Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A unified approach to shear and torsion in reinforced concrete

  • Rahal, Khaldoun N. (Department of Civil Engineering, Kuwait University)
  • Received : 2019.04.24
  • Accepted : 2021.01.09
  • Published : 2021.03.10
⟨ Previous Next ⟩

Abstract

Reinforced concrete (RC) beams can be subjected to a complex combination of shear forces (V), torsional moments (T), flexural moments (M) and axial loads (N). This paper proposes a unified approach for the analysis of these elements. An existing model for the analysis of orthogonally reinforced concrete membrane elements subjected to in-plane shear and normal stresses is generalized to apply to the case of beams subjected to the complex loading. The combination of V and T can be critical. Torsion is modelled using the hollow-tube analogy. A direct equation for the calculation of the thickness of the equivalent hollow tube is proposed, and the shear stresses caused by V and T are combined using a simple approach. The development and the evaluation of the model are described. The calculations of the model are compared to experimental data from 350 beams subjected to various combinations of stress-resultants and to the calculations of the ACI and the CSA codes. The proposed model provides the most favorable results. It is also shown that it can accurately model the interaction between V and T. The proposed model provides a unified treatment of shear in beams subjected to complex stress-resultants and in thin membrane elements subjected to in-plane stresses.

Keywords

References

  1. ACI 318 (2019), Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19), American Concrete Institute, Farmington Hills, MI, U.S.A.
  2. Andre, H. (1987), "Toronto/Kajima study on scale effects in reinforced concrete elements", M.A.Sc. Thesis, The University of Toronto, Toronto, Canada.
  3. Badawy, H.E.I., McMullen, A.E. and Jordaan, I.J. (1977), "Experimental investigation of the collapse of reinforced concrete curved beams", Mag. Concrete Res., 29(99), 59-69. https://doi.org/10.1680/macr.1977.29.99.59.
  4. Bentz, E.C., Vecchio, F.J. and Collins, M.P. (2006), "Simplified modified compression field theory for calculating shear strength of reinforced concrete elements", J. Am. Concrete Inst., 103, 614-624. https://doi.org/10.14359/16438.
  5. Bræstrup, M.W. (1974), "Plastic analysis of shear in reinforced concrete", Mag. Concrete Res., 26, 221-228. https://doi.org/10.1680/macr.1974.26.89.221.
  6. Bresler, B. and Scordelis, A.C. (1963), "Shear strength of reinforced concrete beams", ACI J. Proc., 60(1), 51-72. https://doi.org/10.14359/7842.
  7. Chiu, H.J., Fang, I.K., Young, W.T. and Shiau, J.K. (2007), "Behavior of reinforced concrete beams with minimum torsional reinforcement", Eng. Struct., 29(9), 2193-2205. https://doi.org/10.1016/j.engstruct.2006.11.004.
  8. Choi, C.K. and Cheung, S.H. (1994), "A simplified model for predicting the shear response of reinforced concrete membranes", Thin Wall. Struct., 19(1), 37-60. https://doi.org/10.1016/0263-8231(94)90004-3.
  9. Clark, A. (1951), "Diagonal tension in reinforced concrete beams", ACI J. Proc., 48(10), 145-156. https://doi.org/10.14359/11876.
  10. CSA-A23.3 (2014), Design of Concrete Structures (A23.3-14), Canadian Standards Association, Canada.
  11. Fang, I.K. and Shiau, J.K. (2004), "Torsional behavior of normal-and high-strength concrete beams", ACI Struct., 101(3), 304-313. https://doi.org/10.14359/13090.
  12. Fisher, G.P. and Zia, P. (1964), "Review of code requirements for torsion design", J. Am. Concrete Inst., 61(1), 1-44. https://doi.org/10.14359/7764.
  13. Fouad, E., Ghoneim, M., Issa, M. and Shaheen, H. (2000), "Combined shear and torsion in reinforced normal and highstrength concrete beams (1): Experimental study", J. Eng. Appl. Sci., 47(6), 1059-1078.
