Designatio Desig nation: n: C 469 – 02
Standard Test Method for
Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression1 This standard is issued under the fixed designation C 469; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript supersc ript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Sco Scope pe
3. Signi Significanc ficancee and Use
1.1 This tes testt met method hod cov covers ers det determ ermina inatio tion n of ( 1) cho chord rd modulus modu lus of elast elasticit icity y (Y (Young’ oung’s) s) and ( 2) Poi Poisso sson’s n’s rat ratio io of molded concrete cylinders and diamond-drilled concrete cores when under longitudinal compressive stress. Chord modulus of elasticity and Poisson’s ratio are defined in Terminology E 6. 1.2 The values stated in inch-pound inch-pound units are to to be regarded as the standard. standa ndard rd does not purport purport to add addre ress ss all of the 1.3 This sta safe sa fety ty co conc ncer erns ns,, if an anyy, as asso soci ciat ated ed wi with th it itss us use. e. It is th thee responsibility of the user of this standard to establish appro priate safety and health practices and determine the applicability of regulatory limitations prior to use.
3.1 This test method provides provides a stre stress ss to stra strain in ratio value and an d a ra rati tio o of la late tera rall to lo long ngit itud udin inal al st stra rain in fo forr ha hard rden ened ed conc co ncre rete te at wh what atev ever er ag agee an and d cu curi ring ng co cond ndit itio ions ns ma may y be designated. 3.2 The modulus of elast elasticit icity y and Poisson’s Poisson’s rati ratio o valu values, es, applicabl appli cablee with within in the customary customary worki working ng stre stress ss range (0 to 40 % of ult ultim imate ate con concre crete te str streng ength) th),, are use used d in siz sizing ing of reinforced and nonreinforced structural members, establishing the quantity of reinf reinforcem orcement, ent, and comp computing uting stress for observed strains. 3.3 The modulus of elas elastici ticity ty values obtained will usually be les lesss tha than n mod moduli uli der derive ived d und under er rap rapid id loa load d app applic licati ation on (dynamic or seismic rates, for example), and will usually be greater than values under slow load application or extended load duration, given other test conditions being the same.
2. Referenced Documents 2.1 ASTM Standards: C 31/C 31M Practice for Making and Curing Concrete Concrete Test Test Specimens in the Field 2 C 39/C 39M Test Method for Compressive Compressive Strength Strength of Cylindrical Concrete Specimens 2 C 42/C 42M Test Method for Obtaining and Testing Testing Drilled Cores and Sawed Beams of Concrete 2 C 174/ 174/C C 174M Test Meth Method od for Meas Measuring uring Thic Thickness kness of Concrete Elements Using Drilled Concrete Cores 2 C 192/C 192/C 192M Pract Practice ice for Makin Making g and Curin Curing g Concr Concrete ete Test Specimens in the Laboratory 2 C 617 617 Pra Practi ctice ce for Cap Cappin ping g Cyl Cylind indric rical al Con Concre crete te Spe Specicimens2 E 4 Practices for Force Verification Verification of Testing Testing Machines 3 E 6 Termi erminolo nology gy Relat Relating ing to Meth Methods ods of Mech Mechanica anicall Test3 ing E 83 Prac Practice tice for Verific erification ation and Class Classificat ification ion of Exte Extenn3 someter E 177 Pract Practice ice for Use of the Terms Terms Precision Precision and Bias in 4 ASTM Test Methods
4. Appa Apparatus ratus Testing Machine—Us 4.1 Testing —Usee a tes testin ting g mac machin hinee cap capabl ablee of imposing a load at the rate and of the magnitude prescribed in 6.4. The machine shall conform to the requirements of Practices E 4 (Constant-Rate of-Traverse C RT RT-Ty -Type pe Te Testing sting Machines section). The spherical head and bearing blocks shall conform to the Apparatus Section of Test Test Method C 39/C 39M. 5 4.2 Compressometer —Fo —Forr det determ ermini ining ng the mod modulu uluss of elasticity use a bonded (Note 1) or unbonded sensing device that measures to the nearest 5 millionths the average deformation of two diametrically opposite gage lines, each parallel to the axis, and each centered about midheight of the specimen. The effective length of each gage line shall be not less than three times the maximum size of the aggregate in the concrete nor more tha than n two thirds thirds the height height of the specimen specimen;; the preferred length of the gage line is one half the height of the specimen. Either use gage points embedded in or cemented to the specimen, and read deformation of the two lines independently; or use a compressometer (such as is shown in Fig. 1) consisting of two yokes, one of which (see B , Fig. 1) is rigidly attached to the specimen and the other (see C , Fig. 1) attached at two diametrically opposite points so that it is free to rotate.
