1、Designation: C78/C78M 16Standard Test Method forFlexural Strength of Concrete (Using Simple Beam withThird-Point Loading)1This standard is issued under the fixed designation C78/C78M; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision,
2、 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.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope*1.1 This test method c
3、overs the determination of the flexuralstrength of concrete by the use of a simple beam withthird-point loading.1.2 The values stated in either SI units or inch-pound unitsare to be regarded separately as standard. The values stated ineach system may not be exact equivalents; therefore, eachsystem s
4、hall be used independently of the other. Combiningvalues from the two systems may result in non-conformancewith the standard.1.3 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 app
5、ro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C31/C31M Practice for Making and Curing Concrete TestSpecimens in the FieldC42/C42M Test Method for Obtaining and Testing DrilledCores and Sawed Be
6、ams of ConcreteC192/C192M Practice for Making and Curing Concrete TestSpecimens in the LaboratoryC617/C617M Practice for Capping Cylindrical ConcreteSpecimensC1077 Practice for Agencies Testing Concrete and ConcreteAggregates for Use in Construction and Criteria forTesting Agency EvaluationE4 Practi
7、ces for Force Verification of Testing Machines3. Significance and Use3.1 This test method is used to determine the flexuralstrength of specimens prepared and cured in accordance withTest Methods C42/C42M or Practices C31/C31M or C192/C192M. Results are calculated and reported as the modulus ofruptur
8、e. For the same specimen size, the strength determinedwill vary if there are differences in specimen preparation,curing procedure, moisture condition at time of testing, andwhether the beam was molded or sawed to size.3.2 The measured modulus of rupture generally increases asthe specimen size decrea
9、ses3,4,5and it has been shown that thevariability of individual test results increases as the specimensize decreases.3,43.3 The results of this test method may be used to determinecompliance with specifications or as a basis for mixtureproportioning, evaluating uniformity of mixing, and checkingplac
10、ement operations by using sawed beams. It is used primar-ily in testing concrete for the construction of slabs andpavements.4. Apparatus4.1 Testing MachineThe testing machine shall conform tothe requirements of the sections on Basis of Verification,Corrections, and Time Interval Between Verification
11、s of Prac-tices E4. Hand operated testing machines having pumps that donot provide a continuous loading in one stroke are notpermitted. Motorized pumps or hand operated positive dis-placement pumps having sufficient volume in one continuousstroke to complete a test without requiring replenishment ar
12、e1This test method is under the jurisdiction of ASTM Committee C09 onConcrete and Concrete Aggregates and is the direct responsibility of SubcommitteeC09.61 on Testing for Strength.Current edition approved July 1, 2016. Published August 2016. Originallyapproved in 1930. Last previous edition approve
13、d in 2015 as C78/C78M 15b.DOI: 10.1520/C0078_C0078M-16.2For 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 standards Document Summary page onthe ASTM website.3Tanes
14、i, J; Ardani, A. Leavitt, J. “Reducing the Specimen Size of ConcreteFlexural Strength Test (AASHTO T97) for Safety and Ease of Handling,“ Trans-portation Research Record: Journal of the Transportation Research Board, No.2342, Transportation Research Board of National Academies, Washington, D.C.,2013
15、.4Carrasquillo, P.M. and Carrasquillo, R. L “Improved Concrete Quality ControlProcedures Using Third Point Loading”, Research Report 119-1F, Project 3-9-87-1119, Center For Transportation Research, The University of Texas at Austin,November 1987.5Bazant, Z. and Novak, D. “Proposal for Standard Test
16、of Modulus of Ruptureof Concrete with its Size Dependence,“ ACI Materials Journal, January-February2001.*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 States1permitted and sha
17、ll be capable of applying loads at a uniformrate without shock or interruption. The testing machine shall beequipped with a means of recording or holding the peak valuethat will indicate the maximum load, to within 1 % accuracy,applied to the specimen during a test.4.2 Loading ApparatusThe third poi
18、nt loading methodshall be used in making flexure tests of concrete employingbearing blocks that will ensure that forces applied to the beamwill be perpendicular to the face of the specimen and appliedwithout eccentricity. A diagram of an apparatus that accom-plishes this purpose is shown in Fig. 1.4
