ASTM_D_790-15.pdf

Designation:D790-15INTERNATIONALStandard Test Methods forFlexural Properties of Unreinforced and Reinforced Plasticsand Electrical Insulating MaterialsThis standard is issued under the fixed designation D790;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(s)indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S.Department of Defense.1.Scope*1.5 The text of this standard references notes and footnotes1.1 These test methods are used to determine the flexuralthat provide explanatory material.These notes and footnotesproperties of unreinforced and reinforced plastics,including(excluding those in tables and figures)shall not be consideredhighmodulus composites and electrical insulating materialsas requirements of the standard.utilizing a three-point loading system to apply a load to simply1.6 This standard does not purport to address all of thesupported beam(specimen).The method is generally appli-safety concerns,if any,associated with its use.It is thecable to both rigid and semi-rigid materials,but flexuralresponsibility of the user of this standard to establish appro-strength cannot be determined for those materials that do notpriate safety and health practices and determine the applica-break or that do not fail yield in the outer surface of the testbility of regulatory limitations prior to use.specimen within the 5.0%strain limit.NoTE 3-This standard and ISO 178 address the same subject matter,1.2 Test specimens of rectangular cross section are injectionbut differ in technical content.molded or,cut from molded or extruded sheets or plates,or cut2.Referenced Documentsfrom molded or extruded shapes.Specimens must be solid anduniformly rectangular.The specimen rests on two supports and2.1 ASTM Standards:2is loaded by means of a loading nose midway between theD618 Practice for Conditioning Plastics for Testingsupports.D638 Test Method for Tensile Properties of Plastics1.3 Measure deflection in one of two ways;using crossheadD883 Terminology Relating to Plasticsposition or a deflectometer.Please note that studies have shownD2309 Tests for Rubber Property-Compression Set In-duced by Nuclear Radiation(Withdrawn 1981)that deflection data obtained with a deflectometer will differfrom data obtained using crosshead position.The method ofD4000 Classification System for Specifying Plastic Materi-deflection measurement shall be reported.alsD4101 Specification for Polypropylene Injection and Extru-NoTE 1-Requirements for quality control in production environmentssion Materialsare usually met by measuring deflection using crosshead position.D5947 Test Methods for Physical Dimensions of SolidHowever,more accurate measurement may be obtained by using anPlastics Specimensdeflection indicator such as a deflectometer.NoTE 2-Materials that do not rupture by the maximum strain allowedD6272 Test Method for Flexural Properties of Unreinforcedunder this test method may be more suited to a 4-point bend test.The basicand Reinforced Plastics and Electrical Insulating Materi-difference between the two test methods is in the location of the maximumals by Four-Point Bendingbending moment and maximum axial fiber stresses.The maximum axialE4 Practices for Force Verification of Testing Machinesfiber stresses occur on a line under the loading nose in 3-point bending andover the area between the loading noses in 4-point bending.A four-pointE691 Practice for Conducting an Interlaboratory Study toloading system method can be found in Test Method D6272.Determine the Precision of a Test Method1.4 The values stated in SI units are to be regarded as the2.2 ISO Standard:standard.The values provided in parentheses are for informa-ISO 178 Plastics-Determination of Flexural Propertiestion only.2 For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMThese test methods are under the jurisdiction of ASTM Committee D20 onStandards volume information,refer to the standards Document Summary page onPlastics and are the direct responsibility of Subcommittee D20.10 on Mechanicalthe ASTM website.Properties.3The last approved version of this historical standard is referenced onCurrent edition approved Dec.1,2015.Published January 2016.Originallywww.astm.org.approved in 1970.Last previous edition approved in 2010 as D790-10.DOI:4 Available from American National Standards Institute(ANSI).25 W.43rd St.10.1520/D0790-15.4th Floor,New York,NY 10036,http:/www.ansi.org.