# ASTM D7199-07 (Reapproved 2012)

Designation: D7199 − 07 (Reapproved 2012)Standard Practice forEstablishing Characteristic Values for Reinforced GluedLaminated Timber (Glulam) Beams Using Mechanics-BasedModels1This standard is issued under the fixed designation D7199; 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 mechanics-based requirements forcalculating characteristic values for the strength and stiffness ofreinforced structural glued laminated timbers (glulam) manu-factured in accordance with applicable provisions of ANSI/AITC A190.1, subjected to quasi-static loadings. It addressesmethods to obtain bending properties parallel to grain, aboutthe x-x axis (Fbxand Ex) for horizontally-laminated reinforcedglulam beams. Secondary properties such as bending about they-y axis (Fby), shear parallel to grain (Fvxand Fvy), tensionparallel to grain (Ft), compression parallel to grain (Fc), andcompression perpendicular to grain (Fc ) are beyond the scopeof this practice. When determination of secondary properties isdeemed necessary, testing according to other applicablemethods, such as Test Methods D143, D198 or analysis inaccordance with Practice D3737, is required to establish thesesecondary properties. Reinforced glulam beams subjected toaxial loads are outside the scope of this standard. This practicealso provides minimum test requirements to validate themechanics-based model.1.2 The practice also describes a minimum set ofperformance-based durability test requirements for reinforcedglulams, as specified in Annex A1. Additional durability testrequirements shall be considered in accordance with thespecific end-use environment. Appendix X1 provides an ex-ample of a mechanics-based methodology that satisfies therequirements set forth in this standard.1.3 Characteristic strength and elastic properties obtainedusing this standard may be used as a basis for developingdesign values. However, the proper safety, serviceability andadjustment factors including duration of load, to be used indesign are outside the scope of this standard.1.4 This practice does not cover unbonded reinforcement,prestressed reinforcement, nor shear reinforcement.1.5 The values stated in SI units are to be regarded asstandard. The mechanics based model may be developed usingSI or in.-lb units.1.6 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.2. Referenced Documents2.1 ASTM Standards:2D9 Terminology Relating to Wood and Wood-Based Prod-uctsD143 Test Methods for Small Clear Specimens of TimberD198 Test Methods of Static Tests of Lumber in StructuralSizesD905 Test Method for Strength Properties of AdhesiveBonds in Shear by Compression LoadingD1990 Practice for Establishing Allowable Properties forVisually-Graded Dimension Lumber from In-Grade Testsof Full-Size SpecimensD2559 Specification for Adhesives for Bonded StructuralWood Products for Use Under Exterior Exposure Condi-tionsD2915 Practice for Sampling and Data-Analysis for Struc-tural Wood and Wood-Based ProductsD3039/D3039M Test Method for Tensile Properties of Poly-mer Matrix Composite MaterialsD3410/D3410M Test Method for Compressive Properties ofPolymer Matrix Composite Materials with UnsupportedGage Section by Shear LoadingD3737 Practice for Establishing Allowable Properties forStructural Glued Laminated Timber (Glulam)D4761 Test Methods for Mechanical Properties of Lumberand Wood-Base Structural MaterialD5124 Practice for Testing and Use of a Random Number1This 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 Oct. 1, 2012. Published October 2012. Originallyapproved in 2006. Last previous edition approved in 2007 as D7199 – 07. DOI:10.1520/D7199-07R12.2For 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.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1Generator in Lumber and Wood Products Simulation2.2 Other Standard:ANSI/AITC A190.1 Structural Glued Laminated Timber33. Terminology3.1 Definitions—Standard definitions of wood terms aregiven in Terminology D9 and standard definitions of structuralglued laminated timber terms are given in Practice D3737.3.2 Definitions of Terms Specific to This Standard:3.2.1 bonded reinforcement—a reinforcing material that iscontinuously attached to a glulam beam through adhesivebonding.3.2.2 bumper lamination—a wood lamination continuouslybonded to the outer side of reinforcement.3.2.3 compression reinforcement—reinforcement placed onthe compression side of a flexural member.3.2.4 conventional wood lamstock—solid sawn wood lami-nations with a net thickness of 2 in. or less, graded eithervisually or through mechanical means, finger-jointed andface-bonded to form a glulam.3.2.5 development length—the length of the bond line