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Thiss test method is und Thi under er the jur jurisd isdicti iction on of ASTM Com Commit mittee tee C09 on Concrete and Concrete Aggreg Concrete Aggregates ates and is the direct responsibility responsibility of Subcommittee Subcommittee C09.61 C09. 61 on Testing Testing for Strength. Current edition approved Aug. 10, 2002. Published Published Octobe Octoberr 2002 2002.. Origin Originally ally published publi shed as C469 – 61. Last previo previous us edition C469 – 94 1. 2 Annual Book of ASTM Standard Standardss, Vol 04.02. 3 Annual Book of ASTM Standard Standardss, Vol 03.01. 4 Annual Book of ASTM Standard Standardss, Vol 14.02. e
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C 469 – 02
d = displacement due to specimen deformation r = displacement due to rotation of the yoke about the pivot rod a = location of gage b = support point of the rotating yoke c = location of pivot rod g = gage reading
FIG.. 2 FIG
Diagra Dia gram m of Dis Displa placem cement ents s
where: d = total total deformat deformation ion of the specime specimen n thr throug oughou houtt the effective gage length, µin. (µm), g = gage read reading, ing, µin. (µm) (µm),, er = the perpendi perpendicular cular distan distance, ce, measured measured in inches inches (mil(millimetres) to the nearest 0.01 in. (0.254 mm) from the pivot rod to the vertical plane passing through the two support points of the rotating yoke, and perpendicular distance, measured in inches inches (milli(millieg = the perpendicular metres) to the nearest 0.01 in. (0.254 mm) from the gagee to the ver gag vertic tical al pla plane ne pas passin sing g thr throug ough h the two support points of the rotating yoke. Proced Pro cedure uress for cal calibr ibrati ating ng str strain ain-me -measu asurin ring g dev device icess are given in Practice E 83. FIG. 1
Suitable Suita ble Compr Compressom essometer eter
NOTE 1—Although bonded strain gages are satisfactory on dry specimens, they may be difficult, if not impossible, to mount on specimens continually continu ally moist-c moist-cured ured until tested tested..
At on onee po poin intt on th thee ci circ rcum umfe fere renc ncee of th thee ro rota tati ting ng yo yoke ke,, midway between the two support points, use a pivot rod (see A, Fig. 1) to maintain a constant distance between the two yokes. At the opposite point on the circumference of the rotating yoke, the change in distance between the yokes (that is, the gage read re adin ing) g) is eq equa uall to th thee su sum m of th thee di disp spla lace ceme ment nt du duee to specimen deformation and the displacement due to rotation of the yoke about the pivot rod (see Fig. 2). 4.2.1 Meas Measure ure deformatio deformation n by a dial gage used directly directly or with a lever multiplying system, by a wire strain gage, or by a linear variable differential transformer. If the distances of the pivot rod and the gage from the vertical plane passing through the support points of the rotating yoke are equal, the deformation of the specimen is equal to one-half the gage reading. If these the se dis distan tances ces are not equ equal, al, cal calcul culate ate the def deform ormati ation on as follows: d 5 ge r / ~er 1 eg!
4.3 Extensometer 5—If Poisson’s ratio is desired, the transverse strain shall be determined ( 1) by an unbonded extensometer capable of measuring to the nearest 25 µin. (0.635 µm) the change in diameter at the midheight of the specimen, or ( 2) by two bonded strain gages (Note 1) mounted circumferentially at diametrically opposite points at the midheight of the specimen and capable of measuring circumferential strain to the nearest 5 mill milliont ionths. hs. A combi combined ned compr compressom essometer eter and exte extensome nsometer ter (Fig. 3) is a convenient unbonded device. This apparatus shall contain a third yoke (consisting of two equal segments) located halfway between the two compressometer yokes and attached to the specimen at two diametrically opposite points. Midway between these points use a short pivot rod ( A , see Fig. 3), adjacent to the long pivot rod, to maintain a constant distance between the bottom and middle yokes. Hinge the middle yoke at the pivot point to permit rotation of the two segments of the 8
(1)
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C 469 – 02 5. Test Specimens
FIG. 3
5.1 Molded Cylindrical Specimens —Mold test cylinders in accordance with the requirements for compression test specimens in Practice C 192/C 192M, or in Practice C 31/C 31M. Subject specimens to the specified curing conditions and test at the age for which the elasticity elasticity information information is desi desired. red. Test Test specimens within 1 h after removal from the curing or storage room. Specimens removed from a moist room for test shall be kept moist by a wet cloth covering during the interval between removal and test. 5.2 Drilled Core Specimens—Cores shall comply with the requirements for drilling, and moisture conditioning applicable to com compre pressi ssive ve str streng ength th spe specim cimens ens in Test Met Method hod C 42/ C 42M 42M,, exc except ept tha thatt onl only y dia diamon mond-d d-dril rilled led cor cores es hav having ing a length-to-diameter ratio greater than 1.50 shall be used. Requirem qui rement entss rel relati ative ve to sto storag ragee and to am ambie bient nt con condit dition ionss immedi imm ediate ately ly pri prior or to tes testt sha shall ll be the same as for molded molded cylindrical specimens. 5.3 The ends of the test specimens specimens shall be made perpendicular to the axis ( 6 0.5°) and plane (within 0.002 in.). If the specimen as cast does not meet the planeness requirements, planeness shall be accomplished by capping in accordance with Prac Pr acti tice ce C 61 617, 7, or by la lapp ppin ing, g, or by gr grin indi ding ng.. It is no nott prohibited to repair aggregate popouts that occur at the ends of specimens, provided the total area of popouts does not exceed 10 % of the specimen area and the repairs are made before capping or grinding is completed (Note 2). Planeness will be considered within tolerance when a 0.002 in. (0.05 mm) feeler gage will not pass between the specimen surface and a straight edge held against the surface.