*A Summary of Changes section appears at the end of this standardCopyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United StatesD790-153.Terminologystress may not always occur in the outer surface of the test specimen.Laminated beam theory must be applied to determine the maximum3.1 Definitions-Definitions of terms applying to these testtensile stress at failure.If Eq 3 is used to calculate stress,it will yield anmethods appear in Terminology D883 and Annex A2 of Testapparent strength based on homogeneous beam theory.This apparentMethod D638.strength is highly dependent on the ply-stacking sequence of highlyorthotropic laminates.4.Summary of Test Method5.1.2 Flexural Stress for Beams Tested at Large Support4.1 A test specimen of rectangular cross section rests on twoSpans(6,)-If support span-to-depth ratios greater than 16 to 1supports in a flat-wise position and is loaded by means of aare used such that deflections in excess of 10%of the supportloading nose located midway between the supports.Unlessspan occur,the stress in the outer surface of the specimen fortesting certain laminated materials(see 7 for guidance),aa simple beam is reasonably approximated using equation(Eqsupport span-to-depth(of specimen)ratio 16:1 shall be used.4)in 12.3(see Note 7).The specimen is deflected until rupture occurs in the outerNoTE 7-When large support span-to-depth ratios are used,significantsurface of the test specimen or until a maximum strain(seeend forces are developed at the support noses which will affect the5.1.6)of 5.0%is reached,whichever occurs first.moment in a simple supported beam.Eq 4 includes additional terms thatare an approximate correction factor for the influence of these end forces4.2 Procedure A is designed principally for materials thatin large support span-to-depth ratio beams where relatively large deflec-break at comparatively small deflections and it shall be used fortions exist.measurement of flexural properties,particularly flexural5.1.3 Flexural Strength()-Maximum flexural stressmodulus,unless the material specification states otherwise.sustained by the test specimen(see Note 6)during a bendingProcedure A employs a strain rate of 0.01 mm/mm/min(0.01test.It is calculated according to Eq 3 or Eq 4.Some materialsin./in./min)and is the preferred procedure for this test method.that do not break at strains of up to 5%give a load deflection4.3 Procedure B is designed principally for those materialscurve that shows a point at which the load does not increasethat do not break or yield in the outer surface of the testwith an increase in strain,that is,a yield point(Fig.1,Curvespecimen within the 5.0%strain limit when Procedure Ab),Y.The flexural strength is calculated for these materials byconditions are used.of these test methods and it shall be usedletting P(in Eq 3 or Eq 4)equal this point,Y.for measurement of flexural strength only.Procedure B em-ploys a strain rate of 0.10 mm/mm/min(0.10 in./in./min).For a discussion of these effects,see Zweben,C.,Smith,W.S.,and Wardle,M.Procedure B employs a strain rate of 0.10 mm/mm/min(0.10W.,Test Methods for Fiber Tensile Strength,Composite Flexural Modulus andin./in./min).Properties of Fabric-Reinforced Laminates,Composite Materials:Testing and4.4 Type I tests utilize crosshead position for deflectionDesign(Fifth Conference).ASTM STP 674,1979,pp.228-262.measurement.5%strain limit4.5 Type II tests utilize an instrument(deflectometer)fordeflection measurement.OM=OYB4.6 The procedure used and test type shall be reportedNoTE 4-Comparative tests may be run in accordance with eitherYprocedure,provided that the procedure is found satisfactory for theOMBimaterial being tested.Tangent modulus data obtained by Procedure AOTBtends to exhibit lower standard deviations than comparable resultsobtained by means of Procedure B.OfC5.Significance and Use5.1 Flexural properties as determined by this test method areespecially useful for quality control and specification purposes.They include:5.1.1 Flexural Stress(6,)-When a homogeneous elasticmaterial is tested in flexure as a simple beam supported at twopoints and loaded at the midpoint,the maximum stress in theouter surface of the test specimen occurs at the midpoint.Flexural stress is calculated for any point on the load-deflectioncurve using equation(Eq 3)in Section 12(see Notes 5 and 6).NorE 5-Eq 3 applies strictly to materials for which stress is linearlyErBEIMErBproportional to strain up to the point of rupture and for which the strainsEfare small.Since this is not always the case,a slight error will beNoTE 1-Curve a:Specimen that breaks before yielding.introduced if Eq 3 is used to calculate stress for materials that are not trueCurve b:Specimen that yields and then breaks before the 5%strainHookean materials.The equation is valid for obtaining comparison datalimit.and for specification purposes,but only up to a maximum fiber