1、Designation: D 2915 03Standard Practice forEvaluating Allowable Properties for Grades of StructuralLumber1This standard is issued under the fixed designation D 2915; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last
2、revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe mechanical properties of structural lumber depend upon natural growth characteristics andmanufacturing practices. Seve
3、ral procedures can be used to sort lumber into property classes or stressgrades, the most widely used being the visual methods outlined in Practice D 245. With each, amodulus of elasticity and a set of from one to five allowable stresses may be associated with eachstress grade. The allowable stresse
4、s are extreme fiber stress in bending, tension parallel to the grain,compression parallel to the grain, shear, and compression perpendicular to the grain. This test methodfor evaluation of the properties of structural lumber defines an allowable property as the value of theproperty that would normal
5、ly be published with the grade description.This practice is useful in assessing the appropriateness of the assigned properties and for checkingthe effectiveness of grading procedures.For situations where a manufactured product is sampled repeatedly or lot sizes are small, alternativetest methods as
6、described in Ref (1)2may be more applicable.1. Scope1.1 This practice covers sampling and analysis proceduresfor the investigation of specified populations of stress-gradedstructural lumber. Depending on the interest of the user, thepopulation from which samples are taken may range from thelumber fr
7、om a specific mill to all the lumber produced in aparticular grade from a particular geographic area, during somespecified interval of time. This practice generally assumes thatthe population is sufficiently large so that, for samplingpurposes, it may be considered infinite. Where this assumptionis
8、inadequate, that is, the population is assumed finite, many ofthe provisions of this practice may be employed but thesampling and analysis procedure must be designed to reflect afinite population. The statistical techniques embodied in thispractice provide procedures to summarize data so that logica
9、ljudgments can be made. This practice does not specify theaction to be taken after the results have been analyzed. Theaction to be taken depends on the particular requirements of theuser of the product.1.2 The values stated in inch-pound units are to be regardedas the standard.1.3 This standard does
10、 not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Stand
11、ards:D 198 Test Methods of Static Tests of Timber in StructuralSizes3D 245 Practice for Establishing Structural Grades and Re-lated Allowable Properties for Visually Graded Lumber3D 1990 Practice for Establishing Allowable Properties forVisually-Graded Dimension Lumber from In-Grade Testsof Full-Siz
12、e Specimens3E 105 Practice for Probability Sampling of Materials43. Statistical Methodology3.1 Two general analysis procedures are described underthis practice, parametric and nonparametric. The parametricapproach assumes a known distribution of the underlyingpopulation, an assumption which, if inco
13、rrect, may lead to1This practice is under the jurisdiction of ASTM Committee D07 on Wood andis the direct responsibility of Subcommittee D07.02 on Lumber and EngineeredWood Products.Current edition approved April 10, 2003. Published June 2003. Originallyapproved in 1970 as D 2915 70 T. Last previous
14、 edition approved in 2002 asD 2915 02.2The boldface numbers in parentheses refer to the list of references at the end ofthis practice.3Annual Book of ASTM Standards, Vol 04.10.4Annual Book of ASTM Standards, Vol 14.02.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohock
15、en, PA 19428-2959, United States.inaccurate results. Therefore, if a parametric approach is used,appropriate statistical tests shall be employed to substantiatethis choice along with measures of test adequacy (2, 3, 4, 5, 6,7). Alternatively a nonparametric approach requires fewerassumptions, and is
16、 generally more conservative than a para-metric procedure.3.2 Population:3.2.1 It is imperative that the population to be evaluated beclearly defined, as inferences made pertain only to that popu-lation. In order to define the population, it may be necessary tospecify ( 1) grade name and description
17、, (2) geographical areaover which sampling will take place (nation, state, mill, etc.),(3) species or species group, (4) time span for sampling (adays production, a month, a year, etc.), (5) lumber size, and(6) moisture content.3.2.2 Where possible, the sampling program should con-sider the location
18、 and type of log source from which the piecesoriginated, including types of processing methods or marketingpractices with respect to any influence they may have on therepresentative nature of the sample. Samples may be collectedfrom stock at mills, centers of distribution, at points of end useor dir
