1、Designation: C 78 07Standard Test Method forFlexural Strength of Concrete (Using Simple Beam withThird-Point Loading)1This standard is issued under the fixed designation C 78; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the yea
2、r of last revision. A number in parentheses indicates the year of last reapproval. A superscriptepsilon (e) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the Department of Defense.1. Scope*1.1 This test method covers the de
3、termination of the flexuralstrength of concrete by the use of a simple beam withthird-point loading.1.2 The values stated in inch-pound units are to be regardedas the standard. The SI equivalent of inch-pound units has beenrounded where necessary for practical application.1.3 This standard does not
4、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:
5、2C 31/C 31M Practice for Making and Curing Concrete TestSpecimens in the FieldC 42/C 42M Test Method for Obtaining and Testing DrilledCores and Sawed Beams of ConcreteC 192/C 192M Practice for Making and Curing ConcreteTest Specimens in the LaboratoryC 617 Practice for Capping Cylindrical Concrete S
6、peci-mensC 1077 Practice for Laboratories Testing Concrete and Con-crete Aggregates for Use in Construction and Criteria forLaboratory EvaluationE4 Practices for Force Verification of Testing Machines3. Significance and Use3.1 This test method is used to determine the flexuralstrength of specimens p
7、repared and cured in accordance withTest Methods C 42/C 42M or Practices C 31/C 31M or C 192/C 192M. Results are calculated and reported as the modulus ofrupture. The strength determined will vary where there aredifferences in specimen size, preparation, moisture condition,curing, or where the beam
8、has been molded or sawed to size.3.2 The results of this test method may be used to determinecompliance with specifications or as a basis for proportioning,mixing and placement operations. It is used in testing concretefor the construction of slabs and pavements (Note 1).4. Apparatus4.1 The testing
9、machine shall conform to the requirementsof the sections on Basis of Verification, Corrections, and TimeInterval Between Verifications of Practices E4. Hand operatedtesting machines having pumps that do not provide a continu-ous loading in one stroke are not permitted. Motorized pumpsor hand operate
10、d positive displacement pumps having suffi-cient volume in one continuous stroke to complete a testwithout requiring replenishment are permitted and shall becapable of applying loads at a uniform rate without shock orinterruption.4.2 Loading ApparatusThe third point loading methodshall be used in ma
11、king flexure tests of concrete employingbearing blocks which will ensure that forces applied to thebeam will be perpendicular to the face of the specimen andapplied without eccentricity. A diagram of an apparatus thataccomplishes this purpose is shown in Fig. 1.4.2.1 All apparatus for making flexure
12、 tests of concrete shallbe capable of maintaining the specified span length anddistances between load-applying blocks and support blocksconstant within 60.05 in. (61.3 mm).4.2.2 The ratio of the horizontal distance between the pointof application of the load and the point of application of theneares
13、t 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 should not be morethan 212 in. (64 mm) high, measured from the center or the axisof pivot, and should extend entirely across or beyond the
14、fullwidth of the specimen. Each case-hardened bearing surface incontact with the specimen shall not depart from a plane bymore than 0.002 in. (0.05 mm) and shall be a portion of acylinder, the axis of which is coincidental with either the axisof the rod or center of the ball, whichever the block is
15、pivoted1This 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 Aug. 15, 2007. Published September 2007. Originallyapproved in 1930. Last previous editi
16、on approved in 2002 as C 78 02.2For 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.1*A Summary of Changes section
17、 appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.upon. The angle subtended by the curved surface of each blockshould be at least 45 (0.79 rad). The load-applying andsupport blocks shall be maintaine
18、d in a vertical position and incontact with the rod or ball by means of spring-loaded screwsthat hold them in contact with the pivot rod or ball. Theuppermost bearing plate and center point ball in Fig. 1 may beomitted when a spherically seated bearing block is used,provided one rod and one ball are
19、 used as pivots for the upperload-applying blocks.5. Testing5.1 The test specimen shall conform to all requirements ofTest Method C 42/C 42M or Practices C 31/C 31M or C 192/C 192M applicable to beam specimens and shall have a testspan within 2 % of being three times its depth as tested. Thesides of
20、 the specimen shall be at right angles with the top andbottom. All surfaces shall be smooth and free of scars,indentations, holes, or inscribed identification marks.5.2 The technician performing the flexural strength testshould be certified as an ACI TechnicianGrade II, or by anequivalent written an
21、d performance test program.NOTE 1The testing laboratory performing this test method may beevaluated in accordance with Practice C 1077.6. Procedure6.1 Flexural tests of moist-cured specimens shall be made assoon as practical after removal from moist storage. Surfacedrying of the specimen results in