19、.2.1 All apparatus for making flexure tests of concrete shallbe capable of maintaining the specified span length anddistances between load-applying blocks and support blocksconstant within 61.0 mm 60.05 in.4.2.2 The ratio of the horizontal distance between the pointof application of the load and the
20、 point of application of thenearest reaction to the depth of the beam shall be 1.0 6 0.03.4.2.3 If an apparatus similar to that illustrated in Fig. 1 isused: the load-applying and support blocks shall not be morethan 65 mm 2.50 in. high, measured from the center or theaxis of pivot, and should exten
21、d entirely across or beyond thefull width of the specimen. Each case-hardened bearing surfacein contact with the specimen shall not depart from a plane bymore than 0.05 mm 0.002 in. and shall be a portion of acylinder, the axis of which is coincidental with either the axisof the rod or center of the
22、 ball, whichever the block is pivotedupon. The angle subtended by the curved surface of each blockshall be at least 0.80 rad 45. The load-applying and supportblocks shall be maintained in a vertical position and in contactwith the rod or ball by means of spring-loaded screws that holdthem in contact
23、 with the pivot rod or ball. The uppermostbearing plate and center point ball in Fig. 1 may be omittedwhen a spherically seated bearing block is used, provided onerod and one ball are used as pivots for the upper load-applyingblocks.5. Test Specimens5.1 The test specimen shall conform to all require
24、ments ofTest Method C42/C42M or Practices C31/C31M or C192/C192M applicable to beam specimens and shall have a testspan within 2 % of being three times its depth as tested. Thesides of the specimen shall be at right angles with the top andbottom. All surfaces shall be smooth and free of scars,indent
25、ations, holes, or inscribed identification marks.5.2 Provided the smaller cross-sectional dimension of thebeam is at least three times the nominal maximum size of thecoarse aggregate, the modulus of rupture can be determinedusing different specimen sizes. However, measured modulus ofrupture generall
26、y increases as specimen size decreases.3,4(Note 1).NOTE 1The strength ratio for beams of different sizes dependsprimarily on the maximum size of aggregate.5Experimental data obtainedin two different studies have shown that for maximum aggregate sizebetween 19.0 and 25.0 mm 34 and 1 in., the ratio be
27、tween the modulusof rupture determined with a 150 by 150 mm 6 by 6 in. and a 100 by 100mm 4 by 4 in. may vary from 0.90 to 1.073and for maximum aggregatesize between 9.5 and 37.5 mm 38 and 112 in., the ratio between themodulus of rupture determined with a 150 by 150 mm 6 by 6 in. and a115 by 115 mm
28、4.5 by 4.5 in. may vary from 0.86 to 1.00.45.3 The specifier of tests shall specify the specimen size andnumber of specimens to be tested to obtain an average testresult (Note 2). The same specimen size shall be used forqualification and acceptance testing.NOTE 2It has been shown that the variabilit
29、y of individual test resultsincreases as the specimen size decreases.3,4NOTE 1This apparatus may be used inverted. If the testing machine applies force through a spherically seated head, the center pivot may be omitted,provided one load-applying block pivots on a rod and the other on a ball.FIG. 1 S
30、chematic of a Suitable Apparatus for Flexure Test of Concrete by Third-Point Loading MethodC78/C78M 1626. Procedure6.1 Moist-cured specimens shall be kept moist during theperiod between removal from moist storage and testing.NOTE 3Surface drying of the specimen results in a reduction in themeasured
31、flexural strength.NOTE 4Methods for keeping the specimen moist include wrapping inmoist fabric or matting, or keeping specimens under lime water incontainers near the flexural testing machine until time of testing.6.2 When using molded specimens, turn the test specimenon its side with respect to its
32、 position as molded and center iton the support blocks. When using sawed specimens, positionthe specimen so that the tension face corresponds to the top orbottom of the specimen as cut from the parent material. Centerthe loading system in relation to the applied force. Bring theload-applying blocks
33、in contact with the surface of the speci-men at the third points and apply a load of between 3 and 6 %of the estimated ultimate load. Using 0.10 mm 0.004 in. and0.40 mm 0.015 in. leaf-type feeler gages, determine whetherany gap between the specimen and the load-applying orsupport blocks is greater o
34、r less than each of the gages over alength of 25 mm 1 in. or more. Grind, cap, or use leathershims on the specimen contact surface to eliminate any gap inexcess of 0.10 mm 0.004 in. in width. Leather shims shall beof uniform 6 mm 0.25 in. thickness, 25 to 50 mm 1.0 to 2.0in. width, and shall extend