19、ectly from current production at the grading chains ofmanufacturing facilities.3.3 Sampling Procedure:3.3.1 Random Sampling The sampling unit is commonlythe individual piece of lumber. When this is not the case, see3.3.3. The sampling shall assure random selection of samplingunits from the populatio
20、n described in 3.2 with all members ofthe population sharing equal probability of selection. Theprinciples of Practice E 105 shall be maintained. When sam-pling current production, refer to Practice E 105 for a recom-mended sampling procedure (see Appendix X3 of this practicefor an example of this p
21、rocedure). If samples are selected frominventory, random number tables may be used to determinewhich pieces will be taken for the sample.3.3.2 Sampling with Unequal ProbabilitiesUnder somecircumstances, it may be advisable to sample with unequal butknown probabilities. Where this is done, the genera
22、l principlesof Practice E 105 shall be maintained, and the samplingmethod shall be completely reported.3.3.3 Sequential SamplingWhen trying to characterizehow a certain population of lumber may perform in a structure,it may be deemed more appropriate to choose a sampling unit,such as a package, that
23、 is more representative of how thelumber will be selected for use. Such a composite samplingunit might consist of a sequential series of pieces chosen topermit estimation of the properties of the unit as well as thepieces. Where this is done, the principles in 3.3.1 and 3.3.2apply to these composite
24、 sampling units and the samplingmethod shall be completely reported.3.4 Sample Size:3.4.1 Selection of a sample size depends upon the propertyor properties to be estimated, the actual variation in propertiesoccurring in the population, and the precision with which theproperty is to be estimated. For
25、 the five allowable stresses andthe modulus of elasticity various percentiles of the populationmay be estimated. For all properties, nonparametric or para-metric techniques are applicable. Commonly the mean modu-lus of elasticity and the mean compression perpendicular to thegrain stress for the grad
26、e are estimated. For the four otherallowable stresses, a near-minimum property is generally theobjective.3.4.2 Determine sample size sufficient for estimating themean by a two-stage method, with the use of the followingequation. This equation assumes the data is normally distrib-uted and the mean is
27、 to be estimated to within 5 % withspecified confidence:n 5 ts/0.05 X!25St0.05CVD2(1)where:n = sample size,s = standard deviation of specimen values,X= specimen mean value,CV = coefficient of variation, s/ X,0.05 = precision of estimate, andt = value of the t statistic from Table 1.Often the values
28、of s, X, and t or CV and t are not knownbefore the testing program begins. However, s and X,orCV,may be approximated by using the results of some other testprogram, or they may simply be guessed (see example, Note1).NOTE 1An example of initial sample size calculation is:Sampling a grade of lumber fo
29、r modulus of elasticity (E). Assuming a95 % confidence level, the t statistic can be approximated by 2.s = 300 000 psi (2067 MPa)X= assigned E of the grade = 1 800 000 psi (12 402 MPa)CV = (300 000/1 800 000) = 0.167t =2n =S20.053 0.167D25 44.622 45 pieces!Calculate the sample mean and standard devi
30、ation and use them toestimate a new sample size from Eq 1, where the value of t is taken fromTable 1. If the second sample size exceeds the first, the first sample wasinsufficient; obtain and test the additional specimens.NOTE 2More details of this two-stage method are given in Ref (8).3.4.3 To dete
31、rmine sample size based on a tolerance limit(TL), the desired content (C) (Note 3) and associated confi-dence level must be selected. The choice of a specified contentand confidence is dependent upon the end-use of the material,economic considerations, current design practices, code re-quirements, e
32、tc. For example, a content of 95 % and aconfidence level of 75 % may be appropriate for a specificproperty of structural lumber. Different confidence levels maybe suitable for different products or specific end uses. Appro-priate content and confidence levels shall be selected before thesampling pla
33、n is designed.NOTE 3The content, C, is an estimate of the proportion of thepopulation that lies above the tolerance limit. For example, a tolerancelimit with a content of 95 % describes a level at which 95 % of thepopulation lies above the tolerance limit. The confidence with which thisinference is
34、to be made is a separate statement.3.4.3.1 To determine the sample size for near-minimumproperties, the nonparametric tolerance limit concept of Ref (8)D2915032may be used (Table 2). This will provide the sample sizesuitable for several options in subsequent near-minimumanalyses. Although the freque