Suitable Suita ble Combined Combined Compre Compressom ssometereter-Exte Extensome nsometer ter
yoke in the horizon yoke horizontal tal plane. plane. At the opposite opposite point on the circumference, connect the two segments through a dial gage or oth other er sen sensin sing g dev device ice cap capabl ablee of mea measur suring ing tra transv nsvers ersee deformation to the nearest 50 µin. (1.27 µm). If the distances of the hinge and the gage from the vertical plane passing through the support points of the middle yoke are equal, the transverse deformation of the specimen diameter is equal to one-half the gage reading. reading. If thes thesee dist distances ances are not equal, calc calculate ulate the transverse deformation of the specimen diameter in accordance with Eq 2. d 5 g e h / ~e 8
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1 e g! 8
NOTE 2—Repairs may be made by epoxying the dislodged aggregate back in place or by filling the void with capping material and allowing adequate time for it to harden.
5.4 Measu Measure re the diameter diameter of the test specimen specimen by caliper to the nearest nearest 0.0 0.01 1 in. (0. (0.25 25 mm mm)) by ave averag raging ing two diameter diameterss measured at right angles to each other near the center of the length of the specimen. Use this average diameter to calculate the cross-sectional area. Measure and report the length of a molded specimen, including caps, to the nearest 0.1 in. (2.54 mm). Measure the length of a drilled specimen in accordance with Test Method C 174/C 174M; report the length, including caps, to the nearest 0.1 in. (2.54 mm).
(2)
where: the specimen specimen diameter diameter,, µin. d = transverse deformation of the (µm), g = trans transverse verse gage readi reading, ng, µin. µin. (µm), (µm), e h = the perpendicu perpendicular lar distance, distance, measured measured in inches inches (millimeters) to the nearest 0.01 in. (0.254 mm) from the hinge to the vertical plane passing through the support points of the middle yoke, and e g = the perpendicu perpendicular lar distance, distance, measured measured in inches inches (millimeters) to the nearest 0.01 in. (0.254 mm) from the gage to the vertical plane passing through the support points of the middle yoke. 4.4 Balance or Scale, accurate to 0.1 lb (0.045 kg) shall be used if necessary. 8
6. Proc Procedur eduree 6.1 Mainta Maintain in the amb ambien ientt tem temper peratu ature re and hum humidi idity ty as constant as possible throughout the test. Record any unusual fluctuation in temperature or humidity in the report. 6.2 Use companion specimens specimens to determine the compressive compressive strength in accordance with Test Method C 39/C 39M prior to the test for modulus of elasticity. 6.3 Place the speci specimen, men, with the strain-measur strain-measuring ing equipmentt att men attach ached, ed, on the lower platen platen or bea bearin ring g blo block ck of the testing machine. Carefully align the axis of the specimen with the center of thrus thrustt of the spher spherical ically-se ly-seated ated upper beari bearing ng bloc bl ock. k. No Note te th thee re read adin ing g on th thee st stra rain in in indi dica cato tors rs.. As th thee
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C 469 – 02 spherically-s spherical ly-seated eated block is broug brought ht slow slowly ly to bear upon the specimen, rotate the movable portion of the block gently by hand so that uniform seating is obtained. 6.4 Load the specimen at at least twice. Do not record record any data during the first loading. Base calculations on the average of the results of the subsequent loadings (Note 3).
machinee loa machin load d by the cro crossss-sec sectio tional nal are areaa of the spe specim cimen en determined in accordance with 5.4. 7. Calc Calculat ulation ion 7.1 Calcu Calculat latee the mod modulu uluss of ela elasti sticit city y, to the nea neares restt 50 000 psi (344.74 (344.74 MPa) as follows: E 5 ~S 2 2 S 1! / ~e 2 2 0.000050!
NOTE 3—At least two subsequent loadings are recommended so that the repeatability of the test may be noted.