strain ofCurve c:Specimen that neither yields nor breaks before the 5%strain5%in the outer surface of the test specimen for specimens tested by thelimit.procedures described herein.FIG.1 Typical Curves of Flexural Stress(a,)Versus FlexuralNoTE 6-When testing highly orthotropic laminates,the maximumStrain()D790-155.1.4 Flexural Offset Yield Strength-Offset yield strength isspecification or by customer contract.The chosen stress orthe stress at which the stress-strain curve deviates by a givenstrain points used for the determination of the chord modulusstrain(offset)from the tangent to the initial straight line portionshall be reported.Calculate the chord modulus,E using Eq 7of the stress-strain curve.The value of the offset must be givenin 12.5.2.whenever this property is calculated.5.2 Experience has shown that flexural properties vary withNoTE 8-Flexural Offset Yield Strength may differ from flexuralspecimen depth,temperature,atmospheric conditions,andstrength defined in 5.1.3.Both methods of calculation are described in thestrain rate as specified in Procedures A and B.annex to Test Method D638.5.3 Before proceeding with these test methods,refer to the5.1.5 Flexural Stress at Break()-Flexural stress at breakASTM specification of the material being tested.Any testof the test specimen during a bending test.It is calculatedspecimen preparation,conditioning,dimensions,or testingaccording to Eq 3 or Eq 4.Some materials give a loadparameters,or combination thereof,covered in the ASTMdeflection curve that shows a break point,B,without a yieldmaterial specification shall take precedence over those men-point(Fig.1,Curve a)in which case oB=M.Other materialstioned in these test methods.Table 1 in Classification Systemgive a yield deflection curve with both a yield and a breakD4000 lists the ASTM material specifications that currentlypoint,B(Fig.1,Curve b).The flexural stress at break isexist for plastics.calculated for these materials by letting P(in Eq 3 or Eq 4)equal this point,B.6.Apparatus5.1.6 Stress at a Given Strain-The stress in the outer6.1 Testing Machine-A testing machine capable of beingsurface of a test specimen at a given strain is calculated inoperated at constant rates of crosshead motion over the rangeaccordance with Eq 3 or Eq 4 by letting P equal the load readindicated and comprised of the following:from the load-deflection curve at the deflection corresponding6.1.1 Load Frame-The stiffness of the testing machineto the desired strain(for highly orthotropic laminates,see Noteshall be such that the total elastic deformation of the system6).does not exceed 1%of the total deflection of the test specimen5.1.7 Flexural Strain,e-Nominal fractional change in theduring testing,or appropriate corrections shall be made.length of an element of the outer surface of the test specimen6.1.1.1 Fixed Member-A fixed or essentially stationaryat midspan,where the maximum strain occurs.Flexural strainmember holding the specimen supports;is calculated for any deflection using Eq 5 in 12.4.6.1.1.2 Movable Member-A movable member carrying the5.1.8 Modulus of Elasticity:loading nose.5.1.8.1 Tangent Modulus of Elasticity-The tangent modu-6.1.2 Loading Noses and Supports-The loading nose andlus of elasticity,often called the modulus of elasticity,is thesupports shall have cylindrical surfaces.ratio,within the elastic limit,of stress to corresponding strain.6.1.2.1 The radii of the loading nose and supports shall beIt is calculated by drawing a tangent to the steepest initial5.00.1 mm(0.1970.004 in.)unless otherwise specified instraight-line portion of the load-deflection curve and using Eqan ASTM material specification or as agreed upon between6 in 12.5.1(for highly anisotropic composites,see Note 15).interested parties.NoTE 9-Shear deflections can seriously reduce the apparent modulus6.1.2.2 Other Radii for Loading Noses and Supports-of highly anisotropic composites when they are tested at low span-to-Alternative loading noses and supports are permitted to be useddepth ratios.For this reason,a span-to-depth ratio of 60 to 1 isin order to avoid excessive indentation or failure due to stressrecommended for flexural modulus determinations on these composites.concentration directly under the loading nose or if required byFlexural strength should be determined on a separate set of replicatespecimens at a lower span-to-depth ratio that induces tensile failure in thean ASTM material specification.If alternative loading nose andouter fibers of the beam along its lower face.Since the flexural modulussupport radii are used,the dimensions of the loading nose andof highly anisotropic laminates is a critical function of ply-stackingsupports shall be clearly identified in the test report andsequence,it will not necessarily correlate with tensile modulus,which isreference shall be made to any applicable specifications.not stacking-sequence dependent.