35、ncy with which the tolerancelimit will fall above (or below) the population value, corre-sponding to the required content, is controlled by the confi-dence level selected, the larger the sample size the more likelythe tolerance limit will be close to the population value. It is,therefore, desirable
36、to select a sample size as large as possiblecommensurate with the cost of sampling and testing (see also4.7).3.4.3.2 If a parametric approach is used, then a tolerancelimit with stated content and confidence can be obtained forany sample size; however, the limitation expressed in 3.4.3.1applies. Tha
37、t is, although the frequency that the tolerance limitfalls above (or below) the population value, corresponding tothe required content is controlled, the probability that thetolerance limit will be close to the population value depends onthe sample size. For example, if normality is assumed, thepara
38、metric tolerance limit (PTL) will be of the form PTL = X Ks, (see Ref (8), and the standard error (SE) of this statisticmay be approximated by the following equation:SE 5 s1n1K22n 2 1!(2)where:s = standard deviation of specimen values,n = sample size, andK = confidence level factor.The sample size,
39、n, may be chosen to make this quantitysufficiently small for the intended end use of the material (Note4).NOTE 4An example of sample size calculation where the purpose isto estimate a near minimum property is shown in the following calcula-tion:Estimate the sample size, n, for a compression parallel
40、 strength test inwhich normality will be assumed. A CV of 22 % and a mean C11of 4600psi are assumed based on other tests. The target PTL of the lumber gradeis 2700 psi. The PTL is to be estimated with a content of 95 % (5 % PTL)and a confidence of 75 %.CV = 0.22X= 4600 psi (31.7 MPa)s = (0.22) (4600
41、) = 1012 psi (7.0 MPa)K=(X PTL)/s = 1.877From Table 3:K = 1.869 for n =30Therefore n 30 specimens.SE 5 101213011.8772230 2 1!(3)5 310.5 psi 2.1 MPa!Consequently, although 30 specimens is sufficient to estimate the 5 %PTL with 75 % confidence, the standard error (approximately 12 % of thePTL) illustr
42、ates that, with this size sample, the PTL estimated by test maynot be as close to the true population fifth percentile as desired. A largern may be desirable.TABLE 1 Values of the t Statistics Used in CalculatingConfidence IntervalsAdfn 1CI =75% CI =95% CI =99%1 2.414 12.706 63.6572 1.604 4.303 9.92
43、53 1.423 3.182 5.8414 1.344 2.776 4.6045 1.301 2.571 4.0326 1.273 2.447 3.7077 1.254 2.365 3.4998 1.240 2.306 3.3559 1.230 2.262 3.25010 1.221 2.228 3.16911 1.214 2.201 3.10612 1.209 2.179 3.05513 1.204 2.160 3.01214 1.200 2.145 2.97715 1.197 2.131 2.94716 1.194 2.120 2.92117 1.191 2.110 2.89818 1.1
44、89 2.101 2.87819 1.187 2.093 2.86120 1.185 2.086 2.84521 1.183 2.080 2.83122 1.182 2.074 2.89123 1.180 2.069 2.80724 1.179 2.064 2.79725 1.178 2.060 2.78726 1.177 2.056 2.77927 1.176 2.052 2.77128 1.175 2.048 2.76329 1.174 2.045 2.75630 1.173 2.042 2.75040 1.167 2.021 2.70460 1.162 2.000 2.660120 1.
45、156 1.980 2.617 1.150 1.960 2.576AAdapted from Ref (8). For calculating other confidence levels, see Ref (8).TABLE 2 Sample Size and Order Statistic for Estimating the 5 %Nonparametric Tolerance Limit, NTLA75 % Confidence 95 % Confidence 99 % confidenceSampleSizeBOrderStatisticCSampleSizeOrderStatis
46、ticSampleSizeOrderStatistic28 1 59 1 90 153 2 93 2 130 278 3 124 3 165 3102 4 153 4 198 4125 5 181 5 229 5148 6 208 6 259 6170 7 234 7 288 7193 8 260 8 316 8215 9 286 9 344 9237 10 311 10 371 10259 11 336 11 398 11281 12 361 12 425 12303 13 386 13 451 13325 14 410 14 478 14347 15 434 15 504 15455 20
47、 554 20 631 20562 25 671 25 755 25668 30 786 30 877 30879 40 1013 40 1115 401089 50 1237 50 1349 50AAdapted from Ref (12). For other tolerance limits or confidence levels, see Ref(12) or (8).BWhere the sample size falls between two order statistics (for example, 27 and28 for the first order statisti
48、c at 75 confidence), the larger of the two is shown in thetable, and the confidence is greater than the nominal value.CThe rank of the ordered observations, beginning with the smallest.D2915033TABLE 3 K Factors for One-Sided Tolerance Limits for Normal DistributionsA75 % Confidence (g = 0.25) 95 % C
49、onfidence (g = 0.05) 99 % Confidence (g = 0.01)1 p 0.75 0.90 0.95 0.99 0.75 0.90 0.95 0.99 0.75 0.90 0.95 0.99n3 1.464 2.501 3.152 4.397 3.805 6.156 7.657 10.555 8.726 13.997 17.374 23.9004 1.255 2.134 2.681 3.726 2.617 4.162 5.145 7.044 4.714 7.381 9.085 12.3895 1.151 1.962 2.464 3.422 2.149 3.407 4.203 5.742 3.453 5.362 6.580 8.9416 1.087 1.859 2.336 3.244 1.895 3.007 3.708 5.063 2.847 4.412 5.407 7.3367 1.043 1.790 2.251 3.127 1.732 2.756 3.400 4.643 2.490 3.860 4.729 6.4138 1.010 1.740 2.189 3.042 1.617 2.582 3.188 4.355 2.253 3.498 4.286 5.8139 0
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