21

23 Table 1. Bending Test Cell Summary Data All Data Given at 15% MC Test Spans vary with size MOR given in psi Select Structural Unclassified Data 2x4 2x8 2x10 Sample Size Median MOR Mean MOR Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit No.2 Unclassified Data 2x4 2x8 2x10 Sample Size Median MOR Mean MOR Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit

24 Table 2. Tension Test Cell Summary Data All Data Given at 15% MC Tension Gauge Length is 96 UTS given in psi Select Structural Unclassified Data 2x4 2x8 2x10 1 Sample Size Median UTS Mean UTS Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit No.2 Unclassified Data 2x4 2x8 2x10 1 Sample Size Median UTS Mean UTS Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit x10 SS and #2 already reduced for GQI check 23

25 Table 3. Stiffness Test Cell Summary Data All Data Given at 15% MC 21:1 l/d ratio MOE given in million psi Select Structural Unclassified Data 2x4 2x8 2x10 1 Sample Size Median MOE Mean MOE Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit No.2 Unclassified Data 2x4 2x8 2x10 1 Sample Size Median MOE Mean MOE Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit x10 SS and #2 already reduced for GQI check 24

26 Table 4. Compression Test Cell Summary Data All Data Given at 15% MC No Length Effect UCS given in psi Select Structural Unclassified Data 2x4 2x8 1 2x10 1 Sample Size Median UCS Mean UCS Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit No.2 Unclassified Data 2x4 2x8 2x10 Sample Size Median UCS Mean UCS Standard Deviation th Percentile Pt. Est th Percentile Tol. Lim Upper 75% Conf. Limit Lower 75% Conf. Limit SS 2x8 and 2x10 already reduced for GQI check 25

27 Table 5. Summarized Test Data All Data Given at 15% MC Converted to Characteristic Size: 2x8, 144 MOE given in million psi MOR, UTS, UCS given in psi Select Structural Unclassified Data Dense Data NonDense Data SS DSS SSN Sample Size (MOR) MOR 5% Tol. Limit Factor Sample Size (UTS) UTS 5% Tol. Limit Factor Sample Size (MOE) Mean MOE Factor Median MOE MOE 5% Tol. Lim Sample Size (UCS) UCS 5% Tol. Limit Factor No.2 Unclassified Data Dense Data NonDense Data No.2 No.2D No.2N Sample Size (MOR) MOR 5% Tol. Limit Factor Sample Size (UTS) UTS 5% Tol. Limit Factor Sample Size (MOE) Mean MOE Factor Median MOE MOE 5% Tol. Lim Sample Size (UCS) UCS 5% Tol. Limit Factor

28 Grade SS No.2 Table 6. Test Cell Data Checks for MOR All Data Given at 15%MC Predicted Values converted to original test spans MOR given in psi Size Sample UCL MOR Char. Predicted Size O.S. UCL Value MOR 2x x x x x x Char. Value Grade SS No.2 Table 7. Test Cell Data Checks for UTS All Data Given at 15%MC Gauge Length = 96 UTS given in psi Size Sample UCL UTS Char. Predicted Size O.S. UCL Value UTS 2x x x x x x Char. Value Grade SS No.2 Table 8. Test Cell Data Checks for UCS All Data Given at 15%MC No Length Effect UCS given in psi Size Sample UCL UCS Char. Predicted Size O.S. UCL Value UCS 2x x x x x x Char. Value

29 Table 9. Characteristic Values - Adjusted for Grade All Values Given at 15%MC Characteristic Size 2x8, 144 MOE given in million psi MOR, UTS, UCS given in psi Grade Bending GQI Mean MOE Median MOE 5% TL MOE 5% TL MOR 5% TL UTS Compression GQI 5% TL UCS 1 SS # # # Stud Construction Standard Utility SS and #2 UCS reduced by 5% for test method before application of grade model 28

30 Table 10. Property Estimates All Data Given at 15% MC Length at Characteristic Size MOE given in million psi MOR, UTS, UCS given in psi Size 2x4 2x6 2x8 2x10 2x12 Grade Tolerance Limits MOR UTS UCS MOE Mean MOE Median MOE SS # # #3, Stud Construction Standard Utility SS # # #3, Stud SS # # #3, Stud SS # # #3, Stud SS # # #3, Stud

31 Table 11. Section 12.6 Checks for MOR All Data Given at 15%MC Predicted Values converted to original test spans MOR given in psi Grade Size Sample Size Pt. Est. MOR Char. Predicted O.S. Pt. Est Value MOR New MOR 2x SS 2x Ok 2x Ok 2x No.2 2x Ok 2x Ok Table 12. Section 12.6 Checks for UTS All Data Given at 15%MC Gauge Length = 96 UTS given in psi Grade Size Sample Size Pt. Est. UTS Predicted Char. Value O.S. Pt. Est. UTS New UTS 2x w/in 100 psi SS 2x Ok 2x Ok 2x w/in 5% No.2 2x Ok 2x Ok Table 13. Section 12.6 Checks for UCS All Data Given at 15%MC No Length Effect UCS given in psi Grade Size Sample Size Pt. Est UCS Predicted Char. Value O.S. Pt. Est UCS New UCS 2x Ok SS 2x w/in 100 psi 2x Ok 2x Ok No.2 2x w/in 100 psi 2x Ok 30

32 Table 14. Southern Pine Design Values Size Grade F b F t F v F c F c E 2x4 2x6 2x8 DSS SS SSN #1D # #1N #2D # #2N #3, Stud Construction Standard Utility DSS SS SSN #1D # #1N #2D # #2N #3, Stud DSS SS SSN #1D # #1N #2D # #2N #3, Stud