# ASTM D7290-06 (Reapproved 2017)

Designation: D7290 − 06 (Reapproved 2017)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 the 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 computingcharacteristic 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 population.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 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.1.3 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards: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 Resistance ofWood-Based Materials and Structural Connections forLoad and Resistance Factor DesignD5574 Test Methods for Establishing Allowable MechanicalProperties 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 Statistics2.2 Other Document:MIL-Handbook-17 Polymer Matrix Composites, Volume 1,Revision F33. Terminology3.1 Definitions—Terminology D3878 defines terms relatingto high-modulus fibers and their composites. TerminologyD883 defines terms relating to plastics. Terminology E6 definesterms relating to mechanical 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 value—a statistically-based materialproperty representing 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 Discussion—The 80 % confidence bound and 5th-percentile levels were selected so that composite materialcharacteristic 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 Discussion—The term “characteristic value” isanalogous to the term “basis value” used in the aerospaceindustry where A- and B-basis values are defined as the 95 %1This practice is under the jurisdiction of ASTM Committee D30 on CompositeMaterials and is the direct responsibility of Subcommittee D30.10 on Compositesfor Civil Structures.Current edition approved Aug. 1, 2017. Published September 2017. Originallyapproved in 2006. Last previous edition approved in 2011 as D7290–06(2011). DOI:10.1520/D7290-06R17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s 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 standard.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1lower confidence bound on the lower 1 % and 10 % values ofa population, respectively.3.2.2 data confidence factor, Ω—a factor that is used toadjust the sample nominal value for uncertainty associated withfinite sample size.3.2.3 nominal value—the 5th percentile value of the datarepresented by a probability density function.3.2.4 outlier—an outlying observation, or “outlier,” is onethat deviates significantly from other observations in thesample in which it occurs.4. Significance and Use4.1 This practice covers the procedures 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 codes 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 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 1—Section 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 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 samples 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 determined 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 allowable 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 Deviation—Calculate the averagevalue and standard deviation for the measured material prop-erty:x¯ 5S(i51nxiDn(1)sn215 ŒS(i51n~xi2 x¯!2D/~n 2 1! (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 Observations—The 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 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 2—Practice E178 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 3—An 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 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 point 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 Samples—For a sample ofsize n, arrange the data 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?xi2 x¯?sn21D(3)6.2.1.1 Calculate the critical MNR value, CV, based on a5 % significance level using the following approximation:CV S2 285=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 denoteda 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 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 4—Eq 4 is an approximate nonlinear regression of critical valuespresented in the MIL-Handbook 17 with a correlation coefficient of 0.998.6.3 Material Property Distribution—For this standardpractice, the material property value probability distributionfunction is assumed to follow the two-parameter Weibulldistribution (Ref 2) expressed in the form:f~x! 5SβαDSxαDβ21expF2SxαDβG(5)D7290 − 06 (2017)2where:β = the shape parameter and is the scale parameter, andα = the scale parameter.NOTE 5—The 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, βˆ,oftheWeibull shape parameter β by numerically solving the equa-tion:(i51nxiβˆln~xi!(i51nxiβˆ21βˆ21n(i51nln~xi! 5 0 (6)6.4.2 Calculate the maximum likelihood estimate, αˆ, of theWeibull scale parameter α using:αˆ 5S(i51nxiβˆnD1βˆ(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 5ŒΓS112βˆD2 Γ2S111βˆDΓS111βˆD(8)where:Γ = the gamma function.6.5 Nominal Value—Calculate the nominal value of thesample data as the 5th-percentile of the two-parameter Weibulldistribution, using:x0.055 αˆ @0.0513#1βˆ (9)6.6 Characteristic Value—Calculate the characteristic valuefor the material property as the 80 % confidence bound on the5th-percentile value using:xchar5 Ω x0.05(10)In which the data confidence factor, Ω, 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 factors 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 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, Ω, and7.1.6 The sample characteristic value.TABLE 1 Data Confidence Factor, Ω, 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 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 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 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 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 (βˆ 24.95), the values for COV = 0.05 shall be used.D7290 − 06 (2017)3REFERENCES(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., “StatisticalCharacterization of Fiber-Reinforced Polymer Composite MaterialProperties for Structural Design,” ASCE Journal of StructuralEngineering, August, 2006, Vol 132 , No. 8, pp. 1320-1327.(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 2: Determination of Material PropertyCharacteristic Values of Fiber-Reinforced Polymeric Composites,prepared for the Federal HighwayAdministration (FHWA), StructuralEngineering, Mechan