1、ACI 421.2R-10Reported by Joint ACI-ASCE Committee 421Guide to Seismic Design ofPunching Shear Reinforcementin Flat PlatesGuide to Seismic Design of Punching Shear Reinforcementin Flat PlatesFirst PrintingApril 2010ISBN 978-0-87031-374-5American Concrete InstituteAdvancing concrete knowledgeCopyright
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10、tacting ACI.Most ACI standards and committee reports are gathered together in the annually revised ACI Manual ofConcrete Practice (MCP).American Concrete Institute38800 Country Club DriveFarmington Hills, MI 48331U.S.A.Phone: 248-848-3700Fax: 248-848-3701www.concrete.orgACI 421.2R-10 supersedes ACI
11、421.2R-07 and was adopted and published April 2010.Copyright 2010, 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
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15、uments, theyshall be restated in mandatory language for incorporation bythe Architect/Engineer.Guide to Seismic Design of Punching Shear Reinforcement in Flat PlatesReported by Joint ACI-ASCE Committee 421ACI 421.2R-10During an earthquake, the unbalanced moments transferred at flat plate-column conn
16、ections can produce significant shear stresses that increasethe vulnerability of these connections to brittle punching shear failure. Thisguide provides recommendations for designing flat plate-column connectionswith sufficient ductility to withstand lateral drift without punching shearfailure or lo
17、ss of moment transfer capacity. This guide treats reinforcedconcrete flat plates with or without post-tensioning.Keywords: ductility; flat plate; post-tensioning; punching shear; seismicdesign; shear reinforcement; stud shear reinforcement.CONTENTSChapter 1Introduction, p. 421.2R-21.1General1.2Scope
18、1.3Objective1.4RemarksChapter 2Notation and definitions, p. 421.2R-32.1Notation2.2DefinitionsChapter 3Lateral story drift, p. 421.2R-53.1Lateral-force-resisting systems3.2Limits on story drift ratio3.3Effects of gravity loads on story drift capacity3.4Design recommendations for flat plates with andw
19、ithout shear reinforcementChapter 4Minimum shear and integrity reinforcements in flat plates, p. 421.2R-7Simon J. Brown Amin Ghali*James S. Lai Edward G. NawyPinaki R. Chakrabarti Hershell Gill Mark D. Marvin Eugenio M. SantiagoWilliam L. Gamble*Neil L. Hammill Sami Hanna Megally*Thomas C. Schaeffer
20、Ramez Botros Gayed*Theodor Krauthammer Michael C. Mota Stanley C. Woodson*Member of the subcommittee that prepared this guide.The committee would like to thank Frieder Seible for his contribution to this guide.Mahmoud E. KamaraChair421.2R-2 ACI COMMITTEE REPORTChapter 5Assessment of ductility, p. 42
21、1.2R-8Chapter 6Unbalanced design moment,p. 421.2R-96.1Frame analysis6.2Simplified elastic analysis6.3Upper limit for MuChapter 7Design of shear reinforcement,p. 421.2R-117.1Strength design7.2Summary of design steps7.3ACI 318 provisionsChapter 8Post-tensioned flat plates,p. 421.2R-138.1General8.2Sign
22、 convention8.3Post-tensioning effects8.4Effective compressive stress fpc8.5Extension of punching shear design procedure topost-tensioned flat plates8.6Research on post-tensioned flat platesChapter 9References, p. 421.2R-179.1Referenced standards and reports9.2Cited referencesAppendix AVerification o
23、f proposed minimum amount of shear reinforcement for earthquake-resistant flat plate-column connections,p. 421.2R-18Appendix BVerification of upper limit to unbalanced moment to be used in punching shear design, p. 421.2R-18Appendix CNotes on properties of shear-critical section, p. 421.2R-20C.1Seco
24、nd moments of areaC.2Equations for vAppendix DDesign examples, p. 421.2R-21D.1GeneralD.2Example 1: Interior flat plate-column connectionD.3Example 2: Edge flat plate-column connectionD.4Example 3: Corner flat plate-column connectionD.5Example 4: Use of stirrupsInterior flat plate-column connectionD.
