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1、ACI 421.2R-07 Seismic Design of Punching Shear Reinforcement in Flat Plates Reported by Joint ACI-ASCE Committee 421 American Concrete Institute Advancing concrete knowledge Seismic Design of Punching Shear Reinforcement in Flat Plates First Printing March 2007 ISBN 978-0-87031-237-3 Copyright by th
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10、Practice (MCP). American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 U.S.A. Phone:248-848-3700 Fax:248-848-3701 www.concrete.org ACI 421.2R-07 was adopted and published March 2007. Copyright 2007, American Concrete Institute. All rights reserved including rights of reprodu
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12、btained from the copyright proprietors. 421.2R-1 ACI Committee Reports, Guides, Standard Practices, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This document is intended for the use of individuals who are competent to evaluate the signif
13、icance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the stated principles. The Institute shall not be liable for any loss or damage arisi
14、ng therefrom. Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they shall be restated in mandatory language for incorporation by the Architect/Engineer. Seismic Design of
15、Punching Shear Reinforcement in Flat Plates Reported by Joint ACI-ASCE Committee 421 ACI 421.2R-07 During an earthquake, the unbalanced moments transferred at flat plate- column connections can produce significant shear stresses that increase the vulnerability of these connections to brittle punchin
16、g shear failure. This report gives recommendations for designing flat plate-column connections with sufficient ductility to go through lateral drift without punching shear failure or loss of moment transfer capacity. Keywords: ductility; flat plate; punching shear; seismic design; shear reinforcemen
17、t. CONTENTS Chapter 1 Introduction, p. 421.2R-2 1.1General 1.2Definitions 1.3Notation 1.4Scope 1.5Objective 1.6Remarks Chapter 2Lateral story drift, p. 421.2R-4 2.1Lateral-force-resisting systems 2.2Limits on story drift ratio 2.3Effects of gravity loads on story drift capacity 2.4Design recommendat
18、ions for flat plates with and without shear reinforcement Chapter 3Minimum shear and integrity reinforcements in flat plates, p. 421.2R-6 Chapter 4Assessment of ductility, p. 421.2R-7 Chapter 5Unbalanced design moment, p. 421.2R-8 5.1Frame analysis 5.2Simplified elastic analysis 5.3Upper limit for M
19、u Chapter 6Design of shear reinforcement, p. 421.2R-11 6.1Strength design 6.2Summary of design steps 6.3ACI 318-05 provisions Chapter 7Research on prestressed flat plates, p. 421.2R-12 Simon J. BrownHershell GillMark D. MarvinEugenio M. Santiago Pinaki R. ChakrabartiNeil L. HammillSami H. Megally*Th
20、omas C. Schaeffer William L. Gamble*Mamoud E. KamaraEdward G. NawyStanley C. Woodson* Amin Ghali*James S. Lai *Member of subcommittee that prepared this report. The committee would like to thank Freider Seible and Ramez Gayed for their contributions to this report. Theodor Krauthammer* Chair 421.2R-
21、2ACI COMMITTEE REPORT Chapter 8References, p. 421.2R-12 8.1Cited references Appendix AVerification of proposed minimum amount of shear reinforcement for earthquake- resistant flat plate-column connections, p. 421.2R-14 Appendix BVerification of upper limit to unbalanced moment to be used in punching
22、 shear design, p. 421.2R-14 Appendix CNotes on properties of shear-critical section, p. 421.2R-16 C.1Second moments of area C.2Equations for v Appendix DDesign examples, p. 421.2R-17 D.1General D.2Example 1: Interior flat plate-column connection D.3Example 2: Edge flat plate-column connection D.4Exa
23、mple 3: Corner flat plate-column connection D.5Example 4: Use of stirrups: Interior flat plate- column connection D.6Example 5: Interior flat plate-column connection of Example 1, repeated using SI units Appendix EConversion factors, p. 421.2R-22 CHAPTER 1INTRODUCTION 1.1General Brittle punching fai
24、lure can occur due to the transfer of shear forces combined with unbalanced moments between slabs and columns. During an earthquake, significant horizontal displacement of a flat plate-column connection may occur, resulting in unbalanced moments that induce additional slab shear. As a result, some f
25、lat plate structures have collapsed by punching shear in past earthquakes (AISI 1964, 1991; Mitchell et al. 1990, 1995). During the 1985 Mexico earth- quake (AISI 1991), 91 waffle-slab and solid-slab buildings collapsed, and another 44 buildings suffered severe damage. Hueste and Wight (1999) studie
26、d a building with a post- tensioned flat plate that experienced punching shear failures during the 1994 Northridge, California earthquake; they provided a relationship between the level of gravity load and the maximum story drift ratio that a flat plate-column connection can undergo without punching
27、 shear failure. The displacement-induced unbalanced moments and resulting shear forces at flat plate-column connections, although unintended, must be designed for to prevent brittle punching shear failure. Even when an independent lateral- force-resisting system is provided, flat plate-column connec
28、- tions must be designed to accommodate the moments and shear forces associated with the displacements during earthquakes. 1.2 Definitions The following terms are used throughout the report. design displacementtotal lateral displacement expected for the design-basis earthquake as required by the gov
29、erning code for earthquake-resistant design. design story driftdesign displacement of one level, or floor, relative to the level above or below. design story drift ratiodesign story drift divided by the story height. ductilityratio of displacement at ultimate strength to the displacement at which yi
30、eld of the flexural reinforcement occurs. flat plateflat slab without column capitals or drop panels. lateral-force-resisting systemportion of the structure composed of members designed to resist forces related to earthquake effects. stud shear reinforcement (SSR)reinforcement composed of vertical r
