1、ACI 445.1R-12Report on Torsion in Structural ConcreteReported by Joint ACI-ASCE Committee 445First PrintingApril 2013Report on Torsion in Structural Concrete Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in who
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10、ation: ACI documents are available in print, by download, on CD-ROM, through electronic subscription, or reprint and may be obtained by contacting ACI.Most ACI standards and committee reports are gathered together in the annually revised ACI Manual of Concrete Practice (MCP).American Concrete Instit
11、ute38800 Country Club DriveFarmington Hills, MI 48331U.S.A.Phone: 248-848-3700Fax: 248-848-3701www.concrete.orgISBN-13: 978-0-87031-810-8ISBN: 0-87031-810-1American Concrete InstituteAdvancing concrete knowledgeA clear understanding of the effects of torsion on concrete members is essential to the s
12、afe, economical design of reinforced and prestressed concrete members. This report begins with a brief and systematic summary of the 180-year history of torsion of structural concrete members, new and updated theories and their applications, and a historical overview outlining the development of res
13、earch on torsion of structural concrete members. Historical theories and truss models include classical theories of Navier, Saint-Venant, and Bredt; the three-dimensional (3-D) space truss of Rausch; the equilibrium (plasticity) truss model of Nielson as well as Lampert and Thrlimann; the compressio
14、n field theory (CFT) by Collins and Mitchell; and the softened truss model (STM) by Hsu and Mo.This report emphasizes that it is essential to the analysis of torsion in reinforced concrete that members should: 1) satisfy the equi-librium condition (Mohrs stress circle); 2) obey the compatibility con
15、dition (Mohrs strain circle); and 3) establish the constitutive relationships of materials such as the “softened” stress-strain rela-tionship of concrete and “smeared” stress-strain relationship of steel bars.The behavior of members subjected to torsion combined with bending moment, axial load, and
16、shear is discussed. This report deals with design issues, including compatibility torsion, span-drel beams, torsional limit design, open sections, and size effects. The final two chapters are devoted to the detailing requirements of transverse and longitudinal reinforcement in torsional members with
17、 detailed, step-by-step design examples for two beams under torsion using ACI (ACI 318-11), European (EC2-04), and Cana-dian Standards Association (CSA-A23.3-04) standards. Two design examples are given to illustrate the steps involved in torsion design. Design Example 1 is a rectangular reinforced
18、concrete beam under pure torsion, and Design Example 2 is a prestressed concrete girder under combined torsion, shear, and flexure.Keywords: combined action (loading); compatibility torsion; compression field theory; equilibrium torsion; interaction diagrams; prestressed concrete; reinforced concret
19、e; shear flow zone; skew bending; softened truss model; spandrel beams; struts; torsion detailing; torsion redistribution; warping.CONTENTSCHAPTER 1INTRODUCTION AND SCOPE, p. 21.1Introduction, p. 21.2Scope, p. 3CHAPTER 2NOTATION AND DEFINITIONS, p. 32.1Notation, p. 32.2Definitions, p. 5ACI 445.1R-12
20、Report on Torsion in Structural ConcreteReported by Joint ACI-ASCE Committee 445Daniel A. Kuchma, Chair Robert W. Barnes Jr., SecretaryPerry AdebarNeal S. AndersonRobert B. AndersonMark A. AscheimOguzhan BayrakZdenek P. BaantAbdeldjelil Belarbi*Evan C. BentzJohn F. BonacciHakim BouadiMichael D. Brow
21、nMichael P. CollinsDavid DarwinWalter H. Dilger*Marc O. EberhardCatherine E. FrenchRobert J. FroschGary G. Greene*Neil M. HawkinsThomas T. C. Hsu*Gary J. KleinZhongguo John MaAdolfo B. MatamorosDenis MitchellYi-Lung Mo*Lawrence C. NovakCarlos E. OspinaStavroula J. PantazopoulouMaria A. PolakJulio A.
