Vol. 21 No. 1 (2018) Cover Image
Vol. 21 No. 1 (2018)

Published: February 28, 2018

Pages: 86-98

Articles

Alternative Strut and Tie Model for Reinforced Concrete Deep Beams

Ahmed Faleh Al-Bayati 1
1 Civil Engineering Department, Al-Nahrain University, Baghdad, Iraq
History
  • Received: September 25, 2017
  • Revised: December 16, 2017
  • Accepted: December 18, 2017
  • Available Online: February 10, 2018
DOI

https://doi.org/10.29194/NJES21010086

Abstract

This paper presents a simple strut and tie model to calculate the shear strength of reinforced concrete deep beams. The proposed model assumes that the shear strength is the algebraic sum of three strength components: concrete diagonal strut, vertical stirrups, and horizontal web reinforcements. The contribution of each strength components was calibrated with the test results of 305 deep beams compiled from previous studies with wide range of geometrical and material properties. The predictions of the proposed model were compared with those of the current codes of practice (ACI-318-14 and ASHTOO 2014) and those of existing model in the literature. Comparisons revealed that the proposed model provided better predictions than other models. The mean of predicted strength to test of the proposed model, the ACI-318-14 model, the ASHTOO 2014 model were 0.98, 0.79, and 0.75, respectively. The corresponding standard deviations were 0.17, 0.28, and 0.49, respectively.