alongthe axis of the beam required to develop the design tensilestrength of the reinforcement.3.2.6 fiber-reinforced polymer (FRP)—any material consist-ing of at least two distinct components: reinforcing fibers anda binder matrix (a polymer). The reinforcing fibers are permit-ted to be either synthetic (for example, glass), metallic, ornatural (for example, wood), and are permitted to be long andcontinuously-oriented, or short and randomly oriented. Thebinder matrix is permitted to be either thermoplastic (forexample, polypropylene or nylon) or thermosetting (forexample, epoxy or vinyl-ester).3.2.7 laminating effect—an apparent increase of lumberlamination tensile strength because it is bonded to adjacentlaminations within a glulam beam. This apparent increase maybe attributed to a redirection of stresses around knots and graindeviations through adjacent laminations.3.2.8 partial length reinforcement—reinforcement that isterminated within the length of the timber.3.2.9 reinforcement—any material that is not a conventionallamstock whose mean longitudinal ultimate strength exceeds20 ksi for tension and compression, and whose mean tensionand compression MOE exceeds 3000 ksi, when placed into aglulam timber.Acceptable reinforcing materials include but arenot restricted to: fiber-reinforced polymer (FRP) plates andbars, metallic plates and bars, FRP-reinforced laminated veneerlumber (LVL), FRP-reinforced parallel strand lumber (PSL).3.2.10 shear reinforcement—reinforcement intended to in-crease the shear strength of the beam. This standard does notcover shear reinforcement.3.2.11 tension reinforcement—reinforcement placed on thetension side of a flexural member.3.3 Symbols:Arm = moment arm, distance between compression andtension force couple applied to beam cross-sectionb = beam widthC = total internal compression force within the beam cross-section (see Fig. 2)CFRP = carbon fiber reinforced polymerd = beam depthE = long-span flatwise-bending modulus of elasticity forwood lamstock (Test Methods D4761; also see Fig. 1)Fb= allowable bending stress parallel to grain3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.FIG. 1 Typical Stress-Strain Relationship for Wood Lamstock, with Bilinear ApproximationD7199 − 07 (2012)2Fx= internal horizontal force on the beam cross-section (seeEq 2)GFRP = Glass fiber-reinforced polymerLEL = lower exclusion limit (point estimate with 50 %confidence, includes volume factor)LTL = lower tolerance limit (typically calculated with 75 %confidence)Mapplied= external moment applied to the beam cross-sectionMinternal= internal moment on the beam cross-sectionMC = moisture content (%)MOE = modulus of elasticityMOR = modulus of ruptureMOR5%= 5 % one-sided lower tolerance limit for modulusof rupture, including the volume factorMORBL5%= 5 % one-sided lower tolerance limit for modu-lus of rupture corresponding to failure of the bumperlamination, including the volume factorm*E = downward slope of bilinear compression stress-straincurve for wood lamstock (see Fig. 1)N.A. = neutral axisT = total internal tension force within the beam cross-section(see Fig. 2)UCS = ultimate compressive stress parallel to grainUTS = ultimate tensile stress parallel to grainY = distance from extreme compression fiber to neutral axis(see Fig. 2)y = distance from extreme compression fiber to point ofinterest on beam cross-section (see Fig. 2)εc= strain at extreme compression fiber of beam cross-section (see Fig. 2)εcult= compression strain at lamstock failure (see Fig. 1)εcy= compression yield strain at lamstock UCS (see Fig. 1)εtult= tensile strain at lamstock failure (see Fig. 1)ε(y) = strain distribution through beam depth (see Fig. 2)ρ = tension reinforcement ratio (%); cross-sectional area oftension reinforcement divided by cross-sectional area of beambetween the c.g. of tension reinforcement and the extremecompression fiberρ = compression reinforcement ratio (%); cross-sectionalarea of compression reinforcement divided by cross-sectionalarea of beam between the c.g. of compression reinforcementand the extreme tension fiberσ(y) = stress distribution through beam depth (see Fig. 2)4. Requirements for Mechanics-Based AnalysisMethodologyNOTE 1—At a minimum, the mechanics-based analysis shall accountfor: (1) Stress-strain relationships for wood laminations and reinforce-ment; (2) Strain compatibility; (3) Equilibrium; (4) Variability of mechani-cal properties; (5) Volume effects; (6) Finger-joint effects; (7) Laminatingeffects; and (8) Stress concentrations at termination of reinforcement inbeams with partial length reinforcement. In addition to the above factors,characteristic values developed using the