1、Designation: D 7290 06Standard Practice forEvaluating Material Property Characteristic Values forPolymeric Composites for Civil Engineering StructuralApplications1This standard is issued under the fixed designation D 7290; the number immediately following the designation indicates the year oforigina
2、l adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the procedures for computingcharacteristic v
3、alues of material properties of polymeric com-posite materials intended for use in civil engineering structuralapplications. The characteristic value is a statistically-basedmaterial property representing the 80 % lower confidencebound on the 5th-percentile value of a specified population.Characteri
4、stic values determined using this standard practicecan be used to calculate structural member resistance values indesign codes for composite civil engineering structures and forestablishing limits upon which qualification and acceptancecriteria can be based.1.2 This standard does not purport to addr
5、ess 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 Standards:2D 883 Terminol
6、ogy Relating to PlasticsD 3878 Terminology for Composite MaterialsD 5055 Specification for Establishing and MonitoringStructural Capacities of Prefabricated Wood I-JoistsD 5457 Specification for Computing Reference Resistanceof Wood-Based Materials and Structural Connections forLoad and Resistance F
7、actor DesignD 5574 Test Methods for Establishing Allowable Mechani-cal Properties of Wood-Bonding Adhesives for Design ofStructural JointsE6 Terminology Relating to Methods of Mechanical Test-ingE 178 Practice for Dealing With Outlying ObservationsE 456 Terminology Relating to Quality and Statistics
8、2.2 Other Document:MIL-Handbook-17 Polymer Matrix Composites, Volume 1,Revision F33. Terminology3.1 DefinitionsTerminology D 3878 defines terms relatingto high-modulus fibers and their composites. TerminologyD 883 defines terms relating to plastics. Terminology E6defines terms relating to mechanical
9、 testing. TerminologyE 456 defines terms relating to statistics. In the event of aconflict between terms, Terminology D 3878 shall have prece-dence over the other documents.3.2 Definitions of Terms Specific to This Standard:3.2.1 characteristic valuea statistically-based materialproperty representin
10、g the 80 % lower confidence bound on the5th-percentile value of a specified population. The character-istic value accounts for statistical uncertainty due to a finitesample size.3.2.1.1 DiscussionThe 80 % confidence bound and 5th-percentile levels were selected so that composite materialcharacterist
11、ic values will produce resistance factors for Loadand Resistance Factor Design similar to those for other civilengineering materials (see Refs 1 and 2).43.2.1.2 DiscussionThe term “characteristic value” isanalogous to the term “basis value” used in the aerospaceindustry where A- and B-basis values a
12、re defined as the 95 %lower confidence bound on the lower 1 % and 10 % values ofa population, respectively.3.2.2 data confidence factor, Va factor that is used toadjust the sample nominal value for uncertainty associated withfinite sample size.3.2.3 nominal valuethe 5th percentile value of the datar
13、epresented by a probability density function.3.2.4 outlieran outlying observation, or “outlier,” is onethat deviates significantly from other observations in thesample in which it occurs.1This practice is under the jurisdiction ofASTM Committee D30 on Compositesand is the direct responsibility of Su
14、bcommittee D30.05 on Structural Test Methods.Current edition approved Sept. 1, 2006. Published October 2006.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the stan
15、dards Document Summary page onthe ASTM website.3Available from U.S. Government Printing Office Superintendent of Documents,732 N. Capitol St., NW, Mail Stop: SDE, Washington, DC 20401, http:/www.access.gpo.gov.4The boldface numbers in parentheses refer to the list of references at the end ofthis sta
16、ndard.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4. Significance and Use4.1 This practice covers the procedures for computingmaterial property characteristic values for polymeric compositematerials intended for use in civil engi
17、neering structuralapplications. A characteristic value represents a statisticallower bound on the material property structural memberresistance factors for civil engineering design codes for com-posite structures.4.2 This practice may be used to obtain characteristic valuesfor stiffness and strength
