Strut-and-Tie Model without Discontinuity for Reinforced Concrete Deep Beams

International Concrete Abstracts Portal

The International Concrete Abstracts Portal is an ACI led collaboration with leading technical organizations from within the international concrete industry and offers the most comprehensive collection of published concrete abstracts.

  


Title: Strut-and-Tie Model without Discontinuity for Reinforced Concrete Deep Beams

Author(s): Jung-Yoon Lee and You Min Kang

Publication: Structural Journal

Volume: 118

Issue: 5

Appears on pages(s): 123-134

Keywords: deep beams; nodal zone; shear span-depth ratio; shear strength; simplified STM; strut-and-tie model (STM)

DOI: 10.14359/51732824

Date: 9/1/2021

Abstract:
The current design codes (including ACI 318-19, EC2-04, CSA-14, and fib model code) recommend the strut-and-tie model (STM) for the design of deep reinforced concrete (RC) members with higher accuracy in predicting the shear strength compared to existing semi-empirical shear design equations. Though the STM in these codes are more rational and effective than the previous semi-empirical formulations, their application is still difficult. Several inconsistencies and contradictions exist in the current STMs—such as a complex design process, the unclear mecha-nism for model selection, inconsistent boundary points between B regions and D regions, and an impractically larger prediction for the required amount of shear reinforcement—which question the reliability of STM and create mistrust among designers. In this study, a model was proposed to design RC deep beams by simpli-fying the current STM of the ACI 318-19 code. The proposed model reduces the calculation efforts required for the design process and eliminates the complexities and contradictions in the current STM, especially the differences in STM and beam theory predictions at the boundary between the B region and D region. The proposed model presents practical solutions for the contradictions in the design process of the existing STM and effectively reduces the calculation efforts needed by introducing a check for bearing and potential nodal failure. The simplified model was verified against an extensive experimental database consisting of 595 RC deep beams collected from the literature. Comparison of the results shows that the proposed STM predicted the strength of deep beams with similar accuracy to that of the detailed STM but with remark-ably less calculation effort compared to the detailed STM.

Related References:

1. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 623 pp.

2. Wight, J. K., and Macgregor, J. G., Reinforced Concrete: Mechanics and Design, seventh edition, Prentice Hall, Upper Saddle River, NJ, 2015, 893 pp.

3. Schlaich, J., and Schafer, K., “Design and Detailing of Structural Concrete Using Strut-and-Tie Models,” Journal of the Institution of Structural Engineers, V. 69, No. 6, 1991, pp. 113-125.

4. Brown, M. D.; Sankovich, C. L.; Bayrak, O.; Jirsa, J. O.; Breen, J. E.; and Wood, S. L., “Design for Shear in Reinforced Concrete Using Strut-and-Tie Models,” CTR Technical Report: 0-4371-2, The University of Texas at Austin, Austin, TX, 2006, 330 pp.

5. Lim, E., and Hwang, S. J., “Modeling of the Strut-and-Tie Parameters of Deep Beams for Shear Strength Prediction,” Engineering Structures, V. 108, 2016, pp. 104-112.

6. Ritter, W., “Die Bauweise Hennebique,” Schweizerische Bauzeitung, V. 33, No. 7, 1899, pp. 49-52.

7. Marti, P., “Basic Tools of Reinforced Concrete Beam Design,” ACI Journal Proceedings, V. 82, No. 1, Jan.-Feb. 1985, pp. 46-56.

8. Collins, M. P., and Mitchell, D., “Rational Approach to Shear Design-The 1984 Canadian Code Provisions,” ACI Journal Proceedings, V. 83, No. 6, Nov.-Dec. 1986, pp. 925-933.

9. Rogosky, D. M., and MacGregor, J. G., “Design of Reinforced Concrete Deep Beams,” Concrete International, V. 8, No. 8, Aug. 1986, pp. 49-58.

10. Brown, M. D., and Bayrak, O., “Design of Deep Beams using Strut-and-Tie Models-Part II: Design Recommendations,” ACI Structural Journal, V. 105, No. 4, July-Aug. 2008, pp. 405-413.

11. Robinson, J. R. and Demorieux, J. M., “Essais de traction-Compression sur modèles d’ame de poutre en Beton Armé,” IRABA Report, Institut de Recherches Appliquées du Béton Armé Part 1, 1968.