25、6Example 5: Interior flat plate-column connection ofExample 1, repeated using SI unitsD.7Post-tensioned flat plate structureD.8Example 6: Post-tensioned flat plate connectionwith interior columnD.9Example 7: Post-tensioned flat plate connectionwith edge columnAppendix EConversion factors, p. 421.2R-
26、30CHAPTER 1INTRODUCTION1.1GeneralBrittle punching failure can occur due to the transfer ofshear forces combined with unbalanced moments betweenslabs and columns. During an earthquake, significanthorizontal displacement of a flat plate-column connectionmay occur, resulting in unbalanced moments that
27、induceadditional slab shear stresses. As a result, some flat platestructures have collapsed by punching shear in past earth-quakes (Berg and Stratta 1964; Yanev et al. 1991; Mitchellet al. 1990, 1995). During the 1985 Mexico earthquake(Yanev et al. 1991), 91 waffle-slab and solid-slab buildingscolla
28、psed, and another 44 buildings suffered severe damage.Hueste and Wight (1999) studied a building with a post-tensioned flat plate that experienced punching shear failuresduring the 1994 Northridge, CA, earthquake. Their studyprovided a relationship between the level of gravity load andthe maximum st
29、ory drift ratio that a flat plate-columnconnection can undergo without punching shear failure. Thedisplacement-induced unbalanced moments and resultingshear forces at flat plate-column connections, althoughunintended, should be designed to prevent brittle punchingshear failure. Even when an independ
30、ent lateral-force-resisting system is provided, flat plate-column connectionsshould be designed to accommodate the moments and shearforces associated with the displacements during earthquakes.1.2ScopeIn seismic design, the displacement-induced unbalancedmoment and the accompanying shear forces at fl
31、at plate-column connections should be accounted for. This demandmay be effectively addressed by changes in dimensions ofcertain members, or their material strengths (for example,shear walls and column sizes), or provision of shear reinforce-ment or a combination thereof. This guide does not addressc
32、hanges in dimensions and materials of such members, butfocuses solely on the punching shear design of flat plateswith or without shear reinforcement.This guide, supplemental to ACI 421.1R, focuses on thedesign of flat plate-column connections with or withoutshear reinforcement that are subject to ea
33、rthquake-induceddisplacement; reinforced concrete flat plates with or withoutpost-tensioning are treated in the guide. Slab shear reinforcementcan be structural steel sections, known as shearheads, orvertical rods. Although permitted in ACI 318, shearheads arenot commonly used in flat plates. Stirru
34、ps and shear studreinforcement (SSR), satisfying ASTM A1044/A1044M, arethe most common types of shear reinforcement for flatplates. Shear stud reinforcement is composed of vertical rodsanchored mechanically near the bottom and top surfaces ofthe slab. Forged heads or welded plates can be used as the
35、anchorage of SSR; the area of the head or the plate is sufficientto develop the yield strength of the stud, with negligible slipat the anchorage. The design procedure recommended in thisguide was developed based on numerical studies (finiteelement method) and experimental research on reinforcedconcr
36、ete slabs subjected to cyclic drift reversals that simulateseismic effects. The finite element analyses, supplemental toSEISMIC DESIGN OF PUNCHING SHEAR REINFORCEMENT IN FLAT PLATES 421.2R-3the experimental research, used software, constitutive relations,and models that were subject to extensive ver
37、ifications bycomparing the results with the behavior observed in tests(Megally and Ghali 2000b).Structural integrity reinforcement near the bottom of theslab extending through the columns should be provided asrequired by ACI 318. This document supplements ACI352.1R and ACI 421.1R, which, respectivel
38、y, includerecommendations such as extending a minimum amount ofbottom integrity reinforcement through the column core andprovide details of design for shear reinforcement in flatplates. ACI 352.1R also provides recommendations for thedesign of flat plate-column connections without slab shearreinforc
39、ement subjected to moment transfer in the inelastic-response range. The equations of this guide predict punchingshear strength and drift capacity, assuming that adequateflexural reinforcement is provided at the flat plate-columnconnections; the present guide does not address the requiredflexural rei
40、nforcement.1.3ObjectiveThe objective is to provide a design recommendation forflat plate-column connections with sufficient ductility toaccommodate the displacement of the selected lateral-force-resisting system without punching shear failure or loss ofmoment transfer capacity. The objective covers
41、reinforcedconcrete slabs with or without post-tensioning.1.4RemarksThis guide gives recommendations for the design of shearreinforcement, considering ductility, that supplement theprovisions of ACI 318 for punching shear design. The term“ductility,” used throughout this guide, is the ratio ofdisplac
42、ement at ultimate strength to the displacement atwhich yielding of the flexural reinforcement occurs. For flatplate-column connections, there is no unique definition forthese two displacements. Pan and Moehle (1989) define theultimate and yield displacements by a graphical bilinearidealization of th
43、e experimental load-displacement response,considering the displacement at a specified load levelbeyond the peak load.ACI 318 allows the analysis of flat plate-column frames asequivalent plane frames. When the frame is not designated aspart of the lateral-force-resisting system and is subjected tohor
44、izontal displacements, the width of slab strip to beincluded in the frame model and how to account for cracking(ACI 318, Section R13.5.1.2) are modeling parameters thatsignificantly affect the resulting computed values of themoments transferred between slabs and columns. This guidecontains a procedu
45、re that determines an upper limit momentthat can be transferred between the slab and column whenthe connection is subjected to an earthquake.Chapter 3 defines the story drift that should be consideredin design. Chapter 4 recommends a minimum amount ofshear reinforcement for certain cases. Chapter 5
46、describesmeans of increasing the shear strength of a flat plate-columnconnection and compares the associated ductilities. Chapter 6presents a method to calculate the unbalanced momentrequired for design. Chapter 7 and Appendix D discuss relevantprovisions of ACI 318 and provide the design procedure
47、andexamples for interior, edge, and corner flat plate-columnconnections. Chapter 8, expanded in this edition, providesrecommendations relevant to post-tensioned flat plates.CHAPTER 2NOTATION AND DEFINITIONS2.1NotationAs= area of flexural reinforcing bars, in.2(mm2)Av= cross-sectional area of shear r
48、einforcementon one peripheral line, in.2(mm2)bo= length of perimeter of shear-critical section, in.(mm)Cd= displacement amplification factor (ASCE/SEI 7)c1to c6= dimensions used in Fig. 8.3, defining a post-tensioning tendon profilecx, cy= column dimensions in the x- and y-directions,respectively, i
49、n. (mm)DRu= ultimate story drift ratio at peak strength (inexperiments), or design story drift ratio of aflat plate-column connectiond = average of distances from extreme compressionfiber to the centroid of the tension reinforce-ment positioned in two orthogonal directions,in. (mm)Ec= elastic modulus of concrete, psi (MPa)e=tendon eccentricity, measured from themidsurface of the slab to the centroid of thepost-tensioned tendon; e is positive for atendon situated below midsurface, in. (mm)fc = specified concrete strength, psi (MPa)fp
