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 Thürlimann; 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’s stress circle); 2) obey the compatibility condition (Mohr’s strain circle); and 3) establish the constitutive relationships of materials such as the “softened” stress-strain relationship of concrete and “smeared” 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.
Table of Contents
CHAPTER 1—INTRODUCTION AND SCOPE
CHAPTER 2—NOTATION AND DEFINITIONS
CHAPTER 3—HISTORICAL OVERVIEW OF TORSION THEORIES AND THEORETICAL MODELS
3.3—Historical development of theories for reinforced concrete members subjected to torsion
CHAPTER 4—BEHAVIOR OF MEMBERS SUBJECTED TO PURE TORSION
CHAPTER 5—ANALYTICAL MODELS FOR PURE TORSION
5.4—Stress strain relationships
5.5—Compression field theory
5.6—Softened truss model
CHAPTER 6—MEMBERS SUBJECTED TO TORSION COMBINED WITH OTHER ACTIONS
6.2—Torsion and flexure
6.3—Torsion and shear
6.4—Torsion and axial load
6.5—Torsion, shear, and flexure
CHAPTER 7—ADDITIONAL DESIGN ISSUES RELATED TO TORSION
7.2—Compatibility torsion and torsional moment redistribution
7.3—Precast spandrel beams
7.4—Torsion limit design
7.5—Treatment of open sections
7.6—Size effect on the strength of concrete beams in torsion
CHAPTER 8—DETAILING FOR TORSIONAL MEMBERS
8.4—Detailing at supports
CHAPTER 9—DESIGN EXAMPLES
9.1—Torsion design philosophy
9.2—Torsion design procedures
9.3—Introduction to design examples
9.4—Design Example 1: solid rectangular reinforced concrete beam under pure torsion
9.5—Design Example 2: Prestressed concrete box girder under combined torsion, shear, and flexure