(1)Alternative supports shall have a minimum radius of5.1.8.2 Secant Modulus-The secant modulus is the ratio of3.2 mm(s in.)When testing specimens 3.2 mm or greater instress to corresponding strain at any selected point on thedepth,the radius of the loading nose and supports are permittedstress-strain curve,that is,the slope of the straight line thatto be up to 1.6 times the specimen depth.joins the origin and a selected point on the actual stress-strain(2)The arc of the loading nose in contact with thecurve.It shall be expressed in megapascals(pounds per squarespecimen shall be sufficiently large to prevent contact of theinch).The selected point is chosen at a pre-specified stress orspecimen with the sides of the nose.Alternative loading nosesstrain in accordance with the appropriate material specificationshall be sufficiently large to prevent contact of the specimenor by customer contract.It is calculated in accordance with Eqwith the sides of the nose.The maximum radius of the loading6 by letting m equal the slope of the secant to the load-nose shall be no more than four times the specimen depth.deflection curve.The chosen stress or strain point used for the6.1.3 Drive Mechanism-A drive mechanism for impartingdetermination of the secant shall be reported.to the movable member a uniform,controlled velocity with5.1.8.3 Chord Modulus(E)-The chord modulus is calcu-respect to the stationary member,with this velocity to belated from two discrete points on the load deflection curve.Theregulated as specified in Procedure A or B.selected points are to be chosen at two pre-specified stress or6.1.4 Load Indicator-A suitable load-indicating mecha-strain points in accordance with the appropriate materialnism capable of showing the total load applied to specimenD790-15when in position on the flex fixture.This mechanism shall be7.3 Sheet Materials(Except Laminated Thermosetting Ma-essentially free of inertia lag at the specified rate of testing andterials and Certain Materials Used for Electrical Insulation,shall indicate the load with an accuracy of 1%of theIncluding Vulcanized Fiber and Glass Bonded Mica):indicated value,or better.The accuracy of the testing machine7.3.1 Materials 1.6 mm(Vi in.)or Greater in Thicknessshall be verified in accordance with Practices E4.Specimen width shall not exceed one fourth of the support span6.1.5 Deflection Measuring Device-The deflection measur-for specimens greater than 3.2 mm(s in.)in depth.Specimensing device used shall be selected from the following two3.2 mm or less in depth shall be 12.7 mm(in.)in width.Thechoices:specimen shall be long enough to allow for overhanging on6.1.5.1 Type I-Crosshead Position Indicating System-Aeach end of at least 10%of the support span,but in no casesuitable deflection indicating mechanism capable of showingless than 6.4 mm(4 in.)on each end.Overhang shall bethe amount of change in crosshead movement.This mechanismsufficient to prevent the specimen from slipping through theshall be essentially free of inertial lag at the specified rate ofsupports.A support span of 161 times the depth of thetesting and shall indicate the crosshead movement.The cross-specimen is used for these specimens.head position indicating system shall be verified in accordance7.3.2 Materials Less than 1.6 mm(Vis in.)in Thicknesswith Practice D2309 and minimally meets the requirements ofThe specimen shall be 50.8 mm(2 in.)long by 12.7 mm(in.)a Class D system.wide,tested flatwise on a 25.4-mm(1-in.)support span.6.1.5.2 Type II-Deflection Indicator(Deflectometer)-Asuitable instrument for more accurately determining the deflec-NoTE 12-Use of the formulas for simple beams cited in these testmethods for calculating results presumes that beam width is small intion of the specimen distance between two designated parison with the support span.Therefore,the formulas do not applyThis instrument shall be essentially free of inertia at therigorously to these dimensions.specified speed of testing.The deflection indicator system shallNoTE 13-Where machine sensitivity is such that specimens of thesebe verified in accordance with Practice D2309 and minimallydimensions cannot be measured,wider specimens or shorter supportmeets the requirements of a Class B system.spans,or both,may be used,provided the support span-to-depth ratio is atleast 14 to 1.All dimensions must be stated in the report(see also NoteNoTE 10-It