22、 RamirezKarl-Heinz ReineckDavid H. Sanders*Raj ValluvanJames K. Wight1ACI Committee Reports, Guides, 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 signi
23、ficance 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 aris
24、ing 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.ACI 445.1R-12 was a
25、dopted and published April 2013.Copyright 2013, American Concrete Institute.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 electronic or mechanical device, printed, written, or oral, or recording fo
26、r sound or visual reproduc-tion or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.*Subcommittee members who produced this report.Subcomittee Chair.The committee would like to thank the following individuals for their co
27、ntribution to this report: Mohammad Ali, Neal S. Anderson, Shri Bhide, Michael D. Collins, Maria Cristina Vidigal de Lima, Leonard Elfgren, Christos Karayannis, Liang-Jenq Leu, Mohammad Mansour, Basile Rabbat, Khaldoun Rahal, and Paul Zia.CHAPTER 3HISTORICAL OVERVIEW OF TORSION THEORIES AND THEORETI
28、CAL MODELS, p. 53.1Naviers theory, p. 53.2Thin-tube theory, p. 53.3Historical development of theories for reinforced concrete members subjected to torsion, p. 63.4Concluding remarks, p. 13CHAPTER 4BEHAVIOR OF MEMBERS SUBJECTED TO PURE TORSION, p. 134.1General, p. 134.2Plain concrete, p. 134.3Reinfor
29、ced concrete, p. 154.4Prestressed concrete, p. 174.5High-strength concrete, p. 184.6Concluding remarks, p. 19CHAPTER 5ANALYTICAL MODELS FOR PURE TORSION, p. 205.1General, p. 205.2Equilibrium conditions, p. 205.3Compatibility conditions, p. 205.4Stress strain relationships, p. 225.5Compression field
30、theory, p. 235.6Softened truss model, p. 255.7Graphical methods, p. 26CHAPTER 6MEMBERS SUBJECTED TO TORSION COMBINED WITH OTHER ACTIONS, p. 286.1General, p. 286.2Torsion and flexure, p. 296.3Torsion and shear, p. 336.4Torsion and axial load, p. 366.5Torsion, shear, and flexure, p. 37CHAPTER 7ADDITIO
31、NAL DESIGN ISSUES RELATED TO TORSION, p. 397.1General, p. 397.2Compatibility torsion and torsional moment redistri-bution, p. 397.3Precast spandrel beams, p. 477.4Torsion limit design, p. 487.5Treatment of open sections, p. 517.6Size effect on the strength of concrete beams in torsion, p. 53CHAPTER
32、8DETAILING FOR TORSIONAL MEMBERS, p. 538.1General, p. 538.2Transverse reinforcement, p. 558.3Longitudinal reinforcement, p. 578.4Detailing at supports, p. 58CHAPTER 9DESIGN EXAMPLES, p. 599.1Torsion design philosophy, p. 599.2Torsion design procedures, p. 599.3Introduction to design examples, p. 679
33、.4Design Example 1: solid rectangular reinforced concrete beam under pure torsion, p. 679.5Design Example 2: Prestressed concrete box girder under combined torsion, shear, and flexure, p. 74CHAPTER 10REFERENCES, p. 86CHAPTER 1INTRODUCTION AND SCOPE1.1IntroductionAccounting for the effects of torsion
34、 is essential to the safe design of structural concrete members, requiring a full knowledge of the effects of torsion and a sound under-standing of the analytical models that can easily be used for design. For over three decades, considerable research has been conducted on the behavior of reinforced
35、 concrete members under pure torsion and torsion combined with other loadings. Likewise, analytical models have been developed based on the truss model concept. Several of these models were developed to predict the full load history of a member, whereas others are simplified and used only to calcula
36、te torsional strength. Many models developed since the 1980s account for softening of diagonally cracked concrete.This report reviews and summarizes the evolution of torsion design provisions in ACI 318, followed with a summary of the present state of knowledge on torsion for design and analysis of
37、structural concrete beam-type members. Despite a vast amount of research in torsion, provisions of torsion design did not appear in ACI 318 until 1971 (ACI 318-71), although ACI 318-63 included a simple clause regarding detailing for torsion. Code provisions in 1971 were based on Portland Cement Ass
