A clear understanding of the effects of torsion on concrete members is essential to the safe, 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 research 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 Th\u00fcrlimann; the compression 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 equilibrium condition (Mohr\u2019s stress circle); 2) obey the compatibility condition (Mohr\u2019s strain circle); and 3) establish the constitutive relationships of materials such as the \u201csoftened\u201d stress-strain relationship of concrete and \u201csmeared\u201d stress-strain relationship of steel bars. The behavior of members subjected to torsion combined with bending moment, axial load, and shear is discussed. This report deals with design issues, including compatibility torsion, spandrel 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 detailed, step-by-step design examples for two beams under torsion using ACI (ACI 318-11), European (EC2-04), and Canadian 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 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 concrete; shear flow zone; skew bending; softened truss model; spandrel beams; struts; torsion detailing; torsion redistribution; warping.<\/p>\n
| PDF Pages<\/th>\n | PDF Title<\/th>\n<\/tr>\n | ||||||
|---|---|---|---|---|---|---|---|
| 3<\/td>\n | CONTENTS CONTENTS <\/td>\n<\/tr>\n | ||||||
| 4<\/td>\n | CHAPTER 1\u2014 INTRODUCTION AND SCOPE CHAPTER 1\u2014 INTRODUCTION AND SCOPE 1.1\u2014Introduction 1.1\u2014Introduction <\/td>\n<\/tr>\n | ||||||
| 5<\/td>\n | 1.2\u2014Scope 1.2\u2014Scope CHAPTER 2\u2014 NOTATION AND DEFINITIONS CHAPTER 2\u2014 NOTATION AND DEFINITIONS 2.1\u2014Notation 2.1\u2014Notation <\/td>\n<\/tr>\n | ||||||
| 7<\/td>\n | 2.2\u2014Definitions 2.2\u2014Definitions CHAPTER 3\u2014 HISTORICAL OVERVIEW OF TORSION THEORIES AND THEORETICAL MODELS CHAPTER 3\u2014 HISTORICAL OVERVIEW OF TORSION THEORIES AND THEORETICAL MODELS 3.1\u2014Navier\u2019s theory 3.1\u2014Navier\u2019s theory 3.2\u2014Thin-tube theory 3.2\u2014Thin-tube theory <\/td>\n<\/tr>\n | ||||||
| 8<\/td>\n | 3.3\u2014Historical development of theories for reinforced concrete members subjected to torsion 3.3\u2014Historical development of theories for reinforced concrete members subjected to torsion <\/td>\n<\/tr>\n | ||||||
| 15<\/td>\n | 3.4\u2014Concluding remarks 3.4\u2014Concluding remarks CHAPTER 4\u2014 BEHAVIOR OF MEMBERS SUBJECTED TO PURE TORSION CHAPTER 4\u2014 BEHAVIOR OF MEMBERS SUBJECTED TO PURE TORSION 4.1\u2014General 4.1\u2014General 4.2\u2014Plain concrete 4.2\u2014Plain concrete <\/td>\n<\/tr>\n | ||||||
| 17<\/td>\n | 4.3\u2014Reinforced concrete 4.3\u2014Reinforced concrete <\/td>\n<\/tr>\n | ||||||
| 19<\/td>\n | 4.4\u2014Prestressed concrete 4.4\u2014Prestressed concrete <\/td>\n<\/tr>\n | ||||||
| 20<\/td>\n | 4.5\u2014High-strength concrete 4.5\u2014High-strength concrete <\/td>\n<\/tr>\n | ||||||
| 21<\/td>\n | 4.6\u2014Concluding remarks 4.6\u2014Concluding remarks <\/td>\n<\/tr>\n | ||||||
| 22<\/td>\n | CHAPTER 5\u2014 ANALYTICAL MODELS \nFOR PURE TORSION CHAPTER 5\u2014 ANALYTICAL MODELS \nFOR PURE TORSION 5.1\u2014General 5.1\u2014General 5.2\u2014Equilibrium conditions 5.2\u2014Equilibrium conditions 5.3\u2014Compatibility conditions 5.3\u2014Compatibility conditions <\/td>\n<\/tr>\n | ||||||
