1、ACI 435R-95 became effective Jan. 1, 1995.Copyright 2003, American Concrete Institute.All rights reserved including rights of reproduction and use in any form or by anymeans, including the making of copies by any photo process, or by electronic ormechanical device, printed, written, or oral, or reco
2、rding for sound or visual reproduc-tion or for use in any knowledge or retrieval system or device, unless permission inwriting is obtained from the copyright proprietors.ACI Committee Reports, Guides, Standard Practices,and Commentaries are intended for guidance in plan-ning, designing, executing, a
3、nd inspecting construction.This document is intended for the use of individuals whoare competent to evaluate the significance and limita-tions of its content and recommendations and who willaccept responsibility for the application of the materialit contains. The American Concrete Institute disclaim
4、sany and all responsibility for the stated principles. TheInstitute shall not be liable for any loss or damagearising therefrom.Reference to this document shall not be made incontract documents. If items found in this document aredesired by the Architect/Engineer to be a part of thecontract document
5、s, they shall be restated in mandatorylanguage for incorporation by the Architect/Engineer.435R-1Control of Deflection in Concrete StructuresACI 435R-95(Reapproved 2000)(Appendix B added 2003)This report presents a consolidated treatment of initial and time-dependentdeflection of reinforced and pres
6、tressed concrete elements such as simple andcontinuous beams and one-way and two-way slab systems. It presents thestate of the art in practice on deflection as well as analytical methods forcomputer use in deflection evaluation. The introductory chapter and fourmain chapters are relatively independe
7、nt in content. Topics include “Deflec-tion of Reinforced Concrete One-way Flexural Members,” “Deflection ofTwo-way Slab Systems,” and “Reducing Deflection of Concrete Members.”One or two detailed computational examples for evaluating the deflec-tion of beams and two-way action slabs and plates are g
8、iven at the end ofChapters 2, 3, and 4. These computations are in accordance with the currentACI- or PCI-accepted methods of design for deflection.Keywords: beams; camber; code; concrete; compressive strength; cracking;creep; curvature; deflection; high-strength concrete; loss of prestress;modulus o
9、f rupture; moments of inertia; plates; prestressing; preten-sioned; post-tensioned; reducing deflection; reinforcement; serviceability;shrinkage; slabs; strains; stresses; tendons; tensile strength; time-depen-dent deflection.CONTENTSChapter 1Introduction, p. 435R-2Chapter 2Deflection of reinforced
10、concrete one-way flexural members, p. 435R-32.1Notation2.2General2.3Material properties2.4Control of deflection2.5Short-term deflection2.6Long-term deflection2.7Temperature-induced deflectionsAppendix A2, p. 435R-16Example A2.1Short- and long-term deflection of 4-spanbeamExample A2.2Temperature-indu
11、ced deflectionsChapter 3Deflection of prestressed concrete one-way flexural members, p. 435R-203.1Notation3.2General3.3Prestressing reinforcement3.4Loss of prestressReported by ACI Committee 435Emin A. Aktan Anand B. Gogate Maria A. PolakAlex Aswad Jacob S. Grossman Charles G. SalmonDonald R. Buettn
12、erHidayat N. Grouni*Andrew ScanlonFinley A. Charney C. T. Thomas Hsu Fattah A. ShaikhRussell S. Fling James K. Iverson Himat T. SolankiAmin Ghali Bernard L. Meyers Maher K. TadrosSatyendra K. Ghosh Vilas Mujumdar Stanley C. WoodsonEdward G. NawyChairmanA. Samer EzeldinSecretary*EditorAcknowledgment
13、is due to Robert F. Mast for his major contributions to the Report, and to Dr. Ward R. Malisch for his extensive input to the various chapters.The Committee also acknowledges the processing, checking, and editorial work done by Kristi A. Latimer of Rutgers University.435R-2 ACI COMMITTEE REPORT3.5Ge
14、neral approach to deformation considerationsCurvature and deflection3.6Short-term deflection and camber evaluation inprestressed beams3.7Long-term deflection and camber evaluation inprestressed beamsAppendix A3, p. 435R-42Example A3.1Short- and long-term single-tee beamdeflectionsExample A3.2Composi
15、te double-tee cracked beamdeflectionsChapter 4Deflection of two-way slab systems,p. 435R-504.1Notation4.2Introduction4.3Deflection calculation method for two-way slabsystems4.4Minimum thickness requirements4.5Prestressed two-way slab systems4.6Loads for deflection calculation4.7Variability of deflec
16、tions4.8Allowable deflectionsAppendix A4, p. 435R-62Example A4.1Deflection design example for long-termdeflection of a two-way slabExample A4.2Deflection calculation for a flat plateusing the crossing beam methodChapter 5Reducing deflection of concrete members, p. 435R-665.lIntroduction5.2Design tec
17、hniques5.3Construction techniques5.4Materials selection5.5SummaryReferences, p. 435R-70Appendix BDetails of the section curvature method for calculating deflections, p. 435R-77B1IntroductionB2BackgroundB3Cross-sectional analysis outlineB4Material propertiesB5Sectional analysisB6Calculation when crac
