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1、Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- Obb2949 054395b 92T W The Design of Two-way Slabs Editor
2、 T. C. Schaeffer international SP-183 Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- 0bb2949 0543957 bb
3、 W DISCUSSION of individual papers in this symposium may be submitted in accordance with general requirements of the AC1 Publication Policy to AC1 headquarters at the address given below. Closing date for submission of discussion is November 1, 1999. Ail discussion approved by the Technical Activiti
4、es Committee along with closing remarks by the authors will be published in the MarcWApril 2000 issue of either AC1 Structu ral Journal or AC1 IWgxids Journal depending on the subject emphasis of the individual paper. The Institute is not responsible for the statements or opinions expressed in its p
5、ublications. Institute publications are not able to, nor intended to, supplant indi- vidual training, responsibility, or judgment of the user, or the supplier, of the information presented. The papers in this volume have been reviewed under Institute publication proce- dures by individuals expert in
6、 the subject areas of the papers. Copyright O 1999 AMERICAN CONCRETE INSTITUTE P.O. Box 9094 Farmington Hills, Michigan 48333-9094 All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any electronic or me
7、chanical device, printed or written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors. Printed in the United States of America Editorial production: Jane D. Carroll
8、 Library of Congress catalog card number: 99-61474 Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- m O66
9、2949 0543958 7T2 m PREFACE At ACIs 1996 fall convention in New Orleans, La., ACI-ASCE Joint Committee 421, Design of Reinforced Slabs, sponsored two technical sessions. The focus of the morning session was “Design of Two-way Slabs using Elastic Frame Analogies,” and the afternoon session concentrate
10、d on “Design of Two- Way Slabs using Theorems of Plasticity.” The sessions were moderated by Hershel1 Gill and Thomas C. Schaeffer. This AC1 Special Publication consists of 10 papers, all of which were presented at the sessions in New Orleans. The current AC1 3 18 Building Code specifically addresse
11、s two methods for the design of two-way slabs. These methods are the Equivalent Frame Method, and the Direct Design Method. However, the Building Code also “.permits a designer to base a design directly on fundamental principles of structural mechanics provided it can be demonstrated explicitly that
12、 all safety and serviceability criteria are satisfied.” The papers contained in this volume should give the designer an overview of some of the different analysis and design techniques that are currently being used. Committee 421 would like to thank all of the authors and presenters for their contri
13、butions to the two technical sessions and to this volume. We would also like to thank the reviewers of the original manuscripts, as well as AC1 staff for their assistance. T. C. Schaeffer Editor Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/11111
14、11001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- Obb2949 0543959 639 CONTENTS CONCEPT AND BACKGROUND OF ELASTIC FRAME ANALOGIES FOR by S. Simmonds . 1 TWO-WAY SLAB SYSTEMS DESIGN FOR SEVERE DYNAMIC LOADS by S.
15、Woodson and T. Krauthammer . 17 DESIGN FOR PUNCHING SHEAR IN CONCRETE by S. Megaily and A. Ghali . 37 DEVELOPMENT IN YIELD LINE THEORY FOR SLABS by W. Gamble 67 USING THEORUMS OF PLASTICITY HISTORY AND CONCEPT by S. Simmonds . 77 STRIP METHOD FOR FLEXURAL DESIGN OF TWO-WAY SLABS by S. Alexander 93 P
16、LANE-FRAME ANALYSIS APPLIED TO SLABS by W. Gamble . 119 DETAILING FOR SERVICEABILITY by D. Rogowsky 13 1 DESIGN AND CONSTRUCTION OF TWO-WAY SLABS FOR DEFLECTION CONTROL by A. Scanlon . 145 STRIP DESIGN FOR PUNCHING SHEAR by S. Alexander 161 V Copyright American Concrete Institute Provided by IHS und
17、er license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- 0bb2949 05439b0 350 SP 183-1 Concept and Background of Elastic Frame Analogies for Two-way Slab Systems by S. Sim
18、monds Synopsis: The justification for using elastic frame analogies to determine design moments in two-way slab systems is discussed. A brief history of two-way reinforced concrete slab design leading to the current code procedures is presented. This history includes a description of the various ela
19、stic frame analogies that have existed in past codes, the reasons for changes and the research leading to improved frame analogies. This is followed by a critical review of the Equivalent Frame Method in the current code with suggestions for improving and simplifying provisions for elastic frame ana
20、logies in future codes. Keywords: analysis; design; elastic frames; history; reinforced concrete slabs 1 Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or net
21、working permitted without license from IHS -,-,- D Obb2947 05437b3 297 2 Simmonds Sidney H. Simmonds, currently Professor Emeritus, University of Alberta was for many years Secretary of the Canadian Concrete Code Committee A23.3. He also served on AC1 Committees; 118 - Computers (Chairman 1979-83),
22、120 - History (Chairman 1991-95), 318F - dc on Slabs, 334 - Shells, 340 - Handbook, 421 - Slabs, and was a founding member and first President of the Alberta AC1 Chapter. WHY AN ELASTIC FRAME ANALOGY? Two-way slab systems are a common structural component in reinforced concrete construction. If aske
23、d how they design these slabs, many designers in North America would answer I use a computer program. If pressed as to the methodology incorporated in the program they would likely respond elastic frame analogy. Why an elastic frame analogy? Traditionally, in reinforced concrete design, one uses a l
24、inear elastic theory to determine design parameters and then proportions members using an ultimate strength procedure. The justification for this apparent anomaly is that by designing for moments determined from elastic theory the amount of moment redistribution at service load conditions will be mi
25、nimized thereby ensuring that serviceability requirements will generally be satisfied. Except for special cases such as deep beams or sudden changes in cross section where elastic theory is not applicable, this technique has served us well. To apply a similar procedure to the design of two-way slab
26、systems it is necessary to have a means of obtaining an elastic analysis. As early as 18 11, Lagrange proposed an elastic theory for thin slabs which requires determining a fiinction that will satis both a fourth-order differential equation and the boundary conditions. Solutions using this approach