31、ods anchored mechanically near the bottom and top surfaces of the slab (ASTM A 1044/A 1044M-05). 1.3Notation As= area of flexural reinforcing bars, in.2 (mm2) Av= cross-sectional area of shear reinforcement on one peripheral line, in.2 (mm2) bo= length of perimeter of shear-critical section, in. (mm
32、) Cd= displacement amplification factor (ASCE 7-05) cx, cy= column dimensions in the x- and y-directions, respectively, in. (mm) d= average of distances from extreme compression fiber to the centroid of the tension reinforce- ments positioned in two orthogonal directions, in. (mm) DRu= ultimate stor
33、y drift ratio at peak strength (in experiments), or design story drift ratio of a flat plate-column connection Ec= elastic modulus of concrete, psi (MPa) fc= specified concrete strength, psi (MPa) fy= specified yield strength of flexural reinforce- ment, psi (MPa) fyt= specified yield strength of sh
34、ear reinforcement, psi (MPa) h= slab thickness, in. (mm) Ic= moment of inertia of gross section of column, in.4 (mm4) IE= occupancy importance factor (ASCE 7-05) Iec= equivalent moment of inertia of columns accounting for torsional members in accordance with Section 13.7.5 of ACI 318-05 (refer to pl
35、ane frame idealization Fig. 5.1) Is= second moment of area of slab accounting for cracking (refer to plane frame idealization Fig. 5.1) Ix= second moment of area of assumed critical section about the x-axis, in.4 (mm4) Iy= second moment of area of assumed critical section about the y-axis, in.4 (mm4
36、) Ixy= product of inertia of assumed critical section about centroidal nonprincipal axes x and y, in.4 (mm4) Jc= property of assumed critical section analogous to polar moment of inertia, defined by Eq. (C-1), taken from ACI 318 SEISMIC DESIGN OF PUNCHING SHEAR REINFORCEMENT IN FLAT PLATES421.2R-3 K
37、c= end rotational stiffness of column, moment per unit rotation Kec= end rotational stiffness of equivalent column, moment per unit rotation l= span length, in. (mm) lc= story height, in. (mm) lx, ly= projections of shear-critical section on its principal axes x and y, respectively, in. (mm) M= unba
38、lanced moment transferred between the slab and the column, in.-lb (N-mm) Mpr= probable flexural moment strength, in.-lb (N-mm) (refer to Section 5.3) Mu= ultimate unbalanced moment, at peak strength, transferred between the slab and the column at shear-critical section centroid, in.-lb (N-mm). This
39、definition applies where capacity is consid- ered. Where demand is considered, Mu is factored unbalanced moment in design. Mux, Muy= components of the unbalanced moment Mu transferred between the slab and the column; positive directions of Mux and Muy are defined in Fig. 2.2. s= spacing between peri
40、pheral lines of shear reinforcement, in. (mm) so= spacing between the first peripheral line of shear reinforcement and column face, in. (mm) V= shear force transferred between the column and the slab, lb (N) Vc= nominal shear capacity of a flat plate-column connection with no shear reinforcement, lb
41、 (N) Vu= ultimate shear force transferred between the slab and the column, lb (N) vc= in presence of shear reinforcement (Eq. (6-1), vc is nominal shear strength (expressed in stress units) provided by concrete, psi (MPa). In the absence of shear reinforcement, vc is nominal shear capacity expressed
42、 in stress units = Vc/(bod) (Vc is given by Eq. (2-1) to (2-3). vn= nominal shear strength (expressed in stress units), psi (MPa) vs= nominal shear strength (expressed in stress units) provided by shear reinforcement, psi (MPa) vu= maximum shear stress at critical section, psi (MPa) x, y= coordinate
43、s of point of maximum shear stress on the critical section with respect to centroidal prin- cipal axes x and y, respectively. Also, as subscripts, x and y refer to the same principal axes. x, y= axes parallel to slab edges at the centroid of the shear-critical section at a corner column m= factor us
44、ed in calculation of the design moment for earthquake-resistant flat plate-column connections s= factor that adjusts vc for support type = ratio of long side to short side of concentrated load or reaction area r= aspect ratio of the shear-critical section at d/2 from column face v= fraction of unbal
45、anced moment transferred by vertical shear stresses at flat plate-column connections e= story drift used in elastic frame analysis, in. (mm) u= design story drift, including inelastic deforma- tions, in. (mm) = clockwise rotation angle of x-axis to x-axis, or y- axis to y-axis = slab flexural reinfo
46、rcement ratio = strength reduction factor according to ACI 318 1.4Scope In seismic design, the displacement-induced unbalanced moment and the accompanying shear forces at flat plate- column connections must be accounted for. This demand may be effectively addressed by changes in dimensions of certai
47、n members and/or their material strengths (for example, shearwalls and column sizes) and/or provision of shear reinforcement. This report does not address changes in dimensions and materials of such members, but solely focuses on the punching shear design of flat plates with or without shear reinfor
48、cement. This report, supplemental to ACI 421.1R-99 (Joint ACI- ASCE Committee 421 1999), focuses on the design of flat plate-column connections with or without shear reinforce- ment that are subject to earthquake-induced displacement. Slab shear reinforcement can be structural steel sections, known
49、as shearheads, or vertical rods. Although permitted in ACI 318, shearheads are not commonly used in flat plates. Stirrups and stud shear reinforcement (SSR), satisfying ASTM A 1044/1044M-05, are the most common types of shear rein- forcement for flat plates. SSR is composed of vertical rods anchored mechanically near the bottom and top surfaces of the slab. The anchorage of SSR can be by forged heads or welded plates; the area of the head or the plate is sufficient to develop the yield strength of the stud, with negligib
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