38、ociation (PCA) tests (Hsu 1968b).These provisions were applicable only to rectangular nonprestressed concrete members. In 1995, ACI 318-95 adopted an approach based on a thin-tube, space truss model previously used in the Canadian Standards Association (CSA-A23.3-77) code and the Comit Euro-Internat
39、ional du Bton (CEB)-FIP code (1978). This model permitted treatment of sections with arbitrary shape and prestressed concrete (Ghoneim and MacGregor 1993; MacGregor and Ghoneim 1995). The ACI 318-02 code extended the appli-cation of the (ACI 318) 1995 torsion provisions to include prestressed hollow
40、 sections. ACI 318 allows the use of alter-native design methods for torsional members with a cross section aspect ratio of 3 or greater, like the procedures of pre-1995 editions of ACI 318 or the Prestressed Concrete Institute (PCI) method (Zia and Hsu 1978).This report reviews and summarizes the p
41、resent state of knowledge on torsion and reviews their use as a frame-work for design and analysis of structural concrete beam-type members. Chapter 3 presents a historical background outlining the development of research on torsion of struc-tural concrete members. The general behavior of reinforced
42、 and prestressed concrete members under pure torsion is discussed in Chapter 4. In Chapter 5, the compression field theory (CFT) and softened truss model (STM) are presented in detail. Chapter 5 also includes a description of two graphical methods (Rahal 2000a,b; Leu and Lee 2000). The behavior of m
43、embers subjected to torsion combined with shear, flexure, American Concrete Institute Copyrighted Materialwww.concrete.org2 REPORT ON TORSION IN STRUCTURAL CONCRETE (ACI 445.1R-12)and axial load is discussed in Chapter 6. Chapter 7 introduces additional design issues related to torsion, such as prec
44、ast spandrel beams, torsion limit design, size effect, open sections, and torsional moment distribution. Detailing of torsional members is described in Chapter 8. Chapter 9 covers detailed design examples of several beams subjected to torsion using ACI 318, EC2-04, and CSA-A23.3-04 design equations,
45、 and additional graphical design methods reported by researchers.1.2ScopeTheories presented in this report were developed and verified for building members of typical size. For application to large-scale members, size effects should be considered. They could present a serious safety issue when using
46、 the shear strength equations provided in the design standard, which cannot take into account the shear strength reduction in large-scale members caused by loss of aggregate interlock behavior. Experimental information on large-scale torsional members is lacking.CHAPTER 2NOTATION AND DEFINITIONSThe
47、material presented is a summary of research carried out worldwide and spanning more than four decades, making unification of the symbols and notations used by the various researchers and design codes a challenge. In some cases, mostly for graphs and figures, the notation is kept as originally publis
48、hed.2.1Notationa = moment arm for bending, mm (in.)ac= geometric property indexao= depth of equivalent rectangular stress block in concrete strut of torsional member, mm (in.)A = area of yield surface, mm2(in.2)Acp= area enclosed by outside perimeter of concrete cross section, mm2(in.2)A= total area
49、 of longitudinal reinforcement to resist torsion, mm2(in.2)Ao= gross area enclosed by shear flow path, mm2(in.2) (noted as Atbin Eq. (7.2.6)Aoh= area enclosed by centerline of outermost closed transverse torsional reinforcement, mm2(in.2)Aps= area of prestressing reinforcement in flexural tension zone, mm2(in.2)As= area of nonprestressed longitudinal tension rein-forcement, mm2(in.2)As = area of longitudinal compression reinforcement, mm2(in.2)At= area of one leg of a closed stirrup resisting torsion within spacing s, mm2(