is desirable,but not essential,that this instrument12).automatically record this distance,or any change in it,as a function of the7.4 Laminated Thermosetting Materials and Sheet andload on the test specimen or of the elapsed time from the start of the test,or both.If only the latter is obtained,it has been found useful to alsoPlate Materials Used for Electrical Insulation,Includingrecord load-time data.Vulcanized Fiber and Glass-Bonded Mica-For paper-base andfabric-base grades over 25.4 mm(1 in.)in nominal thickness,6.2 Micrometers-Apparatus for measuring the width andthe specimens shall be machined on both surfaces to a depth ofthickness of the test specimen shall comply with the require-ments of Test Method D5947.25.4 mm.For glass-base and nylon-base grades,specimensover 12.7 mm(0.5 in.)in nominal depth shall be machined onboth surfaces to a depth of 12.7 mm.The support span-to-depth7.Test Specimensratio shall be chosen such that failures occur in the outer fibers7.1 Test specimens that are cut from sheets,plates,orof the specimens,due only to the bending moment.As amolded or extruded shapes,or molded to the desired finishedgeneral rule,support span-to-specimen depth ratios of 16:1 aredimensions are acceptable.The actual dimensions used shall besatisfactory when the ratio of the tensile strength to shearmeasured in accordance with Test Methods D5947.The depthstrength is less than 8 to 1,but the support span-to-depth ratioof the specimen shall be defined as the thickness of themust be increased for composite laminates having relativelymaterial.The depth shall not exceed the width(see Note 11).low shear strength in the plane of the laminate and relativelyThe crosssection of the specimens shall be rectangular withhigh tensile strength parallel to the support span(32:1 or 40:1opposite sides flat and parallel(0.2 mm)and adjacent sidesare recommended).When laminated materials exhibit lowperpendicular along the full length of the pressive strength perpendicular to the laminations,theyshall be loaded with a large radius loading nose(up to four7.2 Whenever possible,the original surface of the sheetshall be unaltered.However,where testing machine limitationstimes the specimen depth to prevent premature damage to theouter fibers.make it impossible to follow the above criterion on theunaltered sheet,one or both surfaces shall be machined to7.5 Molding Materials(Thermoplastics and Thermosets)provide the desired dimensions,and the location of theThe preferred specimen dimensions for molding materials isspecimens with reference to the total depth shall be noted.12.7 mm(0.5 in.)wide,3.2 mm(0.125 in.)thick,and 127 mmConsequently,any specifications for flexural properties on(5.0 in.)long.They are tested flatwise on the support span,thicker sheets must state whether the original surfaces are to beresulting in a support span-to-depth ratio of 16:1(toleranceretained or not.When only one surface was machined,it must1).Thicker specimens are to be avoided if they exhibitbe stated whether the machined surface was on the tension orsignificant sink marks or bubbles when pression side of the beam.Any necessary polishing of7.6 High-Strength Reinforced Composites,Including Highlyspecimens shall be done only in the lengthwise direction of theOrthotropic Laminates-The span-to-depth ratio shall be cho-specimen.sen such that failure occurs in the outer fibers of the specimensNoTE 11-The value obtained on specimens with machined surfacesand is due only to the bending moment.As a general rule,may differ from those obtained on specimens with original surfaces.support span-to-depth ratios of 16:1 are satisfactory when theD790-15ratio of the tensile strength to shear strength is less than 8 to 1,flexural fixtures that have fixed machined span positions,verifybut the support span-to-depth ratio must be increased forthe span distance the same as for adjustable spans at eachcomposite laminates having relatively low shear strength in themachined position.This distance becomes the span for thatplane of the laminate and relatively high tensile strengthposition and is used for calculations applicable to all subse-parallel to the support span(32:1 or 40:1 are recommended).quent tests conducted at that position.See Annex A2 forFor some highly anisotropic composites,shear deformation caninformation on the determination of and setting of the span.significantly influence modulus measurements,even at span-10.1.4 Calculate the rate of crosshead motion as follows andto-depth ratios as high as 40:1.Hence,for these materials,anset the machine for the rate of crosshead motion as calculatedincrease in the span-to-depth ratio to 60:1 is recommended toby Eq 1:eliminate shear effects when modulus data are required,itR=ZL2/6d(1)should also be noted that the flexural modulus of highlyanisotropic laminates is a strong function of ply-stackingwhere:sequence and will not necessarily correlate with tensileR=rate of crosshead motion,mm(in.)