| 24<\/td>\n | 5.4\u2014Stress strain relationships 5.4\u2014Stress strain relationships <\/td>\n<\/tr>\n | ||||||
| 25<\/td>\n | 5.5\u2014Compression field theory 5.5\u2014Compression field theory <\/td>\n<\/tr>\n | ||||||
| 27<\/td>\n | 5.6\u2014Softened truss model 5.6\u2014Softened truss model <\/td>\n<\/tr>\n | ||||||
| 28<\/td>\n | 5.7\u2014Graphical methods 5.7\u2014Graphical methods <\/td>\n<\/tr>\n | ||||||
| 30<\/td>\n | CHAPTER 6\u2014 MEMBERS SUBJECTED TO TORSION COMBINED WITH OTHER ACTIONS CHAPTER 6\u2014 MEMBERS SUBJECTED TO TORSION COMBINED WITH OTHER ACTIONS 6.1\u2014General 6.1\u2014General <\/td>\n<\/tr>\n | ||||||
| 31<\/td>\n | 6.2\u2014Torsion and flexure 6.2\u2014Torsion and flexure <\/td>\n<\/tr>\n | ||||||
| 35<\/td>\n | 6.3\u2014Torsion and shear 6.3\u2014Torsion and shear <\/td>\n<\/tr>\n | ||||||
| 38<\/td>\n | 6.4\u2014Torsion and axial load 6.4\u2014Torsion and axial load <\/td>\n<\/tr>\n | ||||||
| 39<\/td>\n | 6.5\u2014Torsion, shear, and flexure 6.5\u2014Torsion, shear, and flexure <\/td>\n<\/tr>\n | ||||||
| 41<\/td>\n | CHAPTER 7\u2014 ADDITIONAL DESIGN ISSUES RELATED TO TORSION CHAPTER 7\u2014 ADDITIONAL DESIGN ISSUES RELATED TO TORSION 7.1\u2014General 7.1\u2014General 7.2\u2014Compatibility torsion and torsional moment redistribution 7.2\u2014Compatibility torsion and torsional moment redistribution <\/td>\n<\/tr>\n | ||||||
| 49<\/td>\n | 7.3\u2014Precast spandrel beams 7.3\u2014Precast spandrel beams <\/td>\n<\/tr>\n | ||||||
| 50<\/td>\n | 7.4\u2014Torsion limit design 7.4\u2014Torsion limit design <\/td>\n<\/tr>\n | ||||||
| 53<\/td>\n | 7.5\u2014Treatment of open sections 7.5\u2014Treatment of open sections <\/td>\n<\/tr>\n | ||||||
| 55<\/td>\n | 7.6\u2014Size effect on the strength of concrete beams in torsion 7.6\u2014Size effect on the strength of concrete beams in torsion CHAPTER 8\u2014 DETAILING FOR TORSIONAL MEMBERS CHAPTER 8\u2014 DETAILING FOR TORSIONAL MEMBERS 8.1\u2014General 8.1\u2014General <\/td>\n<\/tr>\n | ||||||
| 57<\/td>\n | 8.2\u2014Transverse reinforcement 8.2\u2014Transverse reinforcement <\/td>\n<\/tr>\n | ||||||
| 59<\/td>\n | 8.3\u2014Longitudinal reinforcement 8.3\u2014Longitudinal reinforcement <\/td>\n<\/tr>\n | ||||||
| 60<\/td>\n | 8.4\u2014Detailing at supports 8.4\u2014Detailing at supports <\/td>\n<\/tr>\n | ||||||
| 61<\/td>\n | CHAPTER 9\u2014 DESIGN EXAMPLES CHAPTER 9\u2014 DESIGN EXAMPLES 9.1\u2014Torsion design philosophy 9.1\u2014Torsion design philosophy 9.2\u2014Torsion design procedures 9.2\u2014Torsion design procedures <\/td>\n<\/tr>\n | ||||||
| 69<\/td>\n | 9.3\u2014Introduction to design examples 9.3\u2014Introduction to design examples 9.4\u2014Design Example 1: solid rectangular reinforced concrete beam under pure torsion 9.4\u2014Design Example 1: solid rectangular reinforced concrete beam under pure torsion <\/td>\n<\/tr>\n | ||||||
| 76<\/td>\n | 9.5\u2014Design Example 2: Prestressed concrete box girder under combined torsion, shear, and flexure 9.5\u2014Design Example 2: Prestressed concrete box girder under combined torsion, shear, and flexure <\/td>\n<\/tr>\n | ||||||
| 88<\/td>\n | CHAPTER 10\u2014 REFERENCES CHAPTER 10\u2014 REFERENCES <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" 445.1R-12 Report on Torsion in Structural Concrete<\/b><\/p>\n |