18、 properties of composite materialsobtained from measurements using applicable test methods.5. Sampling5.1 Samples selected for analysis shall be representative ofthe material property population for which the characteristicvalues are to be calculated.5.2 The minimum number of samples shall be specif
19、ied indesign codes that reference this standard.NOTE 1Section 5.3.1 of the building code requirements for structuralconcrete (ACI 318-05) requires at least 30 samples to determine thestandard deviation of concrete compressive strength for a new batch plantbut allows a reduction to a minimum of 15 sa
20、mples, provided that amodification factor is used to increase the standard deviation if less than30 samples are used (Ref 3). For wood, Specification D 5457 requires aminimum of 30 samples for computing the reference resistance of woodbased materials and structural connections for Load and Resistanc
21、e FactorDesign, and states that extreme care must be taken during sampling toensure a representative sample for sample sizes less than 60. The bendingcapacity of wood I-joists can be determined either by analysis orempirically by testing (Specification D 5055). If the capacity is deter-mined by anal
22、ysis, a minimum of ten confirming tests is required at eachof the extremes of flange size, allowable stress, and joist depth. TestMethods D 5574 requires 60 samples for establishing allowable tensileand shear stresses of wood-bonding adhesives in structural joints. Fifty-nine of the samples are actu
23、ally tested, with the last held in reserve.6. Procedure6.1 Mean and Standard DeviationCalculate the averagevalue and standard deviation for the measured material prop-erty:x 5S(i51nxiDn(1)sn215S(i51nSxi xD2D/Sn 1D(2)where:x = sample mean (average),sn-1= sample standard deviation,n = number of specim
24、ens, andxi= measured or derived property.6.2 Detection of Outlying ObservationsThe data beinganalyzed shall be screened for outliers using the MaximumNormed Residual (MNR) method. A value is declared to be anoutlier by this method if it has an absolute deviation from thesample mean which, when compa
25、red to the sample standarddeviation, is too large to be due to chance. This method detectsone outlier at a time; hence the significance level pertains to asingle decision.NOTE 2Practice E 178 provides several methods for statisticallyanalyzing a dataset for outliers. The MNR method is used here beca
26、use itis a simple method that is unlikely to be miscalculated, misinterpreted ormisapplied.NOTE 3An outlying observation may be an extreme manifestation ofthe random variability of the material property value. For such a case, thevalue should be retained and treated as any other observation in thesa
27、mple. However, the outlying observation may be the result of a grossdeviation from prescribed experimental procedure or an error in calculat-ing or recording the numerical value of the data point in question. Whenthe experimentalist can document a gross deviation from the prescribedexperimental proc
28、edure, the outlying observation may be discarded,unless the observation can be corrected in a rational manner.6.2.1 Outlier Criteria for Single SamplesFor a sample ofsize n, arrange the data values x1, x2, x3, .xn in order ofincreasing magnitude with xnbeing the largest value. Calculatethe MNR stati
29、stic as the maximum absolute deviation from thesample mean divided by the sample standard deviation:MNR 5 maxS?xi x?sn21D (3)6.2.1.1 Calculate the critical MNR value, CV, based on a5 % significance level using the following approximation:CV S285=nD2(4)6.2.1.2 There are no outliers in the sample of o
30、bservations ifthe calculated MNR statistic is smaller than the critical valueCV, that is MNR # CV.IftheMNR statistic is found to begreater than the critical value, then the MNR shall be denoteda possible outlier. The possible outlier shall be investigated todetermine whether there is an assignable c
31、ause for removing itfrom the data set. If no cause can be found, it shall be retainedin the data set. If an outlier is clearly erroneous, it can beremoved after careful consideration provided that the subjec-tive decision to remove the value is documented as part of thedata analysis report. If an ou
32、tlier is removed from the dataset,the sample mean and standard deviation shall be recalculated.This process shall be repeated until the sample of observationsbecomes outlier-free.NOTE 4Eq 4 is an approximate nonlinear regression of critical valuespresented in the MIL-Handbook 17 with a correlation c
33、oefficient of 0.998.6.3 Material Property DistributionFor this standard prac-tice, the material property value probability distribution func-tion is assumed to follow the two-parameter Weibull distribu-tion (Ref 2) expressed in the form:fx! 5SbaDSxaDb21expFSxaDbG(5)where:b = the shape parameter and
