1、Designation: C78/C78M 15aC78/C78M 15bStandard 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
2、 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.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope*1.1 This
3、test method covers the determination of the flexural strength of concrete by the use of a simple beam with third-pointloading.1.2 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in eachsystem may not be exact equivalents; therefor
4、e, each system shall be used independently of the other. Combining values from thetwo systems may result in non-conformance with the standard.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standar
5、d to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C31/C31M Practice for Making and Curing Concrete Test Specimens in the FieldC42/C42M Test Method for Obtaining and Testing Drilled C
6、ores and Sawed Beams of ConcreteC192/C192M Practice for Making and Curing Concrete Test Specimens in the LaboratoryC617 Practice for Capping Cylindrical Concrete SpecimensC1077 Practice forAgencies Testing Concrete and ConcreteAggregates for Use in Construction and Criteria for TestingAgencyEvaluati
7、onE4 Practices for Force Verification of Testing Machines3. Significance and Use3.1 This test method is used to determine the flexural strength of specimens prepared and cured in accordance withTest MethodsC42/C42M or Practices C31/C31M or C192/C192M. Results are calculated and reported as the modul
8、us of rupture. The For thesame specimen size, the strength determined will vary whereif there are differences in specimen size, preparation, moisturecondition, curing, or where the beam has been curing procedure, moisture condition at time of testing, and whether the beam wasmolded or sawed to size.
9、3.2 The measured modulus of rupture generally increases as the specimen size decreases3,4,5 and it has been shown that thevariability of individual test results increases as the specimen size decreases.3,43.3 The results of this test method may be used to determine compliance with specifications or
10、as a basis for proportioning,mixing and placement operations. mixture proportioning, evaluating uniformity of mixing, and checking placement operations byusing sawed beams. It is used primarily in testing concrete for the construction of slabs and pavements.1 This test method is under the jurisdicti
11、on of ASTM Committee C09 on Concrete and Concrete Aggregates and is the direct responsibility of Subcommittee C09.61 onTesting for Strength.Current edition approved May 1, 2015Dec. 1, 2015. Published June 2015January 2016. Originally approved in 1930. Last previous edition approved in 2015 as C78/C7
12、8M 15.15a. DOI: 10.1520/C0078_C0078M-15A.10.1520/C0078_C0078M-15B.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM web
13、site.3 Tanesi, J; Ardani, A. Leavitt, J. “Reducing the Specimen Size of Concrete Flexural Strength Test (AASHTO T97) for Safety and Ease of Handling,“ TransportationResearch Record: Journal of the Transportation Research Board, No. 2342, Transportation Research Board of National Academies, Washingto
14、n, D.C., 2013.4 Carrasquillo, P.M. and Carrasquillo, R. L “Improved Concrete Quality Control Procedures Using Third Point Loading”, Research Report 119-1F, Project 3-9-87-1119,Center For Transportation Research, The University of Texas at Austin, November 1987.5 Bazant, Z. and Novak, D. “Proposal fo
15、r Standard Test of Modulus of Rupture of Concrete with its Size Dependence,“ ACI Materials Journal, January-February 2001.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit
16、 may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section appears at
17、 the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14. Apparatus4.1 Testing MachineThe testing machine shall conform to the requirements of the sections on Basis of Verification,Corrections, and Time Interval Betw
18、een Verifications of Practices E4. Hand operated testing machines having pumps that do notprovide a continuous loading in one stroke are not permitted. Motorized pumps or hand operated positive displacement pumpshaving sufficient volume in one continuous stroke to complete a test without requiring r
19、eplenishment are permitted and shall becapable of applying loads at a uniform rate without shock or interruption. The testing machine shall be equipped with a means ofrecording or holding the peak value that will indicate the maximum load, to within 1 % accuracy, applied to the specimen duringa test