18、king occursB7Tension-stiffeningB8Deflection and change in length of a frame memberB9Summary and conclusionsB10ExamplesB11ReferencesCHAPTER 1INTRODUCTIONDesign for serviceability is central to the work of struc-tural engineers and code-writing bodies. It is also essential tousers of the structures de
19、signed. Increased use of high-strength concrete with reinforcing bars and prestressed rein-forcement, coupled with more precise computer-aided limit-state serviceability designs, has resulted in lighter and morematerial-efficient structural elements and systems. This inturn has necessitated better c
20、ontrol of short-term and long-term behavior of concrete structures at service loads.This report presents consolidated treatment of initial andtime-dependent deflection of reinforced and prestressedconcrete elements such as simple and continuous beams andone-way and two-way slab systems. It presents
21、current engi-neering practice in design for control of deformation anddeflection of concrete elements and includes methodspresented in “Building Code Requirements for ReinforcedConcrete (ACI 318)” plus selected other published approachessuitable for computer use in deflection computation. Designexam
22、ples are given at the end of each chapter showing how toevaluate deflection (mainly under static loading) and thuscontrol it through adequate design for serviceability. Thesestep-by-step examples as well as the general thrust of the reportare intended for the non-seasoned practitioner who can, in as
23、ingle document, be familiarized with the major state of prac-tice approaches in buildings as well as additional condensedcoverage of analytical methods suitable for computer use indeflection evaluation. The examples apply AC1 318 require-ments in conjunction with PCI methods where applicable.The rep
24、ort replaces several reports of this committee inorder to reflect more recent state of the art in design. Thesereports include ACI 435.2R, “Deflection of ReinforcedConcrete Flexural Members,” ACI 435.1R, “Deflection ofPrestressed Concrete Members,” ACI 435.3R, “AllowableDeflections,” ACI 435.6R, “De
25、flection of Two-Way Rein-forced Concrete Floor Systems,” and 435.5R, “Deflection ofContinuous Concrete Beams.”The principal causes of deflections taken into account inthis report are those due to elastic deformation, flexuralcracking, creep, shrinkage, temperature and their long-termeffects. This do
26、cument is composed of four main chapters,two to five, which are relatively independent in content.There is some repetition of information among the chaptersin order to present to the design engineer a self-containedtreatment on a particular design aspect of interest.Chapter 2, “Deflection of Reinfor
27、ced Concrete One-WayFlexural Members,” discusses material properties and theireffect on deflection, behavior of cracked and uncrackedmembers, and time-dependent effects. It also includes therelevant code procedures and expressions for deflectioncomputation in reinforced concrete beams. Numericalexam
28、ples are included to illustrate the standard calculationmethods for continuous concrete beams.Chapter 3, “Deflection of Prestressed Concrete One-WayMembers,” presents aspects of material behavior pertinent topretensioned and post-tensioned members mainly forbuilding structures and not for bridges wh
29、ere more preciseand detailed computer evaluations of long-term deflectionbehavior is necessary, such as in segmental and cable-stayedbridges. It also covers short-term and time-dependent deflectionbehavior and presents in detail the Branson effectivemoment of inertia approach (Ie) used in ACI 318. I
30、t gives indetail the PCI Multipliers Method for evaluating time-dependent effects on deflection and presents a summary ofDEFLECTION IN CONCRETE STRUCTURES 435R-3various other methods for long-term deflection calculationsas affected by loss of prestressing. Numerical examples aregiven to evaluate sho
31、rt-term and long-term deflection intypical prestressed tee-beams.Chapter 4, “Deflection of Two-way Slab Systems,” coversthe deflection behavior of both reinforced and prestressedtwo-way-action slabs and plates. It is a condensation of ACIDocument 435.9R, “State-of-the-Art Report on Control ofTwo-way
32、 Slab Deflections,” of this Committee. This chaptergives an overview of classical and other methods of deflectionevaluation, such as the finite element method for immediatedeflection computation. It also discusses approaches fordetermining the minimum thickness requirements for two-way slabs and pla
33、tes and gives a detailed computationalexample for evaluating the long-term deflection of a two-way reinforced concrete slab.Chapter 5, “Reducing Deflection of Concrete Members,”gives practical and remedial guidelines for improving andcontrolling the deflection of reinforced and prestressed concretee
