1、Designation: D7290 06 (Reapproved 2011)Standard Practice forEvaluating Material Property Characteristic Values forPolymeric Composites for Civil Engineering StructuralApplications1This standard is issued under the fixed designation D7290; the number immediately following the designation indicates th
2、e year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the procedures for computingc
3、haracteristic values 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 popula
4、tion.Characteristic 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
5、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 Standards:
6、2D883 Terminology Relating to PlasticsD3878 Terminology for Composite MaterialsD5055 Specification for Establishing and Monitoring Struc-tural Capacities of Prefabricated Wood I-JoistsD5457 Specification for Computing Reference Resistanceof Wood-Based Materials and Structural Connections forLoad and
7、 Resistance Factor DesignD5574 Test Methods for Establishing Allowable Mechani-cal Properties of Wood-Bonding Adhesives for Design ofStructural JointsE6 Terminology Relating to Methods of Mechanical TestingE178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and S
8、tatistics2.2 Other Document:MIL-Handbook-17 Polymer Matrix Composites, Volume 1,Revision F33. Terminology3.1 DefinitionsTerminology D3878 defines terms relatingto high-modulus fibers and their composites. TerminologyD883 defines terms relating to plastics. Terminology E6 definesterms relating to mec
9、hanical testing. Terminology E456 definesterms relating to statistics. In the event of a conflict betweenterms, Terminology D3878 shall have precedence over theother documents.3.2 Definitions of Terms Specific to This Standard:3.2.1 characteristic valuea statistically-based materialproperty represen
10、ting 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 materialcharacter
11、istic 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 value
12、s are 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 da
13、tarepresented 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 of ASTM Committee D30 on CompositeMaterials and is the direct respons
14、ibility of Subcommittee D30.05 on Structural TestMethods.Current edition approved Aug. 1, 2011. Published December 2011. Originallyapproved in 2006. Last previous edition approved in 2006 as D729006. DOI:10.1520/D7290-06R11.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcont
15、act ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards 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,
16、 http:/www.access.gpo.gov.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.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
17、for computingmaterial property characteristic values for polymeric compositematerials intended for use in civil engineering structuralapplications. A characteristic value represents a statisticallower bound on the material property structural memberresistance factors for civil engineering design cod
18、es for com-posite structures.4.2 This practice may be used to obtain characteristic valuesfor stiffness and strength properties of composite materialsobtained from measurements using applicable test methods.5. Sampling5.1 Samples selected for analysis shall be representative ofthe material property
19、population for which the characteristicvalues are to be calculated.5.2 The minimum number of samples shall be specified 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 thes
20、tandard deviation of concrete compressive strength for a new batch plantbut allows a reduction to a minimum of 15 samples, provided that amodification factor is used to increase the standard deviation if less than30 samples are used (Ref 3). For wood, Specification D5457 requires aminimum of 30 samp
21、les for computing the reference resistance of woodbased materials and structural connections for Load and Resistance 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 de
22、termined either by analysis orempirically by testing (Specification D5055). If the capacity is determinedby analysis, a minimum of ten confirming tests is required at each of theextremes of flange size, allowable stress, and joist depth. Test MethodsD5574 requires 60 samples for establishing allowab
23、le tensile and shearstresses of wood-bonding adhesives in structural joints. Fifty-nine of thesamples are actually 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)sn
24、215S(i51nSxi xD2D/Sn 1D(2)where:x = sample mean (average),sn-1= sample standard deviation,n = number of specimens, 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
25、 declared to be anoutlier by this method if it has an absolute deviation from thesample mean which, when compared 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 E178
26、 provides several methods for statisticallyanalyzing a dataset for outliers. The MNR method is used here because 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 materi
27、al property value. For such a case, thevalue should be retained and treated as any other observation in thesample. 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 p
28、oint in question. Whenthe experimentalist can document a gross deviation from the prescribedexperimental procedure, 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
29、values x1, x2, x3, .xn in order ofincreasing magnitude with xnbeing the largest value. Calculatethe MNR statistic 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 % signif
30、icance level using the following approximation:CV S285=nD2(4)6.2.1.2 There are no outliers in the sample of observations 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 denot
31、eda possible outlier. The possible outlier shall be investigated todetermine whether there is an assignable cause 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
32、 that the subjec-tive decision to remove the value is documented as part of thedata analysis report. If an outlier 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 i
33、s an approximate nonlinear regression of critical valuespresented in the MIL-Handbook 17 with a correlation coefficient 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 Weibul
34、l distribu-tion (Ref 2) expressed in the form:fx! 5SbaDSxaDb21expFSxaDbG(5)where:b = the shape parameter and 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 t
35、he maximum likelihood estimate, b,oftheWeibull shape parameter b by numerically solving the equa-tion:D7290 06 (2011)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 va
36、lues used in the analysis.6.4.3 Calculate the coefficient of variation of the propertyfrom the equation:COV 5GS1 12bD 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:
37、x0.055a0.0513#1b (9)6.6 Characteristic ValueCalculate the characteristic valuefor the material property as the 80 % confidence 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
38、isa function of coefficient of variation, sample size, and referencepercentile. Table 1 provides data confidence factors appropriatefor lower fifth-percentile estimates.7. Report7.1 Report the following information, or references pointingto other documentation containing this information, to themaxi
39、mum extent applicable:7.1.1 The sample size and individual data values,7.1.2 Any data values which were determined to 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 likeli
40、hood estimates of the Weibullshape and scale factors for the sample,7.1.5 The data confidence factor, V, and7.1.6 The 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
41、 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 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.
42、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 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.
43、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 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.
44、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 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
45、0.913 0.895 0.858 0.821ALinear interpolation is permitted. For COV values below 0.05 (b 24.95), the values for COV = 0.05 shall be used.D7290 06 (2011)3REFERENCES(1) Ellingwood, B. R., “Toward Load and Resistance Factor Design forFiber-Reinforced Polymer Composite Structures,” ASCE Journal ofStructu
46、ral Engineering, Vol 129, No. 4, 2003, pp. 449-458.(2) Zureick, A., Bennett, R. M., and Ellingwood, B. R., “StatisticalCharacterization of Fiber-Reinforced Polymer Composite MaterialProperties for Structural Design,” ASCE Journal of Structural Engi-neering, August, 2006, Vol 132, No. 8, pp. 1320-132
47、7.(3) ACI 318-05, “Building Code Requirements for Structural Concreteand Commentary,”American Concrete Institute, Farmington Hills, MI,2005.(4) Zureick, A., Bennett, R. M., and Alqam, M., “Acceptance TestSpecifications and Guidelines for Fiber-Reinforced Polymeric BridgeDecks,” Final Report, Volume
48、2: Determination of Material PropertyCharacteristic Values of Fiber-Reinforced Polymeric Composites,prepared for the Federal Highway Administration (FHWA), Struc-tural Engineering, Mechanics, and Materials, Research Report No.03-6, School of Civil and Environmental Engineering, Georgia Insti-tute of
49、 Technology, http:/www.ce.gatech.edu/groups/struct/reports/.ASTM International takes no position respecting the validity of any patent 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 revise