  14. Gupta, P. (1993), "Behavior of reinforced concrete members subjected to shear and compression", M.A.Sc. Thesis, The University of Toronto, Toronto, Canada.
  15. Haddadin, M.J., Hong, S.T. and Mattock, A.H. (1971), "Stirrups effectiveness in reinforced concrete beams with axial force", ASCE J. Struct. Div., 97(9), 2277-2297. https://doi.org/10.1061/JSDEAG.0002996
  16. Hsu, T.T.C. (1968), "Torsion of structural concrete-behavior of reinforced concrete rectangular members", Torsion in Struct. Concrete, SP-18, 261-306.
  17. Hsu, T.T.C. and Zhang, L. (1997), "Nonlinear analysis of membrane elements by fixed angle softened-truss model", ACI Struct. J., 94, 483-492. https://doi.org/10.14359/498.
  18. Hsu, T.T.C. and Zhang, L. (1998), "Behavior and analysis of 100 MPa concrete membrane elements", ASCE J. Struct. Div., 124, 24-34. https://doi.org/10.1061/(asce)0733-9445(1998)124:1(24).
  19. Ibrahim, M.S., Gebreyouhannes, E., Muhdin, A. and Gebre, A. (2020), "Effect of concrete cover on the pure torsional behavior of reinforced concrete beams", Eng. Struct., 216, 110790. https://doi.org/10.1016/j.engstruct.2020.110790.
  20. Johnson, M.K. and Ramirez, J.A. (1989), "Minimum shear reinforcement in beams with higher-strength concrete", ACI Struct. J., 86(4), 367-382. https://doi.org/10.14359/2896.
  21. Ju, H., Lee, D., Kim, J.R. and Kim, K.S. (2020). "Maximum torsional reinforcement ratio of reinforced concrete beams", Struct., 23, 481-493. https://doi.org/10.1016/j.istruc.2019.09.007.
  22. Khalifa, J. (1986), "Limit analysis of reinforced concrete shell elements", Ph.D. Thesis, University of Toronto, Toronto, Canada.
  23. Kirschner, U. (1986), "Investigating the behavior of reinforced concrete shell elements", Ph.D. Thesis, The University of Toronto, Toronto, Canada.
  24. Klus, J. (1968), "Ultimate strength of reinforced concrete beams in combined torsion and shear", ACI J. Proc., 65(3), 210-216. https://doi.org/10.14359/7468.
  25. Koutchoukali, N.E. and Belarbi, A. (2001), "Torsion of high-strength reinforced concrete beams and minimum reinforcement requirements", ACI Struct. J., 98(4), 462-469. https://doi.org/10.14359/10289.
  26. Lee, J.Y., Kim, K.H., Lee, S.H., Kim, C. and Kim, M.H. (2018), "Maximum torsional reinforcement of reinforced concrete beams subjected to pure torsion", ACI Struct. J., 15(3), 749-760. https://doi.org/10.14359/51701108.
  27. Leonhardt, F. and Schelling, G. (1974), "Torsionsversuche an stahl betonbalken", Bulletin no. 239, Deutscher Ausschuss fur Stahlbeton, Berlin.
  28. Lopes, S.M.R. and Bernardo, L.F A. (2014), "Cracking and failure mode in HSC hollow beams under torsion", Const. Build. Mater., 51, 163-178. https://doi.org/10.1016/j.conbuildmat.2013.10.062.
  29. Marti, P. and Meyboom, J. (1992), "Response of prestressed concrete elements to in-plane shear forces", ACI Struct. J., 89, 503-513. https://doi.org/10.14359/2956.
  30. McMullen, A.E. and Rangan, B.V. (1978), "Pure torsion in rectangular sections-A re-examination", ACI J. Proc., 75(10), 511-519. https://doi.org/10.14359/10963.