20、.4.2 Loading ApparatusThe third point loading method shall be used in making flexure tests of concrete employing bearingblocks that will ensure that forces applied to the beam will be perpendicular to the face of the specimen and applied withouteccentricity. A diagram of an apparatus that accomplish
21、es this purpose is shown in Fig. 1.4.2.1 All apparatus for making flexure tests of concrete shall be capable of maintaining the specified span length and distancesbetween load-applying blocks and support blocks constant within 61.0 mm 60.05 in.4.2.2 The ratio of the horizontal distance between the p
22、oint of application of the load and the point of application of the nearestreaction 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 is used: the load-applying and support blocks shall not be more than65 mm 2.50 in. high, measured from the cent
23、er or the axis of pivot, and should extend entirely across or beyond the full widthof the specimen. Each case-hardened bearing surface in contact with the specimen shall not depart from a plane by more than 0.05mm 0.002 in. and shall be a portion of a cylinder, the axis of which is coincidental with
24、 either the axis of the rod or center ofthe ball, whichever the block is pivoted upon. The angle subtended by the curved surface of each block shall be at least 0.80 rad45. The load-applying and support blocks shall be maintained in a vertical position and in contact with the rod or ball by meansof
25、spring-loaded screws that hold them in contact with the pivot rod or ball. The uppermost bearing plate and center point ball inFig. 1 may be omitted when a spherically seated bearing block is used, provided one rod and one ball are used as pivots for theupper load-applying blocks.5. Testing Test Spe
26、cimens5.1 The test specimen shall conform to all requirements of Test Method C42/C42M or Practices C31/C31M or C192/C192Mapplicable to beam specimens and shall have a test span within 2 % of being three times its depth as tested. The sides of thespecimen shall be at right angles with the top and bot
27、tom. All surfaces shall be smooth and free of scars, indentations, holes, orinscribed identification marks.5.2 Provided the smaller cross-sectional dimension of the beam is at least three times the nominal maximum size of the coarseaggregate, the modulus of rupture can be determined using different
28、specimen sizes. However, measured modulus of rupturegenerally increases as specimen size decreases.3,4 (Note 1).NOTE 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 o
29、n a rod and the other on a ball.FIG. 1 Schematic of a Suitable Apparatus for Flexure Test of Concrete by Third-Point Loading MethodC78/C78M 15b2NOTE 1The strength ratio for beams of different sizes depends primarily on the maximum size of aggregate.5 Experimental data obtained in twodifferent studie
30、s have shown that for maximum aggregate size between 19.0 and 25.0 mm 34 and 1 in., the ratio between the modulus of rupturedetermined with a 150 by 150 mm 6 by 6 in. and a 100 by 100 mm 4 by 4 in. may vary from 0.90 to 1.073 and for maximum aggregate size between9.5 and 37.5 mm 38 and 112 in., the
31、ratio between the modulus of rupture determined with a 150 by 150 mm 6 by 6 in. and a 115 by 115 mm 4.5by 4.5 in. may vary from 0.86 to 1.00.45.3 The individual who tests concrete beams for acceptance testing shall meet the concrete laboratory technician requirementsof Practicespecifier of tests sha
32、ll specify the specimen size and number of specimens C1077 including Test Methodto be tested toC78/C78M as a relevant test.obtain an average test result (Note 2). The same specimen size shall be used for qualification andacceptance testing.NOTE 2The testing laboratory performing this test method may
33、 be evaluated in accordance with It has been shown that the variability of individualtest results increases as the specimen size decreases.Practice3,C1077.46. Procedure6.1 Flexural tests of moist-cured specimens shall be made as soon as practical after removal from moist storage. Surface dryingof th
34、e specimen results in a reduction in the measured flexural strength.6.2 When using molded specimens, turn the test specimen on its side with respect to its position as molded and center it on thesupport blocks. When using sawed specimens, position the specimen so that the tension face corresponds to
