1、ACI 224.2R-92(Reapproved 2004)Cracking of Concrete Members in Direct TensionReported b y ACI Committee 224David Darwin*ChairmanAndrew Scanlon*Peter Gergely*SubcommitteeCo-ChairmenAlfred G. BisharaHoward L. BoggsMerle E. BranderRoy W. CarlsonWilliam L. Clark, Jr.*Fouad H. Fouad Milos PolvikaTony C. L
2、iu Lewis H. Tuthill*LeRoy Lutz* Orville R. WernerEdward G. Nawy Zenon A. Zielinski* Members of the subcommittee who prepared this report.Committee members voting on this minor revision:Grant T. HalvorsenChairmanGrant T. HalvorsenSecretaryRandall W . PostonSecretaryFlorian BarthAlfred G. BisharaHowar
3、d L. BoggsMerle E. BranderDavid DarwinFouad H. FouadDavid W. FowlerPeter GergelyWill HansenM. Nadim HassounWilliam LeeTony C. LiuEdward G. NawyHarry M. PalmbaumKeith A. PashinaAndrew ScanlonErnest K. SchraderWimal SuarisLewis H . TuthillZenon A. ZielinskiThis report is concerned with cracking in rei
4、nforced concrete causedprimarily by direct tension rather than bending. Causes of direct tension CONTENTScracking are reviewed, and equations for predicting crack spacing andcrack width are presented. As crackin g progresses with increasing load,Chapter 1-Introduction, pg. 224.2-2axial stiffness dec
5、reases. Methods for estimating post-cracking axial stiffnessare discussed. The repor t concludes with a review of methods forChapter 2-Causes of cracking, pg. 224.2-2controlling cracking caused by direct tension. 2.1-Introduction2.2-Applied loads2.3-RestraintKeywords: cracking (fracturing); crack wi
6、dth and spacing; loads(forces); reinforced concrete ; restraints;tensile stress; tension; volum e change.stiffness ; strains ; stresseACI Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in designing, plan-ning, executing, or inspecting construction and in pre
7、paringspecifications. Reference to these documents shall not bemade in the Project Documents. If items found in thesedocuments are desired to be part of the Project Documentsthey should be phrased in mandatory language and in-corporated into the Project Documents. Chapter 3-Crack behavior and predic
8、tion equations, pg.224.2-33.1-Introduction3.2-Tensile strengthThe 1992 revisions became effective Mar. 1, 1992. The revisions consisted ofremoving year designations of the recommended references of standards-pro-ducing organizations so that they refer to current editions.Copyright 0 1986, American C
9、oncrete Institute.All rights reserved including rights of reproduction and use in any form or byany means, including the making of copies by any photo process, or by any elec-tronic or mechanical device, printed, written, or oral, or recording for sound orvisual reproduction or for use in any knowle
10、dge or retrieval system or device,unless permission in writing is obtained from the copyright proprietors.224.2R-2 ACI COMMITTEE REPORT3.3-Development of cracks3.4-Crack spacing3.5-Crack widthChapter 4-Effect of cracking on axial stiffness, pg.224.2R-64.1-Axial stiffness of one-dimensional members4.