mechanics-based model need tobe further adjusted to address end-use conditions including moistureeffects, duration of load, preservative treatment, temperature, fire, andenvironmental effects. The development and application of these addi-tional factors are outside the scope of this practice. Annex A1 addressesthe evaluation of durability effects. The minimum output requirements forthe analysis are mean MOE (based on gross section) and 5% LTL MORwith 75 % confidence (based on gross section), both at 12 % MC. Theseanalysis requirements are described below.4.1 Stress-strain Relationships:4.1.1 Conventional Wood Lamstock:4.1.1.1 The stress-strain relationship shall be establishedthrough in-grade testing following Test Methods D198 or TestMethods D4761, or other established relationships as long asthe resulting model meets the criteria established in Section 5.Test lamstock shall be sampled in sufficient quantity fromenough sources to insure that the test results are representativeof the lamstock population that will be used in the fabricationof the beams. Follow-up testing shall be performed annually inNOTE 1—A simplified rectangular block stress distribution can be used but it must be shown that it accurately represents the stress distribution.FIG. 2 Example of Beam Section with Strain, Stress, and Force DiagramsD7199 − 07 (2012)3order to track changes in lamstock properties over time, so thatthe layup designs may be adjusted accordingly.4.1.1.2 The stress-strain relationship shall be linear in ten-sion. The stress-strain relationship shall be nonlinear in com-pression if compression is the governing failure mode. In thiscase, a bilinear approximation is acceptable, and shall be usedthroughout this standard (see Fig. 1). In the bilinear model bothtension and compression MOE shall be permitted to beapproximated by using the long-span flatwise-bending MOEobtained using Test Methods D4761.InFig. 1, m*E is thedownward slope of the compression stress-strain curve, definedas the best-fit downward line through the point (UCS, εcy)onthe compression stress-strain curve. The downward best-fit lineshall be permitted to be terminated at the point where theultimate compressive strain εcuis approximately 1 %.4.1.2 Reinforcement:4.1.2.1 The stress-strain relationship shall be establishedthrough material-level testing in accordance with Test MethodD3039/D3039M and D3410/D3410M.4.1.2.2 Nonlinearities in the stress-strain relationship shallbe included in the analysis, if present.4.1.2.3 Acceptable stress-strain models for unidirectionalE-glass FRP (GFRP), Aramid, or Carbon FRP (CFRP) intension are linear-elastic. Acceptable models for hybridE-glass/Carbon composites in tension are linear or bilinear.Acceptable models for mild steel reinforcement are elastic-plastic. Similar models may also apply in compression.4.2 Strain Compatibility:4.2.1 Fig. 2 shows the cross section of a beam with a linearstrain and bilinear stress distribution, with the neutral axis adistance Y below the top of the beam. Using the extremecompression fiber as the origin, the strain distribution for agiven applied moment (Mapplied) is defined by the equation:ε~y! 5 εc2 εc*~y/Y! (1)4.3 Equilibrium:4.3.1 In order to maintain equilibrium, the cross-sectionshall satisfy the conditions of horizontal equilibrium (Eq 2),and the internal moment (Minternal) shall equal the externalmoment applied to that cross section (Mapplied)(Eq 3). See Fig.2 as an example of strain compatibility and equilibrium:(Fx5 0⇒*depthσ~y!dA 5 0 (2)Mapplied5 Minternal5 C~or T!*Arm 5 *depth2 y*σ~y!*dA (3)4.4 Variability of Mechanical Properties:4.4.1 The model shall properly account for the variability ofthe mechanical properties of the wood lamstock and the FRPreinforcement. This includes variability of individual proper-ties and correlations among those properties as appropriate.The mechanics-based analysis shall address statistical proper-ties for and correlations between Ultimate Tensile Stress(UTS), Ultimate Compressive Stress (UCS) and long-spanflatwise-bending modulus of elasticity (E). One example ofhow this may be achieved is provided in Appendix X1.4.4.2 These correlation values are obtained from test data.Test lamstock shall be sampled in sufficient quantity, fromenough sources to insure that the test results are representativeof the lamstock population that will be used in the fabricationof the beams. Follow-up testing shall be performed annually inorder to track changes in lamstock properties over time, so thatthe layup designs may be adjusted accordingly.4.5 Volume Effects:4.5.1 The model shall properly account for changes in beamstrength properties as affected by beam size. In conv