35、across the full width of thespecimen. Gaps in excess of 0.40 mm 0.015 in. shall beeliminated only by capping or grinding. Grinding of lateralsurfaces shall be minimized inasmuch as grinding may changethe physical characteristics of the specimens. Capping shall bein accordance with the applicable sec
36、tions of Practice C617/C617M.6.3 Load the specimen continuously and without shock. Theload shall be applied at a constant rate to the breaking point.Apply the load at a rate that constantly increases the maximumstress on the tension face between 0.9 and 1.2 MPa/min 125and 175 psi/min until rupture o
37、ccurs. The loading rate iscalculated using the following equation:r 5Sbd2L(1)where:r = loading rate, N/min lb/min,S = rate of increase in maximum stress on the tension face,MPa/min psi/min,b = average width of the specimen as oriented for testing,mm in.,d = average depth of the specimen as oriented
38、for testing,mm in., andL = span length, mm in.7. Measurement of Specimens After Test7.1 To determine the dimensions of the specimen crosssection for use in calculating modulus of rupture, take mea-surements across one of the fractured faces after testing. Thewidth and depth are measured with the spe
39、cimen as orientedfor testing. For each dimension, take one measurement at eachedge and one at the center of the cross section. Use the threemeasurements for each direction to determine the averagewidth and the average depth. Take all measurements to thenearest 1 mm 0.05 in. If the fracture occurs at
40、 a cappedsection, include the cap thickness in the measurement.8. Calculation8.1 If the fracture initiates in the tension surface within themiddle third of the span length, calculate the modulus ofrupture as follows:R 5PLbd2(2)where:R = modulus of rupture, MPa psi,P = maximum applied load indicated
41、by the testing machine,N lbf,L = span length, mm in.,b = average width of specimen, mm in., at the fracture, andd = average depth of specimen, mm in., at the fracture.NOTE 5The weight of the beam is not included in the abovecalculation.8.2 If the fracture occurs in the tension surface outside ofthe
42、middle third of the span length by not more than 5 % of thespan length, calculate the modulus of rupture as follows:R 53Pabd2(3)where:a = average distance between line of fracture and the nearestsupport measured on the tension surface of the beam,mm in.NOTE 6The weight of the beam is not included in
43、 the abovecalculation.8.3 If the fracture occurs in the tension surface outside ofthe middle third of the span length by more than 5 % of thespan length, discard the results of the test.9. Report9.1 Report the following information:9.1.1 Identification number,9.1.2 Average width to the nearest 1 mm
44、0.05 in.,9.1.3 Average depth to the nearest 1 mm 0.05 in.,9.1.4 Span length in mm in.,9.1.5 Maximum applied load in N lbf,9.1.6 Modulus of rupture calculated to the nearest 0.05 MPa5 psi,9.1.7 Curing history and apparent moisture condition of thespecimens at the time of test,9.1.8 If specimens were
45、capped, ground, or if leather shimswere used,9.1.9 Whether sawed or molded and defects in specimens,and9.1.10 Age of specimens.C78/C78M 16310. Precision and Bias10.1 Precision6The single-operator coefficient of varia-tion has been found to be 5.7 %. Therefore, results of twoproperly conducted tests
46、by the same operator on beams madefrom the same batch sample are not expected to differ fromeach other by more than 16 %. The multilaboratory coefficientof variation has been found to be 7.0 %. Therefore, results oftwo different laboratories on beams made from the same batchsample are not expected t
47、o differ from each other by more than19 % (Note 7 and Note 8).NOTE 7This precision statement was determined using 150 by 150 by510 mm 6 by 6 by 20 in. and 115 by 115 by 395 mm 4.5 by 4.5 by 15.5in. specimens and based on two concrete mixtures with flexural strengthof 3.65 and 6.15 MPa 530 psi and 89
48、0 psi4. In a separate study,321mixtures with flexural strength ranging from 4.25 to 7.15 MPa 615 to1040 psi were tested and the single operator coefficient of variation for100 by 100 by 355 mm 4 by 4 by 14 in. specimens obtained was 5.2 %.A complete precision statement for 4 by 4 by 14 in. 100 by 10
49、0 by 355mm specimens is not available but will be prepared. The variability of testresults changes with specimen dimensions3,4and should not be extrapo-lated to specimen sizes different than those reported here.NOTE 8This precision statement was determined using a single brandand model testing machine (Rainhart Series 416, Recording Beam tester).4Different testing machine brands and models may yield results withdifferent variability than those stated here.10.2 BiasBecause there i