34、lements, hence enhancing their overall long-term serviceability.Appendix B presents a general method for calculating thestrain distribution at a section considering the effects of anormal force and a moment caused by applied loads,prestressing forces, creep, and shrinkage of concrete, andrelaxation
35、of prestressing steel. The axial strain and thecurvature calculated at various sections can be used to calculatedisplacements. This comprehensive analysis procedure is foruse when the deflections are critical, when maximumaccuracy in calculation is desired, or both.The curvatures and the axial strai
36、ns at sections of acontinuous or simply supported member can be used tocalculate the deflections and the change of length of themember using virtual work. The equations that can be usedfor this purpose are given in Appendix B. The appendixincludes examples of the calculations and a flowchart thatcan
37、 be used to automate the analytical procedure.It should be emphasized that the magnitude of actualdeflection in concrete structural elements, particularly inbuildings, which are the emphasis and the intent of thisReport, can only be estimated within a range of 20-40 percentaccuracy. This is because
38、of the large variability in the prop-erties of the constituent materials of these elements and thequality control exercised in their construction. Therefore, forpractical considerations, the computed deflection values inthe illustrative examples at the end of each chapter ought tobe interpreted with
39、in this variability.In summary, this single umbrella document gives designengineers the major tools for estimating and thereby controllingthrough design the expected deflection in concrete buildingstructures. The material presented, the extensive reference listsat the end of the Report, and the desi
40、gn examples will help toenhance serviceability when used judiciously by the engineer.Designers, constructors, and codifying bodies can draw on thematerial presented in this document to achieve serviceabledeflection of constructed facilities.CHAPTER 2DEFLECTION OF REINFORCED CONCRETE ONE-WAY FLEXURAL
41、 MEMBERS*2.1NotationA = area of concrete sectionAc= effective concrete cross section after cracking, or area of concrete in compressionAs= area of nonprestressed steelAsh= shrinkage deflection multiplierb = width of the sectionc = depth of neutral axisCc,(CT)= resultant concrete compression (tension
42、) forceCt= creep coefficient of concrete at time t daysCu= ultimate creep coefficient of concreted = distance from the extreme compression fiber to centroid of tension reinforcementD = dead load effectEc= modulus of elasticity of concreteEc= age-adjusted modulus of elasticity of concrete at time tEs
43、= modulus of elasticity of nonprestressed reinforcing steelEI = flexural stiffness of a compression memberfc = specified compressive strength of concretefct, ft = splitting tensile strength of concretefr= modulus of rupture of concretefs= stress in nonprestressed steelfy= specified yield strength of
44、 nonprestressed reinforc-ing steelh = overall thickness of a memberI = moment of inertia of the transformed sectionIcr= moment of inertia of the cracked section trans-formed to concreteIe= effective moment of inertia for computation of deflectionIg= moment of inertia for gross concrete section about
45、 centroidal axis, neglecting reinforcementK = factor to account for support fixity and load conditionsKe= factor to compute effective moment of inertia for continuous spansksh= shrinkage deflection constantK(subscript)=modification factors for creep and shrinkage effectsl = span lengthL = live load
46、effectM(subscript)= bending momentMa= maximum service load moment (unfactored) at stage deflection is completedMcr= cracking momentMn= nominal moment strengthMo= midspan moment of a simply supported beamP = axial forcet = timeTs= force in steel reinforcementwc= specified density of concreteyt= dista
47、nce from centroidal axis of gross section, neglecting reinforcement, to extreme fiber in tension = thermal coefficientc= creep modification factor for nonstandard conditionssh= shrinkage modification factor for nonstandard*Principal authors: A. S. Ezeldin and E. G. Nawy.435R-4 ACI COMMlTTEE REPORTst
48、rain in extreme compression fiber of amember= conditions4 = cross section curvature= strength reduction factor#) -cracked= curvature of a cracked member4mean = mean curvature4uncracked = curvature of an uncracked member%=%(SHh =hH)u =P=pb=P=E=8=6=CTSL=LT=s,_T =ssh=ii=SMS4=strain in nonprestressed st
49、eelshrinkage strain of concrete at time, t daysultimate shrinkage strain of concretenonprestressed tension reinforcement ratioreinforcement ratio producing balanced strainconditionsreinforcement ratio for nonprestressed com-pression steel*fAtJ =*fJtl to =time dependent deflection factorelastic deflection of a beamadditional deflection due to creepinitial deflection due to live loadtotal long term deflectionincrease in deflection due to long-term effectsadditional deflection due to shrinkageinitial deflection due to sustained loady