  31. McMullen, A.E. and Warwaruk, J. (1967), "The torsional strength of rectangular reinforced beams subjected to combined loading", Report No. 2, Civil Engineering Department, University of Alberta, Alberta, Canada.
  32. McMullen, A.E. and Warwaruk, J. (1970), "Concrete beams in bending, torsion and shear", Proc., ASCE, 96, 885-903.
  33. Mitchell, D. and Collins, M.P. (1974a), "Behavior of structural concrete beams in pure torsion", Publication No. 74-06, Department of Civil Engineering, University of Toronto, Toronto, Canada.
  34. Mitchell, D. and Collins, M.P. (1974b), "Diagonal compression field theory-A rational model for structural concrete in pure torsion", J. Am. Concrete Inst., 71(8), 396-408. https://doi.org/10.14359/7103.
  35. Mphonde, A.G. and Frantz, G.C. (1984), "Shear strength of highstrength reinforced concrete beams", Publication No. CE 84-157, University of Connecticut, Connecticut, U.S.A.
  36. Olalusi, O.B. and Viljoen, C. (2019), "Assessment of simplified and advanced models for shear resistance prediction of stirrup-reinforced concrete beams", Eng. Struct., 186, 96-109. https://doi.org/10.1016/j.engstruct.2019.01.130.
  37. Palaskas, M., Attiogbe, E. and Darwin, D. (1981), "Shear strength of lightly reinforced T-beams", ACI J. Proc., 78(6), 447-455. https://doi.org/10.14359/10528.
  38. Pang, X.B. and Hsu, T.T.C. (1995), "Behavior of reinforced concrete membranes in shear", ACI Struct. J., 92, 665-679. https://doi.org/10.14359/9661.
  39. Peng, X.N. and Wong, Y.L. (2011a), "Behavior of reinforced concrete walls subjected to monotonic pure torsion-An experimental study", Eng. Struct., 33(9), 2495-2508. https://doi.org/10.1016/j.engstruct.2011.04.022.
  40. Peng, X.N. and Wong, Y.L. (2011b), "Experimental study on reinforced concrete walls under combined flexure, shear and torsion", Mag. Concrete Res., 63(6), 459-471. https://doi.org/10.1680/macr.10.00133.
  41. Placas, A. and Regan, P.E. (1971), "Shear failure of reinforced concrete beams", ACI J. Proc., 68(10), 763-773. https://doi.org/10.14359/15237.
  42. Porasz, A. (1989), "An investigation of the stress-strain characteristics of high strength in shear", M.A.Sc. Thesis, Dept. of Civil Engineering, The University of Toronto, Toronto, Canada.
  43. Rahal, K.N. (1993), "Behaviour of reinforced concrete beams subjected to combined shear and torsion", Ph.D. Thesis, The University of Toronto, Toronto, Canada.
  44. Rahal, K.N. (2000a), "Shear strength of reinforced concrete: Part II-beams subjected to shear, bending moment and axial loads", ACI Struct. J., 97(2), 219-224. https://doi.org/10.14359/850.
  45. Rahal, K.N. (2000b), "Shear strength of reinforced concrete: Part I-membrane elements subjected to pure shear", ACI Struct. J., 97(1), 86-93. https://doi.org/10.14359/837.
  46. Rahal, K.N. (2001), "Analysis and design for torsion in reinforced and prestressed concrete beams", Struct. Eng. Mech., 11(6), 575-590. https://doi.org/10.12989/sem.2001.11.6.575.
  47. Rahal, K.N. (2002), "Membrane elements subjected to in-plane shearing and normal stresses", ASCE J. Struct. Div., 128, 1064-1072. https://doi.org/10.1061/(asce)0733-9445(2002)128:8(1064).
  48. Rahal, K.N. (2008), "Simplified design and capacity calculations of shear strength in reinforced concrete membrane elements", Eng. Struct., 30, 2782-2791. https://doi.org/10.1016/j.engstruct.2008.03.002.