34、is the scale parameter, anda = the scale parameter.NOTE 5The basis for selecting the Weibull distribution is given inRefs 2 and 4.6.4 Maximum Likelihood Parameter Estimation:6.4.1 Calculate the maximum likelihood estimate, b,oftheWeibull shape parameter b by numerically solving the equa-tion:D729006
35、2(i51nxiblnxi!(i51nxib1b1n(i51nlnxi! 5 0 (6)6.4.2 Calculate the maximum likelihood estimate, a, of theWeibull scale parameter a using:a51(i51nxibn21b(7)where:n = the number of data values used in the analysis.6.4.3 Calculate the coefficient of variation of the propertyfrom the equation:COV 5GS1 12bD
36、 G2S1 11bDGS1 11bD(8)where:G = the gamma function.6.5 Nominal ValueCalculate the nominal value of thesample data as the 5th-percentile of the two-parameter Weibulldistribution, using:x0.055a0.0513#1b (9)6.6 Characteristic ValueCalculate the characteristic valuefor the material property as the 80 % c
37、onfidence bound on the5th-percentile value using:xchar5Vx0.05(10)In which the data confidence factor, V, accounts for theuncertainty associated with a finite sample size. This factor isa function of coefficient of variation, sample size, and referencepercentile. Table 1 provides data confidence fact
38、ors appropriatefor lower fifth-percentile estimates.7. Report7.1 Report the following information, or references pointingto other documentation containing this information, to themaximum extent applicable:7.1.1 The sample size and individual data values,7.1.2 Any data values which were determined to
39、 be outliersand excluded from the data analysis, along with the rationalefor excluding the outlier,7.1.3 The sample nominal value and coefficient of variation,7.1.4 The maximum likelihood estimates of the Weibullshape and scale factors for the sample,7.1.5 The data confidence factor, V, and7.1.6 The
40、 sample characteristic value.TABLE 1 Data Confidence Factor, V, on the 5th-Percentile Value for a Weibull Distribution with 80 % ConfidenceA(Refs 3 and 4)COVn 0.05 0.10 0.15 0.20 0.25 0.30 0.40 0.5010 0.950 0.899 0.849 0.800 0.752 0.706 0.619 0.54111 0.953 0.906 0.860 0.814 0.769 0.725 0.642 0.56712
41、 0.956 0.913 0.869 0.826 0.783 0.741 0.662 0.58913 0.959 0.918 0.876 0.835 0.795 0.755 0.679 0.60914 0.961 0.922 0.883 0.844 0.805 0.767 0.694 0.62615 0.963 0.926 0.889 0.851 0.814 0.778 0.707 0.64116 0.965 0.929 0.894 0.858 0.822 0.787 0.719 0.65518 0.968 0.935 0.902 0.869 0.836 0.803 0.739 0.67820
42、 0.970 0.940 0.909 0.878 0.847 0.816 0.755 0.69822 0.972 0.944 0.914 0.885 0.856 0.827 0.769 0.71424 0.974 0.947 0.919 0.891 0.864 0.836 0.781 0.72826 0.975 0.949 0.923 0.897 0.870 0.844 0.791 0.74128 0.976 0.952 0.927 0.902 0.876 0.851 0.800 0.75230 0.977 0.954 0.930 0.906 0.882 0.857 0.809 0.76132
43、 0.978 0.956 0.933 0.910 0.886 0.863 0.816 0.77034 0.979 0.957 0.935 0.913 0.890 0.868 0.822 0.77836 0.980 0.959 0.938 0.916 0.894 0.872 0.828 0.78538 0.980 0.960 0.940 0.919 0.897 0.876 0.833 0.79140 0.981 0.962 0.942 0.921 0.901 0.880 0.838 0.79742 0.982 0.963 0.943 0.924 0.904 0.883 0.843 0.80344
44、 0.982 0.964 0.945 0.926 0.906 0.886 0.847 0.80846 0.983 0.965 0.946 0.928 0.909 0.889 0.851 0.81348 0.983 0.966 0.948 0.929 0.911 0.892 0.854 0.81750 or more 0.984 0.967 0.949 0.931 0.913 0.895 0.858 0.821ALinear interpolation is permitted. For COV values below 0.05 (b 24.95), the values for COV =
45、0.05 shall be used.D7290063REFERENCES(1) Ellingwood, B. R., “Toward Load and Resistance Factor Design forFiber-Reinforced Polymer Composite Structures,” ASCE Journal ofStructural Engineering, Vol 129, No. 4, 2003, pp. 449-458.(2) Zureick, A., Bennett, R. M., and Ellingwood, B. R., “StatisticalCharac
46、terization of Fiber-Reinforced Polymer Composite MaterialProperties for Structural Design,” ASCE Journal of Structural Engi-neering, August, 2006, Vol 132, No. 8, pp. 1320-1327.(3) ACI 318-05, “Building Code Requirements for Structural Concreteand Commentary,”American Concrete Institute, Farmington
47、Hills, MI,2005.(4) Zureick, A., Bennett, R. M., and Alqam, M., “Acceptance TestSpecifications and Guidelines for Fiber-Reinforced Polymeric BridgeDecks,” Final Report, Volume 2: Determination of Material PropertyCharacteristic Values of Fiber-Reinforced Polymeric Composites,prepared for the Federal
48、Highway Administration (FHWA), StructuralEngineering, Mechanics, and Materials, Research Report No. 03-6,School of Civil and Environmental Engineering, Georgia Institute ofTechnology, http:/www.ce.gatech.edu/groups/struct/reports/.ASTM International takes no position respecting the validity of any p
49、atent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand shou