11、2-Finite element applications4.3-SummaryChapter 5-Control of cracking cause d by direct tension,pg. 224.2R-95.1-Introduction5.2-Control of cracking caused by applied loads5.3-Control of cracking caused by restraint of volumechangeNotation, pg. 224.23-10Conversion factors-S1 equivalents, pg . 224.2R-
12、11Chapter 6-References, pg. 224.2R-116.1-Recommended references6.2-Cited referencesCHAPTER l-INTRODUCTIONBecause concrete is relatively weak and brittle intension, cracking is expected when significant tensilestress is induced in a member. Mild reinforcement and/orprestressing steel can be used to p
13、rovide the necessarytensile strength of a tension member. However, a numberof factors must be considered in both design and con-struction to insure proper control of cracking that mayoccur.A separate report b y ACI Committee 22 4 (ACI 224R)covers control of cracking in concrete members in gen-eral,
14、but contains only a brief reference to tensioncracking. This report deals specifically with cracking inmembers subjected to direct tension.Chapter 2 reviews the primary causes of direct tensioncracking, applied loads, and restraint of volume change.Chapter 3 discusses crack mechanisms in tension mem
15、-bers and presents methods for predicting crack spacingand width. The effect of cracking on axial stiffness isdiscussed in Chapter 4. As cracks develop, a progressivereduction in axial stiffness takes place. Methods forestimating the reduced stiffness in the post-crackingrange are presented for both
16、 one-dimensional membersand more complex systems. Chapter 5 reviews measuresthat should be taken in both design and construction tocontrol cracking in direct tension members.Concrete members and structures that transmit loadsprimarily by direct tension rather than bending includebins and silos, tank
17、s, shells, ties of arches, roof andbridge trusses, and braced frames and towers. Memberssuch as floor and roof slabs, walls, and tunnel linings mayalso be subjected to direct tension as a result of therestraint of volume change. In many instances, crackingmay be attributed to a combination of stress
18、es due toapplied load and restraint of volume change. In the fol-lowing sections, the effects of applied loads and restraintof volume change are discussed in relation to the for-mation of direct tension cracks.2.2-Applied loadsAxial forces caused by applied loads can usually beobtained by standard a
19、nalysis procedures, particularly ifthe structure is statically determinate. If the structure isstatically indeterminate, the member forces are affectedby changes in stiffness due to cracking. Methods for est-imating the effect of cracking on axial stiffness arepresented in Chapter 4.Cracking occurs
20、when the concrete tensile stress in amember reaches the tensile strength. The load carried bythe concrete before cracking is transferred to the rein-forcement crossing the crack. For a symmetrical member,the force in the member at cracking isin whichA,= gross areaft= steel area= tensile strength of
21、concreten = the ratio of modulus of elasticity of the steelto that of concretep= reinforcing ratio = ASIA,After cracking, if the applied force remains un-changed, the steel stress at a crack isfs= f =($ -1 +rJ)fi( 2. 2 )For n = 10, fi = 500 psi (3.45 MPa). Table 2.1 givesthe steel stress after crack
22、ing for a range of steel ratiosp, assuming that the yield strength of the steel =Em=ES=P =that of concreteaxial loadaxial load carried by concreteaxial load at which cracking occursaxial load carried by reinforcementbar spacing, in.effective concrete cover, in.unit weight of concrete , lb/ft3most pr
23、obable maximum crack width, in.factor limiting distribution of reinforcementratio of distance between neutral axis andtension face to distance between neutral axisand centroid of reinforcing steel = 1.20 in.beamsaverage strain in member (unit elongation)tensile strain in reinforcing bar assuming not
24、ension in concretereinforcing ratio = A#$CONVERSION FACTORS-SI EQUIVALENTS1 in. = 25.4 mm1 lb (mass ) = 0.4536 kg1 lb (force) = 4.488 N1 lb/in.2= 6.895 kPa1 kip = 444.8 N1 kip/in.2= 6.89 5 MPaEq. (3.5)2Wm ax= 0.02 fSdc x 10-3Eq. (3.6)Wmax= 0*0145f, Abel, John F.; and Billington, DavidP., “Buckling o
