The design and analysis of structural concrete elements is a topic of practical interest. While sometimes the effect of torsion is only addressed based on simple examples, practicing engineers are faced with the need to include the effects of torsion in their designs of a variety of structures and load arrangements. This Special Publication (SP) contains papers about the design of reinforced and prestressed concrete elements for torsion. The focus of the SP is on practical design examples according to different concrete bridge and building codes. In addition to the design examples, papers dealing with the current state of the art on torsion in structural concrete, as well as recent advances in the analysis and design of concrete elements failing in torsion, are added. The objectives of this SP are to provide practicing engineers with the tools necessary to better understand and design concrete elements for torsion. The need for this SP arose after the development of the State-of-the-Art Report on Torsion of Joint ACI-ASCE Committee 445 “Shear and Torsion” and Subcommittee 445-E “Torsion”. Usually, the attention that is paid to torsion in engineering education is limited to simplified textbook examples. The examples in this SP show applications in bridges and buildings, where the torsion design is combined with the design for flexure and shear. Additionally, the examples in this SP give insight on the different outcomes when using different bridge and building codes. Finally, the papers that include theoretical considerations give practicing engineers a deeper understanding and background on torsion in structural concrete. The views from an international group of authors are included in this SP, subsequently representing a variety of building and bridge codes the engineer may encounter in practice. In particular, authors from the United States, Canada, Ecuador, the Netherlands, Italy, Greece, and the Czech Republic contributed to the papers in this SP. Views from academia and the industry are included. To exchange experience in the design of torsion-critical structures as well as new research insights on torsion, Joint ACI-ASCE Committee 445 and Subcommittee 445-E organized two sessions titled “Examples for the Design of Reinforced and Prestressed Concrete Members under Torsion” at the ACI Fall Convention 2020. This SP contains several technical papers from experts who presented their work at these sessions, in addition to papers submitted for publication only. In summary, this SP addresses numerous practical examples of structural elements under torsion in bridges and buildings, as well as insights from recent research applied to practical cases of elements under torsion. The co-editors of this SP are grateful for the contributions of the authors and sincerely value the time and effort they invested in preparing the papers in this volume, as well as the contributions of the reviewers of the manuscripts.

The paper deals with torsion of rectangular concrete sections. The pre-cracking stage and post-cracking stage are discussed. The various design procedures are briefly mentioned and compared. The deficiencies of some methods are identified and discussed. The major part of the paper deals with the results of an experimental program executed at the Czech Technical University. The large-scale elements were tested under loading by torsion and by interaction of torsion and compression. The results showed that the effect of the compression force on the load carrying capacity of the elements in torsion differs according to the stage of performance. While at the pre-cracking stage the contribution of the compression is rather significant, when approaching the failure, it becomes reduced. Simplified technical methods of design of reinforcement were also discussed. It has been proved that the effect of the angle of the compressed diagonal in code models is rather important. The study showed that this effect is sometimes overestimated. Finally, in conclusions, some recommendations for future research are proposed.

The Joint ACI-ASCE Committee 445 published a document titled Report on Torsion in Structural Concrete that contained an in-depth review of historical theory development, design models, and simplified design procedures for the effect of torsion in concrete structures. That document contained three design examples that were relatively simple. An important goal of this ACI Special Publication is to provide more realistic design examples that are usable by design professionals. This paper satisfies that goal by showing a detailed solution to a realistic example that has been encountered on several occasions by one of the authors. Another goal of the ACI Special Publication is to show applications where torsion is combined with flexure and shear. In this example, the torsional effects are combined with biaxial flexure and biaxial shear forces. This example includes a check of the new provisions in ACI 318-19 for bi-axial shear effects.

This paper shows a detailed solution for the design of a reinforced concrete grade beam subjected to torsional effects combined with biaxial shear and biaxial flexure. The grade beam is a portion of a structural screen wall system. A 25 psf (1.20 kPa) strength level wind pressure acts on a 20 ft (6.10 m) tall CMU wall supported by a continuous grade beam. The 21 in (533 mm) wide by 18 in (457 mm) deep grade beam is isolated from an expansive soil and is supported by drilled shafts 21 ft (6.40 m) on center. The wind load and gravity loads induce torsion, biaxial bending moments, and biaxial shear forces in the grade beam. This example shows how to calculate the internal forces in the grade beam at the critical section and design the required longitudinal and shear reinforcement according to the ACI 318-19 code.

The design of the grade beam includes closed stirrups of #4 (Ø 12) bars spaced at 5.5 in (140 mm), five #8 (Ø 25) bars used near the top and bottom faces and one #6 (Ø 16) bar used at mid-height near the side faces.

A bridge pier cap beam supporting girders of two unequal spans was designed per AASTHTO LRFD Bridge Design Specifications (AASHTO LRFD BDS-17) and the ACI 318 Building Code Requirements for Structural Concrete (ACI 318-19) with consideration of torsional effect. Envelopes of bending moment, shear, and torsional moment are given in the problem statement as the result of a comprehensive structural analysis on the bridge. Flexural design is presented firstly based on the bending moment envelope to determine the required area of longitudinal reinforcement. Then shear and torsion design is presented to determine the required area of transverse reinforcement and additional longitudinal reinforcement. Based on the design calculations, the arrangement of reinforcement is illustrated in a cross-section view for the cap beam. Comparison between the two approaches is also included in terms of the equations used and areas of shear and torsion reinforcement determined.

This paper provides a practical example of the torsion design of an inverted tee bent cap of a three-span bridge. A full torsional design following the guidelines of the ACI 318-19 building code is carried out and the results are compared with the outcomes from CSA-A23.3-04, AASHTO-LRFD-17, and EN 1992-1-1:2004 codes. Then, a summary of the detailing of the cross-section considering the reinforcement requirements is presented. The objective of this paper is to illustrate the application of ACI 318-19 when designing a structural element subjected to large torsional moments.