Keywords

References

  1. Wight, JK, “Reinforced Concrete: Mechanics and Design”, Global Edition, Pearson Education Limited 2016.
  2. Foster SJ, Malik AR, “Evaluation of efficiency factor models used in strut-and-tie modeling of nonflexural members”, ASCE Journal of Structural Engineering, 2002 May, Vol. 128, No. 5, pp. 569-577.
  3. Zhong JT, Wang L, Deng P, Zhou M. “A new evaluation procedure for the strut-and-tie models of the disturbed regions of reinforced concrete structures”, Engineering Structures, 2017 Oct, Vol. 148, pp. 660-72.
  4. Tuchscherer RG, Birrcher DB, Williams CS, Deschenes DJ, and Bayrak O, “Evaluation of existing strut-and-tie methods and recommended improvements”, ACI Structural Journal. 2014 Nov 1, Vol. 111, No. 6, pp.1451-1460.
  5. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318 14)”, Commentary on Building Code Requirements for Structural Concrete (ACI 318M-14), American Concrete Institute, 2014.
  6. AASHTO, “AASHTO LRFD Bridge Design Specifications”, American Association of State Highway and Transportation Officials, 2014.
  7. CSA Committee A23.3, “Design of Concrete Structures: Structures (Design)-A National Standard of Canada”, Canadian Standards Association, 2004.
  8. Matamoros, Adolfo B., and Kuok Hong Wong. “Design of simply supported deep beams using strut-and-tie models”, 2003 Nov., Vol. 100, No. 6, pp. 704-712.
  9. Tang CY, Tan KH, “Interactive mechanical model for shear strength of deep beams”, ASCE Journal of Structural Engineering, 2004 Oct, Vol. 130, No. 10, pp. 1534-44.
  10. Russo G, Venir R, Pauletta M, “Reinforced concrete deep beams-shear strength model and design formula”, ACI Structural Journal. 2005 May, Vol. 102, No. 3, pp. 429-37.
  11. Arabzadeh A, Rahaie AR, Aghayari R, “A simple strut-and-tie model for prediction of ultimate shear strength of RC deep beams”, International Journal of Civil Engineering, 2009 Sep, Vol. 7, No. 3, pp. 141-53.
  12. Kassem W. “Shear strength of deep beams: a mathematical model and design formula”, Structural Concrete, 2015 Jun, Vo. 16, 2. pp. 184-94.
  13. Park JW, Kuchma D, “Strut-and-tie model analysis for strength prediction of deep beams”, ACI Structural Journal, 2007 Nov., Vol. 104, No. 6, pp. 657-660.
  14. Smith KN, Vantsiotis AS, “Shear strength of deep beams”, ACI Journal Proceedings 1982 May 1 Vol. 79, No. 3, pp. 201-213.
  15. Oh JK, Shin SW, “Shear strength of reinforced high-strength concrete deep beams”, ACI Structural Journal, 2001 Mar, Vol. 98, No. 2, pp. 164-173.
  16. Kani G, “How safe are our large reinforced concrete beams?”, In ACI Journal Proceedings 1967 Mar, Vol. 64, No. 3, pp. 128-141.
  17. De Cossio RD, Siess CP, “Behavior and strength in shear of beams and frames without web reinforcement”, ACI Journal Proceedings 1960 Feb, Vol. 56, No. 2, pp. 695-736.
  18. Ahmad SH, Lue DM, “Flexure-shear interaction of reinforced high strength concrete beams”, ACI Structural Journal, 1987 Jul, Vol. 84, No. 4, pp. 330-341.
  19. Yang KH, Chung HS, Lee ET, Eun HC, “Shear characteristics of high-strength concrete deep beams without shear reinforcements”, Engineering Structures, 2003 Aug, Vol. 25, No. 10, pp.1343-1352.
  20. Moody KG, Viest IM, Elstner RC, Hognestad E, “Shear strength of reinforced concrete beams Part 1-Tests of simple beams”, ACI Journal Proceedings 1954 Dec, Vol. 51, No. 12, pp. 317-332.
  21. Ferguson PM, “Some implications of recent diagonal tension tests”, ACI Journal Proceedings 1956 Aug, Vol. 53, No. 8, pp. 157-172.
  22. Kim D, Kim W, White RN, “Arch action in reinforced concrete beams-A rational prediction of shear strength”, ACI Structural Journal, 1999 Jul, Vol. 96, No. 4, pp. 586-593.
  23. De Paiva HA, Siess CP, “Strength and behavior of deep beams in shear”, ASCE Structural Engineering Journal, 1965 Oct, Vol. 91, No. 5, pp.19-41.
  24. Tan KH, Kong FK, Teng S, Guan L, “High-strength concrete deep beams with effective span and shear span variations”, ACI Structural Journal, 1995 Jul, Vol. 92, No. 4, pp. 395-405.
  25. Ghannoum, W.M., “Size effect on Shear Strength of Reinforced Concree Beams,” M.Eng. Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, 1998, 115 pp.
  26. Tanimura Y, Sato T, “Evaluation of shear strength of deep beams with stirrups”, Quarterly Report of RTRI, 2005, Vol. 46, No. 1, pp. 53-58.
  27. Aguilar G, Matamoros AB, Parra-Montesinos GJ, Ramírez JA, Wight JK, “Experimental Evaluation of Design Procedures for Shear Strength of Deep Reinforced Concrete Beams”, ACI Structural Journal, 2002 Jan, Vol. 99, No. 4, pp. 539-548.
  28. Kong FK, Robins PJ, Cole DF, “Web reinforcement effects on deep beams”, ACI Journal Proceedings 1970 Dec, Vol. 67, No. 12, pp. 1010-1018.
  29. Clark AP, “Diagonal tension in reinforced concrete beams”, ACI Journal Proceedings 1951 Oct, Vol. 48, No. 10, pp. 145-156.
  30. Shin SW, Lee KS, Moon JI, Ghosh SK, “Shear strength of reinforced high-strength concrete beams with shear span-to-depth ratios between 1.5 and 2.5”, ACI Structural Journal, 1999 Jul., Vol. 96, No. 4, pp. 549-556.
  31. Lu WY, Lin J, Yu HW, “Shear strength of reinforced concrete deep beams”, ACI Structural Journal. 2013 Jul, Vol. 110, No. 4, pp. 671-680.
  32. Brown MD, Bayrak O, “Minimum transverse reinforcement for bottle-shaped struts”, ACI Structural Journal, 2006 Nov, Vol. 103, No. 6, pp. 813-821.
  33. Hwang SJ, Lu WY, Lee HJ, “Shear strength prediction for reinforced concrete corbels”, ACI Structural Journal, 2000 Jul, Vol. 197, No. 4, pp. 543-52.
  34. Hwang SJ, Lee HJ, “Strength prediction for discontinuity regions by softened strut-and-tie model”, ASC Journal of Structural Engineering, 2002 Dec, Vol. 128, No. 12, pp.1519-1526.
  35. Quintero-Febres CG, Parra-Montesinos G, Wight JK, “Strength of struts in deep concrete members designed using strut-and-tie method”, ACI Structural Journal. 2006 Jul., Vol. 103, No. 4, pp. 577-586.
  36. Nielsen MP, Hoang LC, “Limit analysis and concrete plasticity”, CRC press, 2016.
  37. Vecchio FJ, Collins MP, “The modified compression-field theory for reinforced concrete elements subjected to shear”, ACI Journal Proceedings, 1986 Mar, Vol. 83, No. 2, pp. 219-231.
  38. Vecchio FJ, Collins MP, “Compression response of cracked reinforced concrete”, ASCE Journal of structural engineering, 1993 Dec, Vol. 119, No. 12, pp. 3590-610.
  39. IBM SPSS Statistics 22, “SPSS Statistics 22 Manual”, Version 22, 2016.