(3)
where: E = chord modu modulus lus of elast elasticit icity y, psi, psi, S 2 = stre stress ss cor corresp respondin onding g to 40 % of ultima ultimate te load, load, S 1 = stre stress ss correspo corresponding nding to to a longitudi longitudinal nal strain, strain, e 1, of 50 millionths, psi, and longitudi tudinal nal strai strain n produced produced by by stress stress S 2. e 2 = longi 7.2 Calculate Poisson’s Poisson’s ratio, to the nearest 0.01, as follows:
During the first loading, which is primarily for the seating of the gages, observe the performance of the gages (Note 4) and correc cor rectt any unu unusua suall beh behavi avior or pri prior or to the sec second ond loa loadin ding. g. Obta Ob tain in ea each ch se sett of re read adin ings gs as fo foll llow ows: s: Ap Appl ply y th thee lo load ad continuously and without shock. Set testing machines of the screw type so that the moving head travels at a rate of about 0.05 in. (1.25 mm)/min when the machine is running idle. In hydraulically operated machines, apply the load at a constant rate within the range 35 6 5 psi (241 6 34 kPa)/s. Record, without interruption of loading, the applied load and longitudinal strain at the point ( 1) when the longitudinal strain is 50 millionths and ( 2) when the applied load is equal to 40 % of the ultimate load (see 6.5). Longitudinal strain is defined as the total longitudinal longitudinal defor deformati mation on divi divided ded by the ef effecti fective ve gage length len gth.. If Poi Poisso sson’s n’s ratio is to be det determ ermine ined, d, rec record ord the transverse strain at the same points. If a stress-strain curve is to be det determ ermine ined, d, tak takee rea readin dings gs at two or mor moree int interm ermedi ediate ate points without interruption of loading; or use an instrument that makes a conti continuous nuous record. Immediately Immediately upon reac reaching hing the maximum load, except on the final loading, reduce the load to zero at the same rate at which it was applied. If the observer fails to obtain a reading, complete the loading cycle and then repeat it. Record the extra cycle in the report.
~e2 2 0.000050 ! µ 5 ~et2 2 e t1! / ~e
(4)
where: µ = Po Pois issson on’’s ra rati tio, o, et2 = tran transvers sversee strain strain at midh midheight eight of tthe he specimen specimen proproduced by stress S 2, and et1 = tran transvers sversee strain strain at midheight midheight of the the spec specimen imen proproduced by stress S 1. 8. Repo Report rt 8.1 Repor Reportt the following following info informat rmation: ion: 8.1.1 Specimen identification identification number, number, 8.1.2 Dimen Dimension sionss of speci specimen, men, in inche inchess (or millimetre millimetres), s), 8.1.3 Curin Curing g and environmenta environmentall hist histories ories of the specimen, specimen, 8.1.4 Age of the specimen, specimen, 8.1.5 Stren Strength gth of the concrete, concrete, if dete determin rmined, ed, 8.1.6 Unit weight of the concr concrete, ete, if determined, determined, 8.1.7 Stres Stress-str s-strain ain curves, if plot plotted, ted, 8.1.8 Chord modulus modulus of elasticity elasticity,, and 8.1.9 Poiss Poisson’s on’s ratio, if dete determin rmined. ed.
NOTE 4—Where a dial gage is used to measure longitudinal deformation, it is convenient tion, convenient to set the gage before before eac each h loa loading ding so tha thatt the indicator will pass the zero point at a longitudinal strain of 50 millionths.
9. Prec Precisio ision n and Bias 9.1 Precision—The singl single-ope e-operator rator-mac -machine hine multi multibatch batch precision is 6 4.25 % (R1S %) max, as defined in Practice precision E 17 177, 7, ov over er th thee ra rang ngee fr from om 2. 2.5 5 to 4 3 106 ps psii (1 (17. 7.3 3 to 27.6 3 10 Pa) Pa);; the theref refore ore,, the res result ultss of tes tests ts of dup dupli licat catee cylinders from different batches should not depart more than 5 % from the average of the two. 9.2 Bias—This test method has no bias because the values determined can only be defined in terms of the test method.
6.5 It is not prohibited prohibited to obtain the modulus of elasticity elasticity and strength on the same loading provided that the gages are expendable, removable, or adequately protected so that it is possible to comply with the requirement for continuous loading given in Test Method C 39/C 39M. In this case record several readings and determine the strain value at 40 % of the ultimate by interpolation. 6.6 If intermediat intermediatee read readings ings are taken, plot the results results of each eac h of the three tests with the longitud longitudina inall str strain ain as the abscissa and the compressive stress as the ordinate. Calculate the compressive stress by dividing the quotient of the testing
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10. Keyw Keywords ords 10.1 comp compressi ression on test testing; ing; concr concrete; ete; modu modulus lus of elas elastici ticity; ty; Poisson’s ratio
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C 469 – 02
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