35、 the top or bottom ofthe specimen as cut from the parent material. Center the loading system in relation to the applied force. Bring the load-applyingblocks in contact with the surface of the specimen at the third points and apply a load of between 3 and 6 % of the estimatedultimate load. Using 0.10
36、 mm 0.004 in. and 0.40 mm 0.015 in. leaf-type feeler gages, determine whether any gap between thespecimen and the load-applying or support blocks is greater or less than each of the gages over a length of 25 mm 1 in. or more.Grind, cap, or use leather shims on the specimen contact surface to elimina
37、te any gap in excess of 0.10 mm 0.004 in. in width.Leather shims shall be of uniform 6 mm 0.25 in. thickness, 25 to 50 mm 1.0 to 2.0 in. width, and shall extend across the fullwidth of the specimen. Gaps in excess of 0.40 mm 0.015 in. shall be eliminated only by capping or grinding. Grinding of late
38、ralsurfaces shall be minimized inasmuch as grinding may change the physical characteristics of the specimens. Capping shall be inaccordance with the applicable sections of Practice C617.6.3 Load the specimen continuously and without shock. The load shall be applied at a constant rate to the breaking
39、 point.Applythe load at a rate that constantly increases the maximum stress on the tension face between 0.9 and 1.2 MPa/min 125 and 175psi/min until rupture occurs. The loading rate is calculated using the following equation:r 5Sbd2L (1)where:r = loading rate, N/min lb/min,S = rate of increase in ma
40、ximum 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 for testing, mm in., andL = span length, mm in.7. Measurement of Specimens After Test7.1 To determine the dimensions of the specimen cross
41、 section for use in calculating modulus of rupture, take measurementsacross one of the fractured faces after testing. The width and depth are measured with the specimen as oriented for testing. Foreach dimension, take one measurement at each edge and one at the center of the cross section. Use the t
42、hree measurements foreach direction to determine the average width and the average depth. Take all measurements to the nearest 1 mm 0.05 in. If thefracture occurs at a capped section, include the cap thickness in the measurement.8. Calculation8.1 If the fracture initiates in the tension surface with
43、in the middle third of the span length, calculate the modulus of ruptureas follows:R 5 PLbd2 (2)where:R = modulus of rupture, MPa psi,P = maximum applied load indicated by the testing machine, N lbf,L = span length, mm in.,b = average width of specimen, mm in., at the fracture, andd = average depth
44、of specimen, mm in., at the fracture.NOTE 3The weight of the beam is not included in the above calculation.C78/C78M 15b38.2 If the fracture occurs in the tension surface outside of the middle third of the span length by not more than 5 % of the spanlength, calculate the modulus of rupture as follows
45、:R 53Pabd 2 (3)where:a = average distance between line of fracture and the nearest support measured on the tension surface of the beam, mm in.NOTE 4The weight of the beam is not included in the above calculation.8.3 If the fracture occurs in the tension surface outside of the middle third of the spa
46、n length by more than 5 % of the spanlength, 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 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 l
47、oad in N lbf,9.1.6 Modulus of rupture calculated to the nearest 0.05 MPa 5 psi,9.1.7 Curing history and apparent moisture condition of the specimens at the time of test,9.1.8 If specimens were capped, ground, or if leather shims were used,9.1.9 Whether sawed or molded and defects in specimens, and9.
48、1.10 Age of specimens.10. Precision and Bias10.1 PrecisionPrecision6The single-operator coefficient of variation of test results has been observed to be dependent onthe strength level of the beams. The single operator coefficient of variation has been has been found to be 5.7 %. Therefore, resultsof
49、 two properly conducted tests by the same operator on beams made from the same batch sample are not expected to differ fromeach other by more than 16 %. The multilaboratory coefficient of variation has been found to be 7.0 %. Therefore, results of twodifferent laboratories on beams made from the same batch sample are not expected to differ from each other by more than19 %.19 % (Note 5 and Note 6).NOTE 5This precision statement was determined using 150 by 150 by 510 mm 6 by 6 by 20 in. and 11
