Title:
Pure Torsion—Application of Model of Characteristic Failure Cross Sections
Author(s):
Andor Windisch
Publication:
Structural Journal
Volume:
119
Issue:
1
Appears on pages(s):
55-66
Keywords:
characteristic failure cross sections; concrete contribution; concrete cover; efficiency factor; failure modes; nonlinear sectional models; pure torsion; skew reinforcement; softening concrete
DOI:
10.14359/51733010
Date:
1/1/2022
Abstract:
Torsion in structural concrete members is a discipline where in-depth research is still possible and desirable. Sophisticated computer programs have been developed that deliver the ultimate load-bearing capacities after following the whole loading/deformation process. This paper presents the model of the characteristic failure cross sections (MCFC) and the efficiency factor, ψ, of the skew reinforcement and applies them to fundamental test series from the literature on beams with rectangular cross sections loaded in pure torsion. A simple design formula is proposed and validated on test results from the literature. Failure modes and the influence of concrete strength are discussed. Minimum and maximum rates of reinforcement are defined, and detailing recommendations are given.
Related References:
1. Rausch, E., “Drillung, Schub und Scheren im Stahlbetonbau,” Deutscher Ingenieur-Verlag, Düsseldorf, 1953
2. Hsu, T. T. C., “Shear Flow Zone in Torsion of Reinforced Concrete,” Journal of Structural Engineering, ASCE, V. 116, No. 11, 1990, pp. 3206-3226. doi: 10.1061/(ASCE)0733-9445(1990)116:11(3206)
3. Hsu, T. T. C., and Mo, Y. L., “Softening of Concrete in Torsioning Members-Design Recommendations, ACI Journal Proceedings, V. 82, No. 4, July-Aug. 1985, pp. 443-451.
4. Mitchell, D., and Collins, M. P., “The Behavior of Structural Concrete in Pure Torsion,” Publication 74-06, 1974, University of Toronto, Toronto, ON, Canada.
5. Rahal, K. N., and Collins, M. P., “Analysis of Sections Subjected to Combined Shear and Torsion—A Theoretical Model,” ACI Structural Journal, V. 92, No. 4, July-Aug. 1995, pp. 459-469.
6. Jeng, C. H., and Hsu, T. T. C., “A Softened Membrane Model for Torsion in Reinforced Concrete Members,” Engineering Structures, V. 31, Sept. 2009, pp. 944-954. doi: 10.1016/j.engstruct.2009.02.038
7. Greene, G. G. Jr., and Belarbi, A., “Model for Reinforced Concrete Members under Torsion, Bending, and Shear, Part 1: Theory,” Journal of Engineering Mechanics, ASCE, V. 135, No. 9, 2009, pp. 961-969. doi: 10.1061/(ASCE)0733-9399(2009)135:9(961)
8. Bernardo, L. F. A.; Andrade, J. M. A.; and Lopes, S. M. R., “Modified Variable Angle Truss-Model for Torsion in Reinforced Concrete Beams,” Materials and Structures, V. 45, No. 12, 2012, pp. 1877-1902. doi: 10.1617/s11527-012-9876-4
9. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.
10. Windisch, A., “Das Modell der charakteristischen Bruchquerschnitte. Ein Beitrag zur Bemessung der Sonderbereiche von Stahlbetontragwerken (The model of the characteristic fracture cross-sections. A contribution to the dimensioning of the special areas of reinforced concrete structures),” Beton- und Stahlbetonbau, H. 9, 10, 1988, pp. 251-255, 271-274.
11. Völgyi, I., and Windisch, A., “Experimental Investigation of the Role of Aggregate Interlock in the Shear Resistance of Reinforced Concrete Beams,” Structural Concrete, V. 18, Oct. 2017, pp. 792-800. doi: 10.1002/suco.201600137
12. Windisch, A., “On the Design of Two-Way Reinforcements in R/C,” Studi e ricerche, V. 21, 2000, pp. 283-302.
13. Hsu, T. T. C., “Torsion of Structural Concrete-Plain Concrete Rectangular Sections,” Torsion of Structural Concrete, SP-18, G. P. Fisher, ed., American Concrete Institute, Farmington Hills, MI, 1968, pp. 203-235.
14. Leonhardt, F., and Schelling, G., “Torsionsversuche an Stahlbetonbalken,” Deutscher Ausschuss für Stahlbeton, Wilhelm Ernst & Sohn, Berlin, Germany, 1974, 122 pp.
15. Windisch, A., “Reinforcement Pattern of Reinforced Concrete Members in Pure Torsion,” Fuchs, W. and Reinhardt, Ibidem Verlag, Stuttgart, 2002, pp. 293-301.
16. Gesund, H.; and Boston, L. A., “Ultimate Strength in Combined Bending and Torsion of Concrete Beams Containing Only Longitudinal Reinforcement,” ACI Journal Proceedings, V. 61, No. 11, Nov. 1964, pp. 1453-1471.
17. Hsu, T. T. C., “Torsion of Structural Concrete-Behavior of Structural Concrete Rectangular Members,” Torsion of Structural Concrete, SP-18, G. P. Fisher, ed., American Concrete Institute, Farmington Hills, MI, 1968, pp. 261-306.
18. Rasmussen, L. J., and Baker, G., “Torsion in Reinforced Normal and High-Strength Concrete Beams Part 1: Experimental Test Series,” ACI Structural Journal, V. 92, No. 1, Jan.-Feb. 1995, pp. 56-62.
19. Lee, J.-Y.; Kim, K.-H.; Lee, S. H.; Kim, C.; and Kim, M.-H., “Maximum Torsional Reinforcement of Reinforced Concrete Beams Subjected to Pure Torsion,” ACI Structural Journal, V. 57, No. 3, 2018, pp. 749-760. doi: 10.14359/51701108
20. ACI Committee 318, “Building Code Requirements for Structural Concrete and Commentary (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 520 pp.
21. Comité European de Normalisation (CEN), “Eurocode 2: Design of Concrete Structures, Part 1-1, General Rules and Rules for Buildings (BS EN 1992-1-1),” Lausanne, Switzerland, 2004, 211 pp.
22. CSA A23.3-14, “Design of Concrete Structures for Buildings,” Canadian Standards Association, Mississauga, ON, Canada, 2004, 291 pp.
23. Japan Society of Civil Engineering, “Standard Specifications for Concrete Structures,” Japan Society of Civil Engineering, Tokyo, Japan, 2007, 469 pp.