1、ACI 224.2R-92(Reapproved 2004)Cracking of Concrete Members in Direct TensionReported byACI 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. Liu
2、 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. BisharaHoward L
3、. 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 reinfor
4、ced concrete causedprimarily by direct tension rather than bending. Causes of direct tensionCONTENTScracking are reviewed, and equations for predicting crack spacing andcrack width are presented. As cracking progresses with increasing load,Chapter 1-Introduction, pg. 224.2-2axial stiffness decreases
5、. Methods for estimating post-cracking axial stiffnessare discussed. The report 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 width and
6、spacing; loads(forces); reinforced concrete; restraints;tensile stress; tension; volume change.stiffness; strains; stresseACI Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in designing, plan-ning, executing, or inspecting construction and in preparingspecif
7、ications. 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 prediction equatio
8、ns, 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 Concrete Inst
9、itute.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 knowledge or retri
10、eval 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 members4.2-Finite ele
11、ment applications4.3-SummaryChapter 5-Control of cracking caused 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-11Chapter 6-Re
12、ferences, 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 provide the nec
13、essarytensile 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 by ACI Committee 224 (ACI 224R)covers control of cracking in concrete members in gen-eral, but contains onl
14、y 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-bers and presen
15、ts 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 one-dimensional
16、 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, tanks, shells, ties
17、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 stresses due toapplied
18、 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 analysis procedur
19、es, 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 when the concret
20、e 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 concreten = the
21、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 cracking for a range of s
22、teel 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 probable maximum crack
23、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 notension in concreterei
24、nforcing 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= 6.895 MPaEq. (3.5)2Wmax= 0.02 fSdc x 10-3Eq. (3.6)Wmax= 0*0145f, Abel, John F.; and Billington, DavidP., “Buckling of Cooling-Tower Shells: St
25、ate-of-the-Art,”Proceedings, ASCE, V. 101, ST6, June 1975, pp. 1185-1203.3. Tam, K.S.S., and Scanlon, A., “The Effects ofRestrained Shrinkage on Concrete Slabs,” StructuralEngineering Report No. 122, Department of Civil En-gineering, University of Alberta, Edmonton, Dec. 1984,126 pp.4. Neville, Adam
26、 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), V. 7, No. 20, July 1955, pp. 8
27、7-96.6. Price, Walter H., “Factors Influencing ConcreteStrength,” ACI J OURNAL , 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 Testing (RILEM,Paris), V. 1, No.
28、1, Jan.-Feb. 1968, pp. 61-64.8. Petersson, Per-Erik ,“Crack Growth and De-velopment of Fracture 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 Width and Crack Spacingin Reinforc
29、ed Concrete Members,” ACI J OURNAL , Pro-ceedings V. 62, No. 10, Oct. 1965, pp. 1237-1256.10. Broms, Bengt B.,“Stress Distribution in Rein-forced C oncrete Members With Tension Cracks,” ACIJ OURNAL , Proceedings V. 62, No. 9, Sept. 1965, pp. 1095-1108.11. Broms, Bengt B., and Lutz, Leroy A., “Effect
30、s ofArrangement of Reinforcement on Crack Width andSpacing of Reinforced Concrete Members,” ACIJ OURNAL , Proceedings V. 62, No. 11, Nov. 1965, pp.1395-1410.12. Goto, Yukimasa, “Cracks Formed in ConcreteAround Deformed Tension Bars,” ACI J OURNAL ,Proceedings V. 68, No. 4, Apr. 1971, pp. 244-251.13.
31、 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 Concrete Beams and Slabs Under Short-Term Lo
32、ad,” 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 OURNAL , Proceedings V. 78, No. 3, May-June 1981, pp. 217-225.16. Cusick, R.W., and Kes
33、ler, C.E., “Interim 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 Bond in Concrete (Paisely, June 1982), Ap-plied
34、 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/McGillUniversity, Montreal, 1972, pp. 841-867.28.
35、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 TensileStress-Strain Relationship for Prestressed Concre
36、te,”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 ReactorVessels,” Preprints, 2nd International Conference onSt
37、ructural 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., TensionStiffening in Reinforced Concrete Slabs,” Proceed
38、ings,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 OURNAL ., Proceedings V. 68, No. 4, Apr.1971, pp. 252-262.34. Concrete Manual, 8th Edition, U.S. Bureau ofReclamation, Denver, 1975, 627 pp.