/min,modulus,which is not stacking-sequence dependent.L=support span,mm(in.),d=depth of beam,mm(in.),and8.Number of Test SpecimensZ=rate of straining of the outer fiber,mm/mm/min(in./in./8.1 Test at least five specimens for each sample in the casemin).Z shall be equal to 0.01.of isotropic materials or molded specimens.In no case shall the actual crosshead rate differ from that8.2 For each sample of anisotropic material in sheet form,calculated using Eq 1,by more than 10%.test at least five specimens cut in the desired direction.For the10.1.5 Align the loading nose and supports so that the axespurposes of this test,lengthwise designates the principal axisof the cylindrical surfaces are parallel and the loading nose isof anisotropy and shall be interpreted to mean the direction ofmidway between the supports.Center the specimen on thethe sheet known to be stronger in flexure.Crosswise indi-supports,with the long axis of the specimen perpendicular tocates the sheet direction known to be the weaker in flexure andthe loading nose and supports.The loading nose should beshall be at 90 to the lengthwise direction.The direction of test,close to,but not in contact with the specimen(see Note 14).whether it be lengthwise,crosswise,or some angle relative toNoTE 14-The parallelism of the apparatus may be checked by meansthese shall be noted in the report.of a plate with parallel grooves into which the loading nose and supportswill fit when properly aligned(see A2.3).9.Conditioning10.1.6 Apply the load to the specimen at the specified9.1 Conditioning-Condition the test specimens in accor-crosshead rate,and record simultaneous load-deflection data.dance with Procedure A of Practice D618 unless otherwise10.1.7 Measure deflection either by measurement of thespecified by contract or the relevant ASTM material specifica-motion of the loading nose relative to the supports(crossheadtion.Conditioning time is specified as a minimum.Tempera-position)(Type I)or by a deflection indicator(deflectometer)ture and humidity tolerances shall be in accordance withunder the specimen in contact with it at the center of theSection 7 of Practice D618 unless specified differently bysupport span,the gauge being mounted stationary relative tocontract or material specification.the specimen supports(Type II).Load-deflection curves are9.2 Test Conditions-Conduct the tests at the same tempera-used to determine the flexural strength,chord or secantture and humidity used for conditioning with tolerances inmodulus or the tangent modulus of elasticity,and the totalaccordance with Section 7 of Practice D618 unless otherwisework as measured by the area under the load-deflection curve.specified by contract or the relevant ASTM material specifica-Perform the necessary toe compensation(see Annex Al)totion.correct for seating and indentation of the specimen anddeflections in the machine.10.Procedure10.1.8 Terminate the test when the maximum strain in the10.1 Procedure A:outer surface of the test specimen has reached 0.05 mm/mm10.1.1 Use an untested specimen for each measurement(in./in.)or at break if break occurs prior to reaching theMeasure the width and depth of the specimen to the nearestmaximum strain(Notes 15 and 16).The deflection at which0.03 mm(0.001 in.)at the center of the support span.Forthis strain will occur is calculated by letting r equal 0.05specimens less than 2.54 mm(0.100 in.)in depth,measure themm/mm(in./in.)in Eq 2:depth to the nearest 0.003 mm(0.0005 in.).These measure-D=rL216d(2)ments shall be made in accordance with Test Methods D5947.10.1.2 Determine the support span to be used as described inwhere:Section 7 and set the support span to within 1%of theD=midspan deflection,mm(in.),determined value.r=strain,mm/mm(in./in.),10.1.3 For flexural fixtures that have continuously adjust-L=support span,mm(in.),andable spans,measure the span accurately to the nearest 0.1 mmd=depth of beam,mm(in.).(0.004 in.)for spans less than 63 mm(2.5 in.)and to the nearestNoTE 15-For some materials that do not yield or break within the 5%strain limit when tested by Procedure A,the increased strain rate allowed0.3 mm(0.012 in.)for spans greater than or equal to 63 mmby Procedure B(see 10.2)may induce the specimen to yield or break,or(2.5 in.).Use the actual measured span for all calculations.Forboth,within the required 5%strain limit.