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26、 1984,126 pp.4. Neville, Adam M., Hardened Concrete: Physical andMechanical Aspects, ACI Monograph No. 6, AmericanConcrete Institute/Iowa State University Press, Detroit,1971, 260 pp.5. Wright, P.J.F., “Comments on Indirect Tensile Teston Concrete Cylinders, ” Magazine of Concrete Research(London),
27、V. 7, No. 20, July 1955, pp. 87-96.6. Price, Walter H. ,“Factors Influencing ConcreteStrength,” ACI J OURNA L , Proceedings V. 47, No. 6, Feb.1951, pp. 417-432.7. Evans, R.H., and Marathe, M.S., “Microcrackingand Stress-Strain Curves for Concrete in Tension,”Materials and Structures, Research and Te
28、sting (RILEM,Paris), V. 1, No. 1, Jan.-Feb. 1968, pp. 61-64.8. Petersson, Per-Erik ,“Crack Growth and De-velopment of Fractur e Zones in Plain Concrete andSimilar Materials,” Report No. TVBM-1006, Division ofBuilding Materials, Lund Institute of Technology, 1981,174 pp.9. Broms, Bengt B. , “Crack Wi
29、dth and Crack Spacingin Reinforced Concrete Members, ” ACI J OURNA L , Pro-ceedings V. 62, No. 10, Oct. 1965, pp. 1237-1256.10. Broms, Bengt B. ,“Stress Distribution in Rein-forced Concrete Members With Tension Cracks, ” ACIJ OURNA L , Proceedings V. 62, No. 9, Sept. 1965, pp. 1095-1108.11. Broms, B
30、engt B., and Lutz, Leroy A., “Effects ofArrangement of Reinforcement on Crack Width andSpacing of Reinforced Concrete Members, ” ACIJ OURNA L , Proceedings V. 62, No. 11, Nov. 1965, pp.1395-1410.12. Goto, Yukimasa ,“Cracks Formed in ConcreteAround Deformed Tension Bars, ” ACI J OURNA L ,Proceedings
31、V. 68, No. 4, Apr. 1971, pp. 244-251.13. Goto, Y., and Otsuka, K., “Experimental Studieson Cracks Formed in Concrete Around Deformed Ten-sion Bars, ” Technology Reports of the Tohoku University,V. 44, No. 1, June 1979, pp. 49-83.14. Clark, L.A., and Spiers, D.M., “Tension Stiffeningin Reinforced Con
32、crete Beams and Slabs Unde r Short-Term Load, ” Technical Report No. 42.521, Cement andConcrete Association , Wexham Springs, 1978, 19 pp.15. Somayaji, S., and Shah, S.P., “Bond Stress VersusSlip Relationship and Cracking Response of TensionMembers,” ACI J OURNA L , Proceedings V. 78, No. 3, May-Jun
33、e 1981, pp. 217-225.16. Cusick, R.W., and Kesler, C.E., “Interi m Report-Phase 3: Behavior of Shrinkage-Compensating ConcretesSuitable for Use in Bridge Decks, ” T. Ingraffea, Anthony R.; andGergely, Peter, Tension Stiffening: A FractureMechanics Approach,” Proceedings, International Con-ference on
34、Bond in Concrete (Paisely, Jun e 1982), Ap-plied Science Publishers, London, 1982, pp. 97-106.27. Scanlon, A., and Murray, D.W., “An Analysis toDetermine the Effects of Cracking in Reinforced Con-crete Slabs, ” Proceedings, Specialty Conference on theFinite Element Method in Civil Engineering, EIC/M
35、cGillUniversity, Montreal, 1972, pp. 841-867.28. Lin, Cheng-Shung, and Scordelis, Alexander C.,“Nonlinear Analysis of RC Shells of General Form,”Proceedings, ASCE, V. 101, ST3, Mar. 1975, pp. 523-538.29. Chitnuyanondh, L.; Rizkalla, S.; Murray, D.W.;and MacGregor, J.G. ,“An Effective Uniaxial Tensil
36、eStress-Strain Relationship for Prestressed Concrete,”Structural Engineering Report No. 74 , University ofAlberta, Edmonton, Feb. 1979, 91 pp.30. Argyris, J.H.; Faust, G.; Szimmat, J.; Warnke, P.,and William, K.J., “Recent Developments in the FiniteElement Analysis of Prestressed Concrete ReactorVes
37、sels,” Preprints, 2nd International Conference onStructural Mechanics in Reactor Technology (Berlin,Sept. 1973), Commission of the European Communities,Luxembourg, V. 3, Paper H l/l, 20 pp. Also , NuclearEngineering and Design (Amsterdam), V. 28, 1974.31. Gilbert, R. Ian, and Warner, Robert F., Tens
38、ionStiffening in Reinforced Concrete Slabs, ” Proceedings,ASCE, V. 104, ST12, Dec. 1978, pp. 1885-1900.32. Bazant, Zdenek, and Cedolin, Luigi, “Blunt CrackBand Propagation in Finite Element Analysis,”Proceedings, ASCE, V. 105, EM2, Apr. 1979, pp . 297-315.33. Tuthill, Lewis H., “Tunnel Lining With PumpedConcrete,” ACI J OURNA L ., Proceedings V. 68, No. 4, Apr.1971, pp. 252-262.34. Concrete Manual, 8th Edition, U.S. Bureau ofReclamation, Denver, 1975, 627 pp.