27、have been successful only for slabs with the simplest idealized boundary conditions, generally panels with non-deflecting boundaries. This method has been used to develop design procedures for slabs with beams between all supports. It was the need to provide a simple elastic analysis for column supp
28、orted two-way slab systems that led to the concept of an elastic frame analogy. Even today, although a number of ingenious techniques to obtain solutions for two-way systems have been proposed, for example Ang (1) and, more recently, numerical solutions based on finite element or finite difference t
29、echniques, none have proved practical for routine ofice use. Hence the continuing interest in elastic frame analogies. WHAT IS AN ELASTIC FRAME ANALOGY? The concept behind the use of elastic frame analogies is that satisfactory values for the design moments and shears in two-way slab systems can be
30、obtained by considering a portion of the slab-column structure to form a design frame that can be analyzed as a plane frame. a) define the analogous plane frame including assigning member stiffness The process consists of three parts: Copyright American Concrete Institute Provided by IHS under licen
31、se with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32 MSTNo reproduction or networking permitted without license from IHS -,-,- = 0543qb2 Design of Two-way Slabs 3 b) analyze frame with appropriate loading to obtain maximum frame moments, and c) dis
32、tribute frame moments laterally across the corresponding critical sections of the slab. Frame analogies can be used for both gravity and lateral loading on slab- column structures. The basic approach for defining the geometry of the analogous elastic plane frames has remained essentially unchanged t
33、hrough various codes. The structure is considered to be made up of analogous or equivalent frames centered on the column lines taken longitudinally and transversely through the building, see Fig. 1. Each frame consists of a row of columns or supports and slab-beam strips bounded laterally by the cen
34、terline of the panel on each side of the centerline of the columns or supports. Frames adjacent and parallel to an edge are bounded by that edge and the centerline of the adjacent panel. Each frame may be analyzed in its entirety, or for vertical loading each floor or roof with attached columns may
35、be analyzed separately. Success in applying this analogy depends on the appropriate apportioning of stiffness to the members of the frame so that the elastic analysis of the two- dimensional frame will approximate that of the non-linear three-dimensional slab- beam-column system. This problem is mad
36、e more complex by a fundamental assumption in the analysis of plane frames that does not apply to slab-column systems. In a typical plane frame analysis it is assumed that at a beam-column connection all members framing into that joint undergo the same rotation as shown in Fig. 2(a). For slabs suppo
37、rted by columns this assumption is valid only locally at the column. Portions of the slab laterally removed from the column will rotate lesser or greater amounts depending on the geometry and loading patterns as shown in Fig. 2(b). Furthermore, actual slab systems crack even under service loading, e
38、specially near the face of the column resulting in locally reduced stiffness. To account for the differences in behavior of the actual slab-column system and the idealized plane frame, it is necessary to modi the stiffness of the frame elements. Unfortunately, the modifications required to the membe
39、r stiffness for lateral loading differ fiom those for gravity loading. The definition of the analogous frame, the apportioning of stiffness and the rules for the lateral distribution of design moments across the slab have evolved through successive codes. To follow this evolution, it is helpful to r
40、eview the history of the development of two-way slab construction. TWO-WAY SLABS AND FLAT SLABS Since the 1971 AC1 Code, the term two-way slab refers to all slab systems reinforced for flexure in more than one direction with or without beams between supports. The term flat slab is not used. Prior to
41、 1971, the term two-way slab referred only to those slabs with beams between supports along all sides of each panel and the term flat slab referred to slabs without beams between supports but could have column capitals andlor drop panels. The need for the distinction in earlier codes was because of
42、the different genesis of the two slab types and the resulting differences in design rules. The elastic frame method was initially Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=IHS Employees/1111111001, User=listmgr, listmgr Not for Resale, 03/05/2007 03:02:32
43、MSTNo reproduction or networking permitted without license from IHS -,-,- 9 Obb2949 05439b3 ObT W 4 Sirnrnonds developed for two-way slabs without beams (flat slabs). In the remainder of this paper the term flat slab is used as defined above when discussing design rules prior to 1971. EARLY HISTORY
44、OF SLAB DESIGN Reinforced concrete flat slabs were invented in the sense that they were not a logical extension of elastic theory or construction practice. Credit for this invention is generally given to C. A. P. Turner who constructed his first mushroom slab (a reinforced concrete slab supported on
45、 columns with flared column capitals) for the five-story C. A. Bovey Building in Minneapolis in 1906. Lacking a rational analysis, the validity of his design was verified with a load test. So successful was this slab that almost immediately competitors were constructing slabs using various proprieta
46、ry methods. Since there was no generally accepted procedure for analyzing such slabs, it is not surprising that the amount of reinforcement required varied considerably fiom design to design. A comparison of the amounts of reinforcement required in an interior panel by six different design procedure
47、s made by McMillan (2) in 1910 showed that some designs required four times as quch steel as others. In an attempt to reconcile these difference in designs, many of the slabs that were load tested had measurements of the strains in the reinforcement. Moments in the slab were computed from these stee
48、l strains using a straight line expression. These tests did not resolve the differences in design procedures. In 1914, Nichols (3) examined the statics of a uniformly loaded interior panel of a slab without beams with square panels extending infinitely in both directions. In his original paper, he considered only a quarter of the panel but in the closure to his paper he considered as a free body the half panel designated as A, B, C, and D in Fig. 3. From symmetry no shears or twisting moments exist on faces B, C, and D but bending mo