22、a reduction in the measuredflexural strength.6.2 When using molded specimens, turn the test specimenon its side with respect to its 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
23、specimen as cut from the parent material. Centerthe loading system in relation to the applied force. Bring theload-applying blocks 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 0.004 in. (0.10 mm) and0.015
24、in. (0.38 mm) leaf-type feeler gages, determine whetherany gap between the specimen and the load-applying orsupport blocks is greater or less than each of the gages over alength of 1 in. (25 mm) or more. Grind, cap, or use leathershims on the specimen contact surface to eliminate any gap inexcess of
25、 0.004 in. (0.10 mm) in width. Leather shims shall beof uniform14 in. (6.4 mm) thickness, 1 to 2 in. (25 to 50 mm)width, and shall extend across the full width of the specimen.Gaps in excess of 0.015 in. (0.38 mm) shall be eliminated onlyby capping or grinding. Grinding of lateral surfaces should be
26、minimized inasmuch as grinding may change the physicalcharacteristics of the specimens. Capping shall be in accor-dance with the applicable sections of Practice C 617.6.3 Load the specimen continuously and without shock. Theload shall be applied at a constant rate to the breaking point.Apply the loa
27、d at a rate that constantly increases the maximumstress on the tension face between 125 and 175 psi/min (0.86and 1.21 MPa/min) until rupture occurs. The loading rate iscalculated using the following equation:r 5 Sbd2/L (1)where:r = loading rate, lb/min (N/min),S = rate of increase in maximum stress
28、on the tension face,psi/min (MPa/min),b = average width of the specimen as oriented for testing,in. (mm),d = average depth of the specimen as oriented for testing,in. (mm), andL = span length, in (mm).NOTE 1This apparatus may be used inverted. If the testing machine applies force through a spherical
29、ly seated head, the center pivot may be omitted,provided one load-applying block pivots on a rod and the other on a ball.NOTE 21 in. = 25.4 mm.FIG. 1 Diagrammatic View of a Suitable Apparatus for Flexure Test of Concrete by Third-Point Loading MethodC780727. Measurement of Specimens After Test7.1 To
30、 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 specimen as orientedfor testing. For each dimension, take one measurement at eachedge and one
31、 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 0.05 in. (1 mm). If the fracture occurs at a cappedsection, include the cap thickness in the measurement.8. Calculation8.1 If the
32、 fracture initiates in the tension surface within themiddle third of the span length, calculate the modulus ofrupture as follows:R 5 PL/bd2(2)where:R = modulus of rupture, psi, or MPa,P = maximum applied load indicated by the testing ma-chine, lbf, or N,L = span length, in., or mm,b = average width
33、of specimen, in., or mm, at the fracture,andd = average depth of specimen, in., or mm, at the fracture.NOTE 2The weight of the beam is not included in the abovecalculation.8.2 If the fracture occurs in the tension surface outside ofthe middle third of the span length by not more than 5 % of thespan
34、length, calculate the modulus of rupture as follows:R 5 3Pa/bd2(3)where:a = average distance between line of fracture and thenearest support measured on the tension surface of thebeam, in., (or mm).NOTE 3The weight of the beam is not included in the abovecalculation.8.3 If the fracture occurs in the
35、 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 0.05 in. (1 mm),9.1.3 Average depth to the nearest 0.05 in.
36、(1 mm),9.1.4 Span length in inches (or millimeters),9.1.5 Maximum applied load in pound-force (or newtons),9.1.6 Modulus of rupture calculated to the nearest 5 psi(0.05 MPa),9.1.7 Curing history and apparent moisture condition of thespecimens at the time of test,9.1.8 If specimens were capped, groun
37、d, or if leather shimswere used,9.1.9 Whether sawed or molded and defects in specimens,and9.1.10 Age of specimens.10. Precision and Bias10.1 PrecisionThe coefficient of variation of test resultshas been observed to be dependent on the strength level of thebeams.3The single operator coefficient of va
38、riation has beenfound to be 5.7 %. Therefore, results of two properly con-ducted tests by the same operator on beams made from thesame batch sample should not differ from each other by morethan 16 %. The multilaboratory coefficient of variation hasbeen found to be 7.0 %. Therefore, results of two di
39、fferentlaboratories on beams made from the same batch sampleshould not differ from each other by more than 19 %.10.2 BiasSince there is no accepted standard for deter-mining bias in this test method, no statement on bias is made.11. Keywords11.1 beams; concrete; flexural strength testing; modulus of
40、ruptureSUMMARY OF CHANGESCommittee C09 has identified the location of selected changes to this test method since the last issue,C 78 02, that may impact the use of this test method. (Approved August 15, 2007)(1) Revised 5.1.(2) Revised 6.3.(3) Revised 7.1.3See “Improved Concrete Quality Control Proc
41、edures Using Third PointLoading” by P. M. Carrasquillo and R. L. Carrasquillo, Research Report 119-1F,Project 3-9-87-1119, Center For Transportation Research, The University of Texasat Austin, November 1987, for possible guidance as to the relationship of strengthand variability.C78073ASTM Internati
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45、s, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).C78074