  49. Rahal, K.N. (2010), "Shear-transfer strength of reinforced concrete", ACI Struct. J., 107(4), 419-426. https://doi.org/10.14359/51663814.
  50. Rahal, K.N. (2013), "Torsional strength of normal and highstrength reinforced concrete beams", Eng. Struct., 56, 2206-2216. https://doi.org/10.1016/j.engstruct.2013.09.005.
  51. Rahal, K.N. and Collins, M.P. (1995a), "Analysis of sections subjected to combined shear and torsion-A theoretical model", ACI Struct. J., 92(4), 459-469. https://doi.org/10.14359/995.
  52. Rahal, K.N. and Collins, M.P. (1995b), "Effect of thickness of concrete cover on shear and torsion interaction-An experimental investigation", ACI Struct. J., 92(3), 334-342. https://doi.org/10.14359/9657.
  53. Rahal, K.N. and Collins, M.P. (1996), "Simple model for predicting the torsional strength of reinforced and prestressed concrete sections", ACI Struct. J., 93(6), 658-866. https://doi.org/10.14359/512.
  54. Rahal, K.N. and Collins, M.P. (1999), "Background of the 1994 CSA-A23.3 General Method of shear design", Can. J. Civil Eng., 26(6), 827-839. https://doi.org/10.1139/l99-050.
  55. Rangan, B.V. (1991), "Web crushing of reinforced and prestressed concrete beams", ACI Struct. J., 88(1) 12-16. https://doi.org/10.14359/3050.
  56. Rasmussen, L.J. and Baker, G. (1995), "Torsion in reinforced normal and high-strength concrete beams-part 1: experimental test series", ACI Struct. J., 92(1), 56-62. https://doi.org/10.14359/1476.
  57. Roller, J.J. and Russell, H.G. (1990), "Shear strength of high-strength concrete beams with web reinforcement", ACI Struct. J., 87(2), 191-198. https://doi.org/10.14359/2682.
  58. Taborda, C., Bernardo, L.F.A. and Gama, J.M.R. (2018), "Effective torsional strength of axially restricted RC beams", Struct. Eng. Mech., 67(5), 465-479. http://dx.doi.org/10.12989/sem.2018.67.5.465.
  59. Vecchio, F.J. and Chan, C.C.L. (1990), "Reinforced concrete membrane elements with perforations", ASCE J. Struct. Eng., 116, 72-78. https://doi.org/10.1061/(asce)0733-9445(1990)116:9(2344).
  60. Vecchio, F.J. and Collins, M.P. (1986), "Modified compression field theory for reinforced concrete elements subjected to shear", J. Am. Concrete Inst., 83, 219-231. https://doi.org/10.14359/10416.
  61. Vecchio, F.J., Collins, M.P. and Aspiotis, J. (1994), "High-strength concrete elements subjected to shear", ACI Struct. J., 91, 423-433. https://doi.org/10.14359/4149.
  62. Wang, Q., Qiu, W. and Zhang, Z. (2015), "Torsion strength of single-box multi-cell concrete box girder subjected to combined action of shear and torsion", Struct. Eng. Mech., 55(5), 953-964. https://doi.org/10.12989/sem.2015.55.5.953.
  63. Xie, L., Bentz, E.C. and Collins, M.P. (2011), "Influence of axial stress on shear response of reinforced concrete elements", ACI Struct. J., 108(6), 745-754. https://doi.org/10.14359/51683373.
  64. Yamaguchi, T., Koike, K., Naganuma, K. and Takeda, T. (1988), "Pure shear loading tests on reinforced concrete panels part I: outlines of tests", Proceedings, Japanese Architectural Association, Japan.
  65. You, Y.M. and Belarbi, A. (2011), "Thickness of shear flow zone in a circular column under pure torsion", Eng. Struct., 33, 2435-2447. https://doi.org/10.1016/j.engstruct.2011.04.016.