12. Vecchio, F., and Collins, M. P., “Stress-Strain Characteristics of Reinforced Concrete in Pure Shear,” Advanced Mechanics of Reinforced Concrete, International Association for Bridge and Structural Engineering, Zurich, Switzerland, 1981, pp. 211-225.

13. Mau, S. T., and Hsu, T. T. C., “Formula for the Shear Strength of Deep Beams,” ACI Structural Journal, V. 86, No. 5, Sept.-Oct. 1989, pp. 516-523.

14. Hwang, S. J.; Lu, W. Y.; and Lee, H.-J., “Shear Strength Prediction for Deep Beams,” ACI Structural Journal, V. 97, No. 3, May-June 2000, pp. 367-376.

15. Tuchscherer, R. G.; Birrcher, D. B.; and Bayrak, O., “Reducing Discrepancy between Deep Beam and Sectional Shear-Strength Predictions,” ACI Structural Journal, V. 113, No. 1, Jan.-Feb. 2016, pp. 3-15.

16. Tuchscherer, R. G.; Birrcher, D. B.; Williams, C. S.; Deschenes, D. J.; and Bayrak, O., “Evaluation of Existing Strut-and-Tie Methods and Recommended Improvements,” ACI Structural Journal, V. 111, No. 6, Nov.-Dec. 2014, pp. 1451-1460.

17. Matamoros, A. B., and Wong, K. H., “Design of Simply Supported Deep Beams Using Strut-and-Tie Models,” ACI Structural Journal, V. 100, No. 6, Nov.-Dec. 2003, pp. 704-712.

18. Tan, K. H., “Direct Strut-and-Tie Model for Prestressed Deep Beams,” Journal of Structural Engineering, ASCE, V. 127, No. 9, 2001, pp. 1076-1084.

19. Tan, K. H., “A Direct Method for Deep Beams with Web Reinforcement,” Magazine of Concrete Research, V. 55, No. 1, 2003, pp. 53-63.

20. Zhang, N., and Tan, K. H., “Direct Strut-and-Tie Model for Single Span and Continuous Deep Beams,” Engineering Structures, V. 29, No. 11, 2007, pp. 2987-3001.

21. Yang, K. H., and Ashour, A. F., “Strut-and-Tie Model Based on Crack Band Theory for Deep Beams,” Journal of Structural Engineering, ASCE, V. 137, No. 10, 2011, pp. 1030-1038.

22. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99),” American Concrete Institute, Farmington Hills, MI, 1999, 392 pp.

23. De Paiva, H. A., and Siess, C. P., “Strength and Behavior of Deep Beams in Shear,” Proceedings of ASCE, V. 91, No. ST.5, 1965, pp. 19-41.

24. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02),” American Concrete Institute, Farmington Hills, MI, 2002, 443 pp.

25. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp.

26. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 519 pp.

27. AASHTO, “AASHTO LRFD Bridge Design Specifications,” sixth edition, American Association of State Highway and Transportation Officials, Washington, DC, 2012, 1661 pp.

28. European Committee for Standardization, “Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings (EN 1992-1-1:2005),” CEN, Brussels, Belgium, 2005, 229 pp.

29. Comite Euro-International du Beton, “CEB-FIP Model Code 2010-Final Draft,” International Federation for Structural Concrete, Lausanne, Switzerland, 2011.

30. CSA A23.3-14, “Design of Concrete Structures.” Canadian Standards Association, Toronto, ON, Canada, 2004, 291 pp.

31. Reineck, H. K., Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, MI, 2003, 249 pp.

32. Park, R., and Paulay, T., Reinforced Concrete Structures, seventh edition, Wiley and Sons, New York, 1975, 769 pp.

33. International Federation for Structural Concrete, Structural Concrete Textbook on Behavior, Design and Performance-Updated Knowledge of the CEB/FIP Model Code, International Federation for Structural Concrete (fib), Lausanne, Switzerland, Dec. 1999, 292 pp.

34. Foster, S. J., and Gilbert, R. I., “Experimental Studies on High-Strength Concrete Deep Beams,” ACI Structural Journal, V. 95, No. 4, July-Aug. 1998, pp. 382-390.

35. Foster, S. J., “Design of Non-Flexural Members for Shear,” Cement and Concrete Composites, V. 20, No. 6, 1998, pp. 465-475.


ALSO AVAILABLE IN:

Electronic Structural Journal



  

Edit Module